ABSTRACT
Title of Dissertation: TRIPTYCH IN EMPIRICAL FINANCE
Sylvain Delalay
Doctor of Philosophy, 2022
Dissertation Directed by: Professor Vojislav Maksimovic
Department of Finance
This dissertation contains three chapters that explore topics in empirical finance and
political economy.
In Chapter 1, I study how the fundraising revenues of political campaigns affect the
outcome of U.S. elections. First, I assemble a novel and granular dataset that provides a
comprehensive picture of cash flows and voting intentions during U.S. congressional races.
Then, I extract weekly shocks to the fundraising revenues of campaigns by using machine
learning on the dataset. I find that the effect of revenues on the vote share decreases over
the course of general elections. In races involving an incumbent, an additional $100,000
in challenger revenues increases her vote share by 1.48pp in the first half of the general
election, but has no effect in the second half. Early cash infusions are more valuable than
late cash infusions because they provide flexibility to respond to the opponent?s actions
and mitigate current and future financing constraints.
In Chapter 2, I examine how strategic and financial considerations shape the spending
behavior of political campaign committees. To discipline the empirical analysis, I derive a
dynamic model of strategic investment under financing constraints. I test the predictions
of the model using the revenue shocks constructed in Chapter 1. I find that a committee?s
elasticity of advertising expenditures to the revenue shocks of its opponent is 8%, which is a
third of a committee?s elasticity to its own shocks. Moreover, a committee that is relatively
richer than its opponent reacts more aggressively to its opponent?s shocks, both in levels
and as a fraction of cash reserves. This result suggests that the availability of internal
financing can amplify the competitive aspect of political spending in electoral races.
In Chapter 3, I identify investor overreaction in a setting where information flows
are not observable and learning pertains to multiple dimensions of an asset. Specifically, I
measure how investors react to the information released during merger attempts and
whether they form rational beliefs about the probability of deal completion. Using a
model of distorted learning that generates testable implications, I find evidence of relative
mispricing in the cross-section of merger targets. Empirically, a low price-implied
probability of success underestimates the actual probability of success, and vice versa,
suggesting that investors overreact to deal-specific information. The overreaction is
unrelated to the unconditional merger premium and not driven by exposure to traditional
risk factors.
TRIPTYCH IN EMPIRICAL FINANCE
by
Sylvain Delalay
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
2022
Advisory Committee:
Professor Vojislav Maksimovic, Chair/Advisor
Professor Shrihari Santosh, Co-Advisor
Professor Albert S. Kyle
Professor Geoffrey A. Tate
Professor M. Cecilia Bustamante
Professor Andrew T. Sweeting, Dean?s Representative
?c Copyright by
Sylvain Delalay
2022
Acknowledgments
I owe my gratitude to all the people who have made this dissertation possible through
their help and support. My graduate experience at the University of Maryland would have
been much less enjoyable without them.
First and foremost, I would like to thank my advisor, Max Maksimovic, for providing
invaluable guidance throughout my PhD. Max has always made himself available for help
and advice. It has been a pleasure to learn from such a great scholar.
I would also like to thank my co-advisor, Shri Santosh. Shri is one of the smartest
person with whom I have had the privilege to interact. His ability to explain complex
concepts in simple yet precise terms will never cease to amaze me. I am grateful to count
him as a friend.
Thanks are due to Pete Kyle, Geoff Tate, Cecilia Bustamante, and Andrew Sweeting
for agreeing to serve on my dissertation committee and for providing feedback on my ideas.
I would also like to thank Mark Loewenstein and Pablo Slutzky for the numerous discussions
that helped me get to the finish line.
I am also indebted to my fellow PhD students in the finance and economics
departments for their help during the coursework and research portions of the PhD
program.
Special thanks to Vincent Skiera with whom I have regular discussions about
everything and nothing.
ii
I would like to acknowledge the help and support from the administrative staff at
the Smith School of Business, and in particular from Justina Blanco who runs the PhD
program in a very efficient fashion.
I owe my deepest thanks to my family?my mother, father, and brother who have
always stood by me throughout my career. Words cannot express the gratitude I owe them.
My wife, Kirsten, has been extremely supportive of me throughout my graduate studies
and has made countless sacrifices to help me get to this point.
It is impossible to list everybody who have direcly or indirectly contributed to this
dissertation, and I apologize to those I have inadvertently left out.
Finally, thank you, brave reader, for spending some of your time with my thoughts
and ideas, and thank God!
iii
Table of Contents
Acknowledgements ii
Table of Contents iv
Chapter 1: Political Campaign Financing and Electoral Outcomes 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 FEC Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Other Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.3 Sample Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.4 Summary Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.3.1 Shock Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.3.2 Shock Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.4 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.4.1 Effect of Revenues on the Vote Share . . . . . . . . . . . . . . . . . 24
1.4.2 Timing of Revenues . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
1.4.3 Additional Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Chapter 2: Financial Resource Allocation During General Elections 31
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.2 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.2.3 Parameterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.2.4 Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.3 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.1 Empirical Specifications . . . . . . . . . . . . . . . . . . . . . . . . 57
2.3.2 Response to Revenue Shocks . . . . . . . . . . . . . . . . . . . . . . 58
2.3.3 Role of Financing Constraints . . . . . . . . . . . . . . . . . . . . . 64
2.3.4 Role of Political Capital . . . . . . . . . . . . . . . . . . . . . . . . 66
2.3.5 Additional Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
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Chapter 3: Distorted Learning Around Merger Announcements 71
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.2.2 Information Processing . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.2.3 Relationship between Probability Measures . . . . . . . . . . . . . . 81
3.2.4 Pricing of the Target . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3 Data and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.1 Data Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3.2 Sample Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.3.3 Target Stock Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
3.3.4 Price Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
3.4 Empirical Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.4.1 Mispricing in the Cross-Section of Merger Announcements . . . . . 96
3.4.2 Persistence of the Mispricing . . . . . . . . . . . . . . . . . . . . . . 102
3.4.3 Mispricing and Deal Characteristics . . . . . . . . . . . . . . . . . . 106
3.4.4 Mispricing and Firm Characteristics . . . . . . . . . . . . . . . . . . 109
3.4.5 Parameter Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.4.6 Calendar-Time Portfolios . . . . . . . . . . . . . . . . . . . . . . . . 115
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Appendix A: Supplements to Chapter 1 119
A.1 Dataset Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
A.1.1 FEC Reporting Timeline . . . . . . . . . . . . . . . . . . . . . . . . 119
A.1.2 FEC Form 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
A.1.3 FEC Contribution Limits . . . . . . . . . . . . . . . . . . . . . . . 122
A.1.4 Variable Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
A.1.5 Predictors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
A.2 Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.3 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Appendix B: Supplements to Chapter 2 128
B.1 Model Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
B.1.1 Equilibrium at t = T . . . . . . . . . . . . . . . . . . . . . . . . . . 128
B.1.2 Comparative Statics at T . . . . . . . . . . . . . . . . . . . . . . . 130
B.1.3 Equilibrium at t < T . . . . . . . . . . . . . . . . . . . . . . . . . . 131
B.1.4 Numerical Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
B.1.5 Model with Borrowing . . . . . . . . . . . . . . . . . . . . . . . . . 135
B.2 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
B.2.1 Additional Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
B.2.2 Artificial Neural Network . . . . . . . . . . . . . . . . . . . . . . . . 137
B.2.3 Extended Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
B.2.4 Bootstrapped Standard Errors . . . . . . . . . . . . . . . . . . . . . 143
B.2.5 Placebo Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
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Appendix C: Supplements to Chapter 3 146
C.1 Model Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
C.1.1 Optimism and Pessimism . . . . . . . . . . . . . . . . . . . . . . . . 146
C.1.2 Learning Distortion in the Log Odds Space . . . . . . . . . . . . . . 146
C.1.3 Limiting Case: n?? . . . . . . . . . . . . . . . . . . . . . . . . . 147
C.2 Variable Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
C.2.1 Compustat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
C.2.2 Institutional Ownership . . . . . . . . . . . . . . . . . . . . . . . . 149
C.2.3 Merger Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
C.3 Sample Augmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
C.3.1 Newspaper Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
C.3.2 Tokenization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
C.3.3 Subsamples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
C.3.4 Random Forest Algorithm . . . . . . . . . . . . . . . . . . . . . . . 151
C.4 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
C.4.1 Scaling Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
C.4.2 Offer Price Imputation . . . . . . . . . . . . . . . . . . . . . . . . . 153
C.4.3 Standard Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
C.5 Bias in Returns Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
C.6 Two-Stage Regression with Generated Regressands . . . . . . . . . . . . . 157
Bibliography 160
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Chapter 1: Political Campaign Financing and Electoral Outcomes
1.1 Introduction
How does money affect politics and the electoral system? Anecdotal evidence suggests
that money plays a preponderant role in the electoral process and constitutes a necessary,
yet not sufficient ingredient for electoral success.1 However, more than four decades of
academic research have produced ambiguous findings reagarding the quantification of the
effect of money on electoral outcomes.2 As a result, it is still an open and relevant question.
In this paper, I explore how, when, and for whom money matters in U.S.
congressional elections. The campaign finance literature traditionally seeks to measure
the causal effect of political spending on the vote share. In contrast, I focus on fundraising
revenues and measure how their timing affects the vote share obtained by candidates.
Moreover, I examine the economic mechanisms that drive the value of additional revenues
over the course of a general election. Studying the impact of campaign financing on
electoral outcomes improves our understanding of the role of money in politics and has
direct implications for candidates, donors, and political committees.
1Consider these newspaper headlines as illustration: ?Why money is so important in US elections?,
?Cash, the campaigns? lifeblood?, ?Money doesn?t guarantee a win, but lack of money can guarantee a loss?.
Also see Chapter 10 in Philippon (2019) for a general discussion of the relationship between money and
politics.
2Jacobson (2015) and Stratmann (2019) review the literature on the role of money in elections. Also
see Section 1.1.1 for the main findings in this literature.
1
Measuring the causal effect of revenues on the vote share is difficult because the
cash flows in an electoral race?revenues, spending, and transfers to other political
organizations?arise as equilibrium responses in a strategic game between the candidates.
To overcome the endogeneity generated by these strategic interactions, I use machine
learning on the rich data produced during congressional races in order to extract weekly
shocks that provide exogenous variation in the fundraising revenues of the candidates.
Using these shocks, I find that donations received during the race affect the vote share
on election day. A $100,000 unexpected increase in total challenger revenues increases her
vote share by 0.66 percentage points; however, I do not find a significant effect for the
incumbent. 3 Interestingly, the effect is stronger at the beginning of the race (1.48pp in
the first half of the general election vs 0.10pp in the second half), indicating that early
access to financial resources has a greater impact on outcomes than funds obtained closer
to election day. Early cash infusions provide flexibility to respond to the opponent?s actions
and mitigate current and future financing constraints. This finding suggests that donors
and political organizations should allocate financial resources to financially-constrained
campaigns as early as possible.
Very granular data is generated and disseminated during electoral races. This data
consists of information about the finances of the candidates as well as polls and public
opinion. In particular, federal campaign finance regulations require primary campaign
committees?the legal vehicles through which candidates raise and spend funds in federal
elections?to report detailed data on revenues, spending, and transfers to the Federal
3These results are consistent with the findings of Jacobson (1978) and Gerber (2004) who study the
effect of campaign spending on the vote share.
2
Election Commission (FEC). To construct the revenue shocks, I assemble a novel
high-frequency dataset of committee finances that draws a comprehensive picture of the
dynamics of committee cash flows throughout general election races for the U.S. House of
Representatives.4 I supplement the dataset with polling and TV advertising data
gathered from multiple sources. The dataset captures the information set of the
committees.
I lever the abundance of data produced during electoral races to identify shocks to
the fundraising revenues of campaign committees. To do so, I estimate the conditional
expectation of future fundraising revenues under the assumption that committees form
expectations rationally. The difference between realized and expected revenues
constitutes the shock. This is the ideal setting to apply machine learning as the object of
interest is the shock, not the mapping between information sets and forecasts of future
revenues. Moreover, machine learning has the additional benefit of preventing overfitting,
discarding weak predictors, and capturing potential non-linearities and interactions
between the variables in the information set. I implement the learning with a polynomial
LASSO regression and use a regularized artificial neural network to ensure the robustness
of the results.
The methodology produces shocks that have sound statistical properties. The
shocks are not serially correlated, nor do they exhibit discernible event-time patterns.
The shocks are uncorrelated within races, indicating that they reflect idiosyncratic
innovations in the fundraising revenues of committees rather than systematic effects.
4Two statistics illustrate the richness of the FEC data: to construct the dataset, I process 4.7 million
itemized expenditures and 18.3 million donations from individuals.
3
Moreover, the polynomial LASSO and the neural network generate shocks that are highly
correlated even though these algorithms operate in very different ways. Taken together,
these diagnostics suggest that the shocks cleanly capture the unexpected component of
fundraising revenues.
The remainder of the paper is organized as follows. I review the related literature in
Section 1.1.1. I discuss data sources in Section 1.2 and the methodology in Section 1.3. I
present the empirical findings in Section 1.4. Concluding remarks are in Section 1.5.
1.1.1 Related Literature
This paper primarily relates to the political science literature that examines the role of
money in the electoral process. The bulk of this literature measures the causal impact of
candidate spending during a race on the electoral outcome, typically the vote share of the
incumbent.5
Conceptually, regressing the vote share of the incumbent on incumbent and challenger
spending should recover the causal effect of spending on the vote share if the controls
capture all the other factors that affect the vote share. Jacobson (1978) notes that it is
rarely the case because candidate quality is usually omitted from the specification and
spending is an equilibrium outcome. Political scientists have tackled this endogeneity issue
in several ways: instrumental variables (Green and Krasno, 1988; Gerber, 1998), panel data
(Levitt, 1994), focus on close races (Erikson and Palfrey, 2000), field experiments (Gerber,
2004), and regression discontinuity designs (Spenkuch and Toniatti, 2018), among others.
5The vote share of the incumbent and challenger are considered separately to account for a potential
incumbency advantage (Ansolabehere and Snyder Jr., 2002).
4
Empirical results are ambiguous. Some papers find that spending does not affect electoral
outcomes; some find that it matters only for the challenger; finally, some find that spending
matters for both candidates.
A few papers have studied how the timing of cash flows affect candidate outcomes over
the electoral cycles. Bonica (2017) shows that early fundraising success predicts electoral
outcomes in primary elections. Babenko, Fedaseyeu, and Zhang (2021) document that
business politicians enjoy an early fundraising advantage over their opponents. In this
paper, I show that challenger revenues obtained early in the general election have a larger
effect on the vote share than those received later in the race.
1.2 Data
In this section I discuss the data sources, describe the sample construction, and present
summary statistics. The financial data of political committees comes from the FEC.
Election results are from the MIT Election Lab and information on members of Congress
from the @unitedstates project. I download polling data and favorability ratings from
The Polling Report and FiveThirtyEight, as well as the market-implied probabilities of
controlling either chamber of Congress from the Iowa Electronic Markets. Finally, the
Wesleyan Media Project provides data on political TV ads. Section 1.2.1 presents the
FEC data. The other data sources are discussed in Section 1.2.2.
5
1.2.1 FEC Data
The financial data consists of committee filings and itemized transactions, both
downloaded through the FEC API. Campaign committees are required to complete and
file Form 3 reports at specific points in time during an election cycle. Table A.1 in the
Appendix presents the reporting timeline. Moreover, the FEC performs thorough checks
and audits of the reports to ensure their accuracy. I collect Form 3 data of all authorized
committees linked to candidates who have participated in general elections for the U.S.
House of Representatives between 2004 and 2018.
Form 3 is composed of five parts. The first part provides information about the filing
committee, the reporting period, and the congressional district for which the candidate
associated with the committee is running. It also contains a summary of the cash flows
and cash on hand at the beginning and end of the reporting period. The four other parts,
called schedules, contain granular information on itemized receipts (Schedule A), itemized
disbursements (Schedule B), as well as loans, debts, and obligations (Schedules C and D).
Table A.2 in the Appendix contains a complete description of the items reported in Form
3. Table A.3 reports the accounting identities between the items contained in Form 3.
Schedule A lists contributions from individuals, from the candidate, and from other
committees in addition to loans, offsets to operating expenditures, and other receipts. Each
itemized entry contains information about the contributor, and the date and amount of
receipt. A contribution from an individual donor is itemized in Schedule A if it aggregates
over $200 when added to other contributions received from the same donor during the same
6
election cycle.6 The aggregate amount of unitemized donations is reported in the summary
section of Form 3.
Schedule B provides a detailed picture of the disbursements made by a committee.
Each cash outflow is listed with information about the recipient, date, amount, and
purpose of the disbursement. Outflows are broken down into five subcategories: operating
expenditures, transfers to other committees, loan repayments, refunds of contributions,
and other disbursements.
Schedules C and D list outstanding loans, debts, and obligations. Each liability is
reported along with the counterparty, original amount, cumulative payment to date, and
balance outstanding at the close of the reporting period.
Some campaign expenditures such as rent do not directly contribute to winning the
election. I separate advertising expenditures from other operating expenditures in order to
isolate spending that affects the outcome of the election. I classify itemized expenditures
as advertising or non-advertising based on whether advertising-related keywords appear in
the purpose of disbursement. The keywords used in the classification are listed in Appendix
A.1.4. Although the FEC provides a spending category for each expenditure, I do not use
their classification scheme because 70% of the entries (50% of total spending) fall in the
Other category.
For each committee I construct daily time series of cash movements based on the
itemized data contained in the Schedules. Unitemized contributions from individuals are
allocated within the reporting period in proportion to itemized contributions from
6Prior to 2015 a contribution was itemized in Schedule A if the reporting period amount was $200 or
more.
7
individuals. I then construct daily time series of cash holding based on the cash on hand
at the beginning of a reporting period and on cumulative net cash flows. I also consolidate
similar categories of cash flows together as described in Appendix A.1.4. In particular, I
compute net fundraising by netting refunds from gross donations. Finally, I aggregate
each time series at the weekly level to mitigate intra-week seasonality in reporting; flow
variables are summed, stock variables are averaged. In doing so, I adopt the convention
that a week starts on Tuesday so that the beginning of week 0 corresponds to election day.
Four points are worth mentioning. First, political committees are subject to donation
and transfer limits. In particular, donations per individual, election, and candidate were
capped at $2,700 in 2018. Table A.4 presents a comprehensive list of the limits that apply
to the 2017-2018 election cycle. Additionally, Table A.5 reports the history of the limit for
individual donors, starting in 2004. Second, candidates often set up joint committees to
combine forces for fundraising purposes. Revenues obtained through these committees are
accounted for in committee-to-committee cash transfers. Third, individuals may support
candidates by donating to conduit organizations such as ActBlue or WinRed. Earmarked
donations processed by conduits are forwarded to campaign committees who record them
on Schedule A if they meet the reporting threshold. As such, these donations are not
considered committee-to-committee transfers even though conduits are usually organized
as PACs. Fourth, other committees may spend money in support of a candidate. I collect
corresponding expenditures from the FEC API and control for these external cash flows in
the empirical analysis.
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1.2.2 Other Data Sources
1.2.2.1 Election Returns
I obtain general election returns for the U.S. House of Representatives between 2004 and
2018 from The MIT Election Lab. Results are reported at the congressional district level
and contain a district identifier, candidate names, party affiliations, and number of votes
obtained by each candidate.7 I calculate the vote share of each candidate as the number of
votes obtained divided by the total number of votes cast in the corresponding congressional
district.
1.2.2.2 Incumbency Status
The congress legislators database of the @unitedstates project contains a comprehensive
list of the Members of the United States Congress since its inception in 1789. I use the list
to infer a candidate?s incumbency status during an election. A candidate is the incumbent
if at the time of the election she is the Representative of the congressional district for which
she is running.
1.2.2.3 Polling
The Polling Report is a subscription-based website that provides historical polling data
starting in 1998, with a focus on competitive and high profile races. I parse each page
7I aggregate votes at the candidate level to handle fusion tickets. Under fusion voting, a candidate can
be supported by more than one political party. Therefore, the name of a candidate may appear multiple
times on the same ballot. Fusion voting is currently allowed in Connecticut, Delaware, Idaho, Mississippi,
New York, Oregon, South Carolina, and Vermont.
9
of the website and extract vote intentions for candidates in general election races for the
House of Representatives along with the date of the poll.
FiveThirtyEight proposes a very comprehensive sample of polling surveys for election
year 2018. I collect vote intentions for each candidate after excluding internal surveys and
surveys by pollsters that were given a reliability grade of F by FiveThirtyEight.
The Iowa Electronic Markets are futures markets where contract payoffs are
determined by the outcome of presidential and congressional elections. As such, the price
of a contract reflects the beliefs of bettors regarding the probability of the corresponding
outcome. I back out the probability of either party controlling the House of
Representatives from the time series of contract prices.
1.2.2.4 TV Advertising
The Wesleyan Media Project provides granular data on campaign TV ads broadcasted in
the United States during electoral races. The data is available for election years 2006 and
2010-2018. In particular, for each ad shown on TV, the dataset reports the date, time,
candidate featured in the ad, the ad sponsor, and whether the overall tone is positive or
negative. I construct a measure of ad negativity at the candidate level by calculating the
fraction of negative ads to total ads sponsored during the general election.
1.2.3 Sample Construction
In the empirical analysis, I study the effect of fundraising revenues on the vote share in
races for the U.S. House of Representatives between 2004 and 2018. The sample starts
10
in 2004 because it is the first election after the most recent overhaul of campaign finance
regulations.8 I focus on House elections because they provides a large cross-section of races
in the sample period unlike presidential elections. Senate races are more likely to draw
outside support, both in terms of financing and advertising, which would complicate the
analysis of committee behavior. Finally, gubernatorial committees are regulated by their
home state and not by the FEC. Therefore, committees from different states do not follow
the same campaign finance laws, which creates an additional source of heterogeneity that
is hard to tackle.
I merge the datasets in several steps. First, I map candidates to their principal
campaign committee using a linkage file provided by the FEC. Then, I merge election
results with the FEC financial data based on year, congressional district, and fuzzy string
matching of the name of candidates. Finally, I add incumbency information, as well as
polling, party winning odds, and TV advertising data.
To obtain the final sample, I apply the following filters sequentially:
1. I remove candidates with no registered primary committee or no committee data and
ex post votes less than 20%. Marginal candidates with little resources should not
impact the allocation of resources by other candidates or the outcome of the race.
2. I drop races where a candidate does not have a committee. Campaign committees
likely behave differently if they know their opponent is not marginal and does not
have a legal structure to raise and spend money. Since campaign committees must
be registered with FEC, this information is known at the beginning of the race.
8The Bipartisan Campaign Reform Act of 2002 imposes new limits on raising and spending by national
political party committees and tighter rules on issue advocacy ads. The law became effective on November
6, 2002 and the new limits on January 1, 2003.
11
3. I exclude races with a single candidate as they do not feature meaningful strategic
interactions. The average and median vote share in that sample are both above 90%
for the single candidate.
4. I exclude races with more than two candidates. Spending dynamics and the effect
of revenues on the vote share are likely to be different in races with more than two
candidates.
5. I exclude all Louisiana races. Louisiana uses a two-round system with a non-partisan
blanket primary held on federal election day and a runoff one month later if no
candidate receives a simple majority in the first round.
The final dataset is a panel at the committee-week level, starting 12 weeks before election
day. The sample contains races for which financial and polling data are available. The
races in the sample tend to be tight because polling is more likely to occur in close races.
For robustness purposes, I also construct an extended sample that contains races for which
financial data is available. I use the extended sample to illustrate how the races in the main
sample differ from a typical race. I also use the extended sample for a robustness exercise
in Chapter 2. Committees are indexed with respect to election years in both samples.
1.2.4 Summary Statistics
In this section, I discuss the cross-sectional and time series characteristics of the data.
Table 1.1 presents cross-sectional summary statistics for the main and extended samples
in Panel A and Panel B, respectively. The main sample contains 461 races, or 15% of the
general election races between 2004 and 2018. The percentage of the races covered in the
12
main sample is determined by the availability of polling data. These races are competitive
as reflected by the 9% median vote margin. Committees spend close to 1.5 million dollars
on average during the last 12 weeks of the race. Advertising expenditures make up 75% of
total expenditures. On average, committees spend 92% of their total cash reserves which
corresponds to an end cash balance of $137,000. Fundraising during the last 12 weeks
before the election constitutes 57% of total cash inflows; the remaining 43% comes from
initial cash balances. 65% of the fundraising comes from individual donors and 35% from
committee transfers and loans. Loans are not a main source of financing for campaign
committees as they make up only 5% of all cash inflows and are primarily extended by the
candidate.
The extended sample contains 1,851 races (61% of the races between 2004 and 2018).
The extended sample differs from the main sample in several regards. First, these races are
less competitive, with a median vote margin of 22%. Second, committees spend much less
than in competitive races on average: the mean and median amount are half and a quarter
of those in the main sample. Third, committees spend a lower fraction of their total cash
reserves (73%) and hold larger cash balances at the end of the race on average ($232,000).
Overall, the races in the main sample are tighter ex post and involve larger amounts
of money, both in terms of fundraising and spending. Races are not assigned to the main
sample based on their vote margin, but instead based on the availability of polling data.
Table 3.2 confirms the intuition that pollsters focus on competitive races.
13
Table 1.1
Summary Statistics
This table shows summary statistics for the main sample (Panel A) and the extended sample (Panel B). The
extended sample contains races for which polling data is not available. The sample period is from 2004 to
2018. Monetary figures are in thousand USD. The vote margin is the difference between the vote share of
the winner and that of the runner-up. Amounts raised and spent are the total cash flows between weeks
-12 and +2 of the electoral race. Starting and ending cash reserves are sampled at week -12 and +2 respectively.
Panel A: Main Sample
Obs. Mean SD 10% 25% 50% 75% 90%
Vote Margin 461 0.107 0.089 0.014 0.039 0.089 0.151 0.216
Total Spent 922 1,418.439 1,124.445 337.344 721.318 1,143.617 1,830.816 2,741.685
Advertising Expenditures 922 1,058.030 943.264 136.832 446.405 837.722 1,404.971 2,201.091
Total Raised 922 875.915 838.699 211.456 407.672 689.113 1,036.046 1,631.148
Fundraising From Individuals 922 568.220 655.688 118.890 222.521 390.856 642.074 1,118.677
Cash Start 922 664.970 658.044 60.688 175.949 463.357 976.653 1,497.905
Cash End 922 136.839 277.724 10.633 29.086 66.791 142.655 278.841
Panel B: Extended Sample
Obs. Mean SD 10% 25% 50% 75% 90%
Vote Margin 1,851 0.237 0.152 0.050 0.120 0.220 0.328 0.447
Total Spent 3,702 627.880 853.263 21.633 85.155 297.970 854.182 1,633.625
Advertising Expenditures 3,702 421.328 688.600 3.871 16.663 110.418 569.774 1,219.069
Total Raised 3,702 385.098 586.021 13.847 61.029 208.546 500.784 915.502
Fundraising From Individuals 3,702 248.885 408.864 12.612 43.403 127.028 295.413 555.941
Cash Start 3,702 464.951 617.857 3.627 24.265 235.124 677.827 1,262.054
Cash End 3,702 231.941 450.905 1.758 8.724 59.292 244.677 661.687
Figure 1.1 shows the evolution of average total committee spending between 2004
and 2018 for both samples. The figure reflects the difference in spending levels between
the two samples. Committees tend to spend more in the main sample which contains close
races. The figure also reveals an increasing trend in spending over the past two decades: a
committee in a close race spends on average 72% more in 2018 than in 2004. This suggests
that money is playing an increasingly important role in congressional elections. Finally,
note that similar patterns would obtain if total fundraising were shown instead of total
spending.
14
Figure 1.1. Average Committee Spending By Election Year. This figure shows the
average amount of cash spent by a committee between weeks -12 and +2 of an electoral race.
The yellow diamonds correspond to averages for the main sample. The blue circles correspond to
averages for the extended sample.
Finally, Figure 1.2 presents the event-time patterns of spending, fundraising, and cash
reserves. The top panel shows spending and fundraising as a fraction of total spending and
fundraising between weeks -12 and +2. Spending increases as the election gets closer and
peaks in the last two weeks before the election. The fraction of advertising to total spending
appears stable through time. Fundraising, both total and from individual donors, also
increases as the election draws closer. Interestingly, the series displays a spike in week -6,
which is the last week before the close of books for the FEC October Quarterly report. This
suggests that committees attempt to increase their cash balances before reports are due
by performing additional fundraising efforts. Finally, very little spending and fundraising
occurs after the election. The lower panel shows that cash reserves decrease monotonically
over the course of a race. Cash reserves deplete at a faster rate in the last five weeks before
the election.
15
Figure 1.2. Cash Flows and Cash Reserves in Event Time. The top panel shows the
fraction of total committee spending and fundraising by week in the electoral race. The yellow
continuous line with diamonds corresponds to Total Expenditures. The blue continuous line
with circles corresponds to Total Fundraising. Advertising Expenditures (yellow dotted line with
diamonds) and Individual Fundraising (blue dotted line with circles) are shown as fractions of
Total Expenditures and Total Fundraising respectively. The bottom panel shows average cash
balances by week in the electoral race. In both panels, weeks start on Tuesday and week 0 is the
week of the election.
1.3 Methodology
In this section, I present the construction of the revenue shocks and discuss their statistical
properties.
16
1.3.1 Shock Construction
Campaign revenues, spending, and vote shares arise endogenously as equilibrium outcomes
of a strategic game. In order to estimate the effect of revenues on the vote share, I must
first identify suitable revenue shocks.
I exploit the uncertainty in donations from individuals to construct revenue shocks.
During a race, the amount of cash raised in a given period of time is partly stochastic.
Committees can forecast the amount to a certain extent, but some uncertainty always
remains. To construct the shocks, I decompose the realized revenues from individual
fundraising of committee i in week t into its conditional expectation and a forecast error:
Fit = Et?1 [Fit] + sit (1.1)
where sit is orthogonal to the information set of committee i at t? 1. With an estimate of
the conditional expectation I can recover the shocks as:
s?it = Fit ? E?t?1 [Fit] (1.2)
I estimate the conditional expectation function Et?1 [?] through machine learning
because it is exactly the type of setting where this approach shines. First, Equation (1.1)
characterizes a prediction problem, not an inference one. The object of interest is the
forecast itself, not the parameters that generate the forecast. Second, there are many
potential predictors that can capture the information set which underlies the conditional
17
expectation function. Machine learning is able to detect strong predictors, discard weak
ones, and prevent overfitting through regularization. Finally, the mapping between the
predictors and the dependent variable is likely to be non-linear, a feature that machine
learning can accommodate.
The shocks are considered exogenous if the conditional expectation function
corresponds to the beliefs of the committees. The estimation procedure will yield
reasonable shocks if the set of predictors is rich enough to capture the information set of
committees. Thanks to the very granular data produced during electoral races, including
past decisions made by campaign committees, I am able to capture the relevant
information sets and compute meaningful shocks to revenues. Additionally, it would be
hard to argue that large shocks are actually forecastable by committees since individual
donations are capped by FEC regulations.9 Finally, note that committees do not raise
funds from individual donors exclusively, but can also receive transfers from other
committees. I construct the shocks based on individual donations alone because
forecasting transfers from other committees should be easier since there is a usually a
two-way communication channel between donor and recipient.
In the empirical analysis, I scale the shock and all level variables using the aggregate
cash reserves of the committees in the race in week t? 1:
= s?itSit
Cashi,t?1 +
(1.3)
Cash?i,t?1
In Chapter 2?s model, the spending game is played in levels, that is dollar-for-dollar.
9The limit was set at $2,000 per election per candidate in the 2003-2004 election cycle. The limit is
reviewed and adjusted for inflation every odd year. See Table A.5 for the list of historical donation limits.
18
Presumably, actual political committees operate in the same way.10 Using the total cash
reserves in the race as the denominator reflects this feature since the spending and shocks
of both committees are scaled by the same factor. The scaling methodology is the cross-
sectional equivalent of using the average of the beginning and ending values of a period in
a time series context, for instance when calculating employment growth rates as in Davis
and Haltiwanger (1992).
In the data, the average amount of fundraising revenues from individuals varies greatly
across committees and races. Therefore, I scale fundraising in week t using cash reserves in
week t? 1, which makes the dependent variable comparable across committees. I convert
the forecasts and the shocks to levels at the end of the estimation procedure and rescale
them using total cash reserves as described above. I use a large set of variables that capture
the financial situation, position in the race, and individual characteristics of the candidates
as predictors for the estimation. I provide a list of the variables in Appendix A.1.5.
I use a polynomial LASSO regression as main estimation method and a regularized
artificial neural network for robustness purposes.11 The polynomial LASSO is a linear
regression in which the regressors are elements of the polynomial spanned by the original
predictors, and to which a regularization scheme is applied. For instance, if the original
predictors are x1 and x2, the regressors generated by a second-order polynomial are
(1, x1, x2, x2 21, x2, x1x2). The additional regressors generated by the polynomial help
10For instance, in a November 2020 opinion piece, Charles Lane writes that ?[n]o doubt Biden?s ultimate
victory in November was aided by his ability to match Trump?s campaign dollar for dollar, at around
$1 billion each?. Source: https://www.washingtonpost.com/opinions/one-of-2020s-biggest-losers-was-the-
amount-of-money-wasted-in-the-election/2020/11/23/b0c8a034-2da6-11eb-bae0-50bb17126614_story.html
11See Santosa and Symes (1986); Frank and Friedman (1993); Tibshirani (1996) for seminal work on
the LASSO and Chinco, Clark-Joseph, and Ye (2019) for an implementation in the context of finance. See
Hastie, Tibshirani, and Friedman (2009) for a technical discussion of artificial neural networks.
19
capture non-linearities in the relationship between independent variables and the
dependent variable as well as interactions between the original predictors. Finally, the
regularization scheme prevents the algorithm from overfitting the model by discarding
weak predictors.
I estimate the two learning models in six successive steps. The process is followed
for the main and extended samples separately. First, I split the sample into a training and
a testing sample in a 80%-20% split. Second, I standardize the variables in both samples
based on the moments calculated from the training sample to prevent any look-ahead bias.
Third, I select hyperparameters through a 3-fold cross-validation process.12 Fourth, I fit
the selected model on the training sample and compute its R2. Fifth, I use the fitted
model on the testing sample and compute the corresponding R2. Sixth, I re-estimate the
model using the entire sample, generate forecasts, and compute the shock as the difference
between the vector of dependent variables and the forecasts.
A potential issue would arise if a variable entering the information set of campaign
committees is not explicitly included in the set of predictors. I address this concern in
two ways. First, I consider a large set of predictors as inputs to the learning models.
Moreover, the models generate additional predictors by combining the inputs together,
either through a polynomial (LASSO regression) or with intermediate neuron layers
(artificial neural network). Therefore, the final set of predictors is conceivably rich enough
to span the information sets of campaign committees. Second, when I construct the
shock, I assume that committees have perfect foresight of some of the variables at t. Since
12The hyperparameters of the polynomial LASSO regression are the L1 penalty and the order of the
polynomial spanned by the predictors. The hyperparameters of the regularized artificial neural network
are the L2 penalty and the structure of the network (number of layers and size of each layer).
20
expectations are computed as of t? 1, my approach is conservative.
Finally, it is worth noting that I would not be able to construct the shocks if I
did not have access to granular data, both in terms of number of variables and sampling
frequency. For instance, public firms report their financial data to the Securities and
Exchange Commission (SEC) on a quarterly basis. As such, the SEC data does not capture
intra-quarter changes in variables that may affect the conditional expectation of future
revenues, and I would not be able to estimate it precisely. Moreover, firms invest in different
types of intangibles, for instance knowledge capital, organizational capital, patents, trade
secrets, etc. It is difficult to determine the exact monetary amounts contributing to each
type of intangible capital because public firms only report aggregate investment. These
limitations are not present in the context of committee spending during electoral races,
which highlights the importance the empirical setting to answer the research question.
1.3.2 Shock Diagnostics
The training and test R2 of the polynomial LASSO in the main sample are 0.72 and
0.64.13 The learning algorithm captures a large portion of the variation in fundraising from
individuals as illustrated by the high R2s. Additionally, the change in R2 between the
training and test samples is negligible, indicating that the model is likely not overfitted.
Interactions and higher-order terms of the polynomial capture meaningful variation in the
dependent variable. To illustrate this point, I run an OLS regression on the original set of
predictors and obtain an out-of-sample R2 below 0.50.
13The values for the extended sample are 0.57 and 0.52. The artificial neural network produces R2s of
0.7 and 0.61 in the main sample.
21
Figure 1.3. Shock Diagnostics - Polynomial LASSO. This figure presents diagnostics for
the shock constructed with the polynomial LASSO. The top-left panel shows the histogram of the
shock. The top-right panel shows the scatter plot of a committee?s shock along with the shock of
its opponent. The bottom-left panel shows the average of the shock by week before the election.
The bottom-right panel shows the average of the shock by week in calendar time.
The LASSO shocks possess satisfactory statistical properties as illustrated in Figure
1.3. The top-left panel shows the histogram of the shocks. The shape of the distribution is
well behaved. The average and standard deviation are -0.0019 and 0.0541. The skewness
is positive, with a coefficient of 2.827. The top-right panel shows a committee?s shock on
the horizontal axis and that of its opponent on the vertical axis. The figure is symmetric
around the 45-degree line by construction. The figure shows that there is no systematic
relationship between a committee?s shock and that of its opponent. In a regression of a
committee?s shock on its opponent?s shock and committee and time fixed effects, I obtain
a coefficient of 0.06, a value not significantly different from zero. Finally, the bottom-left
and bottom-right panels show that there is no discernible pattern in the shock average in
22
either event time or calendar time. The figure in calendar time is noisier than that in event
time because each point is calculated based on less observations. The figure for the neural
network is similar and shown in Figure A.1 of the Appendix.
When regressing the shocks on their lags and committee and time fixed effects, I
obtain a coefficient of -0.085, a value statistically different from zero. At first glance, this
result suggests that the shocks are serially correlated. However, I argue that a negative
coefficient is to be expected under the null of no serial correlation because the specification
suffers from the Nickell (1981) bias that plagues inference in dynamic panel data models
with fixed effects.14 To show this, I fix the panel structure of the shocks and replace
them by white noise having the same standard deviation, then regress the newly created
observations on their lags and fixed effects. I repeat this procedure 5,000 times in order
to obtain the distribution of the regression coefficient under the null hypothesis that the
shocks are serially uncorrelated. The results for the LASSO shocks are presented in Figure
1.4 and those for the neural network shock in Figure A.2 of the Appendix. Based on the
figures, I cannot reject the null hypothesis that the shocks are serially uncorrelated when
accounting for the impact of the Nickell bias.
Overall, the results presented in this section suggest that the methodology captures
the unexpected component of revenues from individual fundraising and generates
meaningful shocks.
14The Nickell bias arises because the demeaning process used in the within estimator generates a
correlation between regressor and error. As an illustration, consider the panel AR(1) model xit =
?i + ?xi,t?1 + it where t = 1, . . . , T . The within estimator is xit? x?i,1:T = ?(xi,t?1? x?i,0:T?1) + (it? ?i).
The term ?i contains the lagged error term i,t?1and is therefore correlated with xi,t?1. The size of the bias
depends on the number of time periods in the panel and cannot be mitigated by increasing the number of
individual units.
23
Figure 1.4. Shock Autocorrelation - Polynomial LASSO. This figure shows the results
of the autocorrelation analysis for the shocks constructed with the polynomial LASSO. The red
line corresponds to the estimate ?? in the regression Sit = ?i + ?t + ?Si,t?1 + ?it. The blue bars
correspond to the histogram of ?? from the same regression where Sit and Si,t?1 are replaced by
random noise for all i and t. The histogram is based on 5,000 simulations.
1.4 Empirical Evidence
In this section, I discuss the econometric specifications and present the results of the
empirical analysis. Specifically, I study how committee cash flows and the timing thereof
affect the vote share. I focus on the results obtained with the LASSO shocks in the main
sample. Appendix A.3 presents the results corresponding to the shocks constructed with
the artificial neural network.
1.4.1 Effect of Revenues on the Vote Share
As customary in the political science literature, I consider the effect of money on the
outcome of the incumbents and the challenger separately to account for a potential
incumbency advantage (Ansolabehere and Snyder Jr., 2002). For the remainder of this
24
section I exclude open races and restrict the sample to races involving the congressional
district?s incumbent.
To understand the role of cash flows on electoral outcomes, I convert the weekly
revenue shocks into USD and aggregate them at the committee level:
ShockUSDit = Sit (Cashi,t?1 + Cash?i,t?1) /100, 000 (1.4)
?
AggShockUSD = ShockUSDi it (1.5)
t
Because the weekly shocks are forecast errors, their sum constitutes a plausibly exogenous
source of variation in total committee revenues. Since on average committees in the main
sample hold very low cash reserves at the end of the race, aggregate revenue shocks can be
also be construed as shocks to aggregate spending.
To measure the causal effect of revenues on electoral outcomes I regress the vote share
of the challenger on incumbent and challenger aggregate revenue shocks:
V oteShareC = ?y + ?IAggShockUSDI + ?CAggShockUSD + ??C Controls+  (1.6)
where I denotes the incumbent and C denotes the challenger. I control for year fixed effects,
the initial cash levels of the candidates, the polling of the incumbent at the beginning of
the general election, state-level unemployment, and state-level unemployment interacted
with a dummy variable capturing whether the incumbent is in the same party as the U.S.
president. The last two variables proxy for the economic conditions in the congressional
district.
25
Table 1.2 presents the results. A $100,000 unexpected increase in challenger revenues
translates into a 0.66pp increase in vote share. However, there is no effect of unexpected
incumbent revenues on the vote share. These results are consistent with the findings of
Jacobson (1978) and Gerber (2004) who find a positive and significant effect of challenger
spending on the vote share but no effect for the incumbent.
Table 1.2
Effect of Revenues on the Vote Share (I)
This table reports the results of regressions of the challenger vote share on revenue shocks for races in the main
sample that involve the incumbent. The indices C and I correspond to the challenger and the incumbent,
respectively. SumShocki is the sum of the weekly LASSO shocks of the primary committee for candidate i.
Unemployment is measured at the state level. IncRulingParty is a dummy variable that indicates whether the
incumbent is in the same party as the U.S. president. Monetary variables are expressed as multiples $100,000.
Vote shares and polling variables are expressed in percent. Heteroskedasticity-robust standard errors are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
V oteShareC V oteShareC V oteShareC
SumShockI 0.113 0.071 0.073
(0.176) (0.174) (0.157)
SumShock 0.868??? 0.747???C 0.660???
(0.210) (0.190) (0.179)
InitialPolling ??? ??? ???I -0.464 -0.405 -0.406
(0.088) (0.080) (0.061)
InitialCashI 0.027 0.033
(0.035) (0.035)
InitialCashC 0.476??? 0.471???
(0.078) (0.073)
Unemployment -0.720???
(0.273)
Unemp? IncRulingParty 0.532???
(0.160)
Year FE X X X
R2 0.296 0.385 0.422
N 333 333 333
1.4.2 Timing of Revenues
Next, I analyze how the timing of revenues affects their impact on the vote share. To do
so, I aggregate weekly shocks occurring in the first and last six weeks of the general
26
election separately. The first column of Table 1.3 shows the results. The positive impact
of unexpected challenger revenues on the vote share predominantly operates through
unexpected revenues received in the first half of the race. A $100,000 unexpected increase
in challenger revenues received early in the race translates into a 1.48pp increase in the
vote share, while the same amount received late in the rate only buys 0.10pp. Moreover,
the difference between the two coefficients is statistically significant. This result indicates
that early access to financial resources has a greater impact on outcomes than money
received later in the race and suggests that individual donors, political party committees,
and PACs should contribute to challenger committees as early as possible in the general
election.15
Figure 1.5 shows the evolution of the effect of unexpected challenger revenues on
the challenger vote share over the course of the general election. The figure presents the
coefficients ?Ct in the regression:
?
V oteShare = ? + ? AggShockUSD + ? ShockUSD + ??C y I I Ct Ct Controls+  (1.7)
t
The figure confirms the decreasing effect of unexpected revenues on the vote share as
election day draws nearer. In particular, revenues have no effect on the vote share starting
four weeks before the election.
15This result is also present in the model presented in Chapter 2. The marginal effect of an additional
unit of cash is larger early in the race because committees can reinvest the cash to generate additional
fundraising revenues. Additionally, early cash infusions provide flexibility to respond to the opponent?s
actions and mitigate current and future financing constraints.
27
Figure 1.5. Timing of Revenues and Vote Share. This figure shows the effect of unexpected
challenger revenues on the challenger vote share over the course of the general election.
1.4.3 Additional Analysis
Finally, I consider how the sensitivity of the challenger?s spending to its own (weekly) shocks
and to the shocks of the incumbent affect the impact of unexpected revenues on the vote
share. I start by estimating the baseline specifications for each committee in the sample
to collect the elasticities of advertising expenditures to own and opponent?s unexpected
revenues obtained in Chapter 2.16 Then, I create dummy variables that capture whether
a committee?s elasticity is below or above the cross-sectional median. The second column
of Table 1.3 indicates that unexpected revenues accruing to challengers that react less to
their own revenue shocks have a larger impact on the vote share. This result suggests that
smoothing revenue shocks has a positive effect on outcomes and that financing constraints
prevent challengers from increasing their vote share. The third column of Table 1.3 indicates
16Specifically, I estimate Equation (2.19) and Equation (2.20) at a horizon of one week (h = 1). I drop
the time fixed effects (?t) to prevent multicollinearity in the set of explanatory variables.
28
that a challenger that reacts more to the shocks of the incumbent sees a larger increase
in her vote share for a given amount of unexpected revenues. This result suggests that
challenger spending in response to incumbent spending translates into a better outcome.
Table 1.3
Effect of Revenues on the Vote Share (II)
This table reports the results of regressions of the challenger vote share on revenue shocks for races in
the main sample that involve the incumbent. The indices C and I correspond to the challenger and the
incumbent, respectively. SumShockEarlyi (SumShockLatei) is the sum of the weekly LASSO shocks
of the primary committee for candidate i between weeks -12 and -7 (-6 and -1). HighOwnBetaC and
LowOwnBetaC are dummy variables indicating whether the sensitivity of own spending to own revenue
shocks of the challenger committee is above or below the cross-sectional median. HighOppBetaC and
LowOppBetaC are defined similarly for the sensitivity of the challenger?s spending to shocks of the incumbent.
Unemployment is measured at the state level. IncRulingParty is a dummy variable that indicates whether the
incumbent is in the same party as the U.S. president. Monetary variables are expressed as multiples $100,000.
Vote shares and polling variables are expressed in percent. Heteroskedasticity-robust standard errors are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
V oteShareC V oteShareC V oteShareC
SumShockI 0.073 0.056 0.073
(0.163) (0.158) (0.156)
SumShockEarly 1.479???C
(0.370)
SumShockLateC 0.103
(0.263)
SumShockC ?HighOwnBetaC 0.464??
(0.191)
SumShockC ? LowOwnBetaC 1.001???
(0.279)
SumShock ?HighOppBeta 0.761???C C
(0.208)
SumShockC ? LowOppBetaC 0.448
(0.299)
InitialPollingI -0.397??? -0.404??? -0.404???
(0.061) (0.061) (0.061)
InitialCashI 0.023 0.036 0.037
(0.037) (0.035) (0.035)
InitialCash 0.474??? 0.480??? 0.476???C
(0.073) (0.071) (0.073)
Unemployment -0.722??? -0.727??? -0.698??
(0.274) (0.274) (0.276)
Unemp? IncRulingParty 0.509??? 0.526??? 0.525???
(0.162) (0.160) (0.161)
Year FE X X X
R2 0.429 0.423 0.421
N 333 333 333
29
1.5 Conclusion
In this paper, I study how money affects electoral outcomes. While most of the political
science literature studies how candidate spending affects the vote share, I focus on the
fundraising revenues received by candidates. I assemble a high-frequency dataset of
committee finances that provides a comprehensive picture of cash flows and cash balances
during the race. Then, I use machine learning to extract shocks that capture the
unexpected component of fundraising revenues.
I find that a $100,000 unexpected increase in total challenger revenues increases her
vote share by 0.66 percentage points; however, I do not find a significant effect for the
incumbent. The magnitude of the effect for the incumbent and challenger are consistent
with the findings of Jacobson (1978) and Gerber (2004) who study the effect of campaign
spending on the vote share.
I also find that unexpected revenues received early in the race have a larger impact on
the challenger?s vote share than those received later in the race. Early access to financial
resources allows the challenger to better respond to the incumbent?s actions and mitigate
current and future financing constraints.
30
Chapter 2: Financial Resource Allocation During General Elections
2.1 Introduction
Political spending exploded in the 2020 U.S. federal election with a total cost of $14.4
billion, more than twice the amount spent in the 2016 election.1 Although the role of
aggregate spending in elections has been studied extensively by political scientists, much
less is known about the dynamics of fundraising and spending over the course of electoral
races.2
In this paper, I explore how U.S. congressional candidates deploy financial resources
during general elections and how strategic and financial considerations shape their
advertising expenditures. In particular, I study electoral races using methodological tools
developed in the fields of industrial organization and finance.
Federal campaign finance regulations require candidates to perform fundraising and
spending activities through legal entities called campaign committees. Committees are
financially-constrained organizations?they finance their spending through cash reserves
and donations, but generally do not have access to debt. Committee spending consists
primarily of intangible expenditures, specifically of political messaging that attempts to
1The total cost of the 2016 election was $7 billion. Figures include total spending on presidential and
congressional races and are adjusted for inflation. Source: OpenSecrets.org.
2A small literature studies the dynamics of electoral races (see Section 2.1.1), but the topic remains
underexplored.
31
affect, either positively or negatively, the perception of a candidate by voters. Additionally,
committees operate in a decidedly strategic environment due to the limited number of
opponents and the winner-take-all nature of elections. These characteristics justify studying
committee behavior through the lens of economics and finance.
I discipline the empirical analysis with a dynamic model of strategic intangible
investment under financing constraints. Since campaign committees are narrowly-focused
organizations, they are amenable to a comprehensive analysis. In the model, committees
spend their cash reserves on positive and negative political messaging in order to
influence the outcome of an election. Committees increase their cash reserves through
donations, but the amount raised in a given period is subject to some uncertainty. The
model delivers testable predictions about the response to unanticipated fundraising
revenue shocks, as well as about the effect of cash reserves on the response.
In the model, two campaign committees allocate their cash reserves between two
types of spending over the course of an electoral race. Committees cannot borrow from
external markets, but can increase their cash balances by spending on positive messaging,
which generates fundraising revenues and contributes to their stock of political capital,
an intangible asset that captures their standing in the race. Alternatively, committees
can spend on negative messaging to increase the depreciation rate of their opponent?s
political capital. In equilibrium, committees spend a larger fraction of their cash on negative
messaging when their opponent is stronger, either in terms of cash reserves or political
capital.
To understand the response to revenue shocks, I calibrate the model such that it
captures salient features of the data. Simulating the model delivers four key testable
32
predictions. First, a committee?s response to its own revenue shock is positive. Second,
the sign of a committee?s response to the opponent?s shock depends on the
parameterization, and is positive when negative messaging is relatively more productive
than positive messaging. Third, the response of the opponent is larger when the shock
recipient has lower cash reserves. Finally, the magnitude of the opponent?s response is
larger when the shock recipient is ahead in the race.
I test the predictions of the model in the sample of high-profile electoral races for
the U.S. House of Representatives discussed in Chapter 1. I find strong evidence that
financial conditions affect the response to revenue shocks. In head-to-head races, both
committees increase advertising expenditures following a positive revenue shock to either
of the committees, indicating the presence of strategic interactions and financing
constraints. Specifically, the elasticity of advertising expenditures to own revenue shocks
is 26%, while the elasticity to the opponent?s shocks is 8%. Moreover, the relative amount
of cash reserves directly affects the magnitude of the opponent?s response, which triples
when the cash reserves of the shock recipient are low relative to that of the responding
committee. This result suggests that committees use their financial advantage to
undermine weaker opponents when the latter receive unexpected revenues and that the
availability of internal financing can amplify the competitive aspect of intangible
investment. The response to the opponent?s shock is also stronger in the presence of
negative advertising, a result consistent with the predictions of the model. Finally, the
response is larger when shocks are more likely to be observed, for instance if they are
sizable or occur when FEC reporting requirements are more stringent.
The baseline specification estimates a non-parametric impulse response by
33
regressing future advertising expenditures on the shocks. A potential threat to the
identification would be an omitted variable affecting both the shock and future
advertising, leading to spurious results. I alleviate this concern by controlling for the
shock recipient?s contemporaneous advertising, the opponent?s shock, as well as the
opponent?s contemporaneous and future advertising. Additionally, I show that controlling
for spending by other political organizations does not materially alter the results.
The remainder of the paper is organized as follows. I review the related literature in
Section 2.1.1. In Section 2.2, I present a model of strategic intangible investment under
financing constraints and derive testable implications. I present the empirical findings in
Section 2.3. Concluding remarks are in Section 2.4.
2.1.1 Related Literature
Several papers highlight the importance of considering electoral campaigns from a dynamic
perspective (Box-Steffensmeier, Darmofal, and Farrell, 2009; Carsey, Jackson, Stewart, and
Nelson, 2011; Feigenbaum and Shelton, 2013). Acharya, Grillo, Sugaya, and Turkel (2021)
model the dynamic allocation problem of strategic candidates during an electoral race and
measure the perceived rate of decay in popularity leads. My paper provides additional
evidence of dynamic strategic interactions during U.S. congressional races and explores
how unexpected revenues accruing to one of the committees shape the spending decisions
of its opponent..
This paper contributes to the literature on intangible investment (Almeida and
Campello, 2007; Eisfeldt and Papanikolaou, 2013; Gourio and Rudanko, 2014; Peters and
34
Taylor, 2017; Crouzet and Eberly, Forthcoming). Most papers that study intangible
investment consider perfectly competitive organizations or model market power in
reduced form, although there are notable exceptions, in particular in R&D-intensive
industries such as semiconductors and pharmaceuticals (Megna and Klock, 1993;
Cockburn and Henderson, 1994; Rao, 2020; Krieger, 2021). In this paper, I model
campaign committees as players in a dynamic game of intangible investment with explicit
financing constraints and study their strategic response to revenue shocks.
This paper also contributes to the literature studying the interaction between
financing constraints and strategic behavior (Brander and Lewis, 1986; Maksimovic,
1988). Doraszelski, Gomes, and Nockher (2021) propose a dynamic model of industry
equilibrium in which financial market imperfections impact the strategic interactions
between firms. My paper sheds light on the effect of financing constraints on intangible
investment in strategic settings. Schroth and Szalay (2010) examine whether financing
constraints affect a rival?s decision to pursue innovation. Our papers share the idea that
an organization?s investment is affected by the financial situation of all the competitors in
the industry.
Finally, this paper relates to the concepts of predation and strategic advertising in
industrial organization. Predation is unlikely to occur in theoretical models of industry
equilibrium (McGee, 1958; Telser, 1966), unless additional frictions are involved, for
instance through reputation effects (Kreps and Wilson, 1982; Milgrom and Roberts,
1982), asymmetric information (Benoit, 1984; Fudenberg and Tirole, 1986), or agency
problems (Bolton and Scharfstein, 1990). In my model, cash-rich committees incur a
short-term loss by spending on negative messaging and receive a long-term benefit
35
through the higher depreciation rate of their opponent?s political capital. This mechanism
is verified in the data and similar to predation in spirit. In the model, committees expend
resources on messaging to build voter goodwill as in strategic advertising models (Dub?,
Hitsch, and Manchanda, 2005; Borkovsky, Goldfarb, Haviv, and Moorthy, 2017; Ellison
and Ellison, 2011; Bar and Haviv, 2021).
2.2 Model
In this section, I derive a dynamic model of strategic intangible investment to analyze
how committees respond to revenue shocks during an electoral race. The model construes
committees as firms competing in a closed market?the electoral race?and lacking access to
external capital markets. Therefore, spending must be financed by existing cash reserves
and donations. Spending takes the form of positive and negative political advertising
which I call investment and hindrance, respectively. Investment improves the competitive
position of the committee, while hindrance prevents its opponent from improving their own
competitive position. In the nomenclature proposed by Besanko, Doraszelski, and Kryukov
(2014), investment is advantage-building and hindrance is advantage-denying.
2.2.1 Setup
Two players indexed by i represent the candidates in a general election. No other candidates
can enter the race. There are no agency frictions between the candidates and their campaign
staff, therefore I refer to candidates and committees interchangeably. The game is played
in discrete time and has a finite horizon that corresponds to the election date. Time starts
36
at 0, ends at T + 1, and is indexed by t.
Candidate i wins the election held at T + 1 against candidate ?i if her realized vote
margin Mi is positive. The realized vote margin of candidate i is defined as:
Mi = Ki,T+1 ?K?i,T+1 + ? (2.1)
where K represents political capital and ? is a random variable that follows a centered
Laplace distribution with scale parameter ?.3 In effect, ? captures uncertainty in the
outcome of the race that is orthogonal to the spending patterns and non-monetary
characteristics of the candidates. Political capital captures a candidate?s popularity in
their congressional district and can be construed as a stock of goodwill (Nerlove and
Arrow, 1962).
The probability that candidate i wins the election is:
( )
P [ 0] = Ki,T+1 ?K?i,T+1Mi > F (2.2)
?
where F is the standard Laplace cumulative distribution function. Similar expressions
for the probability of winning appears in the campaign finance literature (see for instance
Erikson and Palfrey (2000)). The probability of winning is increasing in a candidate?s own
political capital and decreasing in the political capital of her opponent. In the model,
the difference in initial political capital captures a candidate?s pre-spending expected vote
3 ?The mean and standard deviation of ? are 0 and 2? respectively. The distributional assumption
is made for computational convenience because the model is solved numerically. However, using any
symmetric distribution with finite second moment and centered at zero would yield similar results.
37
margin.4
Both candidates have the same utility valuation of a win, no utility for leftover money,
and do not derive utility or disutility from campaigning.5 Therefore, candidates do not quit
the race as long their conditional probability of winning is strictly positive, which is always
the case given the distribution of ?. In each period t, committee i allocates its cash reserves
to investment (Iit), hindrance (Hit), and savings in order to maximize the probability of
winning the election, taking the strategy of its opponent ?i as given.6
Investment and hindrance constitute campaign spending that ultimately affects the
vote margin. In practice, this type of spending corresponds to political advertising and
messaging to voters. Previous research in the field of campaign finance suggests that
political advertising does indeed help candidates win elections (Gerber, Gimpel, Green,
and Shaw, 2011; Kendall, Nannicini, and Trebbi, 2015; Spenkuch and Toniatti, 2018). In
the model, investment and hindrance can be construed as positive and negative messaging,
respectively. The empirical section of the paper confirms this interpretation using data
capturing the tone of political TV advertising.
The optimization problem of committee i is:
[ ( )]
max KE i,T+1 ?K?i,T+10 F (2.3)
{Iit,Hit}T ?t=0
4To see this, let mi0(= Ki0 ? K?i0 be the differen)ce in initial political capital and rewrite Equation
(2.2) as P [M ? 0] = F mi0 + ?Ki,0?T +1??K?i,0?T +1i ? ? where ?Ki,t1?t2 corresponds to the change in the
political capital of player i between t1 and t2. Absent any spending, the probability that candidate i wins
the race is F (mi0? ) and her expected vote margin is mi0. Therefore, the difference in initial political capital
captures intrinsic non-monetary heterogeneity that influences the outcome of the election.
5The second assumption is justified by the focus on close races in the empirical exercise. Committees
in those races have minimal cash on hand left after the election. Additionally, I assume that committees
do not precautionarily save for potential recounts and legal challenges that may arise after the election.
6Alternatively, candidates could be maximizing vote share. In footnote, Gerber (2004) states that
?[m]aximizing the probability of victory is the most intellectually satisfying objective function.?
38
subject to:
Wi,t+1 = Wit ? Iit ?Hit ? ?(Iit, Kit) + f(Iit, it) (2.4)
Wit ? Iit +Hit + ?(Iit, Kit) (2.5)
0 ? Iit, Hit,Wit (2.6)
Ki,t+1 = (1? ?)?(H?it)Kit + Iit (2.7)
Wit are the cash reserves of committee i at time t and follow the law of motion given
in Equation (2.4). The term ?(Iit, Kit) captures the cost of installing political capital.
Finally, the term f(Iit, it) represents fundraising revenues.
Period t is broken down into two phases. First, the committee spends cash on
investment, hindrance, and adjustment costs. The realization of the revenue shock it is
not included in the information set of committee i when making decisions at time t.
Then, the committee receives fundraising revenues based on the investment made in the
first phase. A committee cannot increase investment in the first phase by borrowing
against fundraising revenues from the second phase, or against any future revenues.7 This
restriction is captured by the liquidity constraint (or cash-in-advance constraint) in
Equation (2.5). Additionally, Equation (2.6) puts a non-negativity constraint on
investment, hindrance, and cash reserves.
The adjustment costs of political capital are quadratic in investment:
( ) = ?0I
2
? Iit, K itit 2 with ?0 ? 0. Therefore, costs are increasing and convex in investment.Kit
7In Appendix B.1.5, I discuss a version of the model in which committees are allowed to borrow against
future revenues.
39
These properties are consistent with the concept of multiple touchpoints in advertising
(Baxendale, MacDonald, and Wilson, 2015): reaching a potential voter through two
different channels (e.g. a TV ad and a radio ad) is superior to reaching her through the
same channel (e.g. broadcasting the same TV ad twice). As the size of investment
increases, so does the number of channels used by the committee and the corresponding
installation costs. For tractability, hindrance does not entail installation costs.
Fundraising revenues are operationalized by f(Iit,  ?it) = itIit with ? in the open unit
interval. In recent years, the fraction of fundraising revenues coming from small donations
has increased significantly (Bouton, Castanheira, and Drazen, 2021). Therefore, I assume
that positive advertising increases fundraising revenues thanks to the higher visibility of
the candidate. The term it follows a binomial distribution and is a multiplicative revenue
shock that introduces randomness in fundraising by varying the productivity of investment:
???????u with probability p
iid
it ? ??????
(2.8)
d with probability 1? p
The shock it becomes publicly observable after time-t decisions have been made and is
independent of ? for all i and t. The following relationships must hold: u ? 1, 0 ? d ? 1,
and E[it] = 1. Therefore, the parameter d can be expressed as a function of u and p:
d = (1 ? pu)/(1 ? p). The condition pu < 1 must hold to ensure that probabilities lie
in the closed unit interval. The conditional expectation in the maximization problem in
Equation (2.3) is taken with respect to uncertainty about realizations of it. The uncertainty
pertaining to the vote margin, ?, is already captured in the cdf F .
40
Political capital evolves over time according to the law of motion in Equation (2.7).
Spending affects next-period political capital in two ways. First, own investment (Iit)
replenishes the stock of capital like in standard investment models (Abel and Eberly,
1994; Strebulaev and Whited, 2012). Second, the opponent?s hindrance (H?it) affects the
depreciation rate of a committee?s political capital through the hindrance function ?. I
operationalize the hindrance function as ?(H?it) = e??0H?it with ?0 ? 0. That is, ? is
decreasing and convex in hindrance.
The depreciation rate of political capital when the opponent does not spend on
hindrance is ?. The effective depreciation rate of political capital is
?eit = 1 ? (1 ? ?)?(H?it). The effective depreciation rate is committee-specific,
time-varying, and depends on the opponent?s decisions. These properties are intuitive
given the intangible nature of political capital and obtain in a wide range of economic
settings, although they are often not explicitly stated.8
Expending resources on investment is advantage-building as it increases the
competitive position of the spender (Besanko et al., 2014). The advantage is obtained
through three distinct channels. First, investment has a direct effect as it increases the
committee?s stock of political capital and hence its standing in the race. Second,
investment decreases future adjustment costs through its effect on current political
capital. Third, investment generates fundraising revenues that can be used in future
periods to generate further spending.
8For instance, consider a monopolist who owns a design that yields a stream of cash flows. The value
of the design, and consequently of the monopolist?s firm, is the present value of the sum of future cash
flows. Suppose that a potential entrant can invest in order to create and improve a competing design, that
the quality of the design increases with each round of investment, and that higher quality translates into
higher market share for the entrant. As a result, the effective depreciation rate of the monopolist?s design
directly depends on the investment decisions of the potential entrant.
41
On the other hand, spending on hindrance is advantage-denying because it
deteriorates the opponent?s competitive position in the race. The obstruction works
through two channels: lower political capital (direct effect) and higher future capital
installation costs (indirect effect).
2.2.2 Solution
I choose pure strategy Markov perfect Nash equilibrium as the solution concept (Maskin
and Tirole, 2001). The state variables are the cash reserves and the stocks of political
capital of the two committees. The game can be solved by backward induction since it has
a finite horizon. I discuss the solution to the optimization problem of committee 1 without
loss of generality.
In the last period of spending (time T ), the liquidity constraint binds and the
committee spends all its cash reserves since the cumulative distribution function F is
increasing in both choice variables and leftover cash does not confer any utility.
Proposition 2.1. The optimal spending of committee i at date T is given by:
?????????
???0 if ?(0) ? 0?
H?1T = ??????W1T if ?(W1T ) ? 0
(2.9)
?????? ( )?+ K1T ? 1 W K1T 2? W + 0 KW1T 2 2 e 0 1T ?0 1T otherwise?0 ?0 ?0?0(1??)2K22T
?? ?
K ?1T
I? = ?1T 1 + 2?0 (W1T ?H1T ) ? 1? (2.10)?0 K1T
42
( )? 1
where ?(H1T ) = (1 ? ?)K ? e??0H2 0 1TT ? 1 + 2?0(W1T?H1T ) 2 and W is Lambert?s WK1T
function.
Proof. See Appendix B.1.1.
The first two cases in Equation (2.9) are corner solutions; the last case corresponds to
an interior solution. The expression for I?1T in Equation (2.10) is derived from the liquidity
constraint that binds in equilibrium.
In Appendix B.1.2, I compute the marginal effect of each model primitive on
optimal investment and hindrance and provide conditions for an interior solution.
Committees spend less on hindrance as the baseline depreciation rate ? increases because
nature hinders political capital for them. Committees substitute investment for hindrance
as the installation cost of investment captured by ?0 increases. Hindrance decreases in
own political capital because investment installation costs become cheaper with each unit
of existing capital. Finally, hindrance increases with the opponent?s political capital.
Committee decisions are more complicated prior to the last round of spending. In
particular, a committee may not deplete its entire cash reserves at t < T and hence must
decide how much to save for period t + 1. Additionally, the committee must take into
account the role of investment in generating fundraising revenues.
The structure of the problem allows for two simplifications when solving for optimal
decisions at t < T . First, the non-negativity constraint on Iit never binds because the
fundraising revenue function f satisfies the Inada (1963) conditions. In particular, the
marginal productivity of investment is infinite at Iit = 0. Second, the non-negativity
constraint onWit never binds if the starting cash reservesWi0 are positive and all the other
43
constraints are not violated at any point during the game. As a result, the only constraints
that matter besides the law of motions of cash and political capital are the non-negativity
constraint on hindrance and the liquidity constraint.
Proposition 2.2 characterizes the solution of the model for decisions made at t < T
using a system of first-order conditions derived from the Bellman equation of each
committee. In general, this problem does not have a closed-form solution and must be
solved numerically. The solution procedure described in Appendix B.1.4 exploits the
recursive structure of the game and the existence of a closed-form solution in the last
period of spending.
Proposition 2.2. The equilibrium spending of the committees at date t < T is the vector
(I1t, I2t, H1t, H2t, ?1tH , ?2tH , ?1tW , ?2tW ) that solves the following system of equations
simultaneously for (i,?i) ? {(1, 2), (2, 1)}:
[ ( )]
?Vi,t+1 + ?Vi,t+1 ?1? ??(Iit, Kit) + ?f(Iit, E it)t
?Ki,t+1 ?Wi,t+1 ?Iit ?Iit [ ]
+ ??(Iit, Kit)?
[ ( itW
?1? = 0 (2.11)
)] ?Iit
?V
E 1,t+1t (1? ?)??(Hit)
??(Iit, Kit)
K
[ ?it
?1?
?K?i,t+1 ]?Iit [ ]
+ ?Vi,t+1 + ?Vi,t+1 ?f(Iit, it) + ?1? ??(Iit, Kit)Et ?itH = 0 (2.12)
?Ki,t+1 ?Wi,t+1 ?Iit ?Iit
?itHHit = 0 (2.13)
?itW [Wit ? Iit ?Hit ? ?(Iit, Kit)] = 0 (2.14)
?itH , ?itW ? 0 (2.15)
Proof. See Appendix B.1.3.
44
To understand the economics of the proposition, consider an interior solution (?1tW =
?1tH = 0) and rearrange Equation (2.11) and Equation (2.12) into:
[ ( )]
?V
E 1,t+1 + ?V1,t+1 ?f(Iit, it) + ?V1,t+1 ?1? ??(I1t, K1t)t = 0 (2.16)
?K1,t+1 ?W1,t+1 [?Iit ?W1,t+1 ?I1t ]
Et ?
?V1,t+1 + ?V1,t+1 (1? ?)??(H1t)K2t = 0 (2.17)
?W1,t+1 ?K2,t+1
The first equation corresponds to the first-order condition of the committee with
respect to investment. The committee invests such that in expectation, the marginal
benefits and marginal costs of investment are equal. A marginal increase in investment
today increases political capital tomorrow and increases fundraising revenues today, which
increases cash reserves tomorrow. A marginal increase in investment today also decreases
cash reserves tomorrow because of the cash outlay for the investment and adjustment
costs. The second equation to the first-order condition with respect to hindrance. A
marginal increase in hindrance decreases the committee?s cash reserves, but it also
decreases the political capital of its opponent.
2.2.3 Parameterization
I calibrate the parameters of the model before deriving predictions about the responses
to revenue shocks. For simplicity, I specialize the setting to a four-period model with
three rounds of spending at t = 0, 1, 2, and an election held at t = 3. In the calibration,
I select parameters that capture features of the campaign finance data. The resulting
parameterization is listed in Table 2.1.
45
Table 2.1
Baseline Parameterization
This table shows the baseline parameterization of the model. The parameters governing the potency of
hindrance (?0) and capital adjustment costs (?0) are not calibrated. Instead, I consider multiple combinations
(?0, ?0) restricted to the interval [1, 15]? [1, 15].
Parameter Category Description Value
? Revenues Curvature of revenue function 0.85
u Revenues Intensity of positive shock 1.5
p Revenues Probability of positive shock 0.25
?0 Hindrance Hindrance potency [1, 15]
?0 Capital Capital installation cost [1, 15]
? Capital Capital depreciation rate 0.15
? Election Scale of vote margin shock 0.10
Ki0 State Variable Initial stock of political capital 0.05
Wi0 State Variable Initial cash reserves 0.40
First, I set the depreciation rate of political capital to ? = 0.15. The political science
literature finds that campaign messaging mostly has short-term effects (Hill, Lo, Vavreck,
and Zaller, 2013). However, ? captures the decay rate of the total stock of political capital,
which should depreciate at a slower rate than investment flows.
Second, I choose the parameters of the revenue shocks such that they display positive
skewness as in the data.9 I choose the values u = 1.5 and p = 0.25.
Third, I set ? = 0.85 in order to deliver time series patterns consistent with the data.
In event time, advertising expenditures, total expenditures, and fundraising revenues are
all increasing, both in levels and as a fraction of cash reserves. Additionally, cash balances
are decreasing in event time. High values of ? in the unit interval produce the desired
9See Section 1.3 for details on the shock construction and summary statistics.
46
patterns.
Finally, I set the scale parameter of the Laplace random variable to ? = 0.10. This
value implies that the standard deviation of the shock to the vote margin is 0.14.
I do not calibrate ?0 and ?0 based on the data or economic intuition. Instead, I
study how combinations of these parameters influence the response to revenue shocks. In
particular, I focus on the combinations ?0 = ?0 = 5 and ?0 = ?0 = 8 because they deliver
diametrically opposed predictions regarding the sign of the opponent?s response.
Figure 2.1. Model Time Series Patterns. This figure presents the time series patterns
generated by the model. The left column shows the parameterization ?0 = ?0 = 5; the right
column shows the parameterization ?0 = ?0 = 8. The other parameters follow the baseline
calibration in Table C.6. The top row shows spending (the sum of investment and hindrance,
excluding adjustment costs) scaled by cash reserves. The middle row shows fundraising revenues
scaled by cash reserves. The bottom row shows the level of cash reserves.
47
Figure 2.1 illustrates three time series patterns generated by the model: the sum
of investment and hindrance over cash, fundraising over cash, and cash reserves. The
left column uses ?0 = ?0 = 5, the right column ?0 = ?0 = 8. The resulting patterns
are similar under both parameterizations. More importantly, the figure confirms that the
model captures important time series features of the data (see Section 1.2 for the empirical
counterparts). However, note that the model is conceptual in nature and by no means
intended to capture every single aspect of the data. In a robustness exercise not presented
here, I show that slightly modifying the calibrated parameters does not materially affect
the predictions of the model.
2.2.4 Predictions
I simulate the four-period calibrated model to establish testable predictions about the
response to revenue shocks. Since the revenue shock is binary for each committee and
investment period, the simulated model for a combination of initial state variables can be
represented as a quaternary tree with 16 nodes in the last round of spending. I study the
spending decisions of the committees conditional on a positive shock to committee 1 (the
recipient) between time 0 and time 1, and by averaging over the shocks to committee 2
(the opponent). The timeline is presented in Figure 2.2. Specifically, I define the response
to a shock as the expectation of a variable conditional on the realization of the shock in
excess of its unconditional expectation. Moreover, I scale the response with the aggregate
cash reserves in the race before the realization of the shock.10 For instance, the response
10I provide a rationale for the scaling in Section 1.3. The model delivers the same predictions when
responses in levels are scaled by own cash reserves rather than total cash reserves.
48
of committee i to a positive revenue shock to the recipient (r) is:
E [Xi1|r0 = u]? E [Xi1] (2.18)
Wi0 +W?i0
where Xi1 is any variable pertaining to committee i at time 1. In particular, I focus on
investment, hindrance, and the sum of the two.
t = 0 t = 1 t = 2 t = 3
Spending Revenues Spending Revenues Spending Election
Figure 2.2. Model Timeline. This figure presents the timeline of the four-period model.
Spending decisions (Iit and Hit) are made at t = 0, 1, 2. The election is held at t = 3. In each
period, fundraising revenues are received after spending decisions are made. The realization of
the revenue shock is unknown when spending decisions are made. Committees cannot borrow
against future revenues.
The first two predictions outline how the parameters ?0 and ?0 shape the response
to revenue shocks. To generate the predictions, I simulate the model for the 225
combinations (?0, ?0) where ?0 = 1, . . . , 15 and ?0 = 1, . . . , 15, then calculate the
response of the committees to the recipient?s shock. Prediction 2.1 and Prediction 2.2
characterize the response of the recipient and of the opponent, respectively.
Prediction 2.1. The recipient?s response to its own revenue shock is positive.
In the simulation, the response of the recipient to its own shock is positive for all
combinations of ?0 and ?0. This result is intuitive. A positive revenue shock increases the
recipient?s cash reserves and relaxes the liquidity constraint after the shock, which allows
the recipient to increase its spending.
49
Prediction 2.2. The sign of the opponent?s response to the recipient?s revenue shock
depends on the model parameterization. The response is positive for large enough values
of ?0 and ?0, that is when adjustment costs are high and hindrance is potent.
Figure 2.3. Opponent?s Response to the Recipient?s Shock. This figure shows a heatmap
of the direction of the opponent?s response to the recipient?s positive revenue shock. The response
is calculated as (E [X2,t=1|1,t=0 = u]? E [X2,t=1]) / (W1,t=0 +W2,t=0). The blue area on the left
corresponds to a minor response, defined as being less than 10% of the response of the recipient
to its own shock. The red area in the middle corresponds to a negative response by the opponent.
The green area on the right corresponds to a positive response by the opponent.
Figure 2.3 shows the direction of the opponent?s response to the recipient?s shock as
a function of ?0 and ?0. The figure reveals three distinct areas in the parameter space.
The opponent exhibits a minor response to the shock when ?0 takes low values (blue area).
I deem the opponent?s response to be minor if it is less than 10% of the response of the
recipient in absolute value. For larger values of ?0, the response may be either positive
(green area) or negative (red area) depending on the parameters. The figure shows that
we should expect a positive response when hindering the opponent is more effective than
50
building own political capital through investment. Indeed, when ?0 is high, hindrance is
more potent, and when ?0 is high, investment becomes more costly to install. Large values
of ?0 and ?0 correspond to the green area in the figure.
Next, I analyze how differences in cash reserves influence the response to shocks. I
focus on two combinations of (?0, ?0), namely (5, 5) and (8, 8), and vary the initial cash
reserves of the recipient while keeping those of the opponent constant. After simulating the
model, I compute the responses of the committees to a positive shock to the recipient as a
function of the recipient?s initial cash reserves. Prediction 2.3 provides the corresponding
testable implications.
Prediction 2.3. The response of both committees is stronger when the shock recipient has
lower cash on hands.
Figure 2.4 illustrates the prediction. The first column shows the responses when the
opponent?s aggregate response is negative (?0 = ?0 = 5). The second column shows the
responses when the opponent?s aggregate response is positive (?0 = ?0 = 8). The first
row corresponds to the aggregate response (I +H); the second and third rows break down
the responses into investment and hindrance separately. Since in the model committees
cannot borrow from external sources, cash reserves reflect the amount of internal financing
available for current and future spending. The figure clearly shows that the response of
both committees is non-increasing in the cash reserves of the recipient.
The figure also shows that the shock recipient is undermined by her opponent with
deep pockets: the opponent?s response is larger when the recipient has lower cash reserves.
This behavior is similar to predation, whereby the opponent incurs a short-term negative
51
cash flow (the amount spent on hindrance) in exchange for a long-term gain. The long-term
gain can be broken down into two distinct effects. The direct effect captures the fact that
hindrance increases the depreciation rate of the opponent?s political capital, and lowers her
expected vote margin in the election. The indirect effect captures the increase in future
installation costs of investment due to the lower stock of political capital.
The opponent positively responds to the shock when capital adjustment costs are high
and hindrance is potent (second column). This corresponds to a ?catching up? behavior:
the opponent spends in order to counteract the higher spending of the recipient following
the shock and so as not to be left behind in the race. In the first column, the response
is negative, akin to a ?yielding? behavior whereby the opponent decreases investment and
postpones spending to a later period.
The figure also provides additional evidence that the positive response to an
opponent?s shock is driven by hindrance. Under both parameterizations, the opponent?s
investment response is negative. When investment is more effective than hindrance (first
column), committees do not resort to the latter, and thus the opponent?s response to the
shock is negative because it is only driven by investment. However, when investment is
less effective than hindrance, committees make use of the latter as illustrated in the
second column. If the hindrance response is large enough in magnitude, the overall
response turns positive.
52
Figure 2.4. Response to Shocks and Cash Reserves. This figure shows the response of
the committees to a positive revenue shock to the recipient as a function of the recipient?s initial
cash reserves. The left column shows the parameterization ?0 = ?0 = 5; the right column shows
the parameterization ?0 = ?0 = 8. The other parameters follow the baseline calibration in Table
C.6. The top row shows the aggregate response at t = 1 (the sum of investment and hindrance,
excluding adjustment costs) scaled by total cash reserves at t = 0. The middle row shows the
response for investment at t = 1 scaled by total cash reserves at t = 0. The bottom row shows
the response for hindrance at t = 1 scaled by total cash reserves at t = 0. The horizontal axis
corresponds to the cash reserves of the recipient at t = 0. The green (blue) line is the response of
the recipient (the opponent).
Finally, I analyze how a committee?s response varies as a function of the difference
in political capital in the race. I first solve the model under the baseline parameterization
with ?0 = ?0 = 8 and the calibrated model primitive listed in Table C.6. Then, I solve
the same model assuming that the shock recipient?s initial political capital takes a larger
53
value.
Prediction 2.4. The magnitude of the opponent?s response increases with the shock
recipient?s political capital when the opponent?s response is positive.
Figure 2.5. Response to Shocks and Political Capital. This figure shows the response of
the opponent to a positive revenue shock to the recipient for two different values of the recipient?s
political capital. The figure uses the parameterization ?0 = ?0 = 8. The other parameters follow
the baseline calibration in Table C.6. The horizontal axis corresponds to the cash reserves of the
recipient at t = 0. The vertical axis corresponds to the aggregate response of the opponent at
t = 1 (the sum of investment and hindrance, excluding adjustment costs) scaled by total cash
reserves at t = 0. The continuous line shows the response for the baseline parameterization
(K1,t=0 = 0.050). The dotted line shows the response when K1,t=0 = 0.075.
Figure 2.5 shows the prediction visually. The continuous line corresponds to the
baseline response of the opponent. The dotted line represents the opponent?s response
when the recipient?s political capital is larger. A dollar spent on hindrance by the
opponent becomes more efficient as the stock of political capital of the recipient increases,
and therefore the opponent responds more strongly to the shocks of the recipient as its
political capital increases.
Next, I study the policy function of the opponent to shed light on the economic
forces that drive its response to revenue shocks. Figure 2.6 shows the spending policies of
the opponent at t = 1 as a function of the state variables when the response is positive
54
(?0 = ?0 = 8). The opponent spends less on investment and more on hindrance as the
cash reserves of the recipient increase. A rich recipient will have to spend its cash at some
point in the future. Knowing that, the opponent increases hindrance in order to decrease
the recipient?s current political capital and increase its future capital adjustment costs. A
dollar spent on hindrance affects the recipient?s political capital more as capital increases
because the hindrance function affects capital multiplicatively in Equation (2.7). Therefore,
the opponent?s spending on hindrance increases with the political capital of the recipient.
The opponent?s investment increases in its own political capital because adjustment costs
are lower.
In the model, committees tend to use hindrance when their opponent is stronger,
either in terms of cash reserves or political capital. Conversely, committees tend to use
investment when their opponent is weaker. This effect has been documented in actual
elections: the candidates that go negative tend to be those who are behind in the polls
or have access to less financial resources (Lau and Pomper, 2002). A positive revenue
shock shifts the position of the recipient in the cash state space. The opponent responds by
decreasing investment and increasing hindrance because the recipient has gained a financial
advantage. The overall direction of the response depends on the relative magnitude of the
changes in investment and hindrance which itself depends on the parameters driving the
intensity of investment adjustment costs (?0) and the potency of hindrance (?0).
The model is inherently conceptual and illustrates the economic trade-offs facing
campaign committees over the course of an electoral race. Nevertheless, it is able to deliver
sharp testable implications about the direction of the response to revenue shocks. In the
remainder of the paper, I turn to the data to measure the direction and magnitude of
55
the response to revenue shocks and investigate the effect of existing cash reserves on the
response.
Figure 2.6. Policy Function at t < T . This figure shows the policy function of the opponent
for the parameterization ?0 = ?0 = 8 at t = 1. The policies are scaled by the opponent?s
cash reserves at the beginning of the first period. The top-left (top-right) panel shows investment
(hindrance) as a function of the cash reserves of both committees. The bottom-left (bottom-right)
panel shows investment (hindrance) as a function of the political capital of both committees. Axes
are inverted in the top-left graph to improve clarity.
56
2.3 Empirical Evidence
In this section, I present the results of the empirical analysis. First, I measure the response
to revenue shocks by estimating the baseline specification. Then, I explore how differences
in cash reserves and in polling affect the response to shocks. I focus on the results obtained
with the LASSO shocks in the main sample. Appendix B.2 presents the results for the
neural network methodology and for the extended sample. I refer to committee i as the
shock recipient and to committee ?i as the opponent throughout this section.
2.3.1 Empirical Specifications
In the empirical analysis, I measure the the causal effect of revenue shocks on future
intangible spending, with a focus on advertising expenditures. Specifically, I compute
non-parametric impulse responses using local projections (Jord?, 2005; Ramey, 2016).
Local projections have the advantage of being model-free and to accommodate potential
non-linearities in the response to shocks while controlling for other determinants of
advertising expenditures.
The baseline specifications are:
Adv = ? + ? + ? S + ??i,t+h i t h it hControlst + it (2.19)
Adv?i,t+h = ?i + ?t + ?hS ?it + ?hControlst + ?it (2.20)
where ?i and ?t are committee and time fixed effects, Sit is the scaled revenue shock to
committee i in week t, and Advj,t+h the scaled advertising expenditures of committee j in
57
the hth week after the shock. The controls are contemporaneous and past values of
advertising and other expenditures, as well as past values of individual and other
fundraising. I also include past values of the difference in polling between the candidates
to capture the state of the race. Past values are up to two lags but results are robust to
adding more lags. The control vector contains values for both committees.
Committee-year fixed effects absorb constant unobserved heterogeneity across
committees.
I also control for the effect of outside spending, in particular advertising expenditures
sponsored by PACs and super-PACs. I aggregate positive and negative outside spending
for each candidate at the weekly level and add these controls to the regressions. I also
include lags to account for potential asynchronous effects.
Standard errors are clustered by committee-year to allow for potential correlation in
the residuals of a particular committee. Since the shock is a generated regressor, I also
compute standard errors using a block bootstrap procedure to account for the sampling
variance as part of a robustness exercise.
2.3.2 Response to Revenue Shocks
Figure 2.7 provides preliminary evidence that campaign committees react to revenue shocks.
The figure shows that the sensitivity of future advertising expenditures to the recipient?s
shock is positive for both the recipient and the opponent. Moreover, the slope of the
recipient?s response is steeper, suggesting that committees respond more to their own shocks
than to the shocks of their opponent, a finding consistent with the predictions of the model.
58
However, the results could be driven by variables affecting shocks and future advertising
expenditures and not by a direct relationship between the two. To mitigate this concern,
I estimate specifications that control for potential cofounders.
Figure 2.7. Response to Revenue Shocks. This figure shows average committee advertising
expenditures in week t + 1 as a function of the recipient?s revenue shock in week t sorted into
quintiles. The blue line with circles is the response of the shock recipient; the green line with
diamonds is the response of the opponent. Shocks and advertising expenditures are demeaned by
committee and event time.
Table 2.2 reports estimates of the shock recipient?s response. The table reveals that
a 1% unexpected increase in own revenues translates into a 0.26% increase in advertising
expenditures in the following week. The effect is persistent and its magnitude is
unchanged when control variables are included in the regression. The sign of the response
is economically intuitive and consistent with Prediction 2.1 in the model. Upon receiving
a positive revenue shock, the recipient is able to increase advertising expenditures because
the unexpected cash flow relaxes the committee?s financing constraint. Since committees
cannot fully borrow against future revenues, their spending policy is tied to random
fluctuations in fundraising. This finding suggests that financing constraints affect the
59
spending behavior of political committees in a significant manner.
Table 2.2
Recipient?s Response to Revenue Shocks
This table reports the results of the regression Advi,t+h = ?i+?t+?hSit+??hControlst+it for h = 1, 2, 3 on the
main sample. Adv corresponds to advertising expenditures and S to the shock constructed with the polynomial
LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered by committee-year are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Advi,t+1 Advi,t+2 Advi,t+3 Advi,t+1 Advi,t+2 Advi,t+3
S 0.258??? 0.283??? 0.284??? 0.254??? 0.279???it 0.278???
(0.039) (0.040) (0.049) (0.039) (0.041) (0.049)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X X X X
Outside Spending X X X
R2 0.315 0.254 0.229 0.322 0.259 0.232
N 9302 8398 7492 9302 8398 7492
Table 2.3
Opponent?s Response to Revenue Shocks
This table reports the results of the regression Adv ??i,t+h = ?i + ?t + ?hSit + ?hControlst + it for h = 1, 2, 3
on the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the polynomial LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
Adv?i,t+1 Adv?i,t+2 Adv?i,t+3 Adv?i,t+1 Adv?i,t+2 Adv?i,t+3
S 0.084?? 0.139??? 0.173???it 0.075?? 0.134??? 0.167???
(0.037) (0.051) (0.053) (0.036) (0.051) (0.053)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X X X X
Outside Spending X X X
R2 0.307 0.246 0.223 0.314 0.251 0.227
N 9302 8398 7492 9302 8398 7492
Table 2.3 reports estimates of the opponent?s response to the revenue shocks of the
recipient. The table shows that a 1% unexpected increase in the recipient?s fundraising
revenues translates into a 0.08% increase in the opponent?s advertising expenditures in the
60
week following the shock. Interestingly, the effect increases over time, from 0.08% in the
first week after the shock to 0.17% three weeks after the shock.
Table 2.4
Opponent?s Response to Revenue Shocks by Advertising Tone
This table reports the results of the regression Advi,t+1 = ?i + ?t + ?1Sit ? NegativeAdsi + ?2Sit ? (1 ?
NegativeAds ?i) + ? Controlst + it on the main sample. Adv corresponds to advertising expenditures
and S to the shock constructed with the polynomial LASSO methodology. NegativeAdsi is 1 if the
fraction of negative TV ads to total ads broadcasted is in the upper quartile of the Wesleyan dataset
and 0 otherwise. The controls are listed in Section 2.3.1. Standard errors clustered by committee-year are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Adv?i,t+1 Adv?i,t+1
Sit ?NegativeAds?i 0.374??? 0.354???
(0.075) (0.075)
Sit ? (1?NegativeAds?i) 0.214??? 0.199???
(0.062) (0.060)
Comm-Year FE X X
Time FE X X
Controls X X
Outside Spending X
R2 0.229 0.240
N 2970 2970
In the model, Prediction 2.2 stipulates that the opponent?s response to the recipient?s
revenue shocks can be of either sign. Table 2.3 strongly suggests that the response is
positive in the data. Through the lens of the model, this result suggests that hindrance is
potent and investment expensive to install (?0 and ?0 both take high values). In the data,
hindrance can be construed as negative messaging. Table 2.4 shows that the opponent?s
response is larger (i.e. more positive) when the opponent uses a larger fraction of negative
advertising over the course of the race. The variable NegativeAds?i is 1 if the fraction
of negative TV ads to total ads broadcasted is in the upper quartile of the cross-sectional
distribution. Committees that do not broadcast TV ads and races occurring in years for
which TV advertising data is not available are excluded from the sample. The results
61
in Table 2.4 verify the intuition of the model that the opponent?s response is positive
when hindrance is preferred to investment as the coefficient ?1 is larger than ?2 at the 5%
significance level. However, in the data, the response remains positive when the committee
uses less negative advertising, while it is negative in the model. This finding illustrates the
limitations of the model, which is conceptual in nature, and therefore unable to capture
every single nuance of the data.
I also measure the response to revenue shocks in multiple subsamples to better
understand its determinants. The results are reported in Table 2.5.
First, I consider the timing of the shock. I classify a shock as Early if it occurs in the
first half of the race (seven week before the election and earlier), and as Late otherwise. The
first column in the table shows that the recipient?s response is stronger in the second half of
the race. The response is statistically significant in both subsamples. The second column
shows that the same result obtains for the opponent?s response. However, the coefficient is
not significant in the first half of the race, and their difference is not significantly different
from zero either. This pattern is consistent with the fact that shocks should be more
observable to the opponent when the election draws closer, as discussed in Section 1.3.2,
although it could also be driven by additional factors such as time-dependent elasticity of
investment to the recipient?s shock in event time.
Second, I classify a shock as Large if its absolute value is in the upper quartile of the
shock distribution and as Small otherwise. The third column shows that the recipient?s
response does not depend on the size of the shock. More interestingly, the fourth column
shows that the opponent mostly reacts to large shocks. Again, this finding is consistent
with the intuition that large shocks should be more observable by the opponent.
62
Third, I split the sample by the sign of the shock. The results are reported in the
fifth and sixth columns of Table 2.5. The recipient?s response is slightly stronger when the
shock is positive, while the opponent mostly reacts to positive shocks although none of
the differences is statistically significant. If the coefficients in the last column of Table 2.5
were statistically significant, the result would suggest that the opponent?s response to the
recipient shocks is asymmetric: the opponent increases spending when the recipient gets a
positive shocks but does not react to negative shocks.
Table 2.5
Subsample Analysis
This table reports the results of the regressions Advi,t+1 = ?i + ?t + ?1Sit ?Early/Large/Positive+ ?2Sit ?
Late/Small/Negative+ ??Controlst + it and Adv?i,t+1 = ?i + ?t + ?1Sit ?Early/Large/Positive+ ?2Sit ?
Late/Small/Negative + ??Controlst + it on the main sample. Adv corresponds to advertising expenditures
and S to the shock constructed with the polynomial LASSO methodology. A shock is Early it occurs in the
first half of the race (seventh week before the election and earlier) and Late otherwise. A shock is Large if
its absolute value is in the upper quartile of the overall distribution and Small otherwise. The controls are
listed in Section 2.3.1. Standard errors clustered by committee-year are reported in parentheses. ???, ??, and
? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Advi,t+1 Adv?i,t+1 Advi,t+1 Adv?i,t+1 Advi,t+1 Adv?i,t+1
Sit ? Early 0.172??? 0.022
(0.057) (0.063)
Sit ? Late 0.288??? 0.097??
(0.044) (0.043)
S ??? ??it ? Large 0.253 0.085
(0.041) (0.038)
S ? Small 0.277???it -0.054
(0.085) (0.087)
Sit ? Positive 0.297??? 0.105??
(0.057) (0.048)
S ?Negative 0.185??it 0.026
(0.091) (0.088)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X X X X
Outside Spending X X X X X X
R2 0.322 0.314 0.322 0.314 0.322 0.314
N 9302 9302 9302 9302 9302 9302
The model and the empirics assume the shocks and spending are fully observable
63
by both committees. While in practice this may not always be true, it is nevertheless a
reasonable assumption. Empirically, I find that committees respond to the revenue shocks
of their opponent and that the response is larger for large shocks than for small shocks. If
shocks were not observable, I would measure no such response. Therefore, shocks must be
partially observable. Additionally, if some shocks were observable and some were not, my
estimates would be biased towards zero and as such would provide a lower bound for the
true effect. In practice, large shocks should be observable by the opponent, either through
public announcements by campaigns, leaks, spying, etc.11 Finally, FEC regulations require
campaign committees to file a 48-Hour Notice anytime they receive a contribution of $1,000
or more less than 20 days (but more than 48 hours) before the day of an election in which
the candidate is running. Therefore, opponents can directly observe large contributions
made in the last three weeks of a race.
2.3.3 Role of Financing Constraints
I now investigate the effect of financing constraints on the response to revenue shocks.
Since committees have limited access to external markets, they cannot borrow against
future fundraising to smooth revenue shocks. Instead, spending comes from cash reserves
which in effect capture the total amount of internal financing available to committees. In
this context, a committee?s financing constraint is a decreasing function of its own cash
reserves and an increasing function of the cash reserves of its opponent.
11Several campaign managers with whom I had discussions mentioned that they actively monitor their
opponents during electoral races.
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Section 2.3.2 shows that the unconditional response of the recipient and the opponent
to the recipient?s revenue shocks is positive in the data. The model predicts that the
magnitude of the response of both committee increases with the difference between the
cash reserves of the recipient and the opponent (Prediction 2.3). To check this prediction,
I interact the shock with a dummy variable that captures the intensity of the financing
constraint of the recipient. First, I construct quartiles of the difference in the logarithm
of cash reserves in week t ? 1 to create the dummy variable. Then, I regress advertising
expenditures in week t+ 1 on the shock in week t interacted with the dummy variable.
Table 2.6
Financing Constraints - Recipient?s and Oppon?ent?s Response
This table reports the results of the regressions A?dvi,t+1 = ?i + ?t + k ?k ? Sit ?DeltaLogCashki,t?1 +
??Controlst + it and Adv?i,t+1 = ? + ? + ? ? S ?DeltaLogCashk ?i t k k it i,t?1 + ? Controlst + it on
the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the polynomial LASSO methodology. DeltaLogCashki,t?1 is a dummy variable that takes value 1 if
log(Cashi,t?1) ? log(Cash?i,t?1) is in the kth quartile of the distribution. The controls are listed in Section
2.3.1. Standard errors clustered by committee-year are reported in parentheses. ???, ??, and ? denote statistical
significance at the 1%, 5%, and 10% levels, respectively.
Advi,t+1 Advi,t+1 Adv?i,t+1 Adv?i,t+1
Sit ?DeltaLogCashQ1i,t?1 0.328
??? 0.323??? 0.372??? 0.354???
(0.080) (0.076) (0.117) (0.115)
Sit ?DeltaLogCashQ2 ??? ???i,t?1 0.260 0.245 -0.002 -0.026
(0.066) (0.066) (0.062) (0.062)
Sit ?DeltaLogCashQ3i,t?1 0.247
??? 0.250??? 0.100? 0.098?
(0.059) (0.059) (0.059) (0.058)
Sit ?DeltaLogCashQ4i,t?1 0.385
??? 0.375??? 0.131?? 0.127??
(0.076) (0.077) (0.056) (0.055)
Comm-Year FE X X X X
Time FE X X X X
Controls X X X X
Outside Spending X X
R2 0.319 0.325 0.311 0.317
N 9292 9292 9292 9292
The results are in Table 2.6. The first two columns show that unlike in the model,
65
the magnitude of the recipient?s response does not depend on the difference between the
cash reserves of the committees. On the other hand, the last two columns show that the
opponent?s response does depend on the difference in cash reserves. In particular, the
opponent?s response is three times larger when the opponent is relatively richer than it is
when the opponent is relatively poorer as ?1 is larger than ?2, ?3, and ?4 at the 5%
significance level. This result suggests the opponent attempts to undermine the recipient,
and the opponent?s response is larger in magnitude when the shock recipient is more
financially constrained. The opponent spends more in order to prevent the recipient to
get ahead in the race when the recipient receives unexpected revenues. This result
suggests that financing constraints can soften the competitive aspect of intangible
investment in concentrated markets.
2.3.4 Role of Political Capital
Next, I examine how differences political capital affects the magnitude of the response
to revenue shocks. Prediction 2.4 states that the opponent?s response is larger when the
response is positive and when the stock of political capital of the recipient is larger. In the
model, the difference in political capital at any point in the race captures the conditional
probability that a candidate wins the election if the election was held at that time.12 I
use the difference in candidate polling as a proxy for the difference in political capital.
I categorize candidates as Leader or Laggard depending on whether they are ahead of
their opponent in the polls or not. Then, I(regress ad)vertising expenditures on the shock
12In the model, this conditional probability is KF i,t?K?i,t? . In particular, assuming that the election
is held today means that cash balances have no impact on the conditional probability of winning because
the committees do not have time to spend their cash on advertising.
66
interacted with dummy variables that represent this categorization.
Table 2.7 presents the results. The response of the opponent is marginally larger
when the shock recipient leads the race in the week preceding the shock (the difference in
coefficients is not significant). This result is consistent with the prediction of the model.
Table 2.7
Political Capital - Opponent?s Response
This table reports the results of the regression Adv?i,t+1 = ?i + ?t + ?1Sit ? Leader + ?2Sit ? Laggard +
??Controlst + it on the main sample. Adv corresponds to advertising expenditures and S to the shock
constructed with the polynomial LASSO methodology. Candidate i is categorized as Leader or Laggard
depending on whether she is ahead of her opponent in the polls or not. The controls are listed in Section 2.3.1.
Standard errors clustered by committee-year are reported in parentheses. ???, ??, and ? denote statistical
significance at the 1%, 5%, and 10% levels, respectively.
Adv?i,t+1 Adv?i,t+1
S ? Leader ?1 0.151?? 0.149??it i,t
(0.070) (0.071)
Sit ? Laggardi,t?1 0.019 0.021
(0.069) (0.072)
Comm-Year FE X X
Time FE X X
Controls X X
Outside Spending X
R2 0.308 0.315
N 9292 9292
Table 2.8 presents the response to revenue shocks by incumbency status. The first
two columns show that incumbents and challengers react similarly to their own shocks,
although challengers exhibit a slightly higher response. The last two columns show that a
challenger?s response to the incumbent?s shock is larger than an incumbent?s response to
the challenger?s shock. This result echoes the findings from Table 2.7 as challengers trail
in the polls on average, and therefore have a lower stock of political capital in comparison
to incumbents.
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Table 2.8
Response to Shocks by Incumbency Status
This table reports the results of the regressions Advi,t+1 = ?i+?t+?1Sit?Incumbenti+?2Sit?Challengeri+
??Controlst+it and Adv?i,t+1 = ?i+?t+?1Sit?Incumbenti+?2Sit?Challengeri+??Controlst+it on the
main sample. Adv corresponds to advertising expenditures and S to the shock constructed with the polynomial
LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered by committee-year are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Advi,t+1 Advi,t+1 Adv?i,t+1 Adv?i,t+1
Sit ? Incumbent 0.229???i 0.236??? 0.117?? 0.131??
(0.074) (0.074) (0.053) (0.052)
Sit ? Challenger 0.294??? 0.287???i 0.051 0.064
(0.064) (0.064) (0.059) (0.062)
Comm-Year FE X X X X
Time FE X X X X
Controls X X X X
Outside Spending X X
R2 0.303 0.315 0.296 0.310
N 6723 6723 6723 6723
2.3.5 Additional Tests
I run additional tests to ensure the robustness of my findings. First, an omitted variable
could affect the revenue shock in week t and advertising expenditures in week t+1, thereby
biasing the results. It would be unlikely that this omitted variable affects advertising in
week t + 1 without affecting advertising in week t. Therefore, the controls should pick
up the effect of the omitted variable since week-t advertising is included in the controls.
Additionally, I also control for the advertising expenditures of the opponent at t+1. Finally,
it is unlikely that an omitted variable affects both committees since shocks are uncorrelated
within races. In order to fully account for this possibility, I run a regression that includes
both shocks as regressors.13 The results presented in Table B.1 show that these additional
13Note that regressing the opponent?s advertising expenditures on the recipient?s shock is equivalent to
regressing the recipient?s advertising expenditures on the opponent?s shock.
68
controls do not materially change the results.
Second, I show that the results are similar when I use shocks constructed with the
artificial neural network rather than with the polynomial LASSO. This is not surprising
given that the correlation between the two series of shocks is 90% in the main sample. The
tables corresponding to the regressions with the neural network shocks are in Appendix
B.2.2.
Third, I show that similar results obtain when regressions are run on the extended
sample that contains races for which no polling data is available. The corresponding tables
are in Appendix B.2.3. The sign of the estimates are consistent with the results from the
main sample. However, the magnitude of the estimates is lower in the extended sample.
This result makes sense: strategic interactions are likely less important in races that are ex
ante less close.
Fourth, note that the shocks derived from the polynomial LASSO and artificial
neural network constitute a generated regressor. To assess whether this additional source
of variation affects the significance of the results, I calculate standard errors using a
bootstrap procedure. The results presented in Appendix B.2.4 show that the significance
of the results is not affected by accounting for the source of variation coming from the
generated regressors.
Finally, I perform placebo tests by shuffling the shocks across committees and running
the baseline regressions. The figures in Appendix B.2.5 show that the results are very
unlikely to be generated by chance alone.
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2.4 Conclusion
In this paper, I study the dynamics of fundraising and advertising by campaign committees
in electoral races for the U.S. House of Representatives. I derive a dynamic strategic
model that captures the main economic trade-offs faced by committees and delivers testable
implications. To test the predictions of the model, I use the shocks constructed in Chapter 1
as source of exogenous variation in fundraising revenues.
In the data, I find that committees do respond to revenue shocks. In head-to-head
races, both committees increase their spending after one of the committees receives a
positive revenue shock. Additionally, the magnitude of the response depends on the
relative cash reserves of the committees; the magnitude of the opponent?s response triples
when the shock recipient is poorer than the opponent. Cash-rich committees use their
financial advantage to undermine opponents that are financially weaker when the latter
receive unexpected revenues. This result suggests that the availability of internal
financing can amplify the competitive aspect of intangible expenditures in environments
characterized by strong strategic interactions and financing constraints.
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Chapter 3: Distorted Learning Around Merger Announcements
3.1 Introduction
Understanding how investors incorporate information into asset prices is a fundamental
question in financial economics. A large body of the literature documents that investors
are prone to mistakes when they process information.1 Strikingly, whether investors
overreact or underreact to information is highly context-dependent. For instance,
De Bondt and Thaler (1985, 1987) show that stocks with low price-to-earnings ratios earn
larger returns than stocks with high price-to-earnings ratios, consistent with the
hypothesis of overreaction to stock-specific news. In contrast, earnings surprises predict
abnormal returns after earnings announcements, indicating that investors underreact to
the information contained in accounting statements (Ball and Brown, 1968; Foster, Olsen,
and Shevlin, 1984; Bernard and Thomas, 1989, 1990).
All of the above examples provide compelling evidence that investors suffer from
faulty learning which translates into asset mispricing. In practice, investors learn about
multiple dimensions of the assets they trade. Identifying whether investors misprocess
information pertaining to a particular dimension generally requires observing the
corresponding information flows. In this paper, I overcome this challenge and study faulty
1See Barberis (2018) for a review.
71
learning pertaining to a specific dimension of an asset in a setting where information flows
are not directly observable. Specifically, I measure how investors react to the information
released around merger announcements and whether they form rational beliefs about the
probability of deal completion.
Empirically, I find that investors overreact to deal-specific information when learning
about the probability of success of a merger attempt. The overreaction creates a conditional
mispricing in the cross-section of merger targets. In particular, target prices underestimate
the probability of deal success when low and overestimate it when high. This stylized fact
is novel and distinct from the empirical finding that merger targets earn positive abnormal
returns on average because I compare the returns of firms within the set of merger targets.2
If investors collect information about a merger attempt, the post-announcement price
of the target should reflect their subjective assessment of the conditional probability of
success. Moreover, if investors behave in a Bayesian fashion, the post-announcement price
should be an unbiased predictor of the price on the completion day of the merger attempt.3
Conceptually, regressing the price of the target at the time of completion on the price of the
target after the announcement should yield a slope of one if investors process information
rationally. In contrast, investor overreaction to deal-specific information would introduce
a bias in prices, and the regression would produce a slope that is less than one.
Measuring the extent of the learning distortion in the cross-section of merger attempts
presents three empirical challenges. First, estimating the conceptual regression in levels
is infeasible because the cross-sectional heterogeneity in prices would yield a coefficient
2Larcker and Lys (1987); Dukes, Frohlich, and Ma (1992); Mitchell and Pulvino (2001); Baker and
Savasoglu (2002) compare targets to non-targets and study their returns.
3I henceforth refer to the day of completion as the date at which the final outcome of the merget
attempt?either success of failure?is publicly announced.
72
close to one and therefore bias the results towards rationality even if investors misprocess
information.4 Second, a specification based on returns suffers from a similar bias towards
rationality due to heterogeneity in deal premia.5 Third, the information sets of investors
are not directly observable, which prevents the analysis from isolating information that
specifically affects the probability of deal completion.
I overcome these challenges by deriving a model of distorted learning during merger
attempts. In effect, the model disciplines the empirical analysis by imposing structure on
the measurement problem. In the model, a representative investor estimates the probability
of success of a merger attempt after receiving binary signals about the outcome of the deal.
A fully rational investor would use Bayes? rule to update her beliefs upon the arrival of new
information, and her subjective beliefs would at all times coincide with objective beliefs. To
allow the investor to deviate from rationality, I introduce a learning distortion in the model,
which I capture through the parameter ?. Specifically, if ? > 1, the representative investor
updates her beliefs as if the sample size is larger than it actually is, thereby overweighting
new information and underweighting prior beliefs, and vice versa if ? < 1. In effect, the
representative investor exhibits overconfidence in her ability to process information when
? is greater than one. As a result, the investor?s beliefs about the probability of success
become distorted over the course of the attempt.
The model indicates how to extract success probabilities directly from asset prices.
4Consider the case where the impact of deal-specific information is minimized so that cross-sectional
variation in prices one day after the announcement is almost completely driven by prior information.
Then the regression coefficient will be one. This is related to the problem of time series regressions with
nonstationary variables.
5To highlight this issue, I simulate merger attempts under the hypothesis that investors misprocess
information, then regress long-run returns on announcement returns. I obtain a coefficient of one, thereby
showing that the regression does not identify the true extent of the distortion.
73
If investors are risk-neutral, the stock price of the target after the announcement is the
probability-weighted average of the cash price and of the standalone value of the firm. The
probability of success is therefore an affine transformation of the target stock price which
I call scaled price. When calculated after the announcement but before completion, the
scaled price reflects the subjective probability of success held by investors. Contrastingly,
the scaled price on the day of completion equals the objective probability of success plus
noise by iterated expectations.
The model also delivers an affine relationship between the subjective and objective
probability odds ratios that can be tested in the data using scaled prices as empirical
counterparts of success probabilities. Notably, information flows are redundant for the
estimation because they are directly embodied in beliefs. As a result, asset prices are
sufficient for the inference because they reflect all available information about the
probability of success. Regressing the scaled price at completion on the scaled price after
the announcement provides an indication of whether investors process deal-specific
information rationally and constitutes the baseline empirical specification. The regression
exploits the heterogeneity in deal outcomes to identify the coefficient driving the learning
distortion.
Using an incorrect price scaling could mechanically lead to a regression coefficient
that is less than unity. To alleviate this concern, I show that any affine scaling that
removes the cross-sectional heterogeneity in price levels and deal premia recovers the
distortion coefficient in the empirical specification. However, interpreting the scaled price
as a probability of success requires using the correct scaling. Measurement error could
also introduce a downward bias in the estimation, leading to spurious results. Since the
74
regressors consist of returns measured over a short time window, it is unlikely that
measurement error would affect the results in a meaningful way.
I estimate the baseline regression using a sample of 4,760 mergers paid in cash and
find a slope coefficient of 0.74, a value that indicates investors deviate from the Bayesian
paradigm when learning about the probability of a successful merger attempt. The results
suggest that investors predictably overreact to merger announcements and fail to properly
incorporate conditioning information into the target?s stock price. Deals with a low market-
implied probability of success underestimate the actual probability of success, and vice
versa. As a result, the overreaction translates into a significant mispricing in the cross-
section of merger targets.
Furthermore, I find that the mispricing of targets due to investor overreaction is
persistent. Investors overreact to the burst of information that follows a merger
announcement. Afterwards, the mispricing slowly corrects over time as more information
about the merger arrives, a result consistent with the predictions of the model.
The results also have a structural interpretation. In the model, the distortion
parameter ? drives the intensity of the overreaction to information. This parameter
corresponds to the reciprocal of the slope coefficient in the baseline regression. In the
data, the estimate of the distortion parameter ? is 1.35, meaning the representative
investor overweights the sample size by 35% in the model. For instance, if the investor
receives 60 positive signals out of 100 signals, she believes she receives 81 positive signals
out of 135 signals.6 The estimate of the distortion parameter is robust to methodological
6That is, the number of positive signals and the total number of signals are both multiplied by a factor
of 1.35.
75
changes and takes comparable values across subsamples.
Interestingly, I find that the magnitude of the overreaction decreases in the merger
premium and in the target?s pre-announcement price run up. This result suggests that
the overreaction is indeed driven by faulty learning, since investors should be less prone to
overreact when the value of information is higher (higher premium) and when the merger
attempt has been partially anticipated (higher run up). Additionally, I find that the
distortion parameter remains stable even when allowed to vary based on overall M&A
activity, whether the deal is a tender offer, and whether the attempt is successful ex post.
Using calendar-time portfolios, I show that targets with a low market-implied
probability of success earn higher abnormal returns than targets with a high
market-implied probability of success. A long-short portfolio that exploits the conditional
mispricing of targets earns an alpha of 9% per annum on average. Moreover, the portfolio
returns and its alpha are orthogonal to those of a standard merger arbitrage strategy that
exploits the unconditional deal premium. These results provide additional evidence of
mispricing in the cross-section of merger targets.
This paper makes three contributions. First, I highlight that the methodology used
to measure overreaction should depend on the empirical context. In the particular case of
merger attempts, regressions based on returns do not capture the extent of the overreaction.
Second, I derive a model that allows me to estimate overreaction pertaining to a specific
dimension of the target without observing the information sets of investors. The model is
general enough to be applied to other settings with binary events. Third, I document a
new stylized fact: investors overreact to the information released during merger attempts.
76
3.1.1 Related Literature
This paper contributes to four strands of the finance literature. First, it furthers our
understanding of how market participants incorporate information into asset prices by
using merger attempts as a laboratory. The model allows me to recover the probability of
deal success without observing the information flows that shape investors? beliefs, and then
to test for overreaction.
Second, this paper relates to a rapidly growing literature on expectation formation.
Myriad frameworks describe how agents form expectations, for instance through diagnostic
expectations (Bordalo, Gennaioli, and Shleifer, 2018; Bordalo, Gennaioli, LaPorta, and
Shleifer, 2019), extrapolative beliefs (Barberis, Greenwood, Jin, and Shleifer, 2015, 2018;
Da, Huang, and Jin, 2020), learning from experience (Malmendier and Nagel, 2011, 2016),
or exaggerated likelihoods (Santosh, 2021). The model captures faulty learning through
exaggerated likelihoods and generates direct testable implications.
Third, this paper contributes to the literature on merger attempts. There have been
many studies examining the determinants of deal completion (Walkling, 1985; Samuelson
and Rosenthal, 1986; Officer, 2003), returns from merger arbitrage (Larcker and Lys, 1987;
Dukes et al., 1992; Mitchell and Pulvino, 2001; Baker and Savasoglu, 2002), the cross-section
of deal premia (Jindra and Walkling, 2004), and value creation in mergers (Hietala, Kaplan,
and Robinson, 2003; Bhagat, Dong, Hirshleifer, and Noah, 2005; Barraclough, Robinson,
Smith, and Whaley, 2013). However, much less is known about whether asset prices reflect
the objective probability of deal completion during a merger attempt. I fill this gap in
the literature by documenting that investors overreact to the information released around
77
merger announcements.
Fourth, this paper illustrates how investor biases interact with firm decisions (Baker
and Wurgler, 2013; Malmendier, 2018), and during mergers in particular (Dong, 2010).
For instance, Giglio and Shue (2014) show that investors underreact to the information
contained in the passage of time after a merger announcement. Baker, Pan, and Wurgler
(2012) find that cash offer prices are biased toward recent peak prices of the target, which
suggests that interested parties use these peaks as reference points.
3.2 Model
In this section, I present a simple model of distorted learning during merger attempts. The
model indicates how to extract beliefs about the probability of deal completion from asset
prices and delivers testable implications.
3.2.1 Setup
In the model, a representative investor forecasts whether a merger attempt will be
successful. The outcome M = 1 corresponds to success and the outcome M = 0 to failure.
P denotes the objective probability measure and S is the representative investor?s
subjective measure. The unconditional first moment of S under the objective measure is
EP[M ] = P[M = 1] = ??. I assume that both measures agree on the unconditional
probability of success, that is S[M = 1] = P[M = 1] = ??.7
Time is discrete and indexed by t = 0, 1 . . . T . At time 0, the investor?s information is
7Appendix C.1.1 shows the model can be extended to allow for unconditional optimism or pessimism
under the subjective measure.
78
the unconditional distribution of S under the subjective measure. At time T , uncertainty
about M is resolved and the investor learns its realization. At times 1, 2 . . . T ? 1, the
investor receives independent signals about the realization of M . Each signal is a Bernoulli
random variable whose value is either high (H) or low (L). The signals provide information
about the outcome: the probability of receiving a high signal is higher when the merger
attempt is successful than when it is not. Each signal mj satisfies the following:
0 < p0 = P[mj = H|M = 0] < p1 = P[mj = H|M = 1] < 1. (3.1)
Assuming p1 6= p0 ensures signals are informative about the realization of M . Let
nt be the total number of signals received at or before time t. Similarly, let kt be the
total number of signals whose realization is H at or before time t. As nt ? ?, the
representative investor can learn the value of M by calculating the sample average of the
signals and comparing it to p1 and p0. To ease the notation, I fix time t and let n = nt
and k = kt. Additionally, I let {mj} = {m ntj}j=1 be the signals in the information set of the
representative investor at time t.
3.2.2 Information Processing
A Bayesian agent who holds objective beliefs combines the information contained in the
signals with her prior beliefs to compute her posterior beliefs about the probability of
success. Bayes? rule under the objective probability measure is:
( )
n pk(1? p )n?k1 P[M = 1]
P[M = 1| {mj}] = ( ) k 1 ( ) . (3.2)n pk(1? p )n?kP[M = 1] + n pk1 (1? p0)n?k1 0 P[M = 0]k k
79
The posterior odds ratio under the objective probability measure is the product of
the likelihood ratio and prior odds ratio:
?( ) ( ) ?
P[ = 1| { }] ? k 1? n?k ( )M mj = p1 p1 ? ??1 [ = 1 ] 1 . (3.3)? PM | {mj} p0 ? p0 1? ??
The ratio p1 captures the informativeness of the signals. To see this, suppose the
p0
investor receives a single signal m that turns out to be high. Her posterior probability is:
P[M = 1|m = 1] = ( 1) ( ) . (3.4)
1 + p0 1???
p1 ??
P[M = 1|s = 1] is an increasing function of p1 . The higher the ratio, the more
p0
informative the signal. If p1 = 1, the signal is uninformative and the posterior probability
p0
equals the prior. As p1 grows larger, the signal becomes more informative: the high signal
p0
increases the conditional probability of success by a larger amount the larger p1 is.
p0
I introduce a learning distortion under the subjective probability measure by assuming
that the representative investor misprocesses information. Specifically, she distorts the log-
likelihood ratio when she updates her beliefs. The posterior odds ratio under the subjective
probability measure is:
?( ) ( ) ??
S[ = 1| { }] ? k 1? n?k ( )M mj = p1 p1 ? ??1 [ = 1 ] 1 1 , (3.5)? SM | {mj} p0 ? p0 ? ??
where ? is the parameter that controls the learning distortion. If ? > 1 (? < 1), the investor
overweights (underweights) the information contained in the likelihood ratio. In effect, the
representative investor exhibits overconfidence in her ability to process information like in
80
the model of Daniel, Hirshleifer, and Subrahmanyam (1998). The magnitude and sign of
?? 1 may vary depending on the context and is therefore an empirical question.
3.2.3 Relationship between Probability Measures
Substituting the expression for the likelihood ratio from Equation (3.3) into Equation (3.5)
reveals a simple relationship between objective and subjective posterior odds ratios:8
( )
S[M = 1| {mj}] = P[M = 1| {
? ( )
mj}] ?? 1??
1 [ = 1 . (3.6)? SM | {mj}] 1? P[M = 1| {mj}] 1? ??
Simplifying Equation (3.6) and solving for the subjective posterior probability of
success yields:
?? ( ) ??1[ = 1| { }] = 1 + P[M = 1| {m }] ?? ( )?? ??1S jM m ?j 1 [ = 1 . (3.7)? PM | {mj}] 1? ??
Alternatively, the objective probability of success can be expressed as a function of
the subjective posterior probability of success:
?? ( ) ?S[ = 1| { }] ? 1 1 ?1M m ? ( )?? ?1?P[M = 1| { jm }] = 1 + ?j 1? S[M = 1| {mj}] 1 . (3.8)? ??
The relationship in Equation (3.7) is one-to-one, non-linear, and well-defined only on
the open interval (0, 1). The corner solutions can be found by taking the corresponding
8In Appendix C.1.2, I discuss the learning distortion in the log odds space.
81
limits:
lim S[M = 1| {mj}] = x for x ? {0, 1} . (3.9)
P[M=1|{mj}]?x
The two measures are in agreement at the boundaries of the support. As a direct
consequence, the two measures agree on the probability of success as the number of signals
n goes to infinity. In addition, the limiting value of the probability of success under either
measure is the realization of the binary random variable:9
plim S[M = 1| {m }nj ] = plimP[M = 1| {mj}n
?? j=1 ?? j=1
] = M . (3.10)
n n
In the model, the wedge between subjective and objective posterior probability
eventually vanishes, but not because the representative investor?s distortion parameter
varies over time. Instead, the wedge disappears because the objective probability of
success converges in probability to the realization of the random variable as more
information is revealed to the investor and because the two measures become in full
agreement when this happens.
Two cases of Equation (3.7) are of special interest. First, the objective and
subjective conditional probabilities are equal if the biased investor turns out to not be
biased. That is, if ? = 1, then S[M = 1| {mj}] = P[M = 1| {mj}]. Second, ?? is the unique
interior fixed point of the mapping between the two measures. That is, if the objective
posterior probability corresponds to the unconditional probability, then the subjective
9Appendix C.1.3 presents a simple algebraic proof.
82
posterior probability also equals the unconditional probability. In the model, if the
information released upon the merger announcement does not change objective beliefs,
then it does not change the subjective beliefs either.
To assess the intensity of the distortion while abstracting from non-linearities, I
linearize the subjective posterior probability of success around its unconditional mean.
The direct and inverse relationships are
S[M = 1| {mj}] ? ((1? ?)??)+ ?P[M = 1| {mj}] (3.11)
P[M = 1| {mj}] ? 1?
1 + 1?? S[M = 1| {mj}]. (3.12)
? ?
Figure 3.1. Relationship between Subjective and Objective Probability of Success.
This figure shows the relationship between the subjective and objective probability of success
when ? = 1.35 and ?? = 0.77. The dashed blue line is the exact relationship (Equation (3.8)).
The dotted green line is the linear approximation (Equation (3.12)). The solid black line is the
45-degree line.
83
Figure 3.1 illustrates the relationship between S[M = 1| {mj}] and P[M = 1| {mj}]
when ? = 1.35 and ?? = 0.77.10 The dashed blue line is the exact mapping, the dotted
green line is the linear approximation, and the solid black line is the 45-degree line. The
figure shows the investor?s overreaction to information. The subjective posterior is less
than the objective posterior when both are below the unconditional probability of success.
The opposite result obtains when either posterior is above the unconditional probability
of success. The distortion is stronger for subjective probabilities below the unconditional
probability of success. This result arises because the unconditional probability of success
is greater than 50%. The linear function reasonably approximates the relationship in the
interior of the interval but fails to capture the strong curvatures near the boundaries. As
expected, the two measures are in full agreement when S[M = 1| {mj}] ? {0, ??, 1}.
Figure 3.1 also conveys the intuition behind the model dynamics. Suppose the
realization of the random variable M is zero, that is, the merger attempt eventually fails
(the same logic applies to the case M = 1). At time 0, the representative investor has not
received any signal. Her subjective probability of success is ??. As the number of signals
increases, the subjective probability drifts towards zero. The bias (the difference between
the blue line and the black line) is non-monotonic in the subjective probability. It first
increases then decreases as more signals arrive. In reality, information may be released in
chunks and the movement along the blue line may not be continuous.
Finally, note that the distributional assumptions of the signals do not have any strong
implication for the model. The relationship between S[M = 1| {mj}] and P[M = 1| {mj}]
10These values capture the empirical estimates measured in Section 3.4 in the context of merger
announcements.
84
holds for any well-behaved likelihood ratio. This result obtains because the likelihood ratio
drops out of the mapping between subjective and objective posterior probability.
In the model, the representative investor makes expectational errors about a future
outcome that are reflected in asset prices and corrected when she receives incremental
information (Hartzmark and Shue, 2018). The learning distortion can also be thought of as
misconstruing the sample size. The representative investor believes she receives ?? k high
signals out of ??n signals instead of k high signals out of n signals. Therefore, the sample
size is misinterpreted by a factor of ?. The learning distortion specific to the model can be
nested in the general exaggerated likelihoods framework proposed in Santosh (2021).
3.2.4 Pricing of the Target
I now specialize the stylized model of distorted learning to the setting of merger attempts
and derive testable implications. I derive a mapping between stock prices, deal parameters,
and the probability of success under both probability measures. The mapping allows me to
extract the probabilities of success from observable market prices. Substituting the market-
implied probabilities into the relationship from the model delivers the baseline econometric
specification.
The representative investor is risk-neutral and interest rates are zero. At t = 0, a
firm (the acquirer) announces its intent to purchase another firm (the target) using cash.
Let M denote the deal status. The deal expires at time T , either succeeding (M = 1) or
failing (M = 0). The cash offer price as of the merger announcement is C0. The last offer
price before completion is C. Let Pt be the share price of the target at time t and let F be
85
the value of the target if the deal fails (the standalone value).
The share price of the target on deal completion is either the final cash price or the
standalone value (Samuelson and Rosenthal, 1986):
PT = MC + (1?M)F . (3.13)
By definition of the conditional expectation:
PT = EPt [PT ] + ?tT , (3.14)
with EPt [?tT ] = 0 and ?tT orthogonal to the information set at time t. The conditional
expectation can be written as:
( )
EPt [PT ] = EP[F ] + CovPt t (M,C ? F ) + EPt [M ] EPt [C]? EPt [F ] . (3.15)
Therefore,
PT ? EPt [F ]? CovPt (M,C ? F )
P[ ] P[ ] = E
P
t [M ] +
?tT
Et C ? Et F EPt [C]? EPt [F ]
. (3.16)
Before deal completion, the price of the target reflects the beliefs of the representative
investor under the subjective measure:
P = ESt t [PT ] (3.17)( )
P = ES[F ] + CovS(M,C ? F ) + ES St t t t [M ] Et [C]? ESt [F ] . (3.18)
86
The conditional probability of success under the representative investor?s subjective
measure can be expressed as:
P ? ESt t [F ]? CovSt (M,C ? F ) S
S[ ] S[ ] = Et [M ]. (3.19)Et C ? Et F
Finally, I introduce the following notation:
= P
S
t ? Et [F ]? CovSt (M,C ? F )?t ES[C]? ES[ ] (3.20)t t F
P P
?T =
PT ? Et [F ]? Covt (M,C ? F )
EPt [C]
(3.21)
? EPt [F ]
?tT
?tT = EPt [C]? EPt [F ]
. (3.22)
The ? variables are affine functions of the target?s share price. The affine scaling
serves two useful purposes. First, it allows for an interpretation of prices as conditional
success probabilities. Second, it removes the variation created by the price level of the target
and by the deal premium, allowing the model to be estimated using the cross-section of
merger attempts. In Section 3.3.4, I describe the operationalization of the scaling for the
empirical analysis.
Note that EPt [M ] = Pt[M = 1] and ESt [M ] = St[M = 1] since M is a binary random
variable. Therefore, there is a direct relationship between the scaled price of the target and
the conditional probabilities of success in the model from Section 3.2:
Pt[M = 1] = ?T ? ?tT (3.23)
St[M = 1] = ?t. (3.24)
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Replacing posterior success probabilities by their ?-counterparts (Equations (3.23)
and (3.24)) in the linear mapping between subjective and objective posterior probabilities
(Equation (3.12)) yields:
( )
1 1
?T = 1? ?? + ?t + ?tT . (3.25)
? ?
Equation (3.25) constitutes the starting point of the empirical analysis. This
specification can be estimated using ordinary least squares (OLS). In effect, the linear
approximation recognizes the simplicity of the model. Specifically, investors may learn
about additional dimensions of the deal besides its probability of success and the target?s
stock price may move for reasons unrelated to the merger attempt.
3.3 Data and Methodology
In this section, I start by describing the data sources and the sample construction.
Afterwards, I discuss the price scaling procedure.
3.3.1 Data Sources
The data on merger announcements comes from Thomson Reuters SDC Platinum?s
Mergers & Acquisitions database. Stock returns, prices, and market capitalizations are
from CRSP. Factor returns, risk-free rates, and industry portfolios are from Ken French?s
website. The SDC-CRSP mapping is from WRDS. Firm-level accounting data are from
Compustat and institutional ownership data are from Thomson Reuters S34. In
Appendix C.2.1 and Appendix C.2.2, I describe the construction of the accounting and
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institutional ownership variables respectively. I also download newspaper articles from
The New York Times, The Wall Street Journal, and The Washington Post through
ProQuest to impute missing cash offer prices.
3.3.2 Sample Construction
I apply the filters listed in Table 3.1 to construct the sample of merger announcements. I
start with all SDC Platinum deals that involve U.S. public targets and whose form of deal
is either acquisition (A), acquisition of majority interest (AM), or merger (M). Out of
those deals, 67% have status completed (the merger attempt is successful), 20% have
status withdrawn (either the acquirer or target have terminated their plans for the
merger), 5% have status unknown, 3% have status pending (the transaction is currently
being discussed or undertaken), and 5% have some other status. I exclude deals whose
status is not completed or withdrawn and deals that do not have a valid announcement
date or completion date. I also exclude deals announced after December 31, 2018 and
deals whose target has not matched PERMNO in CRSP. Moreover, I exclude deals that
are not fully paid in cash as the model is silent on their pricing. I require merger
announcements to be made with a valid initial cash offer price. Before excluding deals
with missing initial offer price, I attempt to recover those values from newspaper articles
using textual analysis. Using this approach, I augment the sample by 841 deals. In
Appendix C.3, I describe the sample augmentation procedure in detail. Finally, I exclude
deals that finish immediately after the announcement and deals for which expected
returns cannot be calculated due to the low sample size in the returns dataset prior to the
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announcement. The final sample contains 4,760 mergers announced between 1978 and
2018.
Table 3.1
Sample Construction
This table lists the filters applied when constructing the sample of merger announcements. The sample period
is from March 1978 to December 2018. The index t corresponds to event time.
Step Source Filter Observations
1 SDC Keep deals with U.S. public targets with form of deal A, AM, or M 21,709
2 SDC Drop deals with status different from completed or withdrawn 18,720
Drop deals with no announcement and completion/withdrawal dates
3 SDC Drop deals announced after 2018-12-31 18,613
4 SDC Keep deals with consideration structure equal to cash only 7,282
5 CRSP Keep deals with matched target PERMNO 5,880
6 SDC Drop deals with no initial cash offer price 4,837
7 CRSP Drop deals that are completed/withdrawn at t = 0 or t = 1 4,772
8 CRSP Drop deals for which expected returns cannot be calculated 4,760
Final sample 4,760
Table 3.2
Summary Statistics
This table presents summary statistics of the sample of merger announcements. The sample period is from
March 1978 to December 2018. Deal values are measured in U.S. dollars. Deal duration is measured in calendar
days. Success, Tender Offer, and Offer Price Imputed are binary variables.
Obs. Mean SD Min 25% 50% 75% Max
Log(Deal Value) 4,748 19.34 1.73 14.07 18.09 19.28 20.56 24.90
Deal Duration 4,760 116.17 99.65 2.00 51.00 88.00 146.25 1483.00
Success 4,760 0.77 0.42 0.00 1.00 1.00 1.00 1.00
Tender Offer 4,760 0.36 0.48 0.00 0.00 0.00 1.00 1.00
Offer Price Imputed 4,760 0.17 0.38 0.00 0.00 0.00 0.00 1.00
Table 3.2 provides the summary statistics. The average value of a target is USD 250
million. The median deal finishes in approximately three months. The median duration is
independent of whether the deal is successful or not. Seventy-seven percent of the merger
attempts are successful. The sample includes both consensual and hostile attempts. Thirty-
six percent of the attempts are structured as tender offers. Finally, 17% of initial offer prices
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are imputed from newspaper articles.
3.3.3 Target Stock Prices
I match SDC firms to their respective CRSP PERMNO based on their six-digit historical
CUSIP and on CRSP?s stocknames table. If a firm maps to multiple PERMNOs, I keep
the entry with the lowest eight-digit historical CUSIP. Market capitalization is aggregated
by six-digit CUSIP to account for multiple classes of common stock. I use stock data at the
daily frequency in all the tests. I also add delisting returns to the series of holding period
returns.
The model generates testable implications in which the dependent variable is an
affine function of the target?s share price on deal completion. In the model, I assume
risk-neutrality and a constant interest rate of zero over the course of an attempt.
Violations of these two assumptions could potentially affect the results. However,
deflating the target?s prices allows for risk exposure compensation that is heterogeneous
across targets and accounts for a time-varying risk-free rate. If the two assumptions are
relaxed, the price of the target one day after the merger announcement is P P1 = Et [mTPT ],
where mT is the stochastic discount factor (SDF) between time 1 and time T . The SDF
representation of pricing has an equivalent formulation in terms of betas and expected
returns (Ross, 1978; Dybvig and Ingersoll, 1982). I choose to work with abnormal returns
because they are methodologically easier to handle than the SDF to deflate prices and
because it is the standard approach in the event study literature (Kothari and Warner,
2007).
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I compute abnormal returns using multiple popular factor models. Specifically, I use
the CAPM (Treynor, 1961; Sharpe, 1964; Lintner, 1965), the Fama-French three-factor
model (Fama and French, 1993), Carhart?s four-factor model (Carhart, 1994), and the
Fama-French five-factor model (Fama and French, 2015). For each merger target i, I
estimate the following regression via OLS over a 250-business-day window ending 60
business days before the merger announcement date:
Rit ?Rft = ?0i + f ?t?1i + it, (3.26)
where Ri,t is the daily return of the target stock, Rft is the risk-free rate, and ft is a vector
of realized daily returns on the factors in the risk adjustment model. If a stock has less
than 30 observations in the 250-day window, I drop the deal from the sample (step 8 in
Table 3.1).
Since OLS coefficients are subject to estimation error, the estimates of ?1i are
overdispersed. That is, the cross-sectional variance of the estimates is larger than the
cross-sectional variance of the true coefficients. On average, low estimated coefficients
have negative estimation error and high estimated coefficients have positive estimation
error. I apply a multivariate Bayesian shrinkage methodology to mitigate the
overdispersion problem (Vasicek, 1973; Frazzini and Pedersen, 2014; Levi and Welch,
2017). For each risk adjustment model and for each calendar year between 1978 and 2018,
I estimate the coefficient ?1i of each stock with share code equal to 10 or 11 in the CRSP
universe using Equation (3.26). I then shrink the estimated coefficients of the entire
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CRSP cross-section as:
??shrunk1i = ?+ ?(? + ?)?1(??1i ? ?), (3.27)
where ??1i is the vector of unshrunk coefficients for stock i, ? is the CRSP cross-sectional
value-weighted average of ??1i, ? is the cross-sectional variance-covariance matrix of ??1i, and
? is the matrix of average estimation errors. For each risk adjustment model, I compute
the abnormal return of stock i on day t as:
ARit = Rit ? (Rf + f ???shrunkt t 1i ). (3.28)
I also consider unadjusted returns (ARit = Rit), returns in excess of the prevailing
risk-free rate (AR fit = Rit?Rt ), and returns in excess of the corresponding Fama and French
(1997) industry portfolio return ( FF48(i)ARit = Rit ? Rt ). Overall, the risk adjustment
calculations generate seven series of abnormal returns for each merger target: Raw, Rf,
CAPM, FF3, Carhart, FF5, and FF48.
Merger attempts are heterogeneous with respect to deal duration in the sample, taking
from a few days to several years. Events lasting more than a few months are considered long-
horizon events. Inference in the context of long-horizon event studies can be econometrically
challenging. Specifically, errors in the benchmark for expected returns are compounded over
long horizons, compounded returns over long horizons are highly skewed, and statistical
tests tend to have low power.11
Fama (1998) recommends using cumulative abnormal returns (CARs) over buy-and-
hold abnormal returns (BHARs) in event studies because the latter compounds estimation
11See Ang and Zhang (2015) for a review of long-horizon event study methodologies.
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errors in expected returns.12 Therefore, I operationalize the price deflation as:
( ? )t
Pit = Pi1 1 + ARi? for t ? T . (3.29)
?=2
where Pi1 is the target?s price from CRSP one day after the merger announcement and
Pit is the resulting deflated price. In addition to adjusting prices for risk exposures, the
deflation accounts for distributions, splits, and reverse-splits.
3.3.4 Price Scaling
The model delivers a relationship between the scaled prices ?(Pit) and ?(PiT ). The scaling
builds on the fact that a merger attempt yields a binary outcome.13 The scaling performs
two important roles. First, it transforms prices into success probabilities. Second, the
scaling ensures that the variation in ?it is driven by heterogeneity in post-announcement
returns and not by heterogeneity in the price level or in the deal premium.
The scalings described in Equation (3.20) and Equation (3.21) cannot be readily
implemented because the conditional expectations are not observable. I make two
simplifying assumptions to operationalize the scaling. First, I assume that the conditional
expectations of C and F are identical under both measures. This is equivalent to
assuming that distorted beliefs only affect the target?s price and do not affect forecasts of
the final cash offer price or the standalone value. Second, I assume both covariance terms
are zero. That is, the outcome of the deal and the difference between final cash offer price
12The results are robust to using BHARs instead of CARs.
13The outcome is not exactly binary since the deal price can adjust, but it is approximately so.
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and standalone value are uncorrelated.14
In the sample, the cash offer price is revised upwards by 2% on average over the
duration of the merger attempt. Merger announcements reveal information about the
target?s standalone value. Malmendier, Opp, and Saidi (2016) find that targets in failed
cash deals are revalued by 15%, on average, after deal failure. Therefore, I choose the final
scaling to be:
= Pi? ? ?Li?i? . (3.30)
?Ci0 ? ?Li
with ? = 1.02, and ? = 1.15. Li is the target?s price 20 days before the merger
announcement and ?Li proxies the expected target?s standalone value.15 C0i is the initial
cash offer price and ?Ci0 proxies the expected final cash offer price. Finally, Pi? is the
target?s risk-adjusted price. All the information required for the scaling is readily
available upon the announcement. In Appendix C.4.1, I show that the results are robust
to changes in the choice of parameters ? and ?.
Importantly, note that any affine scaling that removes the cross-sectional
heterogeneity in price levels and deal premia recovers the distortion coefficient. By the
definition of the conditional expectation, PiT = Pit + ?i with Et[?i] = 0 holds under the
model assumptions and the additional assumption of no learning distortion (? = 1).
Therefore, any equation of the form PiT?a = Pit?a + ?i with b 6= 0 must also hold.
b b b
However, the probabilistic interpretation of the scaled variable requires the scaling to be
done in the way described in the model.
14In the data, the unconditional correlation between the outcome of the attempt and the difference
between the final cash offer price and the estimated standalone value is only 7%.
15I use the price 20 days before the announcement to mitigate run up effects (Schwert, 1996). The
results are robust to using different lags.
95
3.4 Empirical Evidence
In this section, I present the results. I first estimate the baseline econometric specification
derived from the model and show that target prices overreact to merger announcements.
I then provide evidence that target mispricing persists over the course of the attempt. I
also examine the relation between the distortion parameter, firm characteristics, and deal
characteristics. Finally, I provide additional evidence using calendar-time portfolios.
3.4.1 Mispricing in the Cross-Section of Merger Announcements
The baseline specification is the empirical counterpart of Equation (3.25) in the model. I
estimate the following reduced-form specification via OLS:
?iT = ? + ??it + ?itT , (3.31)
where T corresponds to deal completion measured in business days. To mitigate the impact
of outliers on the estimates, I perform the regression on observations that satisfy both
?2 ? ?t ? 3 and |?Ci/?Li ? 1| ? 0.05, and winsorize ?T . Since not all deals finish at the
same event time, I set the dependent variable equal to the value of ?i on the completion
day whenever T is greater than the completion of deal i. Standard errors are robust
to heteroskedasticity in the residuals following White (1980). I calculate other types of
standard errors as part of a robustness exercise and present the results in Appendix C.4.3.
The intuition behind the empirical tests is to check whether scaled prices after the
merger announcement are unbiased predictors of future scaled prices. Under the null
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hypothesis of a well-specified model of expected returns and no learning distortion, the
intercept in Equation (3.31) should be 0 and its slope should be 1. The reduced-form
coefficient ? is the inverse of the distortion parameter ? in the model. The unconditional
probab(ility )of success ?? can be backed out from the reduced-form intercept since
? = 1? 1 ?? = (1? ?) ??. Also note that ?? is the unique fixed point of the linear
?
regression since ?? = ? + ???.16
Figure 3.2. Evidence of Distorted Learning Around Merger Announcements. This
figure shows the relation between ?1 and ?500 with Carhart (1994). The specification is ?i,500 =
?+??i,1+?i. The dependent variable is ?? where ? is the deal completion date whenever ? < 500.
The red line is the best fit of the baseline regression. The blue line with the dots represents local
averages by bins of size 0.25. The black line is the 45-degree line.
Figure 3.2 illustrates my main empirical finding. The red line is the fitted baseline
regression with t = 1, T = 500, and Carhart (1994) risk adjustment. The blue dots
represent local averages of the dependent variable ?iT . If investors process information
16A fixed point is a value of the independent variable for which the conditional mean of the dependent
variable equals the independent variable.
97
about merger targets rationally, the blue and red lines should be indistinguishable from
the black 45-degree line. The slope of the linear regression is well below one, providing
evidence of learning distortion around merger announcements. The non-parametric
estimates confirm the OLS results. The blue and red lines intersect the 45-degree line in
the neighborhood of the unconditional probability of success (0.77) as implied by the
model. It is often the case that assets are properly priced on average but that mispricing
appears only when assets are sorted according to a particular variable. In this case, the
sorting variable is the market-implied probability of success ?it. Targets with a high
market-implied probability of success trade at a premium to their ex post rational price.
Similarly, targets with a low market-implied probability of success trade at a discount to
their ex post rational price. Overall, the results in Figure 3.2 strongly suggests there is
misprocessing of information around merger announcements consistent with overreaction
to deal-specific news.
Figure 3.2 also shows that the model from Section 3.2 is inherently stylized and
therefore fails to fully capture the richness of the data. Comparing Figure 3.2 to the
predictions of the model calibrated with the coefficient estimates (Figure 3.1) provides three
insights. First, the linear approximation captures the positive trend in the relationship
between ?1 and ?T . Second, the curvature of the non-linear at the boundaries of the unit
interval does not obtain in the data. Third, some observations of the dependent variable
?T fall outside of the unit interval. The model acknowleges the fact that investors can
learn about other dimensions of the deal besides the probability of success. For instance,
they may gather information about future revisions in the offer price or about the target?s
standalone value. These additional dimensions of learning are captured in the error term
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of the regression.
Despite its limitations, the model provides a useful transformation that removes the
heterogeneity induced by price levels and allows a probabilistic interpretation of the
resulting scaled variable. In Figure 3.3, I plot the distribution of ?i1 computed with
Carhart (1994) risk adjustment. The model does a good job in terms of data
standardization. Pi1 and ?i1 are almost unrelated as their correlation coefficient is only
5%. Moreover, 80% of the observations of ?i1 lie in the unit interval, bolstering the
interpretation of the scaled price ? as the probability of success.
Figure 3.3. Density of ?1. This figure shows the density of ?1 when computed with Carhart
(1994). The width of each bin is 0.025.
Table 3.3 shows the results of the baseline regression (Equation (3.31)) estimated
using all seven risk adjustments. The independent variable ?t is calculated one day after the
merger announcement and the horizon T is 500 business days. The distortion coefficient ?? is
significantly different from one under all specifications. Moreover, the coefficients are similar
across risk adjustments. The increase in ?? between column (1) and column (2) reflects the
contribution of the risk-free rate to the pricing of the target. The increase in ?? between
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column (2) and columns (3) through (7) reflects the compensation for exposure to factor
risk. The estimates of ? are close to 1.35, which corresponds to the representative investor
overweighting the sample size by 35% in the model. The regression-implied unconditional
probability of success (??) in the Carhart (1994) specification is 81%, a value that cannot
be statistically distinguished from the unconditional probability of success in the sample
(77%). The results confirm the presence of conditional mispricing in the cross-section
of merger targets and are consistent with the mechanism of overreaction to information
presented in the model.
Table 3.3
Baseline Results
This table shows the relation between ?1 and ?500 for various risk adjustments. The specification is ?i,500 =
?+??i,1 +?i. The dependent variable is ?? where ? is the deal completion date whenever ? < 500. The model
parameters are calculated as ? = 1? and ?? =
?
1?? . Heteroskedasticity-robust standard errors are in parentheses.
Standard errors for ? and ?? are calculated using the delta method. ???, ??, and ? denote statistical significance
at the 1%, 5%, and 10% levels, respectively.
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
? 0.601??? 0.668??? 0.725??? 0.742??? 0.740??? 0.736??? 0.737???
(0.038) (0.037) (0.038) (0.040) (0.040) (0.042) (0.044)
? 0.421??? 0.332??? 0.226??? 0.201??? 0.211??? 0.211??? 0.184???
(0.033) (0.032) (0.033) (0.034) (0.035) (0.036) (0.039)
? 1.663??? 1.498??? 1.379??? 1.347??? 1.352??? 1.358??? 1.357???
(0.105) (0.083) (0.072) (0.072) (0.073) (0.077) (0.082)
?? 1.055??? 0.998??? 0.824??? 0.779??? 0.809??? 0.799??? 0.702???
(0.032) (0.034) (0.039) (0.046) (0.046) (0.046) (0.052)
Adj R2 0.170 0.208 0.199 0.175 0.176 0.166 0.164
Observations 4128 4113 4086 4094 4086 4104 4085
Can a regression of long-term returns on short-term returns provide insight on the
mispricing of targets and recover the distortion coefficient? Table 3.4 shows the results of
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the specification:
Ri?20?T = ? + ? Ri i0 1 ?20?1 +  , (3.32)
where Ri = P i ? P i .17?20?t t ?20 The slope coefficients are not significantly different from 1
with any of the risk adjustments. This result obtains because the probability of success and
deal premium are combined in returns. The cross-sectional dispersion in deal premia biases
the estimates of the distortion towards 1. Therefore, the estimates from Equation (3.32)
do not identify the true extent of the learning distortion. In Appendix C.5, I illustrate the
bias by simulating the model and running the returns regression on the simulated data. I
also provide additional support for the scaling procedure described above.
Table 3.4
Returns Regressions
This table shows the relation between R?20?1 and R?20?500 for various risk adjustments. The specification
is Ri?20?500 = ?0 + ? Ri1 ?20?1 + ?i. The time-t cumulative return is calculated as Ri i i?20?t = Pt ? P?20.
The price P500 equals P? where ? is the deal completion date whenever ? < 500. Heteroskedasticity-robust
standard errors are in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels,
respectively.
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
?1 1.016??? 1.005??? 0.992??? 0.990??? 0.996??? 0.990??? 0.985???
(0.006) (0.006) (0.006) (0.006) (0.006) (0.006) (0.007)
?0 0.658??? 0.479??? 0.202??? 0.179?? 0.226??? 0.201?? 0.102
(0.077) (0.076) (0.078) (0.085) (0.086) (0.084) (0.088)
Adj R2 0.889 0.887 0.877 0.858 0.858 0.858 0.846
Observations 4128 4113 4086 4094 4086 4104 4085
The question of whether investors overreact to merger announcement is of interest.
In an earlier attempt to answer this question, Bessembinder and Zhang (2015) define the
17Recall that prices are constructed using CARs.
101
initial target price ratio (ITP) as the ratio of the target?s price after the announcement
over offer price and use it as a measure of investor optimism regarding the outcome of a
merger attempt. They find that high ITPs are associated with a low likelihood of deal
success and with significant negative abnormal returns for the target over the two months
following the announcement. They interpret this finding as evidence of overreaction, thus
my results are very similar to theirs. However, their measure of optimism does not
disentangle deal premium from the probability of success.18 Therefore, ITPs may capture
price movements that are not driven by investors? reaction to information regarding the
outcome of the merger attempt. In contrast, my methodology specifically extracts
investors beliefs about the conditional probability of deal completion from asset prices
and tests whether these beliefs are rationally formed. Moreover, I provide an economic
interpretation of the mechanism behind the overreaction using the model of distorted
learning.
In Appendix C.4, I report the results of robustness checks. Specifically, I show that
the results do not depend on the scaling parameters, on the offer price imputation method,
or on the calculation of standard errors.
3.4.2 Persistence of the Mispricing
The results from the baseline regression from Equation (3.31) suggest that investors
overreact to the burst of information released upon a merger announcement. Do
18Consider the case of two identical merger attempts with a price offer of USD 100 per share. Suppose
that both targets trade at USD 80 per share one day after the announcement, yielding identical ITPs.
Suppose that Target A was trading at USD 50 per share before the announcement while Target B was
already trading at USD 80 per share. Intuitively, the market is more optimistic about the success of Deal
A than that of Deal B, despite the identical ITPs.
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arbitrageurs trade against the mispricing of targets and quickly correct it? If this is the
case, running the baseline regression from Equation (3.31) using ?it with t > 1 as the
independent variable should yield a slope coefficient close to one. Figure 3.4 shows the
slope coefficients of this regression for t = 1 . . . 10. The results show that the coefficients
are significantly less than one in the first two weeks of a merger attempt and their
magnitudes are comparable.19 These results suggest that the mispricing induced by the
learning distortion still exists two weeks after the merger announcement.
In Figure 3.5, I extend Figure 3.4 to illustrate the persistence of the target mispricing
over a longer time window. The figure shows the results of the baseline regression from
Equation (3.31) with the independent variable ?it computed at various event times t. The
regression coefficient at time t is computed based on the subsample of merger attempts
that are still outstanding at that time. The slope of the regression increases in event time,
confirming that the initial overreaction slowly corrects over time when more information
about the merger deal trickles in and investors learn about the outcome of the attempt.
Table 3.5 presents the results for all seven risk adjustments. All columns display a consistent
increasing relation between ? and t that indicates the mispricing of targets is persistent
and slowly decays over time. Moreover, the coefficients are similar across risk adjustments.
19The difference between ?1 and ?10 is not statistically significant in a pooled regression of ?T on
?1 ? 1[t = 1] and ?10 ? 1[t = 10].
103
Figure 3.4. Distortion Coefficient After the Merger Announcement. This figure shows
the slope in the relation between ?t and ?500 with Carhart (1994) for 1 ? t ? 10. The specification
is ?i,500 = ? + ??i,t + ?i. The dependent variable is ?? , where ? is the deal completion date
whenever ? < 500. The continuous line corresponds to the point estimates of ?. The dashed lines
represent 2-standard-error confidence intervals. Standard errors are robust to heteroskedasticity.
Figure 3.5. Distortion Coefficient in Event Time. This figure shows the slope in the
relation between ?t and ?500 with Carhart (1994) for 1 ? t ? 500. The specification is ?i,500 =
? + ??i,t + ?i. The dependent variable is ?? where ? is the deal completion date whenever
? < 500. The continuous line corresponds to the point estimates of ?. The dashed lines represent
2-standard-error confidence intervals. Standard errors are robust to heteroskedasticity.
104
Table 3.5
Distortion Coefficient in Event Time
This table shows the relation between ?t and ?500 at various event times t. The specification is ?i,T =
? + ??i,t + ?i. The dependent variable is ?? where ? is the deal completion date whenever ? < 500. The
columns correspond to the risk adjustments described in Section 3.3.3. Heteroskedasticity-robust standard
errors are in parentheses. Panel A reports the slope of the regression. Panel B reports the intercept. ???, ??,
and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Panel A: ?
(1) (2) (3) (4) (5) (6) (7)
t Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
1 0.602??? 0.669??? 0.726??? 0.743??? 0.740??? 0.737??? 0.738???
(0.038) (0.037) (0.038) (0.040) (0.040) (0.042) (0.044)
5 0.637??? 0.714??? 0.776??? 0.753??? 0.756??? 0.781??? 0.788???
(0.035) (0.033) (0.035) (0.039) (0.039) (0.039) (0.040)
20 0.691??? 0.750??? 0.837??? 0.815??? 0.810??? 0.846??? 0.836???
(0.033) (0.031) (0.032) (0.034) (0.033) (0.032) (0.033)
40 0.730??? 0.763??? 0.836??? 0.824??? 0.847??? 0.837??? 0.868???
(0.040) (0.038) (0.035) (0.033) (0.034) (0.035) (0.035)
60 0.737??? 0.788??? 0.866??? 0.837??? 0.877??? 0.858??? 0.827???
(0.050) (0.047) (0.038) (0.036) (0.036) (0.038) (0.039)
Panel B: ?
(1) (2) (3) (4) (5) (6) (7)
t Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
1 0.420??? 0.331??? 0.226??? 0.200??? 0.210??? 0.210??? 0.183???
(0.033) (0.032) (0.033) (0.034) (0.035) (0.036) (0.039)
5 0.389??? 0.293??? 0.182??? 0.191??? 0.198??? 0.174??? 0.138???
(0.031) (0.030) (0.031) (0.034) (0.034) (0.034) (0.035)
20 0.339??? 0.257??? 0.126??? 0.140??? 0.153??? 0.125??? 0.098???
(0.030) (0.029) (0.028) (0.030) (0.030) (0.029) (0.030)
40 0.297??? 0.235??? 0.109??? 0.113??? 0.101??? 0.106??? 0.063??
(0.038) (0.036) (0.031) (0.030) (0.031) (0.032) (0.032)
60 0.291??? 0.201??? 0.074?? 0.101??? 0.073?? 0.072?? 0.080??
(0.047) (0.043) (0.034) (0.034) (0.034) (0.034) (0.036)
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3.4.3 Mispricing and Deal Characteristics
I next investigate whether the learning distortion varies based on ex ante and ex post deal
characteristics. Let Dij be a dummy variable that takes a value of 1 if deal i belongs to
category j. The econometric specification is
?iT = ?0Di0 + ?1Di1 + ?0Di0?it + ?1Di1?it + ?itT . (3.33)
Equation (3.33) includes category-specific slopes and intercepts. The latter is required
because in the model the intercept is a function of the slope: ? = ??(1 ? ?). The pooled
regression is numerically equivalent to estimating the baseline regression (Equation (3.31))
on each category. The former approach has the added advantage that a Wald test can be
used to test the hypothesis that ?j = ?j? .
Does the distortion coefficient vary with the merger premium? The larger the
premium, the larger the shareholder payoff if the attempt is successful. Intuitively, a
larger premium should incentivize investors to process information more carefully.
Additionally, the target?s price prior to a merger announcement may be subject to a run
up that reflects rumors and information gathered by market participants (Schwert, 1996;
Betton, Eckbo, Thompson, and Thorburn, 2014). If the overreaction documented in the
previous sections is due to faulty learning, the overreaction should be lower for deals with
a higher premium and for deals with a higher run up. To test this hypothesis, I compute
the premium C ?L and the run up P?1?L for each merger. Then, I classify mergers into
high and low premium and run up based on the respective cross-sectional medians.
106
Finally, I estimate the regression described in Equation (3.33). I present the results in
Table 3.6. The results suggest that the overreaction is driven by faulty learning. Indeed,
investors overreact less in situations where the value of information is higher (higher
premium) or where actual information collection is plausibly higher (higher run up).
Table 3.6
Results by Deal Premium and Price Run Up
This table shows the relation between ?1 and ?500 by deal premium and announcement run up for various risk
adjustments. The specification is ?i,500 = ?0D0 + ?1D1 + ?0?i,1D0 + ?1?i,1D1 + ?i where D1 is a dummy
variable whose value is 1 if the deal possesses the characteristic and D0 = 1 ? D1. The dependent variable
is ?? where ? is the deal completion date whenever ? < 500. t(?0 ? ?1) is the t-value of the null hypothesis
?0 = ?1. The columns correspond to the risk adjustments described in Section 3.3.3. Heteroskedasticity-robust
standard errors are in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels,
respectively.
Panel A: Merger Premium
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
?0 0.548??? 0.613??? 0.680??? 0.698??? 0.683??? 0.676??? 0.690???
(0.047) (0.046) (0.047) (0.050) (0.050) (0.053) (0.055)
?1 0.715??? 0.801??? 0.840??? 0.856??? 0.885??? 0.898??? 0.860???
(0.056) (0.055) (0.054) (0.059) (0.056) (0.055) (0.067)
?0 ? ?1 -0.167 -0.187 -0.160 -0.158 -0.202 -0.222 -0.170
t(?0 ? ?1) -2.286 -2.605 -2.229 -2.059 -2.696 -2.892 -1.965
Adj R2 0.175 0.212 0.201 0.177 0.179 0.169 0.166
Observations 4128 4113 4086 4094 4086 4104 4085
Panel B: Run Up
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
?0 0.524??? 0.611??? 0.642??? 0.676??? 0.641??? 0.663??? 0.705???
(0.050) (0.049) (0.051) (0.055) (0.054) (0.057) (0.059)
?1 0.736??? 0.772??? 0.883??? 0.847??? 0.912??? 0.866??? 0.794???
(0.053) (0.052) (0.045) (0.051) (0.051) (0.055) (0.063)
?0 ? ?1 -0.212 -0.161 -0.241 -0.172 -0.271 -0.203 -0.089
t(?0 ? ?1) -2.912 -2.250 -3.540 -2.286 -3.642 -2.569 -1.034
Adj R2 0.174 0.210 0.204 0.177 0.181 0.169 0.165
Observations 4128 4113 4086 4094 4086 4104 4085
107
I next examine whether the learning distortion varies based on other observable deal
characteristics. Table 3.7 reports the results. In Panel A, I compare the distortion
coefficient during and outside of merger waves.20 The point estimates are lower during
merger waves, hinting that the distortion is higher when the M&A market is particularly
active. However, the difference in coefficients is not statistically significant. In Panel B, I
show that the distortion coefficients are similar when controlling for the ex post outcome
of the deal. Finally, in Panel C I compare the coefficient for deals that are tender offers
with deals that are not and obtain similar results. Taken together, the three panels
suggest that the mispricing of targets is pervasive and similar in magnitude across
subsamples.
Table 3.7
Results by Other Deal Characteristics
This table shows the relation between ?1 and ?500 by deal characteristics for various risk adjustments. The
specification is ?i,500 = ?0D0 + ?1D1 + ?0?i,1D0 + ?1?i,1D1 + ?i where D1 is a dummy variable whose value
is 1 if the deal possesses the characteristic and D0 = 1 ? D1. The dependent variable is ?? where ? is the
deal completion date whenever ? < 500. t(?0 ? ?1) is the t-value of the null hypothesis ?0 = ?1. The columns
correspond to the risk adjustments described in Section 3.3.3. Heteroskedasticity-robust standard errors are in
parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Panel A: Merger Wave Dummy
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
?0 0.693??? 0.756??? 0.733??? 0.786??? 0.828??? 0.787??? 0.720???
(0.073) (0.074) (0.087) (0.089) (0.085) (0.087) (0.107)
?1 0.573??? 0.639??? 0.723??? 0.730??? 0.717??? 0.722??? 0.736???
(0.044) (0.042) (0.042) (0.044) (0.045) (0.048) (0.049)
?0 ? ?1 0.120 0.117 0.010 0.056 0.112 0.065 -0.016
t(?0 ? ?1) 1.411 1.372 0.101 0.561 1.161 0.654 -0.134
Adj R2 0.170 0.209 0.199 0.175 0.176 0.166 0.165
Observations 4128 4113 4086 4094 4086 4104 4085
20See Appendix C.2.3 for the definition of merger waves.
108
Table 3.7
Results by Other Deal Characteristics (Continued)
This table shows the relation between ?1 and ?500 by deal characteristics for various risk adjustments. The
specification is ?i,500 = ?0D0 + ?1D1 + ?0?i,1D0 + ?1?i,1D1 + ?i where D1 is a dummy variable whose value
is 1 if the deal possesses the characteristic and D0 = 1 ? D1. The dependent variable is ?? where ? is the
deal completion date whenever ? < 500. t(?0 ? ?1) is the t-value of the null hypothesis ?0 = ?1. The columns
correspond to the risk adjustments described in Section 3.3.3. Heteroskedasticity-robust standard errors are in
parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Panel B: Success Dummy
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
?0 0.693??? 0.705??? 0.700??? 0.748??? 0.766??? 0.726??? 0.664???
(0.071) (0.071) (0.075) (0.077) (0.076) (0.082) (0.083)
?1 0.483??? 0.587??? 0.690??? 0.682??? 0.665??? 0.680??? 0.738???
(0.044) (0.041) (0.041) (0.045) (0.046) (0.047) (0.050)
?0 ? ?1 0.211 0.118 0.010 0.065 0.102 0.045 -0.074
t(?0 ? ?1) 2.531 1.444 0.114 0.733 1.138 0.477 -0.762
Adj R2 0.189 0.223 0.209 0.186 0.188 0.180 0.173
Observations 4128 4113 4086 4094 4086 4104 4085
Panel C: Tender Offer Dummy
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
?0 0.579??? 0.649??? 0.708??? 0.745??? 0.734??? 0.740??? 0.711???
(0.045) (0.044) (0.047) (0.048) (0.048) (0.050) (0.053)
?1 0.640??? 0.693??? 0.719??? 0.685??? 0.705??? 0.657??? 0.765???
(0.071) (0.069) (0.061) (0.072) (0.070) (0.079) (0.083)
?0 ? ?1 -0.062 -0.044 -0.012 0.061 0.029 0.083 -0.053
t(?0 ? ?1) -0.733 -0.532 -0.151 0.700 0.336 0.890 -0.539
Adj R2 0.170 0.209 0.202 0.177 0.178 0.170 0.166
Observations 4128 4113 4086 4094 4086 4104 4085
3.4.4 Mispricing and Firm Characteristics
Thus far the specifications estimate the target mispricing unconditionally or within binary
categories. The learning distortion, however, may conceivably vary in the cross-section of
deals based on the characteristics of the players. The analysis proceeds in two steps to
109
check whether this is the case.
First, I estimate the set of deal-specific distortion parameters ?i using time series
regressions. I specialize the relationship from Equation (3.25) to each deal i:
( )
1 1
?iT = 1? ?? + ?it + ?itT for 0 < t < T . (3.34)
?i ?i
Running a regression of ?iT on ?it and a constant would only identify the intercept
since the dependent variable ?iT is constant and has no variation. Replacing ?? by an
estimate ??? yields a reduced-form specification that identifies ? = 1i :?i
( )
? ?? ??iT ? ? = ?i ?it ? ? + ?itT for 0 < t < T . (3.35)
A natural value for ??? is the fraction of successful merger attempts in the sample. I
calculate ?iT at the 500-day horizon with the Fama and French (1997) 48-industry portfolio
risk adjustment to remove variation that is unrelated to the merger attempt. I exclude
mergers that finish less than 20 business days after the announcement as their estimated
learning distortion parameters are extremely noisy.
Second, I regress the cross-section of deal-specific learning distortion estimates on
acquirer and target characteristics:
??i = ?0 + ?? ?1Xi,target + ?2Xi,acquirer + i, (3.36)
where Xi,p is the vector of characteristics of player p. Accounting characteristics are
calculated using Compustat data for the fiscal year preceding the merger announcement
110
and then standardized. Institutional ownership variables are calculated based on
Thomson Reuters? S34 dataset. In Appendix C.2.1 and Appendix C.2.2, I describe the
construction of the variables. The measurement error in ??i does not bias the estimates in
Equation (3.36) because ??i is on the left-hand side of the equation. However, the
measurement error does introduce additional noise to the second stage regression.21
Table 3.8 provides the summary statistics of the cross-section of ??i resulting from the
first stage regression. The average coefficient is 0.73, a value close to the unconditional
coefficient in the baseline specification. Sixty percent of the estimates are below one; 73%
of the coefficients are statistically different from one.
Table 3.8
Distortion Parameter and Characteristics - First Stage ( )
This table shows the cross-sectional distribution of ??i in the time series regressions ?i,T ???? = ?i ?it ? ??? +?it.i
??? = 0.77 is the unconditional probability of deal completion. Ti is deal i?s completion date. ? is based on the
Fama and French (1997) 48-industry risk adjustment described in Section 3.3.3.
Obs. Mean SD Min 25% 50% 75% Max
??i 4,521 0.73 0.72 -8.38 0.25 0.84 1.18 5.35
Ti 4,521 82.87 68.68 20.00 38.00 63.00 102.00 1025.00
Table 3.9 reports the results of the second stage regression for the institutional
ownership variables. In all specifications, I control for announcement-quarter fixed effects.
An increase in the number of institutional investors that own shares in the target
decreases the learning distortion. An increase in the fraction of shares held by
institutional investors increases the distortion. The same patterns obtain for institutional
ownership of the acquirer, although the statistical significance is low due to the smaller
21In Appendix C.6, I derive the standard errors for the second stage regression.
111
sample size.
Table 3.10 reports the results of the second stage for accounting characteristics. In
all specifications, I control for announcement-year fixed effects. The results in column
(1) show that target characteristics do not explain the cross-sectional variation in the
learning distortion parameter. The main determinants are the operating profitability of
the acquirer and whether the players are in the same industry defined at the four-digit SIC
level. A one standard deviation increase in the profitability of the acquirer increases ?i by
5 percentage points (a decrease in the distortion). Mergers between players operating in
the same industry exhibit a higher distortion on average.
Table 3.9
Distortion Parameter and Institutional Ownership
This table shows the relation between institutional(ownership and merger-specific distortion. The specificationis ?? = ? + ??i 0 1X ?i,target + ?2Xi,acquirer + i. Variables are d)efined in Appendix C.2.2. The dependent variable
comes from the time series regression ?i,T ???? = ?i ?it ? ??? +?it. Standard errors account for the measurementi
error in the first stage (see Appendix C.6 for details). ???, ??, and ? denote statistical significance at the 1%,
5%, and 10% levels, respectively.
(1) (2) (3)
log(Relative Number Institutions) Target 0.047??? 0.015
(0.016) (0.029)
Fraction Institutional Holdings Target -0.132? 0.018
(0.067) (0.126)
log(Relative Number Institutions) Acquiror 0.052??? 0.045??
(0.016) (0.017)
Fraction Institutional Holdings Acquiror -0.037 -0.036
(0.056) (0.059)
Adj R2 0.007 0.028 0.023
Observations 4367 1766 1717
Quarter FE Yes Yes Yes
112
3.4.5 Parameter Stability
Although the estimates of the reduced-form coefficient exhibit some cross-sectional
variation when allowed to vary based on observable deal and firm characteristics, their
values remain comparable. In particular, the results are always consistent with
overreaction to information, never with underreaction. The reciprocal of the reduced-form
coefficient corresponds to the distortion parameter in the model. DellaVigna (2018)
recommends that ?[i]n a well-specified model, certain ?deep? [structural] parameters
should have comparable values across different settings.? The results presented in the
previous sections support the interpretation of the mispricing being driven by a deep
parameter. In the model, the wedge in beliefs is a function of the distortion parameter
and of the information received by investors. The stability of the estimates suggests that
most of the variation in belief distortion is driven by changes in information flows, not by
changes in the intensity of the bias itself.
113
Table 3.10
Distortion Parameter and Firm Characteristics
This table shows the relation between player characteristics and merger-specific distortion. The specification is
??i = ?0 +??1X ?i,target +?2Xi,acquirer +i. Variable(s are defi)ned in Appendix C.2.1. The dependent variable comes
from the time series regression ?i,T ? ???i = ?i ?it ? ??? + ?it. Standard errors account for the measurement
error in the first stage (see Appendix C.6 for details). ???, ??, and ? denote statistical significance at the 1%,
5%, and 10% levels, respectively.
(1) (2) (3)
Operating Profitability Target 0.006 0.007
(0.016) (0.026)
Size Target 0.017 0.006
(0.013) (0.021)
Book Leverage Target 0.004 -0.010
(0.013) (0.022)
Investment-to-Assets Target 0.025 0.058??
(0.021) (0.023)
PPENT-to-Assets Target -0.020 -0.024
(0.023) (0.042)
Cash-to-Assets Target 0.004 -0.002
(0.015) (0.028)
Book-to-Market Target -0.006 0.006
(0.008) (0.023)
Operating Profitability Acquirer 0.051??? 0.051???
(0.014) (0.016)
Size Acquirer 0.028 0.015
(0.023) (0.025)
Book Leverage Acquirer 0.030 0.037?
(0.022) (0.021)
Investment-to-Assets Acquirer -0.054? -0.078?
(0.030) (0.040)
PPENT-to-Assets Acquirer 0.069??? 0.067?
(0.025) (0.037)
Cash-to-Assets Acquirer 0.021 0.023
(0.021) (0.020)
Book-to-Market Acquirer -0.004 0.009
(0.024) (0.025)
Same Industry -0.102?? -0.089??
(0.038) (0.043)
Adj R2 -0.002 0.014 0.009
Observations 3593 1237 1091
Year FE Yes Yes Yes
114
3.4.6 Calendar-Time Portfolios
Merger targets earn positive abnormal returns, and target shareholders compensate
arbitrageurs for taking exposure to completion risk (Larcker and Lys, 1987; Dukes et al.,
1992; Mitchell and Pulvino, 2001; Baker and Savasoglu, 2002). Can arbitrageurs benefit
from the target price mispricing by trading against it? To answer this question, I
construct calendar-time portfolios where the scaled price ?1 is used as a selection
variable. While studies thus far have focused on the unconditional deal premium, in this
section I examine the cross-sectional variation in that premium.
In Section 3.4.1, I find that low-?1 targets underestimate the probability of success
and high-?1 targets overestimate it. Therefore, I propose the following long-short trading
strategy that buys low-?1 targets and short sells high-?1 targets. A stock enters the
portfolio one business day after the merger announcement and exits either when the deal
succeeds and the stock is delisted, or one business day after the announcement that the
deal has failed. Stocks are weighted according to their ?1 within each leg of the long-short
portfolio. Stocks with a larger ?1 in absolute value are given a larger weight because the
panel regressions indicate the mispricing is more severe for stocks having very high or very
low ?1 values. I use scaled prices computed with the Carhart (1994) risk adjustment to
create the weights. Deals whose ?1 is below/above the sample average ??1 are assigned
to the long/short ?leg of th?e portfolio. Within each leg, the weight on individual stocks
is proportional to ?? ? ??1 ??1?. The weight on a stock is proportional to the severity of the
mispricing, which is the difference between the red fitted line and the 45-degree line in
Figure 3.2. Stocks are given a weight of zero outside of the merger announcement window.
115
I present the results in Table 3.11. Annualized alphas are multiplied by 100 and
standard errors follow Newey and West (1987) with a 60-day lag. The table shows pooled
regression results of the daily returns on the low-? and high-? portfolios on risk factors.
Performing the regression on the portfolio legs allows unconditional and conditional
mispricing to be examined separately. Both portfolios have a positive and significant
exposure to the market and to the SMB factor. The exposure to other risk factors is
insignificant. The alphas of both portfolios are positive in columns (1) through (5),
confirming the finding that the cross-section of merger targets is mispriced. The low-?
portfolio earns annualized abnormal returns that are above 9 percentage points higher
than those of the high-? portfolio, and this difference is consistent across the various
specifications of risk factors. The annualized alpha of the long-short strategy is
economically and statistically significant.22
Overall, calendar-time portfolios provide results that mirror the findings based on
panel regressions in Section 3.4.1. However, the two methodologies are not perfect
substitutes. The panel regressions abstract from deal premia and isolate the overreaction
embedded in the probability of success. The magnitude of calendar-time portfolio returns
depends on the probability of success (through the portfolio weights) and on merger
premia. Keeping the probability of success constant and conditioning on the success of
the attempt, the returns earned on a deal increase in the deal premium. Finally, note that
like in the panel regression, the alpha earned by this trading strategy is unrelated to the
unconditional merger premium earned by a standard merger arbitrage strategy. Since
both legs of the long-short portfolio contain merger targets, the unconditional merger
22The results are robust to changing the number of lags in the Newey-West standard errors.
116
arbitrage premium cancels out.
Table 3.11
Calendar-Time Portfolios
This table shows the results of the regressions of calendar-time portfolio legs on risk factors. Low and High are
indicator variables for the legs of the portfolio. Alphas and alpha differences are annualized. HAC standard
errors with a 60-day lag are in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively. The sample period is March 1978 to December 2018.
(1) (2) (3) (4) (5)
Constant CAPM FF3 Carhart FF5
Const?Low 19.009??? 16.156??? 15.533??? 15.655??? 15.116???
(4.123) (3.993) (3.979) (3.945) (3.956)
Const?High 7.709? 6.108?? 5.766? 6.281?? 5.306?
(4.123) (2.995) (2.990) (3.112) (2.935)
MKT-RF?Low 0.340??? 0.363??? 0.362??? 0.373???
(0.045) (0.048) (0.052) (0.052)
MKT-RF?High 0.191??? 0.204??? 0.197??? 0.217???
(0.022) (0.025) (0.025) (0.027)
SMB?Low 0.249??? 0.249??? 0.265???
(0.054) (0.053) (0.058)
SMB?High 0.153??? 0.154??? 0.164???
(0.040) (0.038) (0.037)
HML?Low 0.087 0.080 0.081
(0.063) (0.068) (0.075)
HML?High 0.042 0.015 0.013
(0.034) (0.038) (0.053)
MOM?Low -0.013
(0.056)
MOM?High -0.053
(0.034)
RMW?Low 0.059
(0.068)
RMW?High 0.033
(0.047)
CMA?Low 0.026
(0.093)
CMA?High 0.091
(0.093)
? Difference 11.300? 10.048?? 9.767?? 9.374? 9.810??
? Difference Test Statistic (1.938) (2.013) (1.963) (1.866) (1.992)
Adj R2 0.000 0.029 0.034 0.034 0.034
Observations 21080 21080 21080 21080 21080
117
3.5 Conclusion
In this paper, I measure investor overreaction to information pertaining to a specific
dimension of an asset in a setting where information flows are unobservable. In particular,
I measure how investors react to the information released during merger attempts. I
derive a model of distorted learning which provides a natural price rescaling that recovers
investor beliefs from market prices and delivers testable predictions. Empirically, I find
that investors deviate from the Bayesian paradigm when learning about the success
probability of merger attempts and predictably overreact to deal-specific merger news.
The overreaction generates a conditional mispricing in the cross-section of merger
targets: target prices underestimate the probability of deal completion when low and
overestimate it when high. In terms of returns, targets with a low market-implied
probability of success earn larger abnormal returns than targets with a high
market-implied probability of success. I show that this finding is unrelated to the fact
that merger targets earn positive abnormal returns on average. Overall, I document a new
stylized fact and provide a fresh insight on behavioral distortions during merger attempts.
118
Appendix A: Supplements to Chapter 1
A.1 Dataset Construction
A.1.1 FEC Reporting Timeline
Table A.1
FEC Reporting Timeline
This table shows the reporting timeline for congressional committees during election years. Only quarterly
and year-end reports are filed in non-election years. Source: Federal Election Commission.
Report Period Covered Filing Deadline
April Quarterly January 1 to March 31 April 15
July Quarterly April 1 to June 30 July 15
October Quarterly July 1 to September 30 October 15
Pre-General October 1 to October 10-20 8 days after close of books
Post-General October 10-20 to November 20-30 10 days after close of books
Year-End November 20-30 to December 31 January 31
119
A.1.2 FEC Form 3
Table A.2
FEC Form 3 - Receipts, Disbursements, and Cash
This table presents the items reported by congressional committees on FEC Form 3. Source: Federal Election
Commission.
Item Type Description
11a (i) Receipt Itemized Contributions from Individuals/Persons other than Political Committees
11a (ii) Receipt Unitemized Contributions from Individuals/Persons other than Political Committees
11b Receipt Contributions from Political Party Committees
11c Receipt Contributions from Other Political Committees (e.g. PACs)
11d Receipt Contributions from the Candidate
12 Receipt Transfers from Other Authorized Committees
13a Receipt Loans Made or Guaranteed by the Candidate
13b Receipt All Other Loans
14 Receipt Offsets to Operating Expenditures
15 Receipt Other Receipts
17 Disbursement Operating Expenditures
18 Disbursement Transfers to Other Authorized Committees
19a Disbursement Repayment of Loans Made or Guaranteed by the Candidate
19b Disbursement Repayment of All Other Loans
20a Disbursement Refunds of Contributions to Individuals/Persons other than Political Committees
20b Disbursement Refunds of Contributions to Political Party Committees
20c Disbursement Refunds of Contributions to Other Political Committees (e.g. PACs)
21 Disbursement Other Disbursements
23 Cash Cash on Hand at Beginning at Beginning of Reporting Period
120
Table A.3
FEC Form 3 - Accounting Identities
This table presents the accounting identities used by the FEC to aggregate items reported by congressional
committees on FEC Form 3. Source: Federal Election Commission.
Item Type Description Formula
11a Receipt Total Contributions from Individuals = 11a (i) + 11a (ii)
11 Receipt Total Contributions = 11a + 11b + 11c + 11d
13 Receipt Total Loans = 13a + 13b
16 Receipt Total Receipts = 11 + 12 + 13 + 14 + 15
19 Disbursement Total Loan Repayments = 19a + 19b
20 Disbursement Total Contribution Refunds = 20a + 20b + 20c
22 Disbursement Total Disbursements = 17 + 18 + 19 + 20 +21
27 Cash Cash on Hand at Beginning at Close of Reporting Period = 23 + 16 - 22
121
A.1.3 FEC Contribution Limits
Table A.4
FEC Contribution Limits - 2018 Matrix
This table shows the legal donation limits for various types of donors and recipients in election year 2018.
Limits for other election years are available on the FEC website. Each of the following is considered a separate
election with a separate limit: primary election, caucus or convention with the authority to nominate, general
election, runoff election and special election. Source: Federal Election Commission.
Recipient
Candidate PAC (SSF and Party Party Additional
committee nonconnected) committee: committee: national party
state, district, national committee
local accounts
Individual $2,700 per $5,000 per year $10,000 per year $33,900 per year $101,700 per
election (combined) account, per
year
Candidate $2,000 per $5,000 per year Unlimited Unlimited
committee election transfers transfers
PAC: multi- $5,000 per $5,000 per year $5,000 per year $15,000 per year $45,000 per
candidate election (combined) account, per
year
Donor PAC: non $2,700 per $5,000 per year $10,000 per year $33,900 per year $101,700 per
multi- election (combined) account, per
candidate year
Party $5,000 per $5,000 per year Unlimited Unlimited
committee: election (combined) transfers transfers
state, district, (combined)
local
Party $5,000 per $5,000 per year Unlimited Unlimited
committee: election transfers transfers
national
122
Table A.5
FEC Contribution Limits - History
This table shows the the legal donation limits by individuals to congressional candidates between election
cycles 2003/04 and 2017/18. The FEC fixes the 2003 limit to $2,000 and adjusts the limit for inflation on
every odd year. Each of the following is considered a separate election with a separate limit: primary election,
caucus or convention with the authority to nominate, general election, runoff election and special election.
Source: Federal Election Commission.
Election Cycle Cap on Individual Donations
2003/04 $2,000 per candidate per election
2005/06 $2,100 per candidate per election
2007/08 $2,300 per candidate per election
2009/10 $2,400 per candidate per election
2011/12 $2,500 per candidate per election
2013-/14 $2,600 per candidate per election
2015/16 $2,700 per candidate per election
2017/18 $2,700 per candidate per election
A.1.4 Variable Definitions
I define the following variables based on the FEC items from Form 3:
? Net individual fundraising = Item 11a - Item 20a.
? Net other fundraising = Item 11b + Item 11c + Item 11d + Item 12 - Item 18 - Item 20b
- Item 20c.
? Net loans = Item 13a + Item 13b - Item 19a - Item 19b.
? Net other income = Item 14 + Item 15 - Item 21.
? Advertising expenditures = Individual entries in Item 15 tagged as advertising (see keywords
below).
? Other expenditures = Individual entries in Item 15 not tagged as advertising (see keywords
below).
An operating expenditure is classified as advertising expenditure if its Purpose of Disbursement
contains any of the following keywords: AD, ADS, ADVERSTISING, ADVERTISEMENT,
ADVERTISEMENTS, ADVERTISING, ADVERTISMENT, FLYERS, MATERIAL,
MATERIALS, MEDIA, MULTIMEDIA, NEWSPRINT, PRINT, PRINTED, PRINTER,
123
PRINTING, PRINTS, PROMOTIONAL, RADIO, SIGNS, STICKERS, TELEVISION, TV,
YARD, YARDSIGN, YARDSIGNS.
A.1.5 Predictors
The dependent variable is net fundraising from individuals in week t scaled by own cash reserves
in week t ? 1. See Appendix A.1.4 for the definition of the variables. Lagged variables use two
lags unless mentioned otherwise. Predictions are robust to adding more lags. Variables postfixed
by (*) are sampled for the committee and its opponent. I winsorize all ratio variables at 1% in
each tail to discipline the learning.
The predictors for the extended sample are: dummy variable for Republican or Democrat,
dummy variable for incumbency status, dummy variable for week number, probability and change
in probability as of t?1 that the candidate?s party will control the House (*), lagged net individual
fundraising, net other fundraising, and net other income - scaled by previous week cash reserves
and in levels (*), current and lagged advertising and other expenditures - scaled by previous week
cash reserves and in levels (*), current and lagged fraction of advertising expenditures out of total
expenditures (*), lagged log and change in log of advertising expenditures and net fundraising
from individuals (*), and lagged log cash reserves (*).
The predictors for the main sample are: all the predictors for the extended sample,
percentage of vote intentions in week t ? 1, percentage of vote intentions for the opponent in
week t? 1, difference between own and opponent?s percentage of vote intentions in week t? 1.
124
A.2 Shocks
Figure A.1. Shock Diagnostics - Artificial Neural Network. This figure presents
diagnostics for the shock constructed with the artificial neural network methodology. The top-
left panel shows the histogram of the shock. The top-right panel shows the scatter plot of a
committee?s shock along with the shock of its opponent. The bottom-left panel shows the average
of the shock by week before the election. The bottom-right panel shows the average of the shock
by week in calendar time.
Figure A.2. Shock Autocorrelation - Artificial Neural Network. This figure shows the
results of the autocorrelation analysis for the shocks constructed with the artificial neural network.
The red line corresponds to the estimate ?? in the regression Sit = ?i+?t+?Si,t?1 + ?it. The blue
bars correspond to the histogram of ?? from the same regression where Sit and Si,t?1 are replaced
by random noise for all i and t. The histogram is based on 5,000 simulations.
125
A.3 Robustness
Table A.6
Impact of Revenues on the Vote Share (I) - Artificial Neural Network
This table reports the results of regressions of the challenger vote share on revenue shocks for races in the main
sample that involve the incumbent. The indices C and I correspond to the challenger and the incumbent,
respectively. SumShocki is the sum of the weekly artificial neural network shocks of the primary committee
for candidate i. Unemployment is measured at the state level. IncRulingParty is a dummy variable that
indicates whether the incumbent is in the same party as the U.S. president. Monetary variables are expressed
as multiples $100,000. Vote shares and polling variables are expressed in percent. Heteroskedasticity-robust
standard errors are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
V oteShareC V oteShareC V oteShareC
SumShockI -0.017 0.042 -0.020
(0.125) (0.115) (0.117)
SumShockC 0.490?? 0.598??? 0.609???
(0.211) (0.189) (0.179)
InitialPollingI -0.465??? -0.405??? -0.406???
(0.083) (0.075) (0.057)
InitialCashI 0.048 0.048
(0.036) (0.036)
InitialCashC 0.497??? 0.494???
(0.077) (0.072)
Unemployment -0.772???
(0.272)
Unemp? IncRulingParty 0.569???
(0.159)
Year FE X X X
R2 0.273 0.378 0.420
N 333 333 333
126
Table A.7
Impact of Revenues on the Vote Share (II) - Artificial Neural Network
This table reports the results of regressions of the challenger vote share on revenue shocks for races in the main
sample that involve the incumbent. The indices C and I correspond to the challenger and the incumbent,
respectively. SumShockEarlyi (SumShockLatei) is the sum of the weekly artificial neural network shocks
of the primary committee for candidate i between weeks -12 and -7 (-6 and -1). HighOwnBetaC and
LowOwnBetaC are dummy variables indicating whether the sensitivity of own spending to own revenue
shocks of the challenger committee is above or below the cross-sectional median. HighOppBetaC and
LowOppBetaC are defined similarly for the sensitivity of the challenger?s spending to shocks of the incumbent.
Unemployment is measured at the state level. IncRulingParty is a dummy variable that indicates whether the
incumbent is in the same party as the U.S. president. Monetary variables are expressed as multiples $100,000.
Vote shares and polling variables are expressed in percent. Heteroskedasticity-robust standard errors are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
V oteShareC V oteShareC V oteShareC
SumShockI -0.078 -0.034 -0.018
(0.128) (0.121) (0.117)
SumShockEarly 1.532???C
(0.299)
SumShockLateC -0.139
(0.262)
SumShockC ?HighOwnBetaC 0.401??
(0.197)
SumShockC ? LowOwnBetaC 0.917???
(0.280)
SumShockC ?HighOppBeta 0.637???C
(0.215)
SumShockC ? LowOppBetaC 0.541?
(0.291)
InitialPolling -0.389???I -0.403??? -0.405???
(0.057) (0.057) (0.057)
InitialCashI 0.030 0.045 0.049
(0.039) (0.036) (0.036)
InitialCashC 0.428??? 0.498??? 0.495???
(0.070) (0.071) (0.072)
Unemployment -0.752??? -0.774??? -0.764???
(0.271) (0.273) (0.276)
Unemp? IncRulingParty 0.546??? 0.569??? 0.566???
(0.158) (0.159) (0.160)
Year FE X X X
R2 0.434 0.421 0.418
N 333 333 333
127
Appendix B: Supplements to Chapter 2
B.1 Model Derivations
B.1.1 Equilibrium at t = T
The Bellman equation of candidate 1 at T is:
[ ( )]
( ; ; ; ) = max K1,T+1 ?K2,T+1V1T K1T K2T W1T W2T ET F (B.1)
I1T ,H1T ?
subject to:
WiT ? IiT +HiT + ?(IiT ,KiT ) (B.2)
0 ? IiT , HiT ,WiT (B.3)
Ki,T+1 = (1? ?)?(H?iT )KiT + IiT (B.4)
and where:
????12 exp (x) if x ? 0
F (x) = ??? (B.5)1? 12 exp (?x) if x ? 0
Since F is increasing in both I1T and H1T and leftover cash does not confer any utility, the
liquidity constraint binds and the candidate spends all his wealth:
I?1T +H?1T + ?(I?1T ,K1T ) = W1T (B.6)
Given a level of hindrance H1T and the funct?ional form for ?, investment?I1T is therefore:?
= ( ) = K1T ? 1 + 2?0 (W1T ?H1T )I1 ?T I1T H1T ? 1 (B.7)
?0 K1T
128
The maxi?mization problem at T becomes:? ( ) 1 ??(1? ?)?(H )K ? K1T + K1T 1 + 2?0(W1T?H? 1T
) 2
2T 1T ? ? K ? (1? ?)?(H1T )K0 0 1 2T ? I2T ?maxF T ?
H ?1T ?
(B.8)
subject to 0 ? H1T ? W1T . Denoting the Lagrange multipliers on the two inequality constraints
by ?1TH and??1TW , the first-order condition is:( ) ?1 ? 12
F ?(. . . )?? 1 + 2?0 (W1T ?H1T ) + (1? ?)? ?? H0e 0 1TK2 ?T + ?1TH ? ?1TW = 0 (B.9)
? K1T
where the ellipsis corresponds to the argument to the function F in Equation (B.8).
When the solution is interior, the Lagrange multipliers are zero and the first-order condition
reduces to:
K1T K1T
2 +W ?
2?0H1 1TT
?0 2?0(1? ?)2 2 2
e = H1T (B.10)
?0K2T
This equation has a closed-form solutio(n: ( ))
H interior1T =
K1T 1 K1T ?0
W1T + 2 ??0 2
W 2 2 exp 2?0W1T + K1T (B.11)?0 ?0?0(1? ?) K2T ?0
where W is Lambert?s W function.1 The solution that takes into account the non-negativity and
liquidity constraints is: ??????0 if ?(0) ? 0
H?1T = ?????W1T if ?(W1T ) ? 0 (B.12)H interior1T otherwise
where: ( 1
( ?? H 2 ( ? )
)
? W H ? 2
? H1 ) = (1? ?)K2 ?0e 0 1T ? 1 + 0 1T 1TT T (B.13)
K1T
Finally, optimal investment as a function of optimal hindrance is given by I(H?1T ) in Equation
(B.7).
The partial derivatives of the value function at t = T with respect to own capital and own
1W(z) is the solution to z = wew. See Corless and Jeffrey (2015) for a thorough exposition. The
solution to the equation x = a + becx is x = a ? 1cW(?bce
ac). One could argue the solution is not in
closed-form since W is not an elementary function. This debate is beyond the scope of the paper. In any
case, evaluating W is extremely fast in most computing languages.
129
cash reserves are:
1 { [?V ? ] ? ? ?1T = F ?(. . . ) (1? ?) ??( ? )?HH 2T K + ?(H? ) + ?I1T + ?I1T ?H1T1T
?K 2T 2T1T ? ?K1T ?K1T ?H1}T ?K1T?
?(1? ) ?( ? )?H1T ? ?I
? ?I? ?H?
{ ? ? H K 2T ? 2T 2T1T 2T (B.14)?K1T ?K1T ?H2T ?K1T
?V ? ? ? ?1T = 1F ?(. . . ) (1? ?)??( ?HH? ) 2T ?I ?I ?HK + 1T + 1T 1T1T
?W1T ?
2T ?W1T ?W1T ?H1T ?W1T
?H?
}
?(1? ) ?I
? ?I? ?H?
? ??(H? ) 1T K ? 2T1T 2T ? 2T 2T (B.15)?W1T ?W1T ?H2T ?W1T
These partial derivatives are used to solve the game at t < T given the recursive structure of the
problem. Note that at T the optimal choices made by committees, their value functions, and the
partial derivatives thereof are all in closed-form.
B.1.2 Comparative Statics at T
Recall that ?(H1T ) is defined as:
( )? 12
?(H1T ) = (1? )
2?0 (W1T ?H1T )
? K2T? e
??
0 0
H1T ? 1 + (B.16)
K1T
and that the first-order condition at T can be written as:
1
F ?(. . . )?(H1T ) + ?1TH ? ?1TW = 0 (B.17)
?
For an interior solution this equation reduces to ?(H?1T ) = 0. By the implicit function theorem,
for any variable v:
dH?1T = ? ??/?v? (B.18)dv ??/?H1T
The denominator is always negative:
( )
?? ?
3
2
= ?(1? ?)K ?2e??0H ? ?0 1 + 2?0 (W1T 1T ?H1T )2T 0 < 0 (B.19)?H1T K1T K1T
Therefore, it must be that:
(
dH?
) ( )
sign 1T = sign ?? (B.20)
dv ?v
130
The partial derivatives with respect to each of the parameters are:
?? = ?K ?? H2T?0e 0 1T < 0 (B.21)
??
?? = ?0(1? ?)e??0H1T >(0?K2T ( ? ) 2 ( ? ))
(B.22)
3
?? ?= ??0 W1T H1T 1 + ?0 W1T H1T
2
< 0 (B.23)
?K1 2T ( K1T K1T
?? ? 2 )? ? 3= 0 1 + 0(W1T ?H1T ) 2( > 0 (B.24)?W1T K1T K1T ) 3
?? = W1T ?H1T 1 + 2?0(W1T ?H
?
1T ) 2
> 0 (B.25)
??0 K1T K1T
?? = K2T (1? ?)e??0H1T [1? ?0H1T ] (B.26)
??0
?
The sign of dH1Td? depends on the value taken by H
?
1T . The effect is positive if H?1T?0 < 1 and0
negative if H?1T?0 > 1. The candidate spends all his cash on I if ?(0) < 0, which is equivalent to:
( ) 1
(1? ) K1T
2
K2T ? ?0 < (B.27)
K1T + 2?0W1T
The candidate spends all his cash on H if ?(W1T ) > 0, which is equivalent to:
K ?? W2 (1? ?)?0e 0 1TT > 1 (B.28)
Therefore, the candidate spends cash on both I and H if and only if:
( ) 1
K1T 2
+ 2 < K2T (1? ?)?0 < e
?0W1T (B.29)
K1T ?0W1T
B.1.3 Equilibrium at t < T
The Bellman equation of candidate 1 at t is:
V1t (K1t;K2t;W1t;W2t) = max Et [V1,t+1 (K1,t+1;K2,t+1;W1,t+1;W2,t+1)] (B.30)
I1t,H1t
subject to:
W1,t+1 = W1t ? I1t ?H1t ? ?(I1t,K1t) + f(I1t, 1t) (B.31)
W1t ? I1t +H1t + ?(I1t,K1t) (B.32)
0 ? H1t (B.33)
K1,t+1 = (1? ?)?(H2t)K1t + I1t (B.34)
131
The Lagrangian and complementary slackness conditions of candidate 1 at time t are:
L1t = Et [V1,t+1 (K1,t+1;K2,t+1;W1,t+1;W2,t+1)]
+ ?1tHH1t + ?1tW [W1t ? I1t ?H1t ? ?(I1t,K1t)] (B.35)
0 = ?1tHH1t (B.36)
0 = ?1tW [W1t ? I1t ?H1t ? ?(I1t,K1t)] (B.37)
0 ? ?1tH , ?1tW (B.38)
The fi[rst-order conditions o(f committee 1 at time t are: )] [ ]
?V1,t+1 + ?V1,t+1 ?1? ??(I1t,K1t) + ?( ) + ?1? ??(IE 1t,K1t)t f I1t 1t ?1tW = 0
?K1,t+1 ?W1,t+1 ?I1t ?I1t
[ ] (B.39)
E ? ?V1,t+1 + ?V1,t+1 (1? ?)??t (H1t)K2t + ?1tH ? ?1tW = 0
?W1,t+1 ?K2,t+1
(B.40)
I rearrange the first-order conditions of candidate 1 to isolate the Lagrange multipliers which
speeds u[p the numerical solution procedure and establishes Pro]position 2.2:( )
?Vi,t+1 + ?VE i,t+1t ?1?
??(Iit,Kit) + ?f(Iit, it)
?Ki,t+1 ?Wi,t+1 ?Iit ?Iit [ ]
+ ?1? ??(Iit,Kit)[ ( ?itW )] = 0 (B.41)?Iit
?V
E 1,t+1 (1? ) ?( ) ?1? ??(Iit,Kit)t ? ? Hit K?it
?K?i,t+1[ ]?Iit [ ]
+ ?Vi,t+1 + ?Vi,t+1 ?f(IE it, it) ??(Iit,Kit)t + ?itH ?1? = 0 (B.42)
?Ki,t+1 ?Wi,t+1 ?Iit ?Iit
?itHHit = 0 (B.43)
?itW [Wit ? Iit ?Hit ? ?(Iit,Kit)] = 0 (B.44)
?itH , ?itW ? 0 (B.45)
Since the first-order conditions of the other committee have a similar structure, we are
left with a system of four first-order conditions that must hold simultaneously. The pure strategy
Markov perfect Nash equilibria are vectors (I1t, I2t, H1t, H2t, ?1tH , ?2tH , ?1tW , ?2tW ) that solve the
system. There are 16 potential equilibria depending on whether the four constraints are binding or
not. In general, this problem does not have a closed-form solution and must be solved numerically.
Finally, the recursive formulation of the partial derivatives of the value function at t < T
132
is: [ ]
?V1t = ?V1,t+1 (1? ) ( ?V1,t+1 ??(I1t,K1t) ??(I1t,KE 1t)t [ ] ? ? H
?
2t)? ? ?1tW (B.46)?K1t ?K1,t+1 ?W1,t+1 ?K1t ?K1t
?V1t = ?VE 1,t+1t + ?1tW (B.47)
?W1t ?W1,t+1
Note that if the liquidity does not bind, the partial derivatives of the value function have a familiar
form since ?1tW = 0. If the liquidity constraint binds, increasing W1t (K1t) by an infinitesimal
amount has two effects. First, it increases the resources available (decreases the adjustment cost)
in the next period as for an interior case. Second, it relaxes the liquidity constraint in the current
period which allows the candidate to increase current spending.
B.1.4 Numerical Solution
First, I establish some useful properties of the value function. Second, I outline the numerical
procedure used to solve the model.
B.1.4.1 Properties of the Value Function
Since committee 1 makes no decision at the date of the election (T+1), its terminal value function
is simply:
( )
V1,T+1 (K1,T+1;
K1,T+1 ?K2,T+1
K2,T+1;W1,T+1;W2,T+1) = F (B.48)
?
The value function of committee 1 at time t represents its conditional probability of winning the
election:2 [ ( )]
V1t (K1t;K2t;W1t;W2t) = max
K
E 1,T+1
?K2,T+1
t F (B.49)
{I ,H T1s 1s} ?s=t
Intuitively, V1t is increasing in K1t andW1t and decreasing in K2t andW2t. The Bellman equation
of committee 1 at time t is:
V1t (K1t;K2t;W1t;W2t) = max Et [V1,t+1 (K1,t+1;K2,t+1;W1,t+1;W2,t+1)] (B.50)
I1t,H1t
2Specifically, Vit is the conditional p(robability)that candidate i wins the election assuming the race goesto completion. The conditional probability that candidate i wins if the election was held at t (which is the
wording in most polling surveys) is F Kit?K?ii? . The distinction is subtle but important. Vit captures
the expected future contribution of spending to the election outcome in addition to the current relative
level of political capital.
133
Since both committees form expectations using identical probability measures, it must that:
V1t (K1t;K2t;W1t;W2t) + V2t (K1t;K2t;W1t;W2t) = 1 (B.51)
?V1t ( ?V2tK1t;K2t;W1t;W2t) + (K1t;K2t;W1t;W2t) = 0 (B.52)
?x ?x
for any state vector (K1t;K2t;W1t;W2t), state variable x, and time t. These properties speed up
the numerical solution since only four partial derivatives need to be calculated (instead of eight).
B.1.4.2 Solution Method
I solve the model numerically for a given vector of initial state variables (K10;K20;W10;W20) and a
terminal spending period T . The solution can be visualized in a tree form.At each node, the players
choose optimal investment and hindrance based on the current state vector (K1t;K2t;W1t;W2t).
Each node splits into four branches, one for each realization of the revenue shocks (uu, ud, du, dd).
The solution of the model at time t is characterized by the system of equations in Proposition
2.2. The characterization is in recursive form since it involves partial derivatives of the value
function at t+1. Proposition 2.1 provides an exact, closed-form solution of the problem at t = T .
I use a numerical solver to find the vector that satisfies the equilibrium characterization at t. For
each guess of the solution at t, I use the law of motion of cash and political capital to obtain the
state variables at t+ 1 and the partial derivatives of the value function. This solution method is
slow because the model is solved forward at each guess but provides an exact solution at each t.
The problem is well-behaved enough to guarantee existence and uniqueness of the solution
although I am not able to prove it formally. Indeed, spending exhibits decreasing returns in the
fundraising revenues and hindrance functions and adjustment costs are increasing and convex
in investment. Moreover, the payoff function is increasing in a player?s own state variables and
decreasing in the opponent?s state variables. In the numerical procedure I use multiple starting
values in the solver to ensure the solution is indeed unique.
I increase the speed of the algorithm by feeding the solver with starting values that are close
to the actual solution. I use a surrogate model estimated through machine learning to generate
the starting values. Surrogate models are commonly used in engineering and astrophysics because
they provide computationally-efficient approximations of complex models.3 Like the actual model,
the surrogate model can be construed as a mapping between model primitives (parameters, state
variables, and timestamp) and the choice variables of both players (investment and hindrance)
at a particular timestamp. I build the surrogate model in three successive steps. First, I draw
random samples of the model primitives. Second, I solve the true model for each combination of
primitives using arbitrary starting values in the solver. This step is computationally expensive
because the starting values may be far away from the actual solution. Third, I estimate the
3See Forrester, Sobester, and Keane (2008) for a practical guide.
134
mapping between model primitives and optimal decisions through a polynomial regression. This
mapping is then used in the solver to generate starting values given the model primitives.
B.1.5 Model with Borrowing
In the model, campaign committees face a hard financing constraint as they cannot borrow
against any future revenues. As such, current and future spending can only be financed through
existing cash reserves. The model does not feature cross-sectional variation in the intensity of
the borrowing constraint and is silent about the effect of relaxing the constraint for one of the
committees. In an extension of the model, I allow committees to borrow against future revenues.
To simplify the analysis, I endow each committee with a constant amount of guaranteed
revenues in addition to those obtained through the revenue function f , and allow committees to
borrow against a fraction of that revenue stream at the beginning of the race. I also impose a
collateral constraint that increases over time to prevent committees from defaulting at the time
of the election.
I find that borrowing allows a committee to escape current and future liquidity constraints
by providing a financial buffer against shocks. When borrowing is allowed, the magnitude of
the response to own shocks decreases by 15% in situations where any of the two committees is
constrained. I also find that borrowing increases a committee?s financial flexibility for countering
its opponent. In particular, the magnitude of the response to the opponent?s shocks increases
by 5% in situations where any of the two committees is constrained and when committees are
allowed to borrow.
135
B.2 Robustness
B.2.1 Additional Controls
Table B.1
Additional Controls
This table reports the results of the regression Adv ?i,t+h = ?i + ?t + ?hSit + ?hS?it + ?hControlst + it for
h = 1, 2, 3 on the main sample. Adv corresponds to advertising expenditures and S to the shock constructed
with the polynomial LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered
by committee-year are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%,
and 10% levels, respectively.
Advi,t+1 Advi,t+2 Advi,t+3
S 0.283??? 0.315??? 0.325???it
(0.036) (0.041) (0.050)
S? ??it 0.072 0.127?? 0.127???
(0.035) (0.050) (0.048)
E ??? ??? ???t?1[Fundit] 0.289 0.269 0.596
(0.075) (0.077) (0.106)
E ?1[Fund? ] 0.154?t it 0.142 0.238?
(0.080) (0.090) (0.143)
Advit -0.070??? -0.032 -0.108???
(0.017) (0.020) (0.023)
Adv? -0.046???it -0.016 -0.032?
(0.014) (0.016) (0.019)
Adv?i,t+1 -0.029? -0.014 0.002
(0.015) (0.015) (0.018)
Adv +1 -0.075???i,t -0.035?
(0.017) (0.020)
Adv?i,t+2 -0.007 0.030
(0.017) (0.018)
Adv ???i,t+2 -0.070
(0.021)
Adv? 0.052??i,t+3
(0.021)
Comm-Year FE X X X
Time FE X X X
Controls X X X
Outside Spending X X X
R2 0.326 0.267 0.253
N 9292 8388 7482
136
B.2.2 Artificial Neural Network
Table B.2
Recipient?s Response to Revenue Shocks - Artificial Neural Network
This table reports the results of the regression Adv ?i,t+h = ?i + ?t + ?hSit + ?hControlst + it for h = 1, 2, 3
on the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with the
artificial neural network methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
Advi,t+1 Advi,t+2 Advi,t+3 Advi,t+1 Advi,t+2 Advi,t+3
S 0.283???it 0.267??? 0.275??? 0.277??? 0.259??? 0.268???
(0.038) (0.041) (0.046) (0.038) (0.042) (0.046)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X X X X
Outside Spending X X X
R2 0.317 0.253 0.228 0.323 0.257 0.232
N 9302 8398 7492 9302 8398 7492
Table B.3
Opponent?s Response to Revenue Shocks - Artificial Neural Network
This table reports the results of the regression Adv = ? + ? + ? S + ???i,t+h i t h it hControlst + it for h = 1, 2, 3
on the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with the
artificial neural network methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
Adv?i,t+1 Adv?i,t+2 Adv?i,t+3 Adv?i,t+1 Adv?i,t+2 Adv?i,t+3
S 0.117??? 0.159??? 0.171??? 0.105???it 0.151??? 0.160???
(0.040) (0.054) (0.049) (0.040) (0.055) (0.051)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X X X X
Outside Spending X X X
R2 0.308 0.247 0.223 0.315 0.251 0.227
N 9302 8398 7492 9302 8398 7492
137
Table B.4
Opponent?s Response to Revenue Shocks by Advertising Tone - Artificial
Neural Network
This table reports the results of the regression Advi,t+1 = ?i + ?t + ?1Sit ? NegativeAdsi + ?2Sit ? (1 ?
NegativeAds ) + ??i Controlst + it on the main sample. Adv corresponds to advertising expenditures
and S to the shock constructed with the artificial neural network methodology. NegativeAdsi is 1 if the
fraction of negative TV ads to total ads broadcasted is in the upper quartile of the Wesleyan dataset
and 0 otherwise. The controls are listed in Section 2.3.1. Standard errors clustered by committee-year are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Adv?i,t+1 Adv?i,t+1
Sit ?NegativeAds?i 0.376??? 0.356???
(0.071) (0.071)
Sit ? (1?NegativeAds?i) 0.232??? 0.215???
(0.060) (0.059)
Comm-Year FE X X
Time FE X X
Controls X X
Outside Spending X
R2 0.230 0.241
N 2970 2970
138
Table B.5
Financing Constraints - Recipient?s and Opponent?s Response - Artificial
Neural Network ?
This table reports the results of the regressions A?dvi,t+1 = ?i + ?t + k ?k ? Sit ?DeltaLogCashki,t?1 +
??Controlst + it and Adv?i,t+1 = ?i + ?t + k ?k ? Sit ?DeltaLogCashk ?i,t?1 + ? Controlst + it on
the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the artificial neural network methodology. DeltaLogCashki,t?1 is a dummy variable that takes value 1 if
log(Cashi,t?1) ? log(Cash?i,t?1) is in the kth quartile of the distribution. The controls are listed in Section
2.3.1. Standard errors clustered by committee-year are reported in parentheses. ???, ??, and ? denote statistical
significance at the 1%, 5%, and 10% levels, respectively.
Advi,t+1 Advi,t+1 Adv?i,t+1 Adv?i,t+1
S ?DeltaLogCashQ1it i,t?1 0.373
??? 0.364??? 0.453??? 0.430???
(0.078) (0.075) (0.121) (0.118)
Sit ?DeltaLogCashQ2 ??? ???i,t?1 0.307 0.293 0.024 0.004
(0.068) (0.069) (0.062) (0.062)
Sit ?DeltaLogCashQ3 0.274??? 0.276???i,t?1 0.094 0.090
(0.056) (0.056) (0.060) (0.060)
Sit ?DeltaLogCashQ4 ??? ???i,t?1 0.358 0.343 0.160
?? 0.149??
(0.074) (0.074) (0.066) (0.064)
Comm-Year FE X X X X
Time FE X X X X
Controls X X X X
Outside Spending X X
R2 0.319 0.325 0.310 0.317
N 9292 9292 9292 9292
139
Table B.6
Political Capital - Opponent?s Response - Artificial Neural Network
This table reports the results of the regression Adv?i,t+1 = ?i + ?t + ?1Sit ? Leader + ?2Sit ? Laggard +
??Controlst + it on the main sample. Adv corresponds to advertising expenditures and S to the shock
constructed with the artificial neural network methodology. Candidate i is categorized as Leader or Laggard
depending on whether she is ahead of her opponent in the polls or not. The controls are listed in Section 2.3.1.
Standard errors clustered by committee-year are reported in parentheses. ???, ??, and ? denote statistical
significance at the 1%, 5%, and 10% levels, respectively.
Adv?i,t+1 Adv?i,t+1
Sit ? Leader ??i,t?1 0.159 0.147??
(0.074) (0.074)
Sit ? Laggardi,t?1 0.065 0.061
(0.070) (0.072)
Comm-Year FE X X
Time FE X X
Controls X X
Outside Spending X
R2 0.307 0.314
N 9292 9292
Table B.7
Response to Shocks by Incumbency Status - Artificial Neural Network
This table reports the results of the regressions Advi,t+1 = ?i+?t+?1Sit?Incumbenti+?2Sit?Challengeri+
??Controlst + it and Adv ??i,t+1 = ?i + ?t + ?1Sit ? Incumbenti + ?2Sit ? Challengeri + ? Controlst + it
on the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with the
artificial neural network methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
Advi,t+1 Advi,t+1 Adv?i,t+1 Adv?i,t+1
Sit ? Incumbenti 0.281??? 0.283??? 0.167??? 0.174???
(0.087) (0.086) (0.060) (0.056)
S ? Challenger 0.298???it i 0.287??? 0.093 0.101
(0.063) (0.065) (0.076) (0.078)
Comm-Year FE X X X X
Time FE X X X X
Controls X X X X
Outside Spending X X
R2 0.304 0.316 0.297 0.310
N 6723 6723 6723 6723
140
B.2.3 Extended Sample
Table B.8
Recipient?s Response to Revenue Shocks - Extended Sample
This table reports the results of the regression Advi,t+h = ?i + ?t + ?hSit + ??hControlst + it for h = 1, 2, 3
on the extended sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the polynomial LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
Advi,t+1 Advi,t+2 Advi,t+3 Advi,t+1 Advi,t+2 Advi,t+3
S 0.187??? 0.129??? 0.214??? 0.183???it 0.125??? 0.210???
(0.022) (0.025) (0.030) (0.022) (0.025) (0.030)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X X X X
Outside Spending X X X
R2 0.202 0.155 0.140 0.212 0.160 0.143
N 28872 25891 22892 28872 25891 22892
Table B.9
Opponent?s Response to Revenue Shocks - Extended Sample
This table reports the results of the regression Adv ??i,t+h = ?i + ?t + ?hSit + ?hControlst + it for h = 1, 2, 3
on the extended sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the polynomial LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year are reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
Adv?i,t+1 Adv?i,t+2 Adv?i,t+3 Adv?i,t+1 Adv?i,t+2 Adv?i,t+3
S 0.082??? 0.081??? 0.090??? 0.076??? 0.077???it 0.086???
(0.017) (0.022) (0.021) (0.017) (0.022) (0.021)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X X X X
Outside Spending X X X
R2 0.194 0.153 0.131 0.205 0.157 0.134
N 28872 25891 22892 28872 25891 22892
141
Table B.10
Opponent?s Response to Revenue Shocks by Advertising Tone - Extended
Sample
This table reports the results of the regression Advi,t+1 = ?i + ?t + ?1Sit ? NegativeAdsi + ?2Sit ? (1 ?
NegativeAdsi) + ??Controlst + it on the extended sample. Adv corresponds to advertising expenditures
and S to the shock constructed with the polynomial LASSO methodology. NegativeAdsi is 1 if the
fraction of negative TV ads to total ads broadcasted is in the upper quartile of the Wesleyan dataset
and 0 otherwise. The controls are listed in Section 2.3.1. Standard errors clustered by committee-year are
reported in parentheses. ???, ??, and ? denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Adv?i,t+1 Adv?i,t+1
S ?NegativeAds? 0.322??? 0.313???it i
(0.059) (0.059)
Sit ? (1?NegativeAds?i) 0.186??? 0.176???
(0.045) (0.045)
Comm-Year FE X X
Time FE X X
Controls X X
Outside Spending X
R2 0.168 0.178
N 5943 5943
142
Table B.11
Financing Constraints - Recipient?s and Opponent?s Response - Extended
Sample ?
This table reports the results of the regressions A?dv ki,t+1 = ?i + ?t + k ?k ? Sit ?DeltaLogCashi,t?1 +
??Controlst +  k ?it and Adv?i,t+1 = ?i + ?t + k ?k ? Sit ?DeltaLogCashi,t?1 + ? Controlst + it on
the extended sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the polynomial LASSO methodology. DeltaLogCashki,t?1 is a dummy variable that takes value 1 if
log(Cashi,t?1) ? log(Cash?i,t?1) is in the kth quartile of the distribution. The controls are listed in Section
2.3.1. Standard errors clustered by committee-year are reported in parentheses. ???, ??, and ? denote statistical
significance at the 1%, 5%, and 10% levels, respectively.
Advi,t+1 Advi,t+1 Adv?i,t+1 Adv?i,t+1
Sit ?DeltaLogCashQ1i,t?1 0.068 0.055 0.279
?? 0.262??
(0.060) (0.059) (0.131) (0.131)
S ?DeltaLogCashQ2 0.241??? 0.236??? 0.142???it i,t?1 0.133
???
(0.035) (0.035) (0.041) (0.041)
Sit ?DeltaLogCashQ3i,t?1 0.203
??? 0.199??? 0.072??? 0.068???
(0.034) (0.033) (0.024) (0.024)
Sit ?DeltaLogCashQ4 ???i,t?1 0.180 0.173
??? 0.034? 0.028
(0.039) (0.039) (0.018) (0.018)
Comm-Year FE X X X X
Time FE X X X X
Controls X X X X
Outside Spending X X
R2 0.204 0.214 0.197 0.206
N 28776 28776 28776 28776
B.2.4 Bootstrapped Standard Errors
I calculate bootstrapped standard errors to account for the fact that the shocks constitute
generated regressors. First, I draw a sample of races (with replacement) that has the same size
as the original sample. Second, I fit the polynomial LASSO algorithm on the sample. Third, I
run the regressions and collect the coefficients. I repeat this sequence 1,000 times. Finally, I
compute the standard error on the coefficients of interest as the standard deviation of the
estimates across the 1,000 simulations. Table B.12 and Table B.13 show the results of the
baseline regressions on the main sample with the LASSO shocks with bootstrapped standard
errors alongside standard errors clustered by committee-year. The tables do not show
meaningful changes in the standard errors when the additional source of variation is accounted
for. Similar conclusions obtain when calculating bootstrapped standard errors for the neural
network shocks, the extended sample, and the specifications involving subsamples.
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Table B.12
Recipient?s Response to Revenue Shocks - Bootstrapped Standard Errors
This table reports the results of the regression Adv ?i,t+h = ?i + ?t + ?hSit + ?hControlst + it for h = 1, 2, 3
on the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the polynomial LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year and computed through a bootstrap procedure are reported in parentheses. ???, ??, and ?
denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Advi,t+1 Advi,t+2 Advi,t+3 Advi,t+1 Advi,t+2 Advi,t+3
Sit 0.236??? 0.226??? 0.254??? 0.258??? 0.283??? 0.284???
Clustered SE (0.040) (0.041) (0.057) (0.039) (0.040) (0.049)
Boostrapped SE (0.043) (0.045) (0.055) (0.042) (0.045) (0.053)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X
R2 0.279 0.223 0.202 0.315 0.254 0.229
N 9302 8398 7492 9302 8398 7492
Table B.13
Opponent?s Response to Revenue Shocks - Bootstrapped Standard Errors
This table reports the results of the regression Adv ??i,t+h = ?i + ?t + ?hSit + ?hControlst + it for h = 1, 2, 3
on the main sample. Adv corresponds to advertising expenditures and S to the shock constructed with
the polynomial LASSO methodology. The controls are listed in Section 2.3.1. Standard errors clustered by
committee-year and computed through a bootstrap procedure are reported in parentheses. ???, ??, and ?
denote statistical significance at the 1%, 5%, and 10% levels, respectively.
Adv?i,t+1 Adv?i,t+2 Adv?i,t+3 Adv?i,t+1 Adv?i,t+2 Adv?i,t+3
Sit 0.104??? 0.133??? 0.172??? 0.084?? 0.139??? 0.173???
Clustered SE (0.038) (0.050) (0.058) (0.037) (0.051) (0.053)
Boostrapped SE (0.040) (0.052) (0.052) (0.039) (0.053) (0.048)
Comm-Year FE X X X X X X
Time FE X X X X X X
Controls X X X
R2 0.273 0.219 0.198 0.307 0.246 0.223
N 9302 8398 7492 9302 8398 7492
B.2.5 Placebo Tests
I perform placebo tests by shuffling the shocks across committees for a given event time and
running the baseline regressions. I repeat the procedure 1,000 times to obtain the empirical
distribution of the coefficients that capture the response to shocks under the null that the shocks
are drawn randomly from the pool of committees. Figure B.1 and Figure B.1 present the show
the distributions and the actual estimates. The figures show that it is unlikely that the results
144
from the baseline specifications are generated by chance alone.
Figure B.1. Placebo Test - Recipient?s Response to Revenue Shocks This figure shows
the empirical distribution of the coefficient capturing the response to own shocks under the null
that the shocks are drawn randomly from the pool of committees. The first (second) row shows
the coefficients ?h of Equation (2.19) without (with) controls. The three columns correspond to
h = 1, 2, 3, respectively. The red lines correspond to the actual estimates.
Figure B.2. Placebo Test - Opponent?s Response to Revenue Shocks This figure shows
the empirical distribution of the coefficient capturing the response to the opponent?s shocks under
the null that the shocks are drawn randomly from the pool of committees. The first (second)
row shows the coefficients ?h of Equation (2.20) without (with) controls. The three columns
correspond to h = 1, 2, 3, respectively. The red lines correspond to the actual estimates.
145
Appendix C: Supplements to Chapter 3
C.1 Model Derivations
C.1.1 Optimism and Pessimism
The model assumes S[M = 1] = P[M = 1]. Instead, assume the unconditional odds ratio under
the subjective and the objective measures(are linked thro)ugh a (linear r)elationship:S[M = 1] = P[M = 1] ??1? S[M = 1] ? 1? P[M = 1] = ? 1 , (C.1)? ??
where ? ? (0,?). This functional form allows for unconditional optimism or pessimism under
the subjective measure. To see that, solve for the unconditional probability of success under the
subjective measure:
?P[M = 1]
S[M = 1] = 1 + ( 1) [ = 1] . (C.2)?? PM
The case ? = 1 corresponds to the original model presented in Section 3.2. If ? > 1, the
representative investor is optimistic under the subjective measure. The functional is concave in
P[M = 1] and the unconditional probability of success under the subjective measure is always
higher than that under the objective measure, except at P[M = 1] = 0 and P[M = 1] = 1, where
they exactly match. If ? < 1, the implications are reversed and the representative investor is
pessimistic under the subjective measure.
C.1.2 Learning Distortion in the Log Odds Space
Taking the natural logarithm on both sides of Equation (3.6) shows that the subjective posterior
log odds ratio is a convex combination between the objective posterior log odds ratio and the
unconditional prior log odds ratio:
Lo(S[M = 1| {mj}]) = ?Lo(P[M = 1| {mj}]) + (1? ?)Lo(??), (C.3)
where Lo(x) = log x1?x . Zhang and Maloney (2012) consider various patterns of probability
distortion using the log odds space as a unifying concept. They find significant heterogeneity in
the learning distortion parameter ? across a wide range of experiments. They consider the learning
146
distortion in the context of decisions made from experience. Interestingly, more experience leads
to a greater distortion in some settings. Gabaix (2019) analyses Equation (C.3) through the lens
of behavioral inattention. An agent is inattentive to the true (objective) probability when ? =6 1.
The model provides a distinct microfoundation for the log odds ratio representation based on the
misprocessing of information.
Note the similarities between Equation (C.3) and Equation (3.11). In both equations, the
subjective probability is a function of the objective and unconditional probabilities. The relation
is exactly linear in log odds space and approximately linear without the log-odds transformation.
C.1.3 Limiting Case: n??
To show that plimn?? S[M = 1| {mj}
n
j=1] = plimn?? P[M = 1| {m }
n
j j=1] = M , consider the
posterior probability of success under the subjective measure:
[ = 1| { }] = [( ) ( 1SM mj k ) ]n?k ? ( ) . (C.4)
1 + p0 1?p0 1???p1 1?p1 ??
The number of high signals k is a random variable that depends on the total number of
signals n and satisfies the law of large numbe?rs:
??
?
?np if M = 1plim = 1k (C.5)n?? np0 if M = 0
and
???n(1? p ) if M = 1
plim (n? k) = 1 . (C.6)
n?? ??n(1? p0) if M = 0
Therefore,
( ) ( ) ????[( ) ][ p p1
( )
1?p 1?p
n
? ( 0 0
1
p k0 1? p n k0 ?? p ) (1?p ) ]
if M = 1
plim = 1 1 n (C.7)
n?? p1 1? p1 ? p p 1?p0 0 1?p0 0p 1?p if M = 01 1
and
??
?????? [( ) (
1 ) ]n? if M = 1p1 1 1?p11+ p0 ?p0 1???
? p1 1?p ( )1 ??plim S[M = 1| {mj}] =n?? ?????? [( ) ( 1 ) ]
. (C.8)
1? n?
if M = 0
p0 p0
1+ p0 1?p0 ( 1???p1 1?p1 ?? )
147
Given p0 < p1, it must be that:( )p1 (1? )1?p1 ( )p0 (p0 p0 1 p0 1? )p 1?p0 01 < <p1 ? p1 p1 1 . (C.9)? p1
The proof of the first inequality is as follows. Let x = p0, y = p1, and take the log on both
sides of the inequality:
y [log(x)? log(y)] + (1? y) [log(1? x)? log(1? y)] < 0. (C.10)
Let x = y ?  and define:
f(y, ) = y [log(y ? )? log(y)] + (1? y) [log(1? y + )? log(1? y)] (C.11)
for 0 < y < 1 and 0 <  < y. Fix y to an arbitrary value y0. At the boundaries, f(y0, )
takes the following values:
f(y0, 0) = 0 (C.12)
lim f(y , ) = ??. (C.13)
? 0y0
Showing the derivative of f with respect to  is always negative is a sufficient condition for
f(y0, ) to be negative everywhere on its domain:
?f(y0, ) = ?y0 + 1? y0 = ?
? y0 ?  1? y0 +  (y0 ? )(1 + )
<0. (C.14)
? y0 
Since y0 was chosen arbitrarily, f(y, ) < 0 for any y and  satisfying 0 < y < 1 and
0 <  < y. The second inequality can be proven using a similar argument.
Combining Equation (C.8) and Equation (C.9)?yields:??1 if M = 1
plim S[M = 1| {mj}] = ?? . (C.15)n?? 0 if M = 0
Since the last equality holds for any 0 < ? <?, including for ? = 1, I have:
plim S[M = 1| {m nj}j=1] = plim P[M = 1| {m }
n
j ] = M . (C.16)
n?? n?? j=1
148
C.2 Variable Construction
C.2.1 Compustat
I collect firm fundamental data for the target and acquirer from Compustat. I match deals
announced in year y to accounting information and market capitalizations as of the end of year
y?1 based on the mapping provided by WRDS. All firm data are from Compustat annual except
for SHROUT and ALTPRC, which are from the CRSP monthly database. The variables itcb,
cogs, xsga, and xint are replaced by 0 if missing in Compustat. The variables sale, cogs, xsga,
capx, ppent, ni, xint, revt, at, bookequity, bookassets, bookdebt, and cash are winsorized at the
1st and 99th percentiles of their cross-sectional distributions each year. Market capitalization is
aggregated by six-digit CUSIP to account for multiple common share classes.
Table C.1
Compustat Variable Construction
All firm data from Compustat are annual except for SHROUT and ALTPRC which are from the CRSP monthly
database. The variables itcb, cogs, xsga, and xint are replaced by 0 if missing in Compustat. The variables
sale, cogs, xsga, capx, ppent, ni, xint, revt, at, bookequity, bookassets, bookdebt, cash are winsorized at the 1st
and 99th percentiles of their cross-sectional distributions each year. Market capitalization is aggregated by
six-digit CUSIP to account for multiple common share classes.
Variable Computation
Book Debt dltt+dlc
Book Equity As in Bali, Engle, and Murray (2016)
Market Equity SHROUT? |ALTPRC|
Cash ch, or if missing che, or if both missing 0
Size log(at)
Operating Profitability 100*(revt-cogs-xsga-xint)/bookequity
Book Leverage bookdebt/at
Investment-to-Assets capx/at
PPENT-to-Assets ppent/at
Cash-to-Assets cash/at
Book-to-Market bookequity/marketequity
C.2.2 Institutional Ownership
I collect data on institutional ownership from Thomson Reuters? S34 dataset. I match deals
announced in quarter q to institutional ownership information and market capitalizations as of
the end of quarter q ? 1. If a deal is announced on day d, I use d? 30 to compute the quarter of
announcement q to account for potential run up prior to the announcement.
149
Table C.2
Institutional Ownership Variable Construction
Institutional ownership data is from Thomson Reuters S34. Shares outstanding are from CRSP.
Variable Computation
Realtive Number Institutions Number of institutional investors who own shares of the firm divided by
the total number of managers reporting in S34 in that quarter
Fraction Institutional Holdings Number of shares held by intitutions divided by shares outstanding
C.2.3 Merger Waves
I define merger waves based on the sample obtained after applying the first filter in Table 3.1. I
compute the number of mergers announced in each year of the sample. I regress the number of
mergers announced on the year of announcement and a constant to estimate the time trend. I
then remove the time trend from the number of merger announcements. Merger waves are defined
as the years with a number of detrended mergers above zero.
C.3 Sample Augmentation
This section presents the methodology used to impute missing initial offer prices.
C.3.1 Newspaper Articles
I use ProQuest as a primary source of newspaper articles. For each deal, I search for all the
articles published in The New York Times, The Wall Street Journal, and The Washington Post
between three days before and three days after the deal announcement date, and that contain
the name of the target and the acquirer. Specifically, I set the source type to newspapers, the
document type to article, company profile, front matter, front page/cover story, market report,
market research, news, stock quotes, and the language to English. I also remove common suffixes
such as Corp, Inc, LLC, etc from the company names. I then extract the full text of the first 20
articles returned by ProQuest.1 If a merger has no corresponding newspaper article I exclude it
from the augmentation procedure.
C.3.2 Tokenization
Tokens are sequences of characters separated by white spaces. In each article, I identify all the
tokens that contain one or more digits and call these objects numeric tokens. For each numeric
1ProQuest sorts articles by best match rather than date.
150
token I create three dummy variables for whether the token 1) contains the string "-a-share" (has-
a-share), 2) contains a dollar sign (has-dollar-sign), and 3) is formatted like a date (is-like-date).
I then extract the numeric part of the token and call it the numeric value. If a numeric token
contains a percent sign, I multiply the corresponding numeric value by 100. I exclude numeric
tokens whose numeric value is 50% above or below the price of the target one business day before
the announcement to rule out implausible values. I select the 10 closest tokens before and after
each numeric token (total of 20 tokens). I remove punctuation and common stop words from
those tokens using the dictionary from Python?s nltk.corpus.stopwords module.
C.3.3 Subsamples
My sample contains the numeric tokens of all the merger-related articles that survive the filters
described in Section C.3.2. A deal usually contains to more than one numeric token. The objective
of the augmentation exercise is to forecast which numeric value is most likely to be equal to the
initial offer price.
I assign all deals into three subsamples. A deal with no initial offer price goes into the
prediction category (FP). A deal that has an initial offer price goes into the in-sample category
(IS) if the 5th digit of its SDC deal number is even and into the out-of-sample (OS) category if
the 5th digit of its SDC deal number is odd. The breakdown is as follows: 1195 IS deals, 1038
OS deals, and 1137 FP deals.
In the IS and OS subsamples I create a dummy variable (isCorrect) equal to 1 if the numeric
value is equal to the initial offer price and to 0 otherwise. From the IS subsample I select the 50
tokens that appear most frequently around the numeric tokens that satisfy isCorrect=1. Using
this list and for all three categories, I create 50 dummy variables at the numeric token level. Each
dummy variable equals 1 if the frequent token appears in the neighborhood of the numeric token
and 0 otherwise.
Together, the three subsamples (IS+OS+FP) contain 53 independent variables (has-a-share,
has-dollar-sign, is-like-date, and the 50 neighborhood dummy variables). Additionally, the IS and
OS samples also contain the dependent variable (isCorrect).
C.3.4 Random Forest Algorithm
The objective is to find a algorithm to predict the variable isCorrect in- and out-of-sample using
the independent variables, then to predict the missing initial offer prices using the same algorithm.
I use a random forest algorithm that predicts whether a particular numeric value corresponds to
the actual initial offer price of the deal. Random forests leverage on the ability of decision trees
to extract non-linear patterns from the data while avoiding overfitting.2 Specifically, I implement
a random forest regression that outputs the mean prediction of the individual trees.
2See Ho (1995) and Breiman (2001) for seminal papers and Hastie et al. (2009) for a textbook exposition.
151
For each in-sample merger I obtain the forecasted values of the variable isCorrect linked
to every numeric value. The output is a number between 0 and 1. Since numeric value may be
repeated for a specific deal, I aggregate them by calculating the average forecast of each unique
numeric value. I then select the numeric value with the highest score as the best predictor for the
initial offer price, provided that the score is above a 0.2 threshold. Using a threshold rule implies
that some deals do not have an imputed initial offer price. This feature is rationalized by the
fact that the cost of a false negative (a decrease in the sample size and therefore in power) is less
severe than the cost of a false positive (a wrong initial offer price and therefore a wrong scaled
target price).
I assess the in- and out-of-sample performance of the algorithm by building the
corresponding confusion matrices and related precision, recall, and accuracy. Remember that
the algorithm forecasts whether a numeric value in the newspaper article corresponds to the
initial offer price. Let TP be the number of true positive, TN be the total of true negative, FP
be the number of false positive, and FN be the number of false negative. Precision, recall, and
accuracy are defined as:
Precision = TP+ (C.17)TP FP
Recall = TP+ (C.18)TP FN
Accuracy = TP + TN
TP + + + . (C.19)TN FP FN
The results are reported in Table C.3. Finally, I use the fitted random forest algorithm
to forecast the missing initial offer prices in the FP sample. After the procedure, 841 all-cash
mergers are added to the sample.
Table C.3
Random Forest Confusion Matrix
This table shows the confusion matrix of the random forest algorithm.
In-Sample Out-of-Sample
Sample Size 1139 986
Precision 0.914 0.728
Recall 0.998 0.982
Accuracy 0.928 0.759
C.4 Robustness
In this section, I show that the results are robust to various changes in the methodology.
152
C.4.1 Scaling Parameters
Results may be driven by the choice of scaling parameters. Figure C.1 shows the estimate ?? from
the baseline regression with T = 500 and Carhart (1994) risk adjustment for various values of ?
and ?. The estimates are not sensitive to the choice of parameters.
Figure C.1. Robustness to the Choice of Scaling Parameters. This figure shows the
slope in the relation between ?t and ?500 with Carhart (1994) for various values of the scaling
parameters ? and ?. The specification is ?i,500 = ? + ??i,t + ?i. The dependent variable is ??
where ? is the deal expiration date whenever ? < 500. The continuous line corresponds to the
point estimates of ?. The dashed lines represent 2-standard-error confidence intervals. Standard
errors are robust to heteroskedasticity.
C.4.2 Offer Price Imputation
To show that the results are not driven by the offer price imputation procedure, I run the
baseline linear specification on the initial and augmented samples separately. Table C.4 shows
the coefficients are similar across risk adjustments and across samples. If anything, the
distortion is slightly stronger in the initial sample. Standard errors are tighter in the augmented
sample due to the larger sample size.
153
Table C.4
Initial Offer Price Imputation
This table shows the relation between ?1 and ?500 in the initial sample (Panel A) and augmented sample
(Panel B). The specification is ?i,500 = ? + ??i,1 + ?i. The dependent variable is ?? where ? is the deal
expiration date whenever ? < 500. The columns correspond to the risk adjustments described in Section 3.3.3.
Heteroskedasticity-robust standard errors are in parentheses. ???, ??, and ? denote statistical significance at
the 1%, 5%, and 10% levels, respectively.
Panel A: Initial Sample
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
? 0.510??? 0.595??? 0.648??? 0.680??? 0.680??? 0.677??? 0.673???
(0.049) (0.048) (0.051) (0.054) (0.053) (0.056) (0.058)
? 0.498??? 0.396??? 0.292??? 0.257??? 0.262??? 0.265??? 0.241???
(0.042) (0.041) (0.044) (0.047) (0.046) (0.048) (0.051)
Adj R2 0.106 0.144 0.132 0.119 0.121 0.115 0.116
Observations 3454 3446 3420 3426 3418 3436 3422
Panel B: Augmented Sample
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
? 0.601??? 0.668??? 0.725??? 0.742??? 0.740??? 0.736??? 0.737???
(0.038) (0.037) (0.038) (0.040) (0.040) (0.042) (0.044)
? 0.421??? 0.332??? 0.226??? 0.201??? 0.211??? 0.211??? 0.184???
(0.033) (0.032) (0.033) (0.034) (0.035) (0.036) (0.039)
Adj R2 0.170 0.208 0.199 0.175 0.176 0.166 0.164
Observations 4128 4113 4086 4094 4086 4104 4085
C.4.3 Standard Errors
Heteroskedasticity-robust standard errors fail to account for the potential cross-correlation of
target returns during the event window. I use clustered standard errors to check whether this
drives the results. Table C.5 shows the results of the baseline regression in Equation (3.31) with
White standard errors (Panel A), standard errors clustered by announcement month (Panel B),
and standard error clustered by expiration month (Panel C). Standard errors are similar across
the three panels.
154
Table C.5
Alternative Standard Errors
This table shows the relation between ?1 and ?500 in the initial and augmented samples for various types of
standard errors. Panel A shows heteroskedasticity-robust SEs. Panel B shows SEs clustered by announcement
month. Panel C shows SEs clustered by expiration month. The specification is ?i,500 = ? + ??i,1 + ?i. The
dependent variable is ?? where ? is the deal expiration date whenever ? < 500. The columns correspond to
the risk adjustments described in Section 3.3.3. ???, ??, and ? denote statistical significance at the 1%, 5%, and
10% levels, respectively.
Panel A: White SE
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
? 0.601??? 0.668??? 0.725??? 0.742??? 0.740??? 0.736??? 0.737???
(0.038) (0.037) (0.038) (0.040) (0.040) (0.042) (0.044)
? 0.421??? 0.332??? 0.226??? 0.201??? 0.211??? 0.211??? 0.184???
(0.033) (0.032) (0.033) (0.034) (0.035) (0.036) (0.039)
Adj R2 0.170 0.208 0.199 0.175 0.176 0.166 0.164
Observations 4128 4113 4086 4094 4086 4104 4085
Panel B: SE Clustered by Announcement Month
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
? 0.601??? 0.668??? 0.725??? 0.742??? 0.740??? 0.736??? 0.737???
(0.042) (0.041) (0.042) (0.044) (0.045) (0.047) (0.050)
? 0.421??? 0.332??? 0.226??? 0.201??? 0.211??? 0.211??? 0.184???
(0.036) (0.035) (0.038) (0.041) (0.041) (0.043) (0.046)
Adj R2 0.170 0.208 0.199 0.175 0.176 0.166 0.164
Observations 4128 4113 4086 4094 4086 4104 4085
Panel C: SE Clustered by Expiry Month
(1) (2) (3) (4) (5) (6) (7)
Raw Rf CAPM FF3 Carhart FF5 FF48 Ind
? 0.601??? 0.668??? 0.725??? 0.742??? 0.740??? 0.736??? 0.737???
(0.039) (0.037) (0.039) (0.043) (0.044) (0.047) (0.045)
? 0.421??? 0.332??? 0.226??? 0.201??? 0.211??? 0.211??? 0.184???
(0.034) (0.033) (0.036) (0.040) (0.040) (0.044) (0.044)
Adj R2 0.170 0.208 0.199 0.175 0.176 0.166 0.164
Observations 4128 4113 4086 4094 4086 4104 4085
155
C.5 Bias in Returns Regression
I show that regressing RT on R1 does not identify the learning distortion parameter. To do so, I
first simulate the model then run regressions on the simulated data. The steps taken to simulate
the model are as follows. For each of the N merger attempts:
1. Draw the deal?s outcome from a Bernoulli distribution with parameter ??. M = 1 (M = 0)
indicates success (failure).
2. Draw n signals from a Bernoulli distribution with parameter p1 if the deal is successful and
p0 if the deal fails. The number of high signals is k.
3. Compute the objective posterior probability of success P[M = 1|signals] using Equation
(3.2).
4. Compute the subjective posterior probability of success S[M = 1|signals] using the non-
linear relationship (Equation (3.7)).
5. Fix the price before the announcement and the standalone price at L = F = 100.
6. Draw the deal premium CL from a lognormal distribution and calculate the cash offer price
C.
7. Compute the price at expiration: PT = F +M(C ? F ).
8. Compute the price after the announcement: P1 = F + S[M = 1|signals](C ? F ).
9. Compute the returns: R1 = P1 ? F and RT = PT ? F .
10. Compute the scaled prices: ? P ?F1 = 1C?F and ? =
PT?F
T C?F .
I present the model parameterization in Table C.6. The distributions of ?? and CL are calibrated
using the sample of merger attempts described in Section 3.3.2.
Table C.6
Model Parameterization
This table presents the model parameterization used in the simulations.
Variable Description Value
N Number of deals 5000
n Number of signals 10
? = 1/? Inverse of distortion parameter 0.74
?? Unconditional probability of deal success 0.77
M Deal outcome ?Bernoulli(??)
p1 Probability of getting a high signal given M = 1 0.55
p0 Probability of getting a high signal given M = 1 0.45
F Fallback value 100
C/F Deal premium ?Lognormal(0.30, 0.28)
156
I run the following regressions on the simulated data:
?iT = ?+ ??i1 + i (C.20)
RiT = ?+ ?Ri1 + i (C.21)
The first column of Table C.7 reports the results of the regression based on scaled prices.
The regression recovers the distortion coefficient as expected. The results in column (2) show
that the returns regression does not recover the coefficient of interest when there is cross-sectional
dispersion in deal premia.
Table C.7
Simulation Results
This table presents the results of the regressions on the simulated data.
(1) (2)
Scaled Prices Returns
? 0.742 1.014
(0.039) (0.010)
? 0.207 0.028
(0.031) (0.448)
Adj R2 0.066 0.663
Observations 5000 5000
C.6 Two-Stage Regression with Generated Regressands
I next present how to compute the standard errors in the two stage regressions in Section 3.4.4.
For simplicity, rewrite the first stage of merger i (Equation (3.35)) as:
yi = Xi?i + ?i, (C.22)
where Ti is the number of observations in the time series regression of deal i, yi and Xi are Ti? 1
and ?i is 1? 1. Stack the ?i into a vector ? and rewrite the second stage for all N deals with K
characteristics (Equation (3.36)) as:
? = Z? +  (C.23)
where ? and  are N ? 1, Z is N ?K, and ? is K ? 1. The OLS estimator for the first stage of
deal i is:
?? = ? + (X ?X )?1i i i i X ?i?i (C.24)
157
and its variance is:
Var(?? ) = (X ?X )?1X ?i i i iVar(?i)X (X ?X )?1i i i . (C.25)
The first stage for all N deals is:
?? = ? + ? with ? ? (0,?). (C.26)
Assuming the noise in the first-stage estimation is uncorrelated across deals, ? is a diagonal
matrix whose iith element is Var(??i). If the true ? vector is observable (?ideal case?), the second
stage regression is:
? = Z? + . (C.27)
The ?ideal case? OLS estimator and its variance-covariance matrix are
??I = ? + (Z ?Z)?1Z ? (C.28)
Vcov(??I) = (Z ?Z)?1Z ?Vcov()Z(Z ?Z)?1. (C.29)
Combining Equation (C.26) and Equation (C.27) yields a specification that can be estimated
in the data (?noisy case?):
?? = Z? + + ? (C.30)
The ?noisy case? OLS estimator and its variance-covariance matrix are:
?? = ? + (Z ?Z)?1Z ?N (+ ?) (C.31)
Vcov(??N ) = (Z ?Z)?1Z ?Vcov(+ ?)Z(Z ?Z)?1. (C.32)
Assuming that the vector of measurement errors in the first stage (?) is uncorrelated with
the noise in the second stage () , the variance-covariance matrix becomes:
Vcov(??N ) = (Z ?Z)?1Z ?Vcov()Z(Z ?Z)?1 + (Z ?Z)?1Z ?Vcov(?)Z(Z ?Z)?1 (C.33)
= Vcov(??I) + (Z ?Z)?1Z ??Z(Z ?Z)?1. (C.34)
??I and ??N are unbiased estimators of ? but the variance of ??N is larger because of the
measurement noise in the first stage. The distribution of ??I is the relevant one for hypothesis
testing. Therefore, tests are based on the variance-covariance matrix given by:
Vcov(?? )? (Z ?Z)?1N Z ??Z(Z ?Z)?1. (C.35)
The first term can be estimated using the empirical variance-covariance matrix of the second
stage V?cov(??N ). The second term can be estimated using the regressors of the second stage and
the empirical variance-covariance matrix of the first stage V?cov(??). Note that thus far I have made
158
no assumption about the correlation structure of the error terms in the first and second stages. I
use Newey and West (1987) standard errors with 60 lags to account for the high autocorrelation
in the noise of the first stage. I use standard errors clustered by year of announcement in the
second stage.
159
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