Advertising Competition in Presidential Elections∗
Brett R. Gordon
Wesley R. Hartmann
Columbia University
Stanford University
August 19, 2013
Abstract
Presidential candidates choose advertising strategically across markets based on
each state’s potential to tip the election. The winner-take-all rules in the Electoral
College concentrate advertising in battleground states, ignoring most voters. We
estimate an equilibrium model of competition between candidates to evaluate
advertising and voting outcomes. In a direct vote counterfactual, all states receive
positive advertising and both expenditures and turnout increase. Although states’
political preferences drive competition in the Electoral College, candidates focus
on cheap advertising targets in a direct vote. Simulations removing advertising
price variation suggest a direct vote spreads political attention uniformly across
markets with diverse preferences.
Keywords: Political advertising, presidential election, electoral college, direct
vote, resource allocation, voter choice, contests.
JEL: D72, L10, M37.
∗
We thank Jean-Pierre Dubé, Ron Goettler, Mitch Lovett, Sridhar Moorthy, Michael Peress, Stephan
Seiler, Ron Shachar, Ali Yurukoglu, and seminar participants at Chicago Booth, Columbia, Erasmus, Helsinki
(HECER), Kellogg, Leuven, MIT Sloan, NYU Stern, Stanford GSB, Toronto, University of Pennsylvania,
USC, Yale, Zürich, NBER IO, QME, SICS, and SITE for providing valuable feedback. All remaining errors
are our own. Gordon: Columbia University, Columbia Business School, 3022 Broadway, Uris Hall 511, New
York, NY, 10027, [email protected]. Hartmann: Stanford University, Graduate School of Business, 655
Knight Way, Stanford, CA, 94305, [email protected].
1
Introduction
Advertising is a critical instrument of competition between political candidates. In the 2012
elections, three billion dollars was spent on television advertising, representing the largest
component of candidates’ media expenditures (TVB, 2013). In the general election for
president, candidates strategically allocate advertising to media markets most likely to tip
the election’s outcome. Most advertising focuses on swaying a minority of voters who reside
in battleground states where significant uncertainty exists over the eventual winner of the
state’s contest. In contrast, candidates pay scant attention to the majority of the electorate
who reside in more polarized states where the outcome is predictable. Furthermore, evidence
suggests that candidates’ focus on battleground states extends beyond campaigns to both
policies and federal resources targeted at pivotal voters.1
The battleground state distinction arises under the Electoral College because most states
allocate all of their electoral votes to the candidate who receives a plurality of the state’s
popular vote.2 Marginal votes are only valuable in states where voters’ preferences are closely
divided between candidates. A direct (popular) vote is an oft-proposed alternative that
would eliminate the state-level contests and count each vote equally in a national contest. By
equalizing the relevance of marginal votes for the election outcome, a popular vote may more
equitably balance voters’ influence on candidates’ campaigns and policies.
To evaluate the distribution of candidate attention under a direct vote, we estimate an
1
Garrett and Sobel (2003) and Reeves (2011) find that presidents direct a disproportionate share of FEMA
disaster declarations and expenditures to battleground states. Berry, Burden, and Howell (2010) show that
swing states receive more federal funds after accounting for differences in electoral votes quantities. Outside
the US, Bloom et al. (2013) document that governing parties in the UK are less likely to close hospitals in
areas with narrow expected vote margins. For anecdotal evidence, see Page (2002), Pittman (2004), Solomon
et al. (2007), and Baker and Lipton (2012). One illuminating example is the case of Pennsylvania, which in
2011 contemplated changing its allocation rule to one that might have threatened the state’s battleground
status. Long-time Senator Arlen Specter opposed the move, arguing that “it’d be very bad for Pennsylvania
because we wouldn’t attract attention from Washington on important funding projects for the state. It’s
undesirable to change the system so presidents won’t be asking us always for what we need,” (Liptak, 2012).
The Senator’s explanation highlights the potential link between campaign incentives under the Electoral
College and policy formation preferences.
2
The two exceptions are Maine and Nebraska, which have used a congressional district method since 1972
and 1996, respectively. In practice, however, both states have always allocated all of their votes to a single
candidate.
1
equilibrium model of multimarket advertising competition between presidential candidates.
A direct vote counterfactual reveals that the new distribution of advertising would be more
uniform across markets. However, advertising price variation across markets and funding
disparities between candidates distort the advertising distribution, producing an allocation
that remains correlated with voters’ political leanings. Recomputing the equilibrium in a
counterfactual that equalizes advertising prices and candidates’ funding, we find candidates’
attention would be nearly uniformly distributed across markets despite extensive differences
in voters’ political preferences. This counterfactual likely represents how voters’ influence on
candidates’ policy formulation would change under a direct vote.
Our modeling approach is inspired by recent work on empirical games in industrial
organization (IO). Vote shares arise from an aggregate discrete-choice model in the style of
Berry (1994), where local demand shocks induce advertising endogeneity. Unlike standard IO
applications, however, we assume candidates do not perfectly observe the demand shocks,
which are realized when voters vote on Election Day but after candidates set advertising.
Candidates form rational expectations over these shocks, and set advertising levels to equate
their local marginal benefits of advertising to local advertising prices. A candidate’s local
marginal benefit of advertising is the product of (i) the change in the probability of winning
the election, which depends on the electoral mechanism, voters’ preferences, and candidates’
demand uncertainty, and (ii) the dollar value of such a change, which is a candidate-election
structural parameter that translates the marginal probability of winning into dollar terms
and allows us to endogenize spending levels. We refer to this parameter as the candidate’s
financial strength because of its ability to guide budget changes across election regimes.3
We apply the model to detailed data on votes and advertising from the 2000 and 2004
presidential elections. After estimating voter preferences, we form moments in a GMM
specification around the first-order conditions (FOCs) for candidates’ advertising decisions.
A candidate’s financial strength is identified based on a candidate’s average spending level.
Identification of candidates’ demand uncertainty stems from joint variation in advertising
3
Section 2.2 discusses this interpretation in more detail and describes how our model abstracts away from
a formal fundraising and budget process.
2
and vote shares: a candidate’s willingness to spend money in states with large ex-post voting
margins indicates a degree of uncertainty over voting outcomes.
In a counterfactual experiment with a direct vote in 2000, we find that all states receive
positive advertising. Aggregate spending on advertising increases by 25 percent due to the
expanded set of competitive markets. Advertising in former battleground states declines
by 42 percent and advertising increases in former non-battleground states by 130 percent.
The new distribution of advertising is more equitable, with the standard deviation across
markets in exposures per person dropping by 63 percent. However, advertising exposures
are “tilted” such that markets with left-leaning voter preferences receive 20% fewer exposures
per person. This discrepancy is due to systematically greater advertising costs per voter
in left-leaning markets. Although Gore loses about 50,000 popular votes under this new
advertising equilibrium, he wins the election with about a 450,000 popular vote margin.
Interestingly, we find a direct vote in the 2004 election produces an equilibrium without
advertising by either candidate. This outcome is due to Bush’s 2.5 percent national popular
vote advantage. Whereas advertising competition could overcome the 0.5 percent vote margin
in 2000, advertising’s effect on voters’ choices—relative to advertising prices—is not strong
enough to justify candidate spending in 2004. Of course, a direct vote would probably lead
candidates to alter other dimensions of competition (e.g., policy choices), and these changes
could make the election close enough to warrant positive advertising levels. However, we
must hold these factors fixed in our counterfactual analysis. Without such policy adjustments
to make the election more contestable, the endogenous spending component of our model
predicts that donors would be unwilling to fund advertising in the election. Extant models,
such as Shachar (2009) and Strömberg (2008), which hold budgets fixed, are unable to make
such an assessment and would potentially predict candidate spending even in effectively
uncontested elections.
These results highlight an important distinction between the two election mechanisms:
the collection of state-level contests in the Electoral College is more likely to produce a
set of contests with narrow absolute voting margins compared to the national contest in a
3
direct vote. Each presidential election between 1972 and 2008 had at least five states with
vote margins below the national popular vote margin (2012 had four). Advertising, or other
campaign activities, can be geographically targeted towards a narrow group of pivotal voters
in attempts to tip these contested states in a candidate’s favor. In contrast, in a direct vote,
voters’ influence on candidates is more diffuse, thereby requiring campaign resources and
policy allocations directed toward large groups of voters.
Our work contributes to several literatures. Early game-theoretic analyses in political
science primarily sought to explain observed resource allocations in the Electoral College
(Friedman, 1958; Brams and Davis, 1974; Owen, 1975). Snyder (1989) extends this work to
study two-party competition under more realistic modeling assumptions. Recent research,
such as Grofman and Feld (2005) and Strömberg (2008), examine how states’ size and
competitiveness affect presidential candidates’ strategies.
In contrast to the political science literature, we pursue a structural econometric approach
to study resource allocation in the Electoral College and a direct vote. The aggregate model of
voter choice accommodates instrumental variables to identify the causal effect of candidates’
controls, in contrast to earlier work’s use of probabilistic-voting models (e.g., Lindbeck and
Weibull, 1987; Strömberg, 2008). On the candidate side, we impose the model’s equilibrium
on the data to recover the primitives governing candidates’ decisions. Uncertainty is therefore
inferred from a comparison of candidates’ ex-ante advertising allocations and ex-post demand
realizations.
The analysis of presidential elections extends the structural econometric literature on
advertising. The relevant empirical literature on advertising considers a variety of issues:
the informational effects of advertising (e.g., Ackerberg, 2003; Goeree, 2008), measuring
dynamic effects (e.g., Sahni, 2012), and firms’ inter-temporal advertising decisions (e.g., Dubé
et al., 2005; Doganoglu and Klapper, 2006). Although these issues are likely relevant in
presidential campaigns, the primary strategic dimension for candidates is, however, geographic.
Advertising decisions in our model are interdependent across markets, yielding a multimarket
equilibrium in advertising allocations. Thus, we extend the econometrics of advertising to the
4
context of presidential elections where the stakes of advertising are arguably more important
than in many other applications.
Finally, this paper is relevant to the literature on contests (e.g., Tullock, 1980; Dixit, 1987).
The Electoral College is a nested contest where the final contest outcome depends on the
weighted sum of binary outcomes across state-level contests. In this literature’s terminology,
the contest success function determines a player’s probability of success as a function of
all players’ efforts (Skaperdas, 1996). We construct an empirical contest success function
using our estimates of voters’ preferences and the structure of the candidates’ game. To
econometrically analyze such a contest, we present a computational approach to calculate the
marginal effect of an agent’s effort (e.g., funds directed towards advertising, R&D, lobbying,
etc.). To the best of our knowledge, our work is among the first to estimate an empirical
contest model.
2
Model
We develop a model of strategic interaction between presidential candidates in the general
election. The game has two stages. First, candidates campaign in election t through advertising
to influence voters’ preferences. This campaign activity occurs in a single period as candidates
j = 1, . . . , J form rational expectations about voter preferences and simultaneously choose
advertising levels Atmj across M media markets. A market is composed of a collection
of counties c ∈ Cm , with each county populated by Nc voters. Advertising decisions are
made at the market level, such that advertising is the same across counties within a market,
Atcj = Atmj , ∀c ∈ Cm .
Second, Election Day signifies the conclusion of campaigning. Voters perfectly observe
the demand shocks ξtcj and candidates’ advertising choices. A voter chooses the candidate
who yields the highest utility or opts not to vote. Voting outcomes across all counties are
realized and one candidate is deemed the winner. In our application, we set J = 2 and ignore
minor party candidates for simplicity.
The model differs in an important way from standard equilibrium models of differentiated
5
products in the industrial organization literature (e.g., Berry et al., 1995). Typically firms
set prices to clear the market while observing the demand shocks ξ that influence consumers’
decisions. In our setting, candidates must choose advertising levels before votes are cast and
without perfect knowledge of ξ. As a result, candidates form beliefs over the demand shocks
at the time of their advertising decisions.
2.1
Voters
A voter who resides in county c ∈ Cm receives the following indirect utility for party j:
uitcj = βtj + g (Atmj ; α) + φ0 Xtc + γmj + ξtcj + εitcj
(1)
= δtcj + εitcj
where δtcj is the mean utility of the candidate. βtj is the average national preference for a
party in election t. We set g(Atmj ; α) = α log (1 + Atmj ) to permit advertising to exhibit
diminishing marginal effects. Xtc is a vector of observables at the county or market level that
shift voters’ decisions to turnout or their decisions to vote for a particular candidate. γmj
is a market-party fixed effect that captures the mean time-invariant preference for a party
in a given market (e.g., Democrats consistently attract votes in Boston and Republicans
consistently do well in Dallas). ξtcj is an election-county-party demand shock that voters
observe on Election Day but which is unobserved by candidates when they choose advertising.
εitcj captures idiosyncratic variation in utility. If a voter does not turnout for the election,
she selects the outside good and receives a utility of uitc0 = εitc0 .
Assuming that {εitcj }j are i.i.d. extreme-valued shocks, integrating over them implies
county-level vote shares of the form:
stcj (Atm , ξ; θv ) =
1+
exp (βtj + g (Atmj ; α) + φ0 Xtc + γmj + ξtcj )
P
exp (βtk + g (Atmk ; α) + φ0 Xtc + γmk + ξtck )
(2)
k∈{1,...,J}
where Atm = [Atm1 , . . . , AtmJ ]0 and θv is the vector of voter parameters. Gordon and
Hartmann (2013) explore a number of flexible specifications for voter demand, including
one with heterogeneous advertising preferences. However, since they do not find significant
6
heterogeneity, we focus on the model above with homogeneous preferences.
Our model assumes that voters are not strategic, such that a voter’s beliefs about the
likelihood their vote will be pivotal do not affect their voting decision. This assumption seems
reasonable given the extremely small probability that any given voter’s vote is pivotal in the
presidential election. However, it is possible that a voter’s (potentially biased) perception of
her pivotal probability could change under an alternative election mechanism, whereas our
model assumes that voters do not respond to such a change. Devising a method to incorporate
some notion of strategic voting into our advertising game is an important extension we leave
to future research.4
2.2
Candidates
We begin by discussing how candidates form beliefs over voting outcomes, and then present
a candidate’s objective function for advertising. We suppress the t subscript when possible
since our model treats elections as independent observations.
2.2.1
Candidate Belief Formation
Candidates set advertising without perfectly observing the demand shocks ξcj . Prior to
making their decisions, candidates gather information through campaign research and other
sources about the nature of potential demand shocks in each county. This information
provides the candidate with an expectation ξ¯cj of each shock’s realized value ξcj . Candidates
set advertising levels while forming beliefs according to
ξcj = ξ¯cj + ηmj ,
ηmj ∼ N (0, σ 2 )
(3)
where ηmj is common to all counties c ∈ m and σ is candidates’ ex-ante uncertainty over
voting outcomes. The shock ηmj enters at the market level, as opposed to the county level,
because candidates choose advertising at the market level.5
4
See Shachar and Nalebuff (1999) and Kawai and Watanabe (2013) for different approaches to inferring
strategic voting in large elections.
5
The specification of the shocks could be extended to allow for correlation across markets. This would,
however, increase the computational burden of estimation.
7
The ηmj represent all unknown factors at the time candidates set advertising that will
become known to voters on Election Day. Uncertainty over voting outcomes is an inherent
feature of political contests: unexpected gaffes, surprising news stories, and the weather all
contribute to candidates’ uncertainty over voters’ preferences on Election Day. For example,
Gomez, Hansford, and Krause (2007) find that rain differentially suppresses the turnout
of one party. Since the market-party fixed effects absorb time-invariant unobservables, the
realized value of ξcj captures election-candidate-specific deviations, such as whether it actually
rained in a county on Election Day.
2.2.2
Candidates’ Advertising Decisions
Candidates choose advertising levels Aj = [A1j , . . . , Amj , . . . , AM j ]0 based on the local marginal
costs and benefits of advertising. The marginal cost of advertising is simply the local price of
advertising faced by the candidate, ωmj . To characterize the marginal benefit of advertising,
let dj (A, ξ; θv ) indicate whether candidate j wins the election and let E [dj (A, ξ; θv )], taken
over ηmj , be the probability candidate j wins the election. The marginal benefit of advertising
in market m, expressed in probability units, is the derivative of E [dj (A, ξ; θ)] with respect to
advertising—the increase in the probability of winning the election given a small increase in
candidate j’s ads in market m. A candidate’s first-order conditions (FOCs) for advertising
must satisfy
Rj
∂E [dj (A, ξ; θv )]
≤ ωmj , for m = 1, . . . , M ,
∂Amj
(4)
where Rtj is an unknown structural parameter that translates the probability of winning into
dollar terms, placing both sides of the condition in equivalent units. Thus, the FOCs balance
the value of an increase in the candidate’s probability of winning the election relative to the
marginal cost of one unit of advertising.
Below we show that Rj has a natural interpretation when a candidate’s objective function
is specified in a form consistent with work on either candidate resource allocation or contest
theory. Both approaches yield advertising FOCs consistent with equation (4). We are agnostic
8
as to the precise interpretation of Rj beyond its ability to reasonably guide advertising in
different election regimes, as manifested in the particular form of dj (·).
Optimization with a Budget Constraint. Suppose each candidate sets advertising to
maximize his probability of winning subject to a budget constraint. As in Strömberg (2008)
and Shachar (2009), we do not specify an explicit model of budget formation. Unlike these
papers, however, we do not assume the budget is exogenous. Instead the observed budgets in
our model arise from the optimal allocation of resources among a pool of potential donors.
First, consider a candidate’s constrained objective function:
max E [dj (A, ξ; θv )]
Aj
s.t.
M
X
(5)
ωmj Amj ≤ Bj
m=1
where Bj is the budget. Both the Lagrangian Lj (B) and its multiplier λj (B) depend on all
the budget levels B = [B1 , . . . , BJ ] in the election due to the strategic interaction between
candidates. At a solution, the associated FOC is
∂Lj (B)
∂E [dj (A, ξ; θv )]
:
= λj (B) ωmj for m = 1, . . . , M .
∂Amj
∂Amj
(6)
Inspecting this FOC makes evident its equivalence with the FOC in equation (4). Second,
suppose there exists a pool of representative donors each faced with the decision of whether
to allocate funds to the candidate’s campaign or to an outside opportunity. Our assumed
optimal allocation of donor resources implies that in equilibrium,
λj (B ∗ ) =
M UI
, for j = 1, . . . , J.
Rj
Normalizing the marginal utility of income M UI to one, 1/Rj represents donors’ opportunity
cost of investing in the campaign relative to the utility they expect from the candidate
winning. In equilibrium, donors contribute funds until the shadow price of an additional
dollar, λj , is equal to 1/Rj , yielding the set of optimal budgets B ∗ = [B1∗ , . . . , BJ∗ ].
Thus, Rj is a policy-invariant parameter, independent of campaign fundraising, that
9
we refer to as a candidate’s financial strength. This specification provides a simple way to
conceptualize the endogenous formation of the budget. For example, consider a policy change
that alters dj to some d˜j . The previously optimal budgets B ∗ may imply that λj (B ∗ ; d) is
greater or less than 1/Rj because the left-hand side of equation (6) changes (i.e., moving to
d˜j changes the marginal benefit of advertising). Such an imbalance will result in a new set of
∗
∗ ˜
efficient budgets B̃ that equate each λj B̃ ; d = 1/Rj . We assume that political campaign
contributions are small relative to the broader fundraising market such that the return to
donors’ outside opportunities is invariant to the election mechanism and outcome. This
specification also ignores public good problems in funding candidates who would generate
non-exclusive benefits through their policies as president.6
Optimization in a Contest. Another formulation for a candidate’s objective function
that is consistent with equation (4) draws on contest theory (e.g., Tullock, 1980). Such
models consider the following unconstrained problem where the candidate balances the value
of winning against the total cost of advertising:
πj (A, ξ; θ) = Rj E [dj (A, ξ; θv )] −
M
X
ωmj Amj ,
(7)
m=1
where Rj is the value associated with candidate j winning.
Since the second term above is candidate j’s total spending, scaling the first term by Rj
converts the probability of winning into monetary terms. The key distinction relative to
the objective in equation (5) is the lack of a budget constraint imposed on the candidate.
The contest literature commonly refers to Rj as the “prize” of winning, e.g., Baron (1989)
interprets Rj as the candidate’s expected stream of benefits associated with winning office
6
We do not consider a donor’s expected utility from an election outcome and assume that Rj is invariant
to the actual amount of money donated. This implies two features of donor behavior. First, the marginal
utility of donor income must be independent of the amount they donate to the campaign. This is reasonable
unless policy changes significantly alter the proportion of a donor’s lifetime income that is offered to the
campaign. Second, the expected utility from the candidate winning cannot be contingent on the amount
donated. This assumption may be stronger because of common speculation that large donations earn political
favors. Nevertheless, such issues are beyond the scope of the paper. We merely hope that these assumptions
are reasonable for small local changes in donation amounts.
10
and any future election opportunities if he is successful.7 In contests, such as elections,
lobbying activities, and R&D races, participants expend resources no matter if they win or
lose. An important component of such models is the contest success function which determines
the probability of winning the prize given each participant’s (sunk) effort. In our model,
E [dj (A, ξ; θv )] plays the equivalent role.
2.2.3
Election Mechanism in the Electoral College
The function dj (·) encapsulates the rules of the election system that determine how votes
are tallied to select the winner. We focus here on the observed Electoral College mechanism
and discuss the direct vote mechanism in section 5. The relevance of states in our model
arises through the Electoral College, which aggregates popular votes at the state level to
electoral votes at the national level. The distinction between markets and states requires
some additional notation because multiple markets may exist in a state, m ∈ Ms . Counties
lie within an intersection of a state and market, c ∈ Cms . Finally, let dsj indicate whether a
candidate receives the plurality of a state’s votes,
(
)
X X
X X
dsj (As , ξ; θv ) = 1·
Nc scj (Am , ξ; θv ) >
Nc sck (Am , ξ; θv ), ∀k 6= j (8)
m∈Ms c∈Cms
m∈Ms c∈Cms
where As is the vector of advertising levels across candidates and markets in state s. Under a
winner-take-all rule, a candidate wins all of a state’s Electoral College votes if dsj (As , ξ; θv ) = 1.
Thus, a candidate wins the general election by obtaining a majority of the Electoral College
votes,
( S
)
X
dj (A, ξ; θv ) = 1·
dsj (As , ξ; θv ) · Es ≥ Ē
(9)
s=1
where Es is the state’s electoral votes and Ē = 270 is the minimum number required for a
majority.
7
These benefits could include the perceived monetary value of winning the election, the ability to implement
policies consistent with the candidate’s preferences, or simply the candidate’s “hunger” for the office.
11
3
Data
Four sources of data are combined for the analysis. First, we use advertising spending by
candidate within each of the top 75 designated media markets (DMAs). These markets
account for 78% of the national population. Second, to instrument for advertising levels in
the voter model, we obtain data on the price of advertising across markets. Third, voting
outcomes are measured at the county level. Fourth, we include a collection of control variables,
drawn from a variety of sources, based on local demographics, economic conditions, and
weather conditions on election day. Below we describe the key features of the data and refer
the reader to Gordon and Hartmann (2013) for further details.
3.1
Advertising
We measure advertising as the average number of exposures a voter observes. The advertising
industry commonly refers to this advertising measure as Gross Rating Points (GRPs), which
is equal to the percent of the population exposed (reached) multiplied by the number of times
each person was exposed (frequency). For example, 1,000 GRPs indicates that, on average,
each member of the relevant population was exposed 10 times.
Our advertising data come from the Campaign Media Analysis Group (CMAG) and
contains detailed information about each political advertisement.8 Although the data do not
directly contain GRPs, we derive them using the expenditure for an advertisement divided
by the cost-per-point (CPP) for the appropriate daypart (i.e., one of eight timeslots during
the day) of the ad in a given market.9 The CPPs by daypart come from SQAD, a market
research firm, and we aggregate exposures across dayparts into one advertising quantity, Amj ,
measured in thousands of GRPs. Ads are sponsored by a candidate, a national party, a
8
Freedman and Goldstein (1999) describe the creation of the CMAG data set in more detail.
The price of political advertising in the 60-days prior to the general election is subject to laws which
require the station to offer the purchaser the lowest unit rate (LUR). However, advertising slots purchased
with the LUR may be “preempted” by the TV station and replaced with a higher paying advertiser. The
TV station is only required to deliver the contracted amount of GRPs within a specific time frame, allowing
them to substitute less desirable slots for the original slot. According to the former president of CMAG,
well-financed candidates in competitive races rarely pay the LUR because they want to avoid the possibility
that their ads will be preempted by another advertiser (such as another candidate).
9
12
Table 1: Descriptive Statistics for Candidate Advertising
Obs
Mean Std. Dev.
Min
Max
2000 Election
GRPs Bush
GRPs Gore
Expenditures Bush ($ K)
Expenditures Gore ($ K)
CPMs Bush
CPMs Gore
75
75
75
75
75
75
5.82
4.78
879.84
681.53
8.07
8.11
5.59
0
15.89
5.67
0
17.94
1,218.73
0 6,185.45
1,072.94
0 5,941.61
2.07 3.47
16.73
2.12 3.47
16.87
2004 Election
GRPs Bush (K)
GRPs Kerry (K)
Expenditures Bush ($ K)
Expenditures Kerry ($ K)
CPMs Bush
CPMs Kerry
75
7.81
75
9.73
75 1,123.76
75 1,349.32
75
7.78
75
7.73
10.44
0
35.98
12.81
0
46.22
1,863.43
0 8,386.41
2,207.18
0 9,856.52
2.21 4.24
15.60
2.08 4.15
15.60
hybrid candidate-party group, or an independent interest group. We aggregate advertising
across sponsors when forming Amj for our estimation.
Table 1 reports the GRPs, expenditures, and average cost-per-thousand impressions
(CPMs) for each candidate. CPMs convert the CPPs to a per impression measure that
facilitates comparison across markets of different sizes. The CPMs in table 1 are a weighted
average across dayparts, with weights equal to a candidates’ share of advertising in that
market-daypart (see Appendix A for more details on the construction of advertising levels
and prices). Average CPMs paid decreased from 2000 to 2004 reflecting both decreases in the
actual CPMs in the data and some shifts in the distribution of candidates’ spending across
dayparts.
Figure 1, which plots GRPs by state against a state’s vote margin, illustrates the strategic
allocation of advertising across markets. The winner-take-all rule in the Electoral College
creates sharp incentives for candidates to concentrate their advertising in battleground states,
which contain only 41% of voters but receive 81% of advertising spending. Candidates do not
advertise at all in some markets with large vote margins.
A key point is that the breadth of advertising across vote margins in Figure 1 reveals the
13
Figure 1: GRPs by State-level Voting Margin in 2000 Election: Horizontal axis is
the state-level Republican vote share minus the Democrat vote share. Vertical axis is in hundreds of
GRPs, such that one unit indicates one exposure per voter, on average. Bubbles are proportional to
the state’s voting-age population.
180.0
Republican
Democrats
160.0
Gross Rating Points (00s)
140.0
120.0
100.0
80.0
60.0
40.0
20.0
0.0
-0.5
-20.0
-0.4
-0.3
Democat Stronghold
-0.2
-0.1
0.0
0.1
State Voting Margin (%)
0.2
0.3
0.4
0.5
Republican Stronghold
degree of candidate uncertainty about eventual vote outcomes. Advertising observed in a
state with a significant vote margin suggests a candidate might have been better off moving
those funds to a state at the (ex-post) margin of zero to potentially shift the state’s outcome.
Thus, ex-ante uncertainty about outcomes allows our model to rationalize candidate spending
in states with large realized vote margins.
3.2
Votes, Instruments, and Controls
Table 2 summarizes the data used to estimate the voter model. Voting outcomes at the county
level in 2000 and 2004 come from www.polidata.org and www.electiondataservices.com.
14
We restrict the analysis to the 1,607 counties contained in the 75 DMAs for which we observe
advertising. When estimating the candidate model and analyzing counterfactual policies,
voting behavior is held fixed in counties representing the remaining 22% of the population. In
each county, we observe the total number of votes cast for all candidates and the voting-age
population (VAP). The VAP serves as our market size for the county, which we use to
calculate voter turnout (i.e., the percentage of voters who choose the inside option to vote for
any candidate).10
As described in the model section, advertising is endogenous because candidates possess
knowledge about local demand shocks ξ¯cj . A variable naturally excluded from the demand
side that enters a candidate’s decision problem is the price paid for advertising. However,
particular realizations of the unobservable could induce a candidate to purchase enough
advertising to alter its market clearing price, violating the independence assumption required
for a valid instrument. Stories in the popular press confirm this suspicion (e.g., Associated
Press 2010). To avoid this concern, we use the prior year’s advertising price (i.e., 1999 for
2000 and 2003 for 2004) because there are no presidential, gubernatorial, or congressional
elections in odd-numbered years. Specifically, the instruments are the CPMs by daypart from
SQAD, interacted them with candidate dummies because candidates select different mixes of
dayparts across markets.
The DMA-party fixed effects, γmj , absorb time-invariant geographic variation in the
mean preferences for a given political party. These help establish the orthogonality of the
instruments and unobservables because political preferences and advertising prices tend to
be spuriously correlated across markets. We also include three categories of variables that
serve to explain election outcomes as well as address other potential correlations between
unobservables and instruments: (1) variables that measure local political preferences, (2)
variables that affect voter turnout but not candidate choice, and (3) demographic and
economic variables.
First, data from the National Annenberg Election Surveys (NAES) measures the percentage
10
A more accurate measure of turnout is the voting-eligible population (VEP) because it removes non-citizens
and criminals. However, data on the VEP is only available at the state level.
15
Table 2: Descriptive Statistics: Variables used in the voter model. County-level variables have
1,607 observations and market-level variables have 75 observations per year and party. All averages
are unweighted. LagCPM refers to the one-year lagged cost-per-thousand (CPM) impressions for
a particular daypart, reported in dollars. % identification variables come from the pooled NAES
surveys.
2000
Mean Std. Dev.
2004
Mean Std. Dev.
County-Level Variables
Republican Votes
Democrat Votes
Rain (in.)
Snow (in.)
% Aged 25 to 44
% Aged 45 to 64
% Aged 65 and up
Unemployment Rate
Average Salary (thous.)
Distance*100 (miles)
23,721
25,639
0.20
0.08
0.38
0.32
0.19
4.09
24.99
9.49
51,787
77,929
0.27
0.40
0.05
0.03
0.05
1.56
6.63
4.11
29,349
29,785
0.28
0.02
0.34
0.33
0.19
5.61
27.92
9.49
63,178
89,030
0.51
0.12
0.05
0.03
0.05
1.66
6.93
4.11
Market-Level Variables
LagCPM in Early Morning
LagCPM in Day Time
LagCPM in Early Fringe
LagCPM in Early News
LagCPM in Prime Access
LagCPM in Prime Time
LagCPM in Late News
LagCPM in Late Fringe
% Identifying Republican
% Identifying Democrat
4.18
4.85
5.88
6.26
7.06
12.37
8.50
7.18
0.29
0.30
0.95
1.11
1.45
1.63
1.91
3.47
2.10
1.81
0.06
0.05
5.47
4.89
6.67
7.93
10.41
16.17
12.26
8.30
0.33
0.31
1.55
1.08
1.34
1.73
2.54
4.66
2.56
1.94
0.06
0.06
16
of voters in a market who identify as Democrat or Republican. These data capture variation
in preferences across parties, and hence candidates, within a market. We include interactions
between the Democrat and Republican choice intercepts and the two party identification
variables to allow for asymmetric effects across parties. We also include an indicator for
whether the incumbent governor’s party is the same as the presidential candidate.
Second, we include two types of variables that should solely affect voters’ decisions to
turnout. Gomez, Hansford, and Krause (2007) show that weather can affect turnout in
presidential elections, and so we include county-level estimates of rain and snowfall on
Election Day. The other is a dummy if a Senate election occurs in the same market and
year, since strongly contested Senate races could spur additional turnout for the presidential
election.
Third, we add a set of demographic and economic variables to control for unobserved
changes in these conditions which could be correlated with within-market changes in voter
preferences and the advertising instruments. We use the county-level percentage of the
population in three age-range bins (e.g., 25 to 44) from the Census, the county-level unemployment from the Bureau of Labor Statistics, and the county-level average salary from the
County Business Patterns. Interactions between each candidate’s choice intercepts and the
demographic and economic variables capture differences across parties in voters’ responses to
these conditions.
4
Empirical Application
This section applies our model of advertising competition to data from two elections. We
begin with a discussion of the identification of our parameters, followed by our estimation
strategy, and the parameter estimates.
4.1
Identification
The voter parameters are θv = (β, α, φ, γ) and the candidate parameters are θc = (R, σ).
Identification of θv follows from standard arguments when estimating aggregate market share
17
models. In our particular setting, we use a combination of market-party fixed effects and
advertising prices as instruments to identify advertising effects. We first estimate the voter
model, then take those parameters as given when estimating the candidate model. As the
voter model is a standard differentiated-products logit, the rest of this section focuses on the
candidate model.
For the candidate parameters, inspection of the FOC in equation (4) reveals that the
Rj parameters are identified based on a candidate’s average advertising level in an election.
Identification of candidates’ uncertainty σ relies on systematic variation in advertising levels
and vote margins across markets. Figure 1 shows candidates purchased advertising in states
far from the zero voting margin. To justify such spending, candidates must have believed the
variance of the demand shocks was large enough to give these states a reasonable probability
of being on the margin, such that advertising might tip them in the candidate’s favor. Thus,
candidate uncertainty σ is identified by the degree to which candidates advertise in ex-post
uncontested markets.
To understand this intuition, recall that a candidate forms beliefs concerning the probability
of winning the election, E [dj (A, ξ; θv )], where this expectation depends on σ through equation
(3). A component of this election-level probability is the belief that a candidate wins the
state-level popular vote in s, E dsj (As , ξ; θv ) , where dsj (·) is defined in equation (8). If one
candidate in state s is strongly favored, both candidates’ incentives to advertise in markets in
s will be close to zero because dsj (·) is far from the indifference condition for both candidates.
Small changes in advertising will have little effect on E dsj (As , ξ; θv ) and, consequently, little
effect on E [dj (A, ξ; θv )]. Larger values of σ increase the returns to advertising by increasing
the probability that a demand shock could put dsj (·) close to the indifference point.
An alternative way of understanding the identification is to consider extreme values of σ.
If observed advertising levels were uncorrelated with differences in vote margins across states,
candidates would view outcomes as purely random, such that σ ≈ ∞. Otherwise, if σ ≈ 0, it
is hard to rationalize spending levels in many states with significant realized voting margins.
It is useful to contrast our identification strategy in two ways with the approach in
18
Strömberg (2008). First, he does not estimate the effect of candidates’ decisions (state-level
visits) on votes because visits vary little across candidates within states and the outcome
variable only measures the relative vote share of the two candidates. Second, he does not allow
candidates’ decisions to inform their uncertainty about election outcomes. The empirical
analysis recovers candidate uncertainty as the variances from a time random-effects regression
of state-level Democrat vote shares against various observables (e.g., polls, GDP growth,
etc.). Uncertainty is therefore identified solely through variation in vote shares. Although
this variation may be related to a candidate’s uncertainty, such variation would exist even if
candidates had perfect foresight regarding voting outcomes.
4.2
Estimation
To make the candidate model estimable, we add a stochastic component. Decompose the
true marginal cost of advertising into
ωmj = wmj + vmj ,
(10)
where wmj is an observed estimate of the marginal cost and vmj is a structural error observed
by the candidate but unobserved to the econometrician. The error term vmj forms the basis
of our estimation strategy.11
Given that advertising is a continuous choice variable, we form moments based on the
FOCs of the candidate’s decision problem. Our approach assumes the collection of advertising
choices we observe constitute a (pure-strategy) equilibrium of the advertising competition
game. Note that our model under the Electoral College may possess multiple equilibria but
our estimation strategy does not require us to solve the equilibrium. The primary complication
is that we observe some advertising choices on the boundary.
To explain our approach, first consider observations with positive advertising, where a
11
The unobserved cost shock therefore absorbs any other differences between the observed choices and the
model, such as differences across markets in the degree of uncertainty about outcomes. Note that including
the structural error vmj on the demand side, such as entering through the marginal effect of advertising, is
difficult because the non-linearities in dj (·) prevent inversion of an additively linear error term.
19
solution to the candidate’s FOCs exists and we can recover the econometric unobservable,
Rj
∂E [dj (A, ξ; θv )]
− wmj = vmj .
∂Amj
Given a suitable set of instruments z that satisfy E [v|z] = 0, we could form an estimator
around this moment. However, the equality above does not hold when A∗mj = 0. One
solution is to drop these observations. Although this action would reduce the efficiency of the
estimator, the more serious concern is that it might invalidate the moment condition because
possibly E [v|z, A > 0] 6= 0.
We argue that the specific context of a candidate’s decision problem should minimize
the concern that focusing on positive advertising markets results in a selection problem on
vmj . Whether this selection problem is an issue for estimation hinges on our beliefs about
the potential importance of vmj . In our data the observed marginal costs wmj are SQAD’s
forecasts for the election season. The vmj represent deviations between these forecasts and
candidates’ actual advertising costs. If a sufficiently large vmj draw would lead a candidate
to not advertise in a market, then dropping observations with zero advertising will lead to a
selection problem, such that E [v|z, A > 0] 6= 0.
Such an explanation seems unlikely because the zero advertising outcomes are primarily
due to demand-side shocks which, through the structure of the Electoral College, reduce the
incentives of candidates to advertise in non-battleground states. The more likely situation
is that a candidate only observes realizations of vmj after the candidate commits to some
positive amount of advertising in the market. Since we recover the demand-side shocks
ξcj using revealed preferences in the voter model, this reduces the concern of selection on
unobservable candidate-side shocks. We therefore assume that E [v|z, A > 0] = 0 because
candidates select markets in which to advertise based on wmj and the candidates’ beliefs
about ξ¯cj . We observe the former in our cost data and recover the latter from the demand
estimation.
Under these assumptions, estimation relies on the following moment condition:
∂E [dj (A, ξ; θv )]
E Rj
− wmj |zmj , Amj > 0 = 0 .
∂Amj
20
Let Mj+ denote the set of markets in which candidate j has A∗mj > 0 and M + =
P
j
Mj+ .
The relevant sample moment is
M+
j J
1 XX
∂E [dj (A∗ , ξ; θv )]
m(θ) =
Rj
− wmj ⊗ g(zmj ) ,
JM + j=1 m=1
∂A∗mj
where g(·) is any function and ⊗ is the Kronecker product. For instruments, we use DMA
voting margins differenced across two prior elections (e.g., for 2000, we difference the voting
margin for 1996 and 1992). Differencing removes any location-specific unobservable and
retains information that should relate to a candidate’s uncertainty about voting outcomes in
that market. We interact these variables with party-year dummies to form z.
4.3
Computing the Marginal Effect of Advertising
Calculating the marginal effect of advertising,
∂E[dj (A,ξ;θv )]
,
∂Amj
is challenging because the expec-
tation involves an M × J dimensional integral in the market-candidate specific shocks ηmj
and dj (·) is non-differentiable in Amj . The derivative is therefore only non-zero when a small
amount of advertising can alter the election outcome (i.e., dj (·) changes). We develop an
approach to calculate the derivative that takes advantage of this tipping point and reduces
the effective dimensionality of the integration.12
For a particular candidate j and market m in state s, two conditions define a tipping point
for dj (·). First, the number of electoral votes the candidate can gain (lose) in s, Es , must
surpass the candidate’s national electoral vote deficit (surplus) outside state s. Otherwise,
the election’s outcome is invariant to state s’s outcome. Second, within s, the candidate’s
vote advantage within market m must equal the candidate’s vote deficit outside the market
(i.e across other markets within the state). We state this condition in terms of a candidate’s
internal and external margin, IMmj (Am , ηm ) = EMmj (A−m , η−m ).13
12
Calculating the derivative by simulating E [dj (·)] in conjunction with finite differences will be imprecise
because small deviations from a given Amj are unlikely to shift the election outcome in dj (·). Larger steps
around a given Amj could be used, but this increases the bias of the finite difference estimate of the derivative.
13
It is also possible that there are not enough attainable votes within the market for advertising to place
the internal margin equal to the external margin. We address this and other details, such as when media
markets intersect multiple states, in Appendix B.
21
r
r
Our integration strategy simulates r = 1, . . . , N S draws over ηmk
and EMmj
, and given
r∗
the rth draw, solves for the critical value ηmj
that equates the internal and external margins,
r
r∗
r
r
r
IMmj
= EMmj
. Letting the PDF of η be f (·), we show more
Am , ηmj
, ηmk
A−m , η−m
formally in Appendix B that the marginal effect of advertising is equal to:
r
r
X
,
η
−∂η
A
,
EM
1 X
∂E [d\
(A, ξ; θv )]
m
mj
mk
r∗
=
f ηmj
if Es >
E`k (A` , η`r )−E`j (A` , η`r )
∂Amj
NS r
∂Amj
`6=s
r∗
where ∂η/∂Amj is evaluated at ηmj
. Intuitively, the derivative we seek equals the probability
∗
of drawing a critical value ηmj
times the derivative of this critical value with respect to
advertising. The condition on the right requires that the state be pivotal in the election’s
outcome: the number of electoral votes at stake, Es , must be larger than the candidate’s
electoral deficit outside that state, otherwise the derivative at the rth draw is zero. A
benefit of this approach is that the Monte Carlo integration is effectively over ηmk and EMmj ,
∗
combined with an analytic expression for ηmj
, instead of the original M × J dimensional
integral. Appendix B provides a derivation that generalizes to other contests or goals involving
multidimensional effort and provides more detail on the computation of the derivative in the
Electoral College and the direct vote.
4.4
Voter Model Estimates
Table 3 presents parameter estimates from the voter model. The advertising coefficient is
positive and highly significant. To help interpret the demand estimates, consider that the
average own advertising elasticity is about 0.03. This estimate is smaller than the median
advertising elasticity of 0.05 reported in a meta-analysis of consumer goods in Sethuraman et
al. (2011). We refer the reader to Gordon and Hartmann (2013) for more discussion of the
estimation results from the voter model.
We use the voter estimates to calculate two quantities. First, we measure the political
leaning of media markets and states by removing advertising’s effects while holding all other
factors fixed. Let s0jm be the vote share of candidate j ∈ {R, D} in market m when all
advertising is set to zero. We define the political leaning of a market as the Republican share
22
of the two-party vote in the absence of advertising:
Lm =
s0Rm
.
s0Rm + s0Dm
This provides a summary measure of voters’ party preferences without the potential contaminating effects of advertising.
Second, we calculate the cost per marginal vote at the observed advertising levels in each
media market:
CP Vmj = where smj (Am , ξ; θv ) =
P
c∈Cm
CP Pm
∂smj (Am ,ξ;θv )
∂Atmj
,
(11)
Nm
Nc scj (Am , ξ; θv ) and CP Pm is calculated to be the common
cost per point across candidates.14
Figure 2 plots the cost per marginal vote in the 2000 election against the political leaning
of the media market. The majority of markets with substantial advertising tend to have
a cost per marginal vote around $75. The highest cost, $204 per vote for Republicans in
the Miami-Ft. Lauderdale market, is over twice that faced by the Democrats in the same
market. Inspecting equation (11) indicates that the disparity in costs must arise solely
through asymmetries in the marginal effect of advertising, ∂smj /∂Amj . The Republican’s
marginal effect of advertising is lower in Miami-Ft. Lauderdale for two reasons. First, in the
absence of advertising, this market leans substantially to the left with a political leaning
of Lm = 0.41, such that it is generally more difficult for Republicans to generate votes in
the market. Second, the Republicans purchased 64% more GRPs in Miami-Ft. Lauderdale
than the Democrats, leading to greater diminishing marginal effects of advertising for the
Republicans. Figure 2 also depicts many markets with low costs per marginal vote, yet the
marginal benefit of these votes is generally small because they are in polarized states that are
unlikely to tip.
14
The CP Pm in the equation (11) differs slightly from the wmj used to estimate the candidate model. To
facilitate comparison, we calculate CP Pm as the common cost across candidates, weighting each daypartspecific CP P by the fraction of total exposures purchased in the entire election in that daypart, as opposed
to using candidate-specific weights.
23
Table 3: Voter Model Estimates. Parameter estimates from the two-candidate voter model
with 6,428 observations. Robust standard errors clustered by DMA-Party are in parentheses. F-stat
of excluded instruments is 88.2. ‘*’ significance at α = 0.05 and ‘**’ significance at α = 0.01. Some
coefficients omitted due to space.
Candidate’s Advertising
Senate Election
Gov. Incumbent Same Party
Rain (in.)
Rain × 2004
Snow (in.)
Snow × 2004
Distance*100 (miles)
% 25 ≤ Age < 44
% 25 ≤ Age < 44 × 2004
% 25 ≤ Age < 44 × Republican
% 45 ≤ Age < 64
% 45 ≤ Age < 64 × 2004
% 45 ≤ Age < 64 × Republican
% 65 ≤ Age
% 65 ≤ Age × 2004
% 65 ≤ Age × Republican
% Unemployment
% Unemployment × 2004
% Unemployment × Republican
Average Salary
Average Salary × 2004
Average Salary × Republican
Fixed Effects
Party
Year-Party
DMA-Party
24
Coefficient
Std. Err.
0.0693**
0.0134
0.0090
0.0300
-0.0201
-0.0108
-0.2210**
0.0036
-0.7317**
-1.2942**
0.9047*
3.7490**
0.3468
1.6595**
0.1538
-1.6048**
1.6091**
0.0019
0.0101*
-0.1229**
0.0161**
0.0038**
-0.0195**
0.0159
0.0098
0.0106
0.0293
0.0285
0.0072
0.0606
0.0025
0.2186
0.1987
0.3535
0.3345
0.2247
0.5279
0.3771
0.1700
0.5254
0.0108
0.0050
0.0123
0.0020
0.0007
0.0024
Y
Y
Y
Figure 2: Cost Per Marginal Vote in the 2000 Election. Horizontal axis is a market’s
political leaning Lm . Bubbles are proportional to a candidate’s GRPs in the market.
$250
Republican
Democrat
Cost per Marginal Vote
$200
$150
$100
$50
$0
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
Republican Share of 2-Party Vote in DMA (Net of Ad Effects)
4.5
Candidate Model Estimates
Table 4 presents the parameter estimates from the candidate model. In 2000, Bush outspent
Gore by 29%, and the corresponding Rj estimates imply that Republicans had a 45% greater
financial strength. In 2004, overall spending increased and Kerry outspent Bush, yet Bush’s
Rj is slightly higher than Kerry’s. Bush’s lower spending level may reflect greater confidence
in securing this less contested election rather than weaker financial support.
Uncertainty in 2004 is almost half of that in 2000. To explore the degree of candidate
uncertainty, we consider the implications for both state and national outcomes in the 2000
election. Figure 3 presents candidates’ beliefs about the likelihood of a Republican victory in
25
Table 4: Candidate Model Estimates: Standard errors in parentheses.
Parameters
σ
Rj ($M)
Observed Spending ($M)
2000 Bush
2000 Gore
0.157 (0.010)
146.4 (2.743)
100.8 (2.233)
66.0
51.1
2004 Bush
2004 Kerry
0.079 (0.007)
284.8 (5.999)
282.1 (5.637)
84.2
101.7
each state. The shaded bars represent those states in which each candidate has at least a
ten percent chance of winning. Among these, we see well-known battleground states such
as Florida, New Mexico, and Pennsylvania. The variation in state outcomes translates into
a distribution of electoral vote margins depicted in Figure 4. Although the distribution is
centered around zero because of the closeness of this election, the standard deviation is about
55 electoral votes, indicating a reasonable degree of uncertainty over the election outcome.
Most of this variation is due to the fact that several battleground states, such as Florida,
Ohio, and Pennsylvania, possess a large number of electoral votes.
5
Counterfactuals
We consider a counterfactual election system with a direct (popular) vote, in which the
candidate with the most popular votes is deemed the winner. Although other Electoral
College reforms have been considered, such as the proportional allocation of Electoral College
votes, a direct popular vote has come the closest to being passed (Congressional Research
Service, 2009). Conducting such a counterfactual allows us to understand how candidates
reallocate their resources (e.g., advertising dollars) under a new electoral process and how
voters subsequently respond.
In conducting this counterfactual, we assume other factors remain fixed. Such factors
0
are presently absorbed into a candidates’ local mean utility net of advertising, δcj
= δcj −
α log (1 + Amj ), and include candidates’ other campaign activities (e.g., get-out-the-vote
efforts) and voters’ preferences over their policy positions. The extent to which these
26
Figure 3: Candidates’ Beliefs by State: Each bar represents the probability that the
Republican candidate will win a majority of a state’s popular vote. Shaded bars indicate those
states in which each candidate has at least a ten percent chance of winning.
1
0.9
Probability of Republican Victory
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0
DC
Hawaii
New York
Vermont
Massachusetts
Rhode Island
Maryland
Connecticut
California
New Jersey
Illinois
Delaware
Michigan
Pennsylvania
Maine
Washington
Minnesota
Iowa
Oregon
Wisconsin
New Mexico
Florida
New Hampshire
Nevada
Missouri
Ohio
Tennessee
Arizona
Arkansas
Colorado
West Virginia
Virginia
Georgia
Louisiana
North Carolina
Kentucky
Oklahoma
Indiana
Alabama
Kansas
Alaska
Idaho
Mississippi
Montana
Nebraska
North Dakota
South Carolina
South Dakota
Texas
Utah
Wyoming
0.1
factors could impact our counterfactual results depends on their relationship with advertising
incentives.
5.1
Direct Vote Model
To implement the direct popular vote, we modify the election mechanism represented by dj (·).
The total number of popular votes a candidate receives is
Ṽj (A, ξ; θv ) =
X X
m∈M c∈Cm
27
Nc scj (A, ξ; θv ) .
Figure 4: Candidates’ Beliefs about the Distribution of Electoral Vote Margins.
Simulated distribution of electoral vote margins in 2000 given candidates’ estimated beliefs.
-200 -180 -160 -140 -120 -100
-80
-60
-40
-20
0
20
40
60
80
100
120
140
160
180
200
Republican Electoral Votes - Democrat Electoral Votes
With J = 2, candidate j wins the election if his vote count exceeds the opposing candidate’s
votes,
n
o
d˜j (A, ξ; θv ) = 1· Ṽj (A, ξ; θv ) > Ṽk (A, ξ; θv ) .
In what follows, we express dj (·) as a function of η because we set ξ¯ equal to the recovered
value, ξ, while the model solution requires explicit integration over η. The direct vote objective
function is
M
h
i X
π̃j (A; θ) = Rj E d˜j (A, η; θv ) −
ωmj Amj ,
m=1
with new FOC for advertising of
28
(12)
h
i
∂E d˜j (A, η; θv )
Rj
∂Amj
≤ ωmj , for m = 1, . . . , M .
(13)
Existence of a pure-strategy equilibrium follows from basic results because a candidate’s
objective is continuous and quasi-concave in his advertising variables. To compute the
equilibrium, we solve the 150 advertising choices that simultaneously set the FOC to zero for
each candidate.15 Discussed more fully in Appendix B, the marginal effect of advertising on
the probability of winning is:
r
r
∂ηmj Am , EMmj
, ηmk
1 X
∂E [d\
(A, η; θv )]
r∗
=
−fηmj ηmj
∂Amj
NS r
∂Amj
1 X
α
r∗
=
fηmj ηmj
NS r
1 + Amj
!
.
r
r
r
r∗
where EMmj
≡ EMmj
A−m , η−m
is the external margin in market m and ηmj
=
r
r
ηmj Am , EMmj
, ηmk
is the critical value of the shock that equates the external and internal margins. The derivative of η(·) with respect to Amj in our application is
−α
1+Amj
because Amj and ηmj are perfectly substitutable within the utility function as follows:
δcj = δ̃cj + α log (1 + Amj ) + ηmj . We have suppressed an indicator function that sets the
r
derivative for the rth draw equal to zero when Nm < EMm
. Thus, we compute the equilibrium
by solving the system below for the advertising levels:
"
#
NS
1 X
α
r∗
R`
fη (ηm`
)
− ω`m ≤ 0, for m = 1, . . . , M and ` = j, k
N S r=1
1 + Am`
r∗
r
r
s.t. ηm`
= ηmj Am , EMmj
, ηmk
, for r = 1, . . . , N S
Am` ≥ 0 for m = 1, . . . , M and ` = j, k
15
We set the residuals to zero in all counterfactuals, such that ωmj = wmj . Relatively large residuals
in some markets tend to be correlated within a state (e.g., we recover large unobservables for Bush in all
California DMAs in 2000). These instances likely represent a forecast error in the candidate’s belief about
the probability tipping a given state. However, state boundaries are meaningless in a direct vote. Given
this, we do not expect such residuals to carry over from the Electoral College to the counterfactual. Note
that we did not explicitly model candidate-side unobervables in demand because they are inseparable from
unobserved costs and are not additively separable in the candidate’s FOCs. Our residuals therefore include a
combination of candidates’ demand-side and cost unobservables.
29
subject to a set of complementarity conditions between the FOCs and the advertising choice
variables to allow for zero advertising outcomes.
5.2
Outcomes under a Direct Vote
Table 5 summarizes the counterfactual equilibrium and compares outcomes to those in the
Electoral College. In the direct vote, all markets receive positive advertising and total spending
increases by 25.2%. The advertising levels in the direct vote provide an assessment of the
extent to which battleground states attract disproportionate attention from candidates in the
Electoral College. Advertising intensity, in terms of average exposures per vote, decreases by
about 42% in battleground states and increases by roughly 130% elsewhere. This reallocation
of advertising away from battleground states to many large markets results in a significant
decrease in the overall variation in campaign attention across the county. Despite the fact that
average exposures increases nationally by 26 percent from 91 to 115, the standard deviation
in exposures across markets declines from 110 to 41, or 63 percent.
The new distribution of advertising in the counterfactual flips the popular vote in four
states (Iowa, New Mexico, Oregon, and Wisconsin) from favoring Gore to Bush. Although
Gore loses about 50,000 votes, the net result is that Gore wins with a popular vote margin of
about 450,000 votes. California plays a important role in the counterfactual, as illustrated in
Figure 5, which shows how voting outcomes change between the Electoral College and the
direct vote. Under the direct vote, Democrats lose votes in most states, even those where
they enjoy voters’ support (i.e., Lm < 0.5). Turnout increases in former non-battleground
states because of increased advertising, and turnout declines in former battleground states
due to the reduction in advertising. However, the votes Gore gains in California (bubble in
upper portion of Figure 5) compensate for the votes lost in the smaller states.16
Figure 6 plots the new advertising levels against each market’s political leaning. The
figure makes clear that Bush advertises more than Gore in nearly all markets due to his
higher value for Rj . Although significant variation remains, the distribution of advertising
is generally flatter in the direct vote compared to the Electoral College (recall Figure 1).
16
See Appendix C for a comparison of voter turnout under each election mechanism.
30
Figure 5: Outcomes under the Direct Vote: The vertical axis presents the change in
the Democrat’s state-level voting margin against a measure of a state’s political leaning net of
advertising effects. The bubbles are proportional to the absolute change in voter turnout within
each state, with empty bubbles indicating a reduction in voter turnout. The large bubble in the
upper part of the figure is California.
6%
Democrat Change in Vote Margin
5%
4%
3%
2%
1%
0%
-1%
-2%
-3%
0.2
0.3
0.4
0.5
0.6
0.7
Republican Share of Two-Party Vote (Net of Ad Effects)
31
0.8
Figure 6: Advertising under the Direct Vote. Baseline result from the counterfactual
under a direct vote. The horizontal axis is the political leaning of the market Lm , as defined by
the Republican share of the two-party vote with advertising set to zero. Each bubble’s size is
proportional to the population in the market.
140
Republican
120
Democrat
GRPs (00)
100
80
60
40
20
0
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
Republican Share of Two-Party Vote in DMA (Net of Ad Effects)
32
0.7
0.75
Table 5: Comparison of Observed and Counterfactual Results in 2000: List of battleground
states taken from Cook’s Political Report, September 2000 classification of state competitiveness.
Voting
Votes (m)
Popular Vote Margin (m)
% Voter Turnout
Observed
Bush
Gore
Direct Vote
Bush Gore
50.46 51.00
-0.54
61.89
51.52 52.02
-0.49
63.17
Advertising
Total Spending ($ m)
117.1
Spending ($ m)
66.0
51.1
Avg. Exposures
90.68
Std. Dev. of. Exposures
109.78
Avg. Exposures (K)
50.53 40.15
Avg. Exposures in
Battleground states
115.14 108.59
Non-battleground states 29.89 18.29
146.7
87.1 59.6
114.66
40.81
68.23 46.43
79.30 51.87
64.69 44.69
Table 6 summarizes the population-weighted total GRPs separately for left-, center- and
right-leaning markets, where center markets are defined as those with a political leaning of
Lm ∈ [.45, .55]. The winner-take-all nature of state-level competition in the Electoral College
effectively excluded campaigns from advertising in the most left- and right-leaning markets.
In the counterfactual, voters in left-leaning states receive 21% fewer advertising exposures
compared to voters in centrist states.17 In the next section, we show this discrepancy in
advertising allocations is not simply due to the asymmetry in candidates’ Rj ’s, but depends
on a combination of factors, most notably variation in advertising prices across markets.
5.3
Decomposing the Geographic Distribution of Advertising
Figure 6 reveals significant variation in advertising levels despite the switch to the direct
popular vote. Variation in advertising levels arises through three sources: asymmetries in the
candidates (Rj ), market-level variation in advertising costs (ωmj ), and county-level variation
17
This result is in contrast to the belief in Grofman and Feld (2005) that moving to a direct vote would
lead candidates to focus entirely on the largest media markets.
33
Table 6: GRPs By Political Leaning. GRPs in units of 100 with population-weighted
averages across DMAs. DMAs in the center are those defined to have between a political leaning of
between 45% and 55%, as measured using the Republican share of the two-party vote excluding
advertising. Left-leaning markets are those with less than a 45% political leaning and right-leaning
markets have greater than a 55% political leaning.
Political Leaning of State (Net of Advertising)
Left
Center
Right
GRPs % from
GRPs
% from
GRPs
Center
Center
Electoral College
26.34
Direct Vote
Baseline
97.34
Symmetric Candidates 61.45
Constant CPMs
119.94
Symmetric Candidates 62.07
& Constant CPMs
-85%
177.12
-98%
3.42
-21%
-20%
7%
-9%
122.59
77.25
111.80
68.33
0%
5%
-15%
-3%
122.74
80.79
101.80
66.55
0
in voters’ political preferences (δcj
). To gain a better understanding of the relative importance
of each factor in determining the equilibrium vote and advertising outcomes, we consider a
sequence of simulations that remove the asymmetries in Rj and the variation in ωmj .
Symmetric Rj . The upper panel of Figure 7 presents the equilibrium advertising levels
after setting each candidate’s Rj equal to the average of their estimated values. Both
the Republican and the Democratic advertising levels decline. Advertising levels are more
symmetric across candidate and less dispersed, with the majority of markets receiving six
thousand GRPs or fewer. However, Table 6 documents that even when candidates have
symmetric financial abilities, right-leaning markets receive 5 percent more GRPs than the
center and 31 percent more than the left.
To understand the variation in advertising levels in this symmetric model, it is important
to consider the role of geographic variation in advertising costs. Figure 8 plots the 2000 CPM
against each market’s political leaning. The cheapest media markets are in the center, which
likely explains the greater ad levels in the center in the upper panel of Figure 7. The next
cheapest CPM markets are to the right while more of the expensive markets are to the left.
34
Figure 7: Equilibrium Advertising in a Direct Popular Vote: Upper panel sets makes
each candidates’ Rj symmetric by setting the values equal to the average of the estimates. Middle
panel equalizes the advertising price per exposure across markets. Bottom panel makes symmetric
the Rj values and equalizes advertising prices.
140
Republican
Democrat
120
GRPs (00)
100
80
60
40
20
0
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
140
120
GRPs (00)
100
80
60
40
20
0
140
120
GRPs (00)
100
80
60
40
20
0
35
Republican Share of Two-Party Vote in DMA (Net of Ad Effects)
Figure 8: CPM by Political Leaning of the DMA in 2000: Vertical axis is the costper-thousand impressions (CPM). Bubble size is proportional to market population.
$18
$16
$14
$12
CPM
$10
$8
$6
$4
$2
$0
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Republican Share of 2-Party Votes in DMA (Net of Ad Effects)
Constant CPM. To remove the geographic variation in advertising prices, we solve the
equilibrium after equalizing the CPMs across markets, setting it to the population-weighted
average price. This change makes the cost of reaching voters constant across markets. The
middle panel of Figure 7 presents the advertising levels under constant CPMs and with
the (asymmetric) estimated Rj values. Two features stand out in this panel. First, each
candidate’s advertising distribution is flatter across markets of different political leanings. In
fact, the advertising tilts slightly to the left, with left-leaning markets receiving 7 percent more
GRPs than the center and 17 percent more than the right. Second, Republican advertising is
greater than Democrat’s in all but one market. This arises from Bush’s greater Rj .
36
Symmetric Rj and constant CPM. The bottom panel of Figure 7 presents the advertising levels under both symmetric Rj and constant CPMs.18 Advertising exposures are
nearly symmetric across markets. This model with symmetric Rj and equal ad costs across
markets therefore approaches the theoretical ideal of nearly uniform candidate attention
across the country. The standard deviation of exposures is reduced to 10 exposures per
person, whereas the top and middle panels involved standard deviations of 27.5 and 14.4.
Markets in the center still receive slightly more exposures, but the left now has less than 10%
fewer exposures than the center. This remaining variation likely derives from differences in
advertising elasticities across political leanings.
The lack of advertising price and funding variation suggests that this counterfactual may
be more representative of how other dimensions of candidates strategies might be adjusted in
a direct vote. The winner-take-all rule in the Electoral College leads politicians to choose
policies aimed at narrow constituencies in battleground states, rather than developing broad
programs and investment in general public goods.19 Just as a direct vote would lead to a
nearly uniform distribution of advertising attention in the absence of price variation, it may
similarly eliminate candidates’ incentives to cater their policies toward battleground states.
6
Conclusion
States’ winner-take-all rules for electoral votes concentrate advertising in closely contested
states. This concentration of candidate resources minimizes the political role of roughly
two-thirds of voters who reside in more polarized states. This paper develops a tractable
empirical model of advertising competition between presidential candidates to understand
how candidates’ attention changes under different election mechanisms. We recover voter
18
0
Note that making the δcj
constant across markets would effectively make the entire country one large
undifferentiated market, such that advertising would be constant across all markets.
19
Recent theoretical work highlights the economic policy implications of electoral rules (e.g., Lizzeri and
Persico, 2001; Persson and Tabellini, 2009). A wealth of evidence supports the view that incumbent presidents
enact policies to favor battleground states, e.g., see footnote 1 in the introduction. One journalist, commenting
on the 2012 election, wrote that if a presidential candidate needs to carry Florida, “it elevates the already
ever-present need candidates feel to pander to elderly voters, Cuban-Americans, orange-growers and any
other group that can deliver a bloc of Floridians. The same thing with Iowa and ethanol subsidies and other
agriculture-friendly policies,” (Black, 2012)
37
preferences using an aggregate discrete choice model and address the endogeneity of advertising
levels. Estimating the candidate side allows us to identify the primitives that guide candidates’
advertising allocations. With only three candidate structural parameters, the model is
parsimonious yet flexible. Under a direct vote in the 2000 election, we find total advertising
spending increases by 25 percent, with significant shifts across markets: advertising intensity
in former battleground states drops by almost half and more than doubles in other states.
Perhaps the greatest contrast between the election mechanisms is the role of political
preferences in candidates’ strategies. In the Electoral College, the political preferences of
voters in contested states dominate candidates’ strategies. Our countefactuals in the 2000
election illustrate that local political preferences would play a minimal role under a direct vote
and, in the case of advertising, are overwhelmed by local variation in the cost of reaching voters.
Although our focus has been on advertising, the structural change in candidates’ incentives
(through our contest success function) generalizes to the consideration of other candidate
strategies, such as policy platforms during elections and policy decisions in anticipation of
future contests. It is therefore reasonable to expect that a direct vote would similarly diminish
the role that local political preferences currently play in the formulation of policy.
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40
Appendices for Online Publication
Appendix A: Advertising and Advertising Prices
We construct a market-candidate observed aggregate advertising level and advertising price
(Amj and wmj ) based on two observed variables. Expendituremjad is CMAG’s estimate of
the dollars spent by candidate j in market m on an advertisement a in daypart d. CP Pmd
is SQAD’s reported advertising price for the 18 and over demographic in market m during
daypart d. We use the CPP from the 3rd quarter of the election year.20
Let the daypart level of advertising by candidate j in market m be:
P
a∈Amjd Expendituremjad
GRPmjd =
P8
d=1 CP Pmd
where Atmjd is the set of advertisements for a candidate in a market and daypart. Then total
advertising by candidate j in market m is:
Amj =
8
X
GRPmjd .
d=1
The market-specific advertising price for candidate j is defined as follows:


CP Pmd GRPmjd
if Amj > 0
Amj
wmj =

CP Pm
if Amj = 0
where
CP Pm =
8
X
d=1
"
PM
m=1 GRPmjd
j=1
CP Pmd PJ PM P8
j=1
m=1
d=1 GRPmjd
PJ
#
.
In other words, we use a weighted average across the dayparts in which candidate j advertised
in market m if the candidate did in fact advertise there, or a weighted average based on both
candidates advertising in all markets within each daypart if the candidate did not advertise
in the market.
20
While the advertising primarily spans both September (3rd quarter) and October (4th quarter), it is
problematic using a separate cost for each quarter because a discontinuity in costs would be artificially be
generated on October 1. Furthermore, 4th quarter ad costs are likely not a good estimate of the true cost of
the ad because they include the holiday season.
41
The advertising price in our candidate-side estimation is ωmj = wmj + vmj where vmj is the
candidate’s market-specific unobservable component of advertising. (Recall that the SQAD
prices are forecasts) When we analyze the cost per marginal vote, we use CP Pm in all markets
to highlight the role of diminishing marginal effectiveness and political leaning in the costs of
acquiring an additional vote. Finally, when we solve the direct vote counterfactual, we use wmj
as the price of advertising. This avoids odd implications from large local residuals that likely
do not relate to costs, but retains a source of local variation in advertising. We remove both the
candidate and local market ad price variation in the final simulation by setting an equal price
P P
2
M
1
per thousand people (CPM) such that w̃mj =
CP
M
×
P
op
/100.
mj
j=1
m=1
2M
Appendix B: Computing the Marginal Effect of Advertising
We compute the marginal effect of advertising,
∂E[dj (A,ξ;θv )]
∂Amj
using a hybrid approach that
simulates all but one of the unobservables. The method is applicable to any problem where an
agent (or agents) exerts observed effort to pass a threshold while facing some unobservables.
The general objective function under a threshold goal for agent j ∈ J ≥ 1 choosing effort
allocations Aj ∈ RM
+ is
max πj (A; θ) = Rj · E [dj (A, η; θ)] − ω 0 A ,
Aj
where Rj ∈ R≥0 is the agent’s prize for success, A ∈ RJM
≥0 is the collection of effort choices
k
across agents, ω ∈ RM
≥0 is the cost of effort, and θ ∈ Θ is a set of structural parameters.
dj ∈ {0, 1} is the success function that determines whether agent j wins the prize, such that
E [dj ] is the probability of success that integrates over the unobservable η ∈ RJM with known
CDF Fη . An important component of dj is the scoring function sjm (A, η; θ) ∈ R≥0 , which
determines the agent’s score given all effort choices and the unobservables. For all m, we
assume sjm (A, η; θ) is strictly increasing in Ajm and ηjm and strictly decreasing in Akm and
ηkm , for k 6= j. These conditions ensure that s (A, η) is invertible in η, which is necessary for
the computational approach. We suppress θ for the rest of the exposition.
42
Single agent with scalar uncertainty. The simplest application involves a single agent
(J = 1) who chooses a single effort level A ≥ 0 (M = 1) with a scalar unobservable η in an
attempt to exceed threshold V . The success function is
d (A, η) = 1· s (A, η) > V .
The scoring function produces a value v = s(A, η), which is a random variable due to the
presence of η. Assume the scoring function can produce a value high enough to exceed the
threshold, such that s(A, η) ≥ V for some combination of A and η. Otherwise, the agent
is guaranteed to fail and she will not exert any effort. The probability of success can be
expressed a
E [d (A, η)] = Pr s (A, η) > V
= 1 − Fv s (A, η) ≤ V
,
where Fv (·) is the unknown CDF of the score v. Let s−1 (A, v) be the inverse of s(·, ·) through
the η argument. Given the known distribution function for η, we use a change-of-variables to
re-express the cumulative distribution Fv in terms of η,
Fv s (A, η) ≤ V
= Fη s−1 (A, v) ≤ s−1 A, V
= Fη η ≤ η ∗ A, V ,
,
(14)
(15)
where η ∗ ≡ η ∗ A, V = s−1 A, V is the critical value of the shock that equates the score
and the threshold, s (A, η ∗ ) = V . Thus, given a particular value of A , the marginal effect of
A on the probability of success is:
∂ 1 − Fη η ≤ η ∗ A, V
∂E [d (A, η)]
=
∂A
∂A
−1
∂s
A,
V
= −fη η ∗ A, V
.
∂A
If s−1 and ∂s−1 /∂A have closed forms, then knowledge of fη yields an analytic expression for
the marginal effect of effort.
43
Multiple markets and a competing agent. Our presidential election application involves an extension to a competing agent and multiple markets, where each market requires
an action and has an agent-market specific unobservable. The success function in such a
contest is:
dj (A, η) = 1·{sj (A, η) > sk (A, η)} .
The scoring function is
sj (A, η) =
X
smj (Am , ηm ) ,
m
where Am and ηm are those values relevant to market m across all agents. For a given market,
we can rewrite the success function in the following way:
(
)
dj (A, η) = 1· smj (Am , ηm ) − smk (Am , ηm ) >
X
snk (An , ηn ) − snj (An , ηn )
n6=m
= 1·{IMmj (Am , ηm ) > EMmj (A−m , η−m )}
Intuitively, an agent’s score relative to his opponent’s in market m must be greater than his
deficit across all other markets. We refer to these terms as the internal margin IMmj and
external margin EMmj . The inversion to obtain a critical η ∗ is now in terms of the internal
margin instead of a single agent’s score. Note that an inverse of IMmj through ηmj exists due
to our shape assumptions on s (A, η). The probability of success can now be expressed as
E [dj (A, η)] = Pr (sj (A, η) > sk (A, η))
= 1 − FIM (IMmj (Am , ηm ) ≤ EMmj (A−m , η−m ))
−1
−1
= 1 − Fη IMmj
(Am , smj − smk , ηmk ) ≤ IMmj
(Am , EMmj (A−m , η−m ) , ηmk )
−1
∗
= 1 − Fη ηmj ≤ IMmj
Am , ηmj
, ηmk
Given values for A−m and η−m , EMmj is just a scalar representing agent j’s deficit or
surplus outside market m. Thus the critical value of agent j’s shock in market m is the
∗
∗
∗
ηmj
≡ ηmj
(Am , EMmj , ηmk ) that sets IMmj Am , ηmj
, ηmk = EMmj (A−m , η−m ).
44
We combine this result with Monte Carlo simulation over the opponent’s shock inside
market m and the collection of shocks outside market m to produce an estimate of the
marginal effect of Ajm . The key steps are:
r
r
r
r
1. Simulate r = 1, . . . , N S draws over ηmk
and η−m
= η−nj
, η−nk
using the known
n6=m
distributions fηmj . In our application, these are N (0, σ 2 ), which can be generalized at
higher computational cost.
r
r
r
r
2. Use η−m
to calculate the JM values of EMmj
≡ EMmj
, given some particA−m , η−m
ular value A−m .
r∗
r∗
r
r
r
r∗
r
≡ ηmj
Am , EMmj
, ηmk
that set IMmj
Am , ηmj
, ηmk
=
3. Solve for the critical values ηmj
r
EMmj
for all m and j.
4. The estimate of the marginal effect of Amj is:
r
r
,
η
∂η
A
,
EM
1 X
∂E \
[d (A, η)]
m
mj
mk
r∗
=
− fηmj ηmj
.
∂Amj
NS r
∂Amj
(16)
−1
r∗
where ∂η(·)/∂Amj ≡ ∂IMmj
(·)/∂Amj and evaluated at ηmj = ηmj
.
The next two sections discuss the details of implementing this general form of the derivative
in the direct vote and Electoral College, respectively.
Application to a Direct Vote. The realities of an election place certain restrictions on
the empirical analogues of the score functions. Under a direct vote, equation (16) describes
the derivative if it is always feasible for the internal margin of votes to exceed the external
margin of votes in all markets. In practice, bounds on the internal margin are implied by
the number of voters in the market, giving us the following expression for the derivative in a
direct vote:
r
r
∂η
A
,
EM
,
η
∂E \
[d (A, η)]
1 X
m
mj
mk
r∗
r
=
− fηmj ηmj
1· Nm > EMmj
∂Amj
NS r
∂Amj
45
where Nm =
P
c∈Cm
r
Nc is the total number of voters in the market. If Nm < EMmj
, then
r∗
there does not exist a ηmj
to equate the internal and external margins and the derivative at
the rth draw is zero.
Application to the Electoral College. The Electoral College introduces an added layer
of complexity because of the state-level contests. We need to introduce additional notation
corresponding to multiple markets intersecting a single state and markets intersecting multiple
states. Let Ms(m) be the set of all markets intersecting state s (m), where m is the focal
market for the derivative. Let Cms denote the set of counties intersecting both state s and
market m. Finally, let S̃ (m) denote the set of states that market m intersects.
The Electoral College involves two relevant thresholds for winning an election: (i) the
electoral vote margin and (ii) the state-level popular vote margin. For a given r, the derivative
is non-zero only if the electoral votes attainable through advertising in market m are greater
than the electoral vote deficit implied by the shocks in all other markets:
X
Es >
X
Es0 k (ηsr0 ) − Es0 j (ηsr0 ) .
s0 ∈
/ S̃(m)
s∈S̃(m)
If a market is “in play” based on the electoral votes, then the state-level margin can be
separated into an internal and external margin as above. If a market intersects multiple
states there is a potentially relevant internal and external margin for each:
rs
IMmj
=
X
Nc (scj (Am , ηmj , ηmk ) − sck (Am , ηmj , ηmk ))
c∈Cms
rs
EMmj
=
X
X
Nc (sck (Am , ηn ) − scj (Am , ηn )) .
n∈Ms(m) \m c∈Cns
∗rs
We therefore calculate an ηmj
, as described above, for each state s ∈ S̃ (m). Next, we define
∗r
the relevant critical value, ηmj
, to be the smallest of these shocks that yields enough electoral
votes to offset the electoral vote deficit implied by the rth set of draws.
46
The derivative for the rth draw is therefore:

r
r

r∗ ∂η (Am ,EMmj ,ηmk )


−fηmj ηmj

∂A
mj


∂E [d (A, η)] r 
=

∂Amj





0
r
> EMmj
P
P
and
Es >
Es0 k (ηsr0 ) − Es0 j (ηsr0 ) .
if
P
c∈Cms Nc
s∈S̃(m)
s0 ∈
/ S̃(m)
otherwise
and the overall derivative is
∂E \
[d (A, η)]
1 X ∂E [d (A, η)] r
=
.
∂Amj
NS r
∂Amj
Note that the above characterizes the marginal effect of effort in a contest with a general
contest success function. One primary focus of the theoretical contest literature has been
on the derivation of analytically tractable success functions (Skaperdas, 1996). In practice,
contests such as elections have their own specific success functions implying CDFs for the
probability of success that may inherently not be analytically tractable. We show that the
above approach is beneficial by compressing a large multidimensional integration problem
into unidimensional external and internal margins.
Appendix C: Comparison of Voter Turnout in the Electoral College and the Direct Vote
Turnout in the direct vote increases by 1.3%, or about 2 million voters. The popular vote in
four states—Iowa, New Mexico, Oregon, and Wisconsin, all with thin margins—flips from
Gore to Bush. Gore, however, gains enough votes in the Democratic stronghold of California
to win the election even though his national vote margin shrinks from about 543,000 to
494,000.
An important distinction between the Electoral College and a direct vote is a state’s
relative influence in the election outcome. Under the Electoral College, a state’s influence
is fixed and proportional to its fraction of the total electoral votes.21 The Electoral College
21
The Constitution specifies the number of a state’s electoral votes as equal to its number of Senators (two)
plus its number of Representatives (proportional to its Census population). This allocation implies that each
47
essentially protects states from political losses if a state implements policies that make
it more difficult or disqualifies certain voters from casting their votes. Furthermore, the
winner-take-all rule gives partisan members of a state’s government strong motivation to
influence voter turnout to favor their own political party (as witnessed recently in the form
of voter identification and anti-voter fraud laws proposed in many states).
In contrast, in a direct vote, a state’s relative influence in the election outcome is
endogenous—it is proportional to the percent of its population that turns out to vote
relative to national voter turnout. Figure 9 depicts the difference in representation of a state
between each electoral mechanism and the representation that their population constitutes
as percentage of the US population over age 18. States are ordered on the left axis by
increasing size of their voting age population. On the top, the series of positive bars reflect the
electoral college’s protection of small states. On the bottom, large states such as California,
Texas and Florida are under-represented in both the electoral college and a direct vote.
Under-representation in the direct vote arises from a smaller fraction of the state’s voting
age population actually voting. Other states such as Georgia, Arizona and Nevada also are
under-represented in a direct vote. Minnesota, Wisconsin, Michigan and Ohio are however
over-represented in a direct vote. A direct vote therefore eliminates both the electoral college’s
protection of small states and the tie in to state population size, as a state is now represented
only by its voters turning out for the election.
elector in a small state represents fewer voters compared to larger states: as of 2008, each of Wyoming’s three
electoral votes represented about 177,000 voters, compared to 715,000 for each of the 32 electors in Texas.
48
Figure 9: States’ Election Influence under the Electoral College and Direct Vote:
The horizontal axis reports the difference between a state’s relative influence in the election outcome
under a particular electoral system relative to the state’s voting-age population. Under the Electoral
College, a state’s influence is its number of electoral votes divided by the total number of electoral
votes in the country. Under a direct vote, a state’s influence is its voter turnout divided by the total
voter turnout in the country. Bars to the left of zero indicate that a state has less influence under
that system relative to its share of the total voting-age population. States are sorted from top to
bottom in order of ascending population.
Electoral College
Direct Vote
Wyoming
Alaska
District of Col
Vermont
North Dakota
South Dakota
Delaware
Montana
Rhode Island
Hawaii
Idaho
New Hampshire
Maine
Nebraska
New Mexico
West Virginia
Nevada
Utah
Kansas
Arkansas
Mississippi
Iowa
Oklahoma
Connecticut
Oregon
South Carolina
Kentucky
Colorado
Louisiana
Alabama
Minnesota
Arizona
Maryland
Wisconsin
Missouri
Tennessee
Washington
Indiana
Massachusetts
Virginia
Georgia
North Carolina
New Jersey
Michigan
Ohio
Illinois
Pennsylvania
Florida
New York
Texas
California
-0.02
-0.015
-0.01
49
-0.005
0
0.005
Difference Between Representation and Share of Population over 18
0.01