Structural Equilibrium Analysis of Political Advertising Brett R. Gordon Wesley R. Hartmann Columbia University Stanford University October 2010 Preliminary and incomplete Abstract We present a structural model of political advertising in equilibrium. Candi- dates choose advertising across mediamarkets inordertomaximize the probability of winning the national election. The voter model takes the form of an aggregate random coefficients discrete choice model in which advertising affects a voter’s incentive to vote for either candidate or not to vote at all. We estimate the model using detailed advertising and voting data from the 2000 and 2004 Presidential elections. We use the model to conduct a counterfactual in which we eliminate the Electoral College, and consider a direct national vote. Changing the structure of the electoral process alters candidates’ marginal incentives to advertise in a given market. This leads to a new equilibrium allocation of advertising and potentially a new voting outcome. Furthermore, our model could be used for other counterfactuals, such as considering the effects of 3rd-party candidates or certain campaign finance reforms, and could be applied or extended to races for other offices (e.g. house, senate or gubernatorial) or the primaries. Please note our counterfactual results are in progress and are not yet in the paper. Keywords: Political advertising, voter choice, electoral college, structural model, empirical game, endogeneity, moment inequality. 1 Introduction Concerns about the structure of the Electoral College are twofold. First, that it induces biases in the election process that favor populous states (Nelson 1974, Bartels 1985, Edwards 2004). Second, that a candidate who captures a plurality of the popular vote may fail to receive a plurality of the Electoral College vote. Numerous proposals for comprehensive electoral reform have been made since the founding of the country.1 Public interest in reform became especially strong following the 2000 Presidential election, when George W. Bush won with a majority in the Electoral College despite having a minority of the popular vote. This led many, particularly proponents of reform, to conclude that Al Gore would have won under a direct voting system that eliminated the Electoral College (Time Magazine 2000). Others were quick to note that the Electoral College and popular vote have disagreed only three times in history, suggesting that any such reform is unlikely to impact the final candidate selection. However, such analyses are fundamentally misguided because they ignore the fact that changes in the electoral system may lead candidates to change their campaigning strategies. As a result the outcome of the vote may also change. Under the current winner-take-all allocation rule, the candidate who wins the largest share of the popular vote in a state wins all of that state’s Electoral College votes. This means battleground states—such as Florida and Ohio, where candidates expect a narrow margin of victory—attract significantly more candidate resources than non-battleground states. In contrast, non-battlegrounds states such as New York and Texas barely attract any attention from the candidates; in recent elections, for example, neither major party candidate chose to advertise at all in several states. An alternative vote allocation rule changes the marginal incentives to campaign in a given market and should result in candidates altering their equilibrium allocations. Thus, in the absence of an equilibrium model, it is difficult to determine whether a candidate would or would not have won an election under a different vote allocation rule. Despite the importance 1The first reform proposal was brought before the Senate in 1816. More recently, between 1950 and 1979, proposed amendments for Electoral College reform were debated in the Senate on five occasions and in the House twice, once actually passing by a vote of 339 to 70. 1 of this subject, past empirical work on alternative Electoral College systems ignores the equilibrium implications of changing the allocation rule on candidates’ strategies and voters’ choices (Blair 1979, Gelman, King, and Boscardin 1998, Grofman and Feld 2005, Hopkins and Goux 2008, Str¨omberg 2008). This paper defines a structural equilibrium model of advertising competition between U.S. Presidential candidates in the general election.2 A structural model permits us to conduct counterfactual analyses to consider the implications of moving from the current Electoral College system to various alternatives, such as adopting a congressional district plan, a proportional allocation system, or a direct popular election. We specifically consider the last option since it has come closest to being passed. Our model allows us to examine whether candidates more equitably allocate their resources across states under a direct voting model. In addition, we can analyze how different electoral systems affect voter turnout and how the presence of third-party candidates may differentially affect voting outcomes. We apply the model to data on advertising per candidate and voting outcomes in the 2000 and 2004 elections. First, we use county-level voting data to estimate an aggregate discrete choice model of voter candidate selection with unobserved heterogeneity. We specify voter preferences using the aggregate demand model of Berry, Levinsohn, and Pakes (1995), and estimate it as a mathematical program with equilibrium constraints (MPEC) as detailed in Dub´e, Fox, and Su (2009). This rich model of voting behavior permits the returns to advertising to vary by market and provides us with a flexible basis to predict voters’ responses to changes in candidate advertising. Second, given the voter choice model, we estimate the candidate advertising model as a simultaneous move game. Candidates strategically choose advertising levels across markets while facing uncertainty over local ‘demand’ shocks that could alter voters’ choices. The existence of candidate uncertainty in some form is crucial to the model: if voting outcomes are deterministic functions of advertising choices, then a losing candidate would never choose positive levels of advertising in equilibrium. Prior to Election Day, candidates form unbiased 2Over $750 million was spent on media and advertising in the last Presidential election, and observers predict spending in 2012 to exceed $1.5 billion. Driving this growth in spending is the increasing recognition that a candidate’s marketing campaign plays a critical role in the ultimate election outcome. 2 beliefs about the nature of these shocks, and then set advertising to maximize the expected return from winning the election. On Election Day, voters perfectly observe the shocks and decide whether to vote for a candidate or not to vote at all. The candidate model is computationally challenging to solve and estimate due to the large continuous action space, the existence of corner solutions, and the potential for multiple equilibria. We address these issues by estimating the model using the moment inequality approachinPakes, Porter, Ho, andIshii(2006)(hereafterPPHI).Twokeybenefitsoffollowing PPHI are that we can remain agnostic about the nature of agents’ beliefs over competitors’ privateinformationandthatweavoidexplicitlysolvingforthegame’sequilibrium. Estimation via moment inequalities circumvents these difficulties while still allowing us to find parameters that rationalize the observed outcomes. To our knowledge, we are the first to investigate Electoral College reform using structural empirical methods.3 Brams and Davis (1974) and Owen (1975), among others, initiated a theoretical literature that examines the implications of different electoral allocation rules on election outcomes.4 More recently, Lizzeri and Persico (2001) show that a winner-take-all system provides an arbitrary public good less often than a proportional voting system, and then show that the Electoral College is subject to the same inefficiency. Str¨omberg (2008) incorporates a random-effects regression into a probabilistic voting-model and considers candidates’ resource allocation decisions in uncertain elections.5 Despite the strategic nature of political competition, little work formulates elections as empiricalgames.6 Asinotherdiscrete-choicemodels,ourinclusionofunobservedheterogeneity 3Two recent structural papers in political economy focus on the voter side. Degan and Merlo (2009) model the decision of voters to participate in multiple elections. Kawai and Watanabe (2010) estimate a structural model of strategic voting using Japanese general election data. 4Our model shares some similarities with the theoretical literature on contests, especialy recent work by Kaplan and Sela (2008) on political contests with private entry costs and by Siegel (2009) on all-pay contests. In the latter, each player chooses a costly“score,”representing a (possibly) sunk investment, and the player with the highest score wins the prize. Our model is similar in that candidates engage in a winner-take-all game where each must choose how much to“invest”in advertising, which becomes a sunk cost. Such contests arise naturally in settings where participants must expend resources no matter if they win or lose, such as elections, lobbying activities, and R&D races. 5Che, Iyer, and Shanmugam (2007) use a nested logit model to examine voter turnout and candidate ad type decisions in a non-strategic setting. 6Erikson and Palfrey (2000) investigate the simultaneity problem in estimating the effect of campaign spending on election outcomes. Abstracting away from the voter side entirely, the authors derive testable 3 should better capture substitution patterns across alternatives (i.e candidates). The estimated jointmodelofvoterdecisionsandthecandidates’advertisinggameshouldprovidetherequired structural basis to help make counterfactual predictions in substantially different election regimes. Our counterfactal results are relevant for two audiences. First, candidates and political consultants could use a model to help predict how voters and competitors would respond to a change in the own candidate’s advertising strategy. Second, policy makers seek to understand how the structure of an election may affect voter participation rates and influence candidates’ campaign fundraising and spending activities. The rest of the paper is organized as follows. Section 2 discusses the data set. Section 3 presents the voter and candidate models. Section 4 explains our estimation strategy. 2 Data Thissectiondetailsourdatasourcesandprovidessomereduced-formevidenceofarelationship between advertising and voting outcomes. 2.1 Advertising The primary advertising data come from the Campaign Media Analysis Group (CMAG) for the 2000 and 2004 Presidential elections, and were made available through the University of Wisconsin Advertising Project. CMAG monitors political advertising activity on all national television and cable networks, and assigns each advertisement to support the proper candidate. The data provide a complete record of every advertisement broadcast in each of the country’s top designated media markets (DMAs), representing 78% of the country’s population. Televisionadsarethelargestcomponentofmediaspendingforpoliticalcampaigns according to AdWeek (2009). See Freedman and Goldstein (1999) for more details on the creation of the CMAG dataset. The data contain a large number of individual presidential ads: 247,643 in 2000 and 807,296 in 2004. For each ad, we observe the precise date and time it aired, the candidate implications from the equilibrium solution to a spending game between candidates, which they empirically test using a set of reduced-form regressions. 4 supported (e.g., Democrat, Republican, Independent, etc.), and the sponsoring group (e.g., the candidate, the national party, independent groups, or“hybrid/coordinated”). Another key variable we observe is an estimate of the ad’s cost calculated by CMAG, which will help serve as a basis of estimation in the candidate model. The data allow us to calculate the total length (in seconds) of ads supporting a particular candidate, which we sum over sponsoring groups to yield the observed (to the voter) advertising quantity.7 We restrict attention to advertisements appearing after Labor Day, when the primaries have concluded and competition in the general election begins in earnest. Table 1 displays descriptive statistics. The third-party candidates (Nader and Badnarik) spent more on average per ad because much of their advertising was concentrated in larger, more expensive media markets. Table 1: Descriptive Statistics: Full Sample Total Total Average Popular Election Candidate Party Ads Expenditure Ad Cost Vote 2000 Bush Republican 126814 $89,202,830 $703 47.9% Gore Democrat 119300 $76,902,197 $645 48.4% Nader Green 1256 $1,227,463 $977 2.7% Various Other 269 $373,241 $2370 1.0% Total 247639 $167,605,731 $939 100.0% 2004 Bush Republican 262293 $209,595,807 $799 50.7% Kerry Democrat 544205 $353,848,127 $650 48.3% Badnarik Libertarian 248 $297,717 $1201 0.3% Various Other 550 $197,719 $360 0.7% Total 807296 $563,939,370 $752 100% Total 1054935 $731,545,101 $795 - We also obtained separate advertising cost data from TNS Media Intelligence at the DMA level to use as instrumental variables. The instruments contain the aggregate average cost-per-thousand (CPM) impressions and cost-per-point (CPP) by DMA in each election year.8 These should be valid instruments for advertising because they must be correlated with 7Federal campaign finance law allows political parties to explicitly coordinate certain expenses, including advertising, on behalf of the general election candidates (Garrett and Whitaker 2007). 8Ideally,ourdatawouldcontainaGRP-typeadvertisingvariablethathelpsmeasureexposure,butweonly 5 candidates’ actual advertising costs, but should be uncorrelated with local voting demand shocks. 2.2 Votes The county-level vote data is available from www.polidata.org. For each of the 1,342 counties, we observe the number of votes cast for all possible candidates and the size of the voting-age population (VAP). The VAP estimates serve as our market size parameters, and allow us to calculate a measure of voter turnout at the county level.9 It is important to note that we observe advertising at the DMA level and voting outcomes at the county level. We assign the observed level of advertising at the market level to each of the counties contained in that market.10 We conduct our analysis for all counties for which we observe the DMA-level advertising. Voting behavior, and therefore advertising, in the counties representing the remaining 22% of the population is held fixed when estimating the candidate-side and analyzing the counterfactual candidate policies. We are currently exploring alternative solutions to this issue. 2.3 Reduced-Form Evidence and Discussion To help explore our data, we obtained measures of the competitiveness of a state in a particular election from The Cook Political Report.11 This periodical publishes an index of competitiveness based on factors such as polling, historical voting patterns, and expert opinion. The ratings are published irregularly throughout the election year, and we use the ratings closest to Labor Day. Figure 1 plots the advertising per Electoral College vote for Democrats and Republicans observe advertising quantity (in seconds) and expenditure. Although advertising quantity is more appropriate from the voter perspective, it does not account for variation in exposure rates across markets. Advertising costs should be positively correlated with exposure, but confounds the per unit price and overall quantity of advertising. 9Unfortunately, voting-eligible population (VEP), a more accurate measure to calculate turnout that removes non-citizens and criminals, is only available at the state level. See the web page maintained by Michael McDonald at http://elections.gmu.edu/voter_turnout.htm for more information on measures of voter turnout. 10Of the 1,342 counties, only five belong to multiple DMAs. We use zip code-level population data to weigh the advertising proportionally according to the share of the population in a given state. 11The authors thank Mitchell Lovett for providing this data. 6 against the competitiveness index for each state. The size of each circle is proportional to the number of Electoral College votes in that state. The figure illustrates that candidates tend to spend more per vote in states where the outcome of the election is hardest to predict, such as the battleground states of Ohio, Pennsylvania, and Florida. In contrast California, which the Democrats won with a 10% margin in 2004, receives little advertising from either party. Our model, described in the next section, estimates voter preference parameters by aggregating from the voter level to form county-specific vote shares. We run a series of regressionstotestwhetherthedatacontainreduced-formevidenceofameaningfulrelationship between aggregate voting outcomes and candidate advertising. Table 2 contains the results of several regressions where the dependent variable is the county-specific, difference in logs between the candidate’s vote share and the“outside good’s”vote share, defined here as voters who either did not vote or voted for the third-party candidate.12 The independent variables are a dummy indicating which election, a dummy indicating which party (e.g. Democrat or Republican), an interaction term between the election and party dummies, and the candidate’s advertising quantity observed in that county. Table 2: Reduced-Form Evidence DV: ln(candidate vote share)−ln(outside share) Variable OLS 2SLS 2SLS Intercept -0.657 -0.668 -0.709 Election 0.298 0.299 0.303 Party -0.314 -0.313 -0.307 Election*Party -0.137 -0.141 -0.155 Advertising Quantity 0.109 0.118 0.153 DMA Fixed Effects No No Yes N =6,384, standard errors clustered by DMA All coefficients are significant with p < 0.01. The first column of Table 2 reports OLS results. As expected, advertising appears to have a positive effect on the candidate’s vote share. The second column reports 2SLS results using our ad cost instruments and the third column includes fixed effects at the DMA level. 12We expect to formally model the third-party candidate’s presence in the near future, but chose to ignore them for now to keep the estimation simpler. 7 The advertising coefficient remains positive and strongly significant in each specification, suggesting that the data contain the appropriate variation to help estimate our structural model. Note that controlling for market-specific unobservable shocks through the fixed effects in (moving from the second to third column) leads to an increase in the advertising coefficient. The direction of the change suggests there is a negative correlation between the unobserved shocks and advertising. The results in Figure 1 support this observation: the data show that in stronghold states, where one candidate receives a large, positive unobserved net shock, we see little to no advertising. We find it encouraging to see such consistency across Table 2 and Figure 1. 3 Model In this section we present a two-stage, static model of presidential advertising competition and voter behavior in the general election. We observe the advertising choices and voting outcomes from a collection of T elections. We consider voting outcomes at the county level, such that each voter lives in some county c = 1,...,C, inside a DMA m = 1,...,M, inside a given state s = 1,...,S. We use c ∈ m to denote the set of counties in market m, and m ∈ s to denote the set of markets in state s. The vector θ is the collection of parameters of interest. Figure 2: Model Overview Stage 1 Candidate 1 Candidate 2 … Candidate J A(ˆ) A(ˆ) A (ˆ) 1 2 J MMarkkett realliizes  demand shocks  , ,...,  c1 c2 cJ in each county Stage 2 Voters choose Vote for  Do not vote candidate j*1,,J j*0 8 Figure 2 depicts the basic structure of the game. In the first stage, for a given election t, each candidate j = 1,...,J sets advertising levels {A } across markets. Advertising tmj is the same across counties within a market, such that A = A ,∀c ∈ m. Candidates, tcj tmj however, must allocate advertising before votes are cast and are uncertain about future county-specific demand shocks {ξ } that could influence voters’ decisions. Candidates form tcj rational expectations about these demand shocks and set advertising conditional on these beliefs. The second stage takes place on Election Day, and voters perfectly observe the demand shocks and advertising. If a voter decides to turnout for the election, she chooses for which candidate to vote. Voting outcomes across all counties are realized and one candidate is deemed the winner. Formally, our model abstracts away from the campaign fundraising process, but still allows candidates’“budgets”to flexibly adjust under our counterfactual scenarios. We discuss this issue later at the end of Section 3.2 and consider it an interesting avenue for future research. 3.1 Voters A voter’s utility for candidate j given advertising quantity A in election t is: tcj u = β +α A +γ +ξ +ε , (1) itcj itj i tcj mj tcj itcj where β is a voter-specific taste for a candidate from party j in election t, α is the itj i marginal utility of advertising, γ represents market-party fixed-effects, and ε captures mj itcj idiosyncratic variation in utility, which is i.i.d. across voters, candidates, and periods. ξ tcj is a time-county-candidate specific demand shock that is perfectly observed to voters when casting their votes, but unobserved to candidates (and the researcher) when making their advertising decisions. Candidates’ beliefs about the demand shocks ξ induce endogeneity tcj in candidates’ advertising strategies. If a voter does not turnout for the election, she selects the outside good and receives a utility of u = ε . (2) itc0 itc0 The γ in our model serve the role of location-candidate specific dummies. As the only mj observed characteristic we include is advertising, this helps fit the mean utility level for a 9