A Model of Electoral Accountability

We consider a one-period model with two candidates and one representative voter (for which we reserve the pronoun “she”). Candidates (labeled L and R) compete for an elected office, which they value. Each candidate j∈{R, L} can either commit to a low-effort policy (p _j =0), or to a high-effort policy (p _j =1). Relative to a low-effort policy, the high-effort policy benefits the voter and entails an implementation cost (k>0) for the politician. This simple dichotomy captures the misalignment of incentives between politicians and voters when it comes to the provision of constituency service versus other activities (such as the pursuit of partisan goals, or undertakings associated with private returns for politicians). Electoral accountability in our setting is thus measured by commitment to the high-effort policy.

The voter learns a candidate’s policy platform (p _j ) if and only if the candidate actively advertises it (y _j =1, j∈{L, R}). While this assumption can be weakened (see Appendix B2), it allows us to focus on the informative role of political advertising in its starkest form. Communicating his platform (y _j =1) is costly for a candidate (with symmetric cost c>0), as it requires time and effort on the campaign trail as well as spending on political advertising.

The voter’s payoff is normalized to 0 and 1 when the elected politician implements the low-effort and high-effort policy, respectively. The voter’s utility also depends on partisan shocks {ε _R , ε _L }, revealed to the voter before the election, but after candidates’ platform and communication choices. The partisan shocks capture the voter’s evaluation of candidates’ party label.Footnote ⁸ The shocks ε _j are drawn from two (common knowledge) cumulative distribution functions with support $$\left[ {0,\,\bar{\epsilon }} \right],\,j\in \left\{ {L,\,\,R} \right\}$$ . Let $$ {\Pi}_{j} ={\rm Pr}(\epsilon _{j} \geq \epsilon _{{{\minus}j}} )$$ . Without loss of generality, we assume that П _R ∈ [1/2, 1).Footnote ⁹ The difference between Π _R and Π _L captures the level of partisan imbalance in favor of the right-wing candidate, to whom we then refer as the leading candidate (L is thus the trailing candidate). To simplify the derivation of the results, we also assume that the value of the partisan shocks cannot be too large: $\bar{\epsilon }\,\lt \,1$ . The voter’s utility, as a function of the elected candidate e ∈ {R, L}, is

(1) $$u_{v} (e)=p_{e} {\plus}\epsilon _{e} .$$

Candidates care about holding office.Footnote ¹⁰ If candidate j is elected and implements the low-effort policy, he enjoys a payoff normalized to 1. Such payoff is reduced by an amount k>0 if the elected politician chooses the high-effort policy p=1. We normalize the value of being out of office to 0. After choosing their platform, candidates choose whether to advertise it (at the incremental cost c>0) or not. Candidate j’s payoff is then given by

(2) $$u_{j} (p_{i} ,\,y_{i} )={\Bbb I}_{{\{ e=j\} }} (1{\minus}kp_{j} ){\minus}cy_{j} .$$

The policy cost k captures three possible aspects of an elected official’s job: (i) time and resources for constituency service (e.g., in the example developed in the introduction, time to secure subsidies, and attract private investors), (ii) the political capital required to build consensus and overcome veto players (Hall and Deardorff Reference Jacobson2006), and (iii) the opportunity cost of pursuing committee assignments linked to constituency interests (rather than their more suitable or desirable ones—for a ranking of committees, see Groseclose and Stewart Reference Strömberg1998; Stewart and Groseclose Reference Stewart and Groseclose1999; Stewart Reference Stewart and Groseclose2011).

The timing of the game is as follows:

1. 1. Candidates choose a platform: low-effort (p _j =0) or high-effort (p _j =1) policy.

2. 2. Candidates choose whether or not to advertise their platform: y _j ∈ {0, 1}.

3. 3. For each of the two candidates, the voter observes p _j if and only if y _j =1.

4. 4. The voter observes the realization of the partisan shocks (ε _L , ε _R ).

5. 5. The voter elects one of the two candidates, that is, e ∈ {L, R}.

6. 6. The elected candidate implements p _e , payoffs are realized.

In this model, candidates commit to the policy platform they choose.Footnote ¹¹ We believe that, in this context, the commitment assumption can be justified on empirical grounds: campaign promises have strong predictive power on future behavior in the legislature (Sulkin Reference Sulkin and Swigger2009), especially on relatively more “common value” issues such as attracting new job-creating industries (Ringquist and Dasse Reference Roosevelt2004), even when these positions are implicitly embedded in highly symbolic campaign images (Sulkin and Swigger Reference Sullivan2008). A direct (and technically convenient) implication of this assumption is that communication can only affect a candidate’s chance of being elected. It does not change his payoff once elected.

Our equilibrium concept is perfect Bayesian equilibrium, with the additional restriction of excluding weakly dominated strategies. When multiple equilibria arise, we select the one associated with the highest payoff to the voter. In what follows, the term “equilibrium” refers to this class of equilibria.

Before proceeding to the analysis, we remark that due to the costs associated with the high-effort policy, a candidate commits to p=1 only if he has sufficient electoral incentives to do so. To make electoral accountability at least theoretically possible, we assume throughout that the implementing cost (k) and the campaign cost (c) are not too high compared with the benefit from office: c<1−k.

Campaign Costs and Electoral Accountability

We first study candidates’ advertising choice. Our model predicts a strong correlation between commitment to the high-effort policy and political advertising: a candidate pays the campaign cost if and only if he commits to p=1.Footnote ¹² Candidates thus face a double cost of committing to the high-effort policy: the cost of implementing it (borne only if elected) and the cost of advertising this commitment to the voter (borne regardless of the electoral outcome).

The intuition behind Lemma 1 is clear. A politician incurs the implementation cost k only if he commits to the high-effort policy. Hence, the low-effort policy can be understood as a candidate’s default option: he has no incentive to pay a cost to reveal that he proposes the low-effort policy. But this implies that, when choosing the high-effort policy, a candidate must advertise his platform.

A direct implication of Lemma 1 is that each candidate has effectively two feasible strategies: high-effort policy with a costly advertising campaign or low-effort policy without advertising campaign. When candidates commit to the same strategy, the voter’s electoral decision is driven by the partisan shocks (i.e., vote for R when ε _R >ε _L and vice versa—we can ignore draws which are 0 probability event). When candidates choose different policies, the voter always elects the candidate who proposes the high-effort policy due to our assumptions that the shocks are not too large. Table 1 represents the strategic interaction between the two candidates, and Proposition 1 describes the equilibrium of this electoral game.

Table 1

The Electoral Game Induced by the Voter’s Behavior

PROPOSITION 1: Let $$k^{{\asterisk}} :=1{\minus}{{{\Pi}_{L} } \over {{\Pi}_{R} }}$$ . In equilibrium,

1. (i) If k≥k ^*, both candidates commit to the high-effort policy (p _j =1, y _j =1) if c≤(1−k)Π _L , and to the low-effort policy (p _j =0, y _j =0) otherwise.

2. (ii) If k<k ^*, both candidates commit to the high-effort policy if c≤(1−k)Π _L and choose the low-effort policy if c>Π _R −k. When, instead, c ∈ ((1−k)Π _L , Π _R −k], candidate j commits to the high-effort policy with probability α _j , where

(3) $$\alpha _{L} :={{k{\plus}c{\minus}{\Pi}_{L} } \over {{\Pi}_{R} {\minus}{\Pi}_{L} (1{\minus}k)}};\quad \alpha _{R} :={{1{\minus}k{\minus}c{\minus}{\Pi}_{L} } \over {(1{\minus}k){\Pi}_{R} {\minus}{\Pi}_{L} }}.$$

As pointed out above, a candidate commits to the high-effort policy if and only if the electoral reward is greater than the combined implementation (k) and campaign (c) costs. When these costs are very small, committing to the high-effort policy is a strictly dominant strategy for both candidates. Conversely, when these costs are very large, committing to the high-effort policy is a strictly dominated strategy for both candidates. The case of intermediate costs is more subtle. First, it is important to notice that the leading candidate R has an incentive to choose the same policy as L to take advantage of the favorable partisan shock. L, on the other hand, would prefer distinguishing himself from R (either to gain electorally or to avoid the costs of high effort with little electoral reward). This “hide-and-seek” game implies that the equilibrium can only be in mixed strategies.Footnote ¹³

The mixed strategy equilibrium can only arise when candidate R has a strong incentive to imitate L; that is, when partisan imbalance is sufficiently high. The range of the (c, k) space associated with a mixed strategy equilibrium thus depends on the degree of partisan imbalance: as Π _R approaches 1/2, the support of the mixed strategy equilibrium converges to the empty set. Conversely, as Π _R approaches 1, the area defined by c ∈ ((1−k)Π _L , Π _R −k] approaches the whole parameter space.

Having characterized the equilibrium, we now discuss how candidates’ behaviors are affected by the campaign cost c. When the equilibrium is in pure strategies, an increase in the campaign cost can only decrease candidates’ probability of committing to the high-effort policy. The reason is that the opportunity cost of committing to the high-effort policy increases, while the associated electoral reward remains unchanged. Consequently, voter welfare cannot be improved from c=0. When the equilibrium is in mixed strategies, the relationship between campaign cost and candidates’ incentives to commit to the high-effort policy depends on their ex ante electoral standing: the leading candidate R’s probability of commitment to high effort decreases with c, while it increases for the trailing candidate L.

COROLLARY 1:

1. (i) The voter welfare is maximized when c=0.

2. (ii) When the equilibrium is in mixed strategies, ∂α _L /∂c>0 and ∂α _R /∂c<0.

In a mixed strategy equilibrium (when imbalance is large enough), the two candidates’ decisions to commit to p=1 are affected by fundamentally different forces. The leading candidate R has an incentive to choose the high-effort policy only when the trailing candidate L chooses high effort with sufficiently large probability. In that case, choosing low effort is likely to result in a defeat, while matching the L’s platform allows him to exploit the favorable partisan shock. Conversely, the trailing candidate, who gains from distinguishing himself from the leading candidate, has a stronger incentive to choose high effort when his opponent chooses low effort with sufficiently large probability. As the campaign cost increases, equilibrium requires that the incentive to choose the high-effort policy increases for both candidates. For that to happen, it must be that the trailing candidate’ probability of choosing p=1 increases and that the leading candidate’s decreases. As a result, the overall probability that the trailing candidate wins the election increases with the campaign cost. This is the rebalancing effect.

What are the implications of the rebalancing effect for electoral accountability and voter welfare? When partisan imbalance is low, a greater campaign cost can only lower the probability that candidates commit to high effort and, therefore, can only reduce voter welfare. When partisan imbalance is large and the equilibrium is in mixed strategies, greater campaign cost affects L and R’s strategies in opposite directions, so the effect of higher c at first seems ambiguous. But it is important to notice that the voter benefits from the high-effort policy whenever at least one candidate commits to p=1. So R’s commitment to high effort matters only if the trailing candidate L does not promise the high-effort policy. For campaign cost close to (1−k)Π _L , candidate L does not commit to p=1 with high probability so any reduction in R’s probability to commit to the high-effort policy decreases electoral accountability. For campaign cost close to Π _R −k, candidate L commits to p=1 with high probability so a reduction in R’s probability to commit to the high-effort policy has little effect. As L’s probability to commit to p=1 increases with c, greater campaign cost improves electoral accountability for sufficiently large c (i.e., $$c\in \left[ {{{1{\minus}k} \over 2},{\Pi}_{R} {\minus}k} \right)$$ ).Footnote ¹⁴

Better electoral accountability then translates into higher voter welfare whenever the size of the partisan shocks is not too large.Footnote ¹⁵ This last condition ensures that the gain from obtaining the high-effort policy with greater probability dominates the loss in term of partisan shock from electing the trailing candidate L with higher probability.

PROPOSITION 2:

1. (i) An increase in the campaign cost strictly increases the probability that the high-effort policy is implemented if and only if c ∈ ((1−k)/2, Π _R −k) and k<1−2Π _L , and weakly decreases it otherwise.

2. (ii) There exists $$\hat{\epsilon }\,\gt\, 0$$ such that for all $$\bar{\epsilon }\,\lt \,\hat{\epsilon }$$ , there exists $$\underline {c}(\bar{\epsilon })\in ({{(1{\minus}k)} \mathord{\left/ {\vphantom {{(1{\minus}k)} {2,\,{\Pi}_{R} {\minus}k}}} \right. \kern-\nulldelimiterspace} {2,\,{\Pi}_{R} {\minus}k}})$$ such an increase in the campaign cost increases the voter welfare if and only if $c\in (\underline {c}(\bar{\epsilon }),\,\Pi_{R} {\minus}k)$ and k<1−2Π _L .

To summarize, our results show that an increase in the campaign cost (i) can only hurt the voter when partisan imbalance is low, but (ii) can also improve accountability when partisan imbalance is high, due to the rebalancing effect of higher c. To our knowledge, this result provides novel and qualified formalization of the notion of cash as a “powerful megaphone.” It is important to stress that these results do not rely on equilibrium selection: in the relevant range (c ∈ ((1−k)Π _L , Π _R −k]), the mixed strategy equilibrium that we consider is the unique equilibrium.

Implications for Campaign Finance Regulation

After having studied how exogenous changes in the campaign cost affect platforms and accountability, it seems natural to study the model’s implication for campaign finance regulation. Specifically, we characterize the optimal subsidy when, for a given c (determined by market forces in the media markets included in candidates’ district), the voter pays directly a portion s ∈ [0, c] of a candidate’s advertising cost, while leaving c−s to the candidate’s own fund-raising efforts.

To study the most favorable setting for campaign finance regulation, we assume that the subsidy enters linearly in the voter’s utility (i.e., there is no deadweight loss of taxation). Under this assumption, her objective function becomes p _e +ε _e −s(y _L +y _R ). To simplify the analysis and focus on the effect of campaign cost, we also assume (without significant loss of generality) that (i) k is arbitrarily close to 0 and (ii) the partisan shocks are perfectly negatively correlated and have binary support $(\epsilon _{R} ,\epsilon _{L} )\in \left\{ {(\bar{\epsilon },0),(0,\,\bar{\epsilon })} \right\}$ .Footnote ¹⁶ The voter’s ex ante expected utility as a function of the subsidy s can be written as

(4) $$W(s)=\bar{\epsilon }{\plus}\alpha _{R} (1{\minus}\bar{\epsilon }{\Pi}_{L} ){\plus}\alpha _{L} (1{\minus}\bar{\epsilon }{\Pi}_{R} ){\minus}\alpha _{R} \alpha _{L} (1{\minus}\bar{\epsilon }){\minus}s(\alpha _{L} {\plus}\alpha _{R} ).$$

When c is already low enough so that both candidates already commit to high effort with probability 1 (in this simplified environment, when c<Π _L ), any positive subsidy would simply transfer utility from the voter to the candidates without affecting their behavior. When, instead, the cost is large enough, the voter might gain from a positive subsidy. However, as Proposition 3 shows, the optimal subsidy (for the voter) is not always positive.

PROPOSITION 3: Let $\tilde{c}={\Pi}_{R} {\minus}({\Pi}_{R} {\minus}{\Pi}_{L} )^{2} $ . The voter’s optimal campaign subsidy is

$$s^{{\asterisk}} (c)=\left\{ {\matrix{ 0 \hfill &#x0026; {c\leq \Pi _{L} } \hfill \cr {c{\minus}\Pi _{L} } \hfill &#x0026; {c\in (\Pi _{L} ,\,\tilde{c}]} \hfill \cr 0 \hfill &#x0026; {c\in (\tilde{c},\,\Pi _{R} ]} \hfill \cr {c{\minus}\Pi _{R} } \hfill &#x0026; {c\in (\Pi _{R} ,\,1]} \hfill \cr } .} \right.$$

The voter obtains the high-effort policy whenever at least one candidate proposes it. As the voter must subsidize any candidate who engages in costly political advertising, when c>Π _L , the best scenario for the voter is that one candidate commits to high effort with probability 1, whereas the other does so with probability 0.

This optimal scenario arises in two cases. First, when the campaign cost faced by candidates is Π _R (i.e., c−s=Π _R ), so that the rebalancing effect is strongest and the trailing candidate chooses high effort with probability 1. Second, when the campaign cost faced by candidates is Π _L , so that the rebalancing effect is weakest and the leading candidate chooses high effort with probability 1. Whenever the initial campaign cost satisfies c>Π _R , both c−Π _L and c−Π _R result in the same expected policy payoff, and the voter has a strict preference for the lowest of the two subsidies, c−Π _R .Footnote ¹⁷

When the initial cost is below Π _R , the rebalancing effect cannot be fully exploited. However, the trailing candidate L chooses the high-effort policy with high probability whenever c is close enough to Π _R , while the subsidy c−Π _L required to induce the advantaged candidate to choose high effort with probability 1 is very large. As a result, a campaign subsidy can only reduce voter welfare and the voter prefers 0 subsidy. When c is close to Π _L , the gain from inducing greater effort by the leading candidate outweighs the cost, and the optimal subsidy is again positive.

Interestingly, our theory suggests that the voter would always prefer a tax on campaign spending rather than a subsidy for relatively large c. By raising the campaign cost by an amount Π _R −c, the voter can take full advantage of the rebalancing effect (the probability of getting the high-effort policy increases) without using public resources. This negative subsidy is effectively a form of Pigouvian taxation: the voter would be better off even if she did not enjoy any direct benefit from the associated tax revenues.

In our model, reducing the campaign cost improves the voter welfare because it increases the probability the voter’s preferred policy is implemented. As such, our theoretical framework develops an argument in favor of campaign finance even in the absence of SIGs exchanging contributions for political favors (as in Prat Reference Prato and Wolton2002; Coate Reference Cohen2004; Ashworth Reference Ashworth2005). To the best of our knowledge, the logic behind our results is novel. Our theoretical framework, however, also points out to the difficulty to design an optimal campaign finance reform: the welfare-maximizing subsidy (for the voter) depends critically on the current campaign cost and, under some condition, takes the form of a tax.

Testable Implications and Empirical Evidence

We now return to the positive implications of our model of electoral competition. Our theory predicts that the probability that the elected representative implements the high-effort policy should be as follows:

• ∙ negatively correlated with the campaign cost for low levels of partisan imbalance;

• ∙ positively correlated with the campaign cost for high levels of partisan imbalance;

• ∙ negatively correlated with the degree of partisan imbalance, holding constant the campaign cost.

In this section, we combine existing data sources from the US House of Representatives to present a prima facie cross-sectional empirical assessment of our theory. To perform this exercise, we need to find adequate empirical analogues for our three key variables: candidates’ effort, campaign cost, and partisan imbalance.

Drawing on a large body of research on the determinants of distributive politics in the United States (De Figueredo et al. 2003; Stromberg 2004; Albouy Reference Albouy2009; Berry et al. Reference Bhattacharya2010; Snyder and Strömberg Reference Sorauf2010), our proxy for a congressman’s effort is the amount of discretionary federal spending received by his home district (precisely, high variation non-defense federal outlays for the fiscal years 2006 and 2007).Footnote ¹⁸ It is indisputable that securing federal outlays captures only one dimension of electoral accountability. Furthermore, other political actors can influence the allocations of those funds (Berry et al. Reference Bhattacharya2010). Nonetheless, we believe that this approach has important advantages over alternative measures.

Theoretically, securing federal funds captures important aspects of our notion of high-effort policy. First, it is a relatively non-partisan activity for which the attribution of credit is simpler than other accomplishments (e.g., drafting legislation, or assembling a coalition supporting it), as witnessed by the fact that legislators from both parties heavily advertise these achievements (Druckman et al. Reference Egan2009; Grimmer et al. Reference Groseclose2012; Grimmer Reference Grimmer2013a; Grimmer 2013Reference Grimmer, Messing and Westwoodb). Second, there is robust evidence that voters tend to electorally reward these activities (Levitt and Snyder Reference McAfee and McMillan1997). Third, securing federal funds is a source of opportunity cost for politicians and is correlated with other forms of constituency service. Snyder and Strömberg (Reference Sorauf2010) document how representatives who are relatively more sheltered from electoral pressures due to exogenously low levels of media coverage are less likely to serve in committees representing their constituents’ interests, less likely to vote against their party, and less successful at securing federal funds (while they spend more time pursuing their broad political goals).

Empirically, federal outlays are easily measurable and display a large cross-sectional variance (a great virtue, given the limited availability of data on advertising cost). Moreover, as looking at federal outlays is a very common approach in the literature, our investigation can be guided by established practices and informed by clear benchmarks.

In line with existing literature, we measure partisan imbalance by the absolute distance in the vote share of the two presidential candidates in 2004.Footnote ¹⁹

For the campaign cost, we use data from the Wisconsin Advertising Project (Goldstein and Rivlin Reference Grimmer2007), which includes information on the number, length, and price of a large number of political TV ads aired during the 2004 congressional, gubernatorial, and presidential campaigns. Specifically, we approximate the campaign cost with the per-unit price of political advertising (30-second spot). It is important to point out that this variable captures only part of the cost of informing voters, which is determined by prices (taken as given) as well as quantities of ads necessary for a candidate’s message to reach the electorate (which depends on district characteristics). This is clearly a limitation of our empirical exercise.Footnote ²⁰ However, we do not believe this limitation is too severe as (i) using per-unit average prices allows us to focus on an exogenous variable (not candidates’ strategic decisions), and (ii) total advertising expenditures are positively correlated with the per-unit cost of ads (see Evidence on the Mechanism section, where we also perform our analysis with total expenditures as a robustness check). Using per-unit price of ads also has some advantages. Indeed, we observe a candidate’s advertising expenditures only when he chooses to advertise. But our core comparative statics rely on all candidates, whether or not they advertise. With the per-unit price of ad, we approximate the campaign cost faced by candidates who chose not to advertise.

Due to data availability, our analysis is limited to the 109th Congress.Footnote ²¹ Drawing on our theory (and in line with the existing literature), we estimate the following model:

$$y_{{is}} =\beta _{0} {\plus}\beta _{1} c_{{is}} {\plus}\beta _{3} \pi _{{is}} {\rm {\plus}}\delta \pi _{{is}} {\times}c_{{is}} {\plus}X_{{is}}^{'} \beta _{4} {\plus}\gamma _{s} {\plus}u_{i} .$$

Table 2

Description of Variables

Note: ACS=American Community Survey.

In our baseline specification, y _is is the log of total federal outlays from “high variation programs” awarded to congressional district i in State s. This variable, described in detail in Berry et al. (Reference Bhattacharya2010), captures the amount of discretionary spending received by each district. c _is measures the average price of a 30-second political ad for the 2004 electoral campaign in district i. It is constructed from a population-weighted average of the mean cost in each media market contained in district i. π _is is the partisan imbalance in district i. X _is is a vector of congressman-specific and district-specific controls: information on party, seniority status, membership and chairmanship of various committees, membership of party leadership from Berry et al. (Reference Bhattacharya2010), and on median income, population, shares of urban and minority population from the 2005 American Community Survey. γ _s is a state fixed effects. Table 3 displays summary statistics for the main variables employed in our analysis. We restrict our baseline specification to the 295 congressional districts for which the available measure of ad cost covers at least 90 percent of the district population.

Table 3

Summary Statistics

Note: ACS=American Community Survey.

Table 4 reports the estimated coefficients from our baseline specification. Columns 1–4 show that partisan imbalance is not statistically associated with the level of federal outlays without the inclusion of the interaction term. Once the data are organized according to our theory, the coefficient of partisan imbalance and advertising cost are indeed negative and statistically significant, and the interaction term is positive and statistically significant (all three results are robust to the inclusion of district and congressman-specific covariates, as well as state fixed effects, as shown in columns 5 and 6).

Table 4

Federal Outlays, Campaign Costs, and Partisan Imbalance

Note: Congressman and District covariates include median income, population, minority, urban population, party dummy, leadership dummy, freshman dummy, chair dummies, ranking dummies, and committee membership dummies. t-Statistics in parentheses (standard errors clustered at state level).

FE=fixed effects.

*, **, *** Significant at 10%, 5%, 1%, respectively.

Figure 1 displays the marginal effect of ad cost on federal outlays (and its 95 percent confidence interval) implied by column (4) of Table 4. Consistent with our theory, the marginal effect is negative for low levels of partisanship and positive for high levels of partisanship, as illustrated by Figure 2, which displays the linear prediction of federal outlays as a function of ad cost for various percentiles of partisan imbalance.

Fig. 1

Marginal effect of ad cost

Fig. 2

Predicted value of federal outlays, by percentile of partisan imbalance

Evidence on the Mechanism

Our theory also has implications regarding the source of the joint effect of imbalance and campaign cost on accountability. In particular, under the assumptions of Proposition 2, an increase in the campaign cost should result in (i) higher constituency service (conditional on being elected) from the trailing candidate and (ii) lower constituency service (conditional on being elected) from the leading candidate.Footnote ²²

To look for evidence of these differential effects, we create a dummy variable, Trailing, which equals 1 in districts where the representative comes from a different party than the presidential candidate who received the most votes in either of the two previous presidential elections.Footnote ²³ Our theory predicts that

• ∙ the marginal effect of ad cost on constituency service should always be negative in the sub-sample of leading candidates (i.e., for all levels of imbalance);

• ∙ compared with the baseline estimates, the threshold level of imbalance above which the effect of ad cost is positive should be lower in the sub-sample of trailing candidates.

Figures 3(a) and 3(b) (as well as Table 5) show that the estimated marginal effects are larger for trailing than for leading candidates.Footnote ²⁴ Specifically, in the sub-sample of trailing candidates, the (point estimate of the) marginal effect is positive for values of imbalance slightly above the median level in the overall population. In contrast, in the sub-sample of leading candidates, the (point estimate of the) marginal effect is positive only above the 88th percentile of imbalance.

Fig. 3

Marginal effect of cost for (a) trailing candidates and (b) leading candidates

Table 5

Separating Trailing and Leading Candidates

Note: District covariates include median income, population, minority, urban population. Ranking dummies include party dummy, leadership dummy, freshman dummy, chair dummies, ranking dummies. t-Statistics in parentheses (standard errors clustered at state level).

*, **, *** Significant at 10%, 5%, 1%, respectively.

It is important to stress that in a triple-interaction model, the estimated coefficient of Ad Cost×Imbalance×Trailing is positive, but not statistically different from 0 (see Table D1 in the Supplemental Appendix). Moreover, we cannot reject the hypothesis that the marginal effects of Ad Cost depicted in Figures 3(a) and 3(b) are equal across sub-samples.Footnote ²⁵ While the lack of statistical significance can be due to the small sample size of the trailing sub-sample (only 51 observations), we can only claim that the evidence presented in this sub-section is on balance consistent with our theory, and only suggestive.