Career Concerns and the Dynamicsof Electoral Accountability∗

Matias IaryczowerPrinceton

Gabriel Lopez MoctezumaCaltech

Adam MeirowitzUtah†

May 26, 2020

Abstract

Quantifying the value that legislators give to reelection relative to policysacrifices is crucial to understanding electoral accountability. We estimate thepreferences for office and policy of members of the US Senate, using a struc-tural approach that exploits variation in polls, position-taking and advertisingthroughout the electoral cycle. We then combine these estimates with estimatesof the electoral effectiveness of policy moderation and political advertising toquantify electoral accountability in competitive and uncompetitive elections.We find that senators differ markedly in the value they give to securing officerelative to policy gains: while over a fourth of senators are highly ideological,a sizable number of senators are willing to make relatively large policy con-cessions to attain electoral gains. Nevertheless, electoral accountability is onlymoderate on average, due to the relatively low impact of changes in senators’voting records on voter support.

∗We thank Brandice Canes-Wrone, Michael Gibilisco, Nolan McCarty, Matt Shum, Jorg Spenkuchand audiences at Chicago, Emory, U Penn., Princeton, Rochester, San Andres (Argentina), Stanford,Yale, the ECARES Political Economy conference, and the CIRPEE Conference in Political Economy,for comments. We thank Ashutosh Thakur and Romain Ferrali for excellent research assistance.†Matias Iaryczower: Department of Politics, Princeton University, email: miaryc@princeton.edu;

Gabriel Lopez Moctezuma: HSS, Caltech, email: glopezmo@caltech.edu; Adam Meirowitz: DavidEccles School of Business, University of Utah, email: adam.meirowitz@eccles.utah.edu.

1 Introduction

A core principle of representative democracy is that elections serve to discipline politi-

cians in government. The basic idea is that if a politician were to deviate too much

from the preferences of her constituency, voters would remove her from office (Barro

(1973), Mayhew (1974), Ferejohn (1986)). Thus, politicians who value reelection will

not stray far from voters’ preferred policies.

In practice, however, the power of electoral accountability is not assured, or universal,

but varies across legislators depending on preferences and tradeoffs that are specific to

each politician. In this paper, we estimate a model that decomposes the determinants

of legislative behavior into two components: legislators’ preferences for office versus

policy, and the effectiveness of position-taking and advertising on reelection prospects.

We implement our approach in the US senate. We show that while over a fourth

of senators in our sample are heavily ideological, a sizable number of senators are

generally willing to make relatively large policy concessions to attain electoral gains.

In spite of this, electoral accountability is only moderate on average, because voters

are not highly responsive to position-taking.

Quantifying the value that senators give to reelection relative to policy gains is cru-

cial to understanding electoral accountability, because politicians with different pref-

erences for office and policy have different incentives to cater to voters’ interests.

Indeed, while incumbents who put a large value on reelection would not mind com-

promising their policy ideas to gain any electoral edge, those who put a larger weight

on policy will be less willing to exchange policy concessions for electoral gains (see,

e.g. Alesina and Cukierman (1990)). Moreover, since marginal expected electoral

gains depend on the perceived competitiveness of the election, incumbents with dif-

ferent preferences for office and policy will have different degrees of responsiveness to

voters in safe and competitive elections.

Our approach to estimation exploits variation in polls, position-taking and advertising

expenditures throughout the electoral cycle. To do this, we model explicitly the

dynamic problem of senators running for reelection. The model captures the dynamic

tradeoffs of the politician, as she responds to changing electoral conditions throughout

the electoral cycle.

1

In each period, the senator observes her standing in the polls and chooses a policy

position and TV-ad buys. Both advertising and adopting policies that are in line

with her constituency’s interests affect polls in the next period, but are costly to

the politician. In particular, policy moderation is costly because the senator’s policy

payoff decreases in the distance between the policy position she adopts and her ideal

point. Improving her standing in the polls within cycle doesn’t contribute to the

senator’ payoffs directly, but puts her in a better electoral position as the election

approaches. At election time, the senator gets an office payoff if she attains reelection,

and – to allow the possibility that some senators could also be responsive to voters

even when anticipating large victory margins, as in Bartels (1991) – an additional

benefit from a lopsided win.1

We estimate the model using data for 102 incumbent senators who ran for reelection

at least once between 2000 and 2014 (132 electoral cycles). Identification of the model

parameters relies on the within-cycle dynamics of position-taking and advertising in

response to changing electoral conditions. There are two key ideas here. First, the

level of “effort” exerted in various degrees of competitiveness of the election pins down

the relative value of reelection versus lopsided wins. Larger policy moderation towards

the voter and increased advertising expenditures in “safe” relative to “competitive”

electoral states are consistent with larger values of lopsided wins relative to simply

being reelected. Similarly, higher effort in “competitive” relative to “safe” electoral

states are consistent with a heightened value of reelection relative to a lopsided win.

Second, for any total level of effort, and given the effectiveness of each instrument,

senators who care more about policy will tend to substitute policy responsiveness

with political advertising. Thus, the relative responsiveness of policy and ads in

competitive and safe electoral conditions pins down the relative weight of policy vs

reelection concerns.

Our results provide various novel insights. First, we are able to quantify how each

senator would trade policy concessions for electoral gains, if these were available to

1Whether legislators are differentially responsive when having a large electoral advantage is anempirical question. Bartels (1991) shows that incumbents in safe districts can be as responsive topublic opinion as incumbents in competitive districts. On the other hand, Griffin (2006) and Mian,Sufi, and Trebbi (2010) show that legislators become more responsive to constituency ideology asthe district becomes more competitive. We remain agnostic about the source of this benefit, whichcould include, in addition to a direct valuation of office, a deterrence motive, a stronger bargainingposition within the party, or even the future value of policy decisions upon getting reelected.

2

them. We find that most senators are willing to make significant policy concessions

for a higher probability of retaining office. In particular, the median senator is willing

to give up 2.2% of the distance between party medians (or 5% of the average policy

distance between voters and politicians) for a 1% increase in the probability of reelec-

tion. There is, however, substantial heterogeneity in the importance that senators

give to reelection versus policy. The compensating variation of policy for office gains

is below 1.4% of the distance between party medians for the bottom quartile of our

sample, but above 3.3% for the top quartile.

Second, we consider what tradeoffs are actually available to the politicians. We es-

timate that increasing the incumbent’s TV ads by 1, 000 gross rating points (GRPs)

has a short-run mean impact of increasing its advantage in the polls by about 1 p.p.,

with a smaller long run effect due to decay.2 Our more novel results, in this regard,

are on the electoral return of position-taking. We find that policy moderation towards

the voters increases senators’ advantage in the polls. The effect of position-taking,

thus, varies with the ideological leaning of voters in their state: extreme positions are

penalized in moderate states, but rewarded in more heavily conservative or liberal

ones. Gains and losses from changes in position-taking, however, are moderate in

magnitude. In a moderate state such as Colorado, for instance, a change from a mod-

erate policy position to the most conservative position observed in the data reduces

the incumbent’s advantage in the polls by around 7.9 p.p. on average.

Third, by combining the estimates on senators’ preferences, and the electoral ef-

fectiveness of position-taking and advertising, we are able to assess to what extent

senators would accommodate the preferences of their voters, for varying degrees of

competitiveness of the election. To obtain a comparable measure across senators, we

construct an electoral accountability index (EAI), which measures senators’ predicted

policy positions as a percentage of the distance between their ideal policy and the

vote-maximizing position in their district. We find that for the average senator, elec-

toral accountability is only moderate, reaching a maximum of 30% in competitive

elections, and a minimum of 15% in the presence of a large electoral advantage. Nev-

ertheless, given the heterogeneity in senators’ preferences for office and policy, there

is significant variation in how politicians respond to voters. In fact, in competitive

2Our estimate of the effectiveness of political advertising is in a range consistent with comparableprevious findings in the literature. See Huber and Arceneaux (2007), Stratmann (2009), Gerber,Gimpel, Green, and Shaw (2011), Gordon and Hartmann (2013), Spenkuch and Toniatti (2018).

3

elections, the EAI is close to 70% for senators in the top quartile of career concerns,

and lower than 10% for those in the bottom quartile.

Our results illustrate the usefulness of disentangling politicians’ preferences from the

electoral conditions they face. The results reconcile the general perception that sena-

tors typically do give a large value to being reelected with the relatively low observed

levels of responsiveness to voters on average. We find that the moderate levels of

electoral accountability on average is due to three factors. First, over a fourth of

senators in our sample are heavily ideological, and would only be willing to deviate

from their policy preferences in exchange for a large electoral gain. Second, the elec-

toral return of policy moderation is low, both in absolute terms and relative to the

electoral return of political advertising. Third, a number of senators generally face

a significant advantage in the polls, making them less willing to respond to voters’

preferences in the observed data.

To further clarify the relative role of preferences and the electoral returns of policy

moderation we evaluate a counterfactual exercise in which we increase the electoral

effectiveness of position-taking relative to what we observe in the data. We find that

the relatively low electoral return of policy moderation observed in the data explains

a significant fraction of the difference between observed and ideal levels of electoral

accountability. However, given senators’ preferences, even quadrupling the return of

policy moderation from the levels observed in the data only increases the average

EAI to about 50% in close elections. The even split between voters and politicians

is a substantial concession to voters, but is far from perfect accountability. This

indicates that the weight most senators give to their own ideology is considerable,

and emphasizes the importance of adverse selection on voter welfare.

2 Related Literature

At a broad level, our paper connects with a series of recent papers which have adopted

a structural estimation approach to study how elected politicians respond to electoral

incentives. A key innovation of our paper is to focus on within-cycle dynamics.

In our model, the legislator sequentially makes decisions on policy and advertising

after observing her current advantage in the polls. This allows us to obtain rich

4

heterogeneity in our parameter estimates. In contrast, Diermeier, Keane, and Merlo

(2005) and Lim (2013) focus on the dynamic tradeoffs induced by politicians’ career

decisions. In this context, the relevant dynamics are over terms in office. Likewise,

Sieg and Yoon (2017), Avis, Ferraz, and Finan (2018) and Aruoba, Drazen, and

Vlaicu (2018) focus on the dynamics induced by term limits in models of electoral

competition.3

More specifically, our paper complements a large literature which focused on under-

standing the direct impact of constituency preferences on a legislator’s voting behavior

(Kau and Rubin (1979), Kalt and Zupan (1984), Peltzman (1984), Kalt and Zupan

(1990), Shapiro, Brady, Brody, and Ferejohn (1990), Bender (1991), Levitt (1996),

Mian, Sufi, and Trebbi (2010)). The general finding of this literature is that on aver-

age, legislators are responsive to constituency preferences. In particular, Mian, Sufi,

and Trebbi (2010) use a shock to mortgage defaults that is orthogonal to ideology

among Republicans to separate the influence of ideology from constituent interests,

and conclude that “there is strong evidence that constituent interests affect a politi-

cian’s voting choice”. On the other hand, Lee, Moretti, and Butler (2004) argue that

selection, and not responsiveness to voters, explains the voting behavior in the US

House of Representatives (see also Kau and Rubin (1979)). We contribute to this

literature by estimating senator specific preferences for office vs. policy, and by quan-

tifying how these preferences feedback into heterogeneous responsiveness to electoral

incentives in different electoral conditions. Our results are consistent with the view

that on average senators are (indirectly) responsive to constituency preferences. We

show, however, that the extent of responsiveness varies across legislators and electoral

conditions.

To implement our approach, we estimate the effectiveness of advertising and position-

taking to increase senators’ advantage in the polls. In doing this, we build on a vast

literature.4 As in many of these papers, we use an instrumental variable approach.

3Sieg and Yoon (2017) and Aruoba, Drazen, and Vlaicu (2018) study US governors, Avis, Ferraz,and Finan (2018) focuses on municipalities in Brazil, and Lim (2013) studies elected and appointedjudges in Kansas. Diermeier, Keane, and Merlo (2005) quantify the monetary value of a seat inCongress (i.e., they focus on the value of political office relative to a private sector job, as opposedto relative to policy gains/losses, as in our paper).

4For advertising, see Green and Krasno (1988), Gerber (1998), Huber and Arceneaux (2007),Stratmann (2009), Gerber, Gimpel, Green, and Shaw (2011), Gordon and Hartmann (2013),Spenkuch and Toniatti (2018); for position-taking, see Canes-Wrone, Brady, and Cogan (2002)and Ansolabehere and Jones (2010).

5

However, we estimate the effect of ads and position-taking on a panel, using monthly

variation in polls, position-taking and advertising. Our finding that policy moderation

towards the voters increases senators’ advantage in the polls complements the analysis

of Canes-Wrone, Brady, and Cogan (2002). In their empirical model, the incumbent’s

vote share is assumed to be a function of ideological extremity in roll-call voting,

and Canes-Wrone and coauthors find that incumbents are penalized for ideological

extremity. Our results show that senators are punished for ideological extremity

relative to their district, but that this doesn’t always mean that senators are punished

for taking extreme liberal or conservative positions.

3 Data

Our main data consist of monthly observations of voting support, roll-call votes, and

TV advertising expenditures for 102 incumbent senators who ran for reelection at

least once in the period 2000-2014, for a total of 132 (senator-congress) electoral

cycles.5 We supplement these data with individual characteristics of the senators, as

well as demographic and economic indicators at the state level.

Polls. We use public opinion data for each senate race, collected from Polling Re-

port, Real Clear Politics and Pollster, to measure senators’ advantage in the polls. In

particular, the pointlead of each senator t months away from the election measures

the average difference between the share of respondents in favor of the incumbent

and the challenger in that month. We compute a weighted average over all avail-

able polls, where the weights are inversely proportional to the number of survey

respondents. Whenever possible, we fill gaps in senate races’ opinion data with the

predicted pointlead obtained from incumbent senators’ approval rates, prediction

market data, and national polls that contain individual voters’ congressional approval

(see Appendix F).

Figure 1 illustrates three key facts about the evolution of voter support. First, polls

are informative throughout the electoral cycle. In fact, late realizations of pointlead

are highly predictive of the observed incumbent advantage on election day (upper

5We exclude the electoral cycle 2005/06 since advertising data is not available.

6

0.000

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Figure 1: The upper left panel plots the distribution of realized electoral returns andpointlead a month before the election. The upper right panel plots the correspondingcrossplot. The lower left panel plots the distribution of the average pointlead per senatorover the electoral cycle. The lower right panel plots the distribution of the monthly changein pointlead for each senator and time period.

panel), and throughout the cycle, current values of pointlead are a good predictor

of pointlead in the next period (lower right panel). Second, while on average in-

cumbents enjoy an advantage of close to 20 p.p., there is significant heterogeneity in

electoral security across senators (lower left panel). In particular, the lower quartile

has an advantage of less than 11p.p., while the upper quartile has an average ad-

vantage of more than 28 p.p. Third, there is significant variation in the perceived

electoral advantage a given senator has throughout the cycle. This can be seen in the

lower right panel of Figure 1, which shows the distribution of the monthly change in

pointlead for each senator in the sample.

7

Policy Positions To quantify senators’ policy positions at each point in time,

we use two alternative measures. In our benchmark specification, we use scaling

techniques (Poole and Rosenthal (1985), Clinton, Jackman, and Rivers (2004)) to

obtain a one-dimensional measure capturing variability in senators’ voting records.

Specifically, we define senator i’s position in month t as her “ideal point” estimate

from a Bayesian Quadratic Normal model (Clinton, Jackman, and Rivers (2004)). We

use position only as a summary of senators’ position-taking, and do not interpret

it as a measure of policy preferences, which we then estimate as parameters of the

model. To smooth out the variability of our measure, we use a rolling window of roll

call votes taken within the previous 12 months.

For robustness, we also compute an alternative measure of senators’ policy positions

in each period, partyvote, which we define as the percentage of party votes (votes

for which a majority of Republicans opposes a majority of Democrats) in which the

senator takes the Republican position. The correlation coefficient between partyvote

and position in our sample is 0.83 (see Figure A.1).

The left panel of Figure 2 plots the mean and standard deviation of senators’ policy

positions, where we take as a unit of observation a senator in a specific electoral cycle.

As the figure shows, senators’ policy positions exhibit a relatively large variation

within the cycle, even compared to variation in positions across senators. The figure

also shows that senators who on average take more extreme positions are also those

with a more variable record throughout the cycle. The right panel plots the the

policy positions observed in the data, for Democrat and Republican Senators, vis-a-

vis their advantage in the polls. The figure shows that a larger advantage in the polls

is significantly correlated with more conservative positions for republicans, and more

liberal positions for democrats.6

Advertising. To measure the expenditure in tv-ads of senator i during month t

before the election we use micro data on TV advertisements (Wisconsin and Wes-

leyan Advertisement Project). We compute the monthly TV ad spending for each

incumbent senator by adding the costs of all ads aired during each month on her

6This figure is only intended to describe basic patterns in the data. In the next sections, weuse an instrumental variable approach and the structural model to disentangle the effect of ads andposition taking on next period polls from senators’ choices of ads and position-taking in response totheir perceived advantage in the polls.

8

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Pos

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P−value = 6.595e−05

P−value = 3.15e−06

−2

−1

0

1

2

−40 0 40 80Pointlead

Pol

icy

Pos

ition

Figure 2: Left: Mean and Std. Dev. of Senators’ Policy Positions (by ElectoralCycle). Right: Senators’ Policy Positions and Advantage in the Polls. Red indicatesRepublicans, Blue denotes Democrats.

behalf.7 We then measure the quantity of TV-ad buys in gross rating points using

SQUAD data on ad prices (in dollars per rating point) for the third quarter of each

election year during the period 2002-2010.8 We also use challengers’ TV ad buys,

sponsored by the challenger and third parties on her behalf.

The left panel of Figure 3 plots the cumulative proportion of TV ad expenditures

disbursed up to each month before the election. Senators tend to concentrate TV ad

expenditures in the last 6 months before the election, and typically spend more than

50% of their total TV ads expenditures in the last three months before the election.

Nonetheless, there is considerable variability across senators, with several senators

starting to spend in the third or fourth month before the election. The right panel

of Figure 3 shows that senators tend to spend more in TV ads as elections become

7The estimated cost of airing each TV ad is provided by the Campaign Media Analysis Group(CMAG) based on airing day, time, and media market the ad aired on.

8Ad price data comes from Martin and Peskowitz (2015). Prices are weighted by the fraction ofthe population in each congressional district residing in a given media market. We take the averageacross districts within a state as our measure for price at any given senate race. As the price datais not publicly available for the elections of 2000/01 and 2011/12, for these cycles we use the pricesfor the 2002/03 and 2009/10 elections, respectively.

9

more competitive (no causal emphasis intended).

11 10 9 8 7 6 5 4 3 2 1

Months to Election

Cum

mul

ativ

e T

V−

ads

/ Tot

al T

V−

ads

0.0

0.2

0.4

0.6

0.8

1.0

Close Solid LandslideT

V−

ads

(GR

P P

oint

s)0

5000

1000

015

000

2000

0

Figure 3: Average TV ad buys by time to election and poll advantage.

Additional Variables. We incorporate various senator and race-specific charac-

teristics, including party, gender, seniority, committee service, leadership positions,

and state-level presidential vote share. We also control for contested and uncon-

tested primary elections for incumbents and challengers, demographic characteristics

at the state level (median household income, education, % older population, % black

population, % hispanic population), and economic indicators that vary both across

states and within electoral cycles (unemployment, economic activity). To inform our

measure of district ideology, we follow Canes-Wrone, Brady, and Cogan (2002) and

compute the average vote spread for the period 2000-2012 between the Republican

and Democrat presidential candidates in each state, presrep.margin, using data from

Dave Leip’s Atlas of U.S. Presidential Elections. We refer the reader to Appendix A

for a description of these data, and descriptive statistics of all variables.

10

4 The Model

We consider the decision-making problem of an incumbent politician T months away

from the election. At the beginning of period t, the incumbent observes her advantage

in the polls, pt ∈ P . After observing pt, the incumbent decides (i) a policy position

xt ∈ Πx and (ii) expenditure in TV ads, et ∈ Πe, where we assume for simplicity that

Πx,Πe are finite sets. We let yt ≡ (xt, et) denote the endogenous variables in period

t, and zt ≡ (pt, yt).

Both position taking and TV ads affect next period polls. In particular, we assume

that the incumbent’s advantage in the polls evolves stochastically, with conditional

mean

E[pt−1|zt] = π1pt + π2(xt − ε)2 + π3

√et + Ct,

where ε denote voters’ preferred policy position, and Ct denotes senator and race-

specific controls, including the challenger’s advertisement expenditures.

Investing e dollars in TV ads in period t has an opportunity cost C(et) = γe2t .

Pandering to voters, in turn, is costly to the politician who cares about ideology. In

particular, we assume that when the politician takes a position xt in period t she gets

a flow payoff u(xt, θ) = −λ(xt − θ)2, where θ ∈ R is the politician’s ideal point and

λ is the importance of ideology vis-a-vis office. As is customary in the literature, to

capture other factors that affect the decision of the politician but are unobserved by

the researcher, we assume that a choice yj ≡ (xj, ej) also generates flow payoffs µj,

where µj is known to the politician, but from the perspective of the researcher is an

i.i.d. random variable with pdf g(·).

Voter support at election time, t = 0, determines the result of the election. We

assume that the politician gets an office payoff ω ≥ 0 if she wins the election. To

consider the possibility that some senators could also be responsive to voters even

when anticipating large victory margins, as in Bartels (1991), we assume that the

incumbent obtains an additional benefit α ≥ 0 from a lopsided win.9 We let L =

{p0 ∈ P : p0 < 1/2} denote the event in which the politician loses the election,

M = {p0 ∈ P : p0 ∈ [1/2, p)} denote a close win, and H = {p0 ∈ P : p0 ≥ p} denote

9Note that since the politician’s beliefs are stochastically increasing in current polls pt, thisspecification already induces a continuous increasing continuation value.

11

a lopsided win, for p ∈ [1/2, 1].10 The payoff of losing the election is normalized to

zero.

The Bellman equation for the incumbent is

Wt(pt, µt) = maxyt

{λ(xt − θ)2 − γ(et)

2 + E[W t−1(pt−1)

∣∣ zt]+ µ(yt)}, (4.1)

where W t(pt) ≡ Eµ [Wt(pt, µt)], and

E[W 0(p0)

∣∣ z1

]≡ Pr(p0 ∈M

∣∣z1)ω + Pr(p0 ∈ H∣∣z1)(ω + α).

4.1 Identification: From Model Parameters to Data

The solution to the politician’s problem is a policy function {y∗T−r(·)}T−1r=0 , where

in each t, y∗t (pt, µt) solves (4.1) in state (pt, µt). At each t, the politician balances

the additional cost of ads and position-taking with their marginal return in terms

of increasing the probability of being in a more favorable state next period, and

ultimately winning the election.

Since senators with different preference parameters will resolve these tradeoffs differ-

ently, leading to different choices in each state, observing senators’ choices over the

electoral cycle allows us to recover these preference parameters. We illustrate this

variation in Figure 4.

The first chart plots the policy functions for a politician with a relatively low will-

ingness to compromise her policy position for electoral gains (ω = 0.05, α = 0.21).

The politician in this example maintains a policy position close to her ideal point

regardless of her advantage in the polls, with the brunt of her reelection effort falling

on TV ads. In the second example (center panel) we consider a politician who is

much more willing to concede policy to attain reelection, and gives no value to lop-

sided wins (ω = 0.69, α ≈ 0). Given these preferences, the politician holds a policy

position close to her ideal point (θ = −0.62) when she enjoys a large advantage in the

polls, but significantly moderates her policy position towards the voters’ preferred

10In the main specification, we define a lopsided win as a margin of victory of at least 15 p.p.. InAppendix H, we show that the parameter estimates and policy functions are qualitatively identicalwith alternative thresholds.

12

−20 0 20 40 60

0.45

0.50

0.55

0.60

0.65

Pointlead (pit)

Sta

nce (

x it)

t = 1t = 2t = 3t = 4t = 5

−20 0 20 40 60

−0.

70−

0.65

−0.

60−

0.55

−0.

50−

0.45

−0.

40

Pointlead (pit)

Sta

nce (

x it)

t = 1t = 2t = 3t = 4t = 5

−20 0 20 40 600.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

Pointlead (pit)

Sta

nce (

x it)

t = 1t = 2t = 3t = 4t = 5

−20 0 20 40 60

5000

1000

015

000

Pointlead (pit)

tv−

ads (

e it)

t = 1t = 2t = 3t = 4t = 5

−20 0 20 40 60

500

1000

1500

2000

Pointlead (pit)

tv−

ads (

e it)

t = 1t = 2t = 3t = 4t = 5

−20 0 20 40 60

600

800

1000

1200

1400

1600

1800

2000

Pointlead (pit)

tv−

ads (

e it)

t = 1t = 2t = 3t = 4t = 5

Example 1 Example 2 Example 3

ω = 0.05, α = 0.21 ω = 0.69, α = 0 ω = 0.17, α = 0.31

Figure 4: Predicted Position-Taking (top) and TV-ad buys (bottom) for individualsenators at periods t = 1, . . . , 5. Dashed gray lines depict senators’ ideal policies (θ).

policy (and increases ad expenditures) as the election gets more competitive. In the

third example, we consider a senator who gives a large value to office vis-a-vis policy,

but puts significant value on winning by a large margin (ω = 0.17, α = 0.31). In

this example, the politician is responsive to voters even in safe races. Because the

senator cares about winning by a large margin more than simply winning reelection,

the degree of responsiveness towards the voters is not monotonic in electoral support.

Note that α = 0 implies that the politician is not responsive to voters’ preferences

in uncompetitive elections, as in example 2. Thus, larger changes in position-taking

towards the voter and increased advertising expenditures in “safe” electoral states

relative to “competitive” electoral states are consistent with lower values of ω/α, as

in examples 1 and 3. Similarly, larger changes in position-taking towards the voter

and increased advertising expenditures in “competitive” electoral states relative to

13

“safe” electoral states are consistent with larger values of ω/α, as in example 2.

For any total level of effort, senators who care more about policy will tend to substi-

tute policy responsiveness with political advertising. Thus, the relative responsiveness

of policy and ads in competitive and safe electoral conditions pins down the relative

weight of policy vs reelection concerns, ω/λ. The cost parameter γ/λ then rational-

izes the overall level of ad expenditures. Given these parameters, we can compute

the pattern of responsiveness to voters in each electoral condition. We then obtain

the ideal policy θ as the policy chosen by the senator in electoral states in which she

is not responsive to voters. In the next section, we describe more formally how this

basic intuition translates into our estimation strategy.

5 Estimation

We are interested in the estimation of the structural parameters of the model pre-

sented in Section 4: ideal points, relative weights of ideology vis-a-vis office rents, and

cost parameters. Let ρi ≡ {θi, λi, ωi, αi, γi} denote these individual-specific parame-

ters, with ρ ≡ {ρi}Ni=1, and let ψ denote the parameters of the transition function,

governing the evolution of the state as a function of current state and endogenous vari-

ables, zi,t ≡ (yi,t, pi,t). Given panel data {zi,t} for senators i = 1, . . . , N , the likelihood

of choices yi,t by senator i in period t can be written as the product of the transition

probability Pr(pi,t|zi,t+1;ψ) and the conditional choice probability Pr(yi,t|pi,t; ρi, ψ):

L(ρ, q) =N∏i=1

T∏t=1

Pr(yi,t|pi,t; ρi, ψ)× Pr(pi,t|zi,t+1;ψ), (5.1)

Since the transition function does not depend on either individual-specific parameters

(ρ) or individual unobservable state variables µjt , a consistent estimate of the transi-

tion function can be obtained by estimating it separately. Because this significantly

reduces the computational burden, we estimate the parameters of the model in two

steps. In the first step, we estimate the transition parameters ψ, pooling information

across senators. In the second step, we estimate the individual-specific parameters

ρ given the estimated transition probabilities (see Rust (1994), Aguirregabiria and

Mira (2010)).

14

Suppose first that ψ is known, and consider the problem of estimating the structural

parameters ρ. The difficulty in estimating ρ directly from the likelihood in (5.1) is

that the conditional choice probability Pr(yi,t|pi,t; ρi, ψ) is not a known function of ρi.

Instead, it is given by the optimal response of the politician with characteristics ρi in

each state (pi,t, µi,t). To tackle this problem, we use a version of the nested fixed point

algorithm (NFXP) first proposed by Rust (1987).11In essence, this consists of an outer

and an inner loop. In the inner loop, we obtain the conditional choice probability

Pr(yi,t|pi,t; ρi, ψ) for each given trial parameter ρi, by solving the dynamic problem

of the senator with preferences ρi. To do this, we discretisize the state space, letting

pi,t take values in a finite set. In the outer loop, we search over the parameter space

to maximize the likelihood, with the conditional choice probabilities associated with

each trial parameter given by the inner loop.

To relate senator’s preference parameters to relevant observable attributes, while still

allowing heterogeneity conditional on covariates, we model structural parameters as

latent random variables drawn from distributions with parameters that are functions

of senator characteristics, including party, gender, seniority, and leadership positions.

This allows the preference estimates to be informed by both their effect on conditional

choice probabilities and observable characteristics (see Appendix B for more details).

To estimate the parameters of the transition function, we estimate the linear model

pi,t+1 = π0 + π1pi,t + π2(xi,t − εi)2

+ π3√ei,t + π4

√echi,t +Q

′

itβ + ζc + εi,t.(5.2)

Here ψ = {π, β, φ, ζc} is the vector of first-stage parameters of interest, Qit is a vector

of senator and state specific characteristics that include senator characteristics and

state socio-economic indicators, and ζc are party-Congress fixed effects, which capture

all session-specific shocks to polls for each party.12

11Alternatively, one could in principle use the approach pioneered by Hotz and Miller (1993),and later developed further by Bajari, Benkard, and Levin (2007), in which value functions andstructural parameters are recovered from conditional choice probabilities (CCPs) without explicitlysolving the optimization problem for each trial value of the parameters. Given our data, however,any viable estimation of CCPs capturing heterogeneity across senators would require that we im-pose substantial parametric assumptions to “pool” legislator data. This would impose arbitraryconstraints on legislators’ predicted behavior, leading to significant bias in the resulting estimates.

12Heterogeneity at the senator level is captured via senator-specific covariates. This allows us tolink senators’ characteristics to their policy functions in the dynamic model.

15

The specification in equation (5.2) allows the effect of position (xit) on voter support

to differ based on the incumbent’s state electoral preferences through the term εi ≡a+ b× (presrep.margin), where a and b are coefficients to be estimated. Thus, for

example, an incumbent senator taking a more conservative position can increase voter

support in a conservative state but decrease voter support in a liberal state. This

specification also controls for the effect of unemployment and economic activity, which

vary both across senators and over time. The remaining individual-specific covariates

capture the effect of race characteristics on voter support. We cluster errors at the

senator-congress level to account for heteroskedasticity and serial correlation at the

electoral race level.

Differently than in a static model with observations at the electoral cycle level, equa-

tion (5.2) relies on within-cycle variation. This ameliorates the effect of potential

confounders by controlling for past polls. To account for possible correlation between

time-varying unobservables and tv-ads or position that is not captured in previous

polls, we use an instrumental variable approach.13

As instruments for TV ads of a senator i, we use variation in TV ads in House races

within i’s state, as well as in TV ads from neighboring states. The idea is to use ads

in races that face similar changes in ad costs, but that do not affect senator i’s voter

support directly. We then exploit a similar idea to instrument for policy positions.

In particular, we instrument senator i’s position with the position of the median

House representative from the senator i’s party and state. The exclusion restriction

assumption is that changes in the position-taking of members of the House in the

state of Senator i do not directly affect senator i’s voter support. Instead, changes in

the political environment that is common to both representatives and senator of the

same state lead to similar policy responses by both types of legislators.

As additional instruments for policy positions we use economic conditions, measured

by unemployment (unemployment) and leading indicators of economic activity (lead)

in “neighboring” states. In the definition of neighbor, here we substitute geographical

distances with distances in ideological affinity, as measured by cosponsorship relations.

This builds on the idea that senators will tend to support the positions of like-minded

13A number of papers resorted to IV approaches to estimate the effect of ads on voter support.See Green and Krasno (1988), Gerber (1998), Stratmann (2009), Gordon and Hartmann (2013),Huber and Arceneaux (2007), and Spenkuch and Toniatti (2018). To the best of our knowledge,this issue has not been similarly addressed for position-taking.

16

senators, that are, in turn, a function of their own economic conditions, which are

independent of variation in next period’s voter support of the senator of interest.14

We estimate equation (5.2) on a balanced panel dataset. That is, we impute remaining

missing pointlead observations via the EM algorithm, which is a commonly applied

method to efficiently analyze unbalanced panels (see Appendix G for details). This

allows us to exploit all available information in the data, while avoiding potential

estimation biases in both first and second stages that might arise when the pattern

of missing data is related to observables.15

6 Results

In this section, we report our main results. We begin by describing our estimates

of senators’ preferences for office and policy. To facilitate the interpretation of the

structural parameters, we maintain a fixed policy position x in the final T periods

before reelection. Letting π and π+ denote the probability of a close and a lopsided

win respectively, we can can write senator i’s payoff (ignoring TV advertisement costs)

as

Ui = −λiT (x− θi)2 + ωiπ + (ωi + αi)π+ (6.1)

It follows from (6.1) that the relevant parameter determining how each politician

trades off an increase in the probability of winning office with policy losses is the

ratio ωi/λi. Similarly, the “willingness to pay” for an increase in the probability of

winning by a large margin is given by (ωi +αi)/λi. Figures D.4 and D.5 in Appendix

D plot the estimates of these quantities for each senator in the sample, with 90%

bootstrap confidence intervals.

To provide a more readily interpretable figure of senators’ preferences for office vs

14For robustness, in Appendix C we re-estimate the model using total spending by incumbentsand challengers in the House, and total spending by incumbent and challenger in neighboring states,as instruments for TV ad spending of incumbent and challenger. Table C.3 presents instrumentrelevance, and table C.4 the first stage results. The estimates are qualitatively similar to the resultsin our benchmark specification, while the magnitude of the effect is slightly larger in the alternativespecification.

15The estimates of the first-stage using the incomplete data on voting support are almost identicalto those with the balanced panel. This indicates that the bias induced by the presence of missingpointlead observations is negligible (see Table G.1 and Figure G.3).

17

policy, we compute the change in policy each senator would be willing to concede for

a 1 p.p. increase in the probability of a close win. We refer to this quantity as the

compensating variation. From (6.1), if we consider the change from an initial policy

position x0 = θi,

CVi ≡

√(ωiλi

)1

T∆π (6.2)

Because the underlying space of policies is only identified up to an affine transforma-

tion, in Figure 5 we plot the compensating variation for each senator as a proportion

of the distance between party medians, fixing T = 6.

18

BOXERREED

HATCHDURBININOUYELEAHY

FEINSTEINMIKULSKISHAHEEN

LEVINSCHUMERMURRAY

STABENOWKENNEDY

BAUCUSREID

BYRDGILLIBRAND

CANTWELLMCCONNELL

LAUTENBERGMCCASKILL

LANDRIEUKERRY

ROCKEFELLERROTH

KLOBUCHARCOCHRAN

HAGANLINCOLNMCCAIN

LUGARCASEYKOHL

SARBANESSTEVENS

BEGICHDOLE

JOHNSONFEINGOLDMERKLEY

BROWNPRYORCOONS

GORTONLOTTROBB

CARPERNELSON

HUTCHISONDODD

SPECTERWHITEHOUSE

CARDINSNOWE

WARNERWYDEN

SANDERSCLELAND

UDALLMENENDEZ

BONDFRANKEN

GRASSLEYBAYH

BINGAMANUDALL

DOMENICITESTER

MANCHINCRAPO

COLLINSGREGG

LIEBERMANBROWNBACK

ROBERTSGRAMS

CORNYNALLARDVITTER

BUNNINGHUTCHINSON

RISCHSESSIONSGRAHAM

ABRAHAMVOINOVICH

COLEMANFRIST

SMITHDEWINE

SANTORUMHAGEL

SUNUNUCOBURNWICKER

ALEXANDERBROWNCRAIG

ISAKSONCHAMBLISS

BURR

Percentage Change

0 2 4 6 8 10 12 14

Figure 5: Compensating Variation. Policy concession each senator would be willing togive up for a 1 p.p. increase in the probability of a close win, as a proportion of thedistance between party medians. Blue denotes democrats, red denotes republicans.

As the figure illustrates, most senators are willing to make significant policy conces-

sions for a higher probability of retaining office. The senator at the median of the

distribution is willing to give up 2.2% of the distance between party medians (or 5%

of the average policy distance between voters and politicians) for a 1% increase in

19

the probability of reelection. There is, however, substantial heterogeneity in the im-

portance that senators give to reelection versus policy. The compensating variation

of policy for office gains is below 1.4% of the distance between party medians for the

bottom quartile of our sample, but above 3.3% for the top quartile.

Similarly, we compute the compensating variation for a 1 p.p. increase in the prob-

ability of a lopsided win. This is illustrated in Figure D.6 in the Appendix. The

typical senator gives a non-negligible value to lopsided wins. The median willingness

to pay goes up from 2.2% for a 1 p.p. increase in the probability of a close win, to

3.0% for a corresponding increase in the probability of a lopsided win. This is in

fact the case for most senators in the sample. The upper bound of the lower quartile

increases from 1.4 % of the distance between party medians for a close win to 2.6 %

for a lopsided win, and the upper bound of the third quartile increases from 3.3% to

4.5 %. This indicates that a large fraction of senators will tend to be responsive to

voters even in uncompetitive elections.

The variation in office motivation correlates with observable characteristics of the

senators. We find that party leaders, committee chairmen and more senior senators

are, on average, more willing to sacrifice policy for electoral gains. While the average

backbencher is willing to sacrifice 2.6 p.p. of the distance between party medians for

a 1 p.p. increase in the probability of a close win, the policy concession increases

to 3.7 p.p. for a majority party leader, and to 4.5 p.p. for a committee chairman.

We also find that female senators on average give a larger weight to office than male

counterparts. In particular, the compensating variation increases to 4.5 p.p for female

senators, compared to 2.4 p.p. for male senators. In terms of seniority, the average

policy concession of a member with 16 years in the Senate is about 0.9 p.p. more

than for a senator with 5 years of experience.

We also find that Republicans tend to be more policy motivated on average. The av-

erage policy concession for Republican senators is 1.7 p.p. lower than for Democrats.

This is already clear in Figure 6, where republicans are heavily represented among

the senators with the strongest policy motivation.

Policy Preferences. Because the impact of position-taking on electoral results

varies depending on the senators’ popularity and time to election, certain votes will be

20

more congruent with their policy preferences than others. This implies, quite simply,

that senators’ votes on policy issues are not an unfiltered expression of ideological

preferences, but rather strategic choices conditioned on the competitiveness of the

race at the time of voting.16 Our approach allows us to separate preferences from

strategic position-taking by estimating which votes are more or less likely to be sincere

representations of preference and which are likely to involve adjustments for electoral

reasons.

Taking strategic position-taking into consideration leads to some significant differ-

ences with the sincere voting estimates. In particular, the distribution of ideal points

obtained from our model is more heavily populated in the extremes of the politi-

cal spectrum than the distribution of ideal points in the sincere voting framework.

This is illustrated in Figure 6, which compares our ideal point estimates side by side

with IDEAL estimates (Clinton, Jackman, and Rivers (2004)). The difference in the

two sets of estimates indicates that while some senators are “pandering in” to more

moderate voters, as the conventional wisdom indicates, others are “pandering out”

to relatively more extreme voters.17

All in all, however, we find that the ordering of senators’ ideal policies corresponds

well to the previous estimates. Figure D.1 in the Appendix presents our ideal point

estimates for each senator in the sample, with 90% bootstrap confidence intervals.

Efficacy of Advertising and Position-Taking. In our previous results, we

discussed senators’ preferences for office and policy: the policy concession senators

would be willing to give to attain a gain in the probability of being reelected. In

determining when to compromise in policy, or to what extent, however, senators

must judge the effectiveness of the instruments at their disposal: how much would a

policy concession actually increase voter support. Similarly, in deciding how much to

spend on TV ads, senators must balance the cost of spending with the effectiveness

of TV ads.

16While this statement seems uncontroversial, the available estimates of legislators’ ideal policies(Poole and Rosenthal (1985), Clinton, Jackman, and Rivers (2004)) are derived under the assumptionthat all votes in a legislators’ voting records are sincere reflections of their preferences (see howeverClinton and Meirowitz (2004), Iaryczower, Katz, and Saiegh (2013), Iaryczower and Shum (2012),and Spenkuch, Montagnes, and Magleby (2018).

17This is further illustrated in Figure D.2 in Appendix D, which plots senators’ ideal policies andthe poll-maximizing positions computed from our first stage estimates.

21

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Figure 6: Ideal Point estimates (θ) vs sincere estimates (IDEAL)

In this section, we describe our estimates of the effectiveness of ads and position-taking

to change voter support. Table 6 presents the key estimates (table C.2 in Appendix

C presents the full set of estimates). Column (1) presents the OLS estimates for

a specification without senator and state-specific factors. Column (2) adds senator-

state controls and fixed effects for each party in each electoral cycle. Column (3) – our

main specification – reproduces (2) with instruments for TV-ads and position-taking.

Column (4) maintains the specification in column (3), with our alternative measure

of position-taking (partyvote).

We find that policy moderation towards the voters shifts the distribution of voter

support.18 This induces quite different incentives for senators running for reelection

in moderate, conservative and liberal states. The left panel of Figure 7 plots how voter

support changes with position-taking in a moderate state such as Colorado. As the

figure shows, the poll-maximizing position is a centrist position, and politicians taking

extreme liberal or conservative positions on average suffer an electoral cost. Gains

and losses from changes in position-taking, however, are moderate in magnitude. In

18As can be seen in column 4, this is also the case when we measure position-taking withpartyvote.

22

fact, changing from a moderate position (around 0) to the most conservative position

observed in the state in the sample (about 1), reduces the incumbent’s advantage in

the polls by around 7.9 p.p. on average, at the point estimate.

Table 1: First Stage Results (Compact)

Dependent variable: pi,t−1

OLS OLS IV IV (partyvote)

(1) (2) (3) (4)

pi,t 0.816∗∗∗ 0.763∗∗∗ 0.720∗∗∗ 0.691∗∗∗

(0.023) (0.025) (0.028) (0.032)(xi,t − ε)2 −1.533∗∗∗ −2.199∗∗∗ −10.152∗∗∗

(0.507) (0.829) (3.225)(xpv

i,t − ε)2 −37.049∗∗∗(7.060)√

ei,t 0.017∗∗∗ 0.020∗∗∗ 0.034∗∗ 0.051∗∗∗

(0.007) (0.007) (0.013) (0.015)√echalli,t −0.047∗∗∗ −0.049∗∗∗ −0.053∗∗∗ −0.057∗∗∗

(0.009) (0.010) (0.015) (0.016)

Observations 1,584 1,584 1,416 1,138Senator/District Covariates Yes Yes Yes YesCongress-Party FE No Yes Yes YesAdjusted R2 0.676 0.683 0.640 0.640

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.

Robust standard errors clustered at the senator-congress level in parentheses.

The right panel of Figure 7 plots how voter support changes with position-taking in

a conservative state such as Utah, and a liberal state, Massachusetts. In contrast to

the case of Colorado, senators taking moderate policy positions are penalized at the

polls in both states. In Utah, a change from the most conservative position observed

in the sample (position ≈ 1) to the most liberal policy position observed in the

sample (a moderately conservative position = 0.23) reduces the incumbent’s lead

by about 5 p.p. In Massachusetts, a change from the most liberal position observed

in the sample (position ≈ -1) to the most conservative policy position observed in

the sample (a moderately conservative position = 0.25) reduces voter support by

about 12 p.p.

23

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it)

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it)

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Effect of position on voter support Effect of position on voter support

in a moderate state (Colorado) in a Con/Lib state (Utah/Mass.)

Figure 7: Effect of Position Taking on Voter Support.

Political advertising also shifts the distribution of voter support, for both incumbent

and challenger. At our point estimates, increasing incumbent’s TV ads by 1, 000

GRPs (or 200 ads in 5% rating shows) has an immediate impact of increasing next

period pointlead by around 1 p.p. at the median ad buy. An increase of 1, 000

GRP’s in the challenger’s TV ads decreases the incumbent’s next period pointlead

by around 2.1 p.p.19 The long run effect of ads is considerably smaller, due to the

estimated decay in the effectiveness of ads, which depreciates around one fourth per

month (see Figure 7 in the Appendix).20

19Our estimates are in line with comparable estimates. In House races, Stratmann (2009) findsthat increasing incumbent’s (challenger’s) advertising by 1000 GRP’s increases her pointlead by 2.4p.p. (4.2 p.p.). For Presidential elections, Huber and Arceneaux (2007) estimate a comparable effectof 0.5 p.p. - 0.8 p.p. and Spenkuch and Toniatti (2018) find a comparable effect of 0.7 p.p., whileGordon and Hartmann (2013) estimate a larger effect, of about 3 p.p. for Republicans, and 3.4 p.p.for Democrats.

20This depreciation is consistent with the findings of Gerber, Gimpel, Green, and Shaw (2011). Ina field experiment on the 2006 Gubernatorial campaign in Texas, Gerber et al find a large (5 p.p.)short run effect of ads on vote shares, but a pronounced decay, with advertisement effects vanishingafter a couple of weeks.

24

Electoral Accountability. We now turn to politicians’ behavior in office, to

address electoral accountability. We want to know to what extent senators adjust

their position away from their ideal points and towards the electorate they represent,

and how this varies according to their perceived electoral advantage.

To do this, we combine our estimates of senators’ individual preferences for office and

policy – the policy concession senators would be willing to give to attain a gain in

the probability of being reelected – with the effectiveness of the instruments at their

disposal; i.e., how much would policy concessions or advertising actually increase

voter support. The solution to this problem for each senator i is precisely the policy

function {yi∗T−r(·)}T−1r=0 , where in each t, yi∗t (pt, µt) gives the optimal response of senator

i in state (pt, µt), given preferences ρi, and given the transition function parameter

estimates ψ.

To summarize aggregate patterns of electoral accountability we compute an aggregate

policy function. The first step is to make responsiveness in policy choices comparable

across senators. In order to do this, we construct an electoral accountability index,

EAIit, defined by the relative weight of voters’ preferences in i’s optimal policy posi-

tion at time t and poll advantage p, as given by i’s policy function,

EAIit ≡x∗(p, t, ρi)− θi

(ξi − θi)× 100, (6.3)

where ξi denotes the policy position that maximizes i’s electoral support. An electoral

accountability of 100 in state (pt, t) means that the senator’s predicted position in

state (pt, t) is the policy position that maximizes voter support, x∗(p, t) = ξi, while

EAI= 0 means that the senator is predicted to take a policy position equal to his

preferred ideal policy x∗(p, t) = θi.21

We then compute the average EAI across individual senators, as a function of their

advantage in the polls. In the left panel of Figure 8 we plot the average for the full

sample and for each quartile of the career concern distribution, as ranked by λ.

There are three key takeaways from the figure. First, there is a substantial amount

21Conceptually, this index allows us to contrast the related concepts of accountability and rep-resentation. Accountability involves institutions that induce elected officials to select x close to ξwhereas representation involves institutions that select elected officials with θ close to ξ. In thislight the EAI index measures accountability independent of the degree of representation.

25

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Figure 8: Aggregate policy functions: predicted Electoral Accountability Index andTV advertising as a function of electoral advantage. Quartiles of the distribution ofλ (policy) and λ/γ (ads).

of heterogeneity in politicians’ responses to their voters. Senators in the top quartile

of career concerns have an electoral accountability index close to 70% in close elec-

tions. On the other extreme, senators in the bottom quartile never exceed 10%. As

a result, their policy positions are almost exclusively determined by their own policy

preferences. Second, even at its maximum level (in close elections) the average elec-

toral accountability index is only slightly above 30%, and goes down to about 15%

for a large electoral advantage. Thus, even at its peak, on average politicians’ policy

preferences have a much larger weight than constituency preferences in determining

senators’ policy positions.

Third, our results shed light on the mixed support in the literature for the marginality

hypothesis, which asserts that legislators will tend to be more responsive to voters

when their seat is in danger (see Bartels (1991), Ansolabehere, Snyder Jr, and Stew-

art III (2001), Griffin (2006), Mian, Sufi, and Trebbi (2010)). Our results indicate

that while individual senators can be equally or even more responsive when elections

are not close, on average senators are more responsive to constituency interests in

competitive elections than when they anticipate they will win by a large margin.

26

The right panel of Figure 8 shows a similar exercise with spending in TV ads. Since

TV ad spending is directly comparable across senators, we plot predicted TV ad

spending for the average senator, and for each quartile in the ranking according to

λ/γ, without any further transformation. As with policy, average predicted TV ad-

spending also follows a pattern consistent with the “marginality hypothesis”: the

average TV-ad buy is about 2500 GRPs for large leads (500 ads in 5% rating shows),

but increases to about 6000 GRP’s per month (1200 ads in 5% rating shows) in

close elections. This change is much more pronounced for senators with high career

concerns, who go from an average of less than 7000 GRPs when enjoying large leads,

to about 16000 GRPs in close elections.

Effectiveness of Policy Moderation and Accountability. The analysis in this

paper allows us to disentangle the contribution of politicians’ preferences and of the

electoral effectiveness of policy moderation on electoral accountability. In this section,

we perform a counterfactual exercise to further clarify the extent to which the low

returns of policy moderation hinder electoral accountability. To do this, we recompute

senators’ optimal choices (given the estimated preference parameters) assuming that

the effectiveness of position-taking is twice that estimated from the data. We then

redo the exercise assuming policy moderation has an effect that is four times larger

than in our estimates. Figure 9 shows the average electoral accountability index in

the data and in the counterfactuals, for each quartile of the distribution of career

concerns.

Doubling the return of policy moderation increases the average EAI to about 40% in

close elections, and to more than 30% when the incumbent has an advantage of 20%

in the polls. The top two quartiles experience an even larger change, increasing EAI

for the top quartile to almost 80% in close elections. Senators in the bottom quartile,

however, remain relatively unresponsive, with an EAI below 20% in close elections.

Quadrupling the electoral return of policy moderation, in turn, increases the average

EAI to about 50% in close elections, and to more than 40% when the incumbent has

an advantage of 20% in the polls.

We read these results as offering two conclusions. First, the relatively low electoral

return of policy moderation explains a significant fraction of the difference between

observed and ideal levels of electoral accountability. However, given senators’ prefer-

27

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EA

I %First QuartileSecond QuartileThird QuartileFourth QuartileAverage

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020

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80Polls' Spread %

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data 2x return 4x return

Figure 9: Counterfactual: Electoral Accountability Index in the data, and for anexogenous increase (2x, 4x) of the electoral returns to policy moderation. (Quartilesof the distribution of λ).

ences, even quadrupling the return of policy moderation from the levels observed in

the data only increases the average EAI to about 50% in close elections. The even

split between voters and politicians is a substantial concession to voters, but is far

from perfect accountability. This indicates that the weight most senators give to their

own ideology is considerable, and emphasizes the importance of adverse selection on

voter welfare.

6.1 Model Fit

In Appendix E, we assess the fit of the model. In sample, the model fits the data

remarkably well (see Figure E.1). A more demanding test is to evaluate how the

model fits the data out of sample. To do this, we exploit the fact that our data

contains multiple instances in which senators run two or even three times for office.

Accordingly, we re-estimate the model parameters using only the first instance in

which a senator runs for office in the sample, and use the resulting estimates to

predict their behavior in the second or third run. Overall, we conclude that the

model provides a good approximation to the data, both in and out of sample.

28

6.2 Robustness: Strategic Challenger

In the baseline model we focused on the optimal dynamic behavior of the incumbent,

fixing the challenger’s spending at the levels we observe in the data. This simplified

the presentation of the problem, and allowed us to focus on the core issue of electoral

accountability. The cost of this simplification is that the model doesn’t take into

consideration the strategic responses of the challenger in states that are not observed

in the data. In Appendix I we endogeneize the behavior of the challenger, and estimate

the resulting dynamic game. To avoid multiplicity of equilibria, we assume that in

each stage politicians move sequentially, with the challenger moving first.

−2 −1 0 1 2

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Figure 10: Incumbent’s preference estimates in the Baseline Model and in the Ex-

tended Model with endogenous challenger response.

Figure 10 shows the distribution of the key structural parameter estimates in the

Baseline Model and in the Extended Model with endogenous challenger response. As

the figures show, the incumbent’s parameter estimates of the benchmark model re-

main essentially unchanged. The new parameter in this model is the cost of spending

for the challenger. Our estimates imply that incumbents enjoy a substantial cost ad-

vantage, which partly explains the fact that incumbents outspend challengers almost

four to one (see Figure J.2). Figure J.3 plots the aggregate equilibrium position-taking

and TV ad buys by both the incumbent and challenger, as a function of the incum-

bent’s electoral advantage. As the figure shows, the main results of the benchmark

model are qualitatively unchanged: equilibrium electoral accountability and TV ad

29

buys by the incumbent increase as the election gets closer, when the race is more com-

petitive, and when the incumbent cares more about retaining office. Quantitatively,

the results are also largely similar to the benchmark.

Crowding-Out of Electoral Accountability. Endogeneizing the challenger’s

response allows us to compute a second counterfactual, which is centered on political

advertising. As it is clear from our analysis, politicians see advertising as a substitute

to policy compromise. We are interested in quantifying the extent to which advertis-

ing crowds-out electoral accountability. To do this, we quantify what policy choices

senators would have made in the absence of advertising, and then compare electoral

accountability in the counterfactual with the level of electoral accountability in the

data.22

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Figure 11: Counterfactual: Ban of Political Advertisements

Figure 11 presents the results. As the figure shows, banning advertisement would

increase electoral accountability in close elections by 12 p.p. for the average senator,

22In a related exercise, Gordon and Hartmann (2013) estimate the effect of eliminating ads onvote shares in presidential elections. They show significant changes on electoral returns underno advertisement. Our policy counterfactual complements their results, capturing the effect ofadvertising on policy responsiveness.

30

and by about 25 p.p. for the senators in the top quartile of the distribution of office

motivation. This changes electoral accountability in close elections from 35% to close

to 47% for the average senator, and from 70% to about 95% for senators in the

top quartile of the distribution of office motivation. On the other hand, banning

advertising has a small (< 5 p.p.) effect on electoral accountability independently of

the type of the politician when incumbents enjoy a large advantage in the polls (larger

than 20 p.p.). We conclude that while advertising is not responsible for breaking the

electoral connection between politicians and voters, it does significantly crowd-out

policy accountability in close elections.

7 Conclusion

One of the most basic and widely accepted assumptions in the study of electoral

politics is that legislators have both policy and office motivations. In this paper, we

show that the within-cycle dynamics of position-taking and advertising can be used to

quantify how individual legislators value electoral gains relative to policy concessions,

and how their preferences for office and policy feedback into their responsiveness to

electoral incentives.

We implement our approach for US senators seeking reelection. We find that most

senators are willing to make considerable policy concessions for a higher probability of

retaining office, and that there is substantial heterogeneity in how individual senators

value policy relative to office. By combining the estimates on senators’ preferences

and the electoral effectiveness of position-taking and advertising, we are able to as-

sess to what extent senators would accommodate the preferences of their voters, for

varying degrees of competitiveness of the election. We find that electoral account-

ability is relatively low on average across senators and electoral conditions, although

it increases in competitive elections. Senators in the top quartile of the distribu-

tion are significantly responsive to voters, but those in the lower quartile are largely

unresponsive, even in competitive elections.

Our results illustrate the usefulness of disentangling politicians’ preferences from the

electoral conditions they face. The results reconcile the general perception that sen-

ators typically do give a large value to being reelected with the moderate levels of

31

responsiveness observed on average. This is due to three factors. First, over a fourth

of senators in our sample is heavily ideological, and would only be willing to deviate

from their policy preferences in exchange for a large electoral gain. Second, the elec-

toral return of policy moderation is low, both in absolute terms and relative to the

electoral return of political advertising. Third, a number of senators generally face

a significant advantage in the polls, making them less willing to respond to voters’

preferences on average in the observed data.

The results illustrate the pitfalls of conceiving of accountability as a constant. Re-

sponsiveness is best understood as a form of behavior that is contingent on attributes

of the politician and the nature of the electoral landscape she faces. The exercise in

this paper contributes to a better understanding of this mapping.

32

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35

A Senator Specific Variables and

Descriptive Statistics

We incorporate various senator and race-specific characteristics, including republican

(1 if senator is republican, 0 if democrat), female (1 if senator is female, 0 otherwise),

seniority (number of years of service as a member of the Senate), membership (num-

ber of standing committees a senator is a member of during a congressional session),

com_leader (1 if the senator held a leadership position in a senate committee, 0 oth-

erwise), and leader (1 if the senator was minority or majority leader, 0 otherwise).23

To capture a measure of electoral preferences at the state level, we follow Canes-

Wrone, Brady, and Cogan (2002) and compute the average vote spread for the period

2000-2012 between the Republican and Democrat candidates in the presidential elec-

tion at a given state, presrep.margin, using data from Dave Leip’s Atlas of U.S.

Presidential Elections. To account for primary elections’ characteristics of both in-

cumbents and challengers we include inc_contested and chall_contested which

take a value of 1 if the incumbent (challenger) won the primary election with a spread

of less than 10%

We control for demographic characteristics at the state level including median house-

hold income (income), percent of a state’s population older than 64 years old (pop_64),

percent of a state’s population with less than 9th grade of educational attainment

(educ_9th), percent of a state’s population that is black (black), and percent of a

state’s population that is hispanic (hispanic), all obtained from the 2000 Census’

data. We also include two economic indicators that vary both across states and within

electoral cycles. First, we collected data on state unemployment (unemployment) ob-

tained from the Bureau of Labor Statistics. Second, we obtained a leading indicator

of economic activity (lead) gathered monthly by the Federal Reserve of St. Louis.

23The variables seniority, membership, comleader, and leader are constructed based on datacollected by Charles Stewart III and Jonathan Woon.

36

Table A.1: Summary Statistics: Incumbents’ CharacteristicsVariable Levels n %

∑%

Party Democrat 936 54.5 54.5

Republican 780 45.5 100.0

all 1716 100.0

Membership 0 988 57.6 57.6

1 or more 728 42.4 100.0

all 1716 100.0

Committee Leader No 1417 82.6 82.6

Yes 299 17.4 100.0

all 1716 100.0

Senate Leader No 1625 94.7 94.7

Yes 91 5.3 100.0

all 1716 100.0

Female Male 1443 84.1 84.1

Female 273 15.9 100.0

all 1716 100.0

Table A.2: Summary Statistics: States’ CharacteristicsVariable n Min x x Max s IQR

pointlead 1716 -41.30 19.47 18.63 78.26 15.29 19.30

contributions (1000 $) 1716 -6.25 6160 4946 29526 5067 5589

tv ads (1000 GRP’s) 521 0.00 6.31 2.60 153.35 11.83 5.74

tv ads challenger (1000 GRP’s) 369 0.00 4.47 1.70 93.63 9.14 4.04

tv ads others (1000 GRP’s) 245 0.00 6.49 1.97 58.42 10.58 6.25

tv ads others challenger (1000 GRP’s) 241 0.00 7.07 2.24 149.99 14.47 6.61

position 1716 -2.24 -0.09 -0.25 2.13 0.68 1.15

seniority 1716 1.00 12.45 9.00 45.00 9.90 12.00

unemp 1716 2.29 6.10 5.68 13.72 2.10 2.58

lead index 1716 -5.80 1.25 1.37 6.15 1.31 1.36

pop64 1716 8.20 16.71 16.60 22.80 2.08 1.95

educ 9th 1716 3.20 6.89 5.95 11.70 2.30 3.55

black 1716 0.30 10.78 7.05 36.30 10.04 12.55

hispanic 1716 0.70 7.63 4.30 42.10 9.15 5.80

presrep.margin 1716 -0.26 0.01 -0.03 0.38 0.16 0.24

37

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0.0 0.2 0.4 0.6 0.8 1.0

−2

−1

01

2

Party Vote

Pos

ition

Tak

ing

(ID

EA

L)

cor = 0.83

Figure A.1: Position Taking: Party Vote

38

B Second-Stage Estimation

In this section, we expand on our procedure to estimate the structural parameters

ρ. As we explained in section 5, the difficulty in estimating ρ directly from the

likelihood in (5.1) is that the conditional choice probability Pr(yi,t|pi,t; ρi, ψ) is not a

known function of ρi. Instead, this is given by the optimal response of the politician

with characteristics ρi in each state (pi,t, µi,t), which result from the solution to

maxyt

λ(xt − θ)2 − γ(et)2 + E

[W t−1(pt−1)

∣∣ zt]︸ ︷︷ ︸h(zt)

+µ(yt)

, (B.1)

where Wt(pt, µt) is the value from this problem, W t(pt) ≡ Eµ [Wt(pt, µt)], and

E[W 0(p0)

∣∣ z1

]≡ Pr(p0 ∈M

∣∣z1)ω + Pr(p0 ∈ H∣∣z1)(ω + α).

Since the shocks {µit(y)} are i.i.d. TIEV random variables, we have

Pr(yi,t = y′|pi,t; ρi) =exp [h(pi,t, y

′; ρi)]∑y∈Y exp [h(pi,t, y; ρi)]

and

W i,t(pi,t) = ln

(∑y∈Y

exp [h(pi,t, y)]

)+ C,

where C is Euler’s constant. For each trial parameter ρi. we obtain h(pi,t, y; ρi) by

solving the politician’s problem recursively.

To relate senator’s preference parameters to relevant observable attributes, while still

allowing heterogeneity conditional on covariates, we model structural parameters as

latent random variables drawn from distributions with parameters that are functions

of senator characteristics, including party, gender, seniority, and leadership positions.

This allows the preference estimates to be informed by both their effect on conditional

choice probabilities and observable characteristics.

Specifically, we let φi ≡ {λi, ωi, αi}, and fix λ + ω + α = 1, which is analogous to

estimating normalized office payoffs ωλ

and αλ. To satisfy the normalization, we assume

39

that φi follows a Logistic Normal distribution, which effectively applies a logistic trans-

formation to an underlying bivariate normal distribution, producing a distribution for

(λi, ωi, αi) over the 2-dimensional simplex. The underlying normals are assumed to

have variances σ2ω and σ2

α and means Z′iηω and Z

′iηα, where Zi are senators’ char-

acteristics, including: republican, gender, leader, com_leader, seniority, and

membership. Denote the density of φi as fφ(·; (Z′iηj, σ

2j )j=α,ω). Ideal points θi have

a normal distribution with mean zero, and variance σθ. Denote the density of θi as

fθ(·;σ2θ). The cost parameter γi follows a truncated normal distribution (truncated

at zero) with mean W′iηγ and variance σ2

γ, where Wi includes the vector of charac-

teristics Zi plus senator/race characteristics including: income, pop_64, educ_9th,

black, hispanic, unemployment, lead, and total contributions (contributions).

We denote the density of γi as fγ(·; W′itηγ, σ

2γ).

Our estimation problem is then to choose {φi, θi, γi}Ni=1 and (~η, ~σ) to maximize the

posterior distribution, which is proportional to:

N∏i=1

T∏t=1

Pr(yi,t|pi,t; ρi, ψ)fφ(φi; (Z′

iηj, σ2j )j=α,ω)fθ(θi;σ

2θ)fγ(γi; W

′

itηγ, σ2γ)

To solve this problem, we combine a quasi-Newton gradient method (L-BFGS) with

the value function obtained from the dynamic programming problem of each sena-

tor at each trial parameter. Because this algorithm must fully solve the senator’s

problem for each trial value of the parameters and then compute the gradients of the

likelihood, it can be computationally costly relative to other alternatives proposed in

the literature. In our case, this disadvantage is negligible as we compute the gradi-

ents required for optimization via a reverse-mode automatic differentiation algorithm

(available in the C++ Stan Math Library Carpenter, Hoffman, Brubaker, Lee, Li,

and Betancourt (2015)), which is an extremely fast and efficient way to precisely

compute exact derivatives.24

We measure uncertainty in the structural parameters’ estimates – and other quantities

of interest which are functions of these parameters – via a parametric bootstrap.

That is, after obtaining parameter estimates, we draw 500 pseudo-samples from the

24Usual optimization algorithms use finite differencing, which is a numerical approximation togradient evaluations. This method turns out to be slow and imprecise for nonlinear and highlymultidimensional functions such as the likelihood function we are dealing with in our problem.

40

estimated posterior density and re-estimate the parameters for each sample. We use

the empirical distribution of these 500 estimates to compute confidence intervals and

its sample variance as an estimator of the variance of the structural parameters.

41

C First-Stage Estimates: Additional Results

Table C.1: Instrument Relevance Results

Dependent variable:

(xit − εi)2 √eit

√echallit

(1) (2) (3)

pi,t −0.002 −0.293∗∗∗ −0.309∗∗∗

(0.001) (0.061) (0.055)√ei,t

house 0.0002 0.798∗∗∗ 0.177∗∗

(0.0004) (0.071) (0.069)√echalli,t

house−0.00003 0.304∗∗∗ 0.922∗∗∗

(0.0005) (0.061) (0.062)√ei,t

neighbor 0.001 0.199∗∗∗ 0.099(0.001) (0.069) (0.070)√

echalli,t

neighbor−0.001∗ 0.065 −0.132∗

(0.001) (0.081) (0.079)(xhouseit − εi)2 0.200∗∗∗ 5.879∗∗ 2.746

(0.041) (2.886) (2.347)unemploymentcosp −0.010 −2.770 −5.303∗∗

(0.052) (2.604) (2.200)leadcosp 0.101∗∗∗ −1.104 2.756∗∗

(0.030) (2.047) (1.390)Senator-State Controls Yes Yes YesCongress-Party FE Yes Yes YesIV F-Tests 39.08∗∗∗ 134.31∗∗∗ 223.01∗∗∗

Observations 1,416 1,416 1,416Adjusted R2 0.412 0.741 0.766

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.Robust standard errors clustered at the senator-congress level in parentheses.

42

Table C.2: Complete First Stage Results

Dependent variable: pi,t−1

OLS OLS IV IV

(1) (2) (3) (4)

pi,t 0.816∗∗∗ 0.763∗∗∗ 0.720∗∗∗ 0.691∗∗∗

(0.023) (0.025) (0.028) (0.032)(xi,t − ξ)2 −1.533∗∗∗ −2.199∗∗∗ −10.152∗∗∗

(0.507) (0.829) (3.225)(xpvi,t − ξ)

2 −37.049∗∗∗

(7.060)√ei,t 0.017∗∗∗ 0.020∗∗∗ 0.034∗∗ 0.051∗∗∗

(0.007) (0.007) (0.013) (0.015)√echalli,t −0.047∗∗∗ −0.049∗∗∗ −0.053∗∗∗ −0.057∗∗∗

(0.009) (0.010) (0.015) (0.016)Seniorityi 0.065∗ 0.067∗ 0.020

(0.036) (0.040) (0.051)Membershipi 0.732 0.372 2.625∗

(0.747) (1.058) (1.410)Committee Leaderi −1.293 −0.797 −1.790

(1.012) (1.153) (1.434)Senate Leaderi −1.355 −1.942 −3.640∗∗

(0.828) (1.204) (1.465)Femalei 0.437 −0.884 0.799

(0.685) (0.844) (0.892)Unempit −0.408∗∗ −0.695∗∗∗ −0.453∗∗

(0.172) (0.214) (0.230)Leadit −0.333 −0.306 −0.235

(0.217) (0.292) (0.311)Incomei −0.00001 −0.0001 0.0001

(0.0001) (0.0001) (0.0001)Pop64i 0.261∗ 0.391∗∗ 0.796∗∗∗

(0.144) (0.159) (0.225)Educationi 0.023 −0.139 −0.163

(0.119) (0.194) (0.197)Blacki −0.031 −0.048 −0.015

(0.026) (0.031) (0.035)Hispanici 0.036 0.139∗∗ 0.069

(0.027) (0.058) (0.047)Cont. Primary (Inc.) −1.881 −1.540 0.540

(1.243) (1.991) (2.616)Cont. Primary (Chal.) −0.637 −0.428 −1.849∗

(0.827) (0.834) (0.979)Repi 0.121 0.693 3.461∗

(1.564) (1.555) (1.876)

Observations 1,584 1,584 1,416 1,138Congress-Party FE No Yes Yes YesAdjusted R2 0.676 0.683 0.640 0.640

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.

Robust standard errors clustered at the senator-congress level in parentheses.

43

t+1 t+2 t+3 t+4 t+5

IncumbentChallenger

Month

Cha

nge

in In

cum

bent

's S

prea

d

−3

−2

−1

01

Figure C.1: Short and Long-run effect of TV ads

44

Table C.3: Instrument Relevance Results: Alternative Instruments for TV ads

Dependent variable:

(xit − εi)2 √eit

√echallit

(1) (2) (3)

pi,t −0.002 −0.308∗∗∗ −0.303∗∗∗

(0.001) (0.062) (0.066)√ei,t + echalli,t

house

0.0002 0.198∗∗∗ −0.023

(0.0003) (0.029) (0.025)√ei,t + echalli,t

neighbor

0.0002 0.742∗∗∗ 0.758∗∗∗

(0.0003) (0.038) (0.059)(xhousei,t − ξ)2 0.197∗∗∗ 5.332∗ 4.852

(0.042) (2.987) (3.081)unemploymentcosp −0.011 −3.069 −5.336∗∗

(0.052) (2.672) (2.546)leadcosp 0.098∗∗∗ −1.373 2.318

(0.029) (2.153) (1.872)Senator-State Controls Yes Yes YesCongress-Party FE Yes Yes YesIV F-Tests 37.93∗∗∗ 45.3∗∗∗ 164.16∗∗∗

Observations 1,416 1,416 1,416Adjusted R2 0.410 0.728 0.708

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.Robust standard errors clustered at the senator-congress level in parentheses.

45

Table C.4: First Stage Results with Alternative Instrument for TV ads

Dependent variable: pi,t+1

IV (Baseline) IV (Alternative)

(1) (2)

pi,t 0.720∗∗∗ 0.708∗∗∗

(0.028) (0.030)(xi,t − εi)2 −10.152∗∗∗ −11.262∗∗∗

(3.225) (3.416)√ei,t 0.034∗∗ 0.067∗∗∗

(0.013) (0.023)√echalli,t −0.053∗∗∗ −0.094∗∗∗

(0.015) (0.029)Senator-State Controls Yes YesCongress-Party FE Yes Yes

Observations 1,416 1,416Adjusted R2 0.640 0.628

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.Robust standard errors clustered at the senator-congress level in parentheses.

46

D Structural Estimates: Additional Results

Ideal Point θi

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REEDBROWNCOONSLEAHY

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BEGICHUDALL

KENNEDYINOUYE

SCHUMERWARNERMURRAY

DODDFEINSTEIN

MENENDEZKERRYHAGAN

LEVINFEINGOLD

CANTWELLSTABENOW

SANDERSROBBREID

CARPERWYDENCASEYKOHL

PRYORNELSON

ROCKEFELLERKLOBUCHAR

TESTERLANDRIEU

BINGAMANBAYH

LIEBERMANBAUCUS

BYRDJOHNSONCLELAND

MCCASKILLLINCOLN

MANCHINCOLLINSSTEVENS

SNOWECOLEMAN

BROWNSMITH

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DOLEHUTCHISONVOINOVICH

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ALEXANDERCOCHRAN

GORTONHUTCHINSON

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CHAMBLISSGREGG

GRAHAMSESSIONS

BONDHAGEL

GRASSLEYGRAMS

LOTTBROWNBACK

WICKERCRAIG

MCCONNELLCRAPO

CORNYNISAKSONBUNNING

BURRVITTER

ALLARDMCCAINCOBURN

RISCHROBERTS

−2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5

Figure D.1: Ideal Point Estimates (Solid lines plot 90% bootstrap confidence intervals)

47

−2 −1 0 1 2

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sity

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Figure D.2: Ideal Policy and Poll-maximizing Position

−4 −2 0 2 4

0.0

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Career Concerns, log(ωi λi)

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Figure D.3: Distribution of estimates for ω/λ and (ω + α)/λ.

48

Career Concerns log(ωi λi)

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FRISTHUTCHINSON

RISCHABRAHAMCOLEMANGRAHAM

GREGGSESSIONS

LOTTBROWNBACK

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CRAPOCOCHRANMANCHIN

GRASSLEYTESTERSNOWECASEY

MENENDEZSANDERS

WHITEHOUSECARDIN

DODDCLELAND

COONSSARBANESFRANKEN

UDALLBAYH

MERKLEYDOLE

HUTCHISONBOND

WARNERLINCOLNGORTON

UDALLBEGICH

JOHNSONSTEVENS

BROWNSPECTER

MCCONNELLLUGAR

WYDENSCHUMER

CARPERNELSON

PRYORHAGAN

KOHLROBB

FEINGOLDLANDRIEU

MCCASKILLGILLIBRANDKLOBUCHAR

ROCKEFELLERREID

ROTHDURBIN

SHAHEENCANTWELLSTABENOW

KENNEDYKERRYBYRD

MURRAYLAUTENBERG

BAUCUSLEVIN

FEINSTEINLEAHY

MIKULSKIHATCH

REEDINOUYEBOXER

−4 −2 0 2

Figure D.4: Value of Reelection, ω/λ. Solid lines plot 90% bootstrap confidence

intervals.

49

Career Concerns log((ωi + αi) λi)

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LEAHYMIKULSKI

INOUYEHATCH

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Figure D.5: Value of Lopsided Win, (ω + α)/λ. Solid lines plot 90% bootstrap

confidence intervals.

50

BOXERROBERTS

REEDHATCH

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BEGICHSHAHEENCORNYN

CRAPOBROWN

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WHITEHOUSECANTWELL

MCCASKILLALLARD

COCHRANKOHL

FEINGOLDGORTON

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Figure D.6: Compensating Variation. Proportion of the average distance betweenvoters and politicians that senator i would be willing to give up for a 1 p.p. increasein the probability of a lopsided win.

51

Covariate Estimates ξω

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Senate Leader

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Figure D.7: Career Concerns Covariates. Solid lines plot 90% bootstrap conf. inter-

vals.

52

−4 −2 0 2 4 6 8

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LANDRIEU−113SMITH−110

BROWN−112BROWN−112

SPECTER−108HAGAN−113PRYOR−113

DOLE−110BEGICH−113

LANDRIEU−110MCCASKILL−112

GRASSLEY−111COCHRAN−110COLEMAN−110

NELSON−112CHAMBLISS−110

MCCONNELL−113ALEXANDER−113

WARNER−113REID−111

MCCAIN−111UDALL−113

BURR−111ABRAHAM−106

COLLINS−113SANTORUM−106

CASEY−112VOINOVICH−108

LINCOLN−111MCCONNELL−110

ROBB−106DURBIN−113VITTER−111

FRANKEN−113STEVENS−110BAUCUS−110

BUNNING−108MCCONNELL−107

FEINGOLD−108COLLINS−107

HUTCHINSON−107STABENOW−112

ALLARD−107SMITH−107

GRAHAM−110CLELAND−107ISAKSON−111

SHAHEEN−113GRAHAM−113

MANCHIN−112JOHNSON−110

GRAMS−106GREGG−108

KOHL−106SCHUMER−108LINCOLN−108

MERKLEY−113SUNUNU−110

ALEXANDER−110MENENDEZ−112

LAUTENBERG−110LUGAR−106

BINGAMAN−106COCHRAN−113

DODD−108SNOWE−106

GORTON−106MURRAY−111

GRASSLEY−108SCHUMER−111DOMENICI−107

KLOBUCHAR−112KERRY−110

BAYH−108GILLIBRAND−112

LANDRIEU−107UDALL−113

ROBERTS−113CRAIG−107

COONS−113ROCKEFELLER−110

WYDEN−111SESSIONS−107

DEWINE−106BOND−108

WHITEHOUSE−112SARBANES−106

FRIST−106LIEBERMAN−106

SESSIONS−110MURRAY−108

WYDEN−108HAGEL−107

CARPER−112CARDIN−112

ROCKEFELLER−107ROTH−106

COBURN−111HUTCHISON−106

BROWNBACK−108HATCH−112

REID−108WICKER−112

RISCH−113LEAHY−108

SANDERS−112BYRD−106

CANTWELL−112KENNEDY−106

HATCH−106CRAPO−111LEVIN−110

INOUYE−111LEVIN−107

LEAHY−111DURBIN−107

REED−110INOUYE−108

FEINSTEIN−112MIKULSKI−108

REED−107CORNYN−110CORNYN−113

BOXER−108REED−113

MIKULSKI−111FEINSTEIN−106

ROBERTS−110BOXER−111

LOTT−106

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Figure D.8: Cost Parameter γ/λ: solid lines plot 90% bootstrap conf. intervals.

53

0

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Figure D.9: Density of Variance Structural Parameters

Covariate Estimates ξα

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ContributionsFemale

HispanicBlack

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EducationUnemp

LeadSenate Leader

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Figure D.10: Variance of Structural Parameters: Covariate Estimates. Solid lines

plot 90% bootstrap conf. intervals.

54

E Goodness of Fit

In this section, we assess the fit of the model to the data, both in and out of sample.

The within-sample results are presented in the first two panels of Figure E.1. The

first panel presents a summary of the model fit with respect to position-taking, by

comparing senators’ expected policy positions under their predicted conditional choice

probabilities with their observed policy positions. As the figure shows, the model does

a good job predicting the senators’ observed policy positions on average, with a R2 of

0.94. Note that while the model fits the data remarkably well for moderate choices, it

has more trouble predicting very extreme positions. Examination of the data shows

that this comes not from extreme senators consistently taking extreme positions,

but from the infrequent extreme positions of more moderate senators. To take into

account the uncertainty in senators’ choices, we compute the number of observations

that lie within δ-probability intervals, given the variance of shocks we estimate. We

find that 97% of all observed policy positions fall in a 95% probability interval of the

model predicted choices, and 95% in a 90% probability interval.

The second panel of Figure E.1 shows the overall model fit with respect to the observed

level of tv-ads. The model predicts observed TV ad spending well. In the data,

senators spend a low level of TV ads 70% of the time, compared to 78% in the model,

a moderate amount 24% of the time, against 17% in our model, and a high level 5%

of the time in both the data and the model. When we incorporate the uncertainty

in the conditional choice probabilities, a 90% interval contains more than 99% of the

observed advertisement decisions.

55

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dict

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tanc

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45 Degree−Line

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quen

cy0

100

200

300

400

Out of Sample

Figure E.1: Goodness of Fit, Within and Out of Sample

A more demanding test of the model as the true data generating process, is to evaluate

how the model fits the data out of sample. To do this, we exploit the fact that our

data contains multiple inpositions in which senators run two or even three times for

office (say senator Chuck Shumer, D-NY, 2004 and 2010, or Senator Mitch McConnell,

R-KY, 2002, 2008 and 2012). In our main estimation, we use all the observations,

constraining ideal points and career concern parameter estimates to be constant for

the same individual across periods. For our out-of-sample exercise, we re-estimate

the model parameters using only the first inposition in which a senator runs for office

in the sample, and use the resulting estimates to predict behavior in the second (or

third) run for the subset of senators who ran for reelection multiple times within our

sample.

56

The out-of-sample results are presented in the third and fourth panels of Figure E.1.

On average, the out-of-sample fit of position-taking is reasonably good, with expected

policy positions explaining around 70% of observed policy choices. The difference

with respect to the in-sample fit is in fact due to forecasting errors (and not just

to uncertainty embedded in our game), as in this case only 58% of the observations

on position-taking fall in a 95% probability interval of the model’s predicted choices.

For tv ads, the out-of-sample predicted spending is remarkably close to the observed

spending levels, with more than 99% of the observations falling in a 95% probability

interval. Overall, we conclude that the model provides a reasonable approximation to

the data also out of sample, which makes us confident in the validity of our estimates

and counterfactual predictions.

57

F Measuring Voting Support from Multiple Sources

As described in the paper, we complement opinion data with the predicted pointlead

obtained from three different sources. First, we use incumbent senators’ approval rates

(in 12% of monthly observations) listed by Polling Report, Real Clear Politics and

Pollster. Second, remaining gaps are filled with prediction market data (in 11% of

monthly observations) collected by Intrade in real-time.25 Finally, we use national

polls included in the Roper database that contain individual voter’s congressional

approval (in 7% of monthly observations). To include this information we extrapolate

a linear fit between pointlead and the alternative support measures accounting for

Congress session and monthly random effects.

To create an estimated pointlead from the available measures of voting support,

we regress the incumbent support obtained from polling data (as a proportion of

the two-candidate support) on each alternative measure controlling for congress and

monthly random effects, which we assume normally distributed.

To transform the raw prediction market data into monthly prices, we take the weighted

average of collected prices for the stock that pays out if the incumbent senator wins on

Election Day, where the weights are inversely proportional to the number of individ-

ual trades. Then, we use the transformation suggested by Rothschild (2015) to map

monthly prices onto estimated vote shares as sharet = φ−1(pricet), where sharet is

the estimated incumbent share in month t and φ denotes the normal density function.

Approval data at the monthly level is constructed as the weighted average of incum-

bent approval (as a proportion of the total proportion of respondents that approved

and disapproved the incumbent), where the weights are inversely proportional to

the number of survey respondents. To transform congressional approval from na-

tional polls, first we collected individual information on whether survey respondents

approved the job performed by the party of the incumbent in Congress. Then, we pre-

dict the probability that a voter in a given state and month supports the incumbent

party’s job in Congress by regressing individual binary Congressional job approval on

25Intrade sold contracts for some of the senate races in our sample during the years 2004, 2008,2010, and 2012 that were worth $10 in the event the candidate won and $0 in the event the candidatelost.

58

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mbe

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Sha

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Pol

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Cor = 0.81

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59

G Diagnostics for Balanced Panel Data

The first stage model (5.2) is estimated on a balanced panel dataset, with polls

at every month within a year before election. To fill remaining missing values on

senate races, which are usually intermittently measured over an electoral cycle, we

implement a multiple imputation technique via the EM algorithm. This method uses

the information on all other variables in the observed portion of the data to impute

multiple values for each missing value of electoral support, where the imputations

vary depending on the estimated uncertainty in predicting each missing value. In

particular, we construct ten completed datasets and estimate the parameters of the

first stage for each dataset. Next, we combine the estimated coefficients following

Rubin (2004), where we average point estimates and standard errors across datasets

while incorporating the variation across imputed values into the latter.

Figures G.1, G.2 show diagnostics for the multiple imputations as suggested in Abay-

omi, Gelman, and Levy (2008). As can be seen, there is a significant overlap between

the distributions of observed and imputed values of pointlead, with imputed incum-

bency advantage being slightly higher on average than the observed one. In addition,

when we implement the imputation exercises on the observed pointlead, for which

we know the ground truth, we see that the predicted values are almost identical to

the observed ones.

−40 −20 0 20 40 60 80

0.00

00.

010

0.02

00.

030

Incumbent's Pointlead (p.p)

Rel

ativ

e D

ensi

ty

Observed ValuesImputed Values

Figure G.1: Incumbent’s Observed vs Imputed Pointlead

60

−40 −20 0 20 40 60 80

−60

−40

−20

020

4060

80

Observed versus Imputed Values of spread.comb

Observed Values

Impu

ted

Val

ues

0−.2 .2−.4 .4−.6 .6−.8 .8−1

Figure G.2: Validation of Multiple Imputation on Observed Pointlead

Table G.1 and Figure G.3 present the estimation of the first stage for the observed

unbalanced panel (where observations with missing pointlead are omitted). Overall,

we find that, without including all the information in the observed data -brought

about by the covariates other than support, the results of the first-stage estimation

are almost identical to our main specification, with the effects of position and tv-ads

in the same direction and similar in magnitude as the ones with the balanced panel

dataset.

61

Table G.1: First Stage Results with Unbalanced Panel

Dependent variable:

OLS OLS IV

(1) (2) (3)

pi,t 0.805∗∗∗ 0.753∗∗∗ 0.717∗∗∗

(0.030) (0.031) (0.037)

(xi,t − ξ)2 −0.924∗ −1.468∗ −11.379∗∗

(0.512) (0.842) (5.151)√ei,t 0.020∗∗ 0.023∗∗∗ 0.030∗

(0.009) (0.009) (0.017)√echalli,t −0.042∗∗∗ −0.044∗∗∗ −0.042∗∗

(0.011) (0.010) (0.017)

Senator-State Controls No Yes Yes

Congress-Party FE No Yes Yes

Observations 783 783 681

Adjusted R2 0.709 0.712 0.656

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01.

Robust standard errors clustered at the senator-congress level in parentheses.

62

●(xit − ξ)2●

eitchall ●

Unempit●

Inc_Primary_Conti●

Senate Leaderi

●Femalei●

Blacki

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●Committee Leaderi

●Educationi

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Membershipi●

Leadit

●Repi

●Pop64i

●Seniorityi

●Hispanici

●eit

−40 −30 −20 −10 0 10 20First Difference as a Variable

Moves from Its 1th to Its 99th Percentile

Linear Regression Model of pi,t+1

● IVOLS

Figure G.3: Transition parameters with unbalanced panel

63

H Robustness: Thresholds for Lopsided Wins

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.5

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1.5

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2.5

3.0

Career Concerns (>0%) ω

Den

sity

p=20p=10p=15

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

4

Career Concerns α

Den

sity

p=20p=10p=15

−0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

4

Career Concerns α

Den

sity

p=20p=10p=15

Figure H.1: Career Concerns under Different Thresholds for Lopsided Wins

−20 0 20 40 60

1520

2530

35

Polls' Spread %

EA

I %

p=20p=10p=15

−20 0 20 40 60

3000

4000

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6000

Polls' Spread %

EA

I %

p=20p=10p=15

Figure H.2: Aggregate (Mean) Policy Functions under Different Thresholds for Lop-

sided Wins

I Strategic Challenger

In this appendix, we extend our model to include the strategic spending response of

a challenger. We assume that the challenger gets an office payoff of one if she wins

office and zero otherwise, and that spending ect has a cost γc(ect)2 for the challenger.

The incumbent’s payoffs are as in the benchmark model.

64

To avoid multiplicity of equilibria, we assume that in each stage politicians move

sequentially, with the challenger moving first. In particular, we assume the following

sequence:

1. At the beginning of each period t, incumbent and challenger observe pt, which

evolves according to eq. (5.2);

2. The challenger observes the shocks µc (which are i.i.d. TIEV and unobserved

by the researcher), and chooses a level of TV ad buys ect ;

3. The incumbent then observes ect and shocks µ and chooses (xt, et).

Our solution concept is subgame perfect Nash equilibrium. We solve for the equilib-

rium of the game and associated conditional choice probabilities by backwards induc-

tion. We drop the subindex i for each incumbent for notational convenience. Suppose

there are t = T, . . . , 1 periods remaining to the election, and let zIt ≡ (pt, xt, et, ect).

After observing (pt, µt) and the challenger’s ad expenditure ect , the incumbent solves

maxyt

λ(xt − θ)2 − γ(et)2 + E

[W t−1(pt−1)

∣∣ zIt ]︸ ︷︷ ︸h(zIt )

+µ(yt)

, (I.1)

whereWt(pt, µt, ect) is the value from this problem, W t(pt) ≡ Eµ,µct [Wt(pt, µt, e

ct(pt, µ

ct))],

and

E[W 0(p0)

∣∣ zI1] ≡ Pr(p0 ∈M∣∣zI1)ω + Pr(p0 ∈ H

∣∣zI1)(ω + α).

Since the shocks {µt(y)} are i.i.d. TIEV random variables, the incumbent’s condi-

tional choice probability is given by

Pr(yt = y′|pt, ect) =exp [h(pt, y

′, ect)]∑y∈Y exp [h(pt, y, ect)]

Now consider the challenger. At the beginning of the period, the challenger observes

(pt, µct), and solves

maxect

Eµ [E [W c

t−1(pt−1)∣∣ (pt, e

ct , yt(pt, µt, e

ct))]]− γ(ect)

2︸ ︷︷ ︸hc(pt,ect )

+µc(ect)

, (I.2)

65

where W ct (pt, µ

ct) is the value from this problem, W

c

t(pt) ≡ Eµct [W ct (pt, µ

ct)], and

E[W

c

0(p0)∣∣ p1

]≡ Pr(p0 < 1/2

∣∣p1). From the TIEV distribution of the shocks, the

challenger’s conditional choice probability is given by

Pr(ect = e′c|pt) =

exp[hc(pt, e

′c)]∑

ec∈E exp [hc(pt, ec)].

The structural parameters of the dynamic game include the vector of incumbent

parameters ρ, as well as the challengers’ cost of spending, γc ≡ {γci }Ni=1. We estimate

these structural parameters by first solving for equilibrium strategies for every trial

value of the parameters, and then search for the values that maximize the likelihood

of the data.

Figure J.1 shows the distribution of the estimated structural parameters in the Base-

line Model and in the Extended Model with endogenous challenger response. As the

figures show, the two sets of estimates are remarkably similar.

66

−2 −1 0 1 2

0.0

0.1

0.2

0.3

0.4

0.5

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Ideal Point Estimates

Den

sity

Extended ModelBaseline Model

−4 −2 0 2 4 6 8

0.00

0.05

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0.15

0.20

0.25

Cost of tv−ads log(γi λi)

Den

sity

Extended ModelBaseline Model

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0.0

0.1

0.2

0.3

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Career Concerns, log(ωi λi)

Den

sity

Extended ModelBaseline Model

−2 −1 0 1 2 3

0.0

0.2

0.4

0.6

0.8

Career Concerns, log(ωi + αi λi)

Den

sity

Extended ModelBaseline Model

Figure J.1: Parameter estimates in the Dynamic Game and Baseline Model

67

●

AK−08

MS−08

MS−14

MS−00MT−08

ID−02

NH−04

NY−04

NY−10

NJ−08

CA−04CA−10

IL−14

SD−08NY−12

NJ−12 MS−12

MT−12

AK−14

CA−00

CA−12

LA−08

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0

2

4

−2 0 2 4

Implicit TV ads Cost (Incumbent)

Impl

icit

TV

ads

Cos

t (C

halle

nger

)

Ad Prices

400

800

1200

1600

Figure J.2: Implicit cost of TV ads for Incumbent and Challenger in the Extended

Model with endogenous challenger response.

Figure J.2 plots the estimates for the implicit cost of spending for incumbent and

challengers. Our estimates imply that incumbents enjoy a substantial cost advantage.

This partly explains the fact that incumbents outspend challengers almost four to one.

The figure also shows that races in which the estimated implicit cost of ads is high

tend to also be races where ad prices are high on average, which is reassuring.

Figure J.3 plots the aggregate equilibrium position-taking and TV ad buys by both

the incumbent and challenger, as a function of the incumbent’s electoral advantage.

As the figure shows, the main results of the benchmark model are qualitatively un-

changed. As in the baseline model, equilibrium electoral accountability and TV ad

buys by the incumbent increase as the election gets closer, when the race is more

competitive, and when the incumbent cares more about retaining office.

Quantitatively, the results are also largely similar to the benchmark. The exception is

a moderately higher predicted level of electoral accountability and TV ad spending in

close elections, in particular for senators in the top quartile of office motivation. These

68

differences are not surprising. The simplification in the benchmark is to maintain the

challenger at the observed level of TV ad spending in all states. When we allow

the challenger to choose spending strategically, instead, she tends to spend more the

more competitive the election is. This in turn prompts the incumbent to increase

her effort in close elections (i.e., the game has strategic complementarities). From a

quantitative point of view, however, these results show that introducing the challenger

doesn’t significantly change the conclusions from the benchmark model.

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010

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EA

I %

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5000

1000

015

000

2000

0

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TV

Ads

GR

P's

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1000

2000

3000

4000

5000

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Cha

lleng

er's

TV

Ads

GR

P's

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Figure J.3: Equilibrium Position-Taking (EAI) and TV Advertising by Incumbentand Challenger, as a function of the incumbent’s electoral advantage. Quartiles ofthe distribution of λ (policy) and λ/γ (ads).

69