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: [email protected];
Gabriel Lopez Moctezuma: HSS, Caltech, email: [email protected]; Adam Meirowitz: DavidEccles School of Business, University of Utah, email: [email protected].
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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0.015
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0 40 80
Incumbency Advantage %
Den
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Electoral Results
Polls (October)
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Polls (October)
Ele
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−20 −10 0 10 20Change in pointlead (p.p.)
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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Position Taking Average (Per senator/cycle)
Pos
ition
Tak
ing
Std
. Dev
(P
er s
enat
or/c
ycle
)
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
0.0
0.1
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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
−0.5 0.0 0.5 1.0
−10
010
2030
Policy Position (xit)
Pol
ls (p
it)
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−10
010
2030
Policy Position (xit)
Pol
ls (p
it)
Conservative StateLiberal State
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
−20 0 20 40 60
020
4060
80
Polls' Spread %
EA
I %First QuartileSecond QuartileThird QuartileFourth QuartileAverage
−20 0 20 40 6050
0010
000
1500
0Polls' Spread %
TV
Ads
GR
P's
First QuartileSecond QuartileThird QuartileFourth QuartileAverage
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
−20 0 20 40 60
020
4060
80
Polls' Spread %
EA
I %First QuartileSecond QuartileThird QuartileFourth QuartileAverage
−20 0 20 40 60
020
4060
80Polls' Spread %
EA
I %
First QuartileSecond QuartileThird QuartileFourth QuartileAverage
−20 0 20 40 60
020
4060
80
Polls' Spread %
EA
I %
First QuartileSecond QuartileThird QuartileFourth QuartileAverage
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
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Ideal Point Estimates
Den
sity
Extended ModelBaseline Model
−4 −2 0 2 4
0.0
0.1
0.2
0.3
0.4
0.5
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 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
−20 0 20 40 60
05
1015
20
Polls' Spread %
EA
I(N
o A
ds)
− E
AI(
Bas
elin
e) (
%)
First QuartileSecond QuartileThird QuartileFourth QuartileAverage
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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−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
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Figure D.2: Ideal Policy and Poll-maximizing Position
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Figure D.3: Distribution of estimates for ω/λ and (ω + α)/λ.
48
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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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Figure D.5: Value of Lopsided Win, (ω + α)/λ. Solid lines plot 90% bootstrap
confidence intervals.
50
BOXERROBERTS
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CRAPOBROWN
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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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Figure D.7: Career Concerns Covariates. Solid lines plot 90% bootstrap conf. inter-
vals.
52
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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
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GRAHAM−110CLELAND−107ISAKSON−111
SHAHEEN−113GRAHAM−113
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GRAMS−106GREGG−108
KOHL−106SCHUMER−108LINCOLN−108
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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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Covariate Estimates ξα
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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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0−
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1.0
Observed Stance
Pre
dict
ed S
tanc
e
45 Degree−Line
Low Medium High
ObservedPredicted
Fre
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
state and date random effects.
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Incu
mbe
nt's
Sha
re (
Pol
ls)
Cor = 0.81
0.45 0.50 0.55 0.60 0.65 0.70 0.75
0.4
0.5
0.6
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mbe
nt's
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re (
Pol
ls)
Cor = 0.68
0.45 0.50 0.55 0.60 0.65 0.70 0.75
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mbe
nt's
Sha
re (
Pol
ls)
Cor = 0.55
0.50 0.55 0.60 0.65 0.70 0.75
0.4
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0.7
0.8
Figure F.1: Predicted vs Observed Incumbent Share
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
●Chall_Primary_Conti
●Committee Leaderi
●Educationi
●Incomei●
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
1.0
1.5
2.0
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
5000
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
0.6
Ideal Point Estimates
Den
sity
Extended ModelBaseline Model
−4 −2 0 2 4 6 8
0.00
0.05
0.10
0.15
0.20
0.25
Cost of tv−ads log(γi λi)
Den
sity
Extended ModelBaseline Model
−4 −2 0 2 4
0.0
0.1
0.2
0.3
0.4
0.5
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
−2
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.
−20 0 20 40 60
010
2030
4050
6070
Polls' Spread %
EA
I %
First QuartileSecond QuartileThird QuartileFourth QuartileAverage
−20 0 20 40 60
5000
1000
015
000
2000
0
Polls' Spread %
TV
Ads
GR
P's
First QuartileSecond QuartileThird QuartileFourth QuartileAverage
−20 0 20 40 60
1000
2000
3000
4000
5000
Polls' Spread %
Cha
lleng
er's
TV
Ads
GR
P's
First QuartileSecond QuartileThird QuartileFourth QuartileAverage
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