Corrected Comparative Statics for Presidential Responsiveness to
Public Opinion1
Brandice Canes-Wrone2 and Kenneth W. Shotts3
October 5, 2010
1
2
We thank Sarah Anzia for helpful comments on an earlier draft of this note.
Professor of Politics and Public A¤airs, Department of Politics and Woodrow Wilson School, Princeton
University, Princeton, NJ 08544. Email: bcwrone@princeton.edu.
3
Professor of Political Economy, Stanford GSB, 518 Memorial Way, Stanford, CA 94305.
kshotts@stanford.edu.
Email:
Canes-Wrone and Shotts (2004, henceforth CS) examine how a president’s popularity and the electoral cycle a¤ect congruence between his policy positions and public opinion. Applying a model by
Canes-Wrone, Herron, and Shotts (2001, henceforth CHS), they test multiple hypotheses including
the “Popularity Hypothesis” that in the second half of the term a president of average popularity
is more likely to take actions congruent with public opinion than a president whose popularity is
low or high. Scholars have examined or discussed this hypothesis within the context of British
and Danish prime ministers’ actions (Hobolt and Klemmensen 2008), United States presidents’
speeches (e.g., Rottinghaus 2006; Wood and Lee 2009), and New York City mayors’ budgetary
decisions (Anderson and Smirnova 2006).
The CHS theory does not model a leader’s popularity per se, but rather focuses on voters’perceptions of the likelihood that an incumbent and his challenger are “high quality”in terms of their
policy expertise. CS use presidential popularity as a proxy for these voter perceptions, and implicitly assume that there is a correlation between a president’s popularity and his probability of being
high quality. However, in deriving the Popularity Hypothesis, CS failed to take into account the
fact that in the CHS model, an incumbent that the public believes to be high quality is more likely
to have policy information that recommends the option preferred by voters, under the standard
game theoretic assumption that voters’prior beliefs about the incumbent’s quality are correlated
with his quality. In this erratum we derive the correct comparative static: a nonmonotonic pattern similar to the Popularity Hypothesis, but with an uptick in congruence for extremely popular
presidents. We then discuss implications for the empirical analysis in CS, as well as other empirical
work building on the CHS theory.
The error
The Popularity Hypothesis is based on the equilibrium in CHS’s “Basic Model”when
uncertainty resolution is unlikely, i.e.,
< . In the model, an incumbent who is low quality and
1
whose private policy information indicates that voters misperceive their true interests can have an
incentive to pander by choosing a policy that is in accordance with public opinion (x = A); with
probability
L
s=B .
This probability of pandering varies as a function of voters’initial beliefs about
the probability that the incumbent is high quality,
, and voters’ beliefs about the probability
that the challenger is high quality, . When the absolute di¤erence between
and
is su¢ ciently
large, the incumbent follows his policy information even when it recommends an unpopular policy.
The likelihood of pandering accordingly depends on voters’ ex-ante beliefs about the quality of
the incumbent versus challenger, with pandering being most likely when the candidates’perceived
quality is similar. CS claim that in the CHS model an incumbent’s likelihood of supporting a
popular policy follows the same pattern as the incumbent’s likelihood of pandering. For instance,
CS assert (p. 695) that “The conditions that explain variation in pandering are thus su¢ cient to
characterize variation in policy congruence.”
Under the standard game theoretic assumptions, the claim is incorrect. Game theorists generally assume that actors’prior beliefs about an uncertain outcome are based on the true probability
distribution for that outcome, and CHS do not indicate that their model assumes otherwise. Accordingly, CHS implicitly assume that the voter’s prior belief about the incumbent’s probability of
being high quality equals the actual probability that he is high quality, which doesn’t only a¤ect
L
s=B ,
the probability of pandering, but also has a direct e¤ect on the probability of policy congru-
ence. The probability of seeing signal s = A; which indicates that voters’interests are served by the
popular policy option, is higher for a high quality incumbent –who sees s = A whenever the state is
A; which happens with probability
>
1
2
–than for a low-quality incumbent –who sees the correct
signal with probability q 2 ( ; 1) and thus sees s = A with probability q + (1
) (1
q) < .
A proper analysis of variation in policy congruence in the CHS model must account for this direct
e¤ect.
2
Comparative statics We now derive correct comparative statics for how the incumbent’s prior
probability of being high quality a¤ects congruence in the model, i.e.,
@ Pr(x=A)
:
@
We build on CHS’s
Proposition 1, restating the results in terms of . There are four cases:
1. If the incumbent is far behind the challenger, i.e.,
then
L
s=B
)q
<
(1 )(1 )
)[ (1 q)+(1
L
s=B
H ;
x=A
!=
>
>
L
s=B
(1
(1
=
H ;
x=B
!=
then
L
s=B
is su¢ ciently high such that
)
)
= 1
H
x=B
!=
> ;
= 0.
CS’s derivation of the Popularity Hypothesis stems from the fact that
<
then
)q] :
4. If the incumbent is far ahead of the challenger, i.e.,
then
<
q+(1 )(1 q)
(1 q)+(1 )q :
3. If the incumbent is a bit ahead of the challenger, i.e.,
(1
< ;
= 0.
2. If the incumbent is a bit behind the challenger, i.e.,
(1 q)+(1
H
x=A
!=
is su¢ ciently low such that
and negative when
L
s=B
@
@
is positive when
> . But in doing so they fail to take into account the direct e¤ect of
on Pr(x = A). The correct expression is:
Pr(x = A) =
+ (1
) [ q + (1
) (1
q)] + (1
) [ (1
q) + (1
) q]
L
s=B :
(1)
The …rst term of Equation 1 comes from the fact that high quality incumbents follow their signals:
the probability that the incumbent is high quality is
and the probability that s = A is . The
second term comes from the fact that a low quality incumbent who sees s = A plays x = A:
the probability that the incumbent is low quality is (1
q + (1
) (1
q). The third term is for low quality incumbents who see s = B: the probability
that the incumbent is low quality is (1
L
s=B
) and the probability that s = A is
), the probability that s = B is
(1
q) + (1
is the equilibrium probability that the incumbent panders, choosing x = A:
3
) q; and
@ Pr(x=A)
@
We now …nd
for di¤erent values of ; considering separately cases 1-4 listed above,
and substituting the relevant value of
L
s=B
into Equation 1.
L
s=B
1. When the incumbent far behind the challenger
Pr(x = A) =
Thus
@ Pr(x=A)
@
=
[ q + (1
) (1
+ (1
= 0, so
) [ q + (1
) (1
q)] :
q)] ; which is positive.
2. When the incumbent is a bit behind the challenger, substituting for
Pr(x = A) =
+ (1
+ (1
=
Thus,
@ Pr(x=A)
@
) [ (1
(1
+
=
) [ q + (1
+
) (1
q) + (1
L
s=B
yields
q)]
(1
(1
) q]
)
)
(1
q) + (1
)q
q + (1
) (1
(1 q) + (1
)
> 0.
From cases 1 and 2, we see that the Popularity Hypothesis prediction of a positive correlation
between popularity and congruence for low-popularity incumbents holds unaltered.
3. When the incumbent is a bit ahead of the challenger, substituting for
Pr(x = A) =
+ (1
+ (1
=
Thus,
@ Pr(x=A)
@
=
) [ (1
+ (1
1
) [ q + (1
(1
q) + (1
(1
)
)(1
) (1
)
)
(1
(1
) (1
)
) [ (1 q) + (1
< 0; which is consistent with the Popularity Hypothesis as
4. When the incumbent is far ahead of the challenger,
Thus
@ Pr(x=A)
@
=
[ q + (1
) (1
) q]
:
stated by CS.
Pr(x = A) =
yields
q)]
) q] 1
) (1
L
s=B
+ (1
L
s=B
= 0, so
) [ q + (1
q)] ; which is positive.
4
) (1
q)] :
q)
)q
From case 4, we see that the relationship between congruence and the voters’ ex-ante belief
about the probability that the incumbent is high quality is not fully consistent with the Popularity
Hypothesis as stated in CS. Speci…cally, within the set of incumbents who are extremely popular
the model predicts a positive correlation between congruence and popularity, as long as presidents’
initial popularity is correlated with the probability that they are high quality.
Implications for empirical analysis When might incumbents’actual quality vary? The most
obvious context for presidents is when a new chief executive takes o¢ ce. The CS empirical speci…cation includes president indicators, which control for this type of variation in competence. Thus,
although CS’s derivation and statement of the Popularity Hypothesis is problematic, their empirical speci…cation is nonetheless appropriate for testing the CHS theory. The only situation where
indicators would not be a su¢ cient control variable would be if the actual competence of a president
changed over the course of his term and this change was re‡ected in changes in his approval rating.
In other settings, the di¤erence between the Popularity Hypothesis stated in CS and the correctly derived prediction may be relevant. For example, scholars may not use indicators for individual executives. Also, the competence of a governing coalition could change in parliamentary
democracies due to changes in the set of parties in the coalition. Thus, we want to set the record
straight, to provide a solid basis for future empirical work.
References
Anderson, Stephen H., and Natalia V. Smirnova. 2006. “A Study of Executive Budget-Balancing
Decisions.” American Review of Public Administration 36: 323-336.
Canes-Wrone, Brandice, Michael C. Herron, and Kenneth W. Shotts. 2001. “Leadership and
Pandering: A Theory of Executive Policymaking.” American Journal of Political Science 45:5325
550
Canes-Wrone, Brandice, and Kenneth W. Shotts. 2004. “The Conditional Nature of Presidential
Responsiveness to Public Opinion.” American Journal of Political Science 49:690-706.
Hobolt, Sara Binzer, and Robert Klemmensen. 2008. “Government Responsiveness and Political
Competition in Comparative Perspective.” Comparative Political Studies 41: 309-337.
Rottinghaus, Brandon. 2006. “Rethinking Presidential Responsiveness: The Public Presidency
and Rhetorical Congruency, 1953-2001.” Journal of Politics 68: 720-732.
Wood, B. Dan, and Han Soo Lee. 2009. “Explaining the President’s Issue Based Liberalism:
Pandering, Partisanship, or Pragmatism.” Journal of Politics 71: 1577-1592.
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