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THREE TOPICS ON ELECTIONS

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5108 Kthroj/AccaPreleIRC/Dateoue.indd

THREE TOPICS ON ELECTIONS

By

Makoto Tanaka

A DISSERATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Economics

2008

ABSTRACT

THREE TOPICS ON ELECTIONS

By

Makoto Tanaka

This dissertation consists of three chapters. In chapter one and two, I consider information

transmission problem from politicians to voters about possible outcomes of policies in a

two-period-and-two-elections model (Chapter one) and in an infinite period model with

political parties as overlapping-generations organizations (Chapter two). In Chapter three, I

analyze the choice of policy instrument by an incumbent politician who can use an

inefficient tariff and a less inefficient production subsidy to help domestic manufacturers.

Chapter Qne: “Learning Through Elections”

I consider choices of policy platform at elections when there is uncertainty about outcomes

of policies, and one party has information advantage over another party and voters. This

ability might reflect the ability of the politician in the party. Since the platform choice is

based on the information the politician has, the choice at the election transmits some

information to voters. Then, in one possible equilibrium, I show a case that the higher the

ability of the politician, the worse the information transmission from politicians to voters.

Chapter Two: “Information transmission from overlapping political parties”

I analyze an information transmission problem, again, but in infinite period with two

political parties as overlapping—generations organizations. Policy outcomes depend on the

true state of the world, which changes in each period. Both parties receive information

about the true state. Platform choices are made by old politicians in parties who will retire

soon. So, the next election does not restrict their opportunistic behavior directly. Still, I

show that the OLG party structure restrains the opportunistic choice of platform by old

politicians.

Chapter Three: “The Choice of Inefficient Instruments in a Simple Retrospective Voting

Mgdel with Vgter Abstention”

Tariffs are more inefficient than production subsidies as the instrument to help domestic

industry. Still, tariffs have been used. In this chapter, I propose one explanation about why

governments use inefficient tariffs. The basic idea is the manipulation of voter abstention.

If an incumbent politician decides to help a domestic industry, he also needs to determine

how to distribute the cost of the help among voters. Assuming that some voters’ voting

abstain partially depending on the utility they receive from the incumbent’s policy, the

incumbent could affect the choice of voters to vote or not. Naturally, he will try to take

advantage of it. I analyze if the incumbent has incentive to choose tariff in two cases: same

tax rate for all voter groups, and different tax rates for groups.

To My Mother, Yumiko Tanaka

iv

ACKNOWLEDGEMENT

I have so many people I would like to thank for my dissertation. However, because of
limitation of space, I have to minimize the number of people to thank. First of all, I would
like to thank my committee members. I appreciate the help of my adviser Professor John D.
Wilson. Without his guidance and suggestions, I could not have completed my dissertation. I
thank Professor Anthony Creane for his caring. I really appreciate it when things were rough
for me. I also appreciate the conversations I had with Professor Susan Zhu and Professor
Eric Chang. Because of their help, I could improve my dissertation a lot. Regarding chapter
three, I also want to thank Professor Nelson of Tulane University. The conversation I could
fortunately have with him helped and encouraged me a lot while I was working on the
chapter.

I thank Jennifer Carducci for her professional job and help. She deserves more
chocolate. I also thank Stephanie O. Smith for her help on the format of this dissertation.
I appreciate her kind help and apologize for all of my formatting mistakes. She deserves
more cakes. Finally, but not leastly, I would like to thank all of my friends. They helped
and encouraged me, and sometimes inspired me with their way of life. I appreciate all

the people I met in Michigan.

TABLE OF CONTENTS

LIST OF FIGURES ................................................................................ viii
Chapter 1 Learning through Elections ............................................................... 1
1 .1 Introduction ............................................................................. 1

1.2 Model ..................................................................................... 3

1.3 Updates and Platforms ................................................................ 9

1 .4 Equilibrium ........................................................................... 1 6

1.5 Conclusion of Chapter 1 ............................................................ 20
Appendix of Chapter 1 ........................................................................ 22
Endnotes of Chapter 1 ......................................................................... 33
References ....................................................................................... 35
Chapter 2 Information Transmission from Overlapping Generations parties ................. 36
2.1 Introduction ........................................................................... 36

2.2 Model and Behavior of Politicians ................................................... 41
2.2.1 Model ........................................................................ 42

2.2.2 Behavior of Politicians ...................................................... 52

2.2.3 Definition of equilibrium ................................................... 56

2.3 Results .................................................................................. 58

2.4 Conclusion of Chapter 2 ............................................................. 62
Appendix of Chapter 2 ......................................................................... 68
Endnotes of Chapter 2 ......................................................................... 75
References ....................................................................................... 78

Chapter 3 The Choice of Inefficient Instruments in a Simple Retrospective voting Model

with Voter Abstention ............................................................................... 81
3.1 Introduction ........................................................................... 81

3.2 Model ................................................................................... 83
3.2.1 Economy side ............................................................... 83

3.2.2 Political side .................................................................. 86

3.3 Results with two groups ............................................................... 91
3.3.1 Single Tax Case .............................................................. 91

3.3.2 Different Tax Rates ......................................................... 99

vi

3.4 Three groups: heterogeneity in workers ........................................... 103

3.4.1 The optimal tax rates ....................................................... 105

3.4.2 Will incumbent use tariff? ................................................. 107
3.5 Literature Review ..................................................................... 1 11
3.6 Conclusion of Chapter 3 ............................................................ 115
Appendix of Chapter 3 ...................................................................... 120
Endnotes of Chapter 3 ....................................................................... 124
References ..................................................................................... 1 26

LIST OF FIGURES

Figure 1.1 Flow of Game ........................................................................... 8
Figure 1.2 ............................................................................................... 9
Figure 1.3 .............................................................................................. 11
Figure 1.4 .............................................................................................. 14
Figure 1.5 ............................................................................................. 17
Figure 1.6 ............................................................................................. 19
Figure 1.7 ............................................................................................. 28
Figure 1.8 ............................................................................................. 29
Figure 1.9 ............................................................................................. 31
Figure 2.1 ............................................................................................. 50
Figure 2.2 ............................................................................................. 51
Figure 3.1 ............................................................................................. 90

viii

1 Learning through Elections

1. 1 Introduction

The objective of this chapter is the construction of a model of two consequent elections
with uncertainty about policy outcomes. Tiaditionally, electoral competition models
in Political Economy have assumed that there is no uncertainty about outcomes of
government policies. Clearly, this is a strong assumption. Before the implementar
tions of policies, people can have only beliefs about outcomes. Politicians, however,
might have more information about outcomes than voters. Suppose that a politician
has some private information about possible outcomes. Then, given the information
asymmetry, what policy platform will the politician choose during an election? Since
the politician chooses the platform based on the information he has, the choice of the
platform can be considered as the information transmission from him to voters. Then,
will the politician reveal the information honestly? In other words, will the politician
lie to voters? This is the information transmission problem during the election.
From 19903, many papers have analyzed the problem with various assumptions
about uncertainty (Harrington (1993a), etc.) have. Observing platform choices by
parties during an election, voters can update their beliefs about the uncertainty. How-
ever, there is no reason we can expect this transmission of information to be perfect.
Obviously, the information asymmetry enables politicians to take Opportunistic be-
havior; they can choose a bad policy and lie to voters that it is a good policy. The
common structure of papers in the literature is the following; there is the uncertainty
about policy outcomes, which depend on the state of the world. A politician (or
politicians) has some private information about possible policy outcomes. He chooses
a policy. This choice may be his platform during an election (Heidhues and Lagerof
(2003)), or the policy he implements before the election (Majumdar and Mukand

(2004)). Then, at the election, voters vote for the candidate they prefer. The im-

portant part is this; since the politician’s choice gives voters some information about
the uncertainty, politicians can manipulate preferences of voters on policies and /or
politiciansl.

This situation gives voters two Opportunities of learning about the uncertainty
(i.e., the state of the world); one is when voters observe the choices of parties during
the election, and the other is when voters observe the outcome of the implemented
policy after the election. In multi-election models, the voting decisions at elections
depend on these two opportunities of learning. Thus, politicians have to take into
consideration the impact of the election platform at one election on the election after
that. To model this, I consider a two-period and two-election model. Of these two
elections, the first election is for the information transmission. The second one is for
the retrospective voting based on the result of the implemented policy after the first
election, which guarantees that at least some information is transmitted to voters
during the first election. In addition, I assume that one party has the information
advantage not only over voters but also over the other party. This information advan-
tage can be considered as showing the high ability of the politician in the party. The
symmetry between parties during an election is a common assumption in electoral
competition models without an incumbent. Though Heidhues and Lagerof (2003)
and Bernhardt, Duggan and Squintani (2007) also assume the asymmetry between
parties, the asymmetry in these papers means that parties have different information.
The asymmetry here is stronger since only one party receives the information. This
is a strong and uncommon assumption. However, the asymmetry between parties
in the sense of this chapter is not unnaturalz. As a factor causing such asymmetry
between parties during an election, "valence" has been incorporated into electoral
competition models recently (Schofield (2005), etc.) So, the ability of the politician
in this chapter can be considered as the valence factor in this chapter. Then, I show

that this asymmetry has an interesting implication when the ability of the politician

changes.

The remainder of this chapter is organized as follows; section 1.2 describes the
model. Section 1.3 describes the behaviors of voters and two parties. Section 1.4
shows the existence of equilibrium and other results. Section 1.5 discusses about this

model and its results. All proofs are in the Appendix of this chapter.

1.2 Model

I consider a society with two parties (Party 1 and Party 2) and voters in two periods.
There are two possible policies, at and b. The society can implement only one policy
in one period. There is no uncertainty about the outcome of the policy b. But the
outcome of the policy a. is uncertain. A natural interpretation of these two policies
is that the policy b is the continuation of a current policy, and the policy a is a new
policy. As I explained in the introduction, no one is perfectly sure about the outcome
of the new policy, there is the uncertainty about its outcome. In each period, there
is an election. The society decides which policy it implements in the period by the
election. Candidates from two parties (one from each party) announce one of two
policies as their policy platform. Voters vote for the candidate they prefer, and the
elected politician implements his platform.

Candidates from two parties are new candidates. If a candidate loses the first
election, the game is over for him. At the second election, the party that lost the first
election put up a new candidate. The politician who won the election gets a fixed
rent, which is normalized to one. Let 6 be the common discount factor. The objective
of candidates is the maximization of expected sum of rents from two periods. They
are risk neutral. The outcome of the policy b is the utility 6 6 (0, 1) to voters. The
outcome of the policy a could be success or failure. The outcome depends on the

1

state of the world, w0 and w . If the true state is two, the outcome of the policy

a is failure and the utility 0 to voters. If the state is 2111, the outcome is success

and utility 1 to voters. No one in the society knows the true state. Instead, voters
have belief q 6 (0,1) as the probability of w1 being the true state. This q is lower
than 5. This structure of uncertainty is almost same to the Majumdar and Mukand
(2004). But unlike the paper, one implementation of the policy a is enough to know
the true state of the world. Party 2 candidate also has belief q, same as voters.
Since q < 6, without further information about the uncertainty, the society should
choose the policy b since the expected utility of the policy a is only q. But Party 1
candidate receives a signal about the probability of the true state being w1 before the
first election. To make this model simple, I assume that he receives the probability
of state to1 directly. Denote it as p. This means, the best policy choice of Party
1 candidate for voters is choosing the policy a if p > 5 and choosing the policy b
if p < 6. If p = 6, his choice does not matter. This p is a random variable, and
its distribution depends on the true state of the world. If the true state is wl, the
cumulative distribution function is F (p) If wo, the function is C(p). For 1) E (0, 1),
C(p) > F(p). Moreover, F and G are assumed to be differentiable, F’ (p) > 0 and
G’(p) > 0 on (0,1), and limp__,0 F’(p)/G"(p) = 0, limp_,1F’(p)/G’(p) = 00, and
F' (p) / G’ (p) is monotonically increasing (i.e., monotone likelihood ratio property.)3
These cumulative distribution functions can be considered as representing the ability
of the politician. These properties mean that when the candidate receives the high
value of p it is more likely that the true state is w1 than that the true state is mo,
and vice versa. These distributions are common knowledge.

So, there is an informational asymmetry between Party 1 candidate and vot—
ers/ Party 2 candidate. Then, Party 1 candidate’s policy platform is considered as a
signal from the candidate about the probability of the true state being wl. As the
strategy of Party 1 candidate, I consider the following simple one; before the first
election, the candidate chooses the value T E [0, 1] as the threshold value such that

if he receives p > 7', he will announce the policy a, and if he receives p < T, he will

announce the policy b. If T = p, he will or will not announce the policy a. Since p and
B are the expected utilities of policies a and b, respectively, the value of T different
from ,6 means inefficiency. If T < B, when p E [T, 6), Party 1 candidate would pr0pose
the policy a even though he knows the policy b has higher expected utility for voters.
If T > B, when p E ([3, T), the candidate would propose b even though the policy a
has higher expected utility. With this strategy, T = 1 is interpreted as the candidate
never announces the policy a. T = 0 is that the candidate always announces the
policy (1. Since the choice of a when p > B and the choice of b when p < B is the best
for voters, the best value of T for voters is 5.

Party 1 candidate’s strategy during the second election is simple because of the
assumption about the uncertainty. He announces the policy that voters have higher
expected utility. In a case that he announced the policy a during the first election
and won, then at the start of the second period, every member of society knows the
true state. If the state is wl, it is clear that the policy a is better than the policy b.
Then, the candidate should announce the policy a as the platform during the second
election. If the state is 100, it is also clear that the policy b is better. In the case that
he announced the policy b during the first election and won, he announces the policy
b again during the second election. This is because his platform during the second
election does not give any information to voters. This is intuitively clear. Since the
candidate cares only about the office rent, not the outcome of policies, if announcing
the policy a during the second election is beneficial for him with a certain value of
p, then it is beneficial for the candidate with any value of p to announce the policy
a during the second election because his expected utility during the second election
does not depend on p. Thus, whatever the value of p, Party 1 candidate announces
the policy d. Then, the platform a. does not give any information to voters. There is
no reason for voters to update their belief. Thus they do not update their belief. Since

the belief during the second election is the updated one through Party 1 candidate’s

platform during the first election and it is lower than [5 (since Party 1 candidate
announced the policy b during the first election), it is beneficial for the candidate to
announce the policy b.

The strategy of Party 2 candidate is as follows; during the first election, expecting
the value of T, the candidate uses the mixed strategy. Denote as c the probability of
his announcing the policy a during the first election. His strategy during the second
election is same as Party 1 candidate.

Since during the second election, it is clear that which policy should be proposed,
I do not need to consider about the strategy of the new candidate put up by the party
that lost in the first election.

Knowing Party 1 candidate’s strategy, voters (and Party 2 candidate) try to infer
the value of T rationally and update their beliefs about the state it)1 after observing
Party 1 candidate’s platform, by the Bayesian rule. If Party 1 candidate announces
the policy a, the updated belief is higher than the initial one. If the candidate
announces the policy b, the updated belief is lower.

At each election, voters vote for a party according to their period preference. The
preference consists of three parts. The first part is the expected utility from the
outcome of implemented policy. The second is a random noise. Thus, this model has
an element of probabilistic voting model (Persson and Tabellini (2002)). All voters
receive same noise during each election. This noise represents factors about parties
and candidates other than the utility derived directly from the implemented policy,
like the advent of charismatic candidate or the eruption of scandals. This noise 5 is
an i.i.d. random variable with a distribution H. This s is voters’ bias for Party 1 and
independent of the announced policies by candidates. It can take negative value as
well as positive value. If it is negative, it means bias against Party 1. I assume that
H (0) = 0.5 and H ’ (e) > 0 on its support, the support of H is connected and large

enough, and H is symmetric.

The third part is the assumption of the retrospective voting behavior on the

implementation of the policy a by Party 1 in the first period.

(A) : If the policy a is implemented by Party 1 after the first period and the
outcome is success, voters vote for Party 1 candidate at the second election. If the

outcome is failure, voters vote for Party 2 candidate.

As I wrote above, if policy a was implemented in the first period, there is no un-
certainty in the second period and both parties pr0pose same policy as their platform
during the second election. So, the choice of the party to vote for does not matter
for voters. Thus, voters can use the second election to reward or punish Party 1
(i.e., the retrospective voting.) It is natural to assume that the success increases the
probability of winning the reelection and that the failure decreases the probability.
This is the retrospective voting; voting based on past performance. This (A) is the
simplified and extreme version of such reaction. This works as the incentive for Party
1 candidate to announce the policy a. Without this, as I will show later, there is no
equilibrium.

This voting reaction to the policy a is applied only to Party 1 during the second

election. In other cases, voters vote for Party 1 candidate if,

EU (Party 1 candidate/s platform) + e > EU (Party 2 candidate/s platform)
where, EU means the expected utility
¢=> e > EU(Party 2Is platform) — EU(Party 1/3 platform)

If the opposite inequality holds, voters vote for Party 2 candidate. If the equality
holds, voters vote for Party 1 with probability 0.5. Since a is a random variable, the

probability of Party 1 candidate winning the election is

1-- H(EU(Party 2'splatform) —- EU(party 1'splatform))

The flow of the game in the first period (see figure 1.1)

First period

Flow of Game

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 Signal p

9:

d

5 P l h

m arty c ooses ,_,

g, platform Voters update E? E g 589

g . belief —' 3 g Q a

g E! —" (b '"h "U
(D D (p

Si 53+ 3 :l

: Party 2 chooses 5 g a

co

{3+ platform H l: :3

r»

H.

(D

 

 

 

 

Party 1 chooses threshold 1 for its platform.
Party 2 expects 1.‘ and chooses its platform.

 

 

 

Figure 1.1:

Party 1 candidate receives the signal p.
Candidates announce platforms simultaneously.
Voters observe platforms and update their belief.
Voters receive noise 5, and vote for the party they prefer.
The Elected party implements its platform.
The outcome of the implemented policy is observed.
If the policy was a, then every member’s belief about the state of world is
updated.
Second period.
The equilibrium is defined as the profile of values of T and e such that,
(1) Voters and Party 2 expect the value of T and update their belief rationally
(Bayesian),
(2) With the expectation of T, c is the optimal value for Party 2 candidate.

(3) With the value of c and the expectation about the value of T by voters and

Party 2 candidate, T is the optimal for Party 1 candidate in the sense that it is the
optimal for a candidate with p > T to announce the policy a, and that it is optimal
for a candidate with p < T to announce the policy b.

(4) All expectations are correct.

1.3 Updates and Platforms

In this section, I consider behaviors of voters and party candidates in turn. For
notational simplicity, I abuse notations in denoting not only the threshold value choice
by Party 1 candidate but also all expectations about it as T. I also treat T and p

interchangeably when I consider belief updates.

Voters. (see figure 1.2)

 

‘___qa(t)

 

‘_____qb(t)

 

 

 

12,13

Figure 1.2

Voters update their belief about the probability of the true state being wl after
observing the platform of Party 1 candidate. Let T be the threshold value expected
by voters.

In the case that Party 1 candidate announces the policy a, then the updated belief
is,
= q{1 —F(r)}

qU-JW0f+U-QM1-GUH

This is well defined for T E [0, 1).This updated belief has the following properties.

 

(LUQWU

Lemma 1.1.

 

q“(r)= q 1_G>que(o,1)
4+(1‘qlf_—F‘
lim7-_,1 qa(T) = 1
q
(10 =_____=,
q() q+1_q q

qa’(T) > 0 for all T 6 (0,1)

In the case that Party 1 candidate announces the policy b, the updated belief is,

qFU)
flWfl+ll-®Gfii

 

(Lmq%d=
This is well defined for T E (0, 1]. This updated belief has the following properties.

Lemma 1.2.

 

qb(T) = q C < q for T 6 (0,1)
£1 + (1 — (1)—F“
1iHIT—40 qb(T) : 0
b q
1 = ____._ =
q() 9+0-a) q
TWOZO

Between qa(T) and qb(T), there is the following relations. From Lemma 1 and 2,

the following is obvious.

10

Lemma 1.3.

q"(’r) > qu

_ a q"(T)-q
(1-3) (1’0) —q (T) — qF+(1_q)G

 

Party 1 candidate. (see figure 1.3)

Party 1 candidate’s choice of T during the first election depends on three things;
signal p, his expectation of voters’ expectation of T and Party 2 candidate’s mixed
strategy 0 during first election. Let q“ and qb be Party 1 candidate’s expectation of
voters’ updates (these come from the candidate’s expectation of voters’ expectation

of T.) I consider the candidate’s choice of T depending on different values of c.

 

Q“ qa(p)

b
Kq 1 (p)

 

 

 

LP

Figure 1.3

The case of c = 0: this is the case that Party 2 candidate announces the policy b

during the first election. Then, the expected sum of rents of announcing the policy a

11

for Party 1 candidate with p is,
{1 - H(-qa + {3)}[1 + 5p]

The expected sum of rents of announcing the policy b is,

{1— H(0)}i1 +6{1— H(0)}l = 31—5

It is beneficial for the candidate to announce the policy a if,

{1-1‘1(—q“+fi)}l1+620]23-11E
2+6 a
(1.4) => 1— m 2 H(-q H3)

From this, the necessary minimum level of q“ for the Party 1 candidate with p to
announce the policy a can be defined. Let g? (p) be the value of q“ defined from the

above condition satisfied with equality. Then, the following result can be obtained.

Since qa(0) = q < 5 and qa(1) = 1, this Lemma implies there is a crossing point

The case of c = 1. This is the case that Party 2 candidate announces the policy
a during the first election. Then, the expected sum of rents of announcing the policy

a for Party 1 candidate with p is,

{1- H(0)}l1 +6101 = %

The expected sum of rents of announcing the policy b is,

{1— H(—B+qb)}l1+6{1 — H(0)}i = 2T‘“’{1 — H(—fi+qb)}

12

It is beneficial for the candidate to announce the policy a if,

 

1+6 2+5
2102—2 {1-H(-6+qb)}
1+6p
_ b > __
(1-5) =>H( 6+q)_1 2+6

Same as q‘l’, the necessary minimum level of qb for a candidate with p to announce
the policy a can be defined from this condition. Let qll’(p) be the value of qb defined
from the above condition satisfied with equality. For this qll’ (p), the following results

can be obtained.

Lemma 1.5.

Unlike the case of qa(T) and q? (p), it is possible that there is no crossing point of

qb(T) and q? (p) Between qi” (p) and q? (p), there is a following relation.

Lemma 1.6.

qi’fi?) 2 TM)

The equality holds when p = 0.5.
The case of c E (0, 1) is the combination of above two cases.

Party 2 candidate. (see figure 1.4)

Since Party 2 candidate has the same belief q as voters, it seems at first that he
always announces the policy b. But he knows that the belief will be updated after
Party 1 candidate announces its platform. Following the update, the probability of
Party 2 candidate winning the first election by announcing the policy b changes. If
Party 2 candidate believes that it is very likely that Party 1 candidate announces the
policy a and that the updated belief after that is high enough, it might be beneficial

for the candidate to announce the policy a. Notice that there is a trade-off between

13

the likelihood of Party 1 candidate announcing the policy a and the updated belief.
Since Party 2 candidate does not have any private information about the probability
of the true state being w], announcing the policy b is completely an Opportunistic
behavior. But, since the outcome of the policy depends on the true state not on
which candidate implements the policy, voters do not punish such an Opportunistic

behavior in this model.

a
q2 [q 2(1)

1 /

 

q_

 

 

 

1,1)

Figure 1.4

Again abusing the notation, I denote the value of T expected by Party 2 candidate
as T. Then, Party 2 candidate thinks the probability of Party 1 candidate announcing

the policy a during the first election is,

q{1TF(T)}+(1-q){1-G(T)}= 1-qF(T)-(1-CI)G(T)

14

The expected sum of rents Of Party 2 candidate critically depends on the assumptions
about what happens after Party 2 candidate winning the first election. I restate two
related assumptions. The new candidate put up by Party 1 at the second election
after the defeat Of the Party at the first election does not have any private informa-
tion (actually it does not matter whether or not he has private information since no
information can be transmitted credibly to voters during the second election.) Voters
do not apply (A) to Party 2 candidate even if the candidate implements the policy a
in the first period.

Then, the expected sum Of rents for Party 2 candidate when the candidate an-

nounces the policy a during the first election is,

{1 — qF(T) - (1 - q)G(T)}H(0)[1+ 5151(0)]
+{qF(T) + (1 - Q)G(T)}H(—,5 + qb(T))[1+ 611(0)]
= [0.5 + {qr + <1 — qu}{H(-fi + A — 0.5}12—‘219

The expected sum of rents when the candidate announces the policy b is,

{1 - qF(T) - (1 - q)G(T)}H(-q" + B)I1+ 6H(0)l
+{qF(T) + (1 - q)G(T)}H(0)[1+ 511(0)]
2 + 6

= [H(_qa + 5) + {qF + (1 — q)G}{0-5 — H(€1a + 6)}17

Then, the candidate announces the policy a at the first election if,

0.5 + {qF + (1 — q)G}{H(—fi + qb) — 0.5}
2 H(-q" + [3) + W” + (1 - q)G}{0-5 - H(q" + 5)}
(16) => W” + (1 - q)G}{H(-fi + q”) + H(-q" +13) - 1}

2 H(-q" + fl) - 0-5

Unlike two conditions for Party 1 candidate, this condition (1.6) has both q“ and qb.

Using (1.3), this condition is converted into the one with only q“.

15

a

(17) MP +(1— q)G}{H(—6 + q“ — (11,362”) + Ht—q“ + H) — 1}
2 H(-q" + B) - 0-5

 

Then, the minimum necessary level of q“ for a given T is defined as the value of q“
satisfyng this condition with equality. Denote the minimum level as q§(T). Since
this condition is not easy to handle, I consider also the condition with a given value
of qb. Given the fixed value of qb, the minimum necessary level of q“ for a given T is
obtained from the condition satisfied with equality. Denote the minimum necessary

level for a given qb as q‘2’(T; qb). Then, the following Lemma can be obtained.

Lemma 1.7

For T E (0, 1),
3q§’(T;qb) >

8T
(96130; (1")

qu
(ISO) 2 (1‘2"(T; (1’)

(13(0; (1”) = (13(0) = B

the value of T such that q§’(T) = 1 is lower than 1.

0

<0

1.4 Equilibrium

Firstly, I show there is no equilibrium without voting behavior (A) in this model.

Lemma 1.8. Suppose that voters vote during the second election according to

their period preference without (A). Then, there is no equilibrium.

Thus, (A) is a necessary condition in this model. Next, I state the Proposition of

the equilibrium existence.

Proposition 1.1. With (A), there is an equilibrium in the model.

16

There are four possible cases of the existence of equilibrium. Since these cases are
rather complicated and do not give clear and intuitive characterizations of equilibrium,

I concentrate on only one case that q‘2’(T) and qa(T) do not cross (see figure 1.5.)

(I
q , q [(120)

 

 

 

 

 

 

1 ./
CL
‘ q (r)
[34
q— a
i 4 q1(p’
0 t, p t* 1

Figure 1.5

In this case, the equilibrium value of T and c are T* such that qa(T*) = qi’(T*)
and c = 0. Party 2 candidate never proposes the policy a since qg(T) > qa(T); q"(T)
is never high enough for Party 2 candidate to prOpose the policy. For this case,
there is a simple sufficient condition. Let H (e), the distribution of e, be the uniform
distribution (its support is assumed to be large enough.) Then, (1.7) becomes q 2 fl.
Since 6’ > q, qé’ (p) is always larger than q“ (p) and Party 2 candidate never announces
the policy a. Thus, the case like figure 1.5 is obtained. The equilibrium choice of T
is determined at the crossing of qa(T) and q‘l’“ (p). Denote the equilibrium value of T

as T* . Then, there is no guarantee that T* is equal to 6. T* could be higher or lower

17

than [5. Whichever it is, that means the inefficient choice of Party 1 candidate for
voters.

In this case, a more interesting result can be Obtained; the higher the ability of
Party 1 candidate to discern the true state, the lower the equilibrium outcome value
of T. I give a more formal explanation. As I wrote before, the cumulative distribution
functions F and G can be considered as representing the ability of Party 1 candidate.
Then, a high ability candidate is the one who is more likely to receive high values
of p when the true state is w1 and less likely to receive high values of p when the
true state is wO. Let F 8:67 and F&G be two different sets of distributions. Then, if
150051700) and C701) 2 0(1)) for any I) 6 (0,1) and if 170?) < F00) or @(p) > 0(1))
for some p 6 (0,1), then the candidate with F856} can be considered as having the

higher ability than the one with F &G . Since voter’s updated belief is,

 

 

qa(7.) = q{1 _ F(T)}
q{1— Fng} + (1 - <1){1— 9(7)}
— 1— C(T)
(1+ (1 —Q)m

the updated belief with the higher ability candidate is never smaller than the updated

belief with the lower ability candidate, and strictly higher for some T.

18

(L a

 

 

 

 

(11, q
1 a
q (s=3)
.J
a
’3 q (8:2)
(1‘ a S ta
= i < >
i <— i
>l<>l< 1* l 1'" p
0 t 1: 0.5 1
Figure 1.6

In the figure 1.6, the two different curves of voter’s updated beliefs, q“ for s = 2
and q“ for s = 3 are drawn based on F(p) = p3 and G(p) = 1 -— (1 - p)3. With
these function forms, higher value of 3 means higher ability. On (0, 1), the curve of
q“ (s = 3) is above the curve of q“ (s = 2). Since the change of F and C does not
affect q‘f, the equilibrium value of T moves to left. Since T* < B = 0.6 in figure 1.6,
the outcome with s = 2 is inefficient as the policy b can guarantee the utility 6 to
voters. The candidate with p E (T*, 6) exploits the voters’ trust on the ability of the
candidate. Since T** < T*, with the higher ability candidate the inefficiency worsens

in this case. I state this as a Proposition.

Proposition 1.2. If H is a uniform distribution, the equilibrium exists with T"
such that qa(T*) = qi’(T*) and c = 0. Moreover, in this case, the higher the ability of

Party 1 candidate, the lower T*.

19

This proposition is not saying that having a higher ability candidate is always
bad. If the ability of current candidate is so low that T* with him is to the right of
B, changing him with a higher ability candidate could help voters with T* moving
closer to [3. However, changing candidates with higher and higher ability candidates,
T* eventually passes 6. After that, higher ability candidates make things worse for

voters.

1.5 Conclusion Of Chapter 1

In this chapter, I considered the platform choice in a two-election—and—two—period
model under uncertainty with one party having information advantage. Most papers
in the literature of the policy choice with the uncertainty consider models with only
one election. Since government offices usually allow multiple terms with multiple
elections, candidates must consider about the future elections. Thus it is worth
considering the policy choice of candidates considering future elections as well as the
current election. Harrington (1993b) also considers a two-election model. However,
the interest of the paper is whether politicians will keep their campaign platform after
they win the election, which is different from this chapter since the interest of this
chapter is on what platform a politician will choose.

This chapter assumes strong assumptions. The assumption that only one party
receives the signal is clearly a strong one. In the literature of the information trans-
mission during the election, the more common assumption is that both parties receive
signals (Heidhues and Lagerof (2003) and Bernhardt, Duggan and Squintani (2007),
etc.) However, it is not clear that which is more natural assumption. During elec-
tions, often one party has advantage over the other party (see the Rasmussen reports
(June 21, 2008).) The assumption is a simplified description of such reality. The
other strong assumption is that voters apply (A) only to Party 1 candidate. When

Party 2 candidate implements the policy a and its outcome is failure, the voters does

20

not punish the candidate. Since Party 2 candidate’s choice of policy a is completely
an Opportunistic behavior, this seems unrealistic. It seems very likely that voters
punish the candidate strongly. However, it does not change results qualitatively.
The equilibrium value of T depends on functions and parameters. So, there is
no reason to expect T* = 5. If T* < [3, the candidate with p E (T*,B) announces
the policy a while believing the policy is actually worse than the policy b. Thus,
this could be considered as the inefficiency result. Similar inefficiency happens when
T* > 6. Then the interesting result of this chapter that the higher the candidate’s
ability the lower the equilibrium value of T in the case I explained in the previous
section means that a higher ability candidate could make the inefliciency worse. This
happens because the high ability of the candidate causes voters to update their belief
higher, which gives more opportunity to the candidate to exploit. Though the result
is interesting, to obtain more general result, it might be necessary to consider if the
same result would happen even when two parties receive signals, which is a future

research topic.

21

Appendix of Chapter 1

Lemma 1.1.

90(7) = q > q for T 6 (0,1)

1 - G
q + (1 — 901—17:
limT—d (10.0.) = 1

q
a 0 = —-—-—-—- = _
q() q+1_q q

qa'(T) > 0 for all T 6 (0,1)
Proof. Since C(p) > F(p),1—E%g% < 1 for p 6 (0,1). Then, qa(T) =
q

> q for T 6 (0,1), and q “(0): ——i—-——— — q. From L’HOpital’s
q+1-q

 

 

1—G
F
Inwandumnslaéil

(fl

= 00, limT_,1q"(T) = 1. The derivative of qa(T) with respect

tOTis,

al _ Q{1_q} 0,1 _—__F_
q (T) [q{1-F}+(1—q){1—G}12F{7G” —G 1

—F
Since limT_,0— G =0 andi —G > 1 for T 6 (0,1), q“’ (T) is positive1 for low value
—F
of T. Suppose that q"’ (t);0 at T = t 6 (0,1). This implies -FT:1—_——é - 1< _.O
dl—F F' G’l —F_ dG’l—F _1—FdG’
Then, d—T1—__G— 1—G’F—71———’—<0' Wit this]; [F —GdTF’+
G d 1— F d C" . . . G 1— F1
F72; 1 _ G < 0 since dTF7 < 0. G’This implies, if F71_——67 — 1<0at a certain value
01 F

of T, for all T’ > T, the value of F7I———G_ — 1 < 0. Then, q"(T) is downward sloping

for T’ 2 T. Since lim.,_,1 qa(T) = 1, this is a contradiction. Thus q"’ (T) > 0 for all

 

 

 

T E (0, 1). The updated belief qa(T) goes up from q to 1 as increases from 0 to 1. I

Lemma 1.2.

 

qb(T) = q G < q for T 6 (0,1)
q+(1-®F

limT—->0 qb(T) = 0

b __ q =

guy—0+0-Q) q

leZO

22

q
m+U-q%-

F
I
m— — q. From limT__,0 5—7—8: 3— - O, limT__,0 qb(T) = 0. The deriv-

. . . 1— q} F’ G .
ative of qb T With respect to T 13 q I” T = (A F G' —— — 1 . Since
( ) ( ) [qF +(1— (1)012 [ ]

G’ F
G
— 00 and f > 1 for T E (0, 1), qb’ (T) is positive for T close to 1. Moreover,

Proof. From the definition, qb(T) =

 

< q for T 6 (0,1). Clearly,

$0)=

 

I

‘7—

10:" G , F’ . G _ G’ , F’ , G

limT_,0— G’ F— = 11m7-_,0 a7[lim7_,0 f — lim7-_.0 F7] = llm7-__,0 a7[hm7._,0 F —
Fl

limT_,0 37:] = 0. Suppose that qb’(t) = O at T = t 6 (0,1). This means 6%- — 1 = 0.

d ’F F_’G d F’ d F’
d_% : %2_[—G' —]— "‘ O. Wlth thlS, 'd—'[-G—’%— — gd—‘b—i > 0 SlIlCG

> 0. Since q b(0) = 0, this guarantees q b’(T) 2 0. Thus, the updated belief

limT_,1

Then,

dF’
dTG—’

qb(T) goes up from 0 to q as T increases from O to 1. I

Lemma 1. 4.

8p <0
(11(0 )> B > CF11“)
2 +6 a
Proof. (1.4) 1 — m 2 H(—q +5)

The left hand side of (1.4) is the increasing function of p. The right hand side

of (1.4) is decreasing function of q“ as H’ (s) > 0. Thus, from the implicit function
3__q1 _ 5{2 + (5}

’ 6p 4{1 + 6p}2H’(—q a + a)

qi”(0) > B > qi”(1), substitute p = 0 into the left hand side of (1.4),1

 

< 0. To obtain
_ (2 + 6)

theorem, the derivative of qi‘(p)

< 0.5.

 

Since H (0) = 0.5, —qa + ,8 < 0. Thus, qi‘(0) > H. Substituting p = 1 into the right

 

hand side of (1.4), H(—q‘1‘(1) + B) = 1 — —2+—6— > 0.5. Then, 5 > q‘1’(1). I
4(1 + 6)
Lemma 1.5.
aqll’
3p— < 0
qWM>B>qflU
Proof (15) H(—fi+ b) > 1 — 1 +61)
' ' q — 2+ 6

The left hand side of (1.5) is the increasing function of qb. The right hand side

23

of (1.5) is decreasing fimction of p. Thus, from the implicit function theorem, the
6

(2 + 5)H’(-b’ + qb)
To get this result, substitute p = 0 into the right hand side of (1.5), 1 — -——L— > 0.5.

< 0. Moreover, ql1’(0) > ,8 > q'l’(1).

 

8
derivative of qll’ (p), 5g: = —

2 + 5
Then, —5 + qb > 0 => qf(0) > 3. Substituting p = 1 into the right hand side of (1.5),
1 (5
1— 3:75 < 0.5. Then, H(—B + q’l’(1)) < 0.5 => q’1’(1)< 6. I

Lemma 1.6.
(1%?) Z q'f(p)
The equality holds when p = 0.5.

Proof. To show this result, solve (1.4) and (1.5) satisfied with equality for q‘f (p)
2 + 5 1 + 6p

 

 

 

b a _____ _ -—1 _ __ b = —1 _
311d 91(Pl- Then, (11(1)) l8 H (1 4(1+ 619)), and (11(1)) fl'l'H (1 2 + 6 )-
_ 2+6 _ 1+6p . . .
a __ b = _ 1 _ 1 _
Thus ql (p) q1(p) {H (1 4(1 +6p))+H (1 2 +5 )}. SinceHissymmetric
and H’1(k) 2 (<)0 4:) k 2 (<)O.5, the sigh of the left hand side is same to the sign
2+5 1 +510 52 2
f—1————0.5- 1— —O.5 = 2—1
0’ { 4(1+6p) } { 2+6 } 4(1+6p)(2+6)(p )

=> q‘1‘(p) Z q’l’(p) (the equality holds at p = 0.5.) I

Lemma 1.7.

For T 6 (0,1),
34%(T; (1”)
8T
aqfofh; qb)
6gb
(13(7) 2 43(7; 61")

(13(0; qb) = (13(0) = B
the value of T such that q§l(T) = 1 is lower than 1.

Proof. (1.6) {qF+(1—q)G}{H(—fi+qb)+H(—q“+fi)—1} 2 H(—qa+fi)—0.5
5q§‘(T;qb) 2
8T

>0

<0

The derivatives of q§"(T; qb) with respect to T and qb for T E (0, 1) are,

{qF’ + (1 - q)G’}{1 - H(-fi + (1”) - H(-qa + 6)}
{1 - qF - (1 - a)G}H’(—q“ + fl)
The sign of this is same to the sign of 1 — H(—6 + qb) — H(—qa + 5). Since

 

24

[3 2 qb, q“ > B guarantees that the sign is positive. Unfortunately, it is possible that

B 2 q“. Suppose this. Since H is symmetric, the sign is same to B — qb + q“ - [3 =

 

 

 

a a
a_bTh - - a_b: a,_q-{1-qF-(1-(I)G}q = q -q >
q q. eSignis,q q q qF+(1—q)G qF+(1—q)G“0
Only case this is zero is q“ —- q = 0. This implies T = 0. It is easy to obtain
W21 (T; (1") (W + (1 - Q)G}H'(—fi + q”) 3q§(r; qb) . .
—- = - < 0. Th —— < O h
aqb {1 — qF — (1 — q)G}H'<—qa + a) 9‘" aqb ‘mp es

q‘2"(T) 2 qg’(T; q). If T = 0, the condition (1.6) becomes, 0.5 2 H(—qa +fi) => q“ 2 B.
This does not depend on the value of qb. So, q§‘(0;qb) = q3(0) = B. If T = 1, the

condition (1.6) becomes,

H(-fi+qb)+H(-qa+fl)- 1 2 H(-q“+fi)—0-5
=> H(—5+qb) 2 0.5

=>qb2B

Sincefi > q 2 qb, this condition is never satisfied. This implies that the value of T

such that q§(T) = 1 is lower than 1. I

Lemma 1.8. Suppose that voters vote during the second election according to
their period preference without (A). Then there is no equilibrium.

Proof. No (A) means that the probability of winning second election after the
implementation of the policy a by Party 1 candidate is same to the one after the
implementation of the policy b. Thus, the expected second period rent is same for
both cases. This implies the decision-making during the first election is same to the
case there is only one period. Then, there is no reason for voters to update their
belief. This is the reason of no equilibrium. The following is a formal proof.

Suppose that there is an equilibrium without (A). Let T* and c* be the equilibrium
value of T and 0. Let qa* and qb* be the updated beliefs at the equilibrium.

The expected sum of rents for announcing the policy a is,
(1 - C”‘)(1 - H(-qa* + 6)}[1 + 5(1- H(0)}l + 0*{1- H(0)}[1 + (5(1 - H(0)}l

The expected sum of rents for announcing the policy b is,

25

(1 - C"‘){1 - H(0)}[1 + 5{1 - H(0)}] + C"‘{1 - H(-6 + qb*)}[1 + 5{1 - H(0)}l
The candidate with p announces the policy a if,

(1 - c"‘){1 - H(—q”* + a} + 6*{1- H(0)}

2 <1— c*){1 — mm} + c*{1— H<—/3 + q”*)}
=> (1 - c"‘){H(0) - H(-q“* + {3)} + 6*{H(-fi + 61’”) - H(0)} 2 0
=> 11(0) — H(-q“* H3) +c*{H(—fi+qb*) +H(—q“* +6) - 1} 2 0

Since this condition does not depend on p, if this condition holds for some Party 1
candidate with p, it holds for any Party 1 candidate. This implies T = 0. Since
qa*(0) < q < B, H(O) — H(—qa* + B) < 0. As shown in a previous footnote, H(—B +
qb*) + H (—q"’* + B) — 150. Thus the condition does not hold. This implies that Party
1 candidate never announces the policy a. Then, it has to be T* = 1. In this case, c*
has to be 0. Since H (O) — H (-q“(1) + B) > 0, the condition satisfied, a contradiction.

Proposition 1.1. With (A), there is an equilibrium in the model.

Proof. Since different sets of functional forms and parameters produce different
kind of equilibrium, I cannot obtain a simple general result. So I am going to show
the existence of equilibrium in all possible cases in turn.

The first case is the simplest one. Since q3(0) = B and q§(T) reaches 1 before
reaches 1, and q“(0) = q and qa(1) = 1, it is possible that q§(r) and qa(T) do not

CI‘OSS.

The Case 1: qg'(T) and qa(T) do not cross.

Since q‘1‘(0) > B > q‘f(1) and qa(0) = q and limT_.,1 qa(T) = 1, q? ) and qa(T)
always cross. Moreover, since they are monotone, the crossing point is unique. Let
the point he (T*, q‘”). Then, T = T* E (0, 1) and c = 0 is the equilibrium. Since the

assumption that q§(r) and q"'(T) do not cross implies q§(r) > qa(T), clearly it is never

26

beneficial for Party 2 candidate to announce the policy a during the first election.
Thus c = O. This implies that (ll) (p) is not relevant to Party 1 candidate’s choice

0.

of platform. Only qi”(p) is relevant. Since 951—qu < 0, for p < T*, the updated belief
q“* is lower than the necessary minimum level of the updated belief qi‘ ). Thus,
the candidate with p < T* does not announce the policy a. On the contrary, for the
candidate p > T*, q‘” > q?(p). Thus the candidate with p announces the policy a.

So, the set of T = T* and c = O is the equilibrium.

The case of that qg(T) and qa(T) cross is more complicated. In the case, both
qi"(p) and q? (p) are relevant to the choice of Party 1 candidate, but not the entire
part of them. Let Q E {T 6 [0, 1] : q‘2‘(T) 2 qa(T)}. Then, on Q, q? (p) is relevant
to Party 1 candidate’s choice of platform because on Q Party 2 candidate announces
the policy a.4 On (20 E {T E [0, 1] : q§(r) < qa(T)}, qi”(p) is relevant to Party 1
candidate’s choice of its platform since Party 2 candidate does not announce the
policy a. Depending on functional forms and parameter values, this 9 may be a
convex set or may be a collection of disjoint convex sets. Let {2* C Q be a convex set
such that w* E minw E {2* and w** E maxw E 0* are boundary points of 9. Since
q§‘(T) reaches 1 before T reaches 1, w** < 1. It may be or may not be 9* = D. To
show the existence of the equilibrium, I only need to consider 9*. So, in the following,

I simply assume Q = 9*.

The Case 2 (Figure 1.7): q§(T) and q“ cross, and qf(p) and qa(T) cross on QC

and/or qll’(p) and qb(T) cross on Q.

27

 

a
1 “\q (I)

 
       
 

\

q‘,’<p)

  

 

 

 

 

-—-—- —-----—1--—

A

 

 

< ql1’(p)
1

“RD

0

a“

a
*

Figure 1.7

Suppose qi’(p) and qa(T) cross on QC. Let the crossing point be (T’, q“’). Since
T’ 6 DC, q‘2‘(T') < q“’. This implies that Party 2 candidate does not announce the
policy a at T = T’. Then, with the same logic in the case 1, it can be proven that
T = T’ and c = 0 is the equilibrium.

Next suppose that qll’ (p) and qb(T) cross on 9. Let the crossing point be (T*, qb").
Since T* E Q, q‘2’ (T*) 2 q“*. So, with T = T*, Party 2 candidate announces the policy
a. With Party 2 candidate announcing the policy a, among q‘1”(p) and q’l’(p), only

qi’ (p) is relevant to Party 1 candidate’s choice of platform at p = T* (remember that

b

d
T is the value in [0, 1]. Both p and T take their value on the same axis.) Since fl is

dT
negative, the same logic used in the case 1 shows that the set of T = T* and c = 1 is

the equilibrium.

28

As implied in the Case 2 above, it is possible to have equilibria. Next I consider the
case such that q? (p) and q“ (p) do not cross on QC and qll’ (p) and qb (p) do not cross on
{2. This case also is divided into two cases. Firstly, notice that since qi’ (p) 2 q? (p) and
qa(T) > qb(T), that q‘1’(p) and q“(p) do not cross on QC implies that qi’(w*) > qa(w*)
and qa(w**) > q‘1’(w**). Then two cases are such that; the case of qb(w*) > q?(w*)

and the case that q’l’(w**) > qb(w**).

The Case 3 (Figure 1.8): q§‘(T) and q“ cross, and qb(w*) > q’l’(w*), no crossing

between q‘1’(p) and qa(T) on QC nor between qll’(p) and qb(T) on Q.

 

 

 

      

 

 

 

 

a
a
q ,q’0 q\2(p)
\ E \\qa(r)
13— i
q
qbfilf‘ /qt1’(p)
ql1’(p) ’ i
O (0* g 1 r,p
Figure 1.8

In this case, T = w* and some mixed strategy c 6 (0,1) is an equilibrium. Since

a

q1(w*) > qa(w*), if c = 0, announcing the policy a is not beneficial for Party 1

29

candidate. But qb(w*) > q’1’(w*) implies that if c = 1 it is beneficial for Party 1
candidate to announce the policy a. Since Party 1 candidate with p = 0.2” is not
indifferent between announcing the policy a and announcing the policy b if c = O
or c = 1, T = w* and c = 0 (or c = 1) is not an equilibrium. But there is a value
c* 6 (0,1) such that T = w* and c = c* is the equilibrium. Let q"* E qa(w*) and
qb* = qb(w*). Given some mixed strategy 0, the expected sum of rents of Party 1

candidate for announcing the policy a is,

1+6p

(1 — c){1- H(—q“* + {3)}{1 + 6p} + c 2

 

The expected sum of rents for announcing the policy b is,

2
(1— a2 :1" 5 + (Fig—"p _ H(—B + qb*)}

 

Party 1 candidate announces the policy a if,

 

 

 

 

<1— c){1—- H<—qa* + 5)}{1 + 6p} + c1 1” 5”
2 (1 —c)2+" +33% — H(-fi+q”*)}
: <1— cm - H<—qa* + 3)}{1 + 6p} — 33—9-1
+412” — 2:5{1 — H(—B+qb*)}] 2 0

With T = w*, the coefficient of (1 — c) is negative, and the coefficient of c is positive.

Denote them as (—) and (+). Then, the condition is,

(1 - C)(—) + C(+) = (—) + C{(+) - (-)l 2 0
From this, the value c* E (—+-_—(__—()_—) E (0, 1) is defined as the value that satisfies the
condition with equality. Then the set of T = a2” and c = 0* is an equilibrium. Party 1
candidate with p = w* is indifferent between announcing the policy a and announcing
the policy b. Since both q‘f (p) and qll’ (p) are decreasing functions of p, the values of
(+) and (—) above increase with p. Thus, Party 1 candidate with p 2 w* announces
the policy a. At same time, this means that Party 1 candidate with p < w* does not

announce the policy a. For Party 2 candidate, since the fact that w* is a point of

30

9 means q‘2’(w*) = q“(w*), Party 2 candidate is indifferent between announcing the

policy a and announcing the policy b.

The Case 4 (Figure 1.9): q§(T) and q“ cross, and q’l’(w**) > qb(w**), no crossing

between qi’ (p) and qa(T) on QC nor between qll’ (p) and qb(T) on Q.

a
a b q2(\p)

 

\

\qa(t)

 

.Q
C"
A
c-i
v

/q11)(p)

 

 

 

 

 

LP

 

Figure 1.9

In this case, the combination of T = w** and some mixed strategy 0 6 (0,1) is
an equilibrium. The proof is almost same to the Case 3. Since qa(w**) > q‘1’(w**),
if c = 0, announcing the policy a is beneficial for Party 1 candidate. But qll’(w**) >
qb(w**) implies that if c = 1 it is not beneficial for Party 1 candidate to announce the
policy a. Since Party 1 candidate with p = w* is not indifferent between announcing
the policy a and announcing the policy b if c = O or c = 1, then T = w” and c = 0

(or c = 1) is not an equilibrium. But there is a value c** E (0, 1) such that T = w**

31

b** _

an E qa(w**) and q = qb(w**). Given some

and c = c** is the equilibrium. Let q
mixed strategy c, the expected sum of rents of announcing the policy a for Party 1
candidate is,

(1 - c){1 —— H(—qa** + 5)}{1 + 6p} + c1+ 6p

 

The expected sum of rents of announcing the policy b is,

2 6 2 5
M j; +c—J25—{1-H(—B+q”**)}

Party 1 candidate announces the policy a if,

 

 

 

 

<1— c){1 — H(—qa** + 5)}{1+ 6p} + .1 + 6’
2 (1 - c)2 + 6 + 03121?“ — H(—B + qb**)}
=> (1 -— c){{I — H(-q"'** + mm + 6p} — 11—61
+411,” — 33—511— Heal—gran 2 0

With T = w**, the coefficient of (1 — c) is positive, and the coefficient of c is negative.
Denote them as (+) and (—-). Then, the condition is,
(1- C)(+) + C(-) = (+) + C{(—) — (+)} Z 0

From this, the value c** = —-fi—)—— 6 (O, 1) is defined as the value that satisfies

+ _ _
the condition with equality. Thefi th(e s)et of T = w** and c = c** is an equilibrium.
Party 1 candidate with p = w** is indifferent between announcing the policy a and
announcing the policy b. Since both q‘f (p) and qll’ (p) are decreasing functions of p,
(+) and (—) above increase with p. Thus, Party 1 candidate with p 2 w* announces
the policy a. At same time, this means that Party 1 candidate with p < w* does
not announce the policy a. For Party 2 candidate, since to“ = maxw 6 52 means
q‘2‘(w**) = qa(w**), Party 2 candidate is indifferent between announcing the policy a
and announcing the policy b. Thus the set of T = w** and c = c** is the equilibrium.

Since above four cases cover all possible cases, the proof is completed. I

32

Endnotes of Chapter 1

1. The uncertainty is not restricted only to the policy outcomes in the literature.
The uncertainty about the ability of politicians is often assumed (Majumdar and
Mukand (2004), etc.) Cukierman and Tommasi (1998) and Schultz (2002) consider
the uncertainty about the preference of politicians as well as the policy outcomes.

2. According to the Rasmussen reports (June 21, 2008), voters trust the Demo-
cratic party more than the Republican party on ten key issues including Economy,
National Security, and the war on Iraq. Since the natural interpretation of this "trust"
is competency, this result could be considered as implying that voters assume the abil-
ity gap between two parties. Though even this interpretation is actually inconsistent
with the model of this chapter, at least this implies the meaning of considering the
asymmetry between two parties.

3. As I wrote, this is a simplified, short cut way of modeling the signal. Following
Majumdar and Mukand, this can be stated formally as the following; at first Party
1 candidate has the belief q same as voters. Then the candidate receives a random

signal 3:, which is in [_:r_, is]. This random signal a: has a density 450 if the state is

 

 

 

l
w0 and a density ail if the state is wl. I assume that limxnzg (LO—{:2 = 00 and
1 ¢ (:1?)
limxng Z—ELP—i = 0. Then from this signal, the candidate deduce the new belief p of
a:
the state being w1 using the Bayesian rule,
q¢1(x)
W) = q¢1($) _ we)
q<f>1($) + (1 - (1)9500?) (1)1(33)
4—5—— + (1 — (I)
1 ¢ (:8)
a5 (I)

 

Assuming O :1: is strictly increasing as a function of :13, :1: has a one to one corre-
spondence. Then, from (151 and (to, two distribution F and G can be constructed.

4. Of course, on the bound of Q, Party 2 candidate is indifferent between announc-
ing the policy a and announcing the policy b. So, the candidate might not announce

the policy a on the bound of 9. Actually, the condition that they are indifferent is

33

necessary for the existence of an equilibrium.

34

References

[1] Adams, James AND Samuel Merrill III (2008): “Candidate and Party Strategies
in Two-Stage Elections Beginning with a Primary” American Journal of Political
Science, 52(2), 334-359.

[2] Bernhardt, Dan, John Duggan AND Francesco Squintani (2007): “Electoral com-
petition with privately-informed candidates” Games and Economic Behavior,
2007, 58, 1-29.

[3] Cukierman, Alex AND Mariano Tommasi (1998): “When does it take a Nixon
to go to China?” The American Economic Review, 88(1), 180—197.

[4] Harrington, JR., Joseph, E. (1993a): “Economic policy, Economic performance,
and elections” The American Economic Review, 83(1), 27-42.

[5] Harrington, JR., Joseph, E. (1993b): “The Impact of Reelection Pressures on
the Fulfillment of Campaign Promises” Games and Economic Behavior, 5, 71-97.

[6] Heidhues, Paul AND Johan Lagerof (2003): “Hiding information in electoral
competition” Games and Economic Behavior, 42, 48- 74.

[7] Majumdat, Sumon AND Sharun W. Mukand (2004): “Policy Gambles” The
American Economic Review, 94(4), 1204-22.

[8] Persson, Torsten AND Guido Tabellini (2002): Political Economics Eaplaining
Economic Policy, The MIT press.

[9] Rasmussen reports (2008): “Trust on Issues Democrats Trusted More on All Ten
Electoral Issues”
http: / / www.rasmussenreports.com / public_content / politics / mood__of_ america

/trust_on_issues/trust_on_issues

[10] Schultz, Christian (2002): “Policy biases with voters’ uncertainty about the
economy and the government” European Economic Review, 46, 487-506.

[11] Schofield, Norman (2005): “A valance model of political competition in Britain:
1992-1997" Electoral Studies, 24, 347-370

35

2 Information Transmission from Overlapping

Generations Parties

2.1 Introduction

This chapter considers a model of electoral competition between two overlapping-
generations—organization political parties with uncertainty about policy outcomes.
The interest is on how to restrain opportunistic behavior of politicians who are in their
last period. Suppose that there is an information asymmetry between politicians and
voters of which politicians can take advantage. In multi—period models, usually the
concern about future elections can restrain opportunistic behavior of politicians to
some degree (Austen-Smith and Banks (1989)). This is an intuitive result. However,
what would happen if they are in their last period so that they do not need to worry
about future elections? It seems that in such situations opportunistic behavior of
politicians, i.e., moral hazard, is inevitable. However, unless political parties consisted
only of members who would retire soon, not everyone in parties would be happy to see
such opportunistic behavior. This suggests that there would be conflict of interests
in parties that voters could exploit to restrain politicians. Though the problem of
Opportunistic behavior by politicians in their last periods sounds very artificial since
not all politicians in power are in their last period / term anyway, what I want to show
is that the natural party structure consisting of politicians with various political
life spans can give voters some leverage to restrain party bosses. The opportunistic

behavior of politicians in their last period is a good example to show such possibility.

36

For this objective, I employ a model with OLG political parties that follows Alesina
and Spear (1988) and Harrington (1992).

Traditionally, literature of Political Economy has not paid much attention to the
difference between politicians and political parties. Parties in many electoral compe-
tition models (Calvert (1985), Wittman (1983), etc.) are nothing but labels put on
candidates. Although there are also many papers in which parties are main players
and different subjects from politicians, in those papers parties exist as independent
and consistent entities (for example, Grossman and Helpman (1996).) However, par-
ties in real world are organizations consisting of many individuals who often have
different preferences5. Then, recognizing parties as organizations of individual politi-
cians, not as independent entities, a natural question is what implication parties have
on the behavior of politicians and election outcomes6.

Recently, papers are appearing that consider this question. Snyder and Ting
(2002) formalize the intuitive idea of political parties as brand names and shows how
parties can work as signals about preferences of their candidates to voters. Cail-
laud and Tirole (2002) model the intra-party competition among politicians in the
same party and study what kind of impacts such competitions have on the trust of
voters for politicians and on elections. Levy (2004) considers the endogenous party
formation through stable coalition formations and shows that the existence of par-
ties increases the number of credible election platforms, i.e., that the existence of
parties makes some outcomes feasible that would not be possible otherwise. Most

of papers are finite period models. Alesina and Spear (1988) and Harrington (1992),

however, consider infinite period models in which parties are overlapping-generations-

37

organizations. They consider the problem of policy commitment.

This chapter is one of such papers, and I consider the problem of the informa-
tion transmission from politicians to voters. In short, this is a problem about if
politicians lie or not. I show the party organization can help voters restrain oppor-
tunistic behavior of the party boss. The situation I consider is this; there is the
uncertainty about policy outcomes. No one is sure about outcomes of policies until
policies are really implemented. This is a natural assumption for government policy
decision-makings. The outcomes of almost any political decisions, especially big ones,
are uncertain. Consider big regulation changes, or tax system changes. Maybe the
decision of launching a war is the most evident example. In almost any policy decision-
makings, there is the uncertainty about policy outcomes. However, it can be safely
assumed that politicians have the informational advantage about possible outcomes
over voters. In democracy, politicians choose policies and voters choose politicians.
Thus, to achieve good policy outcomes, it is critically important to make sure that
politicians honestly reveal their information to voters during elections. Given the in-
formational asymmetry, however, this is not guaranteed. There are many papers on
this problem (Harrington (1993), Majumdar and Mukand (2004) and Heidhues and
Lagerlof (2003), etc.) in finite period models. Exact results depend on the structure
of models. But the general conclusion is that it is possible that politicians choose
policies of which they know outcomes are likely to be bad for voters since such poli-
cies are their favorites or since choosing those policies increase the probability of their
winning the next election. As an example, take Heidhues and Lagerlof (2003). They

consider a one—period model in which two parties go to an election with their election

38

platforms. The outcome of implemented policy depends on the state of the world, and
there is the uncertainty about the state of the world. Parties (or candidates) receive
private signals about the state of the world before the election. Candidates have no
preference on policies. Voters, however, have a belief on which state is likely. Since
the objective of the candidates is winning the election, candidates have the incentive
to follow voters’ belief. Thus, it is possible that candidates would propose a policy
that they know is not good for voters. This result is intuitive and also individually
rational for candidates. But, looking at this from the viewpoints of their parties, not
from the viewpoints of individual candidates, this is clearly a bad result. Suppose
that an elected politician in his last political term implements his proposed platform
and a bad outcome realizes. Though the politician does not need to worry about the
next election, the party of the politician will have to face voters in future elections.
Then, it is likely that party will be disadvantaged in the next election, i.e., the lower
probability of the party winning the election (because of the retrospective voting be—
havior.) Thus, there is a conflict of interests in the party; the conflict between current
candidates and other party members (especially candidates who will go to the next
election). I consider a possibility of exploiting this conflict for voters’ benefit.

Since this is an electoral competition model, not only parties but also how people
vote is important. I assume voting depends on party reputations. By “party rep—
utation,” I mean the reputation on a party that the party is revealing information
honestly to voters or not. This party reputation depends, in part, on the behav-
ior of party insiders. To understand how this works, suppose an election between

two parties. Then, pick a voter who does not have any particular party affiliation.

39

Suppose also that the voter is given an opportunity of touring the headquarters of
both parties. Then, in one party’s H.Q., the voter finds that all staff are shirking
and complaining about their candidate. In other party’s H.Q., he finds that all staff
are working hard and talking about what great works their candidate can do for the
country. Then, during the election, for which party will he vote? It is very likely that
he will vote for the party with hard-working staff. Next, suppose that a candidate
from one party chooses a policy based only on his own self-interest and does not
care about what will happen to the party in the future. Then, will the staff work
hard for the candidate? It seems unlikely. This suggests a possible route of a signal
from the party to voters and a possibility of restraining the opportunistic behavior
of current candidates through the route, especially through future candidates. In the
model, I assume that young politicians are supposed to make the election campaign
effort for old politicians during elections. The effort causes negative utility to young
politicians. But they still make the campaign effort since that helps their party and
strong party will help them in future. If old politicians make the choice that hurts the
party, however, the choice will reduce the young’s willingness to make the campaign
effort. The campaign effort is assumed to be observable to voters. At first, I assume
that voters require a certain level of effort (this will be changed later.) The required
effort level is the required disutility level for young politicians during elections. Then,
I consider about the reaction of young politicians to the opportunistic behavior of the

party boss and if it can restrain such opportunistic behavior.

In section 2.2, I explain the model, the behavior of politicians and the definition

40

of equilibrium. I state results in section 2.3. Section 2.4 is the conclusion with a brief

literature review. All proofs and calculations are in the Appendix of this chapter.

2.2 Model and Behavior of Politicians

Before explaining the model, I state a brief description of the flow in each period. At
the start of each period, the nature chooses the state of the world in the period. Then,
two parties receive the same signal about the state of the world. Old politicians in
both parties choose their election platforms, and young politicians choose campaign
effort levels. Observing effort levels, voters update their party reputations and vote
for the party during the election based on the party reputations. The winner of the
election implements the policy of its election platform. The outcome of the policy
is observed by voters and they update party reputations again. In the reputation
update, basically, party reputations get downgraded as punishment for not making
campaign efforts (suggesting suspicious behavior of old politicians) and for choosing
a bad policy (i.e. retrospective voting). These two punishments are instrument and
incentive for young politicians. The reputations are carried over to the next period.
To not have a bad party reputation in the next period, young politicians use the
campaign effort as their instrument to restrain old politicians.

The party reputation in this model means the belief by voters about if the party
honestly reveals its information to voters (i.e., choosing the good policy as its platform
given the information) or not during the election. Basically, old politicians want to

abuse the good reputation and young ones want to keep the good reputation for their

41

election in the future. This “reputation” is different from the one in the literature of
“reputation” like Tadelis (2002), which is a paper of an OLG reputation model. In
this chapter, there is no “good” politician and no “bad” politician. Party reputations
are about if the party is trustable or not. Also, even though reputations are updated
as voters receive new information, the update is not Bayesian. Following Harrington
(1992), the reputation and its update in this model are very simple, and are given by
an assumption7. This is because assuming the Bayesian updating in this model makes
the model unnecessarily complicated; more elaborate update systems naturally lead
to more strategic behavior among politicians, even assuming non-strategic behavior
of voters. Since such complication is not essential to the idea of this chapter, I assume

a simple “reputation” structure in the following.

2.2.1 Model

Society and its members: The society consists of voters and politicians of two
parties (party 1 and party 2.) They are risk neutral. All voters are same and they
do not have any particular affiliation with either party8. Voters care only about
the current period utility; they do not try to maximize the expected utility over
the infinite period. This may be because they are short-lived or myopic. In any
interpretation, this assumption rules out the possibility of their employing complex

strategies.

Parties and politicians: Party 1 and 2 are modeled as overlapping-generations-

organizations with an old politician and a young politician in each party in each

42

period. Following Alesina and Spear (1988), I call the old politicians at the period t as
Presidential candidates (PCs) at the period t. They decide the party platforms of the
period. Correspondingly, I call the young politicians at period t as Vice Presidential
candidates (VPCS) at period t. VPCS make the campaign effort for their parties. The
effort is observable to voters and causes the disutility to VPCS. I call politicians by
the words “PC” and “VPC” in regardless of their being in an election or in office. A
generation t politician of party i 6 {1,2} enters into the party at period t as a VPC
and becomes a PC of party i at period t + 1. Then he retires and leaves the party.
All politicians in a party are same except for their generations. Then, in the election
at the start of each period, old politicians in two parties choose the election platform
of their parties and young politicians make the campaign effort. Assuming the policy

commitmentg, the winning party will implement its platform after the election.

Policies and the state of the world: There are two possible policies: a1 and
a2. Because of the policy commitment, the election determines which policy will be
implemented in the period. However, the policy outcome depends on the state of the
world, and there is the uncertainty about the true state. The number of possible states
of the world is two: w1 and w2. The state of the world is chosen by Nature at the
start of every period with probability % for both states. This is common knowledge.
If the policy of (i E {1, 2}) is implemented in the state wi, then voters receive utility
1. If the policy ai is implemented in the state wj (j aé i), voters receive utility ——1.

Thus, voters can tell the true state in the period after a policy is implemented.

Information: Before the election in each period, parties receive a common signal

43

about the state of the world in the period. From the signal, politicians can derive
the probability of the true state being wl. For the simplicity, I assume that parties
receive the probability directly as the signal. Let r be the probability. This r is a

random variable with the uniform distribution“). Voters do not observe the signal.

Campaign effort: during elections, only VPCS can make the campaign effort.
VPCS suffer the disutility c to make the effort c. Voters can observe the campaign
effort. Since the probability of the realization of each state is common knowledge and
voters can perfectly observe party platforms after they are proposed, the campaign
effort does nothing on informing or deceiving voters about abilities of parties or
platforms. The role of the effort in this model is that the level of the effort can
work as a signal from VPCS to voters about the honesty of PCs. However, if c is too

B
high, VPCS never make the effort c. So, I set the upper bound of c at Z.

Utilities of politicians: If maximizing the welfare of voters is the objective of
politicians, parties would propose their platforms honestly, i.e., proposing policy a1
when they receive signal r > :— and a2 when r < %. But that is not the objective
of politicians. Preferences of politicians are different from voters. Since voters do
not observe the signal, politicians have incentive to lie to voters. Party i 6 {1,2}

politicians receive (dis)utilities at three occasions in their two—period political life.

Politicians’s (dis)utility:
1. Winning election: when Party i wins the election at period t, the PC of
party i at the period receives a fixed benefit B > 1.
2. Implementing policy: PC of party i receives utility 1 when he implements

44

the policy al and receive —1 when he implements aj, j 71$ i. If party j politician
implements a policy, party i politician receives zero utility“. VPCS receive zero
utility fiom the implementation of policies.

3. Making campaign efforts: If VPCS make the campaign effort c during an

election, this gives utility -—c to them. PCs do not make the campaign effort.

Thus, PCs and VPCS do not receive same utility in same period”. The objective
of politicians is the maximization of the sum of utilities from two periods. Since polit-
ical life is just two periods, I do not use a discount factor for calculations of politicians’
utility. Although this specification is for simplifying the model, this reflects reality
to some degree except the assumption that PCs do not make the campaign effort.
What is important for the model is, however, that they receive different utilities in

same period.

In the model, Party 1 and Party 2 are mirror images of each other. PCs of Party
I prefer the policy a1 to the policy a2 and PCs of Party 2 prefer a2 to al. Both
parties receive the same probability r of w1 being the true state as a signal. Also
each state of the world realizes with the same probability %. Since voters are assumed
to have no affiliation with either party, they are basically indifferent between parties.
However, they have preference on party strategies. If Party 1 is honest on the choice of
platforms (r 2 :- —+ a1 and r < :— ——> a2) but Party 2 is dishonest (always proposing
the policy a2), voters prefer honest Party 1 to dishonest Party 2. So, if they thought

Party 1 was more honest than Party 2, they would have a derived preference for Party

1. Since party strategies are unobservable to voters, however, voters need a something

45

that can induce politicians to behave honestly. That “something” is the reputation
on parties and the voting response based on it. Appropriate voting responses based
on party reputations give incentives for VPCS to restrain the opportunistic behavior
of PCs, though there are no honest politicians in the model. When new information
about parties is obtained, the reputation on parties will be updated. I assume very

simple strategies for parties and only two types of party reputations.

Party reputation and Voting response: Voters have only two types of rep-
utations on parties; Honest (H) or Suspicious (S). Honest means that voters think
that the party is likely to pr0pose a1 when r > g and a2 when r < % (when r = %,
choice does not matter.) Suspicious means that voters think that the party is likely
to propose its preferred policy regardless of the signal the party receives. Notice
that reputations are on parties, not on a particular politician, so this is not about
politicians’ type. This reputation system is very coarse compared to the set of PC’S
strategies, which will be explained later. Still, this coarse reputation system can
improve voters’ welfare.

During the election, voters prefer the party with Honest reputation to the party
with Suspicious reputation. They will vote for the honest party over the suspicious
party. Since all voters are assumed to be same, the honest party definitely wins.
If both parties have same reputation (Honest and Honest, or Suspicious and Sus-

picious), following the tradition of the electoral competition literature, both parties

1
have probability § of winning the election.

Reputation update by voters: Voters cannot see signals. Instead, they use

46

the observable campaign effort of both parties and the policy outcome as proxies of
the signal and the strategies. Thus, when they observe VPCs’ effort levels and when
they observe the policy outcome so that they can tell the true state from the outcome,
they update reputations. Zero effort chosen by VPC suggests that the PC of the zero
effort party chose a policy based on his preference, not based on the signal received.
After the policy outcome is observed, voters can tell the true state and which party
chose the bad policy (of when wj, i # j.) Since parties receive a signal about the
true state, the bad policy also suggests that the PC who chose the bad policy chose it
based on his preference, not on the signal. Then, voters downgrade the reputations of
parties that proposed the bad policy as its platform, regardless of whether the party
won the election in the period or not. The update based on VPC’s effort levels can
affect the election outcome in the period. The update based on the policy outcome
can aflect the election outcome in the next period. Though these updates are given

as assumptions exogenously, these are basically simple and intuitive.

Reputation update:

(1) Before the election, if VPC of one party makes the effort level less than c, the
reputation of the party is updated to Suspicious.

(2) After observing the policy outcome, the reputations of parties that proposed

the bad policy are updated to Suspicious.

Above two updates are about downgrading reputations. Since parties have pos-
itive probabilities of choosing the bad policy even if they choose their policies com-

pletely honestly, the opportunities for upgrading reputations are necessary. I assume

47

following two for upgrading.

(3) Before the election, if (1) happens to one party and the reputation of the other
party was Suspicious at the start of the period, the reputation of the other party is
updated to be honest.

(4) After the election, the reputation of the party that was Suspicious at the start
of the period is updated to Honest.

(5) If both parties have Suspicious reputation at the end of period, voters update

their reputations to Honest.

The party reputations are carried over to the next period. (3) strengthens the
punishment of no effort for the case that only one party has Honest reputation.
Without this, it is possible that the PC of the party with Honest reputation prefers
no effort with his opportunistic choice to the effort level c with honest choice. (1) and
(3) make sure that the party of which a VPC does not make the required campaign
effort gets punished during the election. Combined with (2), (4) is essentially saying
that the party that proposed the good policy (of when wi) get rewarded for the choice.
(5) is for the case that both parties obtain Suspicious reputation. Since the fact that
keeping Honest reputation increases the prospect of winning election is the reason
that VPCS can restrain the opportunistic behavior of PCs, upgrading both parties to
Honest is beneficial for voters than keeping two Suspicious parties.

This updating system is just one example of many. Other systems, especially more
complicated systems, might be able to achieve better results. However, the point is

that even this simple system can improve voter welfare.

48

Party strategies: Politicians have two occasions to make decisions; once in each
period of their political life. PCs choose party platforms. Observing PC’s choice,
VPCS decide the level of the campaign effort to make in the period. Then, during
each election, there is an intra-party game in each party between its PC and its VPC;
though it is PCs who determine party platforms, VPCS can have a say in platform
choices through their campaign effort choices. The entire strategy of a politician is
the profile of decisions as a VPC and as a PC. I assume that the strategy is based
only on party reputations and the signal in the current period. So, all politicians in

the same party have the same strategy. I consider the strategy as follows.

Take a PC of Party 1 at period t. Let (A, B) be a profile of Party 1’s reputation
A and Party 2’s B (A, B E {H, S}, H for Honest and S for Suspicious) at the start

of the period. Let r be the signal parties receive. Then, the strategy of the Party 1’s

PCis,
>1=> 1
r — a
_2
<1
7‘ _
2
1
:>(H,H).r2§—eoz>a1
1 0 2
r<——e =>a
2
1
(H,S):r2§—el=>a1
1 1 2
T<——E =>CL
(S,H):a1

Thus, the strategy of Party 1 PCs is the choice of thresholds 50 and 51, or prob-

abilities of lying, for cases of (H, H) and (H, S) (see figure 2.1.)

49

 

 

 

 

 

A A
f T 1| D
0 I 1/2'8 1/2 |1
Figure 2.1

If r 2 %, then there is no reason for Party 1 PCs to lie. It is the happy coincidence
of their preferred policy and the socially Optimal choice. If r < %, there is an incentive
for PCs to lie to voters. Since they do not need to worry about the next election, if
they could choose 50 and 51 freely, they would choose 80 = 51 = %. Since VPCS in
the current period will be PCs in the next period, higher values of 50 and 51 could
benefit VPC if they would have reputation H in the next period. However, such choice
would hurt the prospect of VPCS having reputation H in the next period. Thus, if
PCs choose to lie for very low r, VPCS will not make the required campaign effort c.
The result of this zero effort is that the smaller expected utilities of PCs. To avoid
such loss, PCs might choose values of 50 and 51 that are lower than —1-.As for the
case of (S, H), as long as Party 2 makes the required campaign effort, Party 1 never
wins the election. Thus, actual choice does not matter for PCs. One implication
of this and assumptions about the reputation system is that if (S, H) then Party 1
VPCS will not make the positive campaign effort. This is because the behavior of

VPCS does not matter for the reputation in the next period. This could be changed

so that VPCS in such situation makes the positive campaign effort with apprOpriate

50

changes of reputation update assumptions. Since such change does not alter results
qualitatively, I keep the current update system for the sake of simplicity. I do not
consider the case (S, S) because this happening at the start of a period is ruled out by
the reputation update. The strategies of Party 2 PC, éO and 9:1, can be obtained by
changing (H, S) to (S, H), the inequality signs, negative sings of 50 and 51 to positive

signs, and exchanging a1 and a2 (see Figure 2.2.)

0 1/2 1/2-3. 1

Figure 2.2

As for VPC’s strategy, since VPCS move after PCs in stage games, their decision is
simply about if they should accept the PC’s choice and make the effort c demanded by
voters or should not accept it and make zero effort (when voters demand the positive
level c of the campaign effort, it is meaningless to choose an effort level between 0
and c.) So, the strategy of VPCS is simply to accept PC’s choice of platform only if
it gives expected utility no less than the expected utility of not accepting it. Thus,
the complete set of the strategy for Party 1 politicians can be denoted as (50,51) (the

strategy for Party 2 politicians is (3:0, £1).)

The sequence of the game in period t:

The start of the period t.

51

If (S, S) then (H, H)
Nature chooses the state of the world for the period.

Both parties receive r.

PC chooses platform.
Intra-party game:

VPC decides campaign effort level.
Middle of the period.

Voters observe party platforms and campaign effort levels.
Voters update party reputations.
ElectionzVoters vote according to party reputations.
Suspicious reputation at the start of the period is updated to Honest.
The winner of the election implements its platform.
End of the period.
Voters receive utility from the policy outcome.
Voters update party reputations.

Next period.

2.2.2 Behavior of Politicians

In this subsection, I explain behaviors and conditions for PCs and VPCS in symmetric
equilibrium. In each period, in both parties, a PC and a VPC play a stage game to
decide the party strategy and the campaign effort level in the period. I derive the
expected utilities of politicians in the equilibrium with VPCS making the required

effort c when the party reputation is H.

52

Behaviors of PCs First, I calculate expected utilities of a Party 1 PC at the start
of a period so he knows party reputations but has not received the signal r yet.
Given an equilibrium strategy (50, 51) with VPC making the effort c when the party
reputation is H, let VH, H be the expected utility of Party 1 PC at the start of a

period with (H, H). Then, this is defined as,

1 B—1 1

8+1 B+250
VH,H=(‘2'—50) 2 +(‘2'+50) =

2 2

 

 

 

1
(g — so) of the first term is the probability of r < -2- -— 50 (r has the uniform

2. The probability of his winning

1
distribution.) If r < 5 —- 50, the PC proposes a
1 . . . . . . 1
election is 5, and he Will receive utility B — 1 if he W'lnS. (§ + 50) of the second term
1 1
is the probability of r 2 5 — 50. If r _>_ 2 — 50, he proposes al. The probability of his

1
winning election is 2’ and if he wins, he will receive utility (B + 1).

If (H, S),
1 1 1 1 1
VH,S=(§-‘5 )(B-—l)+(-2-+E )(B+1)=B+2€
If (S, H), Party 1 cannot win as long as Party 2 VPC makes the positive effort.
So,
VS,H = 0

Expected utilities of Party 2 PC can be calculated similarly with (£0, £1). Since
PCs are in their last period, they do not need to worry about the next election.
. . . . 1

Thus, they always want to increase values of 50 and 81 to their maximum, i.e., —.

The behavior of VPCS is more complicated since it involves calculations of expected

utilities.

53

Behavior of VPCS Given an equilibrium strategy (50, 51) with VPC making the
effort c when the party reputation is H, a Party 1 VPC’s expected utilities of accepting
and not accepting PC’s choice are calculated as follows. Notice that when VPCS make
decisions they already know the value of r in their periods. Since PCs’ choice when
r > $- is honest, I do not need to consider the case of r > 1. So, I consider only the

2

1
case of rgé.

(H, H)
1 1 1 1 1
(2.1) a : r[-2-VH,5 + EVH,Sl+(1 — T)[§VS,H + '2'VS,Hl — C

=r(B+2el) —c

This is the expected utility of accepting PC’s choice of a1 when (H, H). The true
state is w1 with probability r and w2 with the probability 1 — r. With (H, H), both
parties have probability :- of winning the election. Party 1 chooses a1 and Party 2
chooses a2 (because r < é.) After the outcome of the policy implemented is observed,
voters can tell which party chose the bad policy (i.e., ai for the true state wj.) So,

the party that chose the bad policy is punished with the bad reputation.

I 1 l l
(2.2) a2: Tl§VH,H + BVH’H] + (1 — T)[§VH,H + EVH’H] — C
_ B+2e0
_ 2

 

This is the expected utility of accepting PC’s choice a2 when (H, H). In this
case, both parties choose the same policy, so, the expected utility for VPCS does not

depend on r.
(2.3) 0: rVHfl + (1 — r)VS,H = g(B + 250)

This is the expected utility of not accepting PC’s choice. Since the reputation of

54

Party 1 becomes Suspicious for no campaign effort, the only case that VPC can have
positive expected utility at the start of the next period is when the choice of Party 2
turns out to be bad. In the case, the reputation of Party 2 would become Suspicious,

too. At the start of the next period, their reputations would be updated to Honest.

(H15)

(2.4) a1: rVH,5 + (1 — r)V5,H —- c = r(B + 251) — c

B+2e0
2

(2.6) 0: rVHfi + (1 — 7:)V5,H = g-(B + 250)

 

(2.5) a2: TVHJJ + (l — TlvH,H - C =

If Party 1 VPCS do not make the effort c when (H, S), reputations become (S, H)
before the election. After the implementation of policy, this will be kept same or be
changed to (H, H), depending the outcome of the implemented policy.

(2.2) and (2.5) are same. Though (2.1) and (2.3) are also same to (2.4) and (2.6)
for the same value of r, respectively, they should be treated as different conditions
because they are for different threshold values. (2.1) and (2.3) are related to 50 and
(2.4) and (2.6) are related to 51. In the case of (S, H), PCs always choose a1 and
VPCS always make zero effort. So, I do not need to consider expected values of VPCS

when (S, H).

Given (H, H) and r, if (2.1) is lower than (2.3), VPCS never accept PCs’ choice of
a1, since VPCS prefer making no campaign effort to accepting a1. Same for (2.2) and
(2.3). So, what is important is the difference between (2.1) and (2.3), and between
(2.2) and (2.3). Same thing can be said for (H, S). Thus, I subtract (2.3) from (2.1)

and (2.2), and (2.6) from (2.4) and (2.5), and denote them as (2.1), (2.2), (2.4) and

55

(2.5), again.

(2.1) g-(B — 250 + 451) — c
(2.2) l—g—WB + 250) — c
(2.4) 721(3 — 250 + 451) — c

(2.5) 1421(3 + 250) — 0

Since B > 1, the derivatives of (2.1) and (2.4) with respect to r is positive. So,
if (2.1) or (2.4) are non-negative at the threshold r0 E g — 50 or r1 E g — 51, it
is positive for r higher than the threshold values. Thus, for any r higher than the
threshold values of r, PCs always propose a1 and VPCS always accept it. Moreover,
since the upper bound of c is g, (2.2) and (2.5) never become negative for any r and
50 in [0, g]. Because of this, I can ignore (2.2) and (2.5). This means VPCS always
accept a2 if PCs choose a2. Thus I need to consider only (2.1) and (2.4). Since what
I am looking for are threshold values of 50 and 51, I substitute the corresponding
threshold values of r, r0 E g — so and r1 E g — 51, into above (2.1) and (2.4). To

distinguish expressions with r and without r, I put “an” to expressions without r.

(2.1)* — eO)(B — 250 + 451) — c

(
(

[\DIF-‘MII-J
[\DIHNIH

(2.4)* — 51x3 — 250 + 451) — 0

2.2.3 Definition of Equilibrium

Consistency and Deviation: Let (50*, 51*) be an equilibrium strategy with VPCS
making the required effort c when the party reputation is H. Then, this (50*,51*)

needs to satisfy the following condition.

56

1
(a) (Consistency) (2.1)* and (2.4)* are non-negative for thresholds r0 = 5 — 50*

for (2.1)* and r1 = g — 81* for (2.4)*.

If this condition does not hold, (50*, 51*) cannot be an equilibrium strategy with
VPCS making the required effort c. The condition (a) is about the consistency of
(50*,51*); if (a) does not hold, VPCS will not accept a1 for thresholds r0 and r1.
Thus, (50 51) that does not satisfy (a) cannot be even an appropriate strategy with
VPCS making the effort c, let alone being an equilibrium strategy. In such case,
VH, H and VH, S cannot be calculated like above since the behavior of VPCS does not
follow (50*, 81*). Then, when PCs prOpose an inconsistent strategy, I assume VPCS
never make the required campaign effort c since they cannot tell making the effort
is beneficial or not. For a successful deviation, the deviated values need to satisfy
(a). Suppose that 50* < :- or 51* < :2- and that the current period Party 1 PC

0:1

of course

_€0*(

deviates from (50*, 51*) when (H, H); proposing a1 when r < r
r 2 0.) Since the party reputation is (H, H), the PC can deviate only from 50*. Let
r = g — '0. This deviation is equal to proposing 50 instead of 50*. If (a) holds for
(3:0, 51*), the current period VPC will accept this deviation. If (a) does not hold, VPC
will not accept al. This is obvious if (2.1)* is negative with (50, 51*). However, even
if (1)* is not negative with (50, 51*), if (2.4)* is negative, the VPC will not accept a1
since (50, 51*) is not a consistent strategy. He cannot calculate VH,S> which is needed
for the calculation of his expected utility. Same holds for (H, S). Thus, for (50*, 51*)

to be an equilibrium strategy, it has to satisfy (a). For Party 2 with (é0*,é1*), similar

1 1
things can be said with thresholds to = 2 + 630* and 7‘1 = 5 + 5:1”. Now, I state the

57

definition of equilibrium.

Equilibrium: Given the voting response of voters and the required campaign
effort level c, Party 1 strategy (50*, 51*) and Party 2 strategy (50*, 5:”) are a pair of
equilibrium strategies if the following conditions hold.

1) Given (220* , 9:1”), there is no consistent strategy (50, 51) that is Pareto superior
to Party 1 PCs in the situation of (H, H) and (H, S) compared to (50*, 51*).

2) Given (50*, 51*), there is no consistent strategy (60, 5‘1) that is Pareto superior

to Party 2 PCs in the situation of (H, H) and (S, H) compared to (é0*, 51*).

Notice that the definition of equilibrium is not saying anything about voters,
though it is them who choose the level of c. In the following, I consider only the

symmetric equilibrium so that (50*, 51*) = (50*,é1’“).

2.3 Results

First, I state about the existence of equilibrium. I consider only r_<_%. Given B > 1,
since c has the upper bound 5, choosing a consistent strategy is always beneficial
than choosing any non-consistent strategy for PCs. Since (2.1) and (2.4) have the
campaign effort c, and positive c can make these values negative for small enough r.
This means that VPCS prefer no campaign effort to accepting a1 for such small r.
Since VPCS always accept a2, choosing a2 for such small values of r is more beneficial
for PCs than accepting the loss of election by no campaign. Thus, PCs choose a2 for
such small r. This means that in all equilibrium strategies VPCS make the required

effort 0 when the party reputation is H. Moreover, since (0,0) makes (2.1)* and

58

B
(2.4)* non negative for any c E [0, 41’ it is obvious that an equilibrium exists for any

B
c 6 [0,1] and B > 1. I state this as a lemma.
B . . . .
Lemma 2.1. For any B > 1 and c 6 [0,1], an equilibrium crists.

Then, what kind of characteristics does the equilibrium have? I consider the easy
case of c = 0 first. Since B > 1, and 50 and 51 take values in [0, g], it is easy to show
that (2.1)* and (2.4)* are always non negative when c = 0. Thus, when c = 0, Party
1 VPCS always accept a1. So, Party 1 PCs always choose al. The same thing also

holds for Party 2 politicians about a2.

011

:5 :—

Lemma 2.2. If c = 0, the only equilibrium is e 2

Next, I consider if positive c can achieve better result for voters, i.e., if positive
c can induce PCs to lie less often. Since both (2.1)* and (2.2)* become —c when
50 = 51 = g, the threshold values of r for positive c must be higher than zero. This
means the threshold values of 50 and 51 are lower than %. The following proposition

is about this, i.e., about the existence of equilibrium with 50 + 51 < 1; Party 1 PCS

do not always lie when c is positive (same for Party 2 PCs when c is positive.)
o o . . . . O 1 . . B
Proposmion 2.1. The equilibrium with e + e < 1 exists with c 6 (0,1).

Of course, 60 + 51 < 1 means the improvement of the voter welfare. I calculate
1 — 16(5051)2
2 + 4030)2 + 4(51)2

(the derivation of this is in the Appendix.) When 50 = 51 = 2’ the long-run average

 

the long-run average voter welfare as the welfare criterion. It is

voter welfare is zero. Since appropriate positive values of c can achieve 50 + 51 < 1,

positive c can make the average welfare positive. So, requiring positive campaign
efforts is beneficial for voters. Then, it is natural to ask if it is possible to achieve

0 = 51 = 0. It is obvious that if B is so large that

the optimal result for voters, i.e., 8
utility gain/ loss from policy preference does not matter to politicians; they behave

more honestly, and vice versa. The following Pr0position is about this point.

B
Proposition 2.2. If B < 2 and c 6 (0,;), there is no equilibrium with 50 =

B
51 = 0. If B 2 2, the equilibrium with 50 = 51 = 0 exists for c = —4—.

Thus, if B Z 2, voters can achieve the Optimal result by requiring c = g. If
B E (1, 2), this is not possible. This impossibility result of 50 = 51 = 0 does
not depend on the upper bound of c. Even if c could take values higher than %,
50 = 51 = 0 is impossible for B 6 (1,2). Then, when B 6 (1,2), what is the

characterization Of the equilibrium?

B
Proposition 2.3. When B 6 (1,2) and c E (0, —4—), equilibria are characterized

by,

1
—>512€0

0 __
E1>2e +2 B

[\D

 

 

8
51: 2—B+2€0+\/(2——B+2€0)2—32c
8

 

1 1
All (50,51) 6 [0, 5] X [0, 5] that satisfy above three conditions are equilibrium.

Given this characterization, what can be said about the Optimal level Of c when B E
1 — 16(5051)2
2 + 4(EO)2 + 4(51)2

 

(1, 2)? Since the long-run average voter welfare is , its indifference

 

— k
curve is 51 = ~1— ——1——02- — k (k is a fixed welfare level.) The closer the curve is
2 k + 4(5 )

60

to the origin, the better for voters. Then, what value of c should voters require to

achieve the highest welfare? The next Preposition is about this.

Proposition 2.4. When B 6 (1,2), the best long-run average voter welfare

16 2 — B B 2 2
achievable is (B _ 2)2 + 32 with 50 = 0 and 51 = T by requiring c = Lg?)—

 

Though the highest achievable average voter welfare by requiring positive 6 when

16
(B — 2)2 + 32

1 . . . . .
2’ it is still better than the average voter welfare 0 With requiring c = 0. However,

B 6 (1,2) is

 

, which is lower than the maximum average voter welfare

the assumption that voters require some positive level Of the election campaign effort

is unrealistic. Moreover, this requires that voters know the value of B. Though the

(B + 2)2

t' f =
calcula ion 0 c 32

is easy if B is known, there is actually an easier way
to achieve the highest average voter welfare; simply, letting parties compete in the

campaign effort level. Change the reputation update during the election from,

(1) Before the election, if VPC Of a party makes the effort level less than c, the

reputation Of the party is updated to Suspicious.
to

(1)’ Before the election, if VPC of a party makes the effort level less than the
effort level the VPC Of the other party makes, the reputation Of the party is updated

to Suspicious.

Then, what is the result of this change? It is clear that PCs will choose 50 and

51 for which VPCS will make positive campaign efforts. Then, what 50, El and effort

level will PCs and VPCS choose?

61

Proposition 2.5. With the reputation update (1)’, if B _>_ 2, the equilibrium is
2 — B

50 = 51 = 0. If B E (1,2), the equilibrium is 50 = 0 and £1: 8

Thus, by letting parties compete in the campaign effort level, the best that can

be achieved by requiring positive c can be achieved automatically for voters.

2.4 Conclusion of Chapter 2

In this chapter, I considered a model of electoral competition between OLG political
parties under the uncertainty about policy outcomes. Exploiting the natural conflict
of interests within parties, I showed the possibility Of restraining the Opportunistic
behavior Of politicians. Requiring young politicians Of making campaign eflorts, it is
possible to deter the Opportunistic behavior Of politicians completely when B _>_ 2.
When B E (1, 2), the restraint on politicians is not perfect. But it can still achieve
higher voter welfare than not requiring the effort. The last Proposition shows the
importance of the competition between parties, which can achieve the best possible
outcome automatically for voters. However, even with the party competition, politi-
cians might lie if B E (1, 2). (H, S) and (S, H) are situations that the trust Of voters
is biased favorably to one party over the other. Such biased trust makes exploiting
the trust too attractive for the trusted party when B is relatively small. Reputation
systems and voting behaviors different from the ones in the chapter could achieve
different results. But, since such possibility of abusing the trust is a part of the re-
ward for young politicians Of restraining Old politicians, the similar exploitation of

the voter trust is inevitable when B is small.

62

The idea of this chapter is based on the party reputation; young politicians make
the campaign effort even though it gives them negative utility, because it helps their
party and the strong party will help them in future. The “strong party” is the party
with good reputation, and young politicians invest in it. Tadelis (2002) is a OLG
reputation paper and considers a model in which retiring agents can sell their firm
names, or reputations. The values of firm names depend on their reputations. To
keep a good reputation so that they can sell firm names at high price at the end Of
their life, even agents in their last period make costly effort. Similarity is clear, but
difference is also clear. In this chapter, it is not Old politicians in their last period
but young politicians with future who make costly efforts. SO, this chapter shows a
different route to keep a good reputation.

The reality is not the major virtue Of this model. Thus, the model depends on
the strong assumptions. However, at same time, explicitly modeling parties as or-
ganizations consisting of individuals is a more realistic way of modeling parties than
treating the parties as consistent existences or simply treating parties only as labels
on candidates. Loosening strong assumptions would change results quantitatively.
But as long as there is the intertemporal conflict of interests and there is some action
observable to voters, the qualitatively same result could be obtained. As I wrote in
the Introduction Of this chapter, there are papers of the retrospective voting models,
in which re-elections in the multi-period partially restrains the incumbent politicians
from practicing selfish behaviors (Austen-Smith and Banks(1989).) Though this chap-
ter could be counted as one of them, unlike usual retrospective voting models in which

the incumbent will face the election on the results of his own policies directly, in the

63

model Of this chapter the incumbent (i.e., PC in Office) will not face the election.
PCs face election only once to become the incumbent. Thus this chapter assumes
out the possibility Of the self-restraint of the incumbent in the usual retrospective
voting models. Still, improving voters’ welfare is possible. Though there is no direct
retrospective voting on politicians, the party structure makes it possible for voters to
use the retrospective voting13. This is different from the case Of repeated elections
between two parties that are consistent entities. Though I consider a particular prob—
lem Of information asymmetry, the same approach in this chapter can be applied to
other moral hazard problems. What important is the conflict Of interests in a party
and the existence Of a way for insiders to send signals to voters.

Although OLG models are Often used in Political Economy literature (see Persson
and Tabellini (2002)) and Alesina and Spear (1988) argue that “the ‘overlapping
generations’ model can be usefully applied to the political arena,” as far as I know,
Alesina and Spear (1988) and Harrington (1992) are only other papers Of electoral
competition model with OLG political parties. Recent papers on how party structures
affect politicians and elections consider static or finite period models (though Snyder
and Ting (2003) consider infinitely repeated game.) As Alesina and Spear (1988)
states, the OLG structure is a good way to capture the intertemporal conflict Of
interests among party members.

As I said, this chapter shares the OLG political party model with Alesina and
Spear (1988) and Harrington (1992). The difference between their papers and this
chapter is about what problem to analyze. Their papers analyze the problem Of

policy commitment. SO, they consider about if politicians keep their choices during

64

elections, and I analyze about what choices they make during elections. Usually
the policy commitment is assumed in electoral competition models (this chapter also
assumes it.) As Alesina (1988) shows, however, the lack Of the assumption could
have a big implication on credible platform choices. Then, Alesina and Spear (1988)
and Harrington (1992) show that the policy commitment could be achieved as the
equilibrium outcome, not as the assumption. Alesina and Spear (1988) consider a
transfer scheme from young politicians to Old politicians for the purpose. The young
politicians make the transfer as they need the Old politicians to keep their promises
for their own future elections. Thus, the logic is based on the conflict Of interest
among party members”.

As one more related paper, I would like to discuss about Caillaud and Tirole
(1999). Based on the conflict of interests among party members, Caillaud and Tirole
(1999) explain why policy convergence does not happen in reality, unlike in many
electoral competition models. It is a one-period model (though implicitly it assumes
the second period) and has an Office-oriented party leader and ideological party rank-
and-files. Because Of the information asymmetry between the party leader and voters,
the leader might not work hard for voters. However, because of the conflict Of interests
between the leader and rank-and-file party members, rank-and—file members can work
as monitors on the behavior of the leader for voters. Such monitoring can increase
the possibility of winning election. But, since only ideological members conduct such
monitoring (since effective monitoring could be costly), only ideological parties can

have such monitoring.

If the results in the paper would be taken literary, they look like implying that

65

the higher level of election campaigns might be good for voters. Clearly this is a
wrong interpretation. What the results really imply is that the party structure that
helps the party boss actually binds his behavior. Since he needs his party for him,
he has to take care of the party, which has the longer life span than the party boss.
Otherwise, party subordinates would send a signal to let voters know what is going
on inside the party. There would be some Obstacles to apply this result directly
to actual election campaigns. Firstly, the campaign effort in this model is different
from the actual campaign effort. In the model, the campaign effort is essentially
the alias of VPCs’ disutility. The costs of actual election campaigns are not entirely
burdened by young politicians who will go to the future elections. This obscures
observability. Also it would lessen the extent of the conflict of interests. For example,
consider a case that VPCS can enjoy some of campaign contributions from special
interests. It might not eliminate the conflict of interests entirely. But if voters are
not sure about the extent to which VPCS can receive the contribution, this would
add uncertainty. Secondly, there might be the information asymmetry between party
leaders and subordinates. In such case, the ability of party subordinates working for
voters is diminished. However, as long as the asymmetry within the party is less
severe than the asymmetry between the party boss and voters, the ability is not zero.

Voters’ appropriate reaction to the actions from party insiders is also very impor—
tant for the results. It does not seem possible to obtain similar results without using
voters’ reaction but with cooperation in OLG organizations (Cremer (1986), Kandori
(1992)”) Although the self-restraint through internal cooperation or inter-party co-

operation might be important, I think, in electoral competition models, assuming a

66

voters’ appropriate reaction is a simpler and more intuitive way.

67

Appendix of Chapter 2

Lemma 2.1. For any B > 1 and c E [0, i], an equilibrium eaists.

Proof. Let D E {(50,231) E [0, g] x [0, g] : (2.1)* 2 0 and (4)* Z 0 for (€0,el)}.
This D is a set of consistent strategies, closed, and non-empty from the assumption
c E [0, g]. If (50,51) ¢ D, the expected utility of PCs from this (50,51) is zero.
If (50,51) 6 D, the expected utility of PCs is positive. Thus, PCS never choose
(60, 51) ¢ D. Then, let P be the set of (£0, 51) E D which is strictly Pareto efficient.

Since D is not an empty set, P is not empty. From the definition of equilibrium, this

non-empty set P is the set of equilibrium strategies. I

B
Proposition 2.1. The equilibrium with 50 + 81 < 1 exists with c E (0, Z).

Proof. (2.1)* éé— — 50)(B — 250 + 451) — c
1 1
(2.4)* 5% — 51x3 — 250 + 451) — c

If e = 0, (1)* and (4)* are zero for 50 = 51 = --21-. Then, slightly increase c from

1
zero. At 80 = 51 = -2-, (1)* and (4)* become negative. However, from the previous

Lemma, an equilibrium must exist. Since (5, 5) ¢ D and all equilibrium strategies

are in D, the equilibrium with so + 51 < 1 must exist. I

The derivation of long-run average voter welfare

0

Since I consider symmetric equilibrium, 5 = 60 and 51 = 61. Then, the transition

probabilities are,

 

1_0 1+0
HH HH'2E ‘d 28r1—rd‘ I ‘
(, ):>(, ).f0 (1—r)r+f%_€0(-2-+ 2 )r+f%+807dr
_§_,02
—, m

68

ULH):(HJWHSEDr§+@%2

ursnwaH)E (H,rn;

[___€1 1+€1
rdr+ _1__1(—1 r) d)r+ rdr+ 1+ 1(—1-—)r )dr
[0 2... 0
21
= Z +(51)2

(Hflfl&6flfl=¢fli$flm$H):g—(EB

From these, the long-run probability of (H, H) at the start of period is derived as

 

 

1 + 4(51)2 . . .
2 + 4(80)2 + 4(51)2’ and the long-run probability of (H, S)&(S, H) is
1 + 4(50)2 . _ .
2 + 4(50)2 + 4 (131)2' Next, the expected voter welfare when reputation is (H, H) 13
2’50 2+50 1 1
f0 {1—r—r}dr+fl_ 0{—(r—(1—r))+—((1—r)—r)}dr
E 2 2
+ [1+8 (1 — r))dr
1
_ 5 _ 2(:0)20

The expected voter welfare when (H, S) or (S, H) is,
l _l_ + 81

-—e

“”0 (1—2r) dr+fl_1(2)r—1dr+f0 (1—2r) dr+f1+ E(QT-1W]
_1_ 12

_2 2(5 )

Thus, the long-run average voter welfare is,

1+4n52 1—4a%2 1+2e%2 114622
2 + 4(50)2 + 4(51)2 2 2 + 4(50)2 + 4(51)2 2
_ 1 — 16(8081)2
_ 2 + 4(80)2 + 4(El)2

 

 

 

B
Proposition 2.2. If B < 2 and c 6 (0,1), there is no equilibrium with 50 =

B
51 = 0. If B 2 2, the equilibrium with 50 = 51 = 0 exists for c = Z.

1(1— 50)(B — 260 + 451) — c

Proof. (21)* 2 2

69

1 1
(2.4)* 212 — 51)(B — 250 +451) — c

Let (50*,51*) be an equilibrium strategy. I stated conditions (a) above that
(50*, 51*) must satisfy to be an equilibrium. Actually, there are more conditions.

0* 1*).

(a) (2.1)* and (2.4)* are non-negative for (e e

(b) At least one of (2.1)* and (2.4)* is zero at (50*,51”).

Denote this one as (25)" (this could be one of (2.1)* and (2.4)* or both.)
(c) At least one of the following two holds.

(c.1) 50* = 51* = —.

(62) For at least one (z)*, the derivative of (z)* with respect to 50 and 61

are non-positive16.

If (a) holds but (b) does not hold, both (2.1)* and (2.4)* would be positive. Then,
PCS could deviate from (50*, 61*) with holding (a). Similar thing can be said to (c);

if (c) does not hold, PCs could deviate successfully. Thus, condition (b) and (c) are

necessary conditions for (60*, 51*) to be an equilibrium strategy. Then, substituting

B B
50* = 51* = 0 into (2)“, I obtain c = Z the maximum of c. Actually, if CZZ’ both

of (2.1)* and (2.4)* are zero for 50* = 51* = 0 (conditions (a) and (b) hold.) This

1* = 0 is an equilibrium. Since

value of c, however, does not guarantee that 60* = e
50* = 51* = 0 cannot satisfy (c.1), it has to satisfy (c2). Derivatives of (2.1)* and

(2.4)* with respect to and 50 and 81 at (50*,51*) are,

 

 

 

8(2.1)* _ 1 0 1 1 O

850 — 2(B 25 +45) (2—e)<0
6(2.1)* 0

851 = 1 — 2e 2 0
a 2.4 * 1

70

2.4 * 1
6(8 1) = ——2-(B—2z-:0-+—4el)+1—2e1
e

 

6(2.1)* 6(2.4)*
851 and 851
Thus, 50* = 61* = 0 cannot be an equilibrium when B < 2. This result does not

Suppose that B < 2. Then, both

 

 

at 50* = 51* = 0 is positive.

B B
depend on the upper bound of c, 4' Even if c can go higher than 71—, 50 = el = 0

could not be obtained. If c > %, all of (2.1), (2.2), (2.3) and (2.4) become negative

0

at e = 51 = 0. VPCS never accept of any of 50 and 51.

Next, suppose that B Z 2 and that there is an equilibrium with (50*, 81*) -,£ (0,0)

0:1,E

B
for c = -4-. Because (5 1*) is Pareto superior to (0,0), if such equilibrium exists,

B B
50* = 0 and 51* = 0 cannot be an equilibrium for c = —. Since c = —, the

0*_1*

. . 1 . .
0* 1*) cannot satisfy (c.1) Since 5 — e = -2- and the pOSitive c

equilibrium (5 ,5
make (2.1)* and (2.4)* negative; (a) cannot hold. SO, (c2) must hold. Then, looking
at (2.1)* and (2.4)*, it is clear that if 50* > 51* then (2.1)* is zero, and if 50* < 51*
then (2.4)* is zero. If 50* = 51* then both are zero. 1 consider these three cases.

Case 1. 50* > 51*

In this case, (2.1)* = 0 and (2.4)* > 0. This case is not consistent with the

assumption that (60*, 51*)

1 a 2.1 * . . . .
50* < 2’ (0 1) = 1 — 250* > 0; condition (C2) is no satisfied.
6

. .. . . 1
IS an equihbrium. Since c > 0, 50* cannot be -2—. For

 

Case 2. 51* > 60*

2.4 *
In this case, (2.4)* = 0 and (2.1)* > 0. Since 3(6) ) < 0 (the equality holds only
6
1*

1
when 6 = 5 and this does not happen as c > 0) and

 

*

061

 

is negative for B Z 2,

(c2) might be satisfied.

1
(2 — 51*)(3 - 250* + 451*) — 2c = 0

71

B
=> ——4(el"‘)2 + (2 — B + 250*)51” — 50* (B and c are cancelled out as c = Z)

1: 2-B+250+\/(2+B+250)2—32c 17
8

 

 

=>€

 

Since 81* > 50*, \/(B — 2 — 2230*)2 — 16.6:1F > (B — 2 — 250*) + 850* 2 0. Ffom
this,
(B — 2 — 250*)2 — 1650* > (B -— 2 — 250*)2 + 1650*(B — 2 — 250*) + 64(50*)2

=> 32(50*)2 +16(B — 1).:0 < 0
B -— 1
2

B - 1
So, 50* E (——2—, 0). However, since 50*

=> 3250* (50* +

 

)<0

is not negative, this is a contradiction.

Case 3. 50* = 51*
In this case, (2.1)* =(2.4)* = 0. Let 5 = 50* = 51*, and substitute 5 into (2.1)*

or (2.4)*. Then,

%(%—e)(B+2e)—c=0

B 1—
:>—2e2+(1—B)e+§—2c=—2e(e——2—B—)=0

2

 

Since < 0, it must be e = 0. Thus, (50*,51”) = 0. I

B
Proposition 2.3. When B 6 (1,2) and c 6 (0,1), equilibria are characterized

H

—>51250
2—B 20
51> + 8

{\D

 

 

 

8
51: 2—B+250+\/(2+B+250)2—32c
8

72

Proof. Let (50, 81) be an equilibrium. The proof of previous Proposition already
showed that the case of 50 > 51 at equilibrium is not possible (this result does not

depend on the value of B.) Thus, always 51 2 50. From this, (2.4)* = —(— —

2—B+250+\/(2+B+250)2—32c
8 .

1
Finally, since c > 0, 51 is less than 2' Then, (c2) in the proof of previous Proposition

BQAY BQAY m2n*
d =
860 an 851 650

1 624* 1
—(§ — 51)_<_0- For ( ) = —-—(B —— 250 + 451) + 1 — 251 to be non positive,

661 2
1> 250+2—B

 

 

51)(B — 250 +451) — c = 0. Solving this, 51 2

must hold for (2.4)*. SO,

 

 

 

must be non-positive.

 

e . Thus, any equilibrium satisfies above three conditions. Then,
1 1
pick (50*,51*) E [0, -2-] x [0, -2—] that satisfies above three. This (80*,81*) satisfies (a),

(b) and (c) in the proof of previous Proposition. I check if PCs have an incentive to

 

 

24* 22 * _*
deviate from (50*,51*). Since 6(651) _<_0 at (50*,51*), %% < 0 and 6:3) $0,
1 1
any point (60,81) 6 [0,-2] X [0,5] such that 60 Z 50*, 51 2 51* and (60*,51*) aé

(50, 51) makes (2.4)* negative. Thus, PCs will not deviate to such points. Any points

satisfying above three conditions are equilibrium. So, above three conditions are the

B
characterization of equilibria for B E (1, 2) and c E (0, —4—). I

Proposition 2.4. When B 6 (1,2), the best long-run average voter welfare

 

 

16 2—B B 22
achievable is (B _ 2)2 + 32 with 50 = 0 and 51 = T by setting c = L%l-.
1 1 20 2—B
Proof. Let E E {(50,51) 6 [0’2] x [0’2] : 51 2 5 +8 }. If (50,51) is

not in E, that (50,51) cannot be an equilibrium. So, I consider only (50,51) in E.

1 — 16(5081)2

 

The long-run average voter welfare is , and its indifference curve

 

2 + 4(50)2 + 4(El)2
is 81 = 1 ——1:—]?—— — k (k is a fixed welfare level.) Since the marginal rate of
2 k + 4(50)2
d1 Ol—k
substitution between 50 and 51 for voters is 3:7)- : —;—(£:222)—), the indifference

73

curve is downward sloping. Because the bottom side of E is upward sloping (on the

l
1
bottom, :7)- = —) and (0,0) ¢ E, it is obvious that voter welfare is maximized at

4
2 — B
the lower left corner of E. The corner is 50 = 0 and 51 = —. I check if this

2 — B
can be an equilibrium for some value of c. Substituting 50 = 0 and 51 = -——,

8
1_2-B+250+\/(2+B+250)2—32c (B+2)2 ,
— 8 ——32 . This

2 _
c= Egg—makes (0,2 B

32
2 — B . . * . 1 1 . u 0
— maximize (2.4) in [0, 2] x [0, 5] when B 6 (1,2), the combination of e = 0

8
2—B B 22 2—B
and 51 = 8 is the only equilibrium when c = Lfigli (0, 8

2 — B 2 0 2 B 2 0 2 — 32
1: + 5+\/(8+ + 5) CandE.Thus,any
1 1 B _2 2
other point in [0, 5] X [0, 2] cannot satisfy even condition for c = ( :2 l

2 — B) the lon run avera e voter welfare is 16 I
’ g g (B — 2)2 + 32'

 

 

5 holds only when c =

 

) an equilibrium strategy. Since 50 = 0 and 51 =

 

 

) is the only

 

intersection of a curve 5
. Finally,

at (0,

 

 

Proposition 2.5. With the reputation update (1)’, if B 2 2, the equilibrium is
2_-2

8
Proof. PCS of both parties want to increase the campaign effort level to the

50 = 51 = 0. If B 6 (1,2), the equilibrium is 50 = 0 and 51:

maximum. This maximum campaign effort level is same to the maximum campaign
effort level that VPCS would accept with the reputation update (1). When B 2 2,
since (0,0) is the only equilibrium with the update assumption (1) and its required

B
level of c is 4’ (0,0) is also the equilibrium result with the assumption (1)’. When
2 — B

B E (1, 2), the combination of 50 = 0 and 51 = T maximizes the value of (2.4)*
1 1 250 2 — B
in E E {(80,81) 6 [0,5] x [0,-é] : 51 2 ——+§——}. Thus, in both cases, the

Optimal with the assumption (1) is obtained with the assumption (1)’. I

74

Endnotes of Chapter 2

5. There are many empirical research papers about special interest groups based
on Grossman and Helpman (1996). They found a “puzzle” that the governments
of US and other countries put much higher weights on consumer welfare than on
contributions from special interests. Gawande and Hoekman (2006) also obtain such
a result on agricultural special interests and argue that such results are due to the
assumption of “unitary” government in Grossman and Helpman (they also talk about
“policy uncertainty”, which is the uncertainty about legislative outcomes, not the
uncertainty about the outcomes of implemented policies in this chapter.)

6. In the literature of the theoretical studies of legislative voting in Political
Science, parties and politicians are different existences, and the function of parties
are big subject (Aldrich & Rohde, Krehbiel & Meirowitz (2002), etc.)

7. Of course, no good/bad politician assumption and the non-Bayesian, simple
reputation update are related to each other. Because of the non-Bayesian update, I
do not need good / bad politicians (or some other assumption about characteristics of
politicians.) Because of no good / bad politicians, a simple Bayesian update does not
work in the model.

8. Alternatively, this can be considered as follows; there are three types of voters:
voters who have the affiliation with party 1, voters who have the affiliation with party
2, and independent voters who have no affiliation with any party. Neither of party 1
and party 2 voter groups is a majority group. Thus, the election outcome depends

on the independents. In other words, they are median voters.

75

9. See Alesina and Spear (1988) and Harrington (1992) for the policy commitment
in OLG political parties models.

10. This is a simplified, short cut way of modeling the signal. Following Majumdar
and Mukand (2004), this can be modeled as follows; at first politicians in both parties
have the belief % as the probability of the true state being wl. Then politicians receive
a common stochastic signal .73, which is in [_a_:, 5:]. This signal a: would be received with
the density function Q51 if the state is wl and the density fimction qfi” if the state is
w2. I assume that limxag (151 (:r)/¢2(:r) = 00 and liqug ¢1(:1:)/¢2(:r) = 0. Then,
from this signal, the candidate deduces new probability 1‘ of the state being wl using

the Bayesian rule,

r(x) = 1

2¢1(x)/<§¢1<x)+ We) = ¢1<x>/¢2<x)/<¢1(x)/¢2<x) + 1) Assuming

2

¢1(:r)/¢2(:z:) is strictly increasing as a function of z, a; has a one to one correspondence.
The distribution of 7‘ is derived from o1 and $2. For example, 451(113) E 2(511— g) / (i—§)2
and (19(1) E 2(33 — .r)/(.i: — §)2 produces the uniform distribution for r.

11. Though this simplifies calculations, this assumption makes an interpretation
of this "preference" difficult. If this “preference” comes from politician’s ideologi-
cal preference, politicians should receive non-zero utility whoever implements those
policies.

One interpretation is that politicians feel good or bad from the act of implement-
ing policies that do or do not fit to their ideologies. Other interpretation is that this
“preference” does not come from politician’s ideologies but from benefits or punish-

ments given by special interests according to policies they implement.

12. If VPCS receive the same utility as PCs do from implementing policies, results

76

described later should be changed quantitatively. But the qualitative result is same.

13. New York Times columnist Thomas Hiedman argued that the fact that Vice-
President Cheney was not going to run for the President partially explains the prob-
lems of President Bush in his second term (New York Times, June 22, 2005).

14. However, Harrington (1992) points out that actually the scheme of Alesina
and Spear (1988) is not credible. Instead, Harrington (1992) provides a different logic.
He assumes that politicians have one more period after they retire. As long as their
parties implement their favored policy, there could be an incentive for them to keep
their campaign platform so that their party would not be disadvantaged against their
opposite party at the election when they retire.

15. The model in this paper is a stochastic one. For the difficulty of cooperation
by OLG organization in stochastic situation, see Messner and Polborn (2003). For

the difficulty caused by limited communication, see Laglmoff and Matsui (2004).
0(2.1)* 0(2.1)* 6(2.4)*
650 051 850

1
and 51 = 5, respectively. So, I can ignore the case that they are zero. However,
8(2.4)* 0(2.4)*
51 (951 = 0, the
. . . . . . . 62(2.4)*
argument in the condition (b) 18 not correct in the strict sense. But, Since W =
e 5

—251 —2 < 0, even the slightest increase of 51 will eventually make (2.4)* negative.

 

 

0:1

1 .
6 2

is always negative. and can be zero only when 5

 

 

. . . 1
can be pOSSIble even when neither of 50 and 51 18 §. When

Thus, I can use the condition (b) in current form.
17. From (2.4)* = 0, 51 = (2 — B + 250 :1: ((2 + B + 250)2 — 32c)0-5)/8 is obtained.
However, 51 = (2 — B + 250 — ((2 + B + 2:30)2 — 32c)0'5)/8 is not answer since this is

negative when c is very low.

77

References

[1] Aldrich, John H. AND David W. Rohde: “Measuring Conditional Party Govern—
ment” Presented at the annual meeting of the Midwest Political Science Associa-
tion, Chicago.

[2] Alesina, Alberto ( 1988): “Credibility and policy convergence in a two-party sys-
tem with rational voters" American Economic Review, 78, 796-806.

[3] Alesina, Alberto AND Stephen E. Spear (1988): “An Overlapping Generations
Model of Electoral Competition” Journal of Public Economics, 37, 359-379.

[4] Austen-Smith, David AND Jeffrey Banks (1989): “Electoral Accountability and
Incumbency” in Models of Strategic Choice in Politics, ed by Peter C. Ordeshook,
Ann Arbor, The University of Michigan Press

[5] Caillaud, Bernard AND Jean Tirole (2002): “Parties as Political Intermediaries”
The Quarterly Journal of Economics, 1453-1489.

[6] Calvert, Randall (1985): “Robustness of the Multidimensional Voting Model:
Candidate Motivations, Uncertainty, and Convergence” American Journal of P0-
litical Science, 39, 69-95.

[7] Cremer, Jacques (1986): “Cooperation in Ongoing Organizations” The Quarterly
Journal of Economics, 101, 33-49.

[8] Friedman, Thomas L. (2005): “Run, Dick, Run” New York Times, June 22, 19.

[9] Gawande, Kishore AND Bernard Hoekman (2006): “Lobbying and agricultural
trade policy in the United States” World bank policy research working paper 3819.

[10] Grossman, Gene M. AND Elhanan Helpman (1996): “Electoral Competition and
Special Interest Politics” Review of Economic Studies, 63, 265-286.

[11] Harrington, Jr., Joseph E. ( 1992): “The Role of Party Reputation in the Forma—
tion of Policy” Journal of Public Economics, 49, 107-121.

[12] Harrington, Jr., Joseph E. (1993): “Economic Policy, Economic Performance,
and Elections” The American Economic Review, 83(1), 27-42.

78

[13] Heidhues, Paul AND Johan Lagerlof (2003): “Hiding information in electoral
competition” Games and Economic Behavior, 42, 48-74.

[14] Kandori, Michihiro (1992): “Repeated Games Played by Overlapping Genera-
tions of Players” Review of Economic Studies, 59, 81-92.

[15] Krehbiel, Keith AND Adam Meirowitz (2002): “Minority Rights and Majority
Power: Theoretical Consequences of the Motion to Recommit” Legislative Studies
Quarterly, 27, 191—217.

[16] Kreps, David M (1990): “Corporate Culture and Economic Theory” in James
E. Alt and Kenneth A. Shepsle, eds., Perspectives on Positive Political Economy.
Cambridge, Ma: Cambridge University Press, 90-143.

[17] Lagunoff, Roger AND Akihiko Matsui (2004): “Organizations and Overlapping
Generations Games: Memory, Communication, and altruism” Review of Economic
Design, 8, 383-411.

[18] Levy, Gilat (2004): “A model of Political Parties.” Journal of Economic Theory,
115, 250-277.

[19] Majumdar, Sumon AND Sharun W Mukand (2004): “Policy Gambles” The
American Economic Review, 94(4), 1207-1222.

[20] Messner, Matthias AND Mattias K. Polborn (2003): “Cooperation in Stochastic
OLG games” Journal of Economic Theory, 108, 152-168.

[21] Morrison, Alan D. AND William J. Wilhelm, Jr. (2004): “Partnership Firms,
Reputation, and Human Capital” The American Economic Review, 94(5), 1682-
1692.

[22] Persson, Torsten AND Guido Tabellini (2002): Political Economy Explaining
Economic Policy, M.I.T. press.

[23] Snyder, Jr., James M. AND Micheal M. Ting (2002): “An Informational Ratio—
nale for Political Parties” American Journal of Political Science, 46(1), 90-110.

[24] Snyder, Jr., James M. AND Micheal M. Ting (2003): “Roll Calls, Party Labels,
and Elections” Political Analysis, 11(4), 419-444.

79

[25] Tadelis, Steven (2002): “The Marker for Reputations as an Incentive Mecha-
nism” Journal of Political Economy, 110(4), 854-882. -

[26] Wittman, Donald (1983): “Candidate Motivation: A synthesis of Alternatives”
American Political Science Review, 77, 142-157.

80

3 The Choice of Inefficient Instruments in a
Simple Retrospective Voting Model with Voter

Abstention

3.1 Introduction

The objective of this chapter is to propose one explanation about why governments use
inefficient policy instruments. Particularly, I consider a case in which an incumbent
politician in office uses a tariff to help an import-competing industry as a decision-
making problem of the incumbent. As every introductory International Economics
textbook explains, the tariff is inefficient compared to the production subsidy as a
policy instrument to help domestic industry. Moreover, as Dixit and Norman (1980)
and Dixit (1986) shows, it is possible to make the transition from the trade with tariffs
to the trade with no tariff Pareto-improving by using appr0priate lump sum transfers
or commodity taxes / subsidies. If so, why at all does the incumbent use tariffs when he
could make every voter better off by using taxes/subsidies instead of tariffs? Given
the natural assumption that the election outcome depends on the utility levels of
voters, the combination of tax and subsidy should be better than tariffs not only for
voters but also for the incumbent’s prospect of winning next election! Though there
is the huge literature of Endogenous Tariff Formation (Mayer (1984), Grossman and
Helpman (1994), Yang (1995), etc), they do not answer this question because they
assume away subsidy, which Rodrik (1995) and Dixit and Roemer (2006) criticize

as restrictions of possible policy instruments. To the question, this chapter tries to

81

provide one explanation. The hinge of the explanation is the voter abstention.

The idea of the explanation is simple; if the incumbent decides to help domestic
industry, other people will have to pick up the tab. Though the incumbent can expect
positive feedbacks during the election from pe0ple who receive the help (as votes,
campaign contributions, etc.), the help will cost the incumbent some votes from people
who finance it involuntarily. However, in reality, unlike many electoral competition
models of Political Economy in which all constituency vote, many peOple actually
abstain from voting. Then, the incumbent might be able to make the loss of votes
small by distributing the cost of the help to people who do not vote. The participation
rates of voter groups depend on characteristics of groups (Lijphart (1997)). Assuming
several different policy instruments, such characteristics must have influence on the
choice of policy instruments by the incumbent. According to empirical researches on
the behavior of voters, one of the important characteristics is income level (Lijphart
(1997)). Generally, the higher the income level of a group, the higher the participation
rate of the group. This does not mean that all political choices are for rich people,
since most of actual voters are middle class or working class anyway18. At margin,
however, different income levels of different voter groups could have an implication
on political choices.

The situation I consider is as follows; an import-competing domestic industry is
lobbying an incumbent to help themlg. The incumbent can use both a tariff and a
production subsidy simultaneously. If the incumbent decides to help them, he has to
choose the combination of the tariff and tax to finance the help. After the decision, the

incumbent will go to election. The outcome of the election depends on utilities voters

82

received. The incumbent is office-motivated, i.e., winning the election is his only
objective. To win the election in this model, the incumbent has to take two things into
his consideration: voter heterogeneity and voter abstention. Voter heterogeneity is the
main idea behind the endogenous tariff formation papers (ex, Mayer (1984)). Because
of the heterogeneity, different voters might prefer different policies. In the model of
this chapter, the heterogeneity comes from different income levels. Combined with
common non-homothetic preference, it derives different consumption patterns among
voter groups. Though voter abstention was incorporated in a model of Mayer (1984),
the idea of abstention has not been explored further in the literature of Endogenous
Tariff Formation. There are many papers about why some people abstain from voting
(Harsanyi (1980), Shachar and Nalebuff (1999), Feddersen and Sandroni (2006). As
surveys of abstention, Aldrich (1993) and Feddersen (2004).) However, since my
attention is not on the abstention itself but on its potential effect for the choice
of policy instruments, I simply assume a voter-abstention model based on the Group
Rule-Utilitarian literature (Feddersen and Sandroni (2006), Coate and Conlin (2004).)
With the voter abstention, the incumbent can manipulate the participation rates
of different voter groups by distributing the cost and benefit of helping domestic
industry among voter groups. Then, he will choose the set of the policy instruments
that maximizes the probability of his winning the election. Within this situation, I

consider under what condition he would use the tariff.

In the following, I describe the model in section 3.2, results in section 3.3 (two

voter groups) and in section 3.4 (three voter groups.) I review related papers briefly

83

in section 3.5. Section 3.6 is the conclusion of this chapter.

3.2 Model

The model is a small country model with two voter groups (I change this to three
groups in section 3.4) that produce two goods. I explain the economy side of the

model first, then the political side.

3.2. 1 Economy side

The two groups in the small country are groups of capitalists and workers, called as
group K and L, respectively. The population is continuum, and groups have popula-
tion NK and NL with NK +NL = land NK < NL. Each capitalist has one unit of
capital, and each worker has one unit of labor. There are two goods, X and Y. Good
X is the exporting good, and one unit of good X is produced by one unit of labor.
Good X is the numeraire. The good Y is the import-competing good, and requires
labor and capital for its production. Let F (k, l ) be its production function with k and
l as units of capital input and labor input. This F is an increasing, differentiable and
constant return to scale technology function. However, since the supply of capital is
fixed, I consider f (l) E F (N K ,l) instead (assuming perfect competition.) This f is
a decreasing return to scale function of the country wide labor input for good Y pro—
duction, l. I treat f as if it is the function of total industry of good Y. The beforetax
incomes of capitalists and workers, 1K and I L, come from profits and wages. Since
one unit of labor can produce one unit of good X, workers receive income I L = 1

from their one unit of labor by producing good X or as wage from working in the

84

production of good Y. Let r and s be the specific tariff of good Y and the production
subsidy per unit of good Y, respectively. The tariff revenue and the income tax, which
I explain later, are used to finance the production subsidy. This assumption might
cause a conceptual problem for the case that the incumbent wants to use only tariff.
However, since I consider in this paper if the incumbent might have an incentive to
use the tariff when he decides to help capitalists, this assumption is innocuous for my
purpose20. Let 'p‘ and p E p+r be the fixed world price and domestic price of good Y,
respectively. Then, the total profit from production of good Y is (p + 7' + s) f (l) — l.

Since the pOpulation size of group K is N K , the before-tax income of a capitalist is

1K: (P+S)f—l
——_NK

Let r“ and y“ be the consumption of good X and good Y by one member of

. I assume that [K > 1, so capitalists are richer than workers.

group a E {K , L}. All members of two groups have same utility function, U (:13, y); no
disutility of labor for workers. Thus, the income tax does not cause distortions, same
as lump-sum tax”. This utility function is an increasing, strictly concave and differ-
entiable function in both arguments. Let y(I“, p) be the common demand function
of good Y of a member of group a E {K , L} derived from the utility maximization
of U (:r, y) with income I 0 (here abusing notation, I a is after-tax, disposable income)
and the domestic price of good Y, p. From this, the demand for good X of a member
of group a E {K, L} is :13“ = I“ — py(p,Ia). Here, deviating from the usual as-
sumption in International Economics, I assume the common utility function U is not
homothetic and that the income elasticity of good Y is less than one. The total and
average demand of good Y is g E N K yK + N LyL. Since f (l) is the total domestic

production of good Y, the import of good Y is defined as m E g —- f (l) The indirect

85

utility function is V(Ia,p) = U(Ia' — py(Ia,p),y(I“,p)), a E {K, L}.

3.2.2 Political side

I assume that voters decide to vote for the incumbent or not based on the utility
they received during the incumbent’s term compared to the utility they would receive
under the policy of the challenger, which is assumed to be the free trade policy. So,
this is the retrospective voting. The incumbent has to take into his consideration the
reactions from his constituency. The objective of the incumbent politician is winning
the election, i.e., the maximization of the probability of winning the election. The
only decisions that incumbent can make before the election are the decision to help
capitalists or not and how to finance the help. The challenger at the election proposes
the free trade policy. His role in this model is just to provide an alternative to voters
and makes the retrospective voting possible for them. He can be considered as a
convinced free trader.

The voting rates of groups are determined by two factors: the voting decision
making, which is also based on voting costs and utility differences between the policies
of the incumbent and the challenger, and stochastic terms. These two determine the

actual number of votes cast and the election outcome.

Voter abstention: Some people do not vote. The problem of the voter ab-
stention, or the paradox of not voting (Feddersen (2004)), is a big issue of Political
Economy, but not a topic of this chapter. So, here, I simply use a modified version

of the Group Rule-utilitarian voting model (Feddersen and Sandroni (2006), Coate

86

and Conlin (2004).) If the incumbent decides to help capitalists, no potential voter
is indifferent between two candidates. Every capitalist prefers the incumbent to the
challenger, and every worker prefers the challenger to the incumbent. Then, they
face two obstacles before actual voting for their preferred candidate. First, voting is
costly. Take a potential voter in group a E {K , L}. Let d“ be the utility difference
between his preferred candidate and the opponent. Let c be his voting cost, which
varies among potential voters. Then, if the voting cost is so high that do” — c < 0,
there is no reason for him to vote. Thus the voting cost is the first obstacle. The
second obstacle is the fact that the probability of being the pivotal voter is essentially
zero unless the number of actual votes is very low. Since the population is continuum
in this model, such probability is zero. So, there is actually no reason for anyone to
vote. Following the Group Rule-utilitarian voting literature, however, I assume that
some people still vote when d“ — c 2 0.22 I call potential voters who do not vote even
when d“ — c 2 0 as free-riders. They do not vote since they think other peOple will
vote for them anyway. The fraction of such free-riders is unknown and stochastic.
Let gba be the participation rate of group a E {K , L} among non free-ride potential
voters. This qb depends on the voting cost function, c(n). This voting cost can be
considered as consisting of time, money and other factors necessary for going to a
voting booth. Different potential voters have different voting costs. Then, the voting
cost function c(n) gives the voting cost of n-th voter in the group when every potential
voters in group a are aligned from the lowest voting cost voter to the highest voting
cost voter. So, n of potential voters in a group have voting cost less or equal to c(n).

I assume that both groups have same cost function and that c’ > 0 and c” < 0. As

87

a simple example giving a cost function of this type, consider a voting district with
one voting booth at the center of the district. Potential voters live uniformly in the
district, and the voting cost of a potential voter is represented by the distance from
his home to the booth. Then, voting function becomes concave like c. Further, I
assume that c(O) < 0, so some people always want to vote, maybe due to the sense of
civic duty or strong partisan feelings. Since both groups have the same voting cost
function c(n), the number of votes is same for both groups when dK = dL = 0. Since
N L > N K , this means qbK > qu at no utility difference. I assume that all actual
capitalist voters vote for the incumbent and all actual working voters vote for the
challenger even when they are indifferent between two candidates. Then, given the

utility difference d“ > 0, the participation rate of the group a, 45“, is defined by,

d“ — c(qbaNa) = 0

From this,

as“ _ 1
Bid—0 _ Mariam) > 0

 

The participation rate d)“ of non free-ride potential voters in group a is determined
by d“ and c. But the actual number of votes is determined by d)“ and stochastic terms
about the fraction of free-riders. This stochastic terms maybe come from many factors
like the conflict of the voters’ sense of the civic duty and the fact of the impossibility
of being the pivotal voter, and all other uncertain factors not resolved until the
election day, like weather, possible transportation troubles, abrupt schedule changes

of potential voters, etc. I assume the following setup; a potential voter in group a

88

is not a free-rider with probability n“. Thus the potential voter is a free-rider with
probability 1 — a“. For simplicity, all members in group a E {K , L} have same a“.
This a“ is a random variable.

K NK ¢K

The number of votes from group K is ,u , and the number of the votes

from group L is uLgbLNL. Thus, the election result is determined by ”K N K qbK —
uLNquL. If ,uK N K 45K —— nLNLdJL > 0, the incumbent wins the election”. Since us
are random variables, this is a random variable, too. Let H (,uK , 111’) be the cumulative
distribution function of ,uK and ,uL. Then, the probability of the incumbent winning
the election can be calculated as fflKNK¢K_#LNL¢L>0dH(luKa”Ll- This is the
objective of the incumbent. Without knowing the exact function form of H, it is

not possible to know the exact value of the probability. However, to analyze the

incumbent’s choice, I do not need to know the exact form. Let A be the intersection
NL L

L K . K L
Of[0,1]><[0,1]and{(/i 1/1' ).l1 2’1 NK¢K

} in [1L X ,uK dimension (see figure

 

3.1.)

89

 

 

”KzuLNL¢L/NK¢K
M/

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.1

Clearly, the maximization of the probability of winning the election is equal to
NL L
NK¢K

 

the maximization of the area of A. Moreover, since ”K = 111’ always holds at

”K = 0 and ML 2 0, the maximization of the area of A is equal to the minimization

L L NK K
. But this is equal to the maximization of —.
NK¢K NL¢L

 

of Thus, the incumbent

does not need to care about the distribution function H. I state this as a claim.

Claim 3.1 The incumbent tries to maximize his probability of winning the election,

prNK¢K_uLNL¢L>OdH(HKa ,uL). This is equal to the maaimization of

NK¢K
NL¢L

90

3.3 Results with two groups

Before stating results, let me briefly describe my strategy of obtaining results. Let
the sum of the production subsidy and the tariff rate as H E s + r. In the following
analysis, firstly I consider if the incumbent has an incentive to use a tax to give
the production subsidy s with zero tariff. Next, I consider if the incumbent has an
incentive to raise the tariff rate r for the given level of H E s + r. Such increase of T
means fl: = —1. Since the objective of this chapter is to consider why the incumbent
might want to use a tariff to give the help when he can give a production subsidy,
this is an easy way to achieve the objective. Because of this order, the tariff does not
cause additional distortions in production; it keeps the distortion in production at
the level previously caused by the production subsidy, though it causes distortions in
consumption. Since the tariff revenue is used to finance the production subsidy (with
the tax revenue from the income tax), higher tariff means lower tax rate. Lower tax
is good news for all people. But because the income elasticity of good Y is less than
one, how good it is is different among people with different income levels. Regarding

the tax rate, I consider two cases; the case of single uniform tax rate and the case of

different tax rates for two groups.

3.3.1 Single tax rate

The incumbent will help capitalists? In this section, I consider if the incumbent
would use the tax to provide the production subsidy to capitalists. I assume, for now,

that the incumbent does not use the tariff. Then, the utility differences of capitalists

91

and workers are defined as follows.

Utility difference:

 

:1: S _ :1: f _ f
dK(t)=V((1——t)(p +1313” l,p*)—V(p f(l ) l 19*)

dL(t) = V(1.p*) - V(1-t,p*)

 

Notice that they are defined as the subtraction of the utility of the non-preferred
candidate’s policy from the utility of the preferred candidate’s policy. When the
government uses only the income tax to provide the subsidy, its budget constraint is

sf (l ) = t(7r + N L ) Taking the derivative of this with respect to t, it is obtained that

gig—n+NL fiom§£=0

ds ,
217“” + Sf (”as dt ‘ Bl

The equilibrium condition for production is, (p* + s) f ’ (l) - 1 = 0. From this,

 

fl = __f’__ = .92
ds (10* +s)f” f”
Thus,
ds_ L _ (_f’fi_1_(rr+NL)f”
Zi_(7r+N )(f S f”) _ff”-S(f’)3
f(l)—8 d
d,{{(t)=l/IK —7V7r—K+—N—%t—} fromazlE =0
dt
dflt): 1L3;
K K

Then, the numerator of the derivative of W with respect to t is,

 

 

ds
1 7r f(l)—
L 1L K K __ _ dt
N o N NKc’(NK¢K)VI { NK + (1 t) K }
1 ds
_NK KNL L_
Q5 NLd<¢LNL)V’ dt
f L
When t = 0, it should be that s = 0 and l = If, so _8_s|t:0 = W—j—iV-fi where If
at f(lf)

and 7rf are l and 71’ at free trade, respectively. Thus the above expression becomes,

92

 

 

1 NL 1
K vK__ NL L _NK KNL vL
NKc’(¢KNK) I NK 4’ (’5 NLduLNL) 1

Moreover, when t = 0, dK = (11’ = 0. So, ¢KNK = gbLNL and c’(NKgbK) =
c’ (N LgbL ) Thus, the expression becomes,

K
1 V,

NLNquLc’(NL¢L)[NK— NL]

 

If this is positive, the incumbent would help capitalists with the production sub-

sidy.

Lemma 3.1. The incumbent will raise tax to help capitalists if the following

condition holds at free trade

vK vL
W _ N_I, > 0 (3.1)
VK VL
Since N L > N K , it is likely that N K NI L > 0 unless the marginal utility of

income decreases very fast. Especially if the marginal utility of income is constant,
it is positive. Thus, the incumbent has an incentive to help capitalists. Though
the logic of this result is a very simple and intuitive, this shows the importance of
considering the voter abstention. The tax and substitution scheme I am considering
here means that taking money from a larger group and giving it to a smaller group.
Because of diflerences in group sizes, the amount of money giving to one person of
the smaller group is larger than the amount of money taken from one person in the
larger group. Thus, naturally, the money given to the smaller group can have bigger
impact on number of votes than the money taken from the larger group. If 10 cents

are taken from everyone in a group with 100 million people, it is unlikely that the 10

93

cents could cause the huge‘increase of votes from the group. However, if everyone can
gain 100 dollars by going to a voting booth, that could cause a big increase of votes
from a group with 100,000 people. Of course, this is same to the usual logic of special
interests, so, anything but new (Persson and Tabellini (2002), pp.159).) However, if
I assumed that everyone votes, this logic could not hold here since 100 million people
would go to voting booths because of their loss of 10 cents! The logic would not hold
anymore. Clearly, this first Lemma shows the possible impact of the voter abstention

on the policy choices of politicians.

How will incumbent help capitalists? In the previous subsection, I showed that
the incumbent is likely to raise the tax and provide the production subsidy. However,
he can also use a tariff to help capitalists; no need for him to stick only to the
production subsidy. But, if he uses both instruments, he would need to consider how

they would affect voting behavior of potential voters24. As I said before, I consider

is

(17'
a given total level of H E s + r > 0, the higher tariff means the lower tax rate. The

the change of the tariff and the subsidy such that = —1, i.e., dH = 0. Thus, for

government budget constraint is now sf (l) = t(7r + N L ) + rm. Since dH = 0, higher

tariff does not change the production level of good Y, the labor employment for the

 

OZ 8 _
production of good Y and the profit. Thus, 5-; = 57’; = 0. Let I E 7r + N L be the
0
average and total income. Then, d7 = — I. T .

The effect of higher tariff on utility:
The higher tariff hurts workers, but it could benefit capitalists if the tariff is not
too high. This is possible since the income elasticity of good Y is less than one.

94

Because of this, the consumption share of workers of good Y is higher than their
income share in the total pOpulation. Thus, the shift from the tax to the tariff is
beneficial for capitalists even if dH = 0. Given the level of H, the level of s is derived
from r. Then, from the government budget constraint, the level of t can be derived

from 7'. Thus, a new indirect utility function of r and H can be defined as

(p*+s+r)f(l)—l
NK

 

VKU:H)=V((1—t)IK,p*+T)=V((1'—tl 40*“)

VL(T:H)=V(1—t,p*+r)

The derivative of VK with respect to r is,

* VK yL yK IK (9m
I I I N y 8T

The sign of this depends on the inside of the bracket. It is natural to assume that

('9

37: < 0. However, since 1K > I L = 1 and the income elasticity of good Y is less than
31" yK

one, 17' — 17 > 025. Thus, the inside of the bracket could be positive. Especially

when r = 0, this is definitely positive. Thus, when H = s + 7' > 0, capitalists prefer
the positive tariffs to zero tariff.

The derivative of VL with respect to r is,

“L VIL KLKyL :9
VT ldH=0=————N I I lI—L-Tfi-N—K‘éfgl

The inside of the bracket is positive. Thus, this is negative. Not surprisingly,

workers always prefer no tariff.

The utility differences

Then, the utility differences are defined as follows.

dK(T:H)=VK(T:H)—VK(020)

95

dL(r : H) = VL(0 : 0) — VL(T : H)

Their derivatives with respect to 7' are d5 = VTK and df’ = —VTL.

 

K K
The effect on N ¢
NL¢L
K K
The derivative of —L- with respect to r is,
1 NL¢
K K K L L_ K K L L L
———(NL,L)2[N caddTN i N ¢ N m]
1 LV_IK LLLL__ VIL KLKKIK 31K
=.——— N I N -——N I N ——-——
07” VIK LLK VIL KK
___... -———~——N
+7"019m!“ f” I +an) f l]

where c(oI) E c(No‘qfia)

At T = 0, this becomes,

L
___IKNKNLZI L 31K L¢L_ VI NK¢K)

I(NL¢L)2 (IL IK —)(NKc’(K' ) NLC'(L)
L K
From the less-than-one income elasticity and the single tax rate t, %L — g—K- > 0
Thus, the sign of this 18 equal to the sign of m LgbL— mNKQSK. This
can be rewritten into,
K L
1 VI 1 VI

 

 

* K K L L _
( ) N Cb N d) [NK¢K NKc'(K) NL¢L NLc’(L)]

Thus, the condition for the incumbent to raise the tariff from zero is,
1 VIK _ 1 V}
NK¢K NKc’(K) NL¢L NLc’(L)
¢> NL NquL/VIL > C’(K)
NK NKQK/VIK C/(L)

>0

 

 

 

This condition can be denoted in terms of elasticities of number of voters with

respect to the utility differences, and-
L L L L K L
N d WI > in g, and > End
K K K K K K K L L rL
N d /VI and N d /VI N d ”I

 

96

At first, this looks a bit weird. If dL is very small and dK is very high, then the
left side of the left inequality would be very small and would make it diflicult for the
condition to hold, even though it sounds like a good condition of the tarifl increase for
the incumbent. Looking at the definition of the elasticity, however, it is clear that the
sizes of ds do not matter since as have d inside, too. Moreover, unless the marginal
utility of income decreases quite fast, the left side cannot be so small. Notice that
Nada ° th ’ 1 ' ' t f ' Th NLdL/VIL

s 088 0 am ms 0 o . e ,
V10 is e group a r g in er me me n NKdK/VIK

ratio of the loss of workers over the gain of capitalists. If the transfer from workers

 

 

is the

to capitalists is done efficiently, the ratio should be one. However, because of the
inefficiency (i.e., dead weight loss), the ratio is likely to be more than one unless
the marginal utility of income decreases very fast. Especially if the marginal utility
of income is constant, the left side should be more than one from the dead weight
loss (this dead weight loss comes from the production subsidy since I am considering
this at r = 0.) Then, the condition says if the voting response of workers to their
utility loss is not so high compared to the voting response of capitalists then the
incumbent would raise the tariff. One simple way to understand the condition is this;
assuming that the constant marginal utility of income, the condition above is equal

K NL/NK

to end—d—K— At T = 0, the dead weight loss from the tarifl is negligible,

> E n ‘15?
so, the marginal transfer rate of the loss of workers to the gain of capitalists by the
tariff at r = 0 is one; one dollar loss of group L means one dollar gain of group
K. Suppose that every worker loses one dollar from the tariff increase. Because of
L

the group size difference, this means N—K- dollar gain for every capitalist. Thus, Zi—L—

can be considered as the ratio of the change in the worker’s utility difference, and

97

NL/NK

dK as the ratio of the change in the capitalist’s utility difference. Then the

elasticities of votes are multiplied to them respectively. Thus, the condition simply
requires that the increase of the votes from capitalists is larger than the increase of

the votes from workers.
Proposition 3.1. Suppose that the incumbent has decided to help capitalists. If

K L

___—___— > _—
NKdK/VIK NLdL/VIL
at 'r = 0, then the incumbent will use the tariflr to help them ( maybe with the produc-

tion subsidy.)

NL ¢L

 

NK¢K
-—a—T-— = 0 defines the optimal value of the tariff for the incumbent, it

is unlikely to be solvable analytically. So, I consider the different characterization of

Though

r
the optimal tariff rate. Let 5d, 2 (12%. From (*), the condition for the optimal tariff

is,
NKag‘dJYNLhL — NKaKNthdI; = 0

KK LL
®N¢N¢[5KEK—EL5L]=0
7. nddr nddr

 

Of course, this means that the impact of tariff on the voting from capitalists is

same to the one on the voting from workers.

Corollary The condition of the optimal tarifi' rate for the incumbent is,

K K _ L L
Erictgd’r _ Endedr

98

3.3.2 Different tax rates

In the previous subsection, I assumed that the incumbent has only one tax rate for two
groups. In this section, I assume different income tax rates for different voter groups.
This changes the result obtained above hugely. I call tax rates of capitalists and
workers as tK and tL, respectively. However, to keep the previous model unchanged
as much as possible, I denote those two tax rates tK and tL in terms of t and tax

burden share h E [0, 1]. So,

tKrr = ht(7r + NL)

#NL=(r—mnn+NL)

Thus, the total income tax payment is still t(7r + N L), but capitalists pay the share
h of that total income tax payment and workers pay the share 1 — h of it. Then,
tK=mm+N%

7f
tL = (1 — h)t(7r + NL)
NL

 

I assume that the incumbent can choose the tax burden share h freely. This means

that in the previous subsection there was a restriction that tK = tL, which means

h = {IV—L. Of course, the change in h affects utility gains and losses of capitalists
II
and workers. Thus, given the total income tax t(7r + N L), the incumbent will choose

the rate h that maximizes {Xi—(15:: Since change in h does not change the total
income tax payment, no change in s happens. So, I do not need to worry whether
the change in h might change it.

In the following, firstly, I consider what rate of h the incumbent would choose for

a given level of t(7r + N L). Then, given that h, I consider if and how the incumbent

99

would provide the protection to capitalists.

The determination of tax rates In this section, I assume 7 = 0, again. Thus,
H = s. Then, given the tax rate t, the indirect utilities of capitalists and workers of

h are given as follows.

 

 

7f— 7T L
VK<h=t>=V< ”32;“ ).p*)

L_ _ 7, L
VL(h:t)=V(N (1 152“ “V ).p*)

From these, utility differences, ds, are derived. Then, the incumbent has to find
NK K K K
—. The derivative of _—
NL¢L NL¢L

the optimal level of h for him to maximize with

respect to h is,

————l L [NchfifdffNquL — NK¢KNL¢5d£1
(NW) )2

_ M _ L L__V_IK_ K Ki
’” (NquL)2[ N ¢ NKd<K>+N f NLd<L>l

The incumbent chooses the value of h such that the inside of the bracket is zero or
corner solutions. However, the corner solution h = 1 does not make sense since this
means that capitalists pay all of the production subsidy they receive (in this section

I assume 7 = 0.) Thus, the possible choice by the incumbent is h E [0, 1).

Lemma 3.2. Given t, if the incumbent can choose the tax burden share h freely,

he will set h at the level such that

VIK > VIL
NKNK¢K6(K) ‘ NLNquLc’(L)

 

 

100

In terms of elasticity and: this condition is equal to

K L
End and

NKdK/V,K — NLdL/VIL

By assumption, N chLc' (L) = NK chc' (K) when t = 0. Thus, the condition
VL VK

becomes figfi at t = 0. So, unless the marginal utility of income decreases

very fast, the strict inequality should hold. So, when t = 0, it is likely that h = 0

(strict inequality means that the inside of the bracket above is negative.) Moreover,

KT L

e 5
it becomes ——-—”d——— > ——"—d—, which is same to 3.2 that I obtained as the
NKdK/VIK NLdL/VIL ( )

condition for the choice of the positive tariff in the previous subsection.
Given the result about h above, then, will the incumbent decide to raise the tax

to help capitalists? The Lemma 3.3 gives a simple condition for that.

If L

V V
Lemma 3.3. If -—If > Ji- at t = 0, then the incumbent will choose the tax rate
N N

t > 0 with tax burden share h = 0.

The proof is in Appendix. Since the objective of the tax is to provide the help
to capitalists, h = 0 is a natural result. Notice that the condition in this Lemma is
the same condition for the incumbent to raise tax in the case of the single tax rate.
The logic for this result is also same. Moreover, I showed the same condition for the
positive tariff holds. However, these same conditions imply one important difference
about the tariff. Given h = 0, there is no incentive for the incumbent to raise the tariff
rate. In the previous single tax rate case, capitalists prefer low but positive tariffs

101

to zero tariff since the positive tariffs mean lower tax burden for them. Though the
higher tariffs have the negative eflect on their utility, as long as the positive effect of
the lower tax outweighs it, capitalists prefer the higher tariffs. Since h = 0 means
capitalists do not pay tax, there is no positive effect of the higher tariff for capitalists.
So, the negative effect cannot be outweighed. Of course, the positive tariff rate means
some transfer of the burden from workers to capitalists. So, it might be possible that
workers would prefer the positive tariff to zero tarifl. Given h = 0, the derivative of

worker’s indirect utility with respect to r at 7' = 0 is

.. vL yL yK
VTleH=0 = —FIL'NKILIK1— — —l

 

 

IL 1K
yL yK
Because of the less-than—one income elasticity of good Y, it is W — I7? > 0.
III" yK
If the tax rate is low, the inside of the bracket, I—L — —I—K—, is still positive. If the tax
yL yK

rate on workers so high that If — 717 < 0 (remember I a is before-tax income),
it could be positive. However, it still can be shown that positive tariffs will lower
NK K VK vL
————L— because of I K 2 I L . Thus, there is no reason for
Ma NKNK¢ c’(K) NLNLq’) c’(L)

the incumbent to use the tariff.

Proposition 3.2. Suppose that the incumbent can choose the tar burden share

VK VL
freely and that N176 > i at t = 0. Then, even when the incumbent use the

production subsidy to help capitalists, he will not use the tarifi.

The proof is in Appendix. In the previous single tax rate case, the condition
K L
and End . . . . .
L gives the reason for the incumbent to raise the tariff since

___—___. > ___—___...
K K L L
NKd /V, N d /V,
the tariff increase causes negligible dead weight loss at r = 0. By raising the tariff,

not by raising the tax and subsidy, the incumbent can help capitalists with the lower

102

dead weight loss. However, if he could change the tax burden share h, this is a better
instrument for the incumbent to provide the help since the burden share change does
not cause any distortion at any level. Thus, when the incumbent can choose the tax
rate freely so that no tax for capitalists is the Optimal for the incumbent, there is no
need for the inefficient tariff. However, this result depends on the assumption that the
workers are homogeneous. If they are heterogeneous, the incentive for the incumbent

to raise the tariff might appear again. I consider this in the next section.

3.4 Three groups: heterogeneity in workers

In this section, I extend the previous model so that it has three groups. Three groups
consist of one capitalist group and two worker groups. The difference between two
worker groups is the income level. Denote two worker groups as group M and group
P, with their group sizes NM, N P and NM + N P = N L. I assume workers in group

P has one unit of labor and workers in group M have 1 + _w_ w > 0, units of labor.

NM’
Thus, workers in group AI are richer than workers in group P, though they are still
poorer than capitalists. A natural interpretation is that group AI is middle class and
group P is poor workers. The total income of two worker groups is N L + w.
The model in previous section cannot incorporate three groups smoothly. To
achieve that, I assume that the group M and P are subgroups of the group L. Let

NM . .
m E N77. For a given level of voting cost 0, I assume that among workers who have
voting cost equal to or lower than c, m of them are group AI workers and 1 — m of

them are group P workers. Horn this assumption, the following voting cost functions

103

for group M and P are defined.

 

NM¢M

Voting cost of group M for the N M ¢M -th voter: c( m ) = c(NquM)
P P

Voting cost of group P for the N P (bP -th voter: c(—1——95—-) = c(NquP)
— m

Since the voting rate (b is determined in the same way, d — c = 0, the derivatives

of qbs of group M and P are defined as follows.
a
1
53% = m for a = Al or P, where c’(a) = c’(NLng)

M M P P
Then, it is defined that ¢L E N ¢ + N ¢

 

. In addition, I assume that group

NL
M and P share same random variable ”L. This means the objective of the incumbent

 

is still which is equal to

W’ N M (W + N1D qu '

Though the total income of workers is now N L + to, not N L , with these new
assumptions, the change from the previous model is minimum from the viewpoint of
the incumbent about what he should do regarding capitalists. In this section, I do
not consider if the incumbent decides to help capitalists or not. There should not be
any qualitative difference from the results in the previous section about this. Thus, I
consider only if the incumbent would use a tariff when he decides to help capitalists,
and about its implication. In addition to above assumptions, I also assume that the
preference is special one; U (11:, y) = :r + u(y), no income effect on good Y and the

marginal utility of income is one. I keep the assumption that the incumbent can

choose tax rates freely.

104

3.4.1 The optimal tax rates

Before I check if the incumbent would use a tariff or not, I consider what is the
optimal tax burden shares for the incumbent. Same as the subsection considering
the same problem in the case of two groups, I assume 7' = 0 in this subsection. Let
t“ be the income tax rate of the group a E (K, M, P}. Then, since the incumbent
can choose the tax rate freely, given a total tax payment from three groups, it is
obvious from the previous section that he imposes tK = 0 on capitalists. This is a
natural result considering the objective of the tax. The implication of this is that

KK

the numerator of the derivative of W with respect to tK with corresponding

changes in taxes on other groups so that no change in the total tax payment is
N L (bLN K (bfdg; — N K ¢KN L (155’de < Oat tK = 0 (I ignore the case that the
equality holds at tK = 0.) Since the group L now consists of two groups, it is not clear
what dL is. However, since N K d5, is the change in the tax burden of capitalists as a
group, NLdtLK /NKd{1{{has a clear interpretation as the ratio of marginal transfers
from capitalists to workers. Since the marginal utility of income is fixed at one and the
total tax payment from three groups does not change so that no change in subsidy and
no change in the production of good Y, this ratio is one: NLdtLK /NKdtI,{( 2 (here
I am considering this with r = 0.). Thus,
NquLaf,‘ — NKhKagNLde/Ndef. > 0 => NLthg‘ > NquKaf;
both dtlk and dig are negative.

Substituting partial derivatives of gb into this,

1 1 NM NP

NKNquKc’(K) > NLNL¢L{NLc’(M) + NLc’(P)}

 

 

105

85d {NM¢M5 51% NquP EPd

NKdK > NLgbL NLdM NLgbL NLdP}

 

 

<=>

vK
I >
NKNKch’(K)

 

Thus, a formula similar to the one in the previous section (i.e.,

vL 8K ELd
I End
41) > —— 15 obtained. Then, what 18 theo timal
NLNL¢La(L) NKdK/V,K NLdL/VIL) p

tax burden share between group M and P for the incumbent? Notice that since the
NK¢K

NM (151” + NP¢P

burden sharing among group M and P does not affect capitalists, the optimal share

 

 

and since the tax

 

objective of the incumbent is the maximization of

h is the one such that minimizes N M ¢M + N P qu . Here, I define t and h, again, and
I use them to denote tM and tP. Now, t is the tax rate on the total income of worker

groups N L + w, and h is the tax burden share of group M. Then,

ht(NL + w) = tM(NM + w)

(1 - h)t(NL + w) = tPNP

From these, I can obtain tM and tP in terms h and t.

 

L
NM+wL
NP

K K
By substituting these into indirect utilities and taking a derivative of W, the

next Lemma can be obtained.

Lemma 3.4. If the incumbent can choose taa: rate freely, he will choose tarz: rates

such that
l I
ATKNK MKC’( ) >NLNL¢LCI(M)

 

 

The proof is in Appendix.

3.4.2 Will incumbent use tariff?

Now I consider if the incumbent would use a tariff or not. Thus, I consider a situation

that the incumbent is using the income tax to provide the production subsidy but
K K

not using a tariff. Then, if the derivative of W with respect to 'r at r = 0 is
positive, the incumbent will use the tariff. Since the tax rate on capitalists is zero,
there is no reason for capitalists to prefer positive tariffs to zero tariff. However,
because of the heterogeneity in workers, workers in group M prefer positive tariffs
to zero tariff. Even in the case of two groups with zero tax on capitalists, there is
some possibility that workers would prefer positive tariffs to zero tariff if tax rate
is very high. Here, such high tax is not required. The logic behind this is same as
the one behind the case that capitalists prefer low but positive tariffs to zero tariff.
Since workers in group M have higher income than workers in group P, their ratio
. . yM . . .
of good Y consumption to income, I—M—, is lower than the ratio of workers in group
P. Thus, raising the tariff rate is equal to the transfer of the tax burden from group
M to group P (as long as the tariff rate is low.) Moreover, since capitalists is not
paying tax, the positive tariff is also equal to the transfer from group M to group K.
Thus they have a reason to prefer low but positive tariffs to zero tariff. Of course,

capitalists and group P workers do not share the reason. However, as long as workers

in group M prefer positive tariffs, it might be possible for the incumbent to use tariffs

107

for his advantage. I am going to consider if this is really the case or not. Of course,

I consider the change of T with dH = 0. The indirect utilities of three groups are

defined as follows.

K_ II
NL+w NM+w

 

 

VM=V l—ht ,*
1—htN +w

Derivatives of them with respect to T at T = 0 with dH = 0 are,

 

 

K K KVPK K
VT =Vp =VI {f—IR-=—y
T _ NM
p <1—h)<f+m)—NPyP
V, =

NP

Since d5 = VTK, dill = —V,M and d5 = —V.,P, the numerator of the derivative of
NK K
NL—qu with respect to T at T = 0 with dH = 0 is,

 

 

 

 

NKc’(K) NLc’(M) NLc’(L)
NK¢KNL¢L K K M M P P
<NKNK¢Kd(K)[f+m_N y -N y -N yl
=0

The inequality holds because of the Lemma in the previous subsection. The last
equality holds since f + m is the supply of good Y and N K yK + N M yM + NPy1D is
the demand of good Y. Thus, even though workers in group IVI prefer positive tariffs,

that is not enough for the incumbent to raise tariff.

Proposition 3.3. If the incumbent can choose tar rates freely, he will not use a

tariff to help capitalists.

108

This is the same result as the one in the previous section. However, this result
depends on the assumption that the incumbent can choose the tax rates freely. This
assumption might be very problematic in three groups setting of this section. The

reason is simple. As I showed, if the incumbent can choose tax rates freely, he would

1 . .
= —— However, Since c” < 0, this means dK = dP.

1
C’ (M) C“(Pl
These utility differences are for each worker in group M and P. At T = 0, these

 

choose tax rates so that

utility differences are tax burdens; the tax burden of each group P worker is same
to the tax burden of each group M worker. Because the income of workers in group
P is lower than the income of workers in group M, the same tax burden means the
higher tax rate for workers in group P than the tax rate for workers in group 114.
Thus, the higher tax rate is put on the lower income group. Though zero tax on
group K might be politically justifiable based on some protectionist and nationalist
sentiments of people for protecting domestic industries, these regressive tax rates for
group AI and P are quite unlikely in usual political situations. Even the zero tax rate
on capitalists might not be possible because of its regressiveness, though it would be
kind of ludicrous considering the purpose of the tax. So, if such regressive tax rate
system is not possible, there is an incentive for the incumbent to use a tariff. The
result of the single tax rate case with two groups is a clear example. With less-than-
one income elasticity of the demand on good Y, the tariff has the same regressive
effect. However, it is less likely that the regressiveness of tariffs become the huge
political problem compared to the regressive tax system. Thus, to achieve the same
regressive treatment of workers, the tariff is a politically better instrument. To show

the possibility of the incumbent using a tariff when he does not have free hand on the

109

choice of tax rates in the case of three groups, consider the following case: the the tax
system is progressrve so that t > t > t . Particularly, t — 0. The pOpulation of
voter groups is N K < NM < Np. Then, suppose that the incumbent is giving the

help to capitalists without using a tariff. Then, the numerator of the derivative of

 

 

NK¢K

with respect to T at T = 0 is,
617}; (NM¢M+NP¢P)_NK¢K( 617M + d5 )
C’(K) 6’0”) 6’0”)

If this is positive, the incumbent would increase the tariff from zero. Because
of the logic for the single tax case in the precious section, higher tariffs reduce the
burden of the help on capitalists. This increases dK , so d5 is positive. Thus, the first
term is positive, i.e., c’tfi) (N M (bM +N P ng ) > 0. The same logic says the burden on

the group P voters rises. So, at? is positive. The effect of the tariff increase on d9”! is

 

ambiguous in general. From the logic, we know a part of the burden on capitalists is
transferred to group M voters. But the same logic also says a part of burden on group
M also goes to group P. The sign of div! depends on which effect is stronger than the
other. However, if NM is much larger than N P and much smaller than N P , d4” would

P
be negative. Moreover, if limd_,0 c’(d) = 00 (like the Inada condition), T 0

-c’—(_P) =
since t1D = 0. Thus, the above value is positive. The incumbent would use the tariff.
The voter abstention and different group sizes give an incentive for the incumbent to
redistribute resource / income. If he can use policy instruments that produce less dead
weight loss, there would be no reason for him to use other instruments that produce

more dead weight loss. However, if he cannot use policy instruments freely, he would

use the inefficient instruments. In the setup of this chapter, if the regressive tax rate

110

system is not possible, that might induce the incumbent to use the inefficient tariff,
as shown in the the example above. Since the reason that the regressive tax system is
not possible in real world is the sense of fairness in the tax system, this might be able
to be said as a trade-off between efficiency and fairness. However, the main problem is
the fact that the voter abstention gives the incumbent the opportunity to manipulate
votes. If all potential voters vote, the incumbent would not help capitalists. Here I

state the main Theorem.

Theorem 3.1 If the incumbent can choose tax rates freely so that he can choose
even regressive tact: rates, he will never use the tariff to help the domestic industry. In

this sense, the inefiiciency of the tariff is the price of the fairness in the tax system.

3.5 Literature Review

There are other papers that consider why tariffs are used. Generally, however, what
they do is the comparison of economic welfare between the case that a tariff is used
and the case that a subsidy is used; they show situations where the tariff achieves
higher welfare than the subsidy. Rodrik (1986) shows that since the tarifl has the
character of public goods, the lobbying effort for the tariff is under-supplied, compared
to the lobbying effort for the firm specific subsidy. So the distortion under the tariff
could be lower than the one under the subsidy. Mayer and Riezman (1987) show
that when the country is small and voters are heterogeneous in factor endowments,
voters prefer the production tax cum subsidy to the tariff. So, if voters will vote on

trade policy like in Mayer (1984), the tariff will not be chosen. But in cases that

111

the country is large or that voters are heterogeneous in both of factor endowment
and consumption preference, they say it is possible for all or some voters prefer tarifl.
Wilson (1990) shows that the efficient instrument can invite more lobbying pressures
so the total distortion can be larger for the efficient instrument than for the inefficient
one. Since politicians care about the level of total distortion which could affect voters’
sentiment toward politicians negatively, there is an incentive for politicians to restrict
the possible policy instruments to the inefficient ones. Mayer and Riezman (1990)
consider several cases in which some voters prefer tariff to subsidy, like the ease of
heterogeneous voters, the case of risk averse voters in the uncertainty about tariff
rate and tax rate, etc., though they do not show how such voter preferences will
be reflected in the political process of choosing policy instruments. In this chapter,
preferences on instruments are also different among different groups. The reason for
such difference is similar to the one in one section of Mayer and Riezman (1990)26.
Naito (2006) shows that given a reasonable information constraint on government,
when government wants to design a tax system to redistribute income to unskilled
workers, tariffs on unskilled labor intensive goods could be Pareto-improving.
Though they do not consider about tariffs directly, Coate and Morris (1995) con-
sider why inefficient instruments are used by government in a model with uncertainties
about two things; one is about the outcome of public project, and another about the
type of the incumbent politician. The incumbent politician has information about
the project outcome and will face re-election. Good type politician will carry on the
project only when the information he has tells him that the project has high proba-
bility of producing good outcome. Bad incumbent wants to transfer money to special

112

interests. He can do that through the direct subsidy or the public project. Voters
update their reputations on the type of politician based on what the incumbent does
and what its outcome is. So, to increase the probability of winning the reelection,
the bad type politician chooses the project over the direct subsidy (this gives him
higher utility than the project) so that he can pretend a good type believing that the
project has high probability of success. Acemoglu and Robinson (2001) consider a
two-period model with a special interest group whose power source is the number of
voters belonging to it. In multi-periods models, policy commitment by politicians is
an important problem. If it is not guaranteed by an assumption, it needs to be guar-
anteed by some mechanism (Harrington (1992)), or no policy commitment (Alesina
(1988)). In the model of Acemoglu and Robinson (2001), the special interest prefers
the inefficient policy to the efficient one since it distorts newcomers’ incentive toward
joining to the special interest, which guarantees the power of the special interest in
the second period and secures the commitment by the government to the transferring
resource to the special interest in the period.

Above, I mentioned papers in which there is no intrinsic difference in the difficulty
of policy implementations. If there is difference in the difficulty of policy implemen-
tations (for example, the cheaper collection cost of tariffs and the higher cost of other
taxes), however, it is actually no wonder that governments would choose the pol-
icy that is easier to implement. Gordon and Li (2005a) argues that governments of
developing countries rely more on tariffs as their revenue sources than the ones of
deveIOped countries because it is more difficult to monitor economic activities of do-

mestic private firms in deveIOping countries than in developed countries. Gordon and

113

Li (2005b) claim that the model of Gordon and Li (2005a) fits actual data better than
the model of Grossman and Helpman (1994). Even in current develOped countries,
the tax collection used to be a difficult problem in the past (maybe still is.) Gard-
ner and Kimbrough (1992) applied to US. this line of explanation about tariffs27.
Though this chapter is different in many aspects from this collection cost type ex-
planation, there is a common element; politicians choose the policy instruments that
have lower political costs. I considered the maximization problem in this chapter.
But votes for the challenger at the election and the loss of votes for the incumbent
can be considered as the political costs of the policy instrument choices. Then, the
same problem can be considered as a political cost minimization problem, like the
expenditure minimization problem28. Then, difference in the nature of the cost could
have a big implication for welfare (maybe even a benevolent planner might decide to
use tariffs when the collection costs of taxes are high. But will the planner use tariffs
for the political cost reason when there is no intrinsic cost difference between tariffs
and taxes?) But from the viewpoint of each politician, whatever the source of the
cost of a policy is (collection costs or loss of votes for him, etc.,) they are political
costs of the policy he wants to implement. So, politicians must try to minimize those
political costs. In this sense, I think this chapter and the collection cost explanation
are in complimentary, looking at different type of costs, not contradicting each other
as the explanation about why tariffs are used.

As I wrote in previous sections, the idea of the paper is that the incumbent
can take advantage of the voter abstention by redistribution costs and benefits of

helping a domestic industry. From this point, this chapter is related to the literature

114

of the Vote Buying/Turnout Buying. Nitchter (2008) analyses turnout-buyings in
Argentina; political party rewarding potential voters who favor the party to its rival
party for voting for the party. Even though they favor the party, they might abstain
from voting without rewarding. Vote Buying is the Opposite; rewarding voters who
do not favor the party for voting for the party. Though the direct rewards for voting
is different from what I consider in this chapter (choice of policy instruments), similar
elements exist; the Optimal choice of policy instruments (or the optimal distribution
of rewards) could increase votes for the incumbent from people who benefit from the
policy of the incumbent and decrease votes for the Opponent from people who suffer

from the policy.

3.6 Conclusion of Chapter 3

In this chapter, I considered why the incumbent might decide to use a. tariff to help
domestic industry. What important in this chapter is the voter abstention. After the
incumbent makes the decision about the help, he will face the election. So, he takes
the election into his consideration when he chooses policy instruments. Because of the
voter abstentions, he might decide to give the help. Then, if there is no restriction
on the choice of efficient policy instruments (the tax and the production subsidy
here), the incumbent would not use the tariff for the help. However, its outcome
does not look politically feasible since it involves the regressive tax rates. So, if the
regressive tax rates are not feasible because of some restrictions on the tax system,

the incumbent would use the tariff to take advantage of the voter abstention. Because

115

of the voter abstention, there is a problem similar to the one under the externality;
the undersupply of the good policy. Though no tariff is better for national welfare,
this would not matter for the incumbent since he might not be rewarded fully for
the good choice because of the voter abstention. So, the incumbent must try to take
advantage of the voter abstention by putting more costs on people who do not vote.
When there is the political restriction on the possible policy instrument choices, this
could lead to the choice of tariffs. For the incumbent, it is the politically low cost
distribution of the burden of his policy.

The less-than-one income elasticity is just one example of the sources for the voter
heterogeneity which the incumbent can exploit. Since it means normal goods, real
world examples are easy to find. Moreover, what I need in this chapter is actually
the consumption pattern difference among diflerent income groups, which is further
easier to find. As an example related to trade restrictions, consider the voluntary
export restriction of Japanese automobiles in 19803. In 19803, Japanese cars were
mostly small to mid size cars, no luxury cars. Thus the rich’s expenditure share
of Japanese cars in 19803 should have been much lower than the middle class and
working class people’s share29. Though it is not related to trade, state lotteries also
can be considered as such a case since it is an easy way for politicians to generate
revenue without offending voters with higher taxes. Garrett and Coughlin (2008)

estimate that the income elasticity of state lotteries is less than one.

The model in this chapter has many moving parts, which might be confusing. So

I briefly explain about the relationships of some important assumptions and results

116

here.

The challenger as Free-trader: The incumbent might not be rewarded for
free-trade policy, which discourages him from pursuing the free-trade policy. He is
not be rewarded not because his challenger is a convinced free trader (there would be
no difference between them if the incumbent chooses the free trade policy.) Even if
the challenger was a protectionist, the results in this chapter still would suggest that
the incumbent might have an incentive to choose the protectionist policy. If choosing
the fiee trade policy against the protectionist challenger were politically beneficial,
he would not have chosen helping the domestic industry in this model.

Endogenous decision of abstention: This is the hinge of the idea in this
chapter. Without this, the incumbent does not have the power of manipulating votes.
What important is that abstention rates vary depending on the utility differences.
Suppose that the some voters abstain, but the rates of election participation among
groups are fixed. This is basically same to the case of no voter abstention with
the different composition of population. To understand this, consider the following
situation; ratios of group populations over total pOpulation are 50% for group P, 25%
for group M and 25% for group K. Moreover, suppose that the participation rates
are 50% for all groups. Then, ratios of actual voters over total actual voters are same
to population ratios. So, this is equivalent to the case of no voter abstention with the
half population size. Since group M and P always prefer challenger, the incumbent
never decides to give the help. Even if participation rates are different among groups,
it is still equivalent to a case of no abstention. If the participation rates are 10%

for group P, 40% for group M and 100% for group K, it is same to a case of no

117

abstention with population ratios of 12.5% for group P, 25% for group M, and 62.5%
for group K. In this case, the incumbent always gives the help. What important for
this chapter is that voting behaviors are influenced by utility differences, which can
be manipulated by the incumbent.

Non-homothetic preference: The incumbent can manipulate voters’ utility
diflerences because of the non-homothetic preference. If preferences are homothetic,
he could not do that. However, what important is not the non-homothetic preference
itself, but the existence of some factors that can give the manipulating power to the

incumbent.

The results in this chapter depend on strong assumptions. However, the basic
logic is more general. For the logic, specific assumptions, like the less-than—one income
elasticity, are not important. If there are more than one policy instruments and there
is heterogeneity, similar results could be obtained. Because of the voter abstention
the incumbent politician can put the cost of his policy on voter groups whose voting
rates are inelastic. Similar to the argument of the Ramsey rule about minimizing the
dead weight loss from commodity taxes, the incumbent can minimize the political
cost of his policy (votes for his challenger) for the same level of political gain (votes
for him) by putting cost on the voting—inelastic voter groups. Then it is natural to
assume that the incumbent wants to use the most efficient policy instrument (e. g. the
tax and production subsidy) for that purpose. However, political restrictions, like the
requirement for fairness, might prevent the use of the most efficient policy instrument

at the optimal level for the incumbent (e.g., regressive income tax rates.) Then, it

118

would be beneficial for the incumbent to use less efficient instruments. In this sense,
the use of inefficient tarifl could be considered as the price of the fairness in the tax

system.

119

Appendix of Chapter 3

K L
Lemma 3.3 If -—1— > —I— at t = 0, then the incumbent will choose the tax rate
NK NL

t > 0 with tar burden share h = 0.
Proof. Proof: The derivative of the capitalist’s indirect utility with respect to t

is,

L d8
—f— h(7r +N )_ht21?f
I NK

L N
As I showed before, 43-— — (7r + N )f

dt ff” — s(f’)3

 

. Thus,

 

 

 

NL 1 — ht ”
NK ff” - 8(f’)
and,
(1— —h)<vr + Nb tff”
VtL_ - _LVI NL [1+ f-‘f” 3(f’)3 3]
. .. K K
Since d5 = VtK and df’ = —V,L, the numerator of the derivative of — with
NL¢>L
respect to t is,
VIK (1 — hon”

 

* K K L L L _

 

_ K K L L L _V_I_ _ tff”
N a N as (7r+N )sgndLNLu h)[1+ff,,_s(f,)3]
V,L V,K

 

< this becomes,

Since the incumbent chooses h so that ,
egndLNL—aggdKNK

 

 

 

* K K L L L VIK (1—htlff” (1- hltf "
( )ZN ¢ N 45 (MN )EKdKjl’rflfftsv'fi —h—1+h_ff”- s<r>3l
V _ II
: NKt’KNLtL‘" + NL)eKdII{NK[f(f1” 28103 ‘ 1]

When t = 0, the inside of the bracket is zero. This means when the incumbent

chooses the corner solution h = 0 so that the strict inequality holds, the derivative of

120

NK K . . . . -
__N L: L at t = 0 1S pOSItive. When the incumbent chooses a non—corner solution so

L K
th VI VI

t =
NLNL¢Lc’(L) NKNquKc’(K)
t = 0. It is easy to prove that the only another value of t that makes the inside of the

, the result means the derivative is zero at

bracket zero is negative, and it is also easy to prove that t = 1 makes the inside —1.
The inside is negative for any t E (0, 1]. This implies that if t > 0 and if the incumbent

is choosing a a non-corner solution for h so that the equality holds, he would have
V,K > V,L
NKNK¢Kd(K) NLNL¢LcI(L)

at t = 0, the incumbent has an incentive to raise the tax rate t. The only consistent

 

 

an incentive to lower the tax rate. However, if

combination of t and h is t > 0 and h = 0. As I showed before, the condition becomes

K L
.‘L>YI_att=o .
NK NL '

Proposition 3.2: Suppose that the incumbent can choose the tar: burden share
K vL

freely and it holds that —I— > —I— at t = 0. Then, even when the incumbent use
NK NL

production subsidy to help capitalists, he will not use tariff.
Proof. Proof: When h = 0, the government budget constraint is sf (1) = tNL +
Tm. The derivative of tax rate t with respect to tariff T for the fixed H E s + T at
dt f + m

T=0isa7= NL.

 

The indirect utilities of capitalists and workers are,
171% : H) = V(IK,p* +T)
VL(T : H) = V(1—t,p* +T)

Then derivatives of them with respect to T at T = 0 with dH = 0 is

 

VTK = VpK = _ IKyK
L
. f + m V
V! = VIL N1. + VI = —N’L (f + m — NLyL)

121

HereIassume VTL>0©f+m—NLyL>0
K K
Then, the numerator of derivative of W with respect to T at T = 0 with

 

 

 

 

 

 

 

dH = 0 is,
KK LL ‘WK .KK If LL
N N N + + —— N
VK VL
From I 2 I andf+m—NLyL>0,
NKNchKc’(K) NLNL¢Ld(L)
_VIK NKyK + VIL (f+m _ NLyL)
NKNKch’(K) NLNL¢Ld(L)
WK KK LL
< + —N —N
= I

Lemma 3.4: If the incumbent can choose tact rate freely, he will choose tax rates

such that
1 > 1
NKNK¢Kd(K) NLNL¢Ld(M)
1 _ 1

d( ) C’(P)

 

Proof. Proof: The indirect utilities of workers in group M and P are defined as

follows.

NL+w NM+w
VM=V1—-ht ,*
<< NM”) NM 1»)

_ L w
_(1 (1)1131; + hp...)

 

 

VP=Vu

The derivatives of these with respect to h are,

VM 2 _fl'fifl
h NM
h NP
Since the help to capitalists hurt them, d5); = —V,:". Thus, the derivative of

122

NMch + NPng with respect to h is,

NM t(NL+w)_ NP t(NL+w)
NLc'(M) NM NLc’(P) NP

 

NMoyth + Npafdf =

_t(NL+w) 1 1
‘ NL (6W) 3(7))

 

If h = 0, all tax burden falls on group P. It would be same to the free trade
situation for group M but that would induce workers in group P to vote. Thus,

c’ (P) < c’ (M) from c” < 0. If h = l, the Opposite would happen. Thus, the

1
incumbent should choose h so that W — d—(1P-) = 0. Substituting this into the

inequality I obtain,
1 1 NM NP 1

NKNchKc’(K) > NLNL¢L{NLc’(M) + NLc’(P)} = NLNLch’(M) I

 

 

 

123

Endnotes of Chapter 3

18. According to CNN exit poll (CNN.com (2004)), 68% of voters of 2004 US.
presidential election made $75,000 or less, and 82% of voters made $100,000 or less.

19. Though I used the word "lobbying", this is not a lobbying model, so, no
campaign contribution from them.

20. This assumption can be changed so that the tariff revenue is distributed to
people, not used to finance the subsidy. Such change makes model more complicated,
but does not change qualitative results.

21. Of course, the production subsidy that is financed by the tax does cause
distortions.

22. Group Rule-Utilitarian voting literature consider more complicated voting
decision making (Feddersen and Sandroni (2006), and Coate and Conlin (2004)) than
the one I employ here. Their decision-making is, as its name suggests, more group-
based.

23. If uKNKgbK — ,uLNquL < 0, the challenger wins. If ,uKNKgbK — uLNLpL =
0, then both candidates have same probability of winning the election.

24. I do not consider the impact of the tariff on the amounts of export and imports.
Though the tariff increase with dH = 0 does not change domestic productions, it
certainly changes domestic consumptions, which changes the amounts of export and
import. However, I simply assume that the change is small enough so that the country
is still exporting good X and importing good Y.

25. Because of the income tax, the good Y consumption - income ratio is actually

124

ya / (1 — t)I“. Since the tax rate is same for both group, I can ignore (1 — t) here.

26. The reason is similar, but not same. In the paper of Mayer and Riezman
(1990), the preference for tariff comes from the difference of income tax rate and the
share of distribution of tariff revenue. In this chapter, the preference comas from the
difference of income share and the consumption share of different consumers (in the
single tax case.)

27. I thank Professor Wilson and Professor Nelson for putting my attention to
those papers and this line of argument.

28. Actually, the previous version of this paper considers the minimization of
votes for challenger for given level of votes for the incumbent.

29. Bordley and McDonald (1993) estimate that income elasticities of automobile
in any segments (small, economy, luxury, etc.) are more than one. This is incon-
sistent with the assumption of this chapter. However, it is natural to suppose that
income elasticities of goods change as income level changes. Bordley and McDonald
(1993) also estimate that the more expensive the automobile segment is, the higher
the elasticity. This is consistent with the conjecture that the elasticity of Japanese

economy cars in 80’s was very low for the rich.

125

References

[1] Aldrich, John H. (1993): “Rational Choice and Turnout” American Journal of
Political Science, 37, 246-78.

[2] Alesina, Alberto (1988): “Credibility and Policy Convergence in a two-Party Sys-
tem with Rational Voters” American Economic Review, 78, 796-805.

[3] Bordley, Robert F. AND James B. McDonald (1993): “Estimating Aggregate Au-
tomotive Income Elasticities fiom the Population Income-Share Elasticity” Journal
of Business 65 Economic Statistics, 11(2), 209-214.

[4] CNN.com. “Election 2004” ,
http: / / www.cnn.com / ELECTION / 2004 / pages / results / states / US / P / 00 / epolls.0

.html

[5] Coate, Stephen AND Stephen Morris (1995): “On the Form of Transfers to Special
Interests” Journal of Political Economy 103, 1210-1235.

[6] Coate, Stephen AND Michael Conlin (2004): “A Group Rule—Utilitarian Ap-
proach to Voter Turnout: Theory and Evidence”, American Economic Review, 94,
5, 1476—1504.

[7] Dixit, Avinash (1986): “Gains from Ti‘ade without Lump Sum Compensation”
Journal of International Economics,'21, 111-122.

[8] Dixit, Avinash AND Victor Norman ( 1980): Theory of International Trade, Cam-
bridge: Cambridge University Press.

[9] Dixit, Avinash AND Thomas Roemer ( 2006): “Political Explanations of Inefficient
Economic Policies - An Overview of Some Theoretical and Empirical literature”
Presentation at IIPF conference “Public Finance: Fifty Years of the Second Best
-and Beyond” in Paphos, Cyprus, August 2006.

[10] Feddersen, Timothy J (2004): “Rational Choice Theory and the Paradox of Not
Voting” Journal of Economic Perspective, 18, 99—112.

[11] Feddersen, Timothy J. AND Alvaro Sandroni (2006): “A Theory of Participation
in Election” American Economic Review, 96, 1271-1282.

126

[12] Gardner, Grant W. AND Kent P. Kimbrough (1992): “Tax Regimes, Tariff
Revenues and Government Spending” Economica, February 1992, 59, 75-92.

[13] Garrett, Thomas A. AND Cletus C. Coughlin (2008): “Inter-temporal Differ-
ences in the Income Elasticity of Demand for Lottery Tickets” Federal Reserve
Bank of St. Louis working paper series 2007—042b (revised version).

[14] Gordon, Roger AND Wei Li (2005a): “Tax Structure in Developing Countries:
Many Puzzles and a Possible Explanation” NBER Working paper No.11267.

[15] Gordon, Roger AND Wei Li (2005b): “Puzzling Tax Structures in DeveIOping
Countries A Comparison of two Alternative Explanations” NBER Working paper
No.11661.

[16] Grossman, Gene M. AND Elhanan Helpman (1994): “Protection for Sale” Amer-
ican Economic Review, 84, 833-50.

[17] Harrington, Jr., Joseph E. (1992): “The role of party reputation in the formation
of policy” Journal of Public Economics, 49, l07-21.

[18] Harsanyi, John C. (1980): “Rule Utilitarianism, Rights, Obligations and the
Theory of Rational Behavior” Theory and Decision, 12, 115-33.

[19] Hinich, Melvin J ., John Ledyard, AND Peter C. Ordeshook (1972): “Nonvot-
ing and the existence of Equilibrium under Majority Rule” Journal of Economic
Theory, 4, pp.144—153.

[20] Lijphart, Arend (1997): “Unequal Participation: Democracy’s Unsolved
Dilemma” American Political Science Review, 91, 1-14.

[21] Mayer, Wolfgang (1984): “Endogenous Tariff Formation” American Economic
Review, 970-85.

[22] Mayer, Wolfgang AND Raymond Riezman ( 1987): “Endogenous choice of trade
policy instruments” Journal of International Economics, 23, 377-81.

[23] Mayer, Wolfgang AND Raymond Riezman (1990): “Voter preferences for trade
policy instruments” Economics and Politics, 2, 259-73.

127

[24] Nichter, Simon (2008): “Vote Buying or Turnout Buying? Machine Politics and
the Secret Ballot” American Political Science Review, 102, 19—31.

[25] Naito, Hisahiro (2006): “Redistribution, production inefficiency and decentral-
ized efficiency” International Tar: and Public Finance, 13, 625-640.

[26] Persson, Torsten AND Guido Tabellini (2002): Political Economics Explaining
Economic Policy, MIT Press

[27] Rodrik, Dani (1986): “Tariffs, subsidies, and welfare with endogenous policy”
Journal of International Economics, 21, 285-99.

[28] Rodrik, Dani (1995): “Political Economy of Trade Policy” in Gene M. Grossman
and Kenneth Rogofl, ed., Handbook of International Economics Vol.3, Elsevier
Science B.V., Amsterdam, The Netherlands, 1457-1494.

[29] Shachar, Ron AND Barry Nalebuff (1999): “Follow the Leader: Theory and
Evidence on Political Participation” American Economic Review, 89, 525-47.

[30] Wilson, John D. (1990): “Are Efficiency Improvements in Government Transfer
Policies Self-Defeating in Political Equilibrium?” Economics and Politics, 2, 241-58.

[31] Yang, C. C. (1995): “Endogenous Tariff Formation under Representative Democ-
racy: A Probabilistic Voting Model” American Economic Review, 85, 956-63.

128

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