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THESIS

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31293 017721188

This is to certify that the

dissertation entitled

Individual Choice and Public Policy
in the United States

presented by

Geoffrey Jenkins

has been accepted towards fulfillment
of the requirements for

Ph . D . degree in Economics

 

 

 

Date 10/19/98

 

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mu mus-p14

INDIVIDUAL CHOICE AND PUBLIC POLICY IN THE UNITED STATES

By

Geoffrey Jenkins

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Economics

1998

ABSTRACT

INDIVIDUAL CHOICE AND PUBLIC POLICY IN THE UNITED STATES

By

Geoffrey Jenkins

This dissertation considers the role of individual choice as a determinant of public policy
and social outcomes. The work is undertaken from the perspective of theoretical macroeconomic
models of individual actions. The models themselves are concerned with social security, medical
subsidies and electoral choice.

In Chapter 2, I model a system of electorally determined social security taxation, wherein
voters, who are differentiated by age and productivity, may choose to vote or abstain, depending
on the costs and perceived benefits of participation. It is found that participation rates will vary
across class and age groups, and in particular, the middle classes will form a much more coherent
political force than their poorer contemporaries.

The Medicare subsidy system is modeled in Chapter 3, wherein agents' decisions about
their medical treatment affect both their health and their incomes. We have found that under
reasonable circumstances, Medicare spending may not only lower the health and welfare of
young agents, but through spillover effects, may also be detrimental to its recipients.

In Chapter 4, I return to a theme examined in Chapter 2, that of alienation. In this chapter,
I examine the US Presidential election data for evidence of alienation within the electorate, and

find that such evidence exists, and is compelling.

‘ '—‘ h __p-——..._f

ACKNOWLEDGEMENTS

I would like to thank the members of my dissertation committee for the advice
and guidance in the preparation of this work. Above all, I would like to thank Rowena
Pecchenino, the chair of my committee, for her unstinting backing, assistance and wealth

of support during the course of my dissertation research.

The comments and suggestions of Robert H. Rasche and Jeffrey Wooldridge have
been invaluable in focusing and clarifying my research. In particular, their comments
with respect to the fourth chapter helped greatly in shaping not only the presentation but

also the structure of work.

iii

TABLE OF CONTENTS

LIST OF TABLES ............................................................................................................ vii
LIST OF FIGURES ........................................................................................................... xi
Chapter 1. Introduction ....................................................................................................... 1

Chapter 2. Alienating the Elecorate:

A Model of Social Security with Intelligent Voters ........................................................... 4
Section I: Introduction ........................................................................................................ 5
Section II: The Framework Of The Model ......................................................................... 9
Section III: The Agents’ Decision .................................................................................... 16
Section IV: Equilibrium .................................................................................................... 24
Section V: Agents’ Combined Political Bliss Points ........................................................ 24
Section VI: Results of the Plurality Maximizing Electoral Game .................................... 30
Section VII: Conclusions and Extensions of the Model ................................................... 43
Appendix 1. The nature of steady state savings and bequests ......................................... 48
Appendix 2. The nature and robustness of agents’ bliss points ........................................ 52
Appendix 3. Changing dominant strategies across different parameter spaces ................ 55

iv

Chapter 3. Does Medicare Make Us Healthy? .................................................................. 58

Section I: Introduction ...................................................................................................... 59
Section II: The Model ....................................................................................................... 61
Section III: Steady-state Equilibrium ................................................................................ 70
Section IV: Conclusion ..................................................................................................... 83
Appendix 1. Baseline Parameter Values ........................................................................... 84
Appendix 2. Simulation Results ....................................................................................... 86

Chapter 4. Empirical Support for the Alienation Hypothesis in

US. Presidential Elections .............................................................................................. 107
Section I: Introduction .................................................................................................... 108
Section II: The Rational Voting Paradox, Alienation, and Participation ........................ 110
Section III: A Simple Model of Participation ................................................................. 114
Section IV: Testing for the Presence of Alienation ........................................................ 123
Section V: Preliminary Evidence of the Voters’ Costs and Preferences ........................ 146
Section VI: Conclusions ................................................................................................. 149

Appendix 1. Comparison of results from linear probability models and
discrete choice models .................................................................................................... 151

BIBLIOGRAPHY ........................................................................................................... 1 54

vi

LIST OF TABLES

Chapter 2

Table 1. Parameter estimates used in baseline and robustness testing of simulations ...... 27

Chapter 3

Table 1. Baseline parameter values .................................................................................. 85

Table 1a. The effects of changes in the medicare subsidy rate for
high-productivity agents ................................................................................................... 87

Table 1b. The effects of changes in the medicare subsidy rate for
low-productivity agents .................................................................................................... 88

Table 2a. The effects of changes in the overall medicare subsidy rate,
holding the difference in low- and high-productivity rates constant ................................ 89

Table 2b. The effects of changes in the overall medicare subsidy rate,
holding the ratio between low- and high-productivity rates constant ............................... 90

Table 2c(i). The effects of changes in the overall medicare subsidy rate,
holding the ratio between low- and high-productivity rates constant ............................... 91

Table 2c(ii). The effects of changes in the overall medicare subsidy rate,
holding the rates for both groups equal to one-another (detail) ........................................ 92

Table 3a. The effects of changes in the social security replacement rate for
high-productivity agents ................................................................................................... 93

Table 3b. The effects of changes in the social security replacement rate for
low-productivity agents .................................................................................................... 94

vii

Table 4a. The effects of changes in the overall social security replacement rate,
holding the difference in low- and high-productivity rates constant ................................ 95

Table 4b. The effects of changes in the overall social security replacement rate,
holding the ratio between low- and high-productivity rates constant ............................... 96

Table 5a. The effects of changes in the health care subsidy rate for young
high-productivity agents ................................................................................................... 97

Table 5b. The effects of changes in the health care subsidy rate for young
low-productivity agents .................................................................................................... 98

Table 5c. The effects of changes in the overall health care subsidy rate for
young agents, holding the difference in low— and high-productivity rates constant ......... 99

Table 5d. The effects of changes in the overall subsidy rate for health care
when young, holding the ratio between low- and high-productivity rates constant ....... 100

Table 6a. The effects of changes in the income tax rate for old agents .......................... 101
Table 6b. The effects of changes in the lump sum tax paid by old agents ..................... 102
Table 7a. The effects of changes in the price of health care for young agents ............... 103
Table 7b. The effects of changes in the price of exercise for young agents ................... 104

Table 8a. The effects of changes in the overall age-dependency rate,
holding the difference in low- and hi gh-productivity rates constant .............................. 105

Table 8b. The effects of changes in the overall age-dependency rate, holding the ratio
between low- and high-productivity rates constant ........................................................ 106

viii

Chapter 4

Table la. Candidate scores and separation, using the thermometer scale ...................... 129

Table 1b. Distances to candidates and candidate separation, using the
Liberal:Conservative scale ................................................................................................. 129

Table 1c. Average participation in different self-assessed political positions ................ 130

Table 2. Sparse regressions of participation as based upon
candidate placement and quality ..................................................................................... 133

Table 3. Candidate placement and quality coefficients in the presence of
assorted demographic characteristic terms. .................................................................... 137

Table 4 Regressing preferred-candidate sub-optimality on: age, sex, race and income. 138

Table 5. Candidate placement and quality coefficients within specific age groups ....... 139

Table 6. The effect of eliminating specific age groups or interview dropouts ............... 140

Table 7. The effects of eliminating liars ......................................................................... 142

Table 8. Candidate placement and quality coefficients in the presence of
assorted demographic characteristic terms, as measured on the
Liberal:Conservative scale. ............................................................................................. 143

Table 9a. Candidate placement coefficients in the presence of assorted
demographic characteristic terms. .................................................................................. 144

Table 9b. Candidate placement coefficients in the presence of demographic
characteristic terms, other than age. ................................................................................ 146

ix

Table 10. Respondents’ interest in the electoral outcome as a function of the
voter’s perception of relative candidate placement ........................................................ 148

Table 11. Uncorrected coefficient estimates and standard errors from the OLS,
Probit and Logit models of participation as a function of candidate placement,
sex, race and income ....................................................................................................... 152

Table 12. Corrected coefficient estimates and standard errors from the OLS and
Logit models ................................................................................................................... 153

Table 13. Corrected coefficient estimates and standard errors from the OLS and
Probit models ................................................ _ .................................................................. 153

LIST OF FIGURES

Chapter 2

Figure 1. Savings equilibrium, as a function of taxation and income group .................... 49
Figure 2. Bequests equilibrium, as a function of taxation and income group .................. 50
Figure 3. The level of bequests, as a function of taxation and income group .................. 51
Figure 4. The distribution of bliss points under baseline parameters ............................... 53

Figure 5. Class- and age-dependent distributions of voter bliss points under
various parameter sets. ...................................................................................................... 54

Figure 6. Typical Nash strategy plots for centrist (left) and polarized (right) games.
Infinite strategy normal forms of the electoral game, for a highly

homogeneous population .................................................................................................. 56
Chapter 4
Figure 1. Proximity- and distance-sensitivity over candidate pairs. ............................... 118

xi

Chapter 1. Introduction

This dissertation is concerned with the relationship between individual choices
and public policies, as examined from a macroeconomic perspective. It employs
theoretical and empirical models of three topics; social security, Medicare and electoral
strategy, in order to examine the often unanticipated consequences of individual
rationality, as played out on a macroeconomic scale.

Chapter 2 models electorally determined social security taxation within an
overlapping generations general equilibrium framework where voters are vulnerable to
alienation. Agents are heterogeneous, and decide upon a preferred tax policy based upon
their own short-term individual economic self interest and the long-term well-being of
their group in society. Given this ideal policy and the policy platforms of political
candidates (which are endogenously determined), agents may or may not participate.
Through simulation, it is found that older agents and the wealthy are disproportionately
likely to participate, and thus wield a disproportionate influence upon the outcome of the
election. Furthermore, the more socially motivated agents are, the more centrist the
equilibrium tax rate and the less sensitive that tax rate is to changes in the income
distribution.

The third chapter deals with the Medicare program, established in 1965 to
improve the health care available to elderly Americans. It has achieved this goal, but we
question the cost at which this has been achieved. To evaluate this cost, this paper
develops an overlapping generations model in which two types, high and low health
status/productivity, of two-period lived agents value health for both utility and human
capital enhancing reasons. The findings include: (i) a reduction in the price of health

care, either directly or via subsidies, for the working population may increase steady-state

healthiness of workers and retirees of both types and may increase capital accumulation;
(ii) an increase in the Medicare subsidy rate need not improve the steady-state healthiness
of retirees, reduces the healthiness of the young and average health, and reduces capital
accumulation; and (iii) increasing the elderly’s share of the cost of the Medicare system,
if financed via lump-sum rather than distortionary taxes, may improve the steady-state
healthiness of workers and retirees, and may increase capital accumulation.

Finally, Chapter 4 seeks to test the assumption upon which Chapter 2 was
predicated, that agents are likely to be alienated by political candidates of sufliciently low
quality, based upon econometric testing of the ICPSR National Election Survey dataset
covering the period 1980 to 1988. Using various measures of voter location, either on an
absolute scale or relative to the candidates' locations, the voter's sensitivity to candidate
placement is tested. It is found that the agent's probability of participation is more
sensitive to changes in the location of the preferred candidate than to changes in the
policy position of the less-preferred candidate. This is consistent with the hypothesis that
voters posses a convex (and hence proximity-sensitive) disutility function over imperfect
policy choices. This in turn implies that given uniform costs of participation, voters
whose policy bliss points are distant from their preferred candidate are less likely to
participate than those whose preferred candidate is close to their ideal, i.e. that voters are

susceptible to alienation.

Chapter 2. Alienating the Electorate: A Model of Social Security with

Intelligent Voters

Section I: Introduction

In a political system without abstention, where voters all exercise the franchise,
the behavior of the individual voter may be modeled as a relatively simple decision, and
from that it is a complex, but tractable, task to model the behavior of politicians. If,
however, one looks at the US, with an electoral system characterized by low
participation rates for the even most important of national elections, then the voters’
decisions, and the candidates’ strategic responses become much less clear-cut.

One of the most promising and persuasive explanations of the low level of turnout
observed in many recent elections is that of alienation, i.e. that voters are increasingly
unlikely to vote for a preferred candidate whose policy position differs greatly fiom the
voter’s ideal policy position. These models are based on a spatial interpretation of
electoral strategy and behavior, following from the work of Hotelling (1929) and Downs
(1957).‘

Early models (e.g. Hinich and Ordeshook (1969)) based upon alienation have
appeal as a partial explanation of low participation rates. Voters face costs of voting, and
as such are unwilling to vote for their preferred candidate irrespective of that candidate’s
qualities, or indeed those of the opposing candidate. Thus, when voters feel that the
candidates are of sufficiently poor quality, participation falls because few voters see the
candidates on offer as being ‘worth the effort’ of voting.

However, if the agent abstains, this increases the probability that the preferred
candidate will lose. As such, the agent must be concerned about not only the benefit to be

gained by the success of the preferred candidate, but also the potential loss suffered

310 0111C

becomes

izeratioi

Ti: and

should the less preferred candidate win, and hence the difference in utility between the
two outcomes. As the preferred outcome becomes better, or the less preferred outcome
becomes worse, the likelihood of alienation should decrease.

Thus, more modern literature (such as Anderson and Glomm (1992)) on
alienation is predicated upon voters who are alienated by the comparative qualities of the
two candidates, rather than merely the location of the preferred candidate.

However, what conventional theoretical models of alienation have not captured as
yet, and what this model does indeed find, is an asymmetry in the distribution of
alienation found in society under equilibrium conditions. While participation rates are
found, of course, to depend on the agent’s location relative to the candidates, agents of
differing ages and classes will possess different levels of alienation, and hence different
participation rates, even if the initial distributions of income and age are symmetric. As
such, certain groups wield a share of the vote out of proportion to their share of the
population as a whole.

What is not considered here is the “paradox of voting”, the question as to why
anyone, within a continuum of voters would feel that their impact on the election was
sufficient to overcome the costs of participation. This issue has received considerable
discussion, but as yet remains unsolved for frameworks within which individual,
uncoordinated voters have zero mass relative to the population. Ledyard (1984), has

shown that within a continuum of voters, the paradox is effectively unavoidable.

 

’ For discussion of the general nature of spatial electoral games, see Enelow and Hinich (1984) and

Enelow and Hinich (1990).

A 1
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Instead, it is assumed that the voters’ level of interest in the election is sufficient
that at least some proportion of the electorate will use their franchise regardless of the
nature of the electoral competition.

The paper presented here is a model of electorally chosen social security taxation,
where not only agents’ consumption decisions, but also their decision to participate and
the candidates’ decisions on policy placement are all based upon utility maximization.

Voters in this model are concerned with three issues. Firstly, they consider the
economic effects of the proposed tax upon themselves. Secondly, in a mildly altruistic
manner, they examine the implications of the tax upon their group in society. Such a
combination of self-interest and mild altruism has found some empirical support, e.g. in
Hudson and Jones (1994) and Shabman and Stephenson (1994). Lastly, based upon the
outcomes of the first two analyses and the candidates’ proposals for the tax, they
determine whether or not they should take part in the election.

In making this final decision, the voters face both potential utility gains from a
preferable outcome of the election, and utility losses from the costs of gathering
information concerning the candidates and then voting. As such, based upon the relative
utility gains and costs, the agent may choose not to vote, if they are indifferent to the
candidate choice presented, or if they are alienated by the lack of quality of the
candidates. Agents decide whether or not to vote based upon the difference the 'choice of
candidates has on their combined economic and social utility, as well as upon their
proximity to candidates (and hence their likelihood of alienation).

The model uses an overlapping generations framework, with agents distributed

into a number of productivity classes. Within each class, there are young and old agents.

This is the only exogenously introduced differentiation between agents in the model.
Their preferences and behavioral patterns are in no other way different from one another.
Their actions, the actions of the politicians, who are assumed to be solely interested in
electoral success, and hence the outcome of the election are all derived from their utility
maximizing behavior given age and productivity.

Agents vote on the level of social security taxation to be imposed in a given
period, and hence the benefits to be received by the current old and the taxes to fall on the
current young. The government may not run a deficit in any period. Thus, unlike models
such as those of Cukiennan and Meltzer (1989) and Alesina and Perotti (1995), the
electoral issue at stake is the level of redistribution between age groups and classes rather
than the level of national debt.

The model’s conclusions may be summarized as follows. Although most agents
possess an economic bliss point for either a zero % tax rate or a 100% tax rate, their
concern for the social well-being of their class leads most agents to possess an interior
bliss point. Secondly, wealthy agents and old agents are disproportionately likely to
participate, and as such have a disproportionate impact on the outcome of the election.

The more economically motivated the agents are (and hence the less socially
concerned), the more likely it is that the electoral outcome is determined by age rather
than income group, and as such, the more polarized the outcome is. This furthermore
implies a high overall level of alienation and low participation.

Likewise, as agents suffer increasing disutility from imperfect candidates, and
hence as alienation rises, the result of the election becomes increasingly polarized and

participation falls.

The equilibrium level of taxation is found to be sensitive to the nature of the
population distribution. However, under mildly restrictive assumptions, the results
outlined above persist strongly, and are highly robust.

The paper is organized as follows. The economic and political framework of the
model is described in Section II. Section III details the conditions required for
equilibrium in such a politico-economic model. Section IV analyses the agent’s
economic, social and political decisions, and the effects of changes in social security
taxation on the level of
bequests, savings and utility. These effects, naturally, alter the bliss points of the agents,
as discussed in Section V. The outcomes of the plurality maximizing form of the electoral

game are presented in Section VI, followed by conclusions in Section VII.

Section II: The Framework Of The Model

Consider a Diamond (1965) style overlapping generations model comprised of
two-period lived agents, firms, and single-period lived politicians. There are n types of
agents, i = 1,...,n. At each date t, N,(t) young agents of type i are born. There is no
population growth.

Agents belong to groups or classes, which differ in productivity. A type i agent
has productivity h,, where h, < h for i < j. Agents of all types supply their labor
inelastically to firms when young, and divide their after tax wage between savings and
consumption. They also may or may not vote. In their age, agents consume from the
returns on their savings and a uniform social security payment, less any bequest they

make, and they also may or may not vote.

315011011

an luv-r
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Agent:

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b

Agents decide whether or not to participate in each election based upon their
economic and social sensitivity to the potential outcomes, their information level
concerning the effects of those outcomes, and their costs of participation. Their level of
interest in the outcome of the election is based upon the direct economic effect of the tax
rate on the agent as well as upon the effect of the tax rate on the long term well-being of

the representative agents from the voter’s own productivity class.

Agents’ Utility

Each agent needs to solve three problems in order to make his fiill political
decision. Firstly, the agent needs to solve the dynamic constrained maximization problem
so as to determine how taxation will directly affect his economic well-being. Secondly,
the agent must determine the solution of the steady state maximization problem for a
member of his class, so as to determine how taxes will affect the social welfare of his
group. Thirdly, the agent must maximize political utility over the participation decision
by determining whether or not the costs and benefits to participation are such as to make
participation itself worthwhile.

Economic preferences are defined over the consumption (when young and when
old) of the individual and the value placed upon bequests given to the members of the

next generation.

U53: = Ln[cit(t)] + l3 Ln[cit(t+l)] + 5 Ln[Bit(t+l)]

[2.1]

10

I
t
M 11
-;-J
71‘.
\1-4'\

Riff:
36d:
1
l

:11

91
.\~
. BI.

Pl

where cm, is the level of consumption of a member of class i of generation t at time t,
cm.” is the consumption of a member of class i of generation t at time t+1 and BM.” is
the bequest made by a member of class i of generation t at time t+1.

Consumption when young is constrained by after tax income, less savings, plus
any bequest received. Bequests are class-specific, so members of a given group receive a

bequest from their direct predecessors, rather than from the population as a whole.

em) = W“ (1 - 1,) - 3,, + BM“,
[2.2]
Consumption when old is constrained by income from previous savings, less any
bequest given, plus a social security payment. The social security payment is equal to a

proportion (8,...) of the average level of wages in a given period (WAN).

em.” = 5,, (l + r...) + e... WAN - BM.”
[2.3]
The agent also derives utility from the welfare of his class. This utility is
determined by the economic utility of agents of the voter’s own type, in steady state. In
this role, the agent acts as a form of social planner, although the agent’s View of society

solely considers the interests of his own group.

Usn = Lnlciy] + l3 Lnlcio] + 5 Ln[Bi1
where

Ciy=Wi(1‘T)'Si+Bi

11

EA}
L.

I1 1‘
i-'*

‘I‘llk.

“A
.‘
L ’4-
«my:

0
t

F}

- w
J

i‘l

and
cio=si(l +r)+ewA-Bi
[2.4]
Thus, the agents political preference for taxation is defined by a weighted political

utility function, Up“, comprising both economic and social utility:

Um = Q UEit + (1 ‘ C) Usa:
[2.5]
The agent must then choose whether or not to participate, based upon the
difference in political utility (AUW) which arises from the difference in candidate tax
manifesto positions (i.e. the comparison of utility under one manifesto tax rate versus

under the other), as well as the cost of information (1“,) and explicit costs of voting (yij).

Thus, the participation of an individual j of type i is dependent on AUW, 1m and 7,].

Pi} = Pij(AUPiuIinl’ij)

[2.6]

Firms

Firms in the economy are perfectly competitive and employ a CRS production
function, the inputs to which are capital (which completely depreciates each period) and
effective labor, which is the sum of the quantity of labor in each class multiplied by the

per capita efficiency of that class:

12

 

’\

v.

F'-

M-

Y: = K.“ (N: h: + N2 hz + + Nn 110"“)

[2.7]
where N, is the number of workers of type i the firm hires, i = 1,...,n, and h; is the

productivity level of an agent of type i. K, is capital at time t, and Yt is output at time t.

In per capita terms:

Y: = k10(91111 + 92 hz + + 9n hull-a)

Yr : kt“ hAil-a)

[2.8]

where h, is the average level of productivity of society, normalized to l, and 0, is the

proportion of type i agents in society.

Capital markets are competitive, and thus capital is paid its marginal product.

(1+ri)=Pi=aK°"

[29]

From profit maximization, wages are equal to the marginal product each class’ labor.

Wit = (1 ' (1) hi kra

[2.10]

These two conditions are also factor market clearing, as young agents supply their

1abor inelastically and old agents supply their saving inelastically.

l3

w.\”

.Js‘» H.

.‘hav*
1.

f

t

.sua

CA

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l:-.§ -

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The Government

The government collects income taxes from the young (at a uniform rate of
income tax), and pays a uniform social security benefit to the old. This governmental
behavior represents the role of an redistributionary income transfer from the young to the

old, so no taxation is placed on capital (and hence upon the old) for simplicity.

n
rtzgiwit = 8! WA:
i=1

[2.11]

The government must run a balanced budget, and may not borrow to cover its

outflows.
Goods Market Clearing

The goods market clearing condition requires that all production in a given period

must be consumed, saved, or bequeathed, and hence:

I! n n n
y: = 2616.10) + 29:91-10) '1' 295311-10) +2 9,-5.1
1:] i=1 i=1 i=1

and hence:

[2.12]

By arbitrage, the return on savings and the return on capital are equal.

14

(1 +11): ptzakia-l

[2.13]

Politicians

Politicians in this model have no ideological preference, and simply desire to win
the election.2 Plurality maximizing politicians have no policy preference, and hence are
identical. As such, clearly, if a unique dominant election-winning strategy exists, both
candidates will choose it as their manifesto position. It is assumed that the rewards to
power-sharing are sufficient to exceed the costs of nomination, i.e. even in the event of a
certain tie, both candidates will compete.

It is assumed that as voters are setting strategy for periods of more than 25 years
(one generation), within which more than one election might be expected in the real
World, credibility is assumed. That is, no candidate can expect to deviate significantly
from his or her manifesto position without losing support. As has been shown (e.g. by
Enelow and Munger (1993) and Alesina (1988)), when either the game is repeated, or
l'eputation effects are present, even ideologically motivated candidates may be able to
Credibly stand on manifesto positions which do not conform with their ideological bliss

P0 ints.3

It may be seen (e.g. in Anderson and Glomm (1992)) that when candidates seek to maximize the
{lumber of votes cast in their favor, rather than the proportion of votes they receive, even ideologically
indifferent candidates may choose not to converge. However, as has been shown by Cox (1990), even vote-
‘g‘m‘lmizing politicians may converge when voters can cast multiple ballots.
While the extension of this model to incorporate ideologically motivated politicians lies beyond
“‘9 S§0pe of the current paper, works by Alesina and Cukierman (1990), Wittrnan (1977, 1990) and others
Provide preliminary evidence of the patterns of candidate behavior which may be expected.

15

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l

 

. ‘1
1.:
If».

'9‘-

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r.

‘8];

-3?

’I‘i’.

Political Structure

Voters take part in an election in each period, which determines the level of
income taxation to be levied upon the young in that period, and hence the level of
benefits to be received by the old in that period. All voters of all classes and ages present
at time t may participate in the election at time t.

Agents decide upon a group- and age-specific optimal policy and then pick the
candidate whose manifesto position most closely mirrors the outcome of the agent’s ideal
policy. Such optimal policy is shared by all members of that age and group, but
individual agents are small relative to the size of the population, and cannot coordinate
their voting. Voters weigh up the costs and benefits of participation, their level of
interest, and the level of information they possess, and decide whether or not to vote.

Candidates, being motivated solely by the desire to win, will each carry out
Strategies which, given the opposing candidate’s strategy, maximize their likelihood of

Winning.

Section III: The Agents’ Decision

Economic Maximization Problem

Initially, the agent calculates his optimal level of bequests and saving, at any
giVen tax rate. Then, by comparing the utility gained from the best response to all
Possible tax rates, the economically optimal rate of tax for agents of that type and age,

SiVen the behavior of other agents, may be determined (i.e. the rate of tax at which the

16

optimal saving and bequest behavior yield the highest level of economic utility). The first

stage in this process, is naturally to determine the optimal saving and bequest functions.

Max UEir (Ln[cit(t)] + flLn[Cit(t+i)] + 5Ln[Bil(t+l)]

51:,Bn(:+1)
s.t.

617(1) = wit (1 _ Tr ) _ Sir + Bil—1(1)

cit(t+1) : Sit(1+ rm ) _ Bit(t+l) + 8m w At+l
[3.1]

These yield the following first order conditions:

(W.r.t. Sit)

(1 + rt+i )fl _ l

Sil(1+ rm ) - Bit(t+1) + 5 WAN Wu (1 - 7:) '1' Bit—10) -

[3 .2]
(W.r.t. Bum”)

a_ ,6 :0

B Sil(1+rt+l)-Bil(l+l) +8 WAt+l

ir(t+l)
[3.3]
SOlving the latter yields:

B : (aw/n+1 + 511(1 + rm ))6
it(t+l) fl + 6

[3.4]

=0

it

Substituting this into the first first order condition and solving for s], yields:

17

35.331111

TI‘EC‘JOF.

s = (1+ r’” )(fl + 6Xw" (I — T' ) + Bil-1(I))_ 5 Wm”
(1+r...)(1+/3+5)

 

[3.5]

Once an agent has determined the optimal savings behavior of all agents, he can
determine the future level of capital from the aggregate savings function, all of which is a
fimction of the level of taxation.

Thus, the agent can measure how the level of taxation effect the capital stock, as
formed by individuals' optimal savings decisions. In other words, an agent can construct:
k,+,[t,], and thus U;E[k,.,], and hence UiE[t,].

Naturally, once the election is concluded and the tax rate is revealed, all agents
will operate along their predetermined optimal response path, found from the solution of
their economic maximization problem.

From Eq.s 2.7, 2.9 and 3.5, and by substituting the solution for the dynamic
bequest chosen by older agents, and the marginal products of capital and labor, the

dynamic capital stock may be constructed:

= a6(a+(l-a)t,)+(l—a)a(,6+6)(l-r,) k“

k i
’* a(1+ [3+5)+(1—a)E,r

 

1+1
[3 .6]

From this determination of the capital stock, agents determine the level of future

Wages and interest rates, as well as the optimal behavior of both generations of current

agents, in terms of savings, consumption and bequests. This, along with the steady state

c'clpital stock found below, allows the agent to determine the political utility functions of

18

‘1
I I )VJ'
."i ‘9‘"
-

Sada]

i'i'ier's

it 501

v
i

all agents, and thus predict their behavior in an election, and hence the agent may form a

rational expectation of the tax rate which will result from the election.

Social Maximization Problem

As well as the process of determining his economically optimal tax rate, the voter
also constructs U,s[t.], which represents the “social welfare” element of taxation. This
element is based upon the agent’s “long term” and (mildly) altruistic beliefs. This
function is not maximized at the agent’s short term optimal tax rate, but rather at the
optimal rate for a member of his class in steady state.

This function is directly analogous to the steady state utility of a member of the
voter’s own group, measured over the range of possible tax rates, and is constructed from

the solution to the steady state form of the agent’s maximization problem:

ng USi (Ln[ciy ] + flLn[Cio ] + 5Ln[Bi ])

s.t.
c,.y = w,(1—t)—s, + 3.-

cm =s,(l+r)—B, +5wA
[3 . 7]

As with the agent’s dynamic behavior, the first order conditions of this
maXimization may be solved so as to yield the steady state savings decision of each
member of each class. Again, by aggregation, this forms the steady state capital stock.

Herice, the agent can construct k,['c], and thus, Us,[k,], and hence USi[t] where k,[t] is the

steady state capital which would result from a stable tax rate of ‘t.
19

In the case of agent’s role as social planner, it is apparent from the time invariant

solution of the first order conditions Eq.s 3.4 and 3.5 that:

S z(1+r)(w,(1-r)+B,)(fl+a)—aw,,

 

 

 

 

" (1+r)(1+,6+6)

[3.8]
= (S,(l+r)+£wA)6

i (.3+5)

[3.9]
And hence:
w,(l—r)(,6+6)+ewA6— ”’4

s. = (1+r)

' (1+fl+6)-6(1+r)
[3.10]

From Eq. 2.7, 2.9, and 3.10, and by substituting the marginal productivities of capital and
labor for the return on saving and the wage rate, the steady state capital stock may be

Written as:

k = a(6+(1—a),6(1—r)))T—75
’ a(,6+6+(l—r))+r

[3.1 1]
All agents now calculate their class’s optimal level of savings, bequests and utility
as a function of the model's parameters and the tax rate (see Appendix One). Thus, agents

may determine the socially optimal tax rate for their group, based upon the rate which

20

would maximize their utility in steady state, holding the behavior of other groups

constant.

Participation and the Agent’s Political Maximization Decision

Now in possession of the functions UEi,[t,] and Us],[t,], representing the economic

and social effects of taxation, the agent must decide whether or not to participate in the

election, i.e. actually vote.

The agent’s decision to vote is based upon three primary components. Firstly, the

agent weighs the economic and social effects of taxation such that overall political utility
may be measured by:
UPit[Tt] = C UEit[Tt] T (1 ' C) Usalth]

[3.12]

and hence the sensitivity of the agent to any candidate choice is reflected by:
AUPitPCAt, Tar] = IUPitLtAt] ' UPit[TBI]|

[3.13]

Where AUHJIN, rm] measures the weighted social and economic utility difference

between the tax rates resulting from candidate A (with manifesto position 1,“) versus

cEilndidate B (with manifesto position 1:3,) being elected.

The agent uses this function, derived from his economic and ideological utility, to

dEtermine an overall “ideal” tax policy, In“. Naturally, the voter then prefers the

x

I Naturally, within each class, there will in fact be two bliss points, one for the old, and one for the
young.

21

‘l ‘
a. r " ‘
119. .1

14“"m1'?‘

1' F...‘AAW

i'vib.‘
IL; “i;

310165 ;

mm:

candidate whose stated policy would, if elected, lead to the outcome closest to this
optimum.

Secondly, the voter possesses an information cost function, 1p],[t,, 1,3], which
describes the voters’ non-economic5

cost of obtaining sufficient information to
participate. In turn, this reflects the level of “free” information available to the agent. As

has been shown from Downs (1957) on through to Popkin (1993)6, voters in elections in

which their mass is trivial relative to the population as a whole, do not have an incentive
to gain information concerning the nature and impact of political alternatives. As such,
their social conditioning generally leads to lower information costs, and hence a higher

level of inforrnedness, for policy alternatives which are close to the agents’ (or the
groups’) bliss points.7

If", and increases as either candidate
moves away from that position. I assume that:

IPit[tAts 181a 131*] = 1‘ (ltAr ' Fifi + I 17m " Tir*l)

[3.14]

Clearly, if [i=0 there is no information cost problem, and agents are fully

informed under all circumstances, and as [1 increases, agents are increasingly narrowly

\

5

These costs are not considered as part of the agents’ consumption decision. Relative to the
economic costs and benefits involved, they are extremely small. They remain significant, however, as
2.‘hihough they are very small relative to the economic and social motivations, the agent has very little
1t“pact on the political outcome, although it has significant impact on the voter. Thus, when the agent
col'lsiders the effect of the election on himself, and his effect on it, the overall effectiveness of his vote is
infliciently small that information costs are a non-trivial determinant in the decision to participate.

This aspects of Downs’ work has received significantly less attention than the predictions
gonceming minimum differentiation and the paradox of participation.

. Lupia (1992) investigates the role of incumbents ability to manipulate the supply of low cost
mformation to “busy” voters, thus deliberately alienating the supporters of their potential opponents.

22

".1 ‘ Let
11 CT

5:!
E3!
‘ri‘

20:15 at:
for tacit
Sill. SC
in: 3536
in]? pm

when

’6 disn
and 1111
.TE'fici

"‘55 p0

informed about the election (i.e. increasingly uninformed about choices which lie distant
from their bliss point).

Thirdly, there are explicit costs to participation, yij for member j of group i. These
costs are uniformly distributed among agents of each class, and the distribution of costs
for each class and age group is the same, such that Min[yi] < 0, Max[yi] > 0, E[yi] > 0. As
such, some agents (those facing negative overall costs) will always participate (even in
the absence of political motivation concerning the candidate choice), but most agents will

only participate if explicit- and information-costs are low, or the agent is highly sensitive

to the policy outcome.

Thus the participation decision for agent j of type i may be seen as:
Mgr [it/sump“, cal—Iiirmrmn;14.)} s.t. P.- e {0,1}

[3.15]

hence in order to maximize utility from participation:

PI] =1 if (AUPitltAptBt]—Iit[TAt’TBI’ 112]) y'j

Pij = 0 otherwise
i 3 .16]

For an individual agent, participation is thus discrete between 0 and 1, however
the distribution of yij is such that participation is a continuous variable within each group,
and that under all circumstances some agents will vote. However, the relative level of
participation between different agent types and age groups is determined by the agents’

bliss points and the positions of the candidates.

23

Senior

{3.3

"mav-
3G, 45.11
A

I a 11’.
fished

it
:1
r:
[:2

C133! 3!

Section

"9 fou

will 1r

4.60

Section IV: Equilibrium

A rational expectations Nash equilibrium for this model is a sequence of taxes
{1,}, a sequence of prices {Wm r,, p,}, a sequence of allocations {CW}, calm], k.} and a
sequence of agent participation levels {PU-(15., t,)} such that at these taxes, prices,
allocations and participation levels, each candidate chooses a strategy which maximizes

that candidate’s utility, agents’ utility is maximized, firms maximize profits, all markets

clear and the govemment’s budget constraint is satisfied.

Section V: Agents’ Combined Political Bliss Points

It is worthwhile at this stage to consider the nature of the agents’ bliss points. The
distribution of the bliss points themselves is a powerful indicator of the forces generating
the equilibrium of the plurality maximizing electoral game.

As has been mentioned, the economic and social utility functions of agents from a
heterogeneous population depend on taxation in a non-linear manner. As such, it is not

possible to algebraically solve the overall political utility function Up].[1:[] for 1,, so as to

find the agent’s bliss point (the tax rate which maximizes lifetime Up],[tl]).

Simulations to determine the nature of Upi,[t,] and 1:]. may be sensitive to the
Choice of initial conditions. Thus, repeated simulations were undertaken with different

initial tax rates (and thus different initial capital stocks). These simulations were
performed iteratively until a stable form for Upi,[t,] and 1']. were found. Furthermore, it
Was found that the system converged to these stable forms very quickly, and that the
nature of Up].[t,] and 1; was almost entirely independent of the initial conditions. From

24

these political utility functions and tax bliss points, it was possible (as is described at the
start of Section VI) to determine the outcome of the electoral game, i.e. the equilibrium
tax rate. This tax rate was then imposed as the initial tax rate, and thus as the determinant
of the initial capital stock. The simulations were then re-run to ensure that future
elections continued to result in this equilibrium tax rate.
Thus, for any parameter set, Up,,['c,], and hence 17,. may be generated numerically.
From Eq.s 3.6 and 3.11, agents determine the dynamic and steady state demand for
capital within the population as a whole. As a result, each agent determines the effect of
taxation on capital, and hence on wages, interest rates, savings, bequests and utility.
In other words, UH,[t,] shows how the agent’s political utility is affected by
changes in the tax rate, to which all agents respond through utility maximization, as
described earlier. Although the dynamic and steady state capital stocks can be solved

analytically, the economic and social utility functions which comprise Um[t,] are highly

non-linear in 1,, and as such must be dealt with through numerical simulation.

From the first order conditions of the agents’ maximization problem, it is possible
to determine each agent’s optimal (steady state and dynamic) savings, bequests and
consumption as a function of taxation. The agent thus possesses the components of
UPithtl'

From Ufi,[t,] it is possible to determine 1],, and t',,,, the tax rates which maximize

lifetime Um,[t,] for young and old agents respectively. In order to determine 12,, and t’,,,,
. . 6U - . . .
the numerical solution of -—;ib] = 0 must be found. For agents whose bliss pomts lie at

1

the comers of the tax policy space, a sufficient condition for a 0% tax bliss point is that

25

%fl<0 (051, $1) and likewise for a 100% bliss point aigllfl>0 (031.31).
I I

The parameter values used in these simulations are described in Table 1.

Proposition 1: Within any productive class, the bliss point of the old will be for a
level of social security taxation greater than or equal to that of the young.
Furthermore, within any age group, the bliss point of wealthier agents will be for

a level of taxation less than or equal to the bliss point of poorer agents.

By assumption, within any productivity group, agents of differing ages will share
their social bliss point, as it derives from the steady state welfare of their class. However,
the economic well-being of each agent is age specific. Under all simulations tested, old
agents uniformly benefit from higher taxation. As taxes rise, they are able to consume
more in old age, and bequeath more to their children. As such, in equilibrium, all old
agents economically prefer a 100% tax rate.

For the young, however, the effects of taxation are almost universally detrimental
to economic utility. Although young agents receive an increased bequest from their

parents, their loss of wage income (through taxation) exceeds the increased bequest
(except for the very poorest young agents, whose incomes are very small, and hence who
are highly sensitive to the size of the bequest that they receive). As such, in equilibrium,

all but the poorest young agents economically prefer a zero tax rate.

26

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27

Given these polarized economic bliss points, but the intrinsically shared socially

optimal tax rate, it is clear that:

T. S 1;, given h,

[5.1]

where 1:2, is the bliss point of a young agent of type i and 1..., is the bliss point of an old
agent of the same type.

Furthermore, within each age group, the tax rate that maximizes overall political
utility is dependent on the agent’s productivity. This result is derived from the agent’s
social utility function, as all old agents and almost all young agents economically desire
100% or zero tax rates respectively.

Most agents do not, in steady state, desire comer solutions to the tax problem. As
taxes rise, agents receive larger social security payments in old age, and also receive
larger bequests when young. Naturally, this also means that they are able to give larger
bequests when old. Countering this effect, however, as the tax rate rises, it can be seen
from Eq. 3.11 that capital, and hence output and wages will fall. Thus, even agents who

benefit from the transfer system are effectively receiving a larger slice of a smaller pie,
and as such they will eventually be made worse off by excessive taxation.

However, these effects are not even across the population, as the social security
System also does transfer income from the wealthy to the poor. As such, in steady state,

although most agents will prefer some interior tax rate, the rate which is optimal depends

inversely on the agent’s productivity. Poorer agents benefit from increased bequests and a

28

larger social security payment, (as well as from increased interest rates) while taxes
diminish the level of pre-and post-tax wages.

Wealthier agents likewise benefit from increased bequests and social security
payments, as well as higher interest rates, over some tax range, but these benefits will
increasingly be overwhelmed by the increased tax burden which the agent faces, i.e. the
agent loses too much wage income to maintain savings, and hence bequests, consumption
and utility.

Thus:

 

 

[5.2]

The inequalities described in proposition 1 and Eq.s 5.1 and 5.2 become strict if,
of n classes of agent, and hence 2n separate bliss points, there are (2n - l) bliss points
for positive taxation and (Zn - 1) for less than 100% taxation. Distributions of bliss points

which conform to this pattern are described hereafier as weakly interior.

Proposition 2: Given a distribution of agents, as agent productivity increases, the

diflerence between agent bliss points within each age group diminishes.

Again, clearly, the distribution of agent bliss points is derived from the agents’
Socially optimal level of tax. While it is not possible to algebraically solve for the form of
11,, it may be determined numerically (for further details, see Appendix 2). From

numerical calculations across a wide range of parameter values, the following pattern is

uniformly observed:
29

 

#20 , 3’20
[5.3]
and hence from Eq.s 3.12 and 5.3:
2 ' 2 ‘

l

[5.4]

Thus, the distribution of the agents’ overall tax bliss points is a convex function of
the agents’ productivities. This behavior appears to be based upon the decreasing nature
of marginal utility. Given the form of the agents’ utility functions, agents who are poor
have (at any tax rate less than 100%) a lower absolute level of utility than rich agents, but
a higher level of marginal utility from consumption and bequests. It may be shown that in
steady state, the change in utility caused by a given change in the tax rate is greater for
poor agents than for wealthy ones. As such, given the existence of some optimal tax rate

for each class of agent, the difference between the bliss points of two wealthy agents will
be less than the difference between the bliss points of two otherwise comparable poor
agents, as the marginal impact of sub-optimal tax rates is far greater on low productivity

agents than it is on the wealthy.

Section VI: Results of the Plurality Maximizing Electoral Game

Once the agents’ bliss points have been determined, in order to locate the

equilibrium, it is necessary to find the set of tax manifesto positions which, given the

30

bib

'2
(1..

6H.

J.

v

'4.)
;‘4

:4

vl

\

'-'

agents’ distribution, and hence the distribution of Uml'CJ functions, that will maximize
the candidates ' utility.

For any combination of strategies, 1,, and 13, each voter must decide on a
preferred candidate (unless the agent is absolutely indifferent between the candidates (an
eventuality which is effectively limited to the case 1,, = 13)), and then each agent must
decide, given the choice of candidates on offer, whether or not to participate.

To do this, Up,,[1:,\] and Upi,[tB] must first be calculated. Which of these is greater
determines whether A or B is the preferred candidate. Given this choice of the more-

desired candidate, the agent’s likelihood of participation must be determined, from Eq.

3.16.

This process must be repeated for the representative agent of each type and age
group within the population. As each of these candidate choices and participation levels
is dependent upon 1,, and 13, each must be recalculated for every combination of possible
candidate strategies. In the case of the simulations used in this paper this demanded the
determination of PU for each age and productivity combination for up to 10,000 strategy
combinations.

Thus, the vote cast for candidate A by members of generation x of type i, given

candidate positions 1,, and TB is:

VM [7.4 ,‘Z'B ] = 0,13; if and only if TA is preferred to TB
= 0 otherwise

[6.1]

31

where T’, is the numerical average of PU within that age and productivity group. As such,

the total number of votes cast for candidate A is:

V.[r.,r.1=::v..[r.,r.1

i=l m—n
[6.2]

By comparing VA[1:A, 13] and the corresponding vote total for candidate B, VB[TA, 133], the
electoral winner may be found, based upon the strategy combination {1A, 13}. It is thus
possible to determine the electoral outcome (in terms of the victor and hence the
“winning” tax rate) from any combination of strategies.

This process generates a winner, and an outcome tax rate from any strategy
combination {1A, TB}. Essentially, this is the direct analog of the normal form of the
strategy game the candidates play, as their payoff functions are zero-sum. Thus, any
strategy combination yields a single payoff, positive for the winner, negative for the
loser, and zero in the event of a tie. From this payoff matrix, it is possible to locate any
Nash equilibria strategy sets.

In this model, without exception, the equilibrium found by simulation was not
only a unique Nash equilibrium, but a Nash equilibrium formed from symmetric
dominant strategies for the two candidates. That is, for each candidate there exists a
unique strategy that yields victory irrespective8 of the opposing candidate’s strategy,

unless the opponent employs an identical strategy, in which case a tie results.

 

3 Hence a more restrictive form of solution than a general Nash equilibrium, in which the

candidate’s strategy is optimal given the opposing candidate’s strategy.
32

However, there may also exist, alongside the dominant strategy, one or more
strategies which, within a different, more restricted, policy space, would be dominant.
Note, this is not merely to say that when the strategy space is restricted such as to remove
the initially dominant strategy, the equilibrium tax rate will be held by a binding
constraint to the edge of the strategy space closest to that strategy. Instead, within such a
restricted policy space, there may exist a dominant strategy in the interior.

Consider an election wherein there are only two blocks of voters, a larger group
which has a bliss point for high taxes, and a smaller group for low taxes. Both groups’
preferences are such that they become alienated rapidly as the candidates move away
from their respective bliss points. Clearly, if they become sufficiently alienated
sufficiently quickly, then candidates may effectively choose between pleasing one group
and pleasing the other. All things being equal, the candidates choose to please the larger
group, and the smaller group is alienated, and fails to participate. '

However, if the strategy space is restricted to low-to-medium tax rates alone, then
there exists some strategy space such that the level of alienation among the supporters of
the high-tax platform will overcome their numerical superiority, and the less numerous
group is decisive across the entire restricted strategy space, and hence the dominant
strategy will be that preferred by the low-tax group. Strategies with the potential to
dominate within restricted spaces prove common in this model, as long as information
costs, and hence the disutility of voting for a poor quality candidate, are non-trivial. For
further discussion of such strategies, see Appendix Three.

Nonetheless, a dominant strategy is found to exist under all parameter

specifications, policy spaces and simulations tested, and that strategy defines the

33

equilibrium outcome of the electoral game. Likewise, although strategies which could
dominate restricted policy spaces are common, they do not exist within all strategy sub-
spaces. As such, for many sub-spaces which eliminate the initial dominant strategy, the
new dominant strategy within the restricted space will be a binding constraint against the
limit closest to the previous dominant strategy.

The existence of strategies which could dominate restricted policy spaces merely
implies the existence of some restricted policy space within which that strategy would
yield the equilibrium of the game.

It may be seen that if there exists a single dominant strategy, across either the
global policy space or some local subspace, then both plurality maximizing candidates
will converge to that point. In that case, voters can perceive no difference between the
candidates, and thus only those agents with negative overall costs participate.

This is not, however, to say that candidate placement and voter participation are
irrelevant in this case. Instead, the voters’ participation decision is what constrains the
candidates to this equilibrium, i.e. how likely the voters would be to participate, if either

candidate moved marginally away from the equilibrium.

INDIVIDUAL CHARACTERISTIC EFFECTS

Proposition 3: Given a weakly interior distribution of agents’ bliss points (as
defined in the discussion of proposition 1), and non-trivial information costs,
agents who are poorer than those whose ideal policy is reflected in the

equilibrium outcome are less likely to participate than voters who are wealthier.

34

Thus, if one constructs the voter whose ideal policy would have been for the
actual outcome, and define that agent’s productivity as hi , it is true that, within either age

group, if the distribution of bliss points is weakly interior:
RU?) <19.1<P.-U7. >13.l,given|72} —I3.|
[6.3]

where Hi is any h, such that [ii at Iii .
This does not necessarily imply that 2%) 0 for all agents. Participation is still

dependent on the agent’s satisfaction with the available candidate choice, as well as on
the agent’s social and economic sensitivity to tax. If the distribution of voters is such that
almost all voters are extremely poor (and hence offset by a handful of “super-rich”), then
the wishes of the poor will dominate, and the result will be that the rich will fail to
participate. However, it does imply, clearly, that the wealthy, in general “punch above
their weight”, i.e. they have a disproportionately large impact on the outcome of the
electoral game.

This result derives from the distribution of bliss points, as described in Section V.
Agents who are wealthier than the mean generally have far less diverse bliss points than
those who are poorer than the mean. Thus, a policy which is ideal for one wealthy group
will also be close to ideal for other wealthy groups, and hence the majority of wealthy

agents will have a high probability of participating in favor of that policy.

35

In contrast, a policy which is ideal for one poor group will also be distant from the
bliss points of other poor groups, so the majority of low productivity agents will have a
low probability of participating in favor of that policy.

If the distribution of agents and the parameter specification leads to a distribution
of bliss points which is not weakly interior, or if information costs are trivial, then the
relative participation rate between wealthy and less-wealthy agents is parameter specific,
although under all simulations tested, Proposition 3 still holds for those agents whose

bliss points are weakly interior.

Proposition 4: Given a weakly interior distribution of agents’ bliss points, the
average level of participation among old agents is greater than the average

among young agents.

Hence, under all simulations:

P... > 17.,
[6.4]

Young voters, although always economically opposed to high taxation, do find
the loss of initial take-home wages somewhat offset by higher bequest receipts, the
interest rate effects of higher taxes, and the increased bequests which they receive from
their parents. The economic utility of the old, however, is unambiguously improved by
increasing taxes. Thus, the economic component of political utility is somewhat more

tax-sensitive for the old wealthy than for the young wealthy, and as such, given

36

candidates at any given distance from the agent’s bliss point to the policy outcome, [the
young will tend to be less likely to participate than the old.

From the propositions 3 and 4, it may be seen that a convergent outcome of the
game reflects the desires of the old over those of the young, and of the wealthy over those
of the poor. Under virtually all simulation run9, this leads to an equilibrium tax rate which
is lower than that of the median agent’s bliss point, as long as the divisions within society

are primarily driven by income, not age.

Proposition 5: As agents become increasingly concerned with the economic
impact of the election ’3 outcome, and hence less sensitive to the social outcome,
society ceases to be polarized by wealth, and is increasingly delineated by age. As
such, taxes increase, and the capital stock, wages and output decrease, while

interest rates rise.

As agents are increasingly focused on the economic effects of taxation, agents’
bliss points diverge rapidly away from the median. Young agents will increasingly prefer
a zero rate of taxation, and old agents will rapidly find the revenue maximizing rate

optimal. This has two principal effects. Firstly, as C (the weighting of economic to social

motivations in Um[t,]) increases, and agents’ bliss points polarize, candidates located

near to any dominant strategy will be increasingly unacceptable to agents from the age

 

9 With the exclusion only of those in which the population distribution was asymmetric and the

costs of participation were very high, such that a single class and age group was likely to dominate the
election. Naturally, in this case, the bliss point of the dominant group was the sole determinant of the
outcome.

37

group whose bliss point lies further from the dominant strategy. As such, one age group
or the other will tend to be almost completely alienated.

Conversely, as Q falls, agents are increasingly willing to accept a centrist policy,
and as such it becomes more likely that (at any parameter specification and voter
distribution) agents will converge to some common centrist policy. As when Q is low, the
majority of agents have similar bliss points, the distance from any agent’s bliss point to
that of any other agent is small, and as such the costs of participation, and hence the level
of alienation are low. Thus, given the parameter specification and population distribution,
as Q falls, the threshold value of u beneath which centrist convergence is possible rises,
and hence even under significant information costs and thus high levels of proximity
sensitivity, the likelihood of alienation will be low.

Secondly, as C; rises, the bliss point of the old will tend to become more important,
and taxation will thus rise. This follows from proposition 4. Because the old are more
sensitive to tax in economic utility terms (as their economic utility responds
unambiguously to increased benefits), if the election is a straight competition between the
young and the old and costs are symmetric, the old will be more likely to participate and

hence dominate the election.

POPULATION DISTRIBUTION EFFECTS

There are three key components to the population distribution. Firstly, there is the
range over which the population is spread (i.e. the minimum and maximum of h,).

Secondly, there is the allocation of agents within that range, which may be broadly

38

characterized as one of four types. Homogeneous distributionslo encompass the perfectly
homogeneous (wherein h,=1.0 for all agents) and low-variance normal distributions.
Uniform distributions contain equal numbers agents from each productivity group.
Bimodal distributions have relatively few agents in either tail, or at the median, but two
“power blocks” located to the lefi and right of the median. Log normal distributions are
asymmetric with a relatively large proportion of the population located below, but close
to the mean, and a long tail above the mean. Thirdly, the number of classes over which
the agents are located is a significant factor in the nature of the equilibrium. Clearly, the
more groups, the smaller the classes and the less effective political mass each class of

agent pOSSCSSCS.

Proposition 6: As the limits of the population distribution expand towards the
limits of weakly interior bliss points, equilibrium taxes will remain steaay or fall.
If the range expands sufliciently that a large proportion of the population has
bliss points at 100% or 0% taxation, then the eflect an equilibrium taxation is

ambiguous.

The narrower the range over which the agents are distributed, the fewer the agents

who possess bliss points for comer solutions. As such, naturally, this will tend to

 

'0 Clearly, within this model, a perfectly “homogeneous society” is something of a misnomer.

Indeed, the homogeneous society is the most polarized of all. Given parameter values, a society comprised
solely of one class of agent splits evenly into two groups; the old, for whom 1;},0 2 1:5 , and the young, for
whom 12p, S 1:5 . There are no other groups with more extreme preferences, nor any with compromise

positions. Obviously, the two age groups are equal in size, and in general their preferences are
approximately equally sensitive to taxation choices away from their bliss points.

39

reinforce the likelihood of centrist convergence, as a greater number of agents will have
broadly similar bliss points. Furthermore, when the range is sufficiently small (i.e. there
are sufficiently few extremely poor or rich agents), the comparative similarity of wealthy
agents’ bliss points as compared with those of the poor ensures that the wealthy agents’
wishes will, in general, be over-represented in the outcome.’1

As the range over which the agents are distributed increases, and the distribution
of bliss points ceases to be weakly interior, more agents will possess a bliss point for
either 100% taxation (in the case of the very poor) or 0% taxation (the very wealthy).
Whether this will lead to a higher or lower tax rate in equilibrium is largely parameter
dependent, and as such, the effect of increased population range on taxation is
ambiguous.‘2

Given the range of agent productivities in the economy, the allocation of those
agents also has a great impact on nature of the outcome of the game. However, as
described above, the effects of changes in the distribution are ambiguous where the range

of the agent distribution generates a large number of voters with comer solutions for bliss

points.

Proposition 7: Relative to the equilibrium outcome of an election with uniformly
distributed agents with weakly interior bliss points, highly homogeneous

distributions have an ambiguous eflect on the outcome, while bimodal

 

” The restricted range require for weakly interior bliss points within this model is in general

relatively small. This results from the overly generous form of social security transfer system. If there was a
significant correlation between the agent’s own productivity and the benefits received, or if there was a cap
on the income against which taxes could be drawn, then a wider range of agents would possess interior tax
bliss points.

40

5i

1

A?
.91

HT
1115;» t

Ween :

ii that

7M} mod:
are for l
gems p0
i 3TB ll}:

Wes Io

distributions lead to higher taxation in the great majority of simulations'3

, and
log-normal distributions lead to higher taxation under all circumstances

simulated.

When the distribution of agents is highly homogeneous, there is little
differentiation between the vast majority of agents in terms of class, but a great deal
between age groups. As such, the findings of propositions 6 and 7 lead us to expect, and
find, that taxes will be higher than in the case of a uniform distribution.

Bimodal distributions also lead to higher levels of taxation, and the stronger the
two modes are, the more reinforced this effect is. Essentially, as two strong modes appear
(one for high tax and one for low tax), the bliss point similarity advantage which wealthy
agents possessed disappears. Once a large proportion of the poor are closely congregated,
as are the bulk of the wealthy, the relative similarity of all wealthy agents’ bliss points
ceases to confer significant advantages to them.

This effect is carried further in the presence of a log-normal population
distribution. Under a log-normal distribution the vast majority of poor agents have similar
bliss points, whereas the rich are now less populace and have a more distended set of
bliss points. As such, their bliss points are no longer mutually supportive, and hence

wealthy agents’ disproportionate ability to draw down the tax rate is diminished.

 

'2 See Appendix 2 for demonstrations of the behavior of agent bliss points under different parameter

specifications.

’ The only exceptions being the case of a very restricted number of classes (e.g. n=3) or very high
costs to participation, such that no group would lend significant support to a candidate located at any other
group’s bliss point.

41

Proposition 8: Increasing the number of classes within a given distribution has a
small and ambiguous eflect an equilibrium taxation, but makes centrist tax rates
more likely, and hence the level of alienation lower. Furthermore, it reduces the
likelihood of the existence of strategies which are dominant in interior of
restricted policy spaces and it implies that any such strategies which do exist will

dominate only within a smaller (more localized) policy space.

As the number of classes increases, each class becomes smaller, and any one class
is thus less likely to be able to dominate the election. However, as the agents who are
removed to form the intermediate classes are spread approximately evenly between a
slightly higher class and a slightly lower one, the net effect on “average” bliss points is
negligible and ambiguous.

However, as each local group becomes weaker, it is less likely that an extreme
solution will result from the election. As powerblocks fade, centrism rises. Clearly, this
will lead to lower levels of alienation, and hence higher overall participation rates.

Equally significantly, it will reduce the number of strategies which could
dominate within the interior of restricted policy spaces. Such strategies rely upon the
existence of a large group of agents with very similar bliss points, but who will largely be
alienated by the initial dominant strategy. As such groups are disbanded, and the
population is instead formed into a continuum of voters, groups of similar agents no
longer share common goals, and hence their ability to appeal as a block fails. In other
words, classes have far greater power through what amounts to a collective political

platform than individual agents can have.

42

However, it should be noted that, dependent on the parameter specification and
the distribution of agents, strategies which dominate the interior of restricted policy
spaces persist under certain circumstances, particularly when information costs are high

(and hence so is alienation) or where the agents are distributed unifonnly or bimodally.

Section VII: Conclusions and Extensions of the Model

Before summarizing the results of this paper, it is important to remember that they
are driven by nothing more than the intrinsic differentiation of the agents, by age and by
productivity. Their personal parameters, distribution and preferences are in all other ways
identical. It is quite possible to generate all manner of interesting electoral results if
agents may be distributed unevenly or given different behavioral patterns, but that is not
the case here. Furthermore, their preferred policy and their participation behavior, and
hence the equilibrium outcome of the election, is derived from utility maximization,
rather than by arbitrary assumption.

The model’s principal conclusions are fivefold. Firstly, when significant numbers
of voters are alienated, pure centrist convergence, with a unique dominant strategy which
persists (either as the active strategy or from a binding constraint) across all policy
spaces, is rare. This is the case almost by definition. Alienation implies the existence of
abstaining voters who would have voted had they been presented with a better candidate.
Likewise, some of the voters whose votes ensure victory for the dominant strategy would
be less likely to participate if such a strategy was not on offer. As such, the role of the

institutional construction of the policy space is critical.

43

It is by no means obvious that the policy space for an issue such as social security
taxation need necessarily be fiom 0% to 100%. If the population structure changes, the
dominant equilibrium should change with them and this may alienate voters who were
pleased with the previous outcome, but not with the new one. If those voters were the
“powerbrokers” of the previous equilibrium, and are permitted to specify the policy space
for the new election, they may be able to restrict the space to one such that their own bliss
points again represent the dominant outcome.

This implies nothing so blatant as restricting the tax level to a constraint against
which the tax rate will be binding, but instead, by specifying a sufficiently limited range,
they may alienate the vast majority of their opponents so effectively that the dominant
solution is within the interior of the restricted policy space. However, such a role in
determining the policy space would clearly change the nature of the electoral game, and
as such lies beyond the scope of this paper, although some inferences may be drawn from
the “agenda setting” literature of committee-based, such as Rosenthal (1990), and models
of information-restriction, e.g. Lupia (1992).

Secondly, within the population as a whole, the old and the wealthy will tend to
have higher participation rates, all things considered, than the poor and the young. This
result, clearly coincides with conventional political wisdom. This result is derived from
the fact that the old are more single-minded in their response to changes in taxation (and
hence benefits) and that the wealthy form a more mutually supportive front in favor of
lower taxes, and as such, are able to disproportionately affect the equilibrium.

Thirdly, as agents become more proximity sensitive, the wealthy will tend to

benefit, i.e. when society becomes polarized, the wealthy form a more coherent force

44

than the poor, and are, as such, able to dominate the outcome, even when they represent
an absolute minority of the population.

Fourth, as the population becomes more socially concerned, and less motivated by
the economic outcome, the political debate will generally be broadly centrist, and based
upon class. If agents are predominantly motivated by economic considerations, then the
debate will tend to polarize, and be characterized by age differences.

It is also worthwhileat this stage, to consider the implications of a less rigid class
structure. Given that voters in this model live for only two periods, it seems reasonable
that they should be fully aware of their own class, but not necessarily that of their
offspring. If agents are unsure of the class of their offspring, they should include more
than one class’s welfare in their social utility calculations. In the extreme case, where
agents are randomly distributed among n classes, the social utility function would be
identical for all agents. This would certainly tend to lead to greater centrism, and a lower
level of alienation, although it would not necessarily ensure the existence of just two bliss
points (one for the old, one for the young), as there would also exist n2 combinations of
old and young within a given period, and hence there would be young poor agents whose
parents would be sufficiently wealthy to not give a large enough bequest to offset taxes.
Overall, however, as agents become concerned with more than their own welfare and that
of their specific class, they are more likely to share some common elements in the
determination of their bliss points, and as such will tend to have less dissimilar bliss
points, leading to a higher level of centrism and lower levels of alienation.

Lastly, as society becomes less unequal, and hence the income range over which

the vast majority of agents is spread diminishes, then the result will tend to reflect both

45

centrism and the wishes of those with as sub-median bliss point for tax. If society
becomes unequal and highly polarized, only then may the poor be able form a sufficiently
large voting block to dominate the election, at which point the equilibrium could shift
violently in their favor. Thus, a more even society, with relatively few poor agents will
tend to be stable and will tend to prefer a low rate of taxation, as we would expect.

The results of this model open fiirther possibilities. It is apparent that under a
shifting social structure, control of the policy space may lead to minority rule, if the
policy space for the next election may be determined by the winners of the present vote.
Likewise, the entry of third candidates may lead to candidate differentiation, and hence
non-convergence. To this point it has been specified that there are only two potential
candidates in any election. As such, when a single dominant policy position exists, they
will converge to it. If, however, there exists the possibility of the entry of a third
candidate, then the position becomes far less obvious.

As has been shown by Osborne (1993), Gutowski and Georges (1993) and other
authors, the strategic behavior of politicians facing potential entrants is likely to be very
different to that of candidates operating in a closed system. Indeed, Chressanthis and
Shaffer (1993) have found evidence that alienation has been a significant factor in the
threat of potential entrants in recent US. presidential elections. Furthermore, Hug (1995)
has demonstrated the possibility of the presence of third parties in the equilibria of spatial
games wherein voters are not fully informed about the candidates’ preferences, as is
particularly likely where candidates have ideological and plurality-seeking motivations.

While third-candidate entry lies beyond this paper’s scope, and would add a

further dimension to the model’s complexity, preliminary simulations indicate that if

46

entry is possible, many of the dominant strategies found in the current model may be
indefensible against the entrant, in particular when there are dominant strategies across
different policy spaces.

Clearly, there is a role for an expansion of this model to incorporate these
changes, as well as introducing ideological motivations for the candidates, under which

circumstances the equilibrium outcome is by no means necessarily convergent.

47

Appendix 1

The nature of steady state savings and bequests

48

From the solution of the derivative of steady state savings with respect to taxation,
it is possible to specify the conditions under which savings will rise in taxes, in the form
of a lower limit on productivity, hf. hf represents the a productivity level so low that,
under prevailing tax rates, savings rise in taxation:

This path clearly depends solely on or, [3, 5 and t. Plotting hf against 1 for
combinations of [3 and 5 ranging from .1 to .75 (assuming or = .3), it is apparent that the
path of hf is not dramatically affected by changes in [3 and 5, and hence that for any
reasonable parameter set, at low tax levels all agents’ savings decrease in taxation, and

even at high tax rates only low productivity agents may have savings which rise in taxes.

 

 

 

2 .* ,
1" Above and to the left of the h, path,
savings decrease in taxation. Below

1.75 and to the left, savings increase.
1. 5
1.25
1
0.75
0.5
0.25

0.2
Figure 1 Savings equilibrium, as a function of taxation and income group

49

 

-~.l|D-.\
Nudt. -
I

h0g1
ml A“ a

i I
“.1,“

LS-lukt
l

etch a.

I .
‘0’, i“! ‘0"
--H-U'\L. "

 

1"
cope

Likewise, it is possible to construct hi++ the productivity requirement such that
bequests will fall in taxation. Plotting h;++ against 1 for combinations of B and 8 ranging
from .1 to .75 (assuming or = .3), it is again clear that the path of hi“ is not critically
dependent on changes in B and 8, and that for any reasonable parameter set, at low tax

levels all agents’ bequests increase in taxation, and even at high tax rates only high

productivity agents may have bequests which fall in taxes.

2-

1.75-

O
o e
' \I
U1 U1 H

O
N
U1

50

r.

t...

 

 

 

 

 

L
t Bequests =
0 .25 _ h. 2.0
. A h, = 1 5
. A
° 2 . h,= 1
A
0 15 - A h. = 0 S
I A
0 1 i A h, = 0 0
. A
0.05 -
A
n J l a J J 1 n l n n a J_ L n L t!
0.2 0.4 0.6 0.8 1
Figure 3 The level of bequests, as a function of taxation and income group

Clearly, for low income groups, bequests consistently rise in taxation, while for

high productivity groups, bequests initially rise, but later fall.

51

Appendix 2

The nature and robustness of agents’ bliss points

52

As has been stated, the nature of ti; and rio‘, the bliss points of young and old

agents of type i, remains analytically insoluble, due to the nonlinear form of UPit[Tt]. As

such, it is necessary to numerically solve the model at this point.

 

0.60 4

0.50 4

      
 

Old: Baseline
0.40 a

0.30 a
0.20 .

Young: Baseline
0.10 «

 

 

0.00

 

m-zs

m-so

hr- 75
hI-IDU-l
hi=l 25
hI=I 50
ht-I 7S
m=2 00 <
m=225«
hisZSO-t
hr=2 75
I'll-3 00

Figure 4 The distribution of bliss points under baseline parameters.

As can be seen by comparing the figure above (simulated under baseline
conditions) to those given in Figure 4, although these parameter changes do have a
significant effect on the location of a given agent’s bliss point, the general pattern

described in proposition 2, Eq.s 5.3 and 5.4 remains valid across a very wide range of

parameter values.

53

 

I.00
.

0.90 t
0.00 4
0.70 r
0.60 4
0.50 4
0.40 4
0.30 i
0.20 *

 

0.00

  
   

Young: Baseline + [[3, 8] = .25

Old: Baseline + [0, 6] = .25

 

 

 

M-.25

1.00

m-sot
m-75
tit-10m .
iii-1.25] '
m-r sol
M"751
III-2 001
m-z 254
I'd-2.501
m-z 75+
m-s 00

 

0.90 d

0.00 4

0.70 d

0.60 -

0.40 ~

0.30 r

0.20 d

0.10 <

 

0.00

 
   
 

OldzBaseline + [g] = .75

Young: Baseline + [Q] = .75

 

Val-.25

Figure 5

 

m-so-
m-75~
m-mo .
um 25 .
m-rso -
um 75 4
01.2.00]
hit-2.25 «
iii-2.504
III-2.75 «
ms 00

Class- and age-dependent distributions of voter bliss points under various
parameter sets.

54

Appendix 3

Changing dominant strategies across different parameter spaces

55

 

 

 

 

 

 

 

 

Figure 6 Typical Nash strategy plots for centrist (left) and polarized (right) games.
Infinite strategy normal forms of the electoral game, for a highly homogeneous
population.

In each plot, the strategy chosen by candidate A is marked on the vertical axis,
and that chosen by candidate B is on the horizontal axis. Strategy combinations {1A, 123}
such that A wins are shown in white, whereas strategy combinations such that B wins are
shown in black. Combinations which yield identical or near-identical tallies for each
candidate are shown in grey.

Clearly, a weakly dominant strategy for candidate A would yield a horizontal
slice of the normal form in which, irrespective of candidate B’s strategy, A would win or
tie. Likewise, a dominant strategy for B would generate a vertical line along which A
always lost, or at best tied.

In the first frame, where information costs (and hence disutility and alienation)
are zero, and thus almost all agents vote, the median voter theorem result occurs. In this
frame, the dominant strategies are r A = 13 = i. In any restricted strategy space such that it
is not available as a strategy, the dominant strategy will be binding against the edge of the

available strategy space closest to i .

56

In the second frame, however, information costs are significant, and agents are
alienated by policy platforms distant from their bliss point. Again, there exists a dominant
strategy, '2 , which will beat or match any other strategy. However, although the strategy,
i is inferior to i , (in that the strategy combination {I A = in, =3 would yield victory
for A), if the strategy set is restricted to 1m >> { , then within that restricted space,

i would be the dominant strategy, rather that a binding constraint approaching i .

57

Chapter 3. Does Medicare make Us Healthy?

58

Section I: Introduction

Medicare was established in 1965 to improve the health care available to and
healthiness of elderly Americans. The policy was, essentially, redistributive, transferring
resources from the working young to the retired old. It has achieved its health care goals,
but at what cost? To evaluate this cost, it is not only necessary to examine the direct
costs of the system, but the indirect costs as well. Many studies have looked at various
ways to make the program cheaper and more effective (see, for example, Moon (1993),
Mazo, et a1. (1994), Aaron and Reischauer (1995) and Moon and Davis (1995)). Few
have examined the indirect costs. A notable exception is Wolfe (1993). These indirect
costs may be substantial if people during their working years postpone health
maintenance until their retirement, or, at least, reduce their expenditures on health
maintenance in response to the difference in the price of maintaining their health now
relative to the price of maintaining it once retired, and/or in response to their lower after-
Medicare-tax income. If people decrease their health care spending in their prime
working years, then they will be less productive during their work life, and they will enter
their retirement less healthy and less wealthy than they would in the absence of the
Medicare system. Thus, the demand for health care by the elderly may be higher than
would have otherwise been the case, and so the cost of maintaining the system could be
higher. A higher cost will lead to increased taxes on the young, reducing their after tax
incomes and their ability to invest in their own health creating a vicious cycle.

This paper develops an overlapping generations model (following Allais (1947),
Samuelson (1958), and Diamond (1965)) in which agents value health for both utility and

human capital enhancing reasons, as in Grossman (1972). Agents are assumed to be two

59

period lived, working in the first period, being retired in the second period. There are
two types of agents: high initial health status and low initial health status. High health
status is assumed to reflect high productivity and therefore high income. Young agents of
both types get utility from consumption and healthiness. Further, their income is a
function of their human capital which depends on their healthiness. The old get utility
fiom consumption and healthiness as well. Healthiness while old depends not only on
health maintenance while old, but also on health maintenance while young. The young
work, pay social security and Medicare taxes, and allocate their after tax earnings to
consumption, health maintenance, and saving for retirement. Health can be maintained
via investments in medical and non-medical care. Medical care may be subsidized by the
government. The old are retired. One lives throughout retirement with probability p,
which is type dependent, and dies at the onset of retirement with probability (l-p).
Retirees allocate the afler tax return on their savings and their social security benefits to
consumption and health maintenance. Medical care for the old is subsidized by the
government. These subsidies are funded by the taxes on the labor income of the young
and by taxes on the return to saving of the old or by lump sum taxes on the old; these
taxes are endogenous. Social security benefits are calculated as a percentage of earnings
while young. These benefits are funded by taxes on the labor income of the young and
taxes on the return to saving of the old or lump-sum taxes on the old; these taxes are also
endogenous. All savings of the short-lived old are left to their children. These bequests
are also taxed.

Previewing some of the results of the model: (i) a reduction in the price of health

care for the working population, either directly or via subsides, may increase steady-state

6O

Sect

healthiness of workers and retirees of both types, and may increase capital accumulation;
(ii) an increase in the Medicare subsidy rate need not improve the steady-state healthiness
of retirees, reduces the healthiness of the young and of the population on average, and
reduces capital accumulation; (iii) increasing the elderly’s share of the cost of the
Medicare system may improve the steady-state healthiness of workers and retirees, and

may increase capital accumulation.

Section II: The Model

Consider an infinitely-lived economy composed of two types of finitely-lived
individuals, and a government. The two types of agents differ in their productivity or
underlying health status. A new generation of each type of individual is born at the
beginning of each period t, (t = l, 2, 3....) and lives for two periods: youth and
retirement. Call this generation t and index type by i, i = 1, 2. Individual agents of each
type are ex ante identical, and face a type specific probability of death at the onset of
retirement of (1-p’)e[0, 1]. There is no population growth. Without loss of generality
assume N‘ of type 1 and N2 agents of type 2 are born at each date, N1 + N2 = 1.

Both types of agents in the first period of their lives work and divide their income
(labor income plus bequests) among current consumption, current health maintenance,
saving for old age, and payment of social security and Medicare taxes. An agent’s health
maintenance expenditures while young enhance his human capital, and thus augment his
effective labor. There are two types of health maintenance expenditures: medical and
non-medical. The former may be subsidized by the government. The latter can be

thought of as expenditures on exercise, nutrition, etc. Such life-style factors have been

61

shown to be important determinants of health status by Gilleskie and Harrison (1998) and
Kenkel (1991), among others. Furthermore, non-medical efforts at one point in time may
reduce the need for subsequent medical expenditures, as explored by Grembowski (1993)
and Stearns et a1. (1998). Although there is not a within-generational link between
medical and non-medical expenditures, there is a cross-generational link between
expenditures on health inputs and health status in this model.

At the beginning of the second period of a type i agent’s life he either lives, with
probability p’, or dies, with probability (1 -p’)." Agents alive in the second period of their
lives are retired. They divide their after tax returns to saving and their social security
benefits between consumption and health care; the medical care component of health care
is subsidized by the Medicare program. Agents who die at the onset of retirement
bequeath their wealth to their children Who are of the same type as their parents.'5 This

assumption allows the health distribution (or income distribution) to remain constant over

 

" Agents in this model face uncertainty about the time of death but not about the maximum possible length
of life. This implies that agents may die before they have exhausted their non-social security wealth, but

not vice versa.

’5 Bequests in this model are assumed to be unintentional, a function of not knowing one’s date of death,
rather than of the desire to make one’s children better off. This assumption is consistent with findings by
numerous researchers: see Hurd (1990), Auerbach, Kotlikoff, and Weil (1992), and Bdrsch-Supan (1993),
as well as the empirical findings of Altonji, Hayashi, and Kotlikoff (1992) that parents and their adult

children are not altruistically linked. But, other research finds an operative bequest motive (Hamennesh

62

time. This also simplifies the model by not having agents that are of a different type then
their parents, as otherwise the bequests would drive the results by generating the income

distribution over time.

Let the representative type i member of generation t’s preferences be represented

U’(t) = lnh;”(t) + lnc,’(t) + p’ lnh,”'(t + l) + p’ lnc,’ (t + l)
where h,” (t) is the health of a type i member of generation t while young, c,’ (t) is
consumption of goods by a type i member of generation t while young, h,"'(t +1) is the
health of a type i member of generation t while old, and c,’ (t + 1) is the consumption of

goods by a type i member of generation t while old.

Assume that a young type i member of generation t’s health is an increasing
concave function of his medical expenditures on health maintenance, m,’ (t) , and his non-
medical expenditures on health maintenance, e," (t). In particular, assume
h,” (t) = .f”m,’(t)”l'e,’(t)“', where ,u’, e[0,1] and vi e[0,l], 5” >0. cf” can either be
considered the initial health stock of the person when he is young, or equivalently, it can

represent his initial productivity type. Assume further that an old member of generation

t’s health is an increasing function of health while young and health maintenance

expenditures, both medical and non-medical, while old, m,’(t+1) and e,’(t+l),

 

and Menchik (1987) and Hurd (1995)), at least among the wealthy. Since the jury is still out, the

assumption of unintentional bequests will be maintained.

63

respectively. Assume h,"’(t+l)= @“mf(t+1)”"e,’(t+l)”’h,y’(t)fl where ,u', e[0,l] and
v; e[0,l] and ,B' e[0,l], If” > 0. 5"" is an age-specific shift to health.
The firms in this economy are perfectly competitive profit maximizers that

produce a single consumption good using the constant returns to scale production
function Y(t)= A(t)K(t)“ H(t)““, where A(t) >0 is a productivity constant, K(t)is the

capital stock at date t, H(t) = ZN ’(t)h,"’ (t) is effective labor at date t which is

comprised of labor hours, N ’ (t) of each type of agent, the productivity of which is

augmented by the workers’ health, h,” (t). Assume physical capital depreciates fully in

the production process. '6

Young type i agents produce medical health goods by converting current

consumption goods into medical health care at a constant rate 7:.“ , and produce non-

medical goods by converting current consumption goods into non-medical health care at
a constant rate 7:, . The government may subsidize the medical health care costs of the
young. If so, the type i young pay only (1— o" )% of their medical costs, the other
0"% is paid by the government. Type i old agents produce non-medical health care by

converting consumption goods into non-medical health goods at a constant rate 72,.

They produce medical health care by converting consumption goods into medical health

goods at a constant rate 7:", . Under Medicare financing of the medical care of the old,

 

’6 The production process is over the course of a generation. Since empirically the depreciation rate is

about 10% per year, capital is all but fully depreciated over the course of a 30 year generation.

64

type i old agents only pay (1— 0’)% of their medical care costs, while the other 6’ % is
paid by the government; 0 is the Medicare subsidy rate. The Medicare program does not
currently differentiate benefits by income, but one may view a higher level of 6’ as
analogous to the subsidy for the dually-eligible elderly who are enrolled in both Medicare
and Medicaid. Although the subsidy rate would be the same for all non-Medicaid
eligible elderly, the non-Medicaid eligible elderly can effectively lower their out-of-
pocket medical price by purchasing Medigap insurance, which we do not model.
Allowing 6 to vary by agent type allows for policy simulations of the effect of
transforming Medicare into an income-related program.

The government in this economy imposes a proportional, type specific, tax on the
wages of young workers, 1'] (t) , and a proportional, type specific, tax on the return on

savings of the old, 1’20), and/or a lump-sum, type specific, tax on the old, l’ (t). The

revenues from these taxes support both the social security system and the Medicare

system. Social security benefits are determined as a type specific fixed proportion, 4" , of
labor income while young. The Medicare system sets the type specific subsidy rate on
health care expenditures of the old, 0’ , and the level of benefits is determined by the
old’s medical care expenditures. The government funds its current expenditures with
current tax receipts, as under the current OASDI and Medicare programs.l7 Thus, it must

adjust the tax rates to ensure that its budget always balances.

 

'7 These programs are required to be in balance over the 75 year planning horizon. We impose the funding

balance requirement generationally.

65

1|

5 ,

III;

9!

The representative type i agent at date t takes as given the return on saving when

old, (1+ p(t+1)), the tax rates r[(t) and r’,(t+1)and/or l” (t+1), social security

benefits T(t+l), and bequests B(t). He chooses health care expenditures while young,

m,’ (t)and e,’ (t) , and old, m,’(t +1) and e,’ (t +1), and saving, s’ (t) , to maximize

l. lnh,” (t) + Inc,i (t) + p’ lnh,"’(t +1)+ p’ lnc,’ (t + 1)
subject to
2. We) = H'V’m.’ (0“? e: (0"

3. h,"’(t + 1) = Ho’m: (t + 1y”: e: (z + 1)“: Ma)”
4 c1(1) = h;"(t)(1- Tl(t)) + 3’0) - S’(t) - 7:...(1- 0’)m,’(t) - 71.810)
5. c,’(t +1) = (1 +p(t +1))(1 — r’,(t +1))s’(t)+ T’(t +1)

-r(z+1>-y:..(1— 6’)m:(t + 1)—ri.ei(t +1)
where constraint 4 encompasses the assumption that bequests are allocated equally across
all members of a type in a generation so that the bequest dependent wealth distribution is
rmiform as in Hubbard and Judd (1987). This assumption maintains the within type
representative agent assumption throughout time. Constraint 5 includes the assumption
that agents do not know the functional linkage between their work effort today and their

social security benefits when old. This follows from the fact that social security benefits

have both insurance and redistributive components, so increasing one’s wage income

66

q‘n
..I.‘::

5.1"
'1

:I ‘
‘mu

today and paying more social security taxes may not lead to proportionately higher
benefits tomorrow. '8

Substituting constraints 2 - 5 into the objective function 1 and maximizing yields
the first-order conditions of the type i agent’s problem with respect to medical goods and

non-medical goods while young, medical goods and non-medical goods while old, and

saving, respectively.

”:0 + m) + #gHrmxtr’r'ejor’i (1 — r20» -r;..(1 - a") = 0

 

 

 

 

 

 

6. . .
m: (t) c: (t)
7 v';(1+ p’fl’) + viHy'm: (0”? e: (0440 — rim) — r1. = O
' e.’ (r) c." (t)

8. fl; _7:n2(1—gi)=

m,'(t+l) c,‘(t+1)
9. Vi2 __ 722 =

e,’(t+l) c,'(t+l)
10. __ .1 +p(1+p(t+_l))(1—r,(t+1))=0.

c1(1) 01(1 +1)

To simplify the analysis, equations 6 and 7 can be combined to solve for e,’ (t) as a

function of m,’ (t):

 

’8 Further, while it is true that the Social Security Administration will provide future benefit information to
workers based on their lifetime earnings up to that point, they will not provide a schedule of how changing
one’s current income by working more hours or by increasing one’s human capital, and thus wage, will
affect one’s future benefits. This also suggests that individuals make human capital investment decisions

without reference to the effects thereof on their Social Security benefits.

67

. l l— i l .
11. e:(t)=3%(—i,)i'flim:(t>.

l yel

while equations 8 and 9 can be combined to solve for e,’ (t + 1) as a function of m,’(t +1) :
12. e,’(t +1) = 291972321171“: +1);
2 7 e2

non-medical goods and medical goods are consumed in fixed proportions while young

and old. Using equations 12 and 8, m,’ (t + 1) can be solved as a function of income when

old

13. m,'(t +1) = I. V3,. 1. [(1+p(t+1))(l— 1;)s’(t)+ T’(t +1)—€i(t+l)]
7220+ V2 +F‘2)

 

Equations 6, 10, 11, and 13 can be combined to yield a system of two equations in two
unknowns, m,’ (t) and s' (t) , which fully characterizes the type i agent’s problem.

The representative firm takes wages and rental rates as given. It hires effective
labor and capital until their marginal products equal their factor prices.
14. (l — a)A(t)K(t)“ H(t)“' = (1— a)A(t)k(t)“[N'h,y’ (t) + Nzhf2 (t)]""I = w(t)
15. aA(t)K(t)“" H(t)” = aA(t)k(t)“"[N‘h,”' (t) + N211;2 (t)]"“" = r(t)
where k(t) is the capital labor-hours ratio. Because of the assumption of constant returns

to scale and agents’ inelastic supply of effective labor, equations 14 and 15 also define

factor market clearing.

The government must maintain a balanced budget at each date t. To do this it
must adjust taxes to meet the Medicare subsidy bill,

Nlpll'luzglml-ral “I“ N21727:.292m12—1 (I) ,

its subsidy of the medical care of the young,

68

N ‘7L.0'M.‘ (t) + N 71.05"? (t),
as well as the social security benefit bill,
T' (t) + T’(t) = p‘N‘;‘h;V_',(t — l)w(t -1)+ p’N’gzhfio — 1)w(t — 1).
That is, at timetthe government must set r[(t), 1,2(1), r;(t), r§(t), €‘(t) and £20) to

satisfy

16. N 'h,” (0710) + N211,” (07? (t) + N 'r'2(t)(l + p(t))s'(: — 1)

+Nzr§(t)(1 + p(t))s2(t — 1) + p'N'll (t) + p2N2l2(t) =

N ‘p'rL29'm,’_. (I) + N ’p’riaBZMit (t) +

N'rl..a'm,‘(0 + N’rilozmflt) + p'N'Chr'rt — 1) + 1221112421212. (2 — 1) .
Clearly, given the Medicare subsidy rates, the subsidy rates on the health care of the
young, and the social security replacement rates, the government is only free to choose
five of the six taxes.

If a type i agent dies at the onset of retirement, his saving is bequeathed in full to
his heirs who must then pay tax on their inheritance. To maintain the representative
agent formulation bequests are equally divided among all the young of the same type
17- 3’0) = (1 - p’)(1 + 10(1))(1 - Ti (t))S'(t - 1) .

The goods market clears when demand for goods equals supply of goods. Goods
market clearing implies that the saving of the young today totally determines the capital
stock tomorrow.

18. N's'(t— 1) + N2s2(t -1) = Nk(t)
Also, by arbitrage
19. (1+ p(t)) = r(t).

69

Section III: Steady-state Equilibrium

A competitive steady-state equilibrium for this economy is a time invariant price
vector {w,r, p} , a time invariant allocation {m” ,m"’ ,e’” ,e‘” ,c” ,c‘” ,s’; i = 1,2} , such that
given these prices and allocations agents’ utility is maximized, firms’ profits are
maximized, and the government’s budget constraint is satisfied.

Equations 6, 10 - 15 and 17, for both types of agents, and 16, 18 and 19 defined at
steady-state characterize the steady-state equilibrium. Steady-state equilibrium is
represented by
20. ,u'](l + p’fl’)c"’ + pjhy’wfl — 7:) —yfn,(l - o")m” = O, i =1, 2
and
21. —c"’+p’r(l—r"2)cy’ =0,i=l,2
where

c” = (1 — a)A(N's' + stz)“(N'hy' + N’hyz)‘“h”

+ (1 —p’ )(1 — r'z)aA(N's' + stz)""’(N'hyl + Nzhfl)” s’
#1 + V'i

-s‘ —y;,(1—a’)(—,—]mr’ i=1,2

I

1
c” = —L— '[(l—z'"2)rs’ +C’hy’w—Z’], i=1,2
1+]u'2 +V'2J

i i 1 VI
h)” = 5W[7ml(li 0' )_V+] (myiyliflfr , i=1,2
el #1

w = (1 — a)A(N‘s' + stz)“(N'hy' + NW2)”

r =aA(NlSl +N282)a—I(Nlhyl +N2hy2)l-a

7O

and given the other tax and subsidy rates I: solves
N'hy'r} + Nzhflrf + N’r’zrs’ + Nzrirs2 + p'N‘IZ' +p2N2€2 =
N'p'ylnzbl'm‘” + szzyidflzmoz + N'yLla'my' + Nzyfnldzmy2 +
p‘N'g'hy' + pzNzgzh”.
Equations 20 and 21, while not analytically tractable, can be solved numerically

for the version of the model that most closely resembles the real world: the tax rate on

the young, 1', = 71W , adjusts to keep the government budget constraint balanced given
the taxes on the income of the old and lump sum taxes on the old. The baseline set of

parameters, listed in Exhibit 1, were chosen for the following reasons. For the price of

medical care for the young, 7:,” , we use the ratio of the CPI for medical care to the CPI,

which is approximately 1.5 (US Bureau of Labor Statistics, 1995). We assume that the

price of non-medical care, 7:], is lower both than the price of overall consumption and
medical care, since much non-medical care, such as exercise is free. Since the price of

medical care to the old, in terms of provider reimbursement, is somewhat lower than the

price charged for the same service to the young, we setyfn2 to 1.25, while leaving the
price of non-medical care for the old equal to that of the young. The Medicare subsidy
rate, 0, is, approximately, the share of medical health care expenditures (not including
nursing home expenditures) by the old that are paid for by Medicare or other public
programs (Hahn and Lefl<owitz, 1992). The social security replacement rate, C (C), is,
according to the Office of the Chief Actuary of the Social Security Administration, .42
for the average earner (.65 for the low wage earner). The Office of the Chief Actuary of

the Social Security Administration has also estimated the current aged-dependency ratio

71

at

COX

0

. -e
‘4
3‘8

’8’
I
:2.“-

to be in the neighborhood of .2. We duplicate this by assuming 70% of the population is
comprised of type 1 agents who have a probability of living into old age, p‘, of .215, and
that 30% of the population is comprised of type 2 agents who have a probability of living
into old age, p2, of .165. (In other words, N'p‘+N’p2=0.2.) The tax on the return to saving
was chosen initially to be equal to 10% for both types of agents since the average elderly
individual falls into a lower tax bracket than the average young individual. We hold the
lump sum tax to zero. The gs, us, vs and B were jointly chosen to yield a ratio of health
care expenditures by the old to health care expenditures by the young in excess on unity,
as found in the data (Hahn and Lefl<owitz, 1992).

The remainder of this section contains simulation results that summarize the
comparative static properties of the model. The first set pertain to policy parameters: the
Medicare subsidy rates, the social security replacement rates, and the tax rates, while the
others examine the cost of medical care, the cost of non-medical care, and the
demographic variables. Among the variables that are potentially affected, we focus on
the implications for capital and health levels because of the relevance of these variables

for the well-being of both the young and the old.

Result 1: (a) Economies with more generous Medicare systems for high productivity

(type 1) agents, higher 0' , have lower rates of saving, thus lower capital, less healthy
young of both types, healthier type 1 old, less healthy type 2 old, healthier old on

average, and a less healthy population overall. (b) Economies with more generous

Medicare systems for low productivity (type 2) agents, higher 02 , have lower rates of

saving, thus lower capital, less healthy young of both types, healthier type 2 old, less

72

I'm!
usbl

in i

from

""l‘
\u

care

healthy type 1 old, first more then less healthy old on average, and a less healthy

population overall.

An increase in the Medicare subsidy rate for either type of agent reduces after tax
lifetime income for both types of agent. Agents respond to this reduction in their income
by decreasing their expenditures across the board, which reduces their income further
since this reduces their human capital investment via both medical and non-medical care.
Further, by reducing the price of health maintenance when old, the relative prices of
capital and health maintenance while young are increased. So agents substitute away
from the now more expensive goods. The reduction of healthiness and capital
accumulation when young reduces income when old. However, since the price of health
care when old is now relatively lower for the targeted group, the old of that group spend a
higher proportion of their (lower) income on health care. While the policy does improve
the health of the targeted group, it does so at the cost of reducing overall healthiness. See
Tables 1a and 1b.

Two policy ramifications follow from these results. First, roughly 16 percent of
the Medicare population is dually eligible for Medicare and Medicaid (Aaron and

Reischauer, 1995). The Medicaid program may, at some level, be interpreted as

constituting a higher 62 for Type 2 agents. Second, even in the absence of the Medicaid
program, the proposal to means test Medicare benefits is equivalent in this model to a
reduction in the Medicare subsidy rate for the type 1 agents, as they have higher incomes
when old than type 2 agents. While this leads to a reduction in healthiness of the old, on

average, in steady state, it improves the health of the low health old. Further, it reduces

73

9".)
“5

f»;
“ibr

f

51

u.

a“

the tax burden on all the young, increasing their investment in capital and health
maintenance, thereby increasing the income of the old and hence their ability to invest in

their own health maintenance. See Table la.

Result 2: (a) Holding the comparative generosity of the Medicare system constant,

62 — 6l constant, economies with higher Medicare subsidy rates have lower rates of
saving, so lower capital, less healthy young agents of both types, more healthy type 1 old,
less healthy type 2 old, higher average health of the old, but lower healthiness of the

population overall. (b) Holding the relative generosity of the Medicare system constant,

6l /62 constant, economies with higher Medicare subsidy rates have lower rates of
saving, therefore capital, less healthy young of both types, more healthy old of type 2,

more healthy type 1 and average old, and a less healthy population overall. (0) Let

6l = 62 , economies with higher Medicare subsidy rates have lower rates of saving,
therefore capital, less healthy young of both types, first more then less healthy old of both

types, and a less healthy population overall.

As is shown in Table 2a, a policy of holding the comparative generosity of the
Medicare system constant biases the system towards the type 1 old as their subsidy rate
rises at a faster rate than that of the type 2 old. However, both groups of young see their
tax rates rising at the same rate. Consequently, type 2 agents are made worse off in every
dimension, since their lower after tax income reduces their expenditures across the board,
and reduces their saving so as to leave them with so much less to spend while old, even at

the lower prices, that their medical expenditures fall. While the type ls do benefit in old

74

heal:

\‘c

age from the higher Medicare subsidy rate, the population as a whole is made less
healthy. In contrast, a policy of holding the relative generosity of the system constant
favors the type 2 old across the board, and at most subsidy rates the type 1 old benefit as
well, as shown in Table 2b. This difference results from the second policy being less
generous than the first, which imposes lower taxes on the young, so they invest more in
their human capital, are more productive (and higher productivity by one group benefits
all), and thus enter old age relatively healthier. However, the better health when old is
bought by worse health when young.

Examination of Tables 2c(i) and 2c(ii) show that increases in the uniform
Medicare subsidy rate first lead to an improvement in the health of the old of both types
up to a subsidy rate of approximately .75; further increases lead to a worsening of the
health of the old (although expenditures on health maintenance by the old continue to
rise). These simulation results therefore suggest that the designers of the Medicare
system may have optimized the benefit to the elderly by not providing first dollar
coverage for all services. Since the health of the young and the average health of all
members of the economy are unambiguously improved by decreasing the Medicare
subsidy rate, reining in the Medicare system may lead to improvements in the overall
health and productivity of the economy for a relatively low concomitant reduction in the
health of the elderly. It is true that beneficiaries may avoid the first dollar coverage or
some increases in beneficiary liability by purchasing supplemental insurance. Indeed,
roughly 65 percent of Medicare beneficiaries have other or supplemental insurance that

covers Medicare deductibles and coinsurance, and 16 percent of beneficiaries have

coverage of these amounts through Medicaid. However, since 62 represents the

75

government’s subsidy of health care for the elderly, these additional sources of coverage
have more to do with the relative price faced by the elderly than with the government

subsidy per se.

Result 3: (a) Economies with higher Social Security replacement rates for high

productivity (type 1) agents, higher 4" , holding the replacement rate for type 2 agents
constant, have first higher then lower rates of saving for type 1 agents, lower rates of
saving for type 2 agents, and lower rates of capital accumulation overall, first more then
less healthy type 1 young and old, lower average health of the young, first higher then
lower average health of the old, and less healthy type 2 young and old. (b) Economies

with higher Social Security replacement rates for low productivity (type 2) agents, higher

{2 , holding the replacement rate for type 1 agents constant, have lower rates of saving
for type 1 agents, higher rates of saving for type 2 agents, lower rates of capital

accumulation, less (more) healthy type I (type 2) young and old, and less healthy old and

young on average.

While counterintuitive, saving may rise with the replacement rate since lifetime
income, for type 1 agents at low replacement rates, and for type two agents at all
replacement rates, rises initially with the replacement rate. As a result, all expenditures
rise, compounding the positive income effect. It is via this mechanism that average
health of the population can be improved via a more generous Social Security System for
the healthy (rich), but this is financed by making the unhealthy (poor) worse off (the poor

share in the costs without receiving any more of the benefits). Higher replacement rates

76

for the poor do improve the lives of the poor, but now since the rich do not receive a

share of the expanded benefits, overall health is not improved. See Tables 3a and 3b.

Result 4: (a) Holding the comparative generosity of the Social Security system constant,

C2 — 4" constant, economies with more generous systems have first higher then lower
rates of saving by type 1 agents, lower rates of saving by type 2 agents, with first higher
then lower capital overall, first more then less healthy type 1 young and old, less healthy
type 2 young and old, less healthy young on average, first more then less healthy old on

average, and a population that is first more then less healthy overall. (b) Holding the

relative generosity of the Social Security system constant, {2 /§' constant, economies
with more generous systems have first higher then lower rates of saving by type 1 agents,
lower rates of saving by type 2 agents, with lower capital overall, less healthy type 1
young, first more then less healthy type 1 old, less healthy type 2 young and old, and less

healthy young and old on average.

The effect of increasing the replacement rate schedule, so as to make the system
more generous, benefits type 1 agents as they see their lifetime incomes rise. Type two
agents who pay more than their share of the increase in generosity see their lifetime
incomes fall, and with it their ability to finance consumption and health care throughout
their lives. Again, to the extent that the overall healthiness of the population is improved,
it is done so to the cost of the poor. These results, in Tables 4a and 4b, point out why the
Social Security system is less redistributive than it appears. The poor do get a higher

replacement rate on their lower wages, but since they have lower life expectancies, their

77

taxes often subsidize the Social Security benefits of the relatively better off, rather than

vice versa.

Result 5: (a) Economies with more generous health care subsidies for the type 1 young,

higher 0' , have higher rates of saving for both types, therefore a higher capital stock, and

healthier young and old of both types. (b) Economies with more generous health care

subsidies for the type 2 young, higher 02 , have lower (higher) rates of saving for type 1
(type 2) agents, a lower capital stock, lower (higher) health for the type 1 (type 2) young
and old, first lower then higher average health for the young, and first lower then higher

average health of the old. (0) Holding the comparative generosity of the health care

subsidy system for the young constant, 0'2 — a"1 constant, economies with more generous
systems have higher rates of saving for both types, higher capital stocks, and more

healthy young and old of both types. ((1) Holding the relative generosity of the health

care subsidy system for the young constant, 0'2 /0l constant, economies with more
generous systems have higher rates of saving for both types, higher capital stocks, and

more healthy young and old of both types.

When the health care of the young is subsidized, they invest more in their health
which improves their human capital, which increases their wage (as well as the other
type’s wage), which increases output. Since type 1 agents outnumber type 2 agents, and
since each additional dollar type 1’s spend on health care increases own as well as
average productivity, these subsidies pay for themselves and benefit all. While such an

external effect exists for type 2 agents’ health expenditures, it is small. Thus, if type 2

78

'11.,“

5A.-
»

‘(J

”(4'

agents are specifically targeted they will benefit, and society on average may benefit as
well, although at the cost of the better off. See Tables 5a - 5d. These results suggest that
the current system of not taxing health insurance benefits is, potentially, beneficial to
society as a whole, at least at low subsidy rates. Clearly, the smaller the external effect of

the benefits, the less beneficial the program.

Result 6: (a) Economies with higher taxes on the saving of the old of both types,

higher 2”, , have lower rates of saving, lower capital, and lower health for all types at all
ages. (b) Holding the taxes on the saving of the old constant, economies with higher

lump sum taxes on the old, higher Z’ , have lower rates of saving for type 1 agents, higher
rates of saving for type 2 agents, and a higher capital stock, first more then less healthy
type 1 young, less healthy type 1 old, more healthy type 2 young and old, first more then
less healthy young on average, less healthy old on average, and a first more then less

healthy population overall.

An increase in the tax on saving reduces the return to saving in all its forms. It
also reduces lifetime income, thereby reducing expenditures when both young and old.
However, to keep the government’s budget balanced, the tax on labor income while
young must adjust, and it falls so agents see higher after tax wage income, inducing them
to invest more in both health maintenance and capital. The net effect on lifetime
healthiness and capital accumulation is, theoretically, ambiguous. The tax on saving
represents one measure of the extent to which the old pay for their own programs. This

suggests that holding the program constant and increasing the elderly’s share of the

79

financing burden may be detrimental to society as a whole in steady-state equilibrium if
the old pay for their programs via a tax on their savings. Even if the old’s share of the
program costs falls because the young’s share of the costs rises, there is no reason to
expect that healthiness of the young, healthiness of the old, and capital accumulation will
increase. This is because the increase in tax reduces agents’ income when young, and
thereby their expenditures on capital and health maintenance. These reductions are offset
all or in part by the increase in income when old, and so the overall effect is again
uncertain. Table 6a suggests that the uniform taxation of the returns to saving is never
beneficial. However, Table 6b shows that making the old pay a greater percentage of the
costs of the program via lump sum taxes can lead to improvements in the health of the
population, particularly the health of the poor. This suggests that holding the tax burden
on the old constant, but shifting from distortionary to lump sum taxation, could improve
the healthiness of the old overall.

Results 1-4 and 6 together suggest that increasing the generosity of programs for
the elderly does not necessarily increase the welfare of the old in steady-state
equilibrium. Clearly, when the increased taxes fall on the young, the first generation of
old benefit, since their benefits rise at no cost to themselves. The current young, by
paying for the increased benefits, see their disposable income reduced, reducing their
ability to invest in their own health, thus productivity, when young, and to save for their
retirement. For them, higher subsidy and replacement rates may translate into lower
overall benefits. Even when the increased costs of the program fall on the old, the
disincentives to saving are such that steady-state welfare may be reduced unless lump

sum taxes are possible.

80

These results seem at odds with casual empiricism that would suggest that
average health, at least measured in terms of life expectancy, has risen since the inception
of the social security and Medicare systems. This may indeed be the case, as
improvements in medical technology may have more to do with improvements in overall
healthiness than the social welfare policies designed for that purpose. However, as
Newhouse (1992) suggests, the Medicare system itself may have enabled or furthered

improvements in technology that might not have occurred in the absence of the system.

Result 7: (a) Economies with higher medical care costs for the young, higheryf,ll , have

lower rates of saving, lower capital, and lower health of all types at all ages. (b)

Economies with higher non-medical care costs for the young, higher 7:, , have lower rates

of saving, therefore capital, and less healthy young and old.

A higher price of health care, either medical or non-medical, for the young
reduces their total expenditures on health care, which reduces their income when young.
This income effect reduces capital accumulation. The reduction of healthiness and
capital accumulation when young reduces income when old, and thus health maintenance
and healthiness when old. See Tables 7a and 7b. This result does not suggest, however,
that the healthiness of the average American has fallen in the post war era during which
medical costs have risen faster than the CPI. It may be the case that the quality adjusted
price index, the true price index, for medical care has actually fallen. If this is the case
the average American should be healthier today. This would also be the case if the price

of non-medical health care has fallen faster than the price of medical care has increased.

81

Result 8: (a) Economies with higher aged dependency ratios, holding population

proportions fixed, and holding comparative probabilities of living into old age constant,

pI - p2 constant, have higher rates of saving for type 1 agents, first higher then lower
rates of saving for type 2 agents, higher capital stocks, more healthy type 1 young and
old, first more then less healthy type 2 young and old, and higher average health of young
and old. (b) Economies with higher aged dependency ratios, holding population

proportions fixed, and holding relative probabilities of living into old aged constant,

pI / p2 constant, have first higher then lower rates of saving by type 1 agents, higher
rates of saving by type 2 agents, first higher then lower capital stocks, first higher then
lower healthiness of type 1 young and old, more healthy type 2 young and old, and first

higher then lower average health of young and old.

As the economy ages the percentage of old in the population increases, and so the
costs of maintaining the programs for the old increase. This increases the taxes on the
young and reduces the bequests received by the young. Both effects lead to a reduced
incentive to save. However, when agents expect to live longer, they save more, both in
terms of human and physical capital, to finance their longer old age. When the latter
effect dominates for all agents, agents at all ages and of all types are healthier. However,
when the former effect dominates on a type, that type sees a reduction in lifetime
healthiness. See Tables 8a and 8b. Clearly, then, population aging in and of itself may

not lead to the demise of the Medicare program.

82

Section IV: Conclusion

This paper has analyzed the steady-state equilibrium effects of a social
security/Medicare program for an economy in which there are two types of agents,
effectively healthy (rich) and unhealthy (poor), where agents’ health is both utility and
productivity enhancing. While the quantitative effects of different funding regimes
differ, the qualitative effects were strikingly similar: increasing the generosity of the
programs for the old does not necessarily lead to increases in steady-state well-being,
although the initial old will benefit if the young pay the bills. Further, the funding of
increases in generosity may be disproportionately born by the poor, making what was
intended to be a progressive policy regressive. Medicare, in the absence of improvements
in health care technology, may make us less healthy.

These results do not mean that the system should be dismantled. The do,
however, point out that the appropriate level of spending must be valued at the margin. If
society as a whole values the elderly, and social welfare is enhanced by the old, whether
rich or poor, being ensured a minimum standard of living, then there may indeed be
welfare gains to having a Medicare program. However, the welfare gains of the program
need to be analyzed in equilibrium, and they need to be analyzed in contrast to the
welfare gains available from other possible health care programs, such as those that
subsidize the health care of the young. We cannot let transitional, initial generation
effects cloud our vision to the stark, unappealing reality that healthier, happier old people
today may come at the cost of less healthy, less happy young today and, possibly, less
healthy, less happy old tomorrow. Planning in full awareness of the societal costs needs

to be the order of the day.

83

Appendix 1

Baseline Parameter Values

84

Table 1 Baseline Parameter Values

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Good Health Poor Health
(i=1) (i=2)
Initial health stock when young (initial in = 1 gyz =
productivity type)
Elasticity of healthiness when young with respect v, = 2 V? = 2
to non-medical health expenditures when young
Elasticity of healthiness when young with respect ,u = 7 ”f = 7
to medical expenditures when young
Price of non-medical inputs for the young 7:” =3 73' :3
Price of medical care for the young 7 ’1'” = 15 7’2"l = 15
Government subsidy of health care costs of the 0' = 0.2 = 0
young
Probability of being alive at retirement pl =215 p2 =.165
Constant shift to health when old 4:01 = 1 4:02 = 1
Elasticity of healthiness when old with respect to v‘, :2 vi :2
non-medical health expenditures when old
Elasticity of healthiness when old with respect to .11; = 5 5 ll: :55
medical expenditures when old
Elasticity of healthiness when old with respect to '31 =5 ’32 =5
healthiness when young
Price of non-medical inputs for the old 7:2 :3 732 :3
Price of medical care for the old 7 L2 = 1-25 7 :2 = 125
Lump sum taxes on the old (I = g2 =
Medicare subsidy rate 91 =70 32 :70
Social security replacement rate 5’ =42 {2 =.65
Tax on return on savings of the old 112 :10 1.: =10
Number of agents (sum to one) N' =. N2 =3
Total Factor Productivity A = 5

 

 

85

 

Appendix 2

Simulation Results

86

Table la

The effects of changes in the medicare subsidy rate for high-productivity agents

era

moi

e01

hY1
[pa
If“
if“
h! (av.)

h? (av.)

lfi‘ni (av.)

1

0.05

0.017955

0.374947

0.0154082

0.106113

0.535638

0.15159

0.140351

0.24317

0.15159

0.336201

0.540455

0.111683

0.177336

0.123471

0.411823

0.164004

0.37052

0.15

0.0177065

0.367847

0.0151203

0.104117

0.525496

0.148739

0.154777

0.23924

0.148739

0.330741

0.533271

0.110209

0.18958

0.121161
0.406352

0.172646

0.367401

3

0.25

0.017394

0.358985

0.0147619

0.10163

0.512835

0.145185

0.172442

0.234332

0.145185

0.323924

0.524244

0.108359

0.203859

0.118285
0.399478

0.182679

0.363345

87

4

0.35

0.0169892

0.347612

0.0143037

0.0984442

0.496588

0.140635

0.19453

0.228032

0.140635

0.315176

0.512562

0.10597

0.220673

0.114604
0.390585

0.194421

0.357891

0

0

0

0

.45

.0164445

.332497

.0136975

.0942216

.474996

.134602

.222836

.219652

.134602

.303545

.496858

.102767

.240611

.10973
.378631

.208218

.350229

0

0

0

0

.55

.0156729

.311459

.0128589

.088364

.444941

.126234

.260125

.207971

.126234

.287339

.474636

.0982524

.264172

.10298

.361721

.224277

.338814

7

0.65

0.0144978

0.28026

0.0116257

0.0797186

0.400371

0.113884

0.310486

0.190592

0.113884

0.263244

0.440832

0.0914202

0.290843

0.0930357
0.336008

0.241885

0.320321

,5:

. 5..

.. n)

. .
vlifi.

.., m?

Table lb

The effects of changes in the medicare subsidy rate for low-productivity agents

eyl

m:31

901

m1
111/2
hol
hoe
11!! (av .)

h° (av.)

him) (av.)

1

0.05

0.0143493

0.276387

0.0114735

0.0786487

0.394839

0.112355

0.358697

0.0595036

0.112355

0.0821828

0.436559

0.0905596

0.322537

0.0386743
0.332759
0.252281

0.319346

0.

0.

0.

.15

.0143104

.275377

.0114338

.0783698

.393396

.111957

.357772

.0663048

.111957

.0915753

.435442

.0903347

.321505

.0418922

33191
252301

318641

0.

0

0.

.25

.0142613

.274103

.0113838

.0780179

.391575

.111454

.356603

.0748604

.111454

.10339

.43403

.0900505

.320202

.0458119

330836

.25229

317745

88

4

0.35

0.0141973

0.272444

0.0113187

0.0775601

0.389206

0.1108

0.35508

0.0859494

0.1108

0.118704

0.43219

0.0896803

0.318505

0.0507078
0.329437
0.252225

0.316569

5

0.45

0.0141105

0.270198

0.0112305

0.0769401

0.385997

0.109914

0.353011

0.100891

0.109914

0.139336

0.429692

0.089178

0.316205

0.0570244
0.327538
0.252057

0.314958

0.

0.

0

0.

0.

0.

0

0.

.55

0139858

266983

.0111045

0760533

381404

.108648

.350042

.122111

.108648

.168638

.426107

.0884572

.312907

.065535

324812

.251683

312624

0.

0.

0

0.

0.

0.

0.

0.

.65

0137917

262001

.0109094

0746801

374287

.106686

.345419

.154608

.106686

.213506

420526

0873361

307788

.0777242
.320569
.250847

.308949

 

 

. s:

.nn.

. k

IfufleHZa
The effects of changes in the overall medicare subsidy rate, holding the difference in low- I

and high-productivity rates constant

1 2 3 4 5 6

91 0.05 0.15 0.25 0.35 0.45 0.55

92 0.2 0.3 0.4 0.5 0.6 0.7

s1 0.0167819 0.0165443 0.0162455 0.0158587 0.0153385 0.0146022
n01 0.341836 0.33525 0.32703 0.316486 0.302477 0.282989
52 0.0140717 0.0138077 0.013479 0.0130587 0.0125026 0.0117331
n02 0.0968291 0.0949898 0.0926973 0.0897616 0.0858703 0.080473
e31 0.488337 0.478929 0.467186 0.452123 0.43211 0.40427
ex? 0.138327 0.1357 0.132425 0.128231 0.122672 0.114961
n61 0.131544 0.145025 0.161521 0.182126 0.208492 0.243145
149 0.449661 0.442359 0.433239 0.421529 0.405952 0.384231
e01 0.138327 0.1357 0.132425 0.128231 0.122672 0.114961
.52 0.621465 0.611329 0.598673 0.582427 0.560823 0.530711
104 0.506585 0.499734 0.491125 0.479986 0.465013 0.443833
10¢ 0.10475 0.103353 0.101601 0.0993376 0.0963032 0.0920249
h91 0.163604 0.174844 0.187935 0.203323 0.221522 0.242931
172 0.189604 0.186034 0.181588 0.175898 0.168363 0.157925
hY (av.) 0.386035 0.38082 0.374268 0.365791 0.3544 0.33829
h? (av.) 0.170039 0.177613 0.186364 0.196535 0.208365 0.221892
109E“ (av ) 0.350035 0.346952 0.34295 0.337582 0.330061 0.318891

89

Table 2b
The effects of changes in the overall medicare subsidy rate, holding the ratio between I

low- and high-productivity rates constant

1 2 3 4 5 6

61 0.05 0.15 0.25 0.35 0.45 0.55

92 0.0625 0.1875 0.3125 0.4375 0.5625 0.6875
31 0.0187875 0.0184533 0.0180184 0.0174228 0.0165323 0.0149017
mvl 0.399058 0. 389317 0.376764 0. 359798 0. 334 919 0. 290868
32 0.0163914 0.0159931 0.015482 0.0147947 0.0137944 0.0120436
mfl 0.112912 0.110161 0.106624 0.101858 0.0948973 0.0826528
eYl 0.570082 0.556167 0.538235 0.513997 0.478456 0.415525
eYZ 0.161304 0.157373 0.15232 0.145511 0.135568 0.118075
1601 0.146604 0.161045 0.17838 0.199287 0.223974 0.247896
1602 0.0831941 0.0972092 0.117204 0.148284 0.203996 0.336875
601 0.161304 0.157373 0.15232 0.145511 0.135568 0.118075
e°2 0.115053 0.134421 0.162047 0.204979 0.281917 0.465338
114/1 0.564554 0.554872 0.542287 0.525075 0.499388 0.452446
hfi 0.116646 0.114649 0.11206 0.108529 0.103283 0.0937628
1101 0.187222 0.19918 0.212629 0.227404 0.24214 0.248838
no? 0.0564502 0.0628952 0.0715439 0.0839878 0.104071 0.144436
hY (av.) 0.430181 0.422805 0.413219 0.400111 0.380557 0.344841
11° (av.) 0.154856 0.16545 0.17771 0.191908 0.207968 0.222999
hull) (av.) 0.384294 0.379912 0.373967 0.365411 0.351792 0.324534

90

Table 20(i)

The effects of changes in the overall medicare subsidy rate, holding the ratio between 3

low- and high-productivity rates constant

61, 92
$1
ngl

S2

11156

hot
h02
hy (av.)
h? (av.)

yuan» (av.)

1

0.

0.

0.

15

.0184957

.390549

.0160434

.110509

.557927

.15787

.161401

.0888726

.15787

.122894

.5561

.114902

.199729

.0588699

.423741

164866

380595

2

0.3

0.0178878

0.373021

0.01533

0.105571

0.532887

0.150816

0.189791

0.103759

0.150816

0.143451

0.53851

0.111284

0.221982

0.0650685
0.410342

0.183146

0.372476

0
0

0

0
0

0

0

91

.45

.0169692

.347054

.0142813

.0982883

.495792

.140412

.22964

.124212

.140412

.171681

.511987

.105853

.249778

.072625

.390146

.205933

.359444

4

0.6

0.0154246

0.304782

0.0125939

0.0865098

0.435403

0.123585

0.288212

0.153194

0.123585

0.211642

0.467491

0.0968047

0.283156

0.0812739
0.356285

0.23319

0.335769

0.

0.

0.

0.

0.

0.

0.

0.

O.

0.

.75

0123155

225027

00946975

0645191

.321467

.0921701

.372235

.19145

.0921701

.264296

.378046

0788373

308824

086679

288283

253843

282543

Table 2c(ii)

The efi‘ects of changes in the overall medicare subsidy rate, holding the rates for both 4

groups equal to one-another (detail)

hyl
th
hol
hoZ
hY (av.)
h? (av.)

Iflaui (av.)

1

0.75

0.0123155

0.225027

0.00946975

0.0645191

0.321467

0.0921701

0.372235

0.19145

0.0921701

0.264296

0.378046

0.0788373

0.308824

0.086679
0.288283

0.253843

0.282543

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

.76

0119948

217215

00916732

0623793

310307

0891132

378164

193886

0891132

267642

368811

0769978

308703

.086477

.281267

.253702

.276673

92

3

0.

0.

0.

0.00884764

0.

0.

77

0116521

20895

060116

2985

.08588

.383909

.196174

.08588

.270784

.35893

.0750315

.308043

.0861191

.273761

.253117

.27032

4

0.78

0.0112849

0.200196

0.00850971

0.0577216

0.285995

0.0824595

0.389365

0.198268

0.0824595

0.273656

0.348337

0.0729269

0.306735

0.0855803
0.265714

0.251999

0.263428

1' ‘ I
.~F, J
5").

a

Table 30

hol
hoZ
rfi'(av.)

hP (av.)

hum) (av.)

1

0.2

0.00103654

0.275296

0.0566425

0.248534

0.393281

0.355048

0.112768

0.689071

0.355048

0.975202

0.435352

0.202638

0.131144

0.364942
0.365538

0.189009

0.336116

2

0.3

0.0106217

0.291291

0.0300142

0.153068

0.41613

0.218669

0.262177

0.403793

0.218669

0.5658

0.452907

0.144335

0.258282

0.205876
0.360336

0.245311

0.341165

3

0.4
0.0137236
0.266725
0.012854
0.0832854
0.381035
0.118979
0.336628
0.204538
0.118979
0.283068
0.425818
0.0942646
0.30362

0.0996501
0.326352

0.253137

0.31415

93

4

0.5

0.0122033

0.220711

0.0054167

0.0463086

0.315302

0.0661551

0.342907

0.106477

0.0661551

0.146125

0.372956

0.0625048

0.288918

0.049647
0.279821

0.229699

0.271467

5

0.6

0.00960793

0.174958

0.00249875

0.0278399

0.24994

0.0397713

0.319768

0.0612581

0.0397713

0.083999

0.316982

0.0437742

0.253495

0.0274412
0.23502

0.197547

0.228774

0

0

0

0

0

0

0

0

The effects of changes in the social security replacement rate for high-productivity agents

.7

.00728646

.136585

.00126441

.0178485

.195122

.0254979

.287988

.0384103

.0254979

.0529979

.26654

.032068

.215629

.0165704
.196199

.166362

.191226

Table 3b

The effects of changes in the social security replacement rate for low-productivity agents

hol
hoZ
ffl'(av.)
f6 (av.)

h‘au’ (av.)

1

0.2

0.0214046

0.314005

0.000743595

0.0234231

0.448578

0.0334616

0.446077

0.0164076

0.0334616

0.0212054

0.477349

0.0387884

0.397642

0.0095042

0.345781

0.301578

0.338413

2

0.3

0.0202611

0.306911

0.00264203

0.0346046

0.438445

0.0494352

0.431694

0.0443387

0.0494352

0.0600596

0.469775

0.0509735

0.384832

0.0231803

0.344134

0.295324

0.335999

94

3

0.4

0.0186068

0.295884

0.00501802

0.046828

0.422691

0.0668972

0.410283

0.0802536

0.0668972

0.110079

0.457894

0.0629948

0.365631

0.0403133

0.339424

0.285115

0.330373

4

0.5

0.0166548

0.281937

0.00750286

0.0586907

0.402767

0.0838439

0.384188

0.120001

0.0838439

0.165368

0.442677

0.0737818

0.342134

0.0590495

0.332008

0.27207

0.322018

5

0.6

0.014632

0.266364

0.00977335

0.0691438

0.380519

0.0987769

0.356098

0.159534

0.0987769

0.220228

0.425415

0.0827518

0.316765

0.0774521

0.322616

0.257535

0.311769

.11

13316

---
4,“)
51$.»

(17
. .

:J-

a}.-

Table 4a
The effects of changes in the overall social security replacement rate, holding the

difference in low- and high-productivity rates constant

1 2 3 4 6

g1 0.2 0.3 0.4 0.5 .6 0.7

g2 0.43 0.53 0.63 0.73 .83 0.93

51 0.00103654 0.0106217 0.0137236 0.0122033 .00960793 0.00728646
601 0.275296 0.291291 0.266725 0.220711 .174958 0.136585
52 0.0566425 0.0300142 0.012854 0.0054167 .00249875 0.00126441
n02 0.248534 0.153068 0.0832854 0.0463086 .0278399 0.0178485
eY1 0.393281 0.41613 0.381035 0.315302 .24994 0.195122
eYZ 0.355048 0.218669 0.118979 0.0661551 .0397713 0.0254979
n61 0.112768 0.262177 0.336628 0.342907 .319768 0.287988
:42 0.689071 0.403793 0.204538 0.106477 .0612581 0.0384103
e°1 0.355048 0.218669 0.118979 0.0661551 .0397713 0.0254979
e92 0.975202 0.5658 0.283068 0.146125 .083999 0.0529979
104 0.435352 0.452907 0.425818 0.372956 .316982 0.26654
in? 0.202638 0.144335 0.0942646 0.0625048 .0437742 0.032068
h91 0.131144 0.258282 0.30362 0.288918 .253495 0.215629
172 0.364942 0.205876 0.0996501 0.049647 .0274412 0.0165704
hY (av.) 0.365538 0.360336 0.326352 0.279821 .23502 0.196199
hP (av.) 0.189009 0.245311 0.253137 0.229699 .197547 0.166362
109”» (av.) 0.336116 0.341165 0 31415 0.271467 .228774 0.191226

95

I...
I

. I
lit

ans

4
‘B

:x

.I. In

Table 4b
The effectsof changes in the overall social security replacement rate,

holding the ratio between low- and high-productivity rates constant

1 2 3 4

g1 0.25 0.35 0.45 0.55

§2 0.386905 0.541667 0.696429 0.85119

51 0.0145205 0.0160724 0.012522 0.0091789
myl 0.369305 0.308757 0.238324 0.181154
32 0.0414088 0.0173114 0.0090122 0.0053689
mYZ 0.189761 0.102515 0.0650436 0.0449875
614 0.527578 0.441082 0.340463 0.258792
ext?- 0.271087 0.14645 0.0929195 0.0642679
1091 0.290724 0.350052 0.334214 0.301627
11192 0.444254 0.239318 0.160887 0.121388
e01 0.271087 0.14645 0.0929195 0.0642679
692 0.635898 0.333859 0.221643 0.167078
1134 0.534749 0.47175 0.393549 0.324799
11112 0.167762 0.109019 0.0792855 0.0612513
1101 0.302812 0.32868 0.290734 0.245344
h°2 0.239454 0.120754 0.0762631 0.0542547
10’ (av.) 0.424653 0.362931 0.29927 0.245734
11° (av.) 0.287131 0.277218 0.237652 0.198049
h<all> (av.) 0.401733 0.348646 0.289 0.237787

96

.. .7... five
4 8‘. .‘u. .33 .n.

Table 5a

The effects of changes in the health care subsidy rate for young high-productivity agents

hy1
hfii
hol
1.102
by (av.)

h° (av.)

tflani (av.)

0.0136477

0.258321

0.0107655

0.0736662

0.369029

0.105237

0.341985

0.178312

0.105237

0.246231

0.416382

0.0865044

0.303997

0.0860867

0.317419

0.250064

0.306193

0.

0.

0.

0.

0.

0.

0.

0.

0.

.05

0152312

29911

0111397

0752715

.405935

.107531

.377651

.182962

.107531

.252769

.456675

0878196

342968

0884381

346018

.279972

33501

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

.1

0170788

348933

011531

0769349

.448628

.109907

.419012

.187799

.109907

.259575

.503209

0891737

389216

0908869

378998

315379

368395

97

0.

0.

0.

0.

0.

0.

0.

0.

O.

0.

0.

0.

.15

0192507

410443

0119396

0786569

498395

.112367

.467343

.192824

.112367

.26665

557367

0905662

44459

093435

417326

357679

407385

0

0

0

0

.2

.0218249

.487294

.0123659

.0804373

.556907

.11491

.524302

.198039

.11491

.273998

.620943

.0919964

.511554

.0960832
.462259

.408725

.453337

6

0.25

0.024904

0.584611

0.012809

0.082275

0.626369

0.117536

0.592072

0.203441

0.117536

0.281616

0.696305

0.093462

0.593443

0.098830
0.515452

0.471026

0.508048

Table 5b

The effects of changes in the health care subsidy rate for young low-productivity agents

02
S 1
“#1
S2
170/2
eY1
efi
mol

moZ

hol

1.102

by (av.)

h? (av.)

lfl‘L” (av.)

1

0.

0.

0.

05

.0133049

.255681

.0113167

.0825975

.365259

.112097

.337126

.189108

.112097

.261016

.413399

.0927624

.299663

.0931557

.317208

248553

305766

2

0.15

0.0125405

0.249667

0.0125511

0.10558

0.356667

0.128204

0.326155

0.214125

0.128204

0.295235

0.406568

0.107731

0.289877

0.110172
0.316917

0.2454

0.304997

3

0.

0

0

0

0

25

.0116544

.242455

.0139947

.138596

.346364

.148495

.313184

.245013

.148495
.337414
.39831

.127112
.278302

.132367
.316951

.242183

.30449

98

4

0.35

0.0106241

0.2337

0.0156998

0.188233

0.333857

0.174788

0.297716

0.284095

0.174788

0.390694

0.388187

0.153045

0.264493

0.162249
0.317645

0.239188

0.304569

5

O.

0

0

0

0

45

.00942472

.222926

.0177433

.267521

.318466

.210195

.279105

.335272

.210195

.460366

.375572

.18931

.247869

.204257
.319693

.237075

.305924

6

0.

0

O.

0.

55

.00803296

209462

0202561

.405429

.299232

.260633

.256516

.405845

.260633

.556382

.359546

.243295

.227676

.26714

.324671

.237443

.310133

Table Sc

The effects of changes in the overall health care subsidy rate for young agents,

holding the difference in low- and high-productivity rates constant

eyl

9w:

hol
hoZ
hY (av.)

h? (av.)

hlau) (av.)

0.05

0.2

0.0140473

0.289498

0.0130444

0.108146
0.392891
0.13132

0.360852
0.220367
0.13132

0.30399

0.446352
0.109558
0.327662
0.113533
0.345314

0.274665

0.333539

0

0

0

.1

.25

.0158117

.338218

.0135651

.110828

.434852

.134576

.40117

.226916

.134576

.313183

.492342

.111452

.372591

.117066

.378075

.309348

.36662

0

0

0

0

0

0

.15

.3
.0178934
.398451
.0141146
.113628
.483834
.137977
.448376
.233784
.137977
.322833
.545917
.113416
.426494
.120776
.416167
.350829

.405277

99

4

0.2

0.35

0.0203699

0.473817

0.0146942

0.11655

0.541505

0.141525

0.504123

0.240982

0.141525

0.332954

0.608871

0.11545

0.491812

0.124671

0.460845

0.400944

0.450861

0

0

0

O

0

.25

.4

.0233438

.569394

.0153047

.119597

.610065

.145225

.570588

.248519

.145225

.343561

.683568

.117554

.571853

.128756

.513764

.462187

.505167

6

0.3

0.45

0.026953

0.692466

0.015947

0.122768

0.692466

0.149076

0.650696

0.2564

0.149076

0.35466

0.773177

0.119728

0.671189

0.133035

0.577142

0.537996

0.570618

Tidfleifld
The effects of changes in the overall subsidy rate for health care when young, holding the

ratio between low- and high-productivity rates constant

1 2 3 4 5

61 0.05 0.1 0.15 0.2 0.25

02 0.1 0.2 0.3 0.4 0.5

31 0.014472 0.015318 0.016151 0.0169047 0.0174554
n91 0.292992 0.333925 0.382357 0.439599 0.506714
s2 0.0123595 0.0143614 0.0169276 0.0202993 0.0248658
as? 0.0952902 0.126738 0.174519 0.251291 0.38415
evl 0.397632 0.429332 0.464291 0.502399 0.542908
er? 0.122516 0.144843 0.174519 0.215392 0.274393
n61 0.366924 0.394106 0.423398 0.454272 0.485361
n62 0.206636 0.242915 0.29061 0.355391 0.447213
e01 0.122516 0.144843 0.174519 0.215392 0.274393
e02 0.285201 0.335074 0.400569 0.489418 0.615167
hYl 0.450116 0.487959 0.530387 0.577748 0.62998
102 0.101422 0.120949 0.147319 0.184376 0.239274
h°1 0.333195 0.366007 0.402652 0.443008 0.486133
tfifl 0.104102 0.128331 0.161989 0.210706 0.285121
by (av.) 0.345508 0.377856 0.415467 0.459736 0.512768
h? (av.) 0.276494 0.307182 0.343088 0.385513 0.436383
trend (av.) 0.334005 0.366077 0.403404 0.447366 0.500037

100

Table 6a

The effects of changes in the income tax rate for old agents

1 2 3 4 5 6

25,25 0 0.05 0.1 0.15 0.2 0.25
s1 0.0165007 0.0150784 0.0136477 0.0122243 0.0108241 0.009
mvl 0.267774 0.263842 0.258321 0.251199 0.242482 0.232
52 0.0135885 0.0121433 0.0107655 0.00946201 0.0082382 0.007
m 0.0842531 0.079005 0.0736662 0.0682698 0.062848 .057
evl 0.382535 0.376917 0.369029 0.358855 0.346402 .331
era 0. 120362 0.112864 0.105237 0. 0975283 0.0897829 .082
mol 0.385661 0.364374 0.341985 0.318686 0.294681 .270
m°2 0.216422 0.197075 0.178312 0.160223 0.142889 .126
e01 0.492083 0.468529 0.443706 0.417815 0.391066 .363
902 0.296137 0.270801 0.246231 0.222542 0.199832 .178
ml 0.426991 0.422591 0.416382 0.408312 0.398341 .386
hfl 0.0950299 0.0908466 0.0865044 0.0820183 0.0774024 .072
1101 0.335761 0.320596 0.303997 0.286117 0.267129 .247
1102 0.104146 0.0950019 0.0860867 0.0774527 0.0691448 .061
M (av.) 0.327403 0.323068 0.317419 0.310424 0.30206 .292
h° (av.) 0.278436 0.264762 0.250064 0.234472 0.218128 .201
111919 (av.) 0.319242 0.31335 0.306193 0.297766 0.288071 .277

101

fable 6t-

Tne et’fe

a?"

'l'.

Table 6b

The effects of changes in the lump sum tax paid by old agents

1',12

“3‘

n02
eyl
e42

mol

e01

hyl
hy2
hol
hoz
hY (av.)

h° (av.)

ruand (av.)

1

0

0

0

0

.0136477

.258321

.0107655

.0736662

.369029

.105237

.341985

.178312

.443706

.246231

.416382

.303997

.317419

.250064

.306193

2

0.01

0.0135925

0.262315

0.0124363

0.0810624

0.374736
0.115803
0.334288
0.199123
0.429428
0.27549

0.420879

.0865044 0.0924962

0.299863

.0860867 0.0967387

0.322364

0.24959

0.310235

3

0

0

0.

0

0.

0

0

0

0

0

0.

0

0

0

.02

.0134134

265534

.0143084

0890708

.379334

.127244

.325002

.221956

.412978

.307678

.424487

.0988019

.294208

108505
.326781

.248247

.313692

102

4

0.03

0.0130997

0.267933

0.0163993

0.0977338

0.382762
0.13962

0.314027
0.246962
0.394218
0.343022
0.427168
0.105434
0.286932

0.121479
0.330648
0.245982

0.316537

5

0.04

0.0126404

0.269466

0.0187265

0.107093
0.384952
0.15299

0.301253
0.274294
0.372997
0.38175

0.428878
0.112405
0.27792

0.135758
0.333936

0.242735

0.318736

6
0.05
0.0120237
0.270079
0.0213076
0.117191
0.385827
0.167415
0.286561
0.304104
0.349152
0.424086
0.42956
0.119722
0.267045

0.15144
0.336609

0.238433

0.320246

Table 7a

The effects of changes in the price of health care for young agents

104
h%2
if“
h02
hY (av.)

h? (av.)

111311) (av.)

1.;

0.0268252

0.761615

0.0211602

0.217193

0.725348

0.20685

0.672191

0.350481

0.87213

0.48398

0.818422

0.170029

0.707499

0.200352

0.623904

0.58198

0.616917

0.0228853

0.590684

0.0180523

0.168447

0.618812

0.176469

0.573462

0.299004

0.744035

0.412895

0.698215

0.145056

0.580084

0.16427

0.532267

0.47717

0.523085

3

1.2

0.0197959

0.468366

0.0156153

0.133566
0.535276
0.152647
0.496048
0.25864

0.643595
0.357157
0.60396

0.125474
0.48391

0.137035

0.460414

0.398059

0.450022

103

4

1.3

0.0173236

0.378344

0.0136651

0.107894

0.468426

0.133583

0.434097

0.226339

0.563217

0.312552

0.528532

0.109804

0.409585

0.115987

0.402914

0.336919

0.391915

5

1.4

0.0153108

0.3105

0.0120774

0.0885462

0.413999

0.118062

0.38366

0.200041

0.497777

0.276236

0.467122

0.0970458

0.350988

0.0993939

.0.356099

0.288719

0.344869

.5

.013647

.258321

.010765

.073666

.369029

.105237

.341985

.178312

.443706

.246231

.416382

.086504

.303997

.086086

.317419

.250064

.306193

Table 7b

hYl
hYZ
hol
hoZ
hY (av.)

h? (av.)

tflaui (av.)

0.0108069

0.235284

0.0153947

0.178374

0.33612

0.16988

0.300493

0.276875

0.389538

0.380857

0.390028

0.148137

0.266972

0.156581
0.31746

0.239651

0.304492

1.1

0.0114934

0.241113

0.0142591

0.14547

0.344448

0.152398

0.310795

0.250878

0.402936

0.345415

0.396767

0.130904

0.276169

0.136725

0.317008

0.241657

0.304449

3

1.2

0.012114

0.24623

0.0132439

0.120517

0.351756

0.137734

0.319947

0.228716

0.414868

0.315168

0.402641

0.116762

0.284338

0.120496
0.316878

0.243787

0.304696

104

0

0

0

0

0

The effects of changes in the price of exercise for young agents

.3

.0126758

.250745

.012332

.101177

.358207

.125266

.328111

.209596

.425533

.289044

.407796

.104973

.291621

.107027

.316949

.245934

.305113

.0131851

.25475

.0115097

.0859087

.363929

.114545

.335419

.19294

.435099

.266262

.412345

.0950132

.298141

.0957054

.317146

.248038

.305628

Table 8a

The effects of changes in the overall age-dependency rate, holding the difference in low-

and high~productivity rates constant
1 2

p1 0.18 0.2
p2 0.08 0.1
51 0.0012764 0.00279838
11171 0.127283 0.158119
32 0.0118309 0.0152635
mfl 0.105469 0.113806
6111 0.181834 0.225884
eY2 0.15067 0.16258
111°1 0.119705 0.162799
m°2 0.266224 0.291979
e°1 0.15067 0.16258
e°2 0.394256 0.42451
1171 0.2537 0.295304
hfl 0.111208 0.117291
11°1 0.109687 0.147593
11°2 0.133693 0.146607
11! (av.) 0.210953 0.2419
11° (av.) 0.113528 0.147419
11mm (av.) 0.198245 0.228172

3

0.22

0.12

0.00483014

0.183296

0.0175157

0.114465

0.261852

0.163522

0.204492

0.297911

0.163522

0.426719

0.327483

0.117766

0.183353

0.148692
0.264568

0.176785

0.250552

105

4

0.24

0.14

0.00716348

0.201879

0.0184839

0.109528

0.288399

0.156468

0.241852

0.288669

0.156468

0.408169

0.350384

0.114187

0.214331

0.142625

0.279525

0.19999

0.265722

Table 8b

The effects of changes in the overall age-dependency rate, holding the ratio between low-

and high-productivity rates constant

hY (av.)
h? (av.)

tflaL” (av.)

0

.215

.1

.00226528

.14895

.0158989

.116238

.212785

.166054

.150267

.301431

.166054

.438389

.28321

.11904

.135932

.151277

.233959

.138482

.21936

.215

.15

.0110061

.23953

.0135669

.088197

.342186

.125996

.304888

.220503

.125996

.3084

.394941

.0981224

.271575

.107792

.305896

.233875

.294118

.215

.2
.0172942
.281506
.00604969
.0500831
.402151
.0715473
.390073
.111415
.0715473
.149476
.442203
.0660289
.345941
.0525535
.329351

.262315

.317693

106

4

0.215

0.25

0.0191044

0.291543

0.00325423

0.0354003

0.416491

0.0505719

0.412614

0.0717036

0.0505719

0.0931268

0.453182

0.0517912

0.365387

0.0332269

0.332765

0.254912

0.318439

.215

.3

.0197055

.294038

.00214037

.0290246

.420055

.0414637

.419578

.0552992

.0414637

.070188

.455893

.0450699

.371152

.0253917

.332646

.241761

.315026

Chapter 4. Empirical Support for the Alienation Hypothesis in
US. Presidential Elections

107

Section I: Introduction

A great deal of academic debate within political economy in the past four decades
has centered on decisions of participation and abstention by rational voters. This paper
seeks to examine the empirical evidence for the existence of one factor in the
participation decision, that of alienation.

Alienation is the process by which voters who can discriminate between the
candidates on offer, but who feel that neither of the candidates is of high enough quality
will tend to abstain from the election. As such, alienation should also be separated from
abstention due to indifference, wherein the agent feels that the candidates (whether their
quality is high or low) are indistinguishable from one another, and thus are not worth
voting for.

Alienation is a function of the quality of the candidates on offer, and while it is
related to the institutional factors which propel conventional abstention, such as
opportunity costs and lack of information, it is distinguished from these factors by dint of
being the only form of abstention which candidate strategy (in terms of policy position)
can directly induce or diminish.

If the alienation hypothesis should be confirmed, there are considerable
theoretical and practical implications for candidate strategies and electoral outcomes.
While this paper concentrates on empirical support for alienation, it is worth noting that

theoretical treatments of the subject19 have yielded equilibrium non-convergence of

 

For example Anderson and Glomm, (1992).
l 08

policy platforms in vote-maximizing games, as well as providing evidence for polarized
campaign strategies in policy models.

The key implication of alienation is the introduction of a “loss of support” into the
candidate’s strategic model. Without alienation, as a candidate converges on the location
of his rival, he can only gain. Every step he takes towards his opponent will “convert”
some of his opponent’s supporters, or at least make them indifferent.

However, when alienation is a possibility, the candidate is aware that any move
will not only increase his support among the voters he is moving towards, but will also
diminish the participation rate of those he moves away from. Essentially, it means that
the tails of the voter distribution (outside of the pair of candidates) are no longer
“guaranteed supporters”, but rather are “potential supporters” whose support must be
wooed every bit as assiduously as those in the traditional battleground between the
candidates.

As a consequence, candidates are less likely to be willing to converge, unless the
reward to convergence, in terms of additional votes, is greater than the losses incurred in
the tails. When it is considered that party activists and donors are generally more extreme
than their parties’ candidates, the costs of convergence may easily outweigh the benefits,
even when the distribution of voters is centrist.

However, there is, as yet, no clear evidence that alienation is a significant factor

in US politics. Firstly, participation studies in the literature of voting have concentrated

109

on the environmental and demographic factors which influence turnout and individual
behavior, rather than the role of the candidates’ strategic decisions.20

Secondly, the whole question of alienation is subject to the rational voting
paradox. If theory implies that candidate strategies should be essentially identical, and
that the motivation to participate on strategic grounds is effectively zero, how much
support can there be for a model that differentiates agents in terms of their participation
responses to strategic alternatives?

To deal with these problems, I intend to present a simple model of participation
which is not subject to the rational voting paradox, but which instead describes rational
participation and abstention. The paradox itself is described in Section II, while the
model of voter behavior is outlined in Section 111.

Section IV then contains the results of a series of econometric analyses of voting
behavior from the 1980-1988 Presidential elections, and finds that not only is alienation
apparent in voting tendencies, but that this behavior is not accounted for by conventional

demographic or institutional factors. Section V offers some indications as to the nature of

the voter’s strategic decision-making process.

Section II: The rational voting paradox, alienation, and participation

The key question here is the strictly limited one of whether alienation is a

significant factor in the behavior of voters in US presidential elections. Alienation has, in

 

2° The most notable attempts at candidate placement implications have naturally (given the post-

Downsian emphasis on convergence and the lack of rational participation) centered on the effects of third

110

the past, been disregarded on the basis that it constitutes a problem only when dealing
with rational voters, and as, under the “rational voting paradox” no such voters exist,
alienation is no more than a theoretical irrelevancy.

Voters whose motivations are drawn from non-strategic, irrational motives may
be alienated, but not on the grounds of rational analysis of candidate placement. As such,
abstention through irrational alienation lies beyond the scope of this paper.

Any reasonable analysis of the question of alienation must also, at least implicitly,
act as a partial answer to the rational voting paradox. This paradox is a direct
consequence of the conclusions of Downs’ seminal 1957 work. Downs found that, within
a simple model of rational voting behavior and rational candidate strategy, (a) there
would be no difference between the policy positions of the two candidates and (b) agents
would be aware that their impact on the election was effectively zero, while participation
would in some sense be costly.

As such, participation resulting from candidate placement should be negligible,
and candidate differentiation should be minimal. As a consequence, neither the
candidates nor the voters should possess any significant strategic motive.

This does not necessarily mean that there are no rational grounds for participation,
and hence that turnout would be zero. Rather, it implies that there are no rational
strategic reasons to participate, and there are no rational strategic motives for candidates
to separate themselves in the case of simple two-party elections.

While in the intervening years many authors have demonstrated limiting cases

within which these conclusions are invalid, these have relied upon highly specific

 

candidates. See Alvarez and Nagler (1995) or Whitten and Palmer (1996), for example.
11 l

K: I "
ham.

behavioral or environmental conditions. When politicians are motivated by factors other
than victory, or when there are n>2 participants, etc., the Downsian result may be
overturned. However, these form exceptions to a much more general rule, that of non-
participation and candidate convergence.“

Thus, this paper employs a simple model of the US election, as a single-shot game
(and thus devoid of reputation effects, credibility issues etc.). Likewise, the description
will be of a two-candidate race, without the possibility of the entry of third candidates.

Such a model is not without its flaws, but is a reasonable analog for US
presidential elections. Separate US presidential elections are generally felt to have limited
dependence on one-another, essentially based upon the limited attention span and short
memory of the archetypal voter. Furthermore, although there exists a history of third
candidates in presidential elections, these candidates have, with the exception of Ross
Perot, mainly been of trivial importance to the electoral outcome. In the case of Mr.
Perot, whose campaigns lie beyond the chronological scope of this paper, it has been
shown22 that the primary impact a “serious” third candidate is to split the race into a trio
of two-candidate races, within which voters behave as they would in a true two-candidate
election.

For the same reason of simplicity, candidates will be considered as lacking an

exogenous policy preference. Thus, their motivations are omitted. This restriction does

 

Consider, for example, Gutowski and Georges (1993) or Osborne (1993).
For example by Alvarez and Nagler (1995).

112

not necessarily alter their strategic behavior”, and has the benefit of removing the
distortionary effects of an arbitrarily-defined policy preference.

Clearly, in a model subject to the rational voting paradox, alienation can have no
real meaning, as strategic motivations in voting behavior have already been eliminated.
Thus, for alienation to be a significant issue, the paradox must be overcome.

Let us assume for the moment that there are factors which overcome the paradox
of rational voting. What effect does this have on voters, and in particular on the
importance of alienation? If we assume that voters do have a rational motivation for
participating in the election, this implies that they once again possess the ability to
distinguish candidates from one another, and to choose between them, based on the
candidates’ policy positions.

The vital question is thus what form of strategic motivation the voters possess.
However, it is most reasonable, I feel, to argue that if strategic motivation re-appears as
the result of factors which overcome the rational voting paradox, then those factors
should encompass the strategic motivation as well.

Thus, I intend to present a simple model, based upon an disaggregated version of
Downs’ own work, in which participation is rational, and in which alienation is a

possible, but not necessary, outcome.

 

23 As in Alesina (1988), wherein convergent or semi-convergent credible manifestos could be

generated under either single-shot non-ideological games, or under multi-shot games with ideologically
motivated politicians.

113

Section III: A simple model of participation

The Downsian view of participation may be expressed as follows. Turnout (at the
aggregate level) is a function of the closeness of the race (R), the importance of the
election (I), the difference between the candidates (D) and the costs (social, economic
and otherwise) of participation (C). As such, turnout (T) is expected to take the form:

T = (R x I x D) — C
[3.1]

Thus, all things being equal, turnout will be higher when the race is close, when
the election is important, and when the candidates are highly differentiated. The level of
turnout will be lower when the net costs of participation are large. All in all, this seems a
reasonable interpretation of group motivation to participation.

An individual voter’s likelihood of participation (Pi) should be based on that
individual’s estimation of the closeness of the race (R1), the importance of the election to
the voter (Ii) and the voter’s perception of the difference between the candidates (Di), as
well as the voter’s personal costs from participation (C1). The average of each of these
individual terms should be the respective group term, and thus the turnout rate should be
the average likelihood of participation by members of the population.

If interest is focussed on the first three terms in the agent’s decision, the closeness
of the race, the importance of the race and the difference between the candidates, then the

paradox appears valid. Given even trivial costs of participation, it is hard to justify a

114

claim that for an individual agent, who knows that his vote has effectively zero mass
relative to that of the population, the benefits of voting outweigh the costs.

However, in a more complex model, especially one in which the agent’s costs are
considered in detail, the conundrum becomes less plausible. Firstly, an additional term
should be entered into the agent’s calculation of the benefit of voting. The agent must
consider the effectiveness of his vote on the outcome, as well as the election’s potential
effect on him. Thus, the benefits of participation increase in closeness, importance and

candidate differences as before, but decrease in the size of the overall voting population.

Thus:

Pim(RiXIiXDi)—Ci
N

 

[3.2]

Secondly, and equally importantly, the agent’s costs must be considered. The
costs an agent faces in voting may be considered in three separate categories. There are
physical and economic costs, such as the time taken, any loss of income incurred, and the
physical effort required. These costs may reasonably be treated as lump sums. There are
also social costs, both to participation and to abstention. It is reasonable to suggest that
these costs are also lump sums, and that they are negative for those individuals for whom
the social costs of abstention outweigh the social costs of participation. Lastly, there are
ideological costs. These reflect the disutility generated by voting for a candidate who is
less than the voter’s ideal, and the risk of the election of a less-preferred alternative who

is even further from the voter’s bliss point.

115

The lump sum costs are particularly important. It has been argued“ that there
exist social benefits from voting which may offset the physical and economic costs of
participation. These social benefits may be considered as negative costs, and are
distributed across the population, such that given the political environment and even a
voter’s ideal policy, two otherwise identical voters may participate differently. The one
who attaches high value to the social benefits of voting may participate in the election,
but the other, whose overall lump sum costs are positive, does not.

The ideological costs reflect a voter’s distaste for having to vote for a candidate
who does not ideologically agree with the voter’s own bliss point. It is reasonable to
assume that these costs are likewise distributed across the population, but the
distributions are not dependent on the political persuasions of the voters they cover.

A useful baseline in considering the magnitude of these costs would be that they
are such that for those agents who gain the greatest social benefit from voting, even the
most distasteful possible preferred candidate would not be so unpleasant as to generate
positive overall costs. However, as some individuals gain almost zero social benefit fiom
voting, those individuals would face positive overall costs even when the ideological
costs were approximately zero, and hence would abstain even under “ideal”
circumstances.

Thus, the agents costs may be considered to take the following form:
C.- = 71+flx1-xll

[3.3]

 

For example by Owen and Grofrnan (1996) and many other post-Downsian writers.

116

where 71, the fixed costs and benefits of voting, may be positive or negative, xi represents
the ideal policy for agent i, and xi. the policy of the preferred candidate. f 'x, —x: l thus
represents the disutility caused by any difference between agent i’s bliss point and the
policy position of the preferred candidate, where f > 0.

Furthermore, the agent is aware that by not voting, he makes the election of the
less preferred candidate more likely. However, by the same logic which generates the
paradox to start with, the agent also knows that his personal decision has a negligible
effect on the outcome, once the voting population is large. This assumption, however, is
critical when confronted with concave agent preferences. Let us assume that voters do
possess social cost structures which make them consider voting. Let us assume that they
also possess some policy preference, and that part of their motivation to vote consists of a
desire to see that policy (or one close to it) succeed in the election. If their aim is to
maximize some form of utility which is dependent upon the policy outcome, and given a
concave form for this utility function, it is clear that the agent will in general choose the
candidate whose position lies closest to the agent’s bliss point.

However, the agent must be aware that there exist two candidates, and hence that
by not voting for the preferred candidate, the agent makes the success of the less-
Preferred candidate more likely. If the two candidates are separated from one another by
a fixed distance, this leads to a problematic conclusion.

When the candidates are close to the agent’s bliss point, the agent can see little
difference between them (in terms of utility gained from the success of the preferred

caIldidate over the less-preferred alternative). When the pair lie further from the agent’s

117

bliss point, however, the voter now sees a great difference between the possible

outcomes, and thus has a far greater motivation to participate:

Agent Utility
L
AUI .........................

     
 

AU,

 
  

 

 

I
I
I
r
I I I I
I I I I
l 1 I I I
I I I I
I I I I
I I I I
I I I I
I I I I
I : : : : .
x x ' ' Candidate
[ Candidate Candidate Placement
| pairl pair 2 (x)
Agent’s Bliss Point
Figure 1 Proximity- and distance-sensitivity over candidate pairs.

AS Ax is the same for the potential candidate pairs 1 and 2, but AU. is far smaller than

AUz. it would follow that voters with these preferences would have a much greater

incentive to vote in a competition between pair 2 than between pair 1.

If this is so, then the following conclusions would seem reasonable:

’ Given the location of either candidate, the greater the separation between the

candidates, the more likely it is that the voter will participate

118

o The effect of the preferred candidate coming closer to the voter’s bliss point should
be smaller than the effect of the less preferred candidate moving away (as the slope of

the utility curve would be far greater further away) by an equal displacement

Hence, given the separation of the pair of candidates, the closer that the pairing lie
to the voter’s preference, the smaller the difference in utility between the two outcomes,
and hence the less likely that the voter will participate. In other words, alienation should
be impossible, as those who should be alienated (i.e. those distant from the candidates)
are in fact those with the greatest incentive to participate.

However, this is all predicated on the assumptions of uniform costs and that
voters participate so as to bring about some particular policy. If alienation is present in
electoral behavior, then there must exist some reason why voters whose bliss point lie far
from the policy position of their favored candidate choose not to vote, while their more
satisfied compatriots do vote. For such behavior to be rational, it must be true that either
the dissatisfied voters face higher costs or lower rewards from voting.

Three alternative explanations could generate alienation under these
circumstances. Firstly, it is possible that the voters do not face uniform costs, and that

their costs are dependent on their position relative to those of the candidates. Secondly, it
is Possible that voters only consider the location of the preferred candidate in deciding to
VOte, i.e. they disregard the risk that their abstention will increase the likelihood of the
lesS-preferred candidate being elected. Lastly, they may consider both of the candidates’

Positions, but their preferences may be drawn over a convex political utility function,

119

such that they are more sensitive to changes in the location of candidates close to their
bliss points.

In order to test these rival hypotheses, and indeed to determine whether alienation
is present at all, I have adopted a form of the Downsian participation framework as the
basis of a simple model of participation.

From Eq. 3.2, it is apparent that the “rewar ” to voting, within this context,
should be based upon the importance and closeness of the race in question, and the
difference between the candidates. However, the importance of the race and the closeness
of the race are both independent of the voter’s location on the policy spectrum.25 The
difference between the candidates, and particularly the relative separation of the
candidates from the voter, clearly is dependent on both the voter’s location and the
voter’s perceptions of the candidates’ positions.

The difference between the candidate’s locations (relative to that of the voter)
may be seen to be D, = “x, — xAl - Ix, —— xBII. Thus, the reward to participation may be
considered as:

(RixlixDi)=(Rixli)xD

 

 

N N "
= [(Ril) +£,)X D,
N

= (§+£,)x||x, -xA|-|x,. ‘30:”
[3.4]

where x, and x3 are the policy positions of candidates A and B.

120

Now, consider the position of the party preferred by agent i (either xA or xB,

whichever is closest to xi) as being denoted by xi", and the position of the less preferred

party by xi'. The distance between X, and xi‘ is then 55,. , and the gap between X, and x{ is

As has been stressed previously, it is vital to know whether the agent’s response
to changing candidate positions is linear, proximity sensitive or distance sensitive. Thus,
the rewards to participation, as expressed in Eq. 3.4 may be rewritten as:

(07 + s,)x (p.55; —,6,5t°,‘)
[3.5]
where 6], ,6) > 0.

If 61:62, then the voter’s response is linear, whereas if 6962, the agent’s response

is distance-sensitive, and if 69,61, the agent’s response is proximity-sensitive.

From equations 3.3 and 3.5, it may be seen that
P. .. «a + 6.1x 044- - 4.2:))-(r. + 71x. - 8|)
[3.6]
hence
P. 0c (67 + admit? —((&’ + 81-).32 + f)?! —r.-

[3.7]
Which is valuable to us, as if (3+e,)/7, >((67+c,),62 + f), then 61>,62, whereas if

(c? + 5, )fl. < ((6 + 2, )fl. + f) then either flz>fl1 or fis large.

\

25
Note that this does not imply that these values are constants, merely that their individual values

depend upon matters other than the location of the voter on the policy scale.

121

Thus, by comparing the voters’ participation rates to differences in the candidates’
positions, we posses a test which should indicate whether the agents are distance
sensitive, or alternatively either proximity-sensitive in their response to policy issues or
strongly proximity-sensitive in their ideological costs.

This model, derived as it is from Downs’ simple model of turnout, treats
candidate placement as exogenously determined. From a theoretical perspective, this is
invalid. Given rational voters, we can only assume the presence of rational politicians.
Rational politicians, aware of the process by which voters determine whether or not to
vote, should choose their positions so as to maximize their utility, presumably by being
elected.

However, such a view of political actions has two inherent flaws for the purpose
of this paper. Firstly, by making candidate placement an endogenously determined
characteristic, the model loses the simplicity and flexibility which gave it its elegance.

Secondly, while the best available dataset with corroborated evidence of
participation and abstention (the NES survey) contains 2000 individual data points per
year, it can only contain a single candidate placement pair per election, and thus the issue

of candidate placement is starved of data.

Furthermore, it has been widely argued that candidate placement is not solely, or
even primarily, determined by considerations of electoral strategy. While undoubtedly
Such considerations are important, internal party politics and the wishes of the usually
SIl‘lall, ideologically motivated grassroots of the party are paramount in the selection of
the party's candidate, and that candidate’s choice of policy position. Further anecdotal

evidence of this may be seen in the lack of total convergence which characterizes US.

122

elections. In electoral games in which victory is the dominant motivation for candidates,
the equilibrium outcome is almost uniformly convergent at something approximate to the
median voter.

A further impediment to incorporating candidate strategy is that what is most
important, in general, is voter’s perception of the candidates’ strategies, rather than those
strategies per se. While constructing a theory of candidate placement is difficult,
constructing one from the voters’ perceptions of candidate strategies is all but impossible,
and certainly would prove an inadequate base from which to try to draw empirical
conclusions.26 Thus, in this paper, I intend to treat candidate strategies as exogenously

given.

Section IV: Testing for the presence of alienation

The question of the presence of alienation implies three subsidiary questions, all
of which must be answered to some degree in order to understand the interaction of
Candidate placement and voter abstention.

Firstly, there is the question as to whether or not voter behavior appears consistent

With the presence of alienation. For this, all we require is that voters whose preferences

are markedly different from those of the candidates are less likely to participate.

K

26 o
Attempts to "reveal" either the voters’ true preferences or the candidates true positions have either

had to rely upon the (dubious) assumption of sincerity, or have otherwise proved inconclusive. Dasgupta
(1 996) demonstrated simultaneously the theoretical possibility and practical uncertainty of attempting to
reVeal the tactical motivations behind candidate strategy.

123

Secondly, we must ask whether or not it appears that this voter behavior is caused
by alienation, or rather by some other institutional or strategic factor. To answer this
question, the agents behavior must be conditioned upon their age, sex, income and level
of interest in the political debate.

Lastly, if it appears that alienation is responsible for some of the observed
behavior of voters, we must ask what form of strategic preference and implicit cost
structure lies behind the observed alienation. In order to do this, is necessary to try to
establish whether the agents utility functions over political questions are proximity
sensitive, or whether the agents simply consider the location of the preferred candidate,
and thus ignore the less preferred candidate, and his potential effect on policy, or
whether, instead, the agents’ costs are proximity-sensitive to a sufficient degree to
overwhelm conventional distance-sensitive utility functions. Any of these three
hypotheses could justify rational alienation, however, their implications for the nature of
voter behavior and hence candidate strategy are widely different.

The data used in this paper originated in the National Election Survey (NES)
under the auspices of the Inter-university Consortium for Political and Social Research
(ICPSR)27, covering the 1980, 1984 and 1988 US presidential elections”. The survey for
these years consist primarily of a pair of interviews, each lasting about 1 hour, and the

Vote Validation Survey, wherein the registration records of the respondents were checked

27 Inter-university Consortium for Political and Social Research, PO Box 1248, Ann Arbor,

glichigan 48106
- Data from the 1992 and 1996 elections were omitted, as the definition of voter participation was
ne lther internally consistent nor reasonably reliable, as data from actual registration records are not
a"ailable for 1992 and 1996. Although a summary variable (constructed by the interviewer) for
Participation does exist, it is only comparable with the previous self-evaluation of participation rather than
e Cross-checked registration record.

124

to determine exactly who had voted (rather than relying on the highly inaccurate basis of
the respondents’ claims to have voted).

Survey households were selected based upon a complex weighting system derived
from US Census data. Individual respondents from these households were selected on a
random basis.

The data for each year contains responses from approximately 2,000 interviewees,
each of whom (other than those who failed to respond to repeated requests) was
interviewed twice, once in the three months prior to the election, and once in the three
months after the conclusion of the campaign. To a large degree, these interviews were
close to the actual polling day (e.g., during the 1988 survey, 55% of the post-election
interviews had been carried out by November 21st, and 82% by December 5th).

While it was naturally impossible to interview all of the initial respondents after
the election, overall approximately 87% of the sample were interviewed on both
occasions. Of those who were not re-interviewed, however, the majority still yielded
some post-election information via the vote validation survey.

The validation survey was deemed successful in approximately 95-98% of the

Cases, the remainder representing a mixture of those who did not give their name, or
Whose registration records were unavailable.29
From the wealth of information obtained in these interviews, certain variables are

0f prime interest to the question of candidate placement and voter behavior. First among

¥

29 Naturally, there also existed a sizable group for whom no registration records could be found

(approximately 15% of the survey cases), but these were reasonably classed as non-voters in most cases.
unherrnore, validation was not carried out on all respondents if the respondent in question claimed to be
unzible or unwilling to vote (for example, those who claimed not to be registered), as the tendency to vote

125

these, of course, is the outcome of the validation test: i.e. whether or not the agent
actually participated. Secondly, there are a conventional set of terms covering the agent’s
demographic and economic characteristics. Thirdly, there are a range of political
questions, fiom which the agent’s views may be determined.

The validation results are obviously of vital importance, as only they reveal the
actual participation or abstention of the voter, rather than simply the indicators for likely
participation, such as interest in the campaign, party membership etc.

The demographic and economic variables are largely self-explanatory. Principal
within the group are terms for age, sex, race and income. The age variable simply
enumerated the respondents age, either as given to the interviewer, or as estimated by the
interviewer. Sex was taken to be equal to zero for female respondents and one for males.
Race was based on a score of zero for non-white respondents and one for whites, the
classification again being either that which was given by the respondent or that which
was estimated by the interviewer.

The income variable recorded the middle income (in 1984 dollars) within 23
bands from an income of less than $3000 per annum (treated as zero dollars) to over
$90,000 (treated as $100,000) per annum. Of the interior bands, eleven were located at
annual incomes of less that $20,000, with seven more for incomes between $20,000 and
$50,000, leaving three bands for incomes between $50,000 and $90,000.

The political variables consist of a number of non-candidate attributes, such as
interest in the campaign, party affiliation (if any) and the respondent’s level of

information about the election, and two scales based upon candidate placement. These

 

while claiming not to is considered trivial by comparison to the likelihood of not voting while claiming to

126

two scales are a 7-point Liberal:Conservative scale on which the respondent must place
themselves, along with the two nominees, and a thermometer scale, which measures the
respondent’s satisfaction with the nominees, other leading figures and the two political
parties. While the Liberal:Conservative scale is technically a purer representation of
candidate placement, it suffers from being only a uni-dimensional measure of position,
whereas the thermometer reading, serving as a proxy for a multi-dimensional placement
system (such that the worse a candidate’s thermometer score, the greater the overall
separation of that candidate’s multiple positions from the agent’s preferred positions)
may be considered a broader and (as a 100 point scale)3O more refined representation of
voter approval of the candidate’s policy positions.

A number of subsidiary variables were created from these two placement scales to
convert them into the relevant measures of distance and quality. In the case of the
Liberal:Conservative scale, this process consisted of determining the distance between
the respondents’ self-assessment of their locations on the scale and the respondents’
views of the candidates’ positions.

For the thermometer scale, more information was available in the dataset. As well
as the nominee’s thermometer scores (both before and after the election), respondents
also gave scores (prior to the election) for the parties themselves, as well as for three
alternative “leading lights” from both parties”. Clearly, these scores are not directly

analogous to a distance scale. Nevertheless, it seems reasonable to assert that an ideal

 

have participated.

3° Although many respondents stuck rigidly to S-point increments, rendering it a 20-point range
instead.
3 ' Typically, these were the individuals among the leaders of the parties who either stood for

nomination or might have been expected to stand. As such, over the course of the three presidential

127

candidate, one who matched the respondent perfectly on every issue, would score a
perfect 100, while a candidate who uniformly opposed the respondent’s views would be
given a zero. Thus, the measure of distance-to-candidate was formed simply from the
difference between an ideal candidate (who would score 100) and the actual nominee’s
score.

As can be seen from Table 1a, using the thermometer scale, few respondents
(20% of those surveyed) gave the best available candidate a score of over 90, while very
few (less than 10%) gave the less-preferred candidate a score in the range 0-10. Indeed,
while 75% of the respondents gave their preferred candidate a score between 70 and 100,
the distribution of scores to the less-preferred candidate was approximately uniform.

Thus, most voters avoided the temptation to polarize their stated views of the
candidates. The mean score of the preferred candidate was approximately 76, while the
mean for the less-preferred rival was about 40. The perceived separation of the candidate
scores appears to be distributed in a manner close to a truncated normal (the more
significant truncation being at 0, and less significantly at 100) around a score of

approximately 30-40, but with significant tails out to a separation of > 90.

 

elections covered, several names recurred (e.g. George Bush, as Vice Presidential nominee for Ronald
Reagan and as Presidential nominee in his own right, in 1988.

128

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From Table lb, it can be seen that analogous patterns appear in the data
concerning the Liberal:Conservative scale. The mean distance to the preferred candidate
is approximately 1.0, while the mean distance to the less-preferred candidate is nearly 3.
The apparent anomaly that the mean separation of the candidates is more than 2.6 (and
hence close to the mean distance to the less-preferred candidate) is explained by the
number of respondents (850 from a total sample of 5911) who felt that they were
straddled by candidates on either side of their own position.

As outlined above, the dataset was tested so as to offer answers on three issues;
whether or not dissatisfied voters are less likely to participate than those who are pleased
with their preferred candidate, whether or not such behavior is accounted for by
alienation, or rather by institutional and demographic factors, and if alienation is found,
the form it seems to take.

As a starting point, Table 1c shows the average probability of participation among

individuals with given positions on the Liberal:Conservative scale.

Table 1c Average participation in different self-assessed political positions

Liberal :Conservative

Placement (1-7) 1 2 3 4 5 6 7
Participation Rate 70% 65% 63% 59% 66% 71% 75%
(Number Of (217) (433) (623) (802) (1083) (735) (364)
respondents)

Voters were asked to place themselves on a 7 point scale from 1 (extremely liberal) to 7
(extremely conservative). As can be seen, there is little overall difference in participation
between the two tails of the distribution, while it appears that participation was lower

among those in the middle-ground.

130

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Testing the null hypothesis that the mean participation rate for groups 3, 4 and 5
(62.9%) was in fact the same as the mean for the other groups (70.3%) led to the rejection
of the null hypothesis at the 5% and 1% levels.32

This “softness” of support in the center is consistent with either a proximity-
sensitive or distance-sensitive model of voter participation, as centrist voters are most
likely to be “straddled” by the two parties and thus face different but equivalently
distasteful alternatives.

It should be noted that the vast majority of respondents placed the candidates
within the range of 3-5, i.e. in broadly centrist positions. Thus, while the highest
participation rates were seen at the extremes of the scale, this was not the location chosen
by most candidates.

In a more complex framework, Table 2 shows the results of a series of regressions
performed on the 1980-1988 combined dataset, in which recorded participation (as
opposed to claims of participation) was regressed upon terms relating to the distance
from the respondent’s position to that of the best candidate on offer (a measure of sub-
optimality), and the difference the respondent perceived between the two candidates (a
measure of candidate dil’ferentiation).

It should be noted at this stage that as the behavior modeled in this paper concerns
discrete choices, it would be natural to conduct the analysis using a Logit or Probit
technique, rather than OLS and the linear probability model.

However, the coefficients derived from such analyses are not easily translated into

intuitively meaningful values, and when the dataset is conventional (especially in that the

 

32 The 95% confidence intervals for the participation rates among members of the mid-range and the

131

majority of predicted participation rates fall between 25 and 75%), the results of the OLS
and Logit regressions should be similar around the mean predicted participation rate. For
ease of interpretation, the results presented in the body of the paper are from OLS
regressions. Appendix 1 details a comparison of the results gained from Logit, Probit and
OLS techniques, and demonstrates that the results are not significantly affected by the
choice of modeling strategy.

From Table 2, it is clear that for any of the first four models, using either pre-
election (model A) or post-election (model B) data, or comparing the candidates to one
another (model C) rather than to the ideal, or using the Liberal:Conservative scale (model
D), the same pattern is consistently replicated, other than in model C, where an inferior
measurement of candidate quality is used, as described below. In all of the other models,
as candidate quality falls, so does participation. Likewise, as the difference between the
candidates increases, participation will rise. It should also be noted that the constant term
dwarfs the effects of placement, even if candidate quality was to move from 0 to 100 (or
0 to 7 for the alternative scale), or if candidates were to converge completely from the
political poles.

Such results are consistent with the preliminary expectations laid out so far. That
the constant term is very large relative to the placement terms is neither surprising nor
worrying, as the coefficients still are significant and remain the only characteristics under
the candidate’s control. The constant, in these sparse regressions, encapsulates all of the
demographic, social and non-strategic political characteristics of the voter and the

election.

 

whole survey being (61.0% to 64.7%) and (64.6% to 67.4%) respectively.
132

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Theory and intuition tell us that the separation of the candidates should be
significant, and that as candidate differentiation increases, so should the incentive to
participate.

Most important, obviously, is the result on the quality (as measured by the
distance to the preferred candidate) term. As the quality of the best available candidate
falls (i.e. the distance increases), so does participation, even given the separation of the
two candidates. Thus, as the voter becomes more distant from a pair of candidates who
are set a fixed distance apart, the voter becomes less likely to vote, not more.

Models A and B are clearly mutually supportive. The slight difference in
coefficient values between them may readily be attributed to the overall decrease in
voters’ opinions of the candidates after the election, such that candidates seemed more
inferior (lowering the coefficient on lack of quality) and less different (increasing the
coefficient on separation) than before.

These models indicate that improving the quality of the preferred candidate by 1°
before or after the election would lead to a .19% or .17% increase in the likelihood of
participating. Similarly, increasing the perceived separation of the candidates by 1°
would have led to a .14% or .15% increase in participation.

Model C, which compares the potential candidates to one another, rather than to
the ideal, contains a somewhat greater coefficient on candidate separation (at .19%
increase in participation per 1° increase in separation), but a markedly lower (.07% per
1°) coefficient on quality. Furthermore, this coefficient is insignificant at the 5%, 10% or

even 20% confidence levels.

134

It transpires that this weakness is in fact primarily a function of the modified
quality variable in use in model C. Whereas the previous quality term measured the
difference between the best nominee and the ideal candidate, in model C it compares the
candidates to the best of a small group of leading politicians. Given an almost infinite
number of potential candidates, there should exist at least one who would score a 100 on
the thermometer scale. If a respondent feels that none of the eight nominees and leading
politicians deserves a high score then that (highly dissatisfied) agent would appear to
have a very low sub-optimality score as measured by model C, but his or her displeasure
becomes apparent under models A and B. For those agents who already felt that one of
the eight possibles was very good, the effect of changing the definition of preferred-
candidate sub-optimality from model A to model C is negligible.

Model D offers broadly similar results to models A, B and C33. In this case, a 1-
point increase (on the 7 point Liberal:Conservative scale) in the distance between the
voter and his or her preferred candidate translates into a 1.5% decrease in the likelihood
of participation, while a 1-point decrease in the separation of the two candidates would
lead to a 4% decrease in participation. The marginally lower level of significance of these
results may well be attributable to the problem of modeling a multi-dimensional process,
such as the decision to vote, through a uni-dimensional scale (the candidate’s placement
on the Liberal:Conservative scale). For agents to whom liberality is not a key issue,
model D says little, whereas for those to whom it is vital, the same evidence will appear

(along with further information) in the multi-dimensional thermometer scale.

 

3’ Furthermore, to demonstrate that the results described so far are not merely the result of the terms’

mathematical construction, if the above regressions are run with a mixture of the two scales (thermometer
and Liberal:Conservative (which are mathematically unrelated» the same general patterns do emerge.

135

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Furthermore, given that the Liberal:Conservative scale encompasses only seven
distinct positions, as opposed to 100 on the thermometer scale, we would expect the
coefficients from the thermometer-based regressions to be approximately 1/14th the size
of those from the uni-dimensional scale. However, it is apparent that the coefficients
from the Liberal:Conservative scale are considerably smaller than this expectation. This
would seem to lend further credence to the belief that the Liberal:Conservative scale is at
best a weak proxy for candidate (and voter) placement.

Owing to the inherent flaws in models C and D, as well as the smaller
independent sample for model B, model A was retained as the “baseline” against which
alternative regressions were tested.34

The two E-models, in which participation was regressed solely on the score of the
preferred (model E1) or less-preferred (E2) candidate, must be considered together.
Comparing E1 to E2, clearly the effect of a 1 degree increase in the quality of the
preferred candidate leads to a far greater increase in participation (model E1, (32%))
than a corresponding decrease in the quality of the worse candidate (E2, (.14%)). This
result is completely at odds with the hypothesis that voters are sensitive to distance, not
proximity. This difference between the coefficients is sufficient to reject the null
hypothesis that the values are equivalent at the 5% level.

Despite these promising results, it must be acknowledged that demographic

characteristics are highly significant in determining the agent’s likelihood of

 

3’ Although model B is based on only a slightly smaller sample, it is dubious to claim that those

individuals who were “lost” from the sample were identical to those who were retained. As would be
expected, they tended to have a lower level of interest in politics, and as a result were less likely to

participate, as well as having markedly different views of the candidates, as compared to the sample as a
whole.

136

participation. Table 3 shows the effects of the presence of key demographic terms on the

coefficients for sub-optimality and candidate separation.

Table 3 Candidate placement and quality coefficients in the presence of assorted
demographic characteristic terms.

Model : Adjusted R2, Prob > Coefficient on Coefficient on Demographic
(number of F-stat distance to preferred candidate Terms Present
observations) candidate (S. E.) differentiation (S. E.)

0.0166 0.0000 -.00189 .00137

A (5217) (.00047) (.00029) None
0.0747 0.0000 -.00072 .00174 Age, sex, race,

F (4611) (.00049) (.00030) income

Note: Income is based upon the median income from the respondent’s selection of one of approximately 22
income bands, based on 1984 incomes.

Clearly, in model F, (which contains data on age, sex, race and income) the
candidate placement coefficients are significantly different from model A. In model F,
however, preferred-candidate sub-optimality is significant only at the 15% level. This
would, initially, appear to suggest that the candidate quality term acts as a proxy for age,
and hence that agents use candidate differentiation (which remains significant at the 5%
level) as the sole determinant of their strategic (as opposed to social) behavior.

This does not, however, appear to be the case. The reason that sub-optimality is
no longer significant is that there is a correlation (with a correlation coefficient of -.114)

between age and suboptimality, as shown in Table 4:

137

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Table 4 Regressing preferred-candidate sub-optimality on: age, sex, race and
income

 

 

suboptimality Coef. Std. Err. t P>It| [95% Conf. Interval]
age I -.1187465 .0138451 -8.577 0.000 -.145889 -.091604

sex I .5254114 .5315969 0.988 0.323 -.5167502 1.567573

race I .9049686 .7051564 1.283 0.199 -.4774452 2.287383
income I .0000148 .0000159 0.931 0.352 -.0000164 .0000461
constant I 27.49609 .8825369 31.156 0.000 25.76594 29.22625

Thus, older voters regard their favored politicians more highly, and as a result, if
age and suboptimality are both present in the regression, the significance of suboptimality
is greatly diminished. Note: this effect is not present for race, sex or income, just age.

This could, however, be taken as an indication that suboptimality was serving
merely as a proxy for age. This seems not to be the case, in the light of age-specific
results obtained from subsequent heterogeneity testing.

The population was split into four age-based quartiles, with the following age
ranges: group 1 = (17 to 29), group 2 = (30 to 40), group 3 = (41 to 58) and group 4 = (59
to 99). Table 5 shows the results obtained by nmning model specification F, which
includes age, sex, race and income data, and four age-specific regressions on sex, race

and income.

138

Table 5 Candidate placement and quality coefficients within specific age groups.

Group Adjusted R2 Prob >

Coefficient on Coefficient on Age range
F-stat distance to preferred candidate
candidate (S. E.) differentiation (S. E.)
(Model F) 0.0747 0.0000 -.00072 .0013? 17-99
(.00049) .00029)
1 0.0416 0.0000 -.00170 .00230 17-29
(. 00089) . 00060)
2 0.0308 0.0000 -.00175 .00154 30-40
(.00087) .00059)
3 0.0418 0.0000 -.00063 .00090 41-58
(. 00085) . 00056)
4 0.0369 0.0000 -.00218 .000924 59-99
(.00084) .00056)

As can be seen, the results are broadly consistent for groups 1, 2 and 4, and
appear to overcome the problems shown by model F, but not for group 3. In group 3,
neither the coefficient on candidate quality nor that on candidate differentiation is
significant at the 5% or 10% levels. Indeed, neither of the placement-based coefficients is
significant even if the other is not present at all.

It is initially difficult to explain why this particular group should respond in such
a markedly different manner from the other groups in the dataset. The problematic
behavior appears to be centered around a group of approximately 500 individuals with
ages between 44 and 51 (i.e. if the 2'“I and 4th quartiles are "stretched" to incorporate
those aged 40-43 and 52-58 respectively, then the revised 2“‘1 and 4th groups still generate

results consistent with those in Table 5).

139

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This group does not appear to be demographically, economically or politically
different from the rest of the sample”. The only respect in which they differ
meaningfully from the sample as a whole or from the groups above and below them is in
the effect of the respondents who "dropped out" between the first and second interviews
(but whose verification data remains available, even though they were only interviewed
once). If model F, with which concern over age-related problems arose, is re-run in the
absence of those who dropped out of the survey (as in model G, below), then although
age remains a significant term, it no longer interferes with the coefficients on either
suboptimality or candidate differentiation. Very similar results are obtained by deleting

only those respondents whose age lies between 44 and 51 (model H), as can be seen in

Table 6.

Table 6 The effect of eliminating specific age groups or interview dropouts

Model Adjusted R2 Coefficient on Coefficient on Demographic Restrictions
(number of distance to preferred candidate terms present
observations) candidate (S. E.) separation (S.E.)

P 0.0747 -.00072 .00137 Age, sex, race, None
(4611) (.00049) (.00029) income

G 0.0718 -.00121 .00135 Age, sex, race, Nodropouts
(4441) (.00051) (.00034) income

H 0.0771 -.00106 .00163 Age, sex, race, Age <44 or
(4120) (.00052) (.00032) income >51

This leads to the possibility that the "problem" with the respondents in the third
quartile relates not to their voting behavior or their political views, but rather, in some

manner, to their reaction to the survey. Specifically, it may be the case that their scores

 

3’ With the exception that they are slightly more conservative than the rest of the sample, but their

140

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reflect either a flippancy of a lack of honesty in their responses. This suggestion appears
to be borne out incorporating a measure of honesty into the sample selection criteria.

During the second interview, respondents were asked whether or not they voted,
and this was then checked, as part of the vote verification survey. Comparing the claim of
participation to evidence of participation, a new variable, truth, was constructed, with
value 1 when the respondent's answer appears to be a lie, and zero if the respondent
appears to have told the truth.

It should be noted that the number of confirmed liars amounted to only
approximately 7% of the population of either the survey or the 3rd quartile.

Survey participants who did not take the second interview were coded as truth=2.
These individuals may have been prepared to tell the truth or lie, but in the absence of a
second interview, it is impossible to tell.

However, by simply omitting respondents whose truth score was 1 (i.e. who
definitely lied), and hence retaining all those respondents who either told the truth or who
did not attend a second interview, the coefficient on suboptimality is significant at the 5%
level across all age groups (model I) and within the third quartile (model J), as can be

seen in Table 7.

 

behavior is not replicated within other, equally conservative subsets of the data.

141

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Table 7 The effects of eliminating liars

Model Adjusted R2 Coefficient on Coefficient on Demographic Restrictions
(number of distance to preferred candidate terms present
observations) candidate (S. E.) separation (S.E.)

F 0.0747 -.00072 .00137 Age, sex, race, None
(4611) (.00049) (.00029) income

1 0.0959 - . 00113 .00184 Age, sex, race, No confirmed liars
(4229) (.00049) (.00030) income

.1 0.0512 —.00164 . 00101 Age, sex, race, No confirmed liars,
(1028) (. 00081) (. 00054) income 3" quartile only

It transpires that the cause of these problems lies not in the number of dishonest
individuals within the four quartiles, which are almost identical“, but rather in the nature
of their dishonesty.

The mean suboptimality score for the sample as a whole is approximately 23.8
(i.e. a candidate score of 76.2), and this mean is not politically or statistically
significantly different from the means of the honest members of the 1St 2nd and 4th
quartiles (24.4 average) or the dishonest members of those groups (23.4) or the honest
members of the 3rd quartile (23.0). It is, however, very different from the mean of the
dishonest members of the third quartile (17.9). A test of the null hypothesis that the mean
score of 1St 2"d and 4’h quartile liars is equal to that for liars in the 3rd group can be easily
rejected at the 1% level.

While there is no apparent explanation as to why one particular age range should
contain individuals whose dishonesty is so radically different from that of the sample as a
whole, it is clear that the presence of such behavior generates an apparent and

problematic correlation between age and suboptimality which is derived primarily from

 

For example, there are 96 confirmed liars in the 3rd quartile, among a total number of 423 liars.

142

the irresponsibility of the dishonest members of the 3rd quartile, rather than from any
underlying political or demographic characteristics.

As such, once this unreliable data has been dropped, a proximity-sensitive picture
once again emerges, even in the presence of the conventional set of demographic
predictors of participation (as in model I in Table 7).

Similarly, if the same tests are performed on models derived from the
Liberal:Conservative scale, and hence from model D, then when the age characteristic is
present (as in model K) it again removes the significance of the sub-optimality term, as

seen in Table 8:

Table 8 Candidate placement and quality coefficients in the presence of assorted
demographic characteristic terms, as measured on the Liberal:Conservative scale.

Model: Adjusted R2, Prob > Coefficient on Coefficient on Demographic Terms
(number of F-stat distance to preferred candidate Present
observations) candidate (S. E.) differentiation (S. E.)
0.0175 - .0152 .0394
D (3492) 0.0000 (.0077) (.0053)
0.0589 - .0149 .0331 Age, sex,
K (3156) 0.0000 (. 0089) (. 0055) race, income
0.0777 -.0224 .0346 Age, sex,
L (2892) 0.0000 (. 0086) (. 0053) race, income

Note: Model L omits those respondents who were demonstrated to have lied about their
participation.

Again, the decrease in the significance of suboptimality between models D and K
is largely attributable to the presence of members of the third age quartile who transpire
to have lied about their participation, as in was the case with the thermometer scale. In

model L, as with model I in Table 7, removing proven liars from the sample greatly

143

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increases the significance of the coefficient on the distance to the preferred candidate.
However, the inherent weakness of the uni-dimensional Liberal:Conservative scale
makes models D, K and L less informative than the thermometer based equivalents
(models A, F and I from Tables 2 and 7).

If the minimalist E-models are combined, and participation is regressed against
just the score of the better candidate and the score of the worse candidate (as in model M
in Table 9a), or against those terms and the demographic characteristics (model N in
Table 9a), then again a proximity-sensitive view of participation emerges.

If we continue to assume that the candidates’ scores are some form of proxy for
their positions relative to the voter, then proximity-sensitivity would indicate that if the
gap between the candidates was fixed, but the candidates moved closer to the voter, the

voter should have more incentive to vote.

Table 9a Candidate placement coefficients in the presence of assorted
demographic characteristic terms.

Model: Adjusted R2, Prob > Coefiicient on Coefficient on Demographic Terms

(number of F-stat Preferred Less-Preferred Present

observations) Cand. (S. E.) Cand. (S. E.)

0.0191 .00339 -.00159 None
M (5318) 0.0000 ( . 00038) (. 00029)

0.0769 .00259 -.00190 Age, sex, race,
N (4618) 0.0000 (. 00040) (. 00030) income

Although the value of the coefficient on the preferred candidate falls in the
PIESence of the demographic characteristics (model N), it remains considerably larger
111311 that on the less-preferred candidate. The coefficient on best candidate’s score is

0.0026, and that on the worse is -0.0019. Consequently, if the thermometer scores of both

144

candidates rose by ten degrees (i.e. both candidates moved closer to the voter’s
preference by the same amount), then the net effect would be an increase of .7% in voter
participation.

However, in model N, we cannot reject the null hypothesis that the two key
coefficients are in fact equal but opposite in sign, i.e. that ,Bprefcmd = -fless-p,efmd at the
95% or 90% confidence levels.37

This discrepancy is yet another result of the lack of honesty of some respondents,
particularly in the 3rd age quartile. If model N is re-written to exclude age (but to still

include race, sex and income), as in model 0 in Table 9b, then the magnitudes of ,Bprcfcmd

and [icsamcfmd are significantly different at the 5% level, as can be seen in Table 9b.38

It should be noted that in none of these models, nor in any of the other models
cited here, did the choice of conventional standard errors (rather than heteroskedasticity
robust stande errors) have any meaningful impact on the significance of any

coefficients.39

\

37

The coefficients are only significantly different in magnitude at approximately the 85% level,

133-Sec! on an F-test of F (I, 4674) = 1.99, and hence Prob > F = 0.1580.

In this case, the appropriate test of the “equal but opposite” hypothesis yields an F-test of

{If I . 4290) = 4.77 and hence Prob > F = 0.0291.

For example, while in model 0 the conventional standard error on the score of the preferred
candidate was (0.00039), the robust one was only slightly higher at (0.00041). Likewise, the coefficient on

SUbOptimality in model 1 has a conventional standard error of (0.00049) while the robust equivalent is only
(0.00051).

145

.01

fl);

Table 9b Candidate placement coefficients in the presence of demographic
characteristic terms, other than age.

Model: Adjusted R2, Prob > Coefficient on Coefficient on Demographic Terms

(number of F-stat Preferred Less-Preferred Present

observations) Cand. (S. E.) Cand. (S. E.)

0.0992 .00311 -.00205 Age, sex, race,
0 (4297) 0.0000 (. 00039) (. 00030) income

Note: Model 0 omits those respondents who were demonstrated to have lied about their
participation.

Under this model specification, if the thermometer scores of both candidates rose

by ten degrees, then the net effect would be an increase of 1.06% in voter participation.40

Section V: Preliminary evidence of the voters’ costs and preferences

From all of the results described in Section IV, and many others which were
carried out simultaneously, it is apparent that voters’ participation decisions do appear
consistent with the concept of alienation. Those who view the preferred candidate as low
quality consistently are less likely to vote than those whose preferred candidate is closer

to the ideal, even given the voters’ perceptions of candidate separation.

Furthermore, these results persist even when the conventional demographic

fac=tors which are assumed to “drive” participation rate differences are present, once the

influence of perceptibly dishonest respondents has been removed. These results offer

‘

‘0 It should be noted that the candidate-placement coefficients and their standard errors from models

M and K are almost identical, as the effects of sex, race and income do not alter the pattern of voter
response to candidates. Instead, sex, race and income set the pre-conditioned level of participation, and
hence predominantly affect the size of the constant term.

146

answers to the first two questions posed at the start of Section IV. However, the third
question, of the motivations which drive the alienated behavior, is less clearcut.

To reiterate, three potential explanations of alienation in the face of rational voters
seem reasonable. First, the voter may possess preferences which are mapped only over
the policy position of the preferred (or less-preferred) candidate, and hence the voter
disregards the consequences of the electoral outcome. Secondly, the voter’s political
utility function may be convex, such that the rate of increased disutility suffered from
unsatisfactory outcomes diminishes in the distance of those outcomes from the voter’s
ideal, i.e. the voter is proximity-sensitive. Lastly, the voter’s costs may be sufficiently
proximity-sensitive that even with a concave political utility function, the overall
response to candidate placement is most pronounced in close proximity to the voter.

From the results described in Section IV, it seems reasonable to eliminate the first
of these possibilities. Voters, although more sensitive to the location of the preferred
candidate than to the location of his rival, are concerned with the nature of both potential

winners.

From Eq. 3.7 and the results outlined above, we can see that the data consistently
suggests that (E + 8,),3, < ((5 + 8,),62 + f) and hence either flz>fll or f is large. ,8; > ,6)
would imply that the utility function itself was convex, whereas a large f with ,6) ,62
would imply strong ideological costs to participating for unsavory candidates, while
maintaining a conventional, concave, utility function.

However, differentiating between these two scenarios is a complex task. Ideally,
one would wish for a measure of the voter’s reluctance to vote, to serve as a proxy for

costs. No such term is available, however.

147

There are, however, some potential proxies for the agent’s concern for the
election’s outcome (i.e. for the agent’s political utility function). This binary variable,
taken from answers to a series of questions concerning the voter’s care for the issues at

stake between the candidates, appears to be strongly proximity sensitive, as is seen in

Table 10.

Table 10 Respondents’ interest in the electoral outcome as a function of the voter’s
perception of relative candidate placement

 

 

carewinl Coef. Std. Err. t P>|t| [95% Conf. Interval]
preferredl .008559 .0003455 24.772 0.000 .0078817 .0092363
less-prefl -.0040107 .0002627 -15.269 0.000 -.0045256 -.0034957
constantl .1394951 .0283597 4.919 0.000 .0838992 .195091

 

It could be argued that this variable, carewin, is acting as a proxy for the whole
decision to participate, incorporating the agent’s utility function and costs. However,
carewin is, on its own, an extremely weak predictor of participation (far weaker, for
example, than the respondent’s intention to vote).41

These results are replicated if the variable interest (representing the respondent’s
overall level of awareness of the campaign) is substituted for carewin. In either case, the
respondents are more sensitive to the preferred candidate, even prior to considering the
costs of participation.

While these results offer no evidence as to the structure of voters’ costs, the fact

that they suggest that, independent of costs, voters are already proximity-sensitive is

 

4' For example, while a sparse regression of participation on carewin generates an R2 of only 3.4%

(or 8.5% in conjunction with demographic terms), a sparse regression on the intention to vote results in an
R2 of 27.8% (or 30.5% with demographic terms).

148

significant on its own. Without having to make any assumptions as to the cost structure, a
rational electoral participant with proximity sensitive political utility is intrinsically
susceptible to alienation. Thus, any politician who intends to use strategic candidate
placement to maximize his or her electoral chances must be aware not only that

convergence and maneuver can win votes, but it can also lose them.

Section VI: Conclusions

The evidence presented in this paper represents a prototypical analysis of the
empirical evidence for alienation in US. elections. The dataset from which it was drawn
holds all of the disadvantages of a multi-purpose, interdisciplinary survey. However, by
presenting the extremely rare data on actual participation, it allows at least some progress
beyond the scope of abstract hypotheses.

Throughout the data, two consistent facts emerge. Firstly, political candidate
placement issues are not the dominant determinant of participation rates. Far more
entrenched personal and demographic characteristics are responsible for the majority of
variation in turnout. However, candidate placement is within the politician’s power to
control, where the other factors are not. As one of the few available levers for a candidate
to use to motivate the electorate, it is sufficient that placement is a key factor, without the
need for it to dominant in itself.

Secondly, within the issue of candidate placement, the role of the preferred
candidate is consistently more important than that of the less-preferred candidate.
Although the separation of the candidates is, as we would expect, vital, even it does not

remove the relative importance of the preferred politician’s perceived position.

149

This result persists in the face of demographic characteristics, and under both a
uni-dimensional scale for candidate placement and a proxy for an infmitely-dirnensioned
scale. Indeed, this consistency is more surprising than the result itself.

Furthermore, there is some evidence that this alienation is driven not by a myopic
concentration on one candidate, nor by ideological costs alone, but rather that the agents’
political utility functions are most sensitive to changes in candidate placement close to
the agent’s ideal, rather than being concave, and hence distance-sensitive. This behavior,
on its own, is sufficient to make alienation not just a potential occurrence but rather a

necessary consequence of candidate strategy.

150

 

Appendix 1

Comparison of results from linear probability models and discrete choice models

151

As is described in the main body of the paper, the results presented there are from
OLS regressions, even though, as we are dealing with a discrete choice model, Probit or
Logit might seem more logical. The models were, however, re-run under Logit and Probit
techniques, and entirely equivalent results were achieved. Presented below is the Logit-
based version of Model G, as well as the Probit version of model G, and Model G itself.

It is immediately apparent that the patterns of significance are replicated across
the models. Furthermore, using the ratios suggested by Maddala (1983), the second and
third tables present the “corrected” coefficient estimates from all three models. As can
clearly be seen, the OLS, Logit and Probit estimates are extremely similar in all cases.

Given that the models generated in this paper were all intended to capture a low
but significant proportion of the motivation to participate, the risk of predicting greater

than certain actions was avoided in all reasonable circumstances.

Table 11 Uncorrected coefficient estimates and standard errors from the
OLS, Probit and Logit models of participation as a function of candidate placement, sex,
race and income.

 

Term: OLS Probit Logit
Coefficient S.E. Coefficient S.E. Coefficient S.E.

Subopt02 —0.0017875 0.0004902 -0.0047789 0.0013297 -0.0077814 0.0021642
Sex —0.0253495 0.0150971 -0.0718568 0.0413574 -0.1266352 0.0677986
Race 0.1655454 0.0205311 0.4306848 0.0551355 0.6937572 0.0886808
Income 3.870E-06 4.490E-O7 0.0000111 1.300E-06 0.0000191 2.260E—06
DiffOl 0.0013864 0.0003029 0.0038390 0.0008337 0.0063709 0.0013753
Constant 0.4172357 0.0280339 -0.2307121 0.0758883 -0.3862869 0.1231478

152

Table 12

Corrected coefficient estimates and standard errors from the OLS and

Logit models

Term:

OLS

Coefficient S.E.

Coefficient
size,
relative to
OLS

100%
100%
100%
100%
100%
100%

Logit

Coefficient S.E.

-0.00194535 0.
-0.03165880 0.

0.17343930
0.00000478
0.00159273
0.40342828

0000

00054105
01694965

.02217020
.00000057
.00034383
.03078695

Coefficient
size,
relative to
OLS

109%
125%
105%
123%
115%
97%

Corrected coefficient estimates and standard errors from the OLS and

Subopt02 -0.0017875 0.0004902
Sex -0.0253495 0.0150971
Race 0.1655454 0.0205311
Income 0.0000039 0.0000004
Diff01 0.0013864 0.0003029
Constant 0.4172357 0.0280339
Table 13

Probit models

Term: OLS

Coefficient S.E.

Subopt02 -0.0017875 0.0004902
Sex -0.0253495 0.0150971
Race 0.1655454 0.0205311
Income 0.0000039 0.0000004
Diff01 0.0013864 0.0003029
Constant 0.4172357 0.0280339

Coefficient
size,
relative to
OLS

100%
100%
100%
100%
100%
100%

Probit

Coefficient S.E.

-0.00191156 0.
-0.02874272 0.

0.17227392
0.00000444
0.00153560
0.40771516

0

000

00053188
01654296

.02205420
.00000052
.00033348
.03035532

Coefficient
size,
relative to
OLS

107%
113%
104%
115%
111%
98%

Note: Correction mechanism (as per Maddala (1983) and others): The OLS coefficients
are considered the baseline to which the Logit and Probit estimates must be “merged”. To
generate equivalent Logit estimates, multiply the Logit coefficients by .25 (or, in the case
of the constant, multiply by .25 and add .5). To generate equivalent Probit estimates,
multiply the Probit coefficients by .40 (or, in the case of the constant, multiply by .40 and

add .5).

153

BIBLIOGRAPHY

154

Aaron, H., and R. Reischauer, 1995, “The Medicare Reform Debate: What Is the Next
Step?” Health Aflairs 14, 8-30.

Alesina, A. (1988). “Credibility and Policy Convergence in a Two-Party System with
Rational Voters.” American Economic Review 78(4): 796-805.

Alesina, A. and A. Cukierrnan (1990). “The Politics of Ambiguity.” Quarterly Journal of
Economics 105(4): 829-850.

Alesina, A. and R. Perotti (1995). “The Political Economy of Budget Deficits.”
International Monetary Fund Stafl Papers 42(1), March 1995: 1-31.

Allais, M., 1947, Economic et Intérét, Imprimerie Nationale, Paris.

Altonji, J. G., F. Hayashi, and L. J. Kotlikoff, 1992, “Is the extended family altruistically
linked? Direct tests using micro data,” American Economic Review 82, 1177-98.

Alvarez, R. M. and J. Nagler (1995). “Economics, Issues and the Perot Candidacy: Voter
Choice in the 1992 Presidential Election.” American Journal of Political Science, 39(3):
714-732

Anderson, S. P. and G. Glomm (1992). “Alienation, Indifference and the Choice of
Ideological Position.” Social Choice and Welfare 9: 17-31.

Auerbach, A. J ., L. J. Kotlikoff, and D. N. Weil, 1992, “The increasing annuitization of
the elderly -- estimates and implications for intergenerational transfers, inequality and
national saving,” NBER Working Paper No. 4182.

B0rsch-Supan, A., 1993, “Aging in Germany and the US: international comparisons,”
NBER Working Paper No. 4530.

Chressanthis, G. A. and S. D. Shaffer (1993). “Major Party Failure and Third Party
Voting in Presidential Elections, 1976-88.” Social Science Quarterly 74(2): 264-273.

155

Council of Economic Advisors, 1994, Economic Indicators, Washington, D. C.: United
States Printing Office.

Cox, G. W. (1990). Multicandidate Spatial Competition. Advances in the Spatial Theory
of Voting Eds. J. M. Enelow and M. J. Hinich. New York, Cambridge University Press.

Cukiennan, A. and A. H. Meltzer (1989). “A Political Theory of Government Debt and
Deficits in a Neo-Ricardian Framework.” American Economic Review 79(4), September
1989: 713-732.

Dasgupta, S. (1996). “Strategic voting with third candidates”. Seminar, Dept. of Political
Science, Michigan State University, October 1996.

Diamond, P. A., 1965, “National debt in a neoclassical growth model,” American
Economic Review 55, 1126-50.

Downs, A. (1957). An Economic Theory of Democracy. New York, Harper.

Enelow, J. M. and M. J. Hinich (1984). The Spatial Theory of Voting. New York,
Cambridge University Press.

Enelow, J. M. and M. J. Hinich, Eds. (1990). Advances in the Spatial Theory of Voting.
New York, Cambridge University Press.

Enelow, J. M. and M. C. Munger (1993). “The Elements of Candidate Reputation: The
Effect of Record and Credibility on Optimal Spatial Location.” Public Choice 77(4): 757-
772.

Gilleskie, D. B., and A. L. Harrison, 1998, “The effect of endogenous health inputs on
the relationship between health and education,” forthcoming, Economics of Education
Review.

Grembowski, D., D Patrick, P Diehr, et al., 1993, “Self-efficacy and Health Behavior
Among Older Adults, Journal of Health and Social Behavior, 34:89—104.

156

 

Grofinan, B. (1996). “Political Economy: Downsian Perspectives” A New Handbook of
Political Science Eds. R. E. Goodin and H. D. Klingemann, Oxford, Oxford University
Press.

Grossman, M., 1972, “On the concept of health capital and the demand for health,”
Journal of Political Economy 80, 223-255.

Gutowski, W. E. and J. P. Georges (1993). “Optimal Sophisticated Voting Strategies in
Single Ballot Elections Involving Three Candidates.” Public Choice 77(2), October 1993:
225-247.

Hahn, B., and D. Lefltowitz, 1992, Annual Expenses and Sources of Payment for Health
Care Services (AHCPR Pub. No. 93-0007). National Medical Expenditure Survey
Research Findings 14, Agency for Health Care Policy and Research, Rockville, MD:
Public Health Service.

Hamermesh, D. S., and P. L. Menchik, 1987, “Planned and unplanned bequests,”
Economic Inquiry 25, 55-66.

Hinich, M. and P. Ordeshook (1969). “Abstentions and Equilibrium in the Electoral
Process.” Public Choice 7: 81-106.

Hotelling, H. (1929). “Stability in competition.” Economic Journal 39: 41 -57.

Hubbard, R. G., and K. L. Judd, 1987, “Social security and individual welfare:

precautionary saving, borrowing constraints, and the payroll tax,” American Economic
Review 77, 630- 46.

Hudson, J. and P. R. Jones (1994). “The Importance of the 'Ethical Voter': An Estimate
of 'Altruism.'.” European Journal of Political Economy 10(3), October 1994: 499-509.

Hug, S. ( 1995). “Third Parties in Equilibrium.” Public Choice 82(1 2): 159-180.

Hurd, M. D., 1990, “Research on the elderly: economic status, retirement and
consumption and saving,” Journal of Economic Literature 28, 565-637.

157

 

Hurd, M. D., 1995, “Using subjective survival probabilities in life cycle models,”
mimeo., Department of Economics, SUNY Stony Brook.

Inter-university Consortium for Political and Social Research (1981, 1985, 1989),
National Election Survey, Ann Arbor, University of Michigan Press

Kenkel, D. S., 1991, “Health behavior, health knowledge, and schooling,” Journal of
Political Economy 99, 287-305.

Ledyard, J. (1984). “The Pure Theory of Large Two-Candidate Elections.” Public Choice
44: 7-42.

Lupia, A. (1992). “Busy Voters, Agenda Control, and the Power of Information.”
American Political Science Review 86: 390-403.

Maddala, G. S. (1983) Limited-dependent and Qualitative Variables in Econometrics,
Cambridge, Cambridge University Press.

Manning, W et al., 1987, "Health Insurance and the Demand for Medical Care: Evidence
from a Randomized Experiment." American Economic Review. Vol. 77, No. 3. June
1987. 251-278.

Mazo, J. F ., A. M. Rappaport, and S. J. Schieber, eds., 1994, Providing Health Care
Benefits in Retirement, Philadelphia: University of Pennsylvania Press.

Moon, M., 1993, Medicare Now and in the Future, Lanham, MD: University Press of
America.

Moon, M., and K. Davis, 1995, “Preserving and Strengthening Medicare,” Health Aflairs
14, 31- 46.

Newhouse, J. (1992) "Medical Care Costs: How Much Welfare Loss?" Journal of
Economic Perspectives, Volume 6, No. 3, 322.

Office of the Chief Actuary, Social Security Administration, 1996.

158

 

Osborne, M. J. (1993). “Candidate Positioning and Entry in a Political Competition.”
Games and Economic Behavior 5(1), January 1993: 133-151.

Physician Payment Review Commission, Annual Report to Congress, 1995.

Popkin, S. (1993). Information Shortcuts and the Reasoning Voter. Information,

Participation and Choice: An Economic Theory of Democracy in Perspective Ed. B.
Grofinan. Ann Arbor, University of Michigan Press.

Powell, G. B. (1986). “American Voter turnout in Comparative Perspective.” American
Political Science Review, 80: 17-43

Rosenthal, H. (1990). The Setter Model. Advances in the Spatial Theory of Voting Eds. J.
M. Enelow and M. J. Hinich. New York, Cambridge University Press.

Samuelson, P, 1958, “An exact consumption-loan model of interest with or without the
social contrivance of money,” Journal of Political Economy 66, 467-82.

Shabman, L. and K. Stephenson (1994). “A Critique of the Self Interested Voter Model:
The Case of a Local Single Issue Referendum.” Journal of Economic Issues 28(4),
December 1994: 1173-1186.

Stearns, S.C., S. Bernard, S. Fasick, R.R. Konrad, R. Schwartz, and G.H. DeFriese, 1998,
"The effect of self-care practices on Medicare reimbursement." Draft paper, UNC.

Uhlaner, C. (1993) What the Downsian Voter Weighs: A Reassessment of the Costs and
Benefits of Action, Information, Participation and Choice: An Economic Theory of
Democracy in Perspective Ed. B. Grofrnan. Ann Arbor, University of Michigan Press.

US. Bureau of Labor Statistics, 1995, CPI Detailed Report, Washington, DC: US.
Government Printing Office.

159

 

Whitten, G. D. and H. D. Palmer (1996). “Heightening Comparativists’ Concern for
Model Choice: Voting Behavior in Great Britain and the Netherlands.” American Journal
of Political Science, 40(1): 231-253

Wittman, D. (1977). “Candidates with Policy Preferences: A Dynamic Model.” Journal
of Economic Theory 14: 180-189.

Wittman, D. (1990). Spatial Strategies When Candidates Have Policy Preferences.
Advances in the Spatial Theory of Voting Eds. J. M. Enelow and M. J. Hinich. New York,
Cambridge University Press.

Wolfe, J. R., 1993, The Coming Health Crisis: Who Will Pay for Care for the Aged in
the Twenty-first Century, Chicago: University of Chicago Press.

160

 

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