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Working Paper 95 1 1
VOTING ON SOCIAL SECURITY:
EVIDENCE FROM OECD COUNTRIES
by Friedrich Breyer and Ben Craig
Friedrich Breyer is a professor of economics at
Universitat Konstanz, Konstanz, Germany, and
Ben Craig is an economist at the Federal Reserve
Bank of Cleveland. For helpful comments, the authors
are grateful to Michael Thies, Furio Camillo Rosati, and
participants at the 1995 European Public Choice Society
meeting and at a seminar held at the University of Bergen.
They would also like to thank Marco Hornung for valuable
assistance in processing the data, and the Deutsche
Forschungsgemeinschaft for financial support under
SFB 178.
'
Working papers of the Federal Reserve Bank of Cleveland
are preliminary materials circulated to stimulate discussion
and critical comment. The views stated herein are those of
the authors and not necessarily those of the Federal Reserve
Bank of Cleveland or of the Board of Governors of the
Federal Reserve System.
November 1995
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Abstract
This article tests the subset of public choice models for social security that have empirical
implications. The data, collected from OECD countries for the years 1960, 1970, 1980,
and 1990, provide some support for each of the theories. Higher median voter age, more
income heterogeneity, greater similarity in family size, and variables that make a public
pension program more profitable are all associated with a larger program. However, none
of the theories explains why the shape of the age distribution and the time trend are so
important. The results are robust under both fixed-effects and random-effects estimation.
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1. Introduction
If a person has a formal pension, the chances are that at least part of his retirement
benefits will be paid for by a form of social security. Indeed, in 1993, Bangladesh,
Myanmar, Thailand, and five African countries were the only nations that did not have a
mandated old-age pension program. Exceptions to the pay-as-you-go approach, such as
Chile's privatized pension system, remain rare. Of the industrial democracies belonging
to the Organisation for Economic Co-operation and Development (OECD), virtually all
have a pay-as-you-go system. Yet there is no immediately obvious reason why this might
be so. Naive models of the adoption of a public pension program assume that a country
chooses the most efficient method of saving for retirement. Following Aaron (1966), a
nation adopts a social security system if its rate of return, equal to the population growth
rate plus the productivity growth rate, exceeds the real interest rate. However, as
Browning (1975) shows, a model of public choice in a democracy can yield inefficiently
high levels of social security. Following Browning's seminal paper, there has evolved a
vast theoretical literature that attempts to explain 1) why these transfers from young to old
exist in democracies even when contributors outnumber recipients, 2) why, if there is a
majority in favor of such transfers, the amounts are not even larger, and 3) what
determines the enormous differences in these programs across countries.'
Empirical work must show which of the many models of public choice proposed
in the literature are good approximations of the political process, in the sense of
predicting future levels of public pension plans. Tests of the various models are also
necessary to make a normative statement of whether the democratic process overshoots
the optimal level of public pensions. Yet the general difficulties that complicate the
testing of public choice models of economic policy are relevant to the public pension
choice as well.
For a comprehensive survey of this theoretical literature, see Breyer (1994).
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Time-series data for the United States do not help to answer these questions, since
individual social security laws are complicated, and it is difficult to determine their longrun effects. Although U.S. social security provisions are unusual in that they are debated
and amended every two years, in fact, there have been only five major legislated changes
in the size of the program since 1950. Statistical inference based on the timing and
magnitude of these five observations (as in Congleton and Shughart [I 9901 and Turner
[I 9841) must necessarily remain imprecise.2 A cross-sectional analysis of the effect of
congressional-district voting patterns on U.S. social security legislation offers its own
difficulties. All that is observed are voting records for the bill as finally presented.
Subsumed beneath the surface are the logrolling and party loyalties that went into crafting
the final form of the legislation and collecting the votes needed for passage (or defeat).
For example, in 1994, HR427 was passed, which restricted benefits paid to alcoholics or
drug addicts under Social Security Insurance and made the Social Security Administration
an independent agency. The vote was 41 3-0 for passage of the bill. It is unclear how one
can test theories of public choice from such data.
This paper compares the behavior of similar countries over wide time intervals.
To this end, we have assembled a data set that properly tests the correspondence of a
country's underlying economic and demographic structure with the public pension
outcome. We have chosen countries that are similar in their democratic processes and
industrial structures both to emphasize the variables that are shifting over this period and
to highlight their effect on the level of pay-as-you-go pensions. Observations in the data
set are for OECD countries in the years 1960, 1970, 1980, and 1990. These large time
intervals allow a country the leeway to change its social security program to the desired
level even if the legislative process moves slowly. Of course, it is difficult to attribute the
different outcomes in data from several nations to differences in the particular set of
explanatory variables we have measured. We use several econometric techniques to
Congleton and Shughart's analysis uses the size of the average benefit as the dependent
variable for yearly observations. To the extent that benefits change without new
legislation, the timing of the legislation becomes less important.
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mitigate this problem and find a similar pattern of results regardless of the approach used.
The empirical work presented in this paper is a clear improvement over previous
empirical tests of public choice theories. Unlike Tabellini's (1990) cross-section of 63
countries, our sample consists of nations that are quite similar in both their level of
industrial development and their strong democratic political process. (Interestingly, it is
within this subsample of countries that Tabellini's results are not all robust.) Compared to
Rizzo's study of the post-war Italian experience or her examination of a single crosssection of OECD members (1990, chapter 7 ) , our panel of countries provides far more
precise estimates.
In section 2, we describe four models
. of public choice for social security, focusing
on the empirical implications of each. We use a similar structure and the same notation
throughout our discussion and do not presume to describe all the theories in the vast
literature on public choice of public pension systems. However elegant or persuasive
excluded theories might have been, our criterion for inclusion was that a theory must have
an unequivocal empirical implication. We found this to be a very small subsample.
We then describe the data set we have gathered for this paper, paying particular
attention to trends in the OECD countries and comparing the general patterns in this
group with the better-known pattern in the U.S. social security program. Finally, we
report the results of our tests and finish with some concluding remarks.
2. Four Models of Public Choice for Public Pensions
Each of the models discussed here is based on the common paradigm of public
choice theory that participants in the political decision process vote to maximize their
utility over lifetime consumption. All are compared to a benchmark case in which the
single decisionmaker is a benevolent dictator, and all are similar in that they describe a
small open economy where the wage and interest rate are exogenously given and constant
over time, and where workers supply one unit of labor to the market. The models cover
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an infinite number of discrete time periods t (t = 0,1,2, ...), with the distance between two
adjacent points corresponding to the age difference between two subsequent generations.
The term "generation t" refers to the group of individuals who are in their first working
age in period t. Only persons in this age group can have children. If M, is the
reproduction rate of the society in period t-1 (i.e., the ratio of the number of people in
generation t to generation t-I), then a sequence of numbers M, (t = 1,2,...) describes the
population path.
If z, is the per capita contribution of workers to the unfunded pension system in
period t, then the payment to each pensioner is
(2.1) Pt = ztMt.
Each worker's and each pensioner's consumption (where c, is a worker's and zt is a
pensioner's consumption in period t, and st is a worker's savings) is
(2.2)
ct = w - zt - st and
(2.3) zt = Rst-, + Pt.
Pensioners do not save, since there is no bequest m ~ t i v e . ~
We test the following four models: a) benevolent dictator, b) direct democracy
with majority rule, c) horizontal redistribution, and d) rational family.
a. Benevolent Dictator
A benevolent dictator model compares the rates of return on contributions to a
pay-as-you-go system (i.e., the population growth rate plus the growth rate of wages due
to technical progress) to the rate of return on capital, which equals the interest rate. In a
world of uncertainty, capital has the additional disadvantage of providing no protection
against unanticipated inflation. Therefore, a benevolent dictator would choose a larger
unfunded system, the higher the sum of the rates of population growth and productivity
Some results rely on the continuous-time model, a different and mathematically more
complex version of the theory in which each individual lives for A periods as a worker
and for T-A periods as a retiree.
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growth relative to the rate of interest, and the higher (and more volatile) the inflation rate.
The same conclusion holds for any model in which politicians behave as if they
maximize a weighted sum of the utilities of the citizens, as they do in Verhoeven and
Verbon (199 1).
b. Direct Democracy with Majority Rule
In the simplest public choice model of Browning (1975) and Greene (1974), each
person votes for the pension system that promises the largest lifetime utility. The major
two assumptions of this model are 1) the voter believes that the program he votes on will
continue at least until he retires, and 2) liquidity constraints prevent borrowing against the
~ voter's beliefs are, in an important sense, irrational
value of future pension c ~ a i m s .The
in this model. If demographic changes occur, then there is strong evidence that the new
voting structure will imply a different contribution level from the one currently being
voted on. Thus, voters believe in a system that is not even consistent within the context
of their own model. Sometimes, as in Browning (1975) and others, this irrational
expectation is defended on the ground that voting takes place infrequently, ensuring
stability of the benefit.
We discuss the model in a continuous-time version. In this case, the desired
contribution level from a voter's point of view increases monotonically with age; thus,
the median voter is generally an older worker. An increase in the population growth rate
has two separate effects: First, the median voter becomes younger, which tends to
depress the equilibrium contribution level. Second, the population growth rate becomes
higher, which increases the growth rate of the economy. From this second effect, the
Browning's model and other similar ones that followed (e.g., Boadway and Wildasin
[1989]) use this as'sumption to explain that the program size is not even higher. An
alternative explanation would be that present voters take into account the negative effects
of too-high contribution rates on the work effort of future generations.
The comparative-static implications of this type of model have been examined by
Townley (1981) and Wickstrom (1984) for the case of a constant growth rate.
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contribution level desired by an individual voter will increase (stay constant, decrease) if
the elasticity of the marginal utility of consumption exceeds (is equal to, falls short of)
unity in absolute terms.
Thus, the effect of a change in the reproduction rate on the level of social security
contributions in a direct voting equilibrium is indeterminate. Also, the change in the size
of the desired pension benefit following an increase in the reproduction rate can be
positive even if the change in the contribution level is negative, since the rate of return
rises. Furthermore, an increase in the rate of productivity growth differs from an increase
in the rate of population growth insofar as it raises the rate of return to pay-as-you-go
pensions without decreasing median voter age. Therefore, although the effect of the
reproduction rate on the optimal values of T, and P, is indeterminate as such, it should be
equal to the conditional effect of a change in M,, holding median voter age constant.
c. Income Heterogeneity and Horizontal Redistribution
In some public pension systems, notably that of the Netherlands, retirement
benefits are practically the same for every retiree, whereas contributions are collected
from workers in strict proportion to their wage income. This feature is used by Tabellini
(1990) in a two-period overlapping generations model with no intertemporal dependence
of contribution rates. Hence, the results would hold even if there were no future after the
period under consideration, meaning that the model is essentially static. The society
consists of a number of retirees ("parents"), each of whom has the same number of
working-age descendants. There is mutual altruism between parents and descendants, but
it is so weak that, in the absence of a social security system, private transfers are zero in
either direction. However, workers are allowed to save for their retirement consumption
as well as to borrow against future pension benefits.
Workers differ with respect to their wage incomes, and thus a flat-benefit,
proportional-contribution social security scheme involves a transfer from workers to
pensioners and from high-income to low-income earners. If voted on in isolation, the
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first kind of transfer would be accepted by all pensioners and rejected by all workers,
since the ratio at which a worker's gift is converted to a benefit to his parent is the same
as in private transfers, and, by assumption, altruism is so weak that these are ruled out. In
contrast, the second kind of transfer, if available on its own, would be accepted by all
families with below-average income earners and rejected by everyone else.
Because the two types of transfers are available only in combination, voters'
preferences with respect to alternative contribution rates can be determined in the
following manner: Among workers, the median-income voter will definitely reject any
positive tax rate 7,, but below a certain income threshold (which is lower than the
median), workers will prefer positive taxes because the ratio of their taxes to their
parent's retirement benefits becomes favorable. Moreover, the lower the income, the
higher is the optimal value of 7,. Conversely, while the parent of a median-income earner
will favor a positive tax rate, the tax rate desired by a pensioner will be a declining
function of his descendant's income, and above a certain threshold, the optimal 7, will be
zero.
Consequently, there is a value of the tax rate, T,*, such that exactly half the voters
(i.e., more than 50 percent of pensioners but less than 50 percent of workers) would
prefer a higher and half would prefer a lower tax rate. Because of the single-peakedness
of individual preferences, 7," constitutes a political equilibrium. Tabellini (1990, section
5) shows that, among other influences, apositive value of 7," is more likely (and, if
positive, its value is larger), the greater the pre-tax income inequality and the lower the
population growth factor M, (the ratio of young to old voters). Thus, a higher median
voter age would reflect a slower growing population and a larger program.
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d. Rational Familv
All the above models of democratic decisionmaking on public pensions are based
on the assumption that each voter, before casting his vote on a particular proposal,
behaves rationally by comparing the costs and benefits accruing to himself alone. In this
comparison, private annuities are considered to be the only alternative to mandatory
public pension plans on a pay-as-you-go basis. Breyer and Schulenburg (1987, 1990)
propose an alternative model of majority voting on a mandatory public pension scheme in
which each family is treated as a decisionmaking unit. Here, a different type of social
contrivance is considered as an additional substitute to public pensions, namely, the
within-family pay-as-you-go system. For a given family, this approach will provide a
higher rate of return than the nationwide system if the ratio between workers and
pensioners within the family itself is higher than in society at large.
The demographic structure of the society is described by the following
assumptions. Each individual lives for three periods (as child, worker, and pensioner).
Therefore, in any period t, society is composed of members of three different generations.
Each worker can have up to two children, where the probabilities of having one or two
children, q, and p,, are time dependent but do not differ across members of the same
generation. For society as a whole, the individual fertility probabilities can be interpreted
as relative frequencies. Thus, in period t, the reproduction rate of the population (the
average number of children per working-age person) is given by
(2.4) Mt = 2pt + q,.
If a "family" is defined as a group consisting of one pensioner and all his direct
descendants, then the assumptions mentioned above imply that in every period, there are
nine types of families that differ in their generational composition, the relative
frequencies of which depend on the fertility parameters of the present and previous
interval.
Analysis of the voting process is simplified by the assumption that in each period,
there is just a yes-no decision on the existence of a mandatory public pension scheme, but
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9
no decision on the level of contributions and benefits. Instead, it is assumed that as long
as such a system survives, the contribution per worker is fixed at 7,whereas the
retirement benefit is determined endogenously by obeying the budget equation for the
pension plan.
All workers and pensioners are eligible to vote in this direct-majority decision,
and it is assumed that all members of a specific family type will vote for abolishing the
system if the discounted value of all present and future contributions from family
members exceeds the corresponding value of their total retirement benefits.
What is interesting for our purposes is, first, how the percentage of "no" votes
behaves when M is decreased, holding the distribution of children constant. Surprisingly,
this percentage does not fall monotonically, so an equally clear-cut result as in most of the
models discussed above does not emerge. What can be said, however, is that for steadystate populations, a majority of votes always goes against the pay-as-you-go system if the
population is shrinking (M < I), whereas this is not the case if it is growing (M > l), as
long as children are fairly evenly distributed. Furthermore, the percentage of "no" votes
is larger the more unevenly children are distributed, i.e., the greater is the variance of the
variable "number of children in a family" in the society.
With respect to the other important determinants of voter behavior, the interest
rate and the rate of productivity growth should play the same role as in the benevolent
dictator model, since the capital reserve system remains as a second alternative to the
public pay-as-you-go system. Predictions resulting from the respective models are
summarized in table 1.
3. Empirical Results
3.1 Description of the Data
Theories of social security determination offer unique problems in empirical
testing. Unlike a community tax, where different regional observations are possible,
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social security is decided at the national level. An observation must reflect the voting of
the entire economy. Yet, unlike the money supply, for example, a social security program
rarely changes, making the use of frequent time series for a single economy problematic.
Our solution is to use a set of similar economies. The low frequency allows us to assume
that the parameters for the economy are exogenously given to the voter. Over a 10-year
span, it is assumed that voters have enough time to change the program to reflect the
outcome of the public choice mechanism. The years chosen are 1960, 1970, 1980, and
1990, which enables us to use detailed demographic data from the decennial censuses that
many countries conducted during these years.
We use OECD data for a variety of reasons. First, more data are available from
these than from other countries, and the information is more reliable and more
comparable between countries than in a data set with more diverse nations. Also, the
political regime is generally democratic in these countries, with a few exceptions that we
exclude from the sample. This allows us to interpret the public pension program as an
outcome of the democratic process.
We measure the size and structure of a pay-as-you-go system along several
dimensions, amounting to five different dependent variables. We use total social security
tax contributions, total benefits paid, and total pensions paid by the government (all as a
fraction of GNP) to measure the size of the program. We also use total benefits per
person over age 60 and total pensions paid by the government per person over age 60
(both in thousands of 1982 U.S. dollars) to determine the benefit received by each
pensioner.
Each of these measures has advantages and disadvantages. The terms social
security contributions and social security benejits can have a variety of meanings to
different countries at different times. Most countries include a measure of the cost of
medical insurance for the elderly in these data. This is clearly a general transfer from the
young to the old and represents much of the outcome of a public choice mechanism that
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I1
would determine the size of the social security program. However, the reported figures
for social security contributions and benefits have the disadvantage that the variance in
the definition of the program creates noise and makes estimates less precise.
Contributions and benefits do not include such items as military retirement
benefits, railroad retirement funds (in the United States), or civil service pension benefits.
The public pension data do include these figures, but do not encompass medical transfers
to the elderly. While programs such as military retirement are a transfer to older people,
the transfer is not sufficiently general to match most public choice models of social
security. In this sense, public pension data are less useful than contributions and
benefits. They have the additional disadvantage of being unavailable for 1990.
Our data set also includes the percentage of social security tax paid by employers
via a hidden employment tax. This variable may account for the fiscal illusion common
among voters of not counting employer contributions as a cost of the program. Over the
full sample period, each dollar of social security tax paid by U.S. workers was matched
by a dollar contributed by employers (50 percent of the total tax). Australia and New
Zealand, which paid for social security out of general tax revenues, were the only OECD
countries not to fund social security with a designated tax.
Table 2 presents the changes in several measures of the public pension system for
~ same variables for the more generally known program
our sample of 20 c ~ u n t r i e s .The
in the United States are also shown for comparison. Benefits and contributions measured
as a fraction of GNP rose dramatically during this period for both the United States and
the OECD sample as a whole. The experience in the United States was consistent with
that of the rest of the OECD countries in that the largest growth in the program occurred
from 1980 to 1990.
The countries are Australia, Austria, Belgium, Canada, Denmark, France, West
Germany, Ireland, Italy, Japan, Luxembourg, the Netherlands, New Zealand, Norway,
Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States.
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Over the entire sample period, the mean values of contributions and benefits as a
share of GNP for the OECD mask great variations in the time-series patterns within a
country. Although public pensions as a fraction of GNP rose for each country with the
passing of every decade, some nations actually cut the size of their program when
measured by contributions or benefits as a fraction of GNP. Others saw explosive
growth in social security during the 1980s, while still others matched the time-series
pattern of the United States. Thus, there is large within-country variation in the size of
public pension programs. This is true for the benefits per capita and benefits per
pensioner measures as well. The U.S. program, at between 6 and 7 percent of GNP in
1990, is relatively small compared to those of most other OECD countries. In 1985, the
size of public pension expenditures ranged from 2.1 percent of GNP in Portugal to 14.5
percent of GNP in Austria. Social security contributions showed the same wide range in
1990, running from 2 to 17 percent of GNP.
The percentage of social security financed by employers is as large as it has ever
been, on average. Again, the pattern varies from country to country. Belgium, for
example, cut the fraction paid by employers between 1960 and 1970 and then increased it
between 1970 and 1990, while Canada increased the fraction between 1960 and 1970 and
cut it thereafter. In short, the 20 countries show wide variation in all dimensions of their
public pension programs. This is true not only in terms of absolute levels, but also in
terms of time patterns within each country. Clearly, there are differences in the data that
the theories need to explain.
Research suggests that a number of explanatory variables should be important in
determining the size of a public pension program. The demographic situation of a
country is represented by two variables: age of the median voter and ratio of the 40- to
60-year-old population to pensioners, which is an approximation of the variable M , . ~
The variable "ratio of population 20 to 40 years of age to population 40 to 60 years of
age," which approximates Mt+l,is highly correlated with median voter age and thus
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This reflects the shape of the age distribution above the age of the median voter. (The
mean of the median voter age is 42.) If this number is high, then the distribution above
the median voter is more concentrated toward the working population (and less toward
pension recipients), if one holds the median voting age constant.
The interest rate, growth rate, and inflation rate are all represented by five-year
averages of the five years preceding and including the year of observation. The interest
rate is the real rate on the longest government security for which data are available, the
growth rate is the real growth rate of GNP, and the inflation rate is the growth rate of the
Consumer Price Index. These variables, plus those describing the size of the public
pension system, could be obtained for 76 core observations representing 20 countries.
The variables measuring variance of children and variance of income are less
straightforward. We found limited household data on the proportion of the population
This turns out to
living in households of four or less for 56 of the 76 core obser~ations.~
be a good approximation for the variance of household size within a population, as a
closely fitted regression suggests.9 We measure income inequality via the Gini
coefficient, which has been shown to be closely related to the variance of income in the
OECD countries.1° The Gini coefficient is calculated on the basis of pre-tax income for
51 of the 76 core observations." All variables are included in a sample of 44
observations. Means and standard deviations of our sample are reported in table 3 for the
76 observations.
cannot be included in an equation with the two other demographic variables.
Richer household size data are not available for many observations.
The regression is PROPORTION IN HOUSEHOLDS OF SIZE 4 OR LESS =
1.03 - .1313 VAR (HOUSEHOLD SIZE), with an R~ of .89 (t-stats are under estimates).
(39.6) (16.5)
lo See Sawyer (1976).
l 1 Of course, a problem connected with both the Gini coefficient and the share of the
population living in households of four or less is that both are affected by the size of the
public pension program (the latter because public pensions increase the independence of
the aged) and thus are not necessarily exogenous.
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3.2 Estimates
The estimation procedure breaks the error term into a classic components scheme:
(3.1) P = XP + ei + eit,
where P is public pension size, P is the vector of parameters of interest, X is the
explanatory variable matrix, ei is the country-specific unobserved error, and ei, is a
random error uncorrelated with X. If ei is assumed to be uncorrelated with X, then we use
a random-effects estimator for P."
Because the random-effects model is heavily influenced by international variation
in the variables, we call these estimates explanations of cross-country differences in
public pension programs. If ei is assumed to be correlated with X, then a fixed-effect
estimate of
p is more appropriate, and we call these estimates explanations of within-
country differences in public pension programs. Our prior belief was that the withincountry estimates are more reliable tests of which public choice models are supported by
the data, because each country has a distinct set of institutions and data measuring
conventions and procedures, which are likely to be correlated with some of the elements
of X. For example, the Gini coefficient is calculated from income figures based on tax
returns from the individual countries. Some countries treat the family as the basic unit of
taxation, while others tax the individual. Clearly, this error -- a component of the
individual country effect ei -- will be correlated with the Gini coefficient.
This prior belief is not supported by the data, however. The last rows in tables 4
and 5 include p-values for the Wald test of the hypothesis that the data could have been
l 2 Both the random-effects and fixed-effects estimates are modified to be consistent and
efficient given the unbalanced panel design, where some countries include more
observations than others. Estimates of the standard errors are also modified to be
efficient and consistent under any reasonable assumption about the time-series structure
of the error term, COV(eit,ei,+,), for any value of s.
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generated by a random- rather than a fixed-effects model.13 The high values listed here
should not be interpreted as evidence that the random-effects model provides more
reliable estimates than the fixed-effects model, but rather as a sign that our data do not
provide precise enough fixed-effects estimates to distinguish between the two models
statistically. The main reason for this appears to be the loss in degrees of freedom in a
fixed-effects estimation, considering the relatively limited sample size.
The dependent variables, which measure the size of the public pension program,
include total benefits as a fraction of GNP and benefits per pensioner.'4 Table 4 contains
estimates of the former and table 5 .includes estimates of the latter. We report estimates
both from the full sample of 76 observations, which does not have observations for the
household size variable or Gini coefficient, and from the reduced sample of 44
observations, which includes all of the explanatory variables.
The most striking result in table 4 lies in the strong and significant positive effect
of median voter age on program size. This empirical pattern is consistent with only two
of the theoretical models discussed in section 2 -- the majority voting model of Browning
and the horizontal redistribution model of Tabellini.
Holding median voter age constant, the nondemographic variables contribute
considerably to explaining differences in the size of the pay-as-you-go system. In the
benevolent dictator model, efficiency considerations predict that increasing the
economy's long-run growth rate should have a positive effect, that increasing the long-run
interest rate should have a negative effect, and that increasing the inflation rate (and thus
the variability of return on the competing real capital assets) should have a positive effect
on the public pension program. Table 4 shows that the estimates are consistent with these
l 3 This test, first suggested by Hausman and Taylor (1984) in a balanced panel design, has
been modified to reflect the unbalanced design of our data.
l 4 Equations with the dependent variable "contributions as a fraction of GNP" yield
essentially the same result as those with the dependent variable "benefits as a fraction
of GNP."
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conjectures, with one exception. The effect of rising interest rates on benefits as a
fraction of GNP is insignificant in the full sample and negative and significant only in the
reduced sample.
Column 3 shows that, given median voter age, the size of the program increases
significantly with the ratio of pensioners to older workers. This effect might have a
public choice explanation: Political decisionmakers in a representative democracy are
responsive to constituencies with a large fraction of pensioners even if these
constituencies are not pivotal in forming a majority on this particular issue. However,
the significance of this variable suggests that public choice theories which rest solely on
the age of the median voter are not rich enough to describe the determination of the size
of the public pension program. The mapping between the age distribution of the
electorate and program size clearly relies on aspects of the distribution other than its
median.I5
The last two columns of table 4 contain the results for the reduced sample,
which can be used to test the last two theories.16 A Gini coefficient increases with the
variance of income, which the horizontal redistribution theory predicts should have a
positive effect on the size of the public pension program (if indeed this has a
redistributive nature). Unlike Tabellini (1990), we think that the best way to test this
proposition is to include an interaction term ("Gini coefficient for a flat benefit rate"),
defined as the product of the Gini coefficient and the dummy variable, which is 1 when
the program provides a flat benefit, and 0 otherwise. Column 4 shows that this variable
has the predicted positive sign and is not quite significant at the 10 percent level, whereas
the Gini coefficient itself is insignificant (which is clear from column 5). Thus, this
finding provides weak support for the horizontal redistribution model as an explanation
The variable "fraction of contributions paid by employer" is insignificant. Including it,
however, has no effect on the other estimates.
l6 Results from regressions that include M, as a right-hand variable yield essentially the
same results, except that standard errors' are wider.
l5
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of the size of the public pension program: Countries with a flat benefit schedule have
larger public pension programs when there is more heterogeneity in income.I7
The family voting model predicts that an increase in the variance of the number of
children should decrease the size of the public pension program. Greater variance in the
number of children is associated with a decrease in the proportion of people living in
households of four or less, so that the family voting model predicts that this variable
should have a positive coefficient. Indeed, the cross-country estimates show this variable
to be positive and significant.
Table 5 contains the estimates with respect to the dependent variable "benefits per
person over age 60." This variable is also positively related to median voter age, although
the effect is now generally insignificant. This result is due to the strong negative
correlation between median voter age and the proportion of pensioners in the population,
which by itself reduces benefits per pensioner, as shown i n equation (2.1). In the full
sample, the effects of the other three variables related to the relative rates of return of the
two alternative pension financing systems have the sign predicted by the benevolent
dictator model in the random-effects estimation, whereas in the fixed-effects estimates,
only the inflation rate is significant and of the predicted sign. The ratio of pensioners to
older workers has no significant effect on benefits per pensioner.
All estimates of the time trend clearly indicate that the size of the public pension
program experienced a secular increase. In fact, this result is the strongest of all our
findings. The secular tendency for public pension programs to grow, even after
accounting for the usual suspects of growth in income or a change in demographic
structure, is puzzling. One is reminded of the crude political arguments against social
security in the 1930s, when opponents predicted that government programs would grow
on their own. Indeed, the coefficient of the time trend is usually about 0.002 when
l 7 The countries with flat retirement benefits are Australia, Ireland, the Netherlands, and
New Zealand.
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"benefits as a fraction of GNP" is the dependent variable. This means that, ceteris
paribus, each decade has seen a secular increase of 2 percent of GNP in the size of the
pay-as-you-go system, making social security the kudzu of government programs.'8
Another possible explanation for the strong positive time trend is that social security
programs were phased in gradually. In Norway, for example, claims to benefits are to
some extent related to previous contributions.
Finally, the coefficient on average income displays a robust pattern with
respect to the data set and estimation technique. As income per capita increases, the
proportion of benefits in GNP falls and the benefit per pensioner rises. Thus, if the public
choice mechanism expresses a demand for public pensions, the total public pension is a
normal necessity.
4. Conclusion
From the many models of public choice of social security, we have listed a
subset that contains empirical predictions along with the expected sign of the explanatory
variables. The bottom line of the exercise is that none of the theories is strongly rejected
when confronted with data that should be well suited to measuring its predictions. OECD
data support the Browning majority-voting model in its most definite prediction
--
that
median voter age has a positive impact on retirement benefits as a fraction of GNP.
Given median voter age, estimates of variables measuring the efficiency of the public
pension program vis-i-vis the competing capital markets generally support the intuition
provided by a benevolent dictator model. Higher growth rates are associated with larger
public programs, whereas higher real interest rates are associated with smaller programs.
"A specification that uses a dummy for each time period has essentially the same
results reported here. Further, the linear specification of a time trend follows the pattern
of the time dummies very well for the fixed-effect estimates. For random-effect
estimates, the pattern of the time dummies shows greater change in the program between
1970 and 1980 than during the other intervals.
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The model proposed by Tabellini, which emphasizes the intragenerational
transfers implicit in many social security programs, gets only weak support for its central
prediction, namely, a positive impact of income heterogeneity on the size of these
programs. Family voting, by contrast, gets confirmed with the caveat that we can
measure its most important explanatory variable -- variance of children -- only indirectly.
The strongly positive time trends pose a further puzzle for theories of
public choice. Why did public pension programs experience a secular increase during
this period that was not accounted for by demographic, financial, or inequality factors
typically considered to be predictors of program size? What mechanism or underlying
change in the structure of the OECD countries can explain the positive time trend?
Clearly, theories can be formulated that account for the empirical patterns
found in our research. To explain the coefficient patterns of the demographic variables,
one might investigate a model in which generations feel responsible for the care of only
their immediate parents. A challenge for public choice theory is to develop a model that
is consistent with our empirical findings, that has additional empirical hypotheses to
which it can be subjected, and that has strong predictions which can aid in policymaking.
Even in the absence of such a model, however, our work has pointed to several
predictions in a reduced-form context. Shrinking populations, if they mean a reduction in
the size of the young cohort relative to the elderly, should increase the size of the social
security program. Events that heighten the efficiency of the public pension program
relative to a private savings alternative, whether an increase in the economy's long-run
growth rate, a decrease in the interest rate, or an increase in the rate of inflation, should
also boost the size of the program. Finally, we find a disturbing secular tendency for
public pension programs to rise rapidly both as a share of GNP and in terms of the
average benefit paid.
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Data Appendix: Sources
1. Demographic variables, such as population size, are taken from various issues of the
United Nations Demographic Yearbook. This is also the primary source for the
household size variable, although where possible, it is supplemented with data from
demographic yearbooks of the individual OECD countries.
2. The growth rate, GNP, inflation rate, and interest rate are computed from the
International Monetary Fund Financial Statistics series on CD-ROM. The interest rate is
the five-year average of the longest rate available on the disc. Price data are
supplemented by purchasing-power-parity figures taken from the OECD publication
Purchasing Power Parity in the OECD, 1986. When this clearly makes no difference in
our results, we use simple exchange-rate data from the CD-ROM.
3. Contributions and benefits for social security programs come from a variety of
sources. The primary source is the OECD publication National Accounts, Detailed
Tables. However, these data were augmented where necessary with information from
various publications, including statistical yearbooks for individual countries. In addition,
we use data on the size of public pension programs reported in the OECD study
Reforming Public Pensions, 1988, which was made available to us by the OECD.
4. Descriptions of the individual public pension programs are largely taken from various
issues of Social Security Programs around the World, published by the U.S. Social
Security Administration.
5. Sawyer (1976) is a primary source for the Gini coefficients. In addition, we use tax
data from two OECD publications: "Income Tax Schedules -- Distribution of Taxpayers
and Revenues," in OECD Studies in Taxation, 1981; and "The Personal Income Tax
Base: A Comparative Study," in OECD Studies in Taxation, 1990. W e also use data from
the World Bank's annual Yearbook, and statistical yearbooks from individual countries
when they are available and contain income distribution or tax data.
clevelandfed.org/research/workpaper/1995/wp9511.pdf
References
Aaron, H. (1966), "The Social Insurance Paradox," Canadian Journal of Economics and
Political Science. 32: 120-145.
Boadway, R., and D.E. Wildasin (1989), "A Median Voter Model of Social Security,"
International Economic Review, 20: 307-328.
Breyer, F., J.-M. Graf v.d. Schulenburg (1987), "Voting on Social Security: The Family
as Decision-Making Unit," Kyklos, 40: 529-547.
Breyer, F., J.-M. Graf v.d. Schulenburg (1990), "Family Ties and Social Security in a
Democracy," Public Choice, 67: 155-167.
Breyer, F. (1994), "The Political Economy of Intergenerational Redistribution," European
Journal of Political Economy, 10: 61-84.
Browning, E.K. (1975), "Why the Social Insurance Budget Is Too Large in a
Democracy," Economic Inquiry, 13: 373-388.
Congleton, R.D., and W.F. Shughart I1 (1990), "The Growth of Social Security:
Electoral Push or Political Pull?" Economic Inquiry, 28: 109-132.
Greene, K.V. (1974), "Toward a Positive Theory of Intergenerational Income Transfers,"
Public Finance. 29: 306-324.
Hausman, J., and W.E. Taylor (1984), "Panel Data and Unobservable Individual
Effects," Econometrics, 49: 1377-1398.
Rizzo, I. (1990), The Hidden Debt, Kluwer Academic Publishers, Dordrecht.
Sawyer, M. (1976), Income Distributions in OECD Countries, Organisation for
Economic Co-operation and Development, Paris.
Tabellini, G. (1990), "A Positive Theory of Social Security," NBER Working Paper No.
3272, National Bureau of Economic Research, February.
Townley, P.G.C. (1981), "Public Choice and the Social Insurance Paradox: A Note,"
Canadian Journal of Economics, 14: 7 12-717.
Turner, Z.A. (1984), "Population Age Structure and the Size of Social Security,"
Southern Economic Journal, 50: 1131- 1146.
clevelandfed.org/research/workpaper/1995/wp9511.pdf
Verhoeven, M.J.M., and H.A.A. Verbon (1991), "Expectations on Pension Schemes
under Non-Stationary Conditions," Economics Letters, 36: 99-103.
Wickstrom, B.A. (1992), "Population Age Structure and the Size of Social Security,"
mimeo, University of Linz.
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Table 1
Signs of Comparative-Statics Influences in
Public Choice Models of Social Security
1
1
Benevolent
dictator
Majority
rule
Horizontal
redistrib.
Rational
family
+
-
+/-
(+I
Mt
R
1
v(ch)
v(inc)
1
Dependent Median
variable
voter
age
Tt
pt
Tt
pt
Tt
pt
Tt
pt
0
0
+
+
+
+
0
0
Mt
Independent Variable
Growth
R
i
rate
+
+
+I-
(+I
+/+/-
(+I
impact positive
impact negative
impact indeterminate
positive impact likely
present (older) workers per pensioner
long-run interest rate
long-run inflation rate
variance of number of children
variance of income (Gini coefficient)
Source: Authors.
+
+
+/+/0
0
0
0
0
0
0
0
+
+
0
0
0
0
0
0
v(ch)
v(inc)
0
0
0
0
0
0
-
0
0
0
0
-
+
+
0
0
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Table 2
Social Security Programs in the OECD
1960
Social Security Measure
Full Sample OECD Countries
Benefits per GNP
0.0633
Contributions per GNP
0.0553
Public pensions per GNP
0.0462
Fraction paid by employer
0.457
Real benefit per capita
0.293
Real contribution per capita 0.265
Public pension per capita
0.228
Real benefit per pensioner
1.962
Public pension per pensioner 1.546
--
United States
Benefits per GNP
Contributions per GNP
Public pensions per GNP
Fraction paid by employer
Real benefit per capita
Real contribution per capita
Public pension per capita
Real benefit per pensioner
Public pension per pensioner
Source: Authors' calculations.
1970
1980
0.0708
0.0634
0.0588
0.383
0.530
0.466
0.433
3.186
2.583
0.1 10
0.0983
0.0924
0.400
0.976
0.869
0.810
5.713
4.653
1990
0.1 19
0.1 10
---
0.580
1.362
1.271
---
7.157
---
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Table 3
Means and Standard Deviations
Variable
Mean
Standard Deviation
Benefits per GNP
Contributions per GNP
Public pensions per GNP
(53 observations)
Log real benefit
per pensionera
Log real public pension
per pensioner (53 observation^)^
0.820
0.862
0.378
0.0760
Ratio of 40- to 60-year-olds
to elderly
Median age
Long-run real interest rate
Long-run real growth rate
Inflation rate
Log real GNP per capitaa
Portion households 1-4
(59 observations)
Gini coefficient (54 observations)
a. In thousands of 1982 U.S. dollars.
Source: Authors' calculations.
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Table 4
Dependent Variable:
Benefits as a Fraction of GNP
Constant
Interest rate
0.202
(1.254)
-0.133
(1.009)
-0.193
(1.447)
Real growth rate
0.103
(0.910)
0.267
(2.823)
0.238
(2.388)
Inflation rate
0.43 1
(2.456)
0.303
(2.382)
0.174
(1.254)
Log GNP per capita
-0.033
(1.269)
0.0032 1
(0.772)
0.000405
(0.107)
0.00389
(2.235)
0.00589
(4.072)
0.00396
(2.761)
*
*
*
*
-0.0357
(2.953)
0.00251
(3.372)
0.00 195
(6.957)
0.00171
(5.929)
*
*
*
*
*
*
*
*
*
*
*
*
Number of observations
76
Error scheme
Fixed
P-value for random effects
76
Random
0.462
76
Random
0.305
Median voter age
M, (Ratio of 40- to 60year-olds to elderly)
Time trend
Gini coefficient
for flat-benefit rate
Gini coefficient
Portion households 1-4
Note: T-statistics are in parentheses under the estimated parameter
Source: Authors' calculations.
44
Random
0.775
44
Random
0.267
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Table 5
Dependent Variable:
Benefits per Pensioner
Constant
Interest rate
2.8
(1.487)
4.45
(2.895)
4.52
(2.991)
Log GNP per capita
0.462
(1.612)
1.08
(19.796)
1.05
(2 1.092)
Median voter age
0.012
(0.469)
0.0262
(1.340)
0.015
(0.806)
*
*
*
*
76
Fixed
76
Random
0.564
Real growth rate
Inflation rate
M, (Ratio of 40- to 60year-olds to elderly)
Time trend
Gini coefficient
for flat-benefit rate
Portion households 1-4
Number of observations
Error scheme
P-value for random effects
76
Random
0.233
Note: T-statistics are presented in parentheses under the estimated parameter.
Source: Authors' calculations.
44
Random
0.55 1
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