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\begin{document}
\title{Ageing population: The complex effect of fiscal leakages on the
politico-economic equilibrium.}
\author{Assaf Razin\thanks{%
Tel-Aviv University, Cornell University, NBER, CERP and CESifo. E-mail
address:\ razin@post.tau.ac.il.} and Efraim Sadka\thanks{%
Tel-Aviv University, CESifo and IZA. E-mail address:\ sadka@post.tau.ac.il.}}
\date{\ Received 24 May 2006; received in revised form 29 May 2006; accepted
7 June 2006 }
\begin{titlepage}
\begin{center}
\textbf{Aging population: the complex effect of fiscal leakages on the
politico-economic equilibrium}
\textbf{Assaf Razin}$^{a,b,}$\textbf{\footnote{%
E-mail address:\ razin@post.tau.ac.il.} and Efraim Sadka}$^{c,d,}$\textbf{%
\footnote{%
E-mail address:\ sadka@post.tau.ac.il.}}
$^{a}$Tel-Aviv University, Cornell University
$^{b}$NBER, CERP and CESifo
$^{c}$Tel-Aviv University
$^{d}$CESifo and IZA
\end{center}
\end{titlepage}\newpage
\section{Introduction: fiscal leakages in the wake of aging}
In an earlier study [Razin, Sadka and Swagel (2002); henceforth RSS] we
analyzed in a stylized model the effect of the aging of the population on
the size of the welfare state in a politico-economic context. We underscore
the existence of two conflicting effects. On the one hand, the aging of the
population strengthens the political clout of the pro-tax/social benefits
coalition. Put differently, the median voter, generally a young working
individual, is poorer and opt for more redistribution. On the other hand,
there is the "fiscal leakage" effect: as the population ages, the
young-working median voter realizes that there are more individuals who
share in her tax money, making her less receptive to raising taxes for
social transfers. Thus, the effect of aging on the politico-economic
equilibrium size of the welfare state depends on the relative strengths of
these two conflicting effects.
In RSS the welfare state is described by a stylized model in which taxes are
collected from the labor income of the working young and transfers are
offered uniformly to all, young and old alike. The uniform transfer captures
on average the many types of transfers which are each not uniform, such as
old-age security, health care, education, children allowances, etc. Some of
these transfers favor the old and some - the young (through their children).
If the number of children rises over time, then a greater portion of the
total transfers goes to the young. This additional fiscal leakage by no
means eliminates the fiscal leakage effect from the young to the old that
aging causes and which is the key effect we aimed to unveil in RSS.
Furthermore, in practice, the overall labor tax does not distinguish between
(or earmarked separately for) the elderly and children; and benefits are not
financed only by payroll taxes. Young families with many children may team
up with the elderly on their support for the generosity of the welfare
state. This is why it may be better to look at total dependency ratio than
at merely the elderly dependency ratio.
Another mechanism whereby aging tends to reduce the size of the welfare
state is offered in Razin and Sadka (2005). Consider a pay-as-you-go,
old-age social security system in which the working young pay social
security contributions in order to finance old-age benefits paid \emph{only}
to the retired old\footnote[1]{%
In RSS benefits were paid to all, young and old, in a form of a uniform
transfer (a demogrant).}. At each point in time, the young are willing to
vote for paying taxes even though the tax revenues are used entirely to pay
for the old, only because they expect the young of the next generation to do
likewise for them, when they grow to become old and retire. The expected
future aging of the population puts such a social security system under
strain. The burden of financing the pension benefits to the old falls on
fewer young shoulders, when population ages. Thus, if the fertility of the
young falls below the fertility rate of their parents, then the share of the
old in the next period will rise. The current young expects the next young
generation to reduce the benefit it pays to the old (current young)
generation. That is, the current young generation expects a smaller benefit
than it actually pays to the current old. As a result, the expected future
aging of the population triggers the current young to vote for lower
benefits (and taxes) for the current old. This incentive persists for the
next generations, self-validating the expectations for lower benefits caused
by aging.
In practice, taxes are levied both on labor and on capital. As the old are
the major holders of capital, the overall burden of taxes falls on both the
young and the old. This gives rise to fiscal leakages in various directions
in the wake of aging, depending on the type of taxes. In the next section we
develop a stylized model of a welfare state with both capital and labor
taxes in order to elicit these leakages when population ages.
\section{The various channels of fiscal leakage}
We model in this section, in a nutshell, a welfare state which levies taxes
on income from \emph{labor and capital} and redistributes the revenues among
its members. As such, it generates a multitude of political forces which
interact with \ each other in forming a politico-economic equilibrium. The
incidence of the labor income tax is relatively strongest on the young
working individuals. By contrast, these individuals have typically little
capital income. It is the (retired) old who have the lion's share of capital
income. Furthermore, this type of income is typically the main, if not the
sole, source of income of the old. At any point in time, the attitude of a
forward looking young towards an income tax is affected not only by how much
tax she will pay on her labor income. She is obviously concerned also by the
tax on her capital income which, though typically small at present, will
increase gradually to become a major source of her income, as she grows
older. The retiree is nevertheless concerned only about the capital income
tax (save for any altruism towards her offspring). At the same time, as the
redistribution done by the welfare state is typically biased in favor of the
old (old-age social security, medicare, etc.), she expects her cohort to
receive the lion's share of the transfers that the income tax revenues can
finance. Thus, the political economics of how the income tax is determined
is very subtle. There is a variety of factors at play, some reinforcing each
other and some conflicting with one another. In particular, aging of the
population has important implications for the transformation of the income
tax in the welfare state.\footnote[2]{%
Oeppen and Vaupel (2002) forecast a continuing strong trend of increasing
life expectancy among the best performing economies. Numerous studies
investigate the implications of such trends on the welfare state; see e.g.
Borsch-Supan, Ludwig and Winter (2004), Tosun (2003) and Razin and Sadka
(2005). They did not, however, focus on the intra and intergeneration
conflicts around the design of the income tax which is at the center of this
paper.}
Consider a representative welfare state which levies taxes on income, and
grants a flat benefit (in cash or in kind) to all its members. We employ an
overlapping-generations framework in which each generation lives for two
periods: in the first period of her life, an individual invests in human
capital and work; in the second period she retires. Thus, in each period
there is one generation (the young) who has labor income only and another
generation (the old) who has capital income only. $\ $Assume further that
the welfare state has a pay-as-you-go type of financing. That is: the
government's budget is balanced every period. This setup yields itself to a
two-type political conflict. First, there is an inter-generational aspect of
the conflict: \ In each period the old would like to tax labor, whereas the
young would prefer to tax capital. Second, there is the standard
intra-generational conflict between the poor (young and old) and the rich
(young and old). The income tax is determined as an equilibrium outcome of
all these forces.
We then study how aging alters the equilibrium outcome. There are two
channels through which aging affects the equilibrium tax rates. First, aging
increases the political clout of the old who favor low capital taxation and
high labor taxation. Second, there is a multitude of leakages of revenues
from one group to the other. On the one hand, the young are more inclined to
raise the income tax rate, because its capital component is levied over a
larger number of old people. But, on the other hand, the tax revenues from
the labor component are leaked to a larger number of old beneficiaries.
At the heart of any politico-economic equilibrium there must be some
underlying distribution of income. As in RSS, we generate an income
distribution based on human-capital formation framework, with an exogenously
given heterogeneity in innate ability.
Evidently, an income tax creates two distortions. As a tax on capital
income, it distorts saving-consumption decisions. As a tax on labor income,
it distorts human capital investment decisions. In each period only the old
have capital income, whereas only the young have labor income. There is
therefore an intergenerational conflict (between the young and the old) in
the determination of the taxes in each period. In each period the young
would prefer to tax only capital income in that period. (The capital income
of the young would be taxed only in the next period in another round of
voting.) On the other hand, the old would like to tax only labor income
(save for altruism for the young offspring).
We assume some kind of an implicit intergenerational contract by which labor
and capital are taxed at a uniform rate $(\tau )$. The revenues are used to
provide a flat benefit $(b)$\footnote[3]{%
This formulation of a flat $b$, which is independent of the taxes
(contributions) paid by the recipient, is of a Beveridgeam type. The spirit
of our analysis continues to hold also in a Bismarckian system, as long as
the benefit does not exactly match the contribution; see Galasso and Profeta
(2007).}$.$ The tax rate and the generosity of the benefit are linked
through the government's budget constraint. In a multi-period setting such
as ours, this simple specification captures the spirit of a pay-as-you-go
tax-transfer system. The features of the transfer can include a uniform per
capita grant (either in cash or in-kind, such as national health care), as
well as age-related benefits such as old-age social security and medicare,
or free public education. The transfer is defined per family so that the
number of children in the family does not affect the attitude of the family
toward the transfer. Therefore, the number of children does not affect the
voting decision of the family. Also, each family (whether young or old and
irrespective of the number of children) consists of the same number of
eligible voters. In addition to the intergenerational conflict, there is
also the standard conflict between the rich and the poor of both
generations. The transfer is defined per family so that the number of
children in the family does not affect the attitude of the family toward the
transfer. Therefore, the number of children does not affect voting decision
of the family. Also, each family (whether young or old and irrespective of
the number of children) consists of the same number of eligible voters.
\subsection{Skill-acquisition decisions}
As in RSS, we assume a stylized economy in which there are two types of
workers: \ Skilled workers who have high productivity and provide $q_{H}$
efficiency units of labor per each unit of labor time, and unskilled workers
who have low productivity and provide only $q_{L}$ efficiency units of labor
per each unit of labor time, where $q_{L}$ $<$ $q_{H}.$ Workers have one
unit of labor time during their first period of life, but are born without
skills and thus with low productivity. Each worker chooses whether to
acquire an education and become a skilled worker or remain unskilled. After
the working period, individuals retire, with their consumption funded by
savings.
There is a continuum of individuals, characterized by an innate ability
parameter, $e,$ which is the time needed to acquire an education. By
investing $e$ units of labor time in education, a worker becomes skilled
after which the remaining $1-$ $e$ units of labor time provide an amount of $%
(1-e)q_{H}$ units of effective labor. Less capable individuals require more
time to become skilled and thus find education more costly in terms of lost
income (education is a full-time activity). We assume that there is also a
positive pecuniary cost of acquiring skills, $\gamma ,$ which is not tax
deductible.\footnote[4]{%
This is typically the case in practice where the out-of-pocket cost of
investment in human capital is not tax-deductible. In contrast, investment
in physical capital is tax-deductible, albeit imperfectly, through annual
depreciation allowances (rather than full dispensing).
\par
{}} The cumulative distribution function of innate ability is denoted by $%
G(e),$ with the support being the interval $[0,1].$ The density function is
denoted by $g=G^{\prime }.$
If an $e-$~individual (namely, an individual with an education-cost
parameter $e)$ decides to become skilled, then her after-tax income is $%
(1-\tau )wq_{H}(1-e)+b-\gamma ,$ where $w$ is the wage rate per efficiency
unit of labor, $\tau $ is the flat tax on labor income, and $b$ is a uniform
benefit (demogrant). If she remains unskilled, her after-tax income is $%
(1-\tau )q_{L}w+b.$ Note that, naturally, acquiring a skill is more
attractive for individuals with low cost of education than for individuals
with higher costs.
Thus, there exists a cutoff level, $e^{\ast },$ such that those with
education-cost parameter below $e^{\ast }$ invest in education and become
skilled, whereas everyone else remains unskilled. This cutoff level is the
cost-of-education parameter of an individual who is just indifferent between
becoming skilled or not:
\begin{equation}
e^{\ast }(\tau )=1-\frac{q_{L}}{q_{H}}-\frac{\gamma }{(1-\tau )q_{H}w}.
\label{one}
\end{equation}
\noindent Note that the higher is the tax rate the lower is $e^{\ast }.$
That is, the fraction of skilled in the labor force falls with the tax rate.
In order to simplify the dynamics of the model we assume, as in RSS, that
factor prices are not variable. We specify a production function which is
effectively linear in labor, $L,$ and capital, $K:$
\begin{equation}
Y=wL+(1+r)K, \label{two}
\end{equation}
\noindent\ where $Y$ is gross output. The wage rate, $w,$ and the gross
rental price of capital, $1+r,$ are determined by the marginal productivity
conditions for factor prices $(w=\partial Y/\partial L$ and $1+r=\partial
Y/\partial K)$ and are already substituted into the production function. The
linearity of the production function can arise as an equilibrium outcome
through either international capital mobility or factor price equalization
arising from goods' trade. For simplicity, the two types of labor are
assumed to be perfect substitutes in production in terms of efficiency units
of labor input, and capital is assumed to fully depreciate at the end of the
production process.
We assume that the population grows at a rate of $n.$ Because individuals
work only in the first period, the ratio of retirees to workers is $1/(1+n),$
and the dependency ratio - retired as a share of the total population -
equals $1/(2+n).$
Each individual's labor supply is assumed to be fixed, so that the income
tax does not distort individual labor supply decisions at the margin. The
total labor supply does, however, depend on the income tax rate, as this
affects the cutoff cost-of-education parameter $e^{\ast }$ and thus the mix
of high and low skill workers in the economy. This can be seen from equation
(1) which implies that $e^{\ast }$ is declining in $\tau ,$ so that the tax
system is distortive.\footnote[5]{%
A further distortion is caused in practice by the progression of the income
tax, as the opportunity cost of investment in human capital (in the form of
foregone income)\ is typically taxed at a lower rate than the return to
investment in human capital.}
An increase in $\tau $ reduces the share of the skilled individuals in the
labor force. This, in turn, reduces the effective labor supply and output.
We denote by $\tau _{t}$ and $b_{t}$\ the tax rate and the benefit,
respectively, prevailing in period $t.$ In this period the total labor
supply is given by:
\begin{equation}
L(\tau _{t})=\left( \int_{0}^{e^{\ast }(\tau
)}(1-e)q_{H}dG+q_{L}\{1-G[e^{\ast }(\tau _{t})]\}\right) N_{0}(1+n)^{t}=\ell
(\tau _{t})N_{0}(1+n)^{t}, \label{three}
\end{equation}
\noindent where $N_{0}(1+n)^{t}$ is the size of the working age population
in period $t$ (with $N_{0}$ the number of young individuals in period 0), \
and $\ell (\tau _{t})=\int_{0}^{e^{\ast }(\tau _{t})}(1-$ $%
e)q_{H}dG+q_{L}\{1-G[e^{\ast }(\tau _{t})]\}$ is the average (per worker)
labor supply in period $t.$ This specification implies that for each $e$ and
$t,$ the number of individuals in period $t,$ with a cost-of-education
parameter less than or equal to $e,$ is $(1+n)^{t}$ times the number of such
individuals in period 0.
\subsection{Saving decisions}
An individual consumes one consumption good in each period of her life:
First-period consumption of an individual born at $t$ is denoted by $c_{1t}$
and second-period consumption of this individual is denoted by $c_{2t}.$
Individuals have identical preferences which are represented by $u(c_{1t},$ $%
c_{2t}).$ The life-time budget constraint of an $e-$ individual is:
\begin{equation}
c_{1t}+\frac{c_{2t}}{1+(1-\tau _{t+1})r}=W(e,\tau _{1t},\tau
_{t+1},b_{t},b_{t+1}), \label{four}
\end{equation}
\noindent where $W(\cdot )$ is her life-time income or wealth:
\begin{equation}
W(e,\tau _{t},\tau _{t+1},b_{t},b_{t+1})=\left\{
\begin{tabular}{ll}
$(1-\tau _{t})q_{H}w(1-e)+b_{t}+\dfrac{b_{t+1}}{1+(1-\tau _{t+1})r},$ & $%
\text{if\ \ }e\leqq e^{\ast }(\tau _{t})$ \\
$(1-\tau _{t})q_{L}w+b_{t}+\dfrac{b_{t+1}}{1+(1-\tau _{t+1})r},$ & $\ \text{%
if\ }e\geqq e^{\ast }(\tau _{t})$%
\end{tabular}%
\right. . \label{five}
\end{equation}
Maximization of $u,$ subject to the budget constraint, yields the
consumption demand functions, $C_{i}(e,\tau _{t},\tau
_{t+1},b_{t},b_{t+1})),\ i=1,2$ , \noindent and the indirect utility
function, $v(e,\tau _{t},\tau _{t+1},b_{t},b_{t+1}).$ The saving of an $e-$
young individual is:
\begin{equation}
s(e,\tau _{t},\tau _{t+1},b_{t},b_{t+1})=\left\{
\begin{tabular}{ll}
$(1-\tau _{t})q_{H}w(1-e)+b_{t}-C_{1}(e,\tau _{t},\tau _{t+1},b_{t},b_{t+1})%
\text{,}$ & $\text{if }e\leqq e^{\ast }(\tau _{t})$ \\
$(1-\tau _{t})q_{L}w+b_{t}-C_{1}(e,\tau _{t},\tau _{t+1},b_{t},b_{t+1})\text{%
, }$ & $\text{if }e\geqq e^{\ast }(\tau _{t})$%
\end{tabular}%
\text{ }\right. \label{six}
\end{equation}
Aggregate saving, denoted by $S(\cdot ),$ is given by:
\begin{equation}
S(\tau _{t},\tau _{t+1},b_{t},b_{t+1})=\int_{0}^{1}s(e,\tau _{t},\tau
_{t+1},b_{t},b_{t+1})dG(e). \label{seven}
\end{equation}
\subsection{The government budget constraint}
The government balances its budgets period-by-period. Its outlays in period $%
t$ are $b_{t}[N_{0}(1+n)^{t-1}+N_{0}(1+n)^{t}],$ as there are $%
N_{0}(1+n)^{t-1}$ old people and $N_{0}(1+n)^{t}$ young people living in
period $t.$ Its revenues come from the income tax on both labor and capital.
Only the old have savings and capital income. The saving of an $e-$ (old)
individual in period $t,$ which is exogenously given, is denoted by $%
s_{t-1}(e).$ Average (per old) saving in period $t,$ denoted by $S_{t-1}$ is
also given in period $t:$
\begin{equation}
S_{t-1}=\int_{0}^{1}s_{t-1}(e)dG. \label{eight}
\end{equation}
Only the young have labor income. Thus, the government's budget constraint
in period $t$ is given by:
\begin{equation}
b_{t}=\frac{\tau _{t}}{2+n}[rS_{t-1}+(1+n)w\ell (\tau _{t})]. \label{nine}
\end{equation}
In period $t,$ $S_{t-1}$ is given, so that the government's budget
constraint determines $b_{t}$ as a function of $\tau _{t}$ and $S_{t-1}:$ $%
b_{t}=B(\tau _{t},S_{t-1})$ $.$
\subsection{\noindent A politico-economic equilibrium}
In period $t,$ the tax rate $\tau _{t}$ is determined by the majority of the
people (old and young) alive in this period. (Recall that this choice of $%
\tau _{t}$ determines also $b_{t}.)$ The old naturally care only about $\tau
_{t}$ (and $b_{t}),$ because period $t$ is their last period of life.
However, the young who will grow to be old in period $t+1$ are aware that
their welfare depends also on the tax rate, $\tau _{t+1},$ and the benefit, $%
b_{t+1},$ that will be determined in period $t+1.$
We now turn to the description of a politico-economic equilibrium. We look
first at the voting decision of an old individual with an education-cost
parameter $e.$ Her saving, denoted by $s_{-1}(e),$ has already been
predetermined. Her \textbf{net }gain from the tax-transfer system, denoted
by $V_{t}^{O}(e),$ is given by:
\begin{equation}
V_{t}^{O}(e)\equiv V^{O}(e,\tau _{t},S_{t-1}^{t})=B(\tau _{t},S_{t-1})-\tau
_{t}rs_{t-1}(e). \label{ten}
\end{equation}
She will vote for raising (lowering) the tax rate $\tau _{t},$ if $\partial
V^{O}/\partial \tau _{t}>(<)0.$ Note that $s_{t-1}(e)$ is strictly declining
in $e$ for all $e(<)0.$ We plausibly assume that $\partial
^{2}v/\partial \tau _{t}\partial e\geq 0.$ That is, if a certain tax hike
benefits a young individual of type $e_{1},$ it must benefit all individuals
with $e>e_{1}$ (that is, who are poorer than her); conversely, if a tax cut
is beneficial for an $e_{1}-$ individual, it must also be beneficial for all
individuals with $e0$), then the young
constitute the majority of the population. The young have no capital income.
Also, as the savings of the old are predetermined, there is no distortion
created by taxing capital, so that raising the tax will always generates
more tax revenues for the benefit of all (young and old). Therefore, the
majority will opt for a 100\% tax on capital (as in the standard
time-inconsistency context).
\subsubsection{Income tax}
We now return to study the object of interest in this section, which is the
effect of aging on the income tax (on both labor and capital). Unlike the
labor tax case where the old were all for raising the tax, now, as the tax
is levied on capital income too, the old are no longer unanimous in their
attitude towards the tax; the rich old may well be against the income tax.
Therefore, the old pivot is also relevant for the determination of the tax
transfer system. Thus, each one of the two cases studied under the labor tax
(the pivot young being either skilled or unskilled) must be separated into
two cases according as to whether the old pivot is skilled or unskilled.
Therefore, there are altogether four cases that we will investigate below.
Note in general that the fiscal leakage factor is no longer clear-cut. As
the income tax base includes both labor and capital income, then the labor
tax component of the income tax is levied on the young only, but the
revenues from it "leak" to the old as well. Similarly, the capital tax
component is levied on the old only, but the revenues from it "leak" to the
young as well. Therefore, the fiscal leakage factor becomes ambiguous.
\bigskip
\textbf{(a)\ Young pivot - unskilled; old - pivot skilled}\footnote[9]{%
Parameter values: $r=2$, $q_{H}=1$, $q_{L}=0.001$, $\gamma =0.0001$, $\beta
=0.5.$}\textbf{\ }
Recall that with a tax on labor only, the first factor vanishes (because the
young is unskilled)\ and the second (the fiscal leakage) factor decreased
the tax rate as population ages. But, with an income tax, the first factor
(the change of the pivot) reemerges because the old pivot is skilled. In our
simulations, $e^{O}$, the education-cost parameter of the old pivot,
declines as population ages. That is, the old pivot changes to a richer
(more skilled) individual whose anti-tax attitude is stronger and she would
have preferred to lower the tax. However, apparently the fiscal leakage
effect becomes strongly in favor of raising the tax, as the young are now
more motivated to raise the tax because there are more old people to be
taxed, so that more revenues from the capital tax can leak to the young. The
latter effect dominates and the politico-economic equilibrium tax rate rises
as the population ages.
\bigskip
\textbf{(b) Young pivot - unskilled; old pivot - unskilled}
This configuration cannot in general produce an equilibrium. When a pivot,
whether young or old, is unskilled, then a small change in the identity of
the pivot does not change her attitude towards the tax. When both pivots are
unskilled, then small changes in the identities of both pivots do not
produce a change in the preferred tax rate. At the same time, both pivots
must prefer the same tax rate in a politico-economic equilibrium. Such a
single tax rate need not exist.
\bigskip
\textbf{(c) Young pivot - skilled; old pivot - skilled}\footnote[10]{%
Parameter values: $r=4$, $q_{H}=1$, $q_{L}=0.01$, $\gamma =0.2$, $\beta
=0.5. $}
In our simulations, as the population ages, the young pivot changes to a
poorer (less skilled) individual who would also like to expand the size of
the welfare state. Similarly, the old pivot also changes in the same
direction, and the new old pivot would like to hike the tax. But apparently,
the fiscal leakage factor stemming from the tax revenues (and especially
those from the labor tax component)\ being spread over a larger population
of the old, dominates:\ as population ages, the income tax rate declines.
\bigskip
\textbf{(d) Young pivot - skilled; old pivot - unskilled}\footnote[11]{%
Parameter values: $r=4$, $q_{H}=1$, $q_{L}=0.5$, $\gamma =0.2$, $\beta =0.5.$%
}
As the population ages, the identity of young pivot, who is skilled, changes
to a more able individual (with a lower cost-of-education parameter). This
new pivot would like to cut the tax rate. The identity of the old pivot
changes too to a more able individual; but this change does not have any
effect on the preferred tax rate of the old pivot, as she is unskilled. In
case (c)\ above, the skilled young pivot became less able and more pro-tax.
Nevertheless, the fiscal leakage effect dominated, and the tax rate
declined, as the population aged. In our case, the tax certainly has to
decline as the population ages, because the young skilled pivot becomes more
able and more anti-tax.\bigskip
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Notes:
\begin{tabular}{l}
$\tau ^{L}$ - the labor tax \\
$\tau $ - the income tax \\
An upward arrow indicates an increase in the relevant variable, as
population ages. \\
A downward arrow indicates a decline in the relevant variable, as population
ages.%
\end{tabular}
\subsection{Summary}
We extend the RSS model to highlight the complexity of the fiscal leakage
effect and the changes in the political power balance. Tax revenues are
generally biased in favor of the old \ (old-age social security, medicare,
etc.). Therefore, one would expect the pro-tax coalition to gain more
political clout as population ages; consequently, aging should tilt the
political power balance in favor of expanding the welfare state. However, a
careful scrutiny of the politico-economic equilibrium reveals also a
multitude of fiscal leakages that are at play. The equilibrium is governed
by the preferences of two voting pivots, one young and one old. Aging may
change the young pivot to a richer, more anti-tax individual. The fiscal
leakage of revenues from the larger number of old taxpayers of the capital
tax component of the income tax to the young may encourage the latter to
vote for more taxes. But, on the other hand, the fiscal leakage from the
young taxpayers of the labor tax component of the income tax to a larger
number of old beneficiaries may tame the appetite of the young for more
taxes. As a result, the welfare state does not necessarily expands, when its
population ages.
\section{Conclusion: testing the model predictions}
In order to illustrate the problems in testing the predictions of the
various voting models, we confine attention to the basic RSS labor-tax
model. We referred specifically to two conflicting factors which determine
how the tax rate changes when population ages: the change in the median
voter and the fiscal leakage effect.
In order to isolate the effect of aging on the tax rate through the fiscal
leakage mechanism, specify the following equation:
\begin{equation}
\tau =\alpha +\beta x+\gamma y+\delta z+\theta v+\varepsilon ,
\end{equation}%
where:
$x$ - elderly dependence ratio,
$y$ - child dependency ratio,
$z$ - a political economy measure proxying the median voter (say, a rise in
z, means a richer median voter).
$v$ - a vector of other control variables.
Now, if only $x$ is included in the regression, as an explanatory variable
(in addition to $v$), then we have two left out variables, $y$ and $z$. We
know [see, for instance, Gujarati (1995)] that in this case the OLS estimate
of $\beta $ is biased. The magnitude of the bias is a function of the true
coefficients of the left out variables and the sample correlations between
these variables and the error term ($\varepsilon $). For instance, if, as in
our theory, $\delta $ is negative, and if the sample correlation between $z$
and the error term is negative, then the OLS estimate of $\beta $ is biased
upward. Furthermore, even if we had a good proxy for the median voter ($z$),
then we would still face serious problems, because $z$ is \emph{jointly}
determined with $x$, $y$, and, in particular, $\tau $. We would have
therefore needed a \emph{good instrument} for $z$. This was unavailable to
RSS as to Disney (2007).
This is why we viewed the analysis of the data in RSS as merely
illustrative: "We show that the data are broadly consistent with the
specific structural model of the theory. The empirical results must thus be
seen as only suggestive, particularly since the regressions do not test
against alternative mechanism" (RSS, p. 911). The main objective of RSS was
to underscore theoretically the fiscal leakage effect. The latter may be
quite complex, but, as we show here, its politico-economic existence in the
wake of aging remains intact.
\newpage
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\end{document}