Aging and the Welfare State: A Political Economy Model

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Aging and the Welfare State A Political
Economy Model

• Assaf Razin, Efraim Sadka and Edith Sand
• October 2005

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Summary

• An income tax is generally levied on both labor
  and capital. The working young bear mostly the
  tax on labor income, whereas the retired old, who
  draws income from her accumulated savings, bear
  the brunt of the capital tax. Therefore, there
  arise two types of conflicts in the determination
  of the income tax the standard
  intra-generational conflict between the poor and
  rich, and an intergenerational conflict between
  the young and the old.

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• The paper analyzes how aging affects the
  resolution of these conflicts, and the
  politico-economic force that is at play the
  fiscal leakages from taxpayers to transfer
  recipients.
• The effect of aging is evaluated in the context
  of two equilibrium concepts Rational Myopic
  Equilibrium (RME) and Rational Forward-Looking
  Equilibrium (RFE).

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Features of the Model

• A standard overlapping-generations model. Each
  generation lives for two periods in the first
  period of life, the individual can invests in
  human capital and work in the second period of
  life the individual retires. In the first period,
  the endowment of time is equal to 1.

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• There are two types of workers, characterized by
  an innate ability parameter, (which is the
  time needed to acquire education).
• percent of the population is assumed to be
  of type , and the rest of type .
• Only type decides to acquire education, and
  thus produce units of effective
  labor. Type remains unskilled, and produces
  only units of effective labor.

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• The production function is linear in labor, ,
  and capital
• (1)
• where is gross output. The wage rate, ,
  and the rental price of capital, , are
  determined by the marginal productivity
  conditions (depreciation rate is 100).

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• Population grows at a rate of . The
  dependency ratio (retired as a share of the
  total population) equals .
• Total labor supply is given by
• (2)
• where is the size of the
  working age population in period (with the
  number of young individuals in period 0), and
• (3)
• is the average (per worker) labor supply.

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• Individuals have identical preferences
• (4)
• where is the first-period consumption of an
  individual born at t and is the
  second-period consumption of this individual.
• The life-time budget constraint of an individual
  is
• (5)
• where is the level of transfer payments.

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• The saving of the young individual is
• (6)
• aggregate saving per capita of the young, denoted
  by , is
• (7)
• The indirect utility function of the young
  individual is given by
• (8)

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• The tax-transfer system is pay as you go The
  government levies a flat income tax, on both
  labor and capital, which fully finances the
  transfer payments to both generations.
• The governments balanced budget constraint
  implies
• (9)

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The Politico-Economic Equilibrium

• The tax rate is determined by the majority
  of the people (old and young) alive.
• Type I Equilibrium Rational Myopic Equilibrium
  (RME) Future policies are taken as given.
• Type II Equilibrium Rational Forward-Looking
  Equilibrium (RFE) Individuals take into account
  the response of future policies to the policy
  chosen by them at present (similar to Krusell and
  Rios-Rull (1999).

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Rational Myopic Equilibrium

• The voting decisions of the young and old
  individual
• (10)
• (11)
• Note that the effect of on all future taxes
  is not taken into account.

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• Note also that the voting decisions do not
  depend on , thus the solution is a corner
  solution.
• The case where takes place when more
  than half of the population favor a higher tax
  rate ( that is, if ,the conditions are
  or
  )
• The case where takes place when more
  than half of the population favor a lower tax
  rate ( that is, if the
• conditions are ,
  or
• ).

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Rational Forward-Looking Equilibrium

• Current voting decisions affect the
  determination of current savings. These in turn
  affect the voting decisions of the next period
  and so on. Individuals are assumed to take into
  account this chain effects.
• That is, individuals internalize the link
  between their current voting decisions and the
  voting decisions in the next period.

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• The Policy Rule
• Assuming that the strategies of the game are
  restricted to Markov strategies, the policy rule,
  , depends only on the state variables at the
  beginning of the period that is, the savings of
  the skilled young and the unskilled young of the
  previous period

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• We first describe the saving decisions.
• Denote the saving choice rules of the young
  skilled and the young unskilled as a function of
  previous-period savings and the current policy
  choice, ,
  .
• The functions and describe what the
  individuals will do given that they expects
  future taxes to be set according to . That is
  and are derived from the first order
  conditions of the young individuals
• (12)
• (13)

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• 2. The tax rate is chosen as to maximize the
  decisive voters utility function, while taking
  the saving choice rules and
  , and the future tax rate to be
  . The first
  order condition is
• (14)
• The fixed-point condition requires that for
  every the solution to the problem will
  be given by .

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Results

• Proposition The RFE has multiple equilibria
  among them is the RME equilibrium.
• The effect of aging on the tax rates, saving
  rates, consumption-equivalent utility and fiscal
  leakage measures (in percents)
• Panel 1

The RME The RME The Non RME The Non RME
Capital Tax Income Tax Capital Tax Income Tax
Tax rate Tax rate Tax rate Tax rate
0 0 0.169468 -18.1088613
Skilled Young Saving Rate Skilled Young Saving Rate Skilled Young Saving Rate Skilled Young Saving Rate
0.6607534- 0.2553414- -1.1283668 0.45168
Unskilled Young Saving Rate Unskilled Young Saving Rate Unskilled Young Saving Rate Unskilled Young Saving Rate
1.2191084- 0.8016346- -7.7312673 -23.2251535
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• Panel 2Consumption Equivalent Utility

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Panel 3 Fiscal LeakageThe
Parameters are
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Observations

• Comparison between capital tax and income tax (in
  the Non RME)
• Aging lowers tax rate in the income tax regime
  but raises the tax rate in the capital tax
  regime.
• Aging lowers the utility level of skilled young
  and unskilled young while raises the utility
  level of skilled old, in the income tax regime.
  Under the capital tax regime, aging has opposite
  effects it raises the utility level of skilled
  young and unskilled young while lowers the
  utility level of skilled old. The unskilled old
  utility level increases in both the capital tax
  and the income tax regimes.

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• Comparison of the Non RME and the RME equilibria
• The effect of aging on the tax rates is zero (a
  corner solution) in the RME. In the income tax
  regime aging lowers the tax rate in the capital
  tax regime aging raises the tax rate.
• The effect of aging on the utility levels of the
  different income and age groups are
• Under the income tax regime, aging has similar
  effects across the tax regimes on the skilled
  young and unskilled old but opposite effects on
  the unskilled young and skilled old.
• Under the capital tax regime, aging has similar
  effects.