aging and the welfare state: a political economy model assaf razin, efraim sadka and edith sand...
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Aging and the Welfare State:
A Political Economy Model
Assaf Razin, Efraim Sadka and Edith Sand
October 2005
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.
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).
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.
• 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 :
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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:
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where is the size of the working age population in period (with the number of young individuals in period 0), and
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is the average (per worker) labor supply.
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Individuals have identical preferences:
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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:
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where is the level of transfer payments.
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The saving of the young individual is:
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aggregate saving per capita of the young, denoted by , is:
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The indirect utility function of the young individual is given by:
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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 government’s balanced budget constraint implies:
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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 :
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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.
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 : ))(),(( 2111 eses ttt
We first describe the saving decisions.
1. 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:
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2. The tax rate is chosen as to maximize the decisive voter’s utility function, while taking the saving choice rules and , and the future tax rate to be: . The first order condition is:
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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 Non RMEThe RME
Income Tax Capital Tax Income TaxCapital Tax
Tax rate
-18.10886130.16946800
Skilled Young Saving Rate
0.45168-1.12836680.2553414-0.6607534-
Unskilled Young Saving Rate
-23.2251535-7.73126730.8016346-1.2191084-
• Panel 2:Consumption Equivalent Utility:
0.6008650.05714273.1631226.0377
Unskilled Old Unskilled Old Unskilled Old Unskilled Old
-0.537294-0.600879-1.4597818.1175
Skilled Old Skilled Old Skilled Old Skilled Old
1.591740.6499210.369484-119.857
Unskilled Young Unskilled Young Unskilled Young Unskilled Young
0.718345-0.382360.0881641-0.0262898
Skilled YoungSkilled YoungSkilled YoungSkilled Young
Capital TaxIncome TaxCapital Tax Income Tax
The RMEThe Non RME
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Panel 3: Fiscal Leakage:
The Parameters are
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Income Tax Capital TaxFiscal Leakage from the Skilled Young Fiscal Leakage from the Skilled Young
-13.87336881 -2.43902Fiscal Leakage from the Unskilled Young Fiscal Leakage from the Unskilled Young
-0.47516888 -2.438985442Fiscal Leakage from the Skilled Old Fiscal Leakage from the Skilled Old
-0.600838202 -0.537294Fiscal Leakage from the Unskilled Old Fiscal Leakage from the Unskilled Old
-0.571387163 -0.600865
The RMEIncome Tax Capital Tax Fiscal Leakage from the Skilled Young Fiscal Leakage from the Skilled Young
-2.391155933 -0.305307398Fiscal Leakage from the Unskilled Young Fiscal Leakage from the Unskilled Young
-0.255408231 -0.305307398Fiscal Leakage from the Skilled Old Fiscal Leakage from the Skilled Old
0.659178274 -1.626453044Fiscal Leakage from the Unskilled Old Fiscal Leakage from the Unskilled Old
-6.713067842 -2.988550973
The Non RME
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Observations
• Comparison between capital tax and income tax (in the Non RME):
a. Aging lowers tax rate in the income tax regime but raises the tax rate in the capital tax regime.
b. 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.
• Comparison of the Non RME and the RME equilibria:
a. 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:
b. 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.