Determinants of the Welfare State: Dependency Ratio, Wage Gap and Low- Skill Migration Assaf Razin, Efraim Sadka, Phillip Swagel

Tax-Transfer Policy in a Political- Economy Equilibrium Two types of workers: skilled workers who have high productivity and provide one efficiency unit of labor per each unit of labor time, and unskilled workers who have low productivity and provide only q<1 efficiency units of labor per each unit of labor time. Workers have one unit of labor time during their first period of life, but are born without skills and thus with low productivity.Two types of workers: skilled workers who have high productivity and provide one efficiency unit of labor per each unit of labor time, and unskilled workers who have low productivity and provide only q<1 efficiency units of labor per each unit of labor time. Workers have one unit of labor time during their first period of life, but are born without skills and thus with low productivity. There is a continuum of individuals, characterized by an innate ability parameter, e, which is the time needed to acquire an education.There is a continuum of individuals, characterized by an innate ability parameter, e, which is the time needed to acquire an education.

We assume also a positive pecuniary cost of acquiring skills,, which is not tax deductible. 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′.We assume also a positive pecuniary cost of acquiring skills,, which is not tax deductible. 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′. Suppose that the government levies a flat tax on labor income in order to finance a flat grant, b.Suppose that the government levies a flat tax on labor income in order to finance a flat grant, b. A simple decision rule:A simple decision rule: Acquire skill iff

Cutoff education-cost parameter:Cutoff education-cost parameter: Rearranging terms gives the cutoff level for the education decisions:Rearranging terms gives the cutoff level for the education decisions:(1) The production function is effectively linear in labor, L, and capital, K:The production function is effectively linear in labor, L, and capital, K:(2) where Y is gross output.

(3) where is the size of the working age population in period t (with N 0 the number of young individuals in period 0), and is the average (per worker) labor supply in period t. The government budget constraint implies: Therefore, the lump-sum grant equals: (4) In period t the total labor supply is:

For any tax rate, dependency ratio (as indicated by n) and wage gap (as indicated by q), equations (1) and (4) determine and as functions of, n, and q.For any tax rate, dependency ratio (as indicated by n) and wage gap (as indicated by q), equations (1) and (4) determine and as functions of, n, and q. The net after-tax lifetime income is given by:The net after-tax lifetime income is given by:

A young individual born in period t chooses her first- and second-period consumption (c 1t and c 2t, respectively) to maximize lifetime utility, u(c 1t, c 2t ), subject to the lifetime budget constraint,.A young individual born in period t chooses her first- and second-period consumption (c 1t and c 2t, respectively) to maximize lifetime utility, u(c 1t, c 2t ), subject to the lifetime budget constraint,. Second-period consumption of a retiree born in period t-1 (that is, consumption of a retiree in period t) is given by:Second-period consumption of a retiree born in period t-1 (that is, consumption of a retiree in period t) is given by:(6) where S t-1 (e,n,q) denotes this individual's savings in period t-1.

Note that: Therefore, if for some e 0, then for all e > e 0. And, similarly, if for some e 0, then for all e e 0. And, similarly, if for some e 0, then for all e < e 0.

Denote the education-cost parameter of the median voter by e M. Then:Denote the education-cost parameter of the median voter by e M. Then: Dividing this equation by N 0 (1+n) t-1 and rearranging terms yields the education-cost parameter for the median voter: (7) The political equilibrium tax rate,, in period t [denoted by ] maximizes the after-tax lifetime income of the median voter: (8)

so that is implicitly defined by the first-order condition: (9) and the second-order condition is: (10)

(11)

The Effect of the Dependency Ratio

The Effect of the Wage Gap Total differentiation of equation (9) with respect to q implies: (15) For the sake of simplicity, we assume that e is uniformly distributed over [0, 1]. Then: and g(e)=1.

Empirical Evidence

Low-skill Migration: Theory and Evidence.