Determinants of the Welfare Determinants of the Welfare State: Dependency Ratio, Wage State: Dependency Ratio, Wage

Gap and Low-Skill MigrationGap and Low-Skill Migration

Assaf Razin, Efraim Sadka, Phillip Assaf Razin, Efraim Sadka, Phillip SwagelSwagel

Tax-Transfer Policy in a Tax-Transfer Policy in a Political-Economy EquilibriumPolitical-Economy Equilibrium

• Two types of workers: skilled workers who Two types of workers: skilled workers who have high productivity and provide one have high productivity and provide one efficiency unit of labor per each unit of labor efficiency unit of labor per each unit of labor time, and unskilled workers who have low time, and unskilled workers who have low productivity and provide only q<1 efficiency productivity and provide only q<1 efficiency units of labor per each unit of labor time. units of labor per each unit of labor time. Workers have one unit of labor time during Workers have one unit of labor time during their first period of life, but are born without their first period of life, but are born without skills and thus with low productivity.skills and thus with low productivity.

• There is a continuum of individuals, There is a continuum of individuals, characterized by an innate ability parameter, characterized by an innate ability parameter, e, which is the time needed to acquire an e, which is the time needed to acquire an education.education.

• We assume also a positive pecuniary cost We assume also a positive pecuniary cost of acquiring skills, , which is not tax of acquiring skills, , which is not tax deductible. The cumulative distribution deductible. The cumulative distribution function of innate ability is denoted by function of innate ability is denoted by GG((ee), with the support being the interval ), with the support being the interval [0,1]. The density function is denoted by [0,1]. The density function is denoted by g=Gg=G′. ′.

• Suppose that the government levies a flat Suppose that the government levies a flat tax on labor income in order to finance a tax on labor income in order to finance a flat grant, flat grant, bb..

• A simple decision rule: A simple decision rule:

Acquire skill Acquire skill iffiff

bqbe 111

• Cutoff education-cost parameter:Cutoff education-cost parameter:

• Rearranging terms gives the cutoff Rearranging terms gives the cutoff level for the education decisions:level for the education decisions:

(1)(1)

• The production function is effectively The production function is effectively linear in labor, linear in labor, LL, and capital, , and capital, KK: :

(2)(2)

where where YY is gross output. is gross output.

.111 * bqbe

1

1* qe

,1 KrLY

(3) (3)

where is the size of the working where is the size of the working age population in period age population in period tt (with N (with N00 the the number of young individuals in period 0), number of young individuals in period 0), and is the and is the average (per worker) labor supply in period average (per worker) labor supply in period tt..

The government budget constraint implies:The government budget constraint implies:

Therefore, the lump-sum grant equals:Therefore, the lump-sum grant equals:

(4) (4)

tt

te

tt

nNel

nNeGqdGeLt

1

111

0*

0

0

*

*

tnN 10

.1

11

0*

10

ttt

tttt

t

nNel

LnnNb

*0

* 11*

t

e

t eGqdGeelt

.2/1* nnelb ttt

In period t the totalIn period t the total labor supply islabor supply is::

• For any tax rate , dependency ratio For any tax rate , dependency ratio ((as indicated by as indicated by nn ) ) and wage gap and wage gap ((as as indicated by qindicated by q)), equations , equations ((11 ) ) and and ((44 ) ) determine and determine and as functions of , as functions of , nn, and , and qq ..

• The net after-tax lifetime income is The net after-tax lifetime income is given by:given by:

qee tt ,** qnbb tt ,,

t

,,1

,,,,1

,1

,,,,11

,,,,5

*

1

*

1

1

qeeforr

qnbqnbq

qeeforr

qnbqnbe

qneW

t

tt

t

tt

tt

• A young individual born in period t A young individual born in period t chooses her firstchooses her first- - and secondand second--period period consumption consumption ((cc1t1t and and cc2t2t, respectively, respectively) )

to maximize lifetime utility, to maximize lifetime utility, uu ((cc1t1t, , cc2t2t)), , subject to the lifetime budget subject to the lifetime budget constraint,constraint, . .

• SecondSecond--period consumption of a retiree period consumption of a retiree born in period born in period tt-1-1 ( (that is, consumption that is, consumption of a retiree in period of a retiree in period tt ) ) is given byis given by::

(6) (6)

where where SSt-1t-1(e,n,q)(e,n,q) denotes this denotes this individual's savings in period individual's savings in period tt-1-1..

qneWrcc tttt ,,,,1/ 121

,,,1,,,, 11,2 qnbrqneSqnec ttt

Note thatNote that::

0/ tW 0/ tW

0/ tW

• Therefore, if for some Therefore, if for some ee00, then , then for all for all e > ee > e00. And, similarly, if . And, similarly, if for some for some ee00, then for all , then for all e < ee < e00..

0/ tW

• Denote the education-cost parameter of Denote the education-cost parameter of the median voter by the median voter by eeMM. Then:. Then:

Dividing this equation by Dividing this equation by NN00(1+n)(1+n)t-1t-1 and and rearranging terms yields the education-rearranging terms yields the education-cost parameter for the median voter:cost parameter for the median voter:

(7)(7)

The political equilibrium tax rate, , in The political equilibrium tax rate, , in period t [denoted by ] maximizes period t [denoted by ] maximizes the after-tax lifetime income of the the after-tax lifetime income of the median voter:median voter:

(8)(8)

qn,0

,,,,maxarg,0 qnneWqn M

so that is implicitly defined by so that is implicitly defined by the first-order condition:the first-order condition:

(9) (9)

and the second-order condition is:and the second-order condition is:

(10) (10)

qn,0

0,,,,,

qnB

qnneW M

.0,,,,,,,

020

2

qnqnB

qnqnneW M

((1111))

The Effect of the Dependency Ratio

The Effect of the Wage GapThe 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 EvidenceEmpirical Evidence

Low-skill Migration: Theory and Low-skill Migration: Theory and EvidenceEvidence..