Unemployment Insurance, Wage Differentials and Unemployment

Unemployment Insurance, Wage Differentials and UnemploymentAuthor(s): Michael BräuningerSource: FinanzArchiv / Public Finance Analysis, Vol. 57, No. 4 (2000), pp. 485-501Published by: Mohr Siebeck GmbH & Co. KGStable URL: http://www.jstor.org/stable/40912943 .

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FinanzArchiv vol.57 no. 4 485

Unemployment Insurance, Wage Differentials and Unemployment Michael Brauninger*

The paper explores the relation between wages, wage differentials, and the level and structure of unemployment within a wage bargaining model. There are two types of individuals: skilled and unskilled. The bar-

gained wage of each group depends on the respective replacement rate and determines unemployment rates. Different institutional settings of the unemployment insurance system are considered in a model which includes earnings-related and flat-rate schemes as special cases. Depending on the institutional setting, replacement rates are either exogenous or

endogenous. Therefore, shocks may or may not change relevant replacement rates and, thereby may have different effects on unemployment. (JEL: H 24, J 24, J 31, J 41, J 65)

1. Introduction

Two central questions in the debate on how to fight unemployment are: why has unemployment increased so much over the last 30 years and why do unemployment rates differ so much between OECD countries? Blanchard and Wolfers (2000) state that, to answer both questions, it is necessary to analyze how shocks affect unemployment given different institutional settings. This paper contributes to the analysis of the role of shocks and institutions by fo- cusing on the point that unemployment is a particular problem of the low skilled.

In most OECD countries (except Italy) the unemployment rate declines with increasing levels of skill (Dreze and Sneessens, 1997). Therefore, the rise in overall unemployment is often associated with the rise in unemployment of the low skilled, which is a result of declining relative demand for low-skilled labor. The decline in relative demand for low-skilled labor requires an increase in the wage differential or else it leads to an increase in low-skilled unemployment. Nickell and Bell (1996, 1997), Siebert (1997) and Freeman and Schettkat (2000) discuss the empirical evidence for international differ-

* I thank two anonymous referees, Michael Carlberg, Laszlo Goerke and Jochen Micha- elis for helpful comments. The usual disclaimer applies.

FinanzArchiv 57(2000), 485-501. ©2001 Mohr Siebeck Verlag - ISSN 0015-2218



486 Michael Brauninger

ences in absolute and relative unemployment rates and wage differentials. However, an analysis based on a single coherent theoretical model seems to be missing. Therefore, this paper explores relations between wage differentials, unemployment, relative unemployment for skilled and unskilled workers, and the proportion of skilled workers within a wage bargaining model. As in all models of equilibrium unemployment, the unemployment rate depends on the level of unemployment compensation. An obvious reason for different levels of unemployment between skilled and unskilled workers might be different replacement rates. As has been pointed out by Atkinson and Micklewright (1991), relevant replacement rates for different groups of individuals depend on many different institutional settings of unemployment insurance.

To answer the question of how unemployment among different skill and income groups is affected by unemployment benefits, it seems to be of particular importance to determine how far unemployment benefits are linked to individual earnings or are paid on a flat rate. Since unemployment compensation in an earnings-related benefits scheme is linked to the individual's previous wage, the replacement rates for all income groups will be the same. In contrast, unemployment benefits are independent of an individual's previous wage in a flat-rate scheme. Replacement rates for low-skilled workers will, therefore, be higher than for skilled workers.

Previous papers concerned with the structure of unemployment insurance analyze a change from earnings-related to flat-rate schemes (Vijlbrief and van de Wijngaert, 1995; Goerke, 2000; Goerke and Madson, 2000). In doing so, they assume homogenous individuals. In contrast, this paper assumes individuals differing with respect to their skills and, therefore, allows us to study the effects of different unemployment insurance systems on relative unemployment and wage rates. Hence, the focus of this paper is different: it plac- es emphasis on the point that relevant replacement rates change endogenous- ly and differently for different income groups.

Section 2 presents the wage bargaining model. Subsection 2.1 shows how bargaining at the firm level determines the wage. Subsection 2.2. analyses the aggregate outcome. In the model, all firms are identical except that they use different types of labor: some firms use unskilled labor while others use skilled labor. It is assumed that capital is fixed at the firm level in the short run. Since firms use either skilled or unskilled labor, there is no substitution between skilled and unskilled workers. However, with some time delay capital is mobile. We take two logical steps: in the first step, capital is mobile between firms on the national level. As a result of this, skilled and unskilled workers become perfect substitutes. For convenience we call this the medium run. In the second step we assume capital to be internationally mobile. As a result, the level of the capital stock becomes endogenous. For convenience we call this the long run.



Unemployment Insurance, Wage Differentials and Unemployment 487

Section 3 analyses how two shocks change relative wages and unemployment rates depending on the institutional arrangement of the unemployment insurance. In subsection 3.1 we first look at the increase in replacement rates which has occurred in all OECD countries (Martin, 1996). The increase in the replacement rate will increase unemployment rates in both skill groups, but only in an earnings-related scheme does it do so proportionally. In any other scheme the unemployment rate of the unskilled increases more than the unemployment rate of the skilled. In subsection 3.2, we consider skilled biased technical progress, which is often regarded as an explanation for changes in relative wages and unemployment (Topel, 1997). We see that in an earnings-related scheme unemployment rates are not affected. In a flat-rate scheme the skilled unemployment rate is reduced and the unskilled unemployment rate stays constant in the short run. However, due to capital reallocation the unskilled unemployment rate might increase in the medium run. International capital mobility will then reverse this effect. Subsection 3.3 illustrates the effect of these shocks in a numerical example.

Section 4 endogenises the proportion of skilled individuals by modelling the education decision. It is shown that the education decision does not depend on relative unemployment rates. However, an increase in the proportion of individuals becoming skilled might have effects on relative unemployment rates depending on the institutional setting of the unemployment insurance.

2. Model

2.1. Wage Bargaining There is a large number of firms. Each firm i uses capital Kt and one type of labor Lh to produce a variety of other goods. All goods are imperfect substitutes and firms act under monopolistic competition. Firm / faces a demand function Yt - pj11 Y, where Yt is the demand for the good produced by firm /, pt is the relative price of that good, r' is the price elasticity of demand, and Y is an index of aggregate demand. Firms maximize profits 77, = Rt - Wi Lt - rKh where Rt = pt Y( is revenue, wt is the wage in firm i, and r is the market interest rate. Insert the inverse demand function to obtain Ri= Yllr] Yf with k = 1-1/ rj. The production function is assumed to be of Cobb-Douglas type Yt = K?(et L^f with a + /? = 1, a, /? > 0 and et as an index of labor efficiency. Profit maximization implies that the marginal revenue of labor equals the wage rate 3^//3L/ = ̂ kRÎL^ = n^.The rate of return on capital is given as revenue minus labor cost per unit of capital rt = (Rt - wÎKi = (1-/3 KjRi/Ki. Capital is owned by domestic and foreign households. Each household holds a portfolio which includes assets from all firms. Since each




firm is small, wage bargaining does not change the expected return on the individual portfolio.

Workers of each firm are represented by a union. Unions maximize the utility of a representative worker, see Booth (1995). The union has Nt members, and utility of a risk-neutral representative member is vt - (1 - ut) (1-0 W; + ut a/5 where 1 - ut is the probability of a union member being employed by firm /, with ut - (Nt - Li)/Nl •. When employed in firm /, the union member receives net income (1 - 1) wh where t is the tax rate. When not employed in firm i, the union member receives the alternative income ^.The alternative income is the income a worker obtains when not employed in firm /. In that case the worker either becomes unemployed, in which case he receives unemployment benefits, or finds a job in another firm, in which case he receives the net wage paid by other firms. The probability of finding a job in another firm depends on the strain on the labor market. This probability as well as wages paid by other firms and the tax rate are exogenous in the bargaining process. Unemployment benefits are either paid in a flat-rate scheme or they might depend (at least to some extent) on an individual's previous wages. Hence, for the small firm, all components of alternative income at as well as the tax rate are given exogenously.The number of union members is also exogenous and, therefore, the union might equivalently maximize

Unions and firms bargain about the real wage. It is assumed that bargaining leads to maximization of the Nash product: Q - (Vt- V,)7 (77)- 77/)1"7, where y defines the relative bargaining power of unions and firms. With y = 1, we have a monopoly union and with y = 0 there is no union power and the wage is set by firms. Vt and 77) are union utility and firms' profits, respec- tively, for the case of no solution to the bargaining process. If no settlement is reached, all union members receive the alternative income Vt = at Nt' while firms will not produce and incur a loss to the extent of the costs of capital fi^-rKi. This implies that the Nash product is: Q = (Lt{{' -t) v^-fl,))7 (Ri-Wi Li)1'7 . Maximization of the Nash product leads to

(l-t)wi=iiai with /i = l-y + -~-. <1) pK

The wage in firm / is set as a fixed mark-up, 'i, of alternative income. The mark-up increases with union power, y , and declines with both competitive- ness, k, and the elasticity of production with respect to labor, /?. With no union power, y = 0, the net wage corresponds to alternative income /i=l.

Union members not employed in firm / become unemployed. Following Layard and Nickell (1990), it is assumed that during each period there are fluctuations on the labor market. Hence, there is a chance for unemployed




workers to become employed during the period. It is assumed that labor markets for heterogenous types of labor are separated and the probability of stay- ing unemployed during the whole period is therefore cp Uj , where Uj is the relevant unemployment rate and (pis negatively related to the size of labor market fluctuations. The probability of becoming employed in another firm is 1 - cp Uj. When unemployed workers find a job they will receive the same net income as those workers employed in other firms, (1 - i) w;.They receive unemployment benefits Bt during unemployment.

From (1) it is obvious that taxes are relevant for the relation between wages and alternative income. Therefore, the tax treatment of alternative income is important. It is natural to assume that wages in all firms are taxed at the same rate. However, the second component of alternative income, unemployment benefits, might not be taxed or be taxed at a different rate. According to the OECD (1997) study, unemployment benefits are either taxed or fixed in relation to net wages in most countries (22 countries). Benefits are not taxed in three countries only (Czech Republic, Japan, Portugal). However, most countries do not levy social security contributions on unemployment benefits. In addition, the tax rate on benefits will be different to the tax rate on wage income, due to a progressive tax system. Therefore, potentially endogenous, variation in the tax rate might change the relevant net replacement rate (Pfliiger, 1997). However, the government might adjust gross benefits to offset the change in net benefits induced by a tax variation. In Ger- many, for example, unemployment benefits are fixed in relation to net wages. However, the gross replacement rate stayed constant from the 1960s to the 1990s. Tax rates increased over this period. Hence, the government increased net replacement rates by deliberate policy action. We will therefore assume that all benefits are taxed at the same rate as wages, which allows the government to steer the net replacement rate directly. Under these assump- tions the alternative income is given by

af=q>Uj(l-t) £/+ (1 -<puj) (l-t)wj. (2)

Now insert (2) into (1) to obtain

wt= 'x (<p Uj Bt + (1 - q> Uj) Wj) . (3)

Obviously, the bargained wage in each firm i depends on the relevant unemployment rate, labor market flows, wages workers might obtain in other firms and on unemployment benefits. It does not depend on the tax rate. This is due to the assumption that benefits and wages are taxed at the same rate. Therefore, endogenous variations in the tax - which always occur if either benefits, or wages, or unemployment rates, or all three change - do not affect the bargaining solution.




Now consider the policy parameter, which is unemployment benefits. In international comparison countries do not only differ with respect to the level of unemployment benefits, they also differ with respect to the deter- mination of benefits. Most OECD countries pay unemployment benefits in earnings-related schemes. Only three countries (Australia, New Zeeland, United Kingdom) have flat-rate schemes. However, all countries with earnings-related schemes have upper ceilings on insurable income and lower bounds on earnings-relations provided by social insurance. Therefore, the earnings-relation holds only for part of the earnings distribution. In addition, it seems to be important that unemployment insurance is paid only for a limited time. After a certain period of unemployment the earnings-related unemployment insurance is replaced by unemployment assistance or social assistance. These are paid as flat-rate schemes in most countries. See OECD (1997) and Goerke (2000) for an overview and classification of existing schemes. Therefore, most schemes may be described as a mixture of earnings-related and flat-rat schemes. To capture differences in unemployment insurance systems, we assume that unemployment benefits depend on a flat-rate component A, and on a component related to previous earnings

Bf. = A + 6 wlW . (4)

The general model of unemployment insurance schemes given in (4) includes three special cases: 1) With A > 0 and b = 0 we have a flat-rate scheme. 2) With b > 0 and A = 0 unemployment benefits are fixed in relation to the previous wage of the worker. We therefore have an earnings-related scheme. 3) With A > 0 and b > 0 we have a mixed scheme, which is probably the most relevant case if all levels of productivity and income differentials are considered.

To see how different unemployment insurance schemes affect the bargained wage, insert (4) into (3) to obtain: wt = /j,((puj(A + b wit_^)+ (1- (puj) iv;). Hence, in each period the bargained wage depends on the bargained wage of the previous period. As long as b stays below a critical level we obtain

dWi/dWj^ = ficpujb < 1. Hence, the wage converges to a steady state

H. Wl =ti<PUjA + (l-<puj)wj) (5) H. Wl (l-fitpujb)

In the following we will concentrate on the steady state wage. It depends on the mark-up, the relevant unemployment rate, wages paid by other firms, the flat-rate component in unemployment benefits, and the earnings-related component in unemployment benefits.




2.2. Aggregate Wages and Unemployment

Now we will analyze the macroeconomic effects of wage bargaining. It is assumed that there are two types of workers (/ e (s, u))' skilled and unskilled. The proportion of skilled workers is jts and the proportion of unskilled workers is nu .The number of firms that use skilled (unskilled) workers corresponds to these proportions. Skilled workers have the efficiency ss > 1 and unskilled workers have the efficiency eu = 1. Therefore, e= es gives the relative efficiency of skilled workers. The aggregate production function for firms using skilled or unskilled labor is Yy = Kf(£jLj)^. All firms are assumed to be equally competitive and, therefore, all prices are the same pt - 1. Thus, revenue is equal to production Rt = Yt. Firms have the right to manage and therefore adjust employment to equalize the marginal product with the bargained wage: Wj= /3 k ef (Kj/Lj)a. Note that Ly = k} '' - uj) N in order to obtain

f K Y Wj={3Ke?'

K J . (6)

The bargained wage in each firm is given in (5). All unions are assumed to be identical. As a consequence, all skilled workers will receive the same wage ws - ws - wi,s and all unskilled workers will receive wu - wu - wiu. The assumption of separated labor markets implies that the probability of skilled workers finding a job in another firm depends on the skilled unemployment rate, and the probability of unskilled workers finding a job depends on the unskilled unemployment rate. Hence, we assume that unskilled workers can- not become skilled during unemployment and that skilled workers will not accept unskilled jobs and therefore only search for skilled jobs. For simplic- ity we focus on the steady state of the bargaining process. Insert wt = vPy into (5) to obtain

WjWj=A with Wj=Wj(b,uJ,^(p) = (l-b)--i1-^. (7) ficpiij

In a purely earnings-related benefit scheme we have A = 0 and an equilibrium requires Wj = 0. Since Wj is independent of productivity we obtain us-uu. For any A > 0 the short-run equilibrium is given by equations (6) and (7). Unemployment rates and wages are jointly determined by the parameters of the unemployment insurance system, the parameters of the bargaining process, the parameters of the production function, the proportion of skilled individuals, and the amount of capital used in each sector. Figure 1 gives a graph- ical representation of the equilibrium. It becomes obvious that we have us - uu only for A - 0. For any A > 0, the unskilled unemployment rate exceeds the skilled unemployment rate.




Figure 1

Unemployment Rates

A YsWs I

/ Vu Wu/

A -/- - -^-

In the medium run, capital is mobile between firms. Hence, the rate of return on capital will equalize rs - rM.The rate of return on capital is (1 - /3 k) Yj/Kj. Equalization of rates of return on capital then implies that each firm uses the same ratio of capital per efficient labor unit. Since e gives the relative efficiency of skilled labor we obtain: Ks/Ls = eKu/Lu. Insert this into (6) to obtain ws/wu = e. Hence, due to capital mobility between firms, the wage differential is given by relative efficiency, and is independent of wage bargaining.

The aggregate level of capital is given: K = Ks + Ku. Now use Ks/Ls =

eKu/Lu to obtain KU=LUK/(LU + eLs) and therefore :KS/LS =sK/[(jcu(1 - uu) + e its (1 - us)) N], Insert the capital labor ratio into (6) to obtain wages after adjustment of capital between firms

ws=£wu=/3ks' - -^ -^-' . (8) {jTu(l-Uu) + £JTs(l-Us) N)

An increase in either rate of unemployment increases the levels of both wages, and has no effect on the wage differential.

In the long run, capital is internationally mobile. For the small open economy the rate of return on capital is exogenously given by rs-ru- r. Use the




production function in r = (1 - /? k) Yj/Kj to obtain the capital labor ratio: Ks/Ls = eKu/Lu = s [(1 - /? K)lr]y P.Then insert the capital labor ratio into (6) to obtain

Ws=eWu=epK(l^lA . (9)

Both wages are fixed by international capital mobility. In the long run neither the wage of the skilled nor the wage of the unskilled depends on the respective unemployment rate (a similar result with homogenous labor is de- rived in Jerger and Michaelis, 1999). The wage differential is constant at e. Given wages, the system can be solved for unemployment rates

O-l)w,

In both sectors the equilibrium rate of unemployment is increasing in both parameters of unemployment benefits. Hence, even though replacement rates have no effect on the long-run level of wages, unemployment rises with replacement rates. The reason is that capital has been exported, and therefore, given the wage level, employment is lower. In addition, (10) reveals that in an earnings-related scheme (A = 0) both unemployment rates are independent of the wage level, and both are the same. This is due to the fact that both replacement rates are the same. As soon as there is some flat-rate component in unemployment benefits (A > 0) the relative replacement rate is higher for low wages. Hence, the unemployment rate declines with the level of wages and, therefore, the skilled unemployment rate is below the unskilled.

As shown, the long-run level of wages is independent of unemployment benefits and unemployment. However, for workers it is not their gross wage that is relevant but their net wage. Hence, we have to consider the tax rate. It is assumed that the unemployment insurance budget balances each period. Therefore, taxes levied on the employed always have to cover unemployment benefits paid to the unemployed: (1 - us) jzs Ntws + (1 - uu) JiuNtwu = us itsN (1 - 1) Bs +uu Jtu N (1 - 1) Bu. Divide by N and rearrange to obtain

t = us nsbws+ uu Jiubwu+usJisA + uu jtu A ('-us{'-b))jzsws+{'-uu('-b))jiuwu+usJZsA + uu7iuA

'

The tax rate increases when either the flat-rate or the earnings-related component of unemployment benefits increases; in addition, it increases with unemployment and it declines with wages. In the short-run and in the me-




dium-run, an increase in benefits leads to a rise in unemployment and to an increase in wages. The increase in benefits and the rise in unemployment both require an increase in the tax. The rise in wages extenuates the necessary tax increase. Howeve'r, in the long run, wages are independent of unemployment benefits. Therefore, the effect which dampens the increase in taxes disappears.

3. Shocks

3.1. Increase in Replacement Rate

The replacement rate depends on the flat-rate component as well as on the earnings-related component in unemployment benefits. First, we will consider an increase in the flat-rate component A. The short-run effects can be obtained directly from figure l.The A-line moves upwards and both unemployment rates increase. Since Ws ws is steeper than Wu wu, the unemployment rate of the unskilled increases more than that of the skilled. As a result, the wage increase for the unskilled is higher than for the skilled. Hence, the wage differential is reduced.

The increase in the relative wage of unskilled workers leads to a decline in the relative rate of return on capital in firms using unskilled labor. Capi- tal therefore adjusts between firms to equalize rates of return in the medium run. Hence, capital moves from firms using unskilled labor to firms using skilled labor. Given the unemployment rates, wages of skilled workers increase while wages of unskilled workers decline. This implies that Ws ws becomes steeper and Wu wu becomes flatter. Hence, unemployment amongst skilled workers declines, while unemployment amongst unskilled workers increases. As (8) shows, the process of adjustment ends when the wage differential is given by e once again. The level of wages for each type of labor depends on both unemployment rates. Therefore, the bargained wage in each sector depends on the bargained wage in the other sector. Now take the ratio from (7), note ws/wu - £, and rearrange to obtain

u (jM-l)g"n s

wuuie-lHl-ty + fi-l'

This means that when a medium-run increase in the unskilled unemployment rate occurs, then the skilled unemployment rate also increases. Hence, the medium-run reduction in skilled unemployment does not compensate for the initial increase. Both unemployment rates are therefore above their original level. As a consequence, both marginal products and wages are above their original levels.




This medium-run wage increase leads to a decline in the rate of return on capital. Capital will therefore be invested abroad. The decline in capital per worker leads to a fall in the marginal product of labor. Given the wage, firms would reduce employment. This puts pressure on the unions. Both types of wages are reduced and in the long run they return to their original level, as is seen from (9). Since international capital mobility reduces wages and the flat-rate component in unemployment benefits stays constant, it leads to an increase in replacement rates. Hence, both unemployment rates increase from the level given in the medium run. The long-run effect on unemployment rates can be obtained from (10). Differentiation shows

duj Uj ~dA~ (l-b)wi-A'

As a result, the rise in the flat-rate component in unemployment benefits leads to an increase in both unemployment rates in the long run. In addition, since uu > us and wu < ws, the increase in unskilled unemployment exceeds the increase in skilled unemployment.

Now consider an increase in the earnings related component of unemployment benefits. An increase in benefits increases the bargained wage and both unemployment rates go up. In figure 1 there is a parallel outward shift for both Ws vvând Wu wu. Hence, unemployment for both types of labor increases. In a purely earnings-related scheme, they increase by the same amount dus = duu. With some flat-rate component (^4 > 0), the increase in the unskilled unemployment rate exceeds the increase in the skilled unemployment rate duu > dw5.To obtain the effect on the relative wage, take ratios from (6) to reach: z = ws/wu = e15 [(jtu (1 - uu) Ks)I(jts (1 - us) iQ]a.Then take the total differential to obtain

& = ( 1 dus _ 1 duu} db

= U1"^) 36

_ (l-uu) db )'

For any A > 0 we have uu > us and dujdb < dujdb. Therefore, the wage differential declines. Only in a purely earnings-related scheme (A = 0), we have uu - us and dujdb < dujdb so that dz = 0. In that case there need not be a reallocation of capital in the medium run. For A > 0 the wage differential declines in the short run and the relative rate of return on capital in firms using unskilled labor is reduced. In the medium run, capital is reallocated to- wards firms using skilled labor. As with an increase in the flat-rate component A, this implies that the unskilled unemployment rate increases while the skilled unemployment rate declines. The process stops when the wage differential returns to e. Both unemployment rates and both wages are above their




original level after the adjustment. This implies that the rate of return on capital is reduced. Long-run international capital mobility then implies that capital is invested abroad. If wages remained at the medium-run level, unemployment would rise period by period. Therefore, capital export puts pressure on unions, and they agree to wage reductions. Hence wages decline to the levels given in (9). The effect on unemployment rates is obtained from (10) as

duj = JKp_ 2 db jix-1

J '

Hence, both unemployment rates increase. In an earnings-related scheme (A = 0) we have us=uu, and both unemployment rates increase by the same amount. As soon as there is some flat-rate component, we have us<uu, and the unskilled unemployment rate increases more than the skilled.

3.2. Skilled Biased Technological Progress

Skilled biased technological progress means that the efficiency of skilled individuals increases while the efficiency of unskilled workers remains unchanged. Hence, e increases. The short-run effect can be obtained from figure l.The increased efficiency of skilled workers leads to an increase in the skilled wage and makes the Ws w^-line steeper. In a purely earnings-related scheme (A = 0) the unemployment rate of skilled workers remains unchanged. However, if there is a flat-rate component (A > 0), skilled unemployment is reduced. The reason is that the replacement rate is reduced due to the wage increase. Initially, neither the wage nor the unemployment rate of the unskilled is affected.

Due to the decline in the skilled unemployment rate, the change in the relative wage is smaller than the change in e. This implies that the relative rate of return on capital in firms using unskilled labor is reduced. Therefore, in the medium run, capital is reallocated between firms. This puts pressure on the unions of unskilled workers and takes pressure off the unions for skilled workers. The wage of skilled workers increases and the wage of unskilled workers declines, so that the wage differential is given by e.The reduction in the unskilled wage leads to an increase in the replacement rate and, therefore, to an increase in unskilled unemployment.

The long-run effect on wages is obtained from (9). An increase in e leads to a proportional increase in the wage of skilled workers and has no effect on the wage of unskilled workers. A comparison with the medium-run effects shows that both wages increase due to international capital mobility. The decline in the unskilled wage as well as the increase in the skilled wage be-




low e implies that the rate of return on capital increases in the medium run. Hence, there is a capital inflow which reduces the rate of return on capital and increases the marginal product of labor. As a consequence of the proportional increase in the skilled wage, the skilled unemployment rate is reduced in the long run. The unskilled unemployment rate returns to the original level.

3.3. Numerical Example

In this section a numerical example illustrates the effects of shocks on some of the endogenous variables. In turn, we consider the short-run, the medium- run and the long-run effects of an increase in the flat-rate component of unemployment benefits, an increase in the earnings-related component, and an increase in productivity of skilled workers.

In the example, a mixed unemployment insurance system is assumed to exist. Initially the flat-rate component of unemployment benefits is A = 0.4 and the earnings-related component is b = 0.4. The relative efficiency of skilled workers is e = 2. For the other assumed parameters see the bottom line of table 1. The long-run equilibrium is calculated on the basis of these parameters. In the long-run equilibrium, the wage of skilled workers is ws = 3.32 and of the unskilled workers wu= 1.66. The unemployment rate among the skilled is us- 4.5% and the unemployment rate among the unskilled is uu - 6%. To finance unemployment benefits, a tax rate of t = 3.2%

Table 1

Changes in Wages, Unemployment Rates and Tax Rates Induced by Shocks

ws wu us uu t

short run 0.5 3.4 6.0 16.2 9.6 A = 0.8 medium run 2.4 2.4 5.9 18.3 10.6

long run 0 0 6.1 18.4 10.7

short run 1 2.3 7.7 13.2 10.6 6 = 0.6 medium run 1.7 1.7 7.6 13.3 8.7

long run 0 0 7.8 13.6 8.9

short run 16.8 0 4.4 6.0 3.1 e = 2.5 medium run 20.9 -3.3 4.3 6.2 3.2

long run 25.0 0 4.3 6.0 3.0

Assumed parameter values: N = 100, r = 0.04, /3 = 0.7, y = 0.05, jzs = 03,k= 0.99, <p =1




is necessary. For the three shocks considered, table 1 gives the percentage increase in wages (columns ws and wu), the level of unemployment rates in percent (columns us and uu) and the level of the tax rate in percent (column t). For each shock, the short-run, the medium-run, and the long-run values are presented.

4. The Education Decision

So far we have treated the proportion of skilled individuals as exogenous. However, since we are dealing with the long run, the proportion of skilled individuals is endogenous and depends on education decisions. To capture the effects of wage and unemployment differentials, a simple approach, devel- oped by Buiter and Kletzer (1993) and Cahuc and Michel (1996), is used. Forgone leisure is the only cost of education in this approach. Individuals live for two periods. In the first they enjoy leisure and possibly receive education. In the second period they supply one unit of labor either as a skilled or as an unskilled worker. Each individual i is born with a specific ability qrTo become skilled, an individual has to participate in the education system and, therefore, has to make an effort ev The necessary effort to become skilled depends on the individual's ability. Let the necessary effort be given by et = (1 - qt)/h with qt e [0, 1] as an index of ability and h as a parameter for the public support for education. An increase in h means an increase in public support for education so that the necessary individual effort is reduced.

Utility of an individual i depends negatively on the effort and positively on the expected income /; obtained either as a skilled or as an unskilled worker

t/^ylogCl-O + Cl-tflog/y. (1D

The individual will become skilled if utility obtained in the skilled sector exceeds utility obtained in the unskilled sector. This is the case if 7 log (1 - et) + (1 - 7) log /, > (1 - 7) log Iu or equivalent^: (1 - et) > (Iu/Is)(1-y)/y. Since the necessary effort depends on individuals' ability, the individual 1 will become skilled if his ability is sufficiently high: qt>q=l-h + h (/M//5)(1~r)/y.

Expected income of skilled (unskilled) individuals /; depends on the wage Wj, unemployment benefits Bj9 the expected times of employment 1 - Uj and unemployment w;. We assume that labor market flows are large enough so that each individual becomes employed and also has a period of unemployment during his working life. The expected time of employment is 1 - Uj and expected time of unemployment is wy. Hence, expected income is given by

/y = (1 - uj) (1-0 wj + uj (1-0 (A + bwj). (12)




Take the ratio IJIS and insert unemployment rates from (10) to obtain: IJIS = wjws. We see that the expected ratio between lifetime income of unskilled and skilled workers is simply the relative wage. This holds, although the expected time of unemployment is lower for skilled individuals. This is due to the fact that the cost of unemployment is also higher for skilled individuals. Since these two effects are just proportionate to each other, the expected income differential is given by the wage differential. This implies that a higher unskilled unemployment rate does not induce an increase in the proportion of skilled individuals. This result contradicts the results obtained for unemployment due to minimum wages (see Cahuc and Michel, 1996 and Saint-Paul, 1996). Minimum wages induce unemployment for low-skilled individuals only and therefore reduce expected relative income for the unskilled.

Since education decisions are long run, we assume that capital is internationally mobile. Hence the wage differential is wjws =11 e. We therefore obtain the threshold level of ability q=l-h + h (l/e)(1-y)/y. The threshold level of ability declines with the public support for education and with the wage differential, which is given by the technological parameter e. An individual will become skilled if his ability exceeds the threshold level. Since all individuals differ with respect to their abilities, the proportion of individuals becoming skilled depends on the distribution of abilities. The ability of an individual g; is a random variable, which is independently and identically distributed on the range [0, 1]. We denote with F(q) the cumulative distribution function of abilities. Hence, the proportion of skilled individuals will be JT=l-F(q).

An increase in public support reduces the threshold level of ability (dq/dh < 0) and, therefore, more individuals become skilled. This has neither an effect on the wage of skilled nor on the wage of unskilled individuals due to international capital mobility. Hence, the relative wage also remains constant. This implies that both unemployment rates do not change. However, in any scheme except for the earnings-related one, the unemployment rate of skilled individuals is below the unemployment rate of unskilled individuals. Therefore, an increase in the proportion of skilled individuals reduces the average unemployment rate.

An increase in e raises the wage of skilled individuals but has no effect on the wage of the unskilled so that the wage differential widens. As a consequence, more individuals become skilled. The average wage increases due to the increase in the wage of the skilled as well as the increase in their proportion. With an earnings-related unemployment insurance scheme, both unemployment rates remain unchanged, and, since both unemployment rates are identical, total unemployment also remains unchanged. With a flat-rate scheme the skilled unemployment rate is reduced. The unskilled unemploy-




ment rate is not affected. The total unemployment rate declines due to two factors: the skilled unemployment rate declines and the proportion of skilled individuals increases.

5. Conclusion

The underlying argument of this paper is that replacement rates for skilled and unskilled workers are the same only in purely earnings-related unemployment insurance schemes. In flat-rate schemes, as well as in mixed schemes, i.e. schemes with some flat-rate components, replacement rates for unskilled workers are higher than for skilled workers. As a consequence, the unemployment rate of unskilled workers is higher. The unemployment rates of different skill groups are the same only in purely earnings-related schemes. In addition, it has been shown that an increase in the flat-rate component increases unemployment among unskilled workers more than among skilled workers. The same applies to an increase in the earnings-related component if there is some flat-rate component.

A second important point is that shocks, which affect productivity and wages, will change relevant replacement rates if there is some flat-rate component. Therefore, unemployment rates will also change. In a medium-run perspective, where the capital stock of the economy is given but capital can be reallocated within the economy, each shock which has a direct effect on only one type of labor leads to a reallocation of capital. It therefore changes productivity and the wages of all workers. Again, with some flat-rate component, this leads to changes in replacement rates, wages, and unemployment rates.

A third point is that unemployment induced by wage bargaining does not influence education decisions. If the unemployment rate of the unskilled exceeds the unemployment rate of the skilled, this is due to a higher replacement rate. Hence, skilled individuals have a smaller chance of becoming unemployed but they also have higher relative costs. These two effects cancel each other out, and, therefore, the education decision is independent of relative unemployment rates. However, if there is some flat-rate component in the unemployment scheme, an increase in the number of individuals becoming skilled reduces the average unemployment rate, since the skilled unemployment rate is below that of the unskilled.




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Michael Brauninger Department of Economics University of the Armed Forces Holstenhofweg 85 22043 Hamburg Germany [email protected].



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Unemployment Insurance, Wage Differentials and Unemployment