EUROPEAN ECONOMIC REVIEW
ELSEVIER European Economic Review 41(1997) 517-524
Unemployment insurance benefits capital accumulation
Harris Dellas *
and human
Centerfor Economic Studies, Catholic University Leuuen, 69 Naamsestraat, 3000 Leaven, Belgium
Abstract
Public unemployment insurance benefits tend to benefit disproportionately the low skilled. Hence they may serve as an income insurance substitute for human capital acquisition. As a result of their negative effect on the incentive to accumulate human capital, they lead to an increased supply of low skilled and to higher unemployment among the low skilled both in the short and long term rate. Accounting for the long term costs of unemployment insurance benefits may greatly increase the cost of the welfare state. 0 1997 Elsevier Science B.V.
JEL classtjication: E24; J24; J65
Keywords: Unemployment insurance; Human capital accumulation; Long term unemployment
The unemployment insurance (UZ) system has been a key feature of the labor markets in modem industrial countries. Its implications for the rate of unemploy- ment as well as the distribution of income have been the subject of a large body of literature. On the one hand, UZ is given credit for sheltering low income individuals from the hardships of labor markets, thus keeping the incidence of poverty lower and the distribution of income more equal. On the other hand, it is accepted that it reduces the incentive to work, leading to higher wages and unemployment (Feldstein, 1976). The welfare state has been assigned a big share of the blame for the high and persistent unemployment rates experienced lately by many industrial countries (Layard et al., 1994, Krugman, 1994).
* E-mail: [email protected], Fax: + 32 16 326796.
0014-2921/97/$17.00 Copyright 0 1997 Elsevier Science B.V. All rights reserved.
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518 H. Dellas / European Economic Review 41(1997) 517-524
The existing literature has been mostly concerned with the effect of UZ on the willingness to work. However, there are other incentives that may be influenced
by UZ, such as the incentive to acquire skills. The key insight of this paper is that UZ may serve as a good substitute for investment in skills from the point of view of income insurance. ’ In particular, if the main beneficiaries of UZ are those with
low levels of skills then the welfare system may reduce the incentive to accumu- late human capital by tilting relative income profiles in favor of the unskilled. The resulting increase in the relative supply of low skilled workers has several implications: First, it applies a downward pressure on the real wage of the low
skilled worsening their employment outlook. Second, if technological progress is skilled biased then the labor force becomes more vulnerable to technological
innovations, a feature that may well lead to higher long-term unemployment. Third, if the rate of technological progress depends on the share of high human capital individuals in the labor force, then UZ may retard the rate of development/implementation of new technologies. And fourth, it lowers the average, long-term quality of labor and hence long-term productivity and per capita income. Needless to say, all of these negative contributions of UZ accentu-
ate the cost of the welfare state. All these are conditional on the low skilled benefiting disproportionately from
UZ. Whether this is true or not depends on several things: the type of the shocks (aggregate vs. factor specific) as well as their persistence; the duration of
unemployment benefits (where longer is not necessarily more detrimental); and the size of the labor adjustment costs. In general, there are circumstances under which unemployment benefits may provide relatively greater insurance to the well
endowed, encouraging thus human capital acquisition.
1. The model
1.1. The environment
There exists a continuum of workers distributed uniformly on the unit interval and two types of labor: skilled and unskilled. Each worker, j, is associated with a
different level of ability and faces a cost 13(j) E [O, 11 (with de(j)/dj > 0) for acquiring skills. Low and high skilled labor differ in their productivity and in the hiring/firing costs they face. Workers live and work for two periods and they must decide whether they will acquire skills at a cost 13(j) before they become
’ Feldstein (1994) has informally made a related point. He has argued that the existence of limited (II benefits in the US has lowered the wage risk premium associated with cyclical/seasonal jobs. This has made the creation of such jobs cheaper - relative to jobs requiring more skills - and has distorted
the composition of employment.
H. Dellas / European Economic Review 41 (1997) 517-524 519
active in the labor market. Within each labor class, all workers are identical from the firms’s point of view. In each period, the firms must hire skilled and unskilled labor in order to produce a single, homogenous good, whose price is normalized to unity. The profits of the representative firm in the first, ml and second period, n2, are
( 1 1 ,Jr1=41 4% --X;+B,y,--y:
2 2 xi -X0)* - WlXXl - WlyYl)
(1.1)
1 1 5.6 +B,Y, - 1~: - ;h( x* -x1)’ - w2xx2 - W*yY*y
(14
where qr > 0, t = 1,2 is an aggregate shock in period t, A, > 0 and B, > 0 are
factor-specific productivity shocks (E, A, > E, B,), x, and yI are the quantities of skilled and unskilled labor employed and wrx and wty are the corresponding wage rates per unit of labor. Eqs. (1.1) and (1.2) assume that skilled labor is subject to adjustment (hiring/firing) costs while unskilled is not. * The parameter h > 0 captures the cost of adjustment. In order to avoid the noise that comes from transitional dynamics it is assumed that the firm can hire x,, units of labor in the beginning of period 1 at no cost (x, is assumed to be equal to the full employment level).
Without loss of generality - because we will mainly focus on the incentives of the workers to acquire skills - we will assume that the firm knows the values of the shocks for both periods before it starts operations in period 1. From the first order conditions the following factor demand equations can be derived
q14+~2+%-w,, q,A2+h-w2, x1 =
q1 + 2h ' x2 q*+h .
y1 =B, - wly
41 y2 =B, - !h
q2 .
(1.3)
(14
The demand for skilled labor in any period depends on the stock of that factor in other periods because of the adjustment costs. On the other hand, unskilled labor is perfectly flexible and hence the demand for it takes the standard static form.
’ Rees (1973) discusses relative costs of hiring/firing for different labor classes based on a group of
manufacturing fvms in Rochester, NY. He reports that the average cost for professional, managerial
and technical workers are twelve times as great as those for the unskilled, while those for the skilled
workers are more than five times as large.
520 H. Dellas/European Economic Review 41 (1997) 517-524
1.2. Full employment
It is instructive to use as a benchmark the case of perfectly flexible wages. In
this case, x, =x2 =x and y, = y2 = y = 1 -x, where x and 1 -x are the stocks of skilled and unskilled labor that are available in the economy (recall that these quantities are chosen by the workers in the beginning of time and are subsequently
supplied inelastically). In order to determine the level of employment for the two types of labor as well as their rental rates one must study the decision problem of the workers. Let us abstract from issues of risk aversion by postulating a linear utility function. If a worker of ability j remains unskilled then his expected lifetime utility (income) is given by E(w, y + wzY) where E is an expectation formed before any of the values of the productivity shocks are known and w1 y and wzY are determined by solving Eqs. (1.4) together with the full employment
conditions. If he decides to become skilled then his lifetime utility is given by
E(W, X + wzx) - t9(j) where wlx and wzX are determined by solving Eqs. (1.3) and using the full employment equilibrium conditions. The decision to become skilled is based on the difference between E(wI, + wzX) - 19(j) and E(w,, +
w,,), which, using (1.3)-(1.4) can be written as
O=Eq,EA,-(Eq,+h)x+Eq,(EA,-x)-B(j)-Eq,(EB,-1+x)
-Eq,(EB,-1+x). (1.5)
The shocks are assumed to be uncorrelated. The criterion then is: acquire skills if R > 0; do not otherwise. With the
suitable choice of the parameters of the model there exists an interior solution, j * ,
such that everybody with j I j * becomes skilled and everybody with j > j * remains unskilled. The equilibrium level of skilled employment is given by
Eq,(EA,-B,+l)+Eq,(EA,-EB,+l)-8(j*) x=
2(Eq, +Eq,) (1.6)
In a stationary equilibrium with q1 = q2 = q, A, = A, = A and B, = B, = B
and under the assumption of a linear cost function such that 0(j) = j (note that j=x)
2q(A-B+ 1) x=
4q++1 . (1.7)
It can be shown that Ew,, > Ewi, for all values of Eq. This implies that the expected demand schedule for skilled labor lies above that of the unskilled. This is a feature that plays an important role in the study of the effects of unemployment insurance.
2. Unemployment insurance
Let us now turn to the examination of the relationship between unemployment insurance benefits and the composition of the labor force. We will consider limited
H. Dellas/ European Economic Review 41 (1997) 517-524 521
(one period) and indefinite (two period) benefit schemes under a variety of shocks
(aggregate vs. idiosyncratic, temporary vs. persistent). UZ takes a very simple form, namely out of work people receive a payment equal to w.
2.1. Aggregate shocks
Let A and B be constant and q vary stochastically. Given the supply of labor
of type i, there are two states of employment. Either the realization of q is good enough so that full employment for type i obtains at a wage rate that exceeds w. Or, the aggregate shock is bad enough so that the full employment equilibrium for i obtains at a wage below w. In the latter case, all workers of type i earn w
independent of their employment status. Let 1 -p, and pX be the probabilities associated with these two states of nature for the skilled and qx the corresponding cut-off point for q. Let 1 - py , py and q y be the unskilled analogues.
2.1.1. A persistent aggregate shock with indefinite UI benefits
Suppose that q is subject to permanent shocks. Let us also assume that unemployed workers are entitled to UI benefits for the full duration of the unemployment spell. The criterion for skill acquisition is then given by
0 = _/q’wff(ddq + /‘“““w,,( df( q)dq + /4hf( q)dq Pmi” 4= 4mn
+ /qmuw~r(df(q)dq - e(j) - 2(“‘wf(q)dq qx 4min
+2 / qmarwy( q)f( q)dq. qy
(2.1)
One can write the expected income gains to the skilled and unskilled as a result of the introduction of UI as
GAINS,, = [w - Ew,,lq”] + [w - Ew,,lq”]
GAINS, = 2[ w - EwylqY] ) (2.2)
where Ew, xI qx = (A - x)EqJq’ is the full employment, expected wage of the skilled in period t conditional on having a realization q < qx. That is, it gives what the high skilled would have earned during ‘bad’ times if there were no unemployment insurance in place. Note that Ew 1 xIqx = Ew,,l qx (because the adjustment costs incurred in a full employment equilibrium are zero). Moreover, it can be easily shown that px = Prob(w, < w) = Prob(q < (w/(A -x)) < pv = Prob(w, < w) = Prob( q < (w/( B - 1 + x)). If the low skilled would also have lower wages than the high skilled during recessions in the absence of Ul then UI favors the low skilled. Hence, the more vulnerable the unskilled to recessions - both in terms of the probability of unemployment and the wages - the smaller
522 H. Dellas/ European Economic Review 41 (1997) 517-524
their incentive to invest in skills. 3 This result is consistent with popular beliefs on the incidence of benefits from UI.
2.1.2. A persistent aggregate shock with limited UI benejits
Suppose now that the unemployed are entitled to unemployment benefits for only one period (the first in this case) and that during the other period (the second)
they receive nothing. In the absence of other real wage rigidities (such as minimum wages) the wage in the second period coincides with the market clearing, full employment wage. Expression (2.2) now takes the form
GAINS,, = [W - Ew,,lq”] + [ &,.I( q*,w) - Ew,,lq’]
GAINS”, = [w-Ew,lqy], (2.3)
where Ew , x I q ’ = Ew, x 1 q ’ is the expected wage of skilled labor in periods 1 and 2 conditional on q < qx and in a no UI regime. Ewzx)(qx,w) is the wage of the skilled in the second period, conditional on q < qx but in the presence of an UZ
benefits system. Note that Ew, x I( q x, w) < Ew, x I q x because the availability of UZ during the first period leads to unemployment during that period. The restoration of full employment when the benefits cease during the second period involves adjustment costs for which the firms need to be compensated (in the form of lower
wages). The question of interest is which type of UZ benefits - indefinite or limited -
favors more the low skilled. Using (2.2) and (2.3) one can see that limited benefits are associated with a greater incentive to invest in skills compared to indefinite benefits when Ew2xl(qx,w) < Ewy )q y. That is, when labor adjustment is so costly that the wage of the skilled in the second period must drop below the level of unskilled wages in order to compensate the firms. Consequently, limited UZ
policies worsen the relative income position of the skilled and thus discourage the accumulation of human capital (while indefinite UI policies do not). This is an interesting, rather unexpected finding. It is due to the fact that the former type of policy leads to intertemporal distortions.
2.1.3. A temporary aggregate shock
Suppose now that recessions may occur only in the first period. The criterion for investing in skills now is based on the comparison of
GAINS,, = [w - Ew,,lq*] + [ Ew& - ~344
GAINS,, = [w-Ewylqy], (2.4)
3 The likelihood of cyclical unemployment is greater for the unskilled. For instance, the probability
of a temporary - cyclical - layoff is a decreasing function of educational attainment (Abowd and
Ashenfelter, 1984).
H. Dellas / European Economic Review 41 (I 997) 517-524 523
where Ew,, is the expected wage in the second period conditional on not having
an 111 system in place. Ew,,lw, on the other hand, is the expected wage in period 2 conditional on having an UI system in place. Again the existence of UI benefits
introduces an intertemporal distortion, forcing skill labor wages in the second period down to cover the adjustment costs. As a result, an economy that is subject to transitory shocks may end up with an inferior quality of labor in comparison to an economy which is subject to more persistent shocks.
2.2. Factor-specific shocks
Let us now consider factor idiosyncratic productivity shocks. The analysis is
similar for skilled and unskilled labor shocks so we will focus only on the former.
If the shocks are permanent and if the benefits are of indefinite duration, then the criterion for becoming skilled depends on the sign of the expression
GAIN&, = [w - Ew,,(q’] + [w - Ew,,lq”] (2.5)
(the gains to the unskilled are zero). Both terms in (2.5) are positive. The existence of unemployment benefits unambiguously improves the relative income position of the skilled, increasing thus the incentive to acquire human capital.
Things seem more ambiguous when the benefits have limited duration. This is due to the fact that there are two opposing forces. Income insurance against intertemporal distortions. Expression (2.5) now becomes
GAIN& = [w - Ew,,(q”] + [ EwzxIw - Ew2*]. (2.6)
The first term of (2.5) is positive while the second is negative. Subsequently, it
is no longer necessarily true that limited unemployment benefits improve the fate of the high skilled when this factor is afflicted by idiosyncratic shocks.
2.3. Additional considerations
We have discussed the implications of UZ for the skill composition of the labor force. The quality of labor is of importance for several reasons.
First, it matters for the average level of labor productivity. An economy with lower labor quality will also have lower per capita income and average living standards.
Second, it is possible that the level of technology (or even the rate of technological progress as has been claimed by the new growth theory) is related to the total or average level of human capital. Better trained individuals may be in a better position to either innovate or implement new technologies. This means that economies that are better endowed in terms of human capital may be able to reap the productivity/output benefits associated with technological innovation (and if the new growth theory is right, they may even grow faster in the long run). This element can be captured by making the average level of A, an increasing function of x (or x/(1 -x)).
524 H. Dellas/ European Economic Review 41 (1997) 517-524
A great deal of attention has been recently devoted to the issue of skilled biased technological progress, and in particular to its implications for long-term unem- ployment and the distribution of income. If technological progress continues to work against the low skilled and if UZ polices encourage the pursuit of low skill activities then they contribute to both higher long-term unemployment and a more skewed long-run distribution of income. The effects on unemployment come from making the labor force more vulnerable to skill biased shocks and are on top of those associated with the discouragement of work that have been emphasized in the existing literature.
All these considerations 4 also imply that the direct cost of the welfare state may be even higher once the additional effects on labor quality are accounted for. Lower long-term productivity and higher long-term unemployment require a higher tax burden.
Acknowledgements
I am grateful to CES of KUL for financial support.
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Similar forces are at work in Dellas (19941, but there they arise from the exercise of macroeco- nomic stabilization policy.
