Unemployment insurance and market structure

Journal of Public Economics 52 (1993) 237-249. North-Holland

Unemployment insurance and market structure

Nicolas Marceau*

DCpartement d’honomique, Universitt! Laval, Quebec, GIK 7P4, Canada

Received September 1991, linal version received June 1992

This paper examines the impact of unemployment insurance (UI) on employment and unemployment in an industry in which the prices can vary due to some market power. Some non-conventional results are obtained. It is shown that, if there is free entry and exit, average industrial employment may be a decreasing function of the experience rating because the number of firms in the industry is itself a decreasing function of this parameter. This contradicts the conventional view which was arrived at using models of a perfectly competitive industry with no entry, and according to which employment should be an increasing function of the experience rating. The general conclusion is that for industries with different degrees of market power, the same UI scheme has different impacts on employment and unemployment.

1. Introduction

This paper examines the impact of unemployment insurance (UI) on employment and unemployment in an industry characterized by Cournot competition. Both the no entry and the free entry cases are considered. It is shown that free entry in the industry might lead to unconventional results.

The analysis is performed within an implicit contract theory framework similar to that developed in the mid 1970s by Baily (1974), Gordon (1974) and Azariadis (1975). Since implicit contract theory is used here, attention is restricted to the impact of unemployment insurance on temporary layoffs. Feldstein’s (1976) demonstration that temporary layoffs represented some 75 percent of the layoffs in the manufacturing industry in the United States for the period 1965-1975 should convince the reader of the importance of this type of layoffs. Also, for the whole Canadian economy in 1991, an average of 8.9 percent of the unemployed that were working before becoming unemployed were on temporary layoffs [Statistics Canada (1991, table 32)]. This number would probably be larger if attention were paid to the manufactur-

Correspondence to: N. Marceau, Dtpartement d’&onomique, Fact&B des Sciences Socialet, Universitt Laval, QuCbec, GIK 7P4, Canada.

*I am indebted to Robin Boadway for valuable comments and suggestions. Helpful comments‘ were also received from Lorne Carmichael, Rick Chaykowski, Chris Ferral, Stephen Jones, Huw Lloyd-Ellis, and two anonymous referees. Financial support from the Fonds pour la Formation de Chercheurs et i’Aide B la Recherche du Qutbec is gratefully acknowledged.

OQ47-2727/93/$06.00 0 1993-Elsevier Science Publishers B.V. All rights reserved

J.PE- D

238 N. Marceau, Unemployment insurance and market structure

ing industry. However, temporary layoffs are more a North American phenomenon than a European one. As reported by Burdett and Wright (1989a, table l), the variations in employment in North America are mostly due to variations in the number of workers, while in Europe they are due to a combination of variations in the number of workers and in the number of hours per worker.’

Several positive analyses of UI have been made using implicit contract models. These include the classic papers by Feldstein (1976) and Baily (1977) but also, more recent work by Topel and Welch (1980), Burdett and Ho01 (1983), Mortensen (1983) and Burdett and Wright (1989a, b) (from now on, BW). In general, those papers argue that UI has an adverse impact on employment.’ More precisely, the conventional view is that increasing the experience-rating parameter, by increasing employment in bad states of the world (the standard effect), should decrease the number of layoffs in those states and thus increase average employment. Many then advocate that an efficient UI scheme would be characterized by full experience rating, and argue that, since the UI schemes in place in the United States are not fully experience rated, UI generates harmful unemployment.

The goal of this paper is not to argue in favor of a fully or partially experience-rated UI scheme, but rather to show that the conventional view according to which an increase in experience rating should increase average employment does not necessarily hold when one pays attention to market structure and to entry. In fact the conventional view has been arrived at using models in which there was perfect competition and fixed prices in the product market. It is shown here that if the industry is characterized by Cournot competition in the output market and there is free entry, it is possible that the average employment level of the industry will fall as a consequence of a higher experience-rating parameter.

It should be noted that the conventional view has also been recently challenged by BW. They showed that the above conventional prediction no longer holds if one allows for the firm size effect, i.e. the fact that the size of the firms, and thus employment and unemployment, is not independent of the UI scheme in place. The current analysis distinguishes another effect. It is referred to as the free entry effect and is understood to be the impact of a UI scheme on the number of firms that ultimately decide to enter an industry. It should be noted that the firm size effect is obtained independently3 of the

‘Burdett and Wright’s explanation of this phenomenon is convincing. They argue that it is due to the presence of short-term compensation paid to workers on reduced hours in Europe, and to the absence of such an institution in North America.

‘This is not true for BW. See below for a detailed examination of their argument. aThis should not be interpreted to mean that, given an industry market size, the number of

firms and the size of the firms in the industry are independent, but rather that the free entry effect would be observed even in the absence of the firm size effect, i.e. if the firm size is exogenous.

N. Marceau, Unemployment insurance and market structure 239

one identified by BW. It may therefore reinforce or contradict the firm size effect.

The above discussion has centered on the impact of experience rating. The U.S. systems are effectively financed through more or less experience-rated taxes. However, elsewhere, payroll taxes are also used to finance those schemes. This is particularly true for Canada where the UI scheme is financed almost exclusively through a payroll tax. The impact of a payroll tax used to finance the UI scheme is therefore considered. Again, some interesting results are obtained when one takes into account the impact of the free entry effect.

The plan of this paper is as follows. In section 2 the basic model is presented. The no entry and the free entry cases are analyzed in sections 3 and 4. It should be noted that the firm size effect described in BW is not

incorporated into the analysis.4*5 Concluding remarks follow in section 5.

2. The model

Consider the following economy. There are m> 1 identical, risk-neutral firms in an industry and each has an exogenous number of workers under contract, N. There is uncertainty in this economy which takes the form of two states6 of demand, 1 and 2, for the good produced by the firms. The good state, 1, occurs with probability A, and the bad state, 2, with probability 1-L The demand’ in state s is

Ps=ks- 2 qsi. i=l

where ps is the price of output in state s, k, is a state-dependent constant, and qsi is the output of firm i in state s. The good state is called good because k, > k,. Thus, the main difference with the previous analyses is that,

“It is not clear whether the firm size effect has to be present when the free entry efIect is, and vice versa. In fact, to answer that question one has to judge whether a lirm re-evaluates its size decision more frequently that its decision to supply some output on the particular market under consideration. For example, if a firm is locked into some constant labor-capital ratio to produce, one might argue that the only thing the firm could do after the UI scheme is modified is to stay or exit the market. On the other hand, the technology might give some flexibility to the firm, which implies that the decision to exit would only be considered as an extreme option.

sThe same analysis, but with the firm size effect, is performed in an appendix available upon request. The qualitative results obtained in section 4 are not changed by the introduction of the firm size effect.

61t is solely for simplicity that only two states of the world are assumed; the qualitative results of the analysis would still be obtained with more possible states.

‘The demand is assumed to be linear so that clear results are obtained. A more general state- dependent demand might well lead to ambiguous results. My concern here is however not to show that the conventional view is never correct but rather that there exist situations in which it is incorrect.


here, the pair of prices {pl,pz} is not given to the firms as with perfect competition but rather determined by their behavior.’

The technology used by the firms to produce output is linear in labor, the single input:’

4si = F(nsi) = %if

where qsi and nsis N are respectively the output and the number of employed workers in firm i and state s. Obviously, n,,s N because it might be in the interest of firm i to layoff (N-n,,) workers in state s. However, when a worker is laid off, a publicly provided UI benefit b is provided to him. To finance the cost of the UI program, the government imposes a UI tax. The tax bill, TB,,, of firm i in state s given Iz,i is

TB,i =eb(N - n,i) + 6N,

where e is the experience-rating parameter and 6 is the rate of the payroll tax. Note that the UI scheme is said to be fully experience rated if e= 1 and partially experience rated if e < 1. lo Typically, in the United States e >O, while for Canada, e = 0 and 6 > 0. It should be noted that no rationale for the public provision of UI is given here and it is assumed that no severance pay is provided by the firms to their laid-off workers. This is acceptable since my intention is only to perform a positive analysis of the existing UI schemes. Moreover, as argued by Oswald (1986) severance pay can be viewed as insurance against technological change and loss in human capital when a job is lost permanently rather than as insurance against temporary unemployment.

Denote by wsi the income paid by firm i in state s to its employed workers and assume that there is a fixed cost c for production to take place. It is assumed that the firms in this economy complete a la Cournot-Nash so that firm i, when making its decisions, takes as given the decisions made by other firms in the industry. Denote by a caret (A) those variables that are taken as given by a firm. The expected profits of firm i are, given the decisions

{n,,,w,,;s=l,2}:

‘It should be noted that the analysis of implicit contracts in the presence of imperfect competition, but without UI, is the subject of a growing program of research. On this, see Chari et al. (1989) or Cooper (1990).

‘The same remarks apply for the choice of the technology and for the choice of the demand. Moreover, considering a more general technology when using a linear demand might lead to a non-concave objective function for the firm, while using a linear technology ensures that

concavity. ‘OIt should be noted that the UI scheme is not required here to be self-financed. See below for

a discussion of this issue.


EIZ’=l k,-n,,- f -tl,iW,i-eb(N-tl,J

j#i 1 k,-n/f Azj -n,iw,i-eb(N-n,i)

j#i 1 -6N-C.

Now consider the workers in this economy. All the workers are assumed to be identical and risk-averse. Each has utility given by u(Z,h), where I is the worker’s income and h his labor supply. It is assumed that labor is indivisible and that it can take only two values: hi (0, l}, where h=O for an unemployed worker and h= 1 for an employed worker. The utility function is strictly concave and has the following properties:

u1 >o; urr ~0; and u,<O.

When a worker joins a firm he knows that he may face the possibility of a layoff. It is assumed that the laid-off workers of a firm are chosen randomly among the N attached workers. Consequently, a worker joining firm i, given the set of decisions {IZ,~, wSi; s= 1,2), will have expected utility

EU’=A +wri, l)+w u(b,O) 1 %U(W,i,l)+ N 2 . (N-n,i) u(b 0) 1

Assuming that the workers could obtain reservation utility RU elsewhere in the economy, an optimal contract between firm i and its workers is a set of decisions {nSi, wSi; s = 1,2} that solves the following problem:”

max EII’ {n.,,wSi:s=l 21

subject to

EUi2RU, nSisN, s=l,2. -

The Lagrangian of this problem is written, using yi, /Iii, and /?2i as Lagrange multipliers:

“As noted by Baily (1977), Burdett and Ho01 (1983), or BW, the dual of the problem (i.e. max EU subject to En>K) would yield the same contract curve. However, since I want to examine the entry decision of the firms, the version of the problem examined in the text has some heuristic advantages.


The first-order conditions of this maximization problem are:‘*

-l.nli+yid~ul(wli, l)=O, (1)

-(l-l)n,i+Yi(l-n)~,l(,zi,l)=O, (2)

~ [

kl-2nli-~ ~lj-Wli+eb+~ [U(Wli, l)-u(b,O)] -Bli=O, 1 (3) j#i

(1-A) k,-2n,,-f ^ jti

n,j-~,i+eb+~[u(w,i, l)-u(b,O)] -B2i=Ol 1 (4)

EU’-RU=O, (5)

N-nSiLO, s=l,2,

Bsi~Oo, S=l,2, (6)

B,i(N-n,i)=O, S= 1,2.

Using eqs. (1) and (2), the following is obtained:

wri=w*i=wi and yiu,(wi, l)-N=O. (7)

Thus, the income offered by firm i to its employed workers is state independent. This is a standard result of the implicit contract theory. Now consider eqs. (3) and (4) and let pIi= jZi =O, i.e. the constraints on the employment levels are not binding; they then imply, respectively, that

k,-2n,,-f Alj-wi+eb+Z=O, j#i

(8)

k2-2n2i-i A2j-wi+eb+Z=0, j#i

where

(9)

“The second-order conditions of this problem are shown to be satisfied in an appendix available upon request.


It will be said, using Burdett and Hool’s (1983) terminoloav, that a contract is a labor contract if Z>O, but that it is a leisure contract it’ Z <O.

Using the first-order conditions, one can get well-defined reaction curves for the endogenous variables {wi,n,i,112i,yi,Bli,82i} as functions of the other firms employment level in the industry: {A, j, hzj;j # i}. In particular, it can be shown that employment is a strategic substitute:r3

an,,<,, an,

s= 1,2, i#j.

Because the reaction curves are well defined, it would be possible to show that there exists a Nash equilibrium.i4 Now, because all firms in the industry are identical, the equilibrium obtained here is a symmetric Nash equilibrium:

nli=nlj=nl, vi,j,

n,,=nzj=n2, vi,j,

wi=wj=w, Vi,j,

/ISi = fiSj = @,, Vi, j; s = 1,2.

Then, using eqs. (8) and (9) it is possible to obtain:

k,-(m+l)n,=k,-(m+l)n,.

This implies that for both m endogenous or m exogenous, n, >n, since k, > k,. Furthermore, this implies that if there are layoffs in state 2, the number of layoffs will be greater than in state 1. For simplicity, I will, from now on, concentrate on the case where n, = N and n, = n< N. It could be demonstrated that a pair of {k,,k,) exists such that it is the case.r’ That

r3This can be obtained in the following way. Recall that it has been assumed that j31i=/?2i=0. Therefore, differentiating eqs. (5), (8), and (9) for the endogenous variables {r~,,,n,~, wi} and the exogenous variables {nlj,naj} yields a system of equations characterizing the contract. Routine manipulations yield that an, Jdn, j < 0, Vi # j, and dn,,/dn,j ~0, Vi # j.

14A Nash equilibrium exists if (a sufficient condition): (1) the number of players is finite; (2) the strategy sets are compact (closed and bounded) and convex; and (3) the payoffs of each player are continuous, bounded and strictly quasi-concave in their own strategies. None of these three conditions seems to pose a particular problem, although it might be necessary to make some further assumptions to satisfy (2).

“See Burdett and Hool (1983) or BW for a similar simplifying assumption.


simplification implies that eq. (3) is no longer relevant and that we can set pzi = 0. Thus, from eqs. (1)<9), only two equations remain that determine the endogenous variables {w, ri} as functions of the exogenous variables of interest here (e, Sj:

k,--(m+l)n-w+eb+ [

a(w, l)-4b,O) =O U,(W 1) 1 ’ (10)

(11)

Let us now turn to the no entry and free entry cases. It will be shown that in the no entry case, the conventional results hold, i.e. an increase in experience rating leads to less layoffs and to an increase in average employment. However, it will be shown that in the case of free entry, an increase in experience rating has a negative impact on the number of firms that enter the industry. This effect, the free effect, will then to a decrease even if layoffs have under a rather weak here the entry would be present even firm effect.

tax, it is shown that

when there free entry. This result same spirit as the one obtained

entry

there is no entry, m is parametric eqs. and for the endogenous

variables {n, w}. The following

Hb>() z=- IDI ’

aw (i-~)bz,~

z= (DI ’ ’ as ZPO,

where H=AN +(l -I)n>O is the average employment per firm, r= -ur r(w, l)/ui(w, 1) >O is the coefficient of absolute risk aversion of the workers, and JDI = --H(m + 1) -( 1 - ;l)rZ’ < 0.

The results obtained here are conventional. The standard effect an/&>O,


i.e. the firm decreases the number of layoffs it makes in bad states of nature as it bears a heavier fraction of the cost of a layoff, has been recognized by Feldstein (1976) and Baily (1977) among others. Using that result, it has been argued previously that increasing e would then increase employment. Indeed, holding m (and N) constant, and defining the average level of layoffs in the industry by L=( 1 -2)m(N - n) and the average level of employment in the industry by M =lmN +(l -Qrrn, it is then possible to obtain that aL/de<O and aM/ae> 0. Thus, average employment increases because average layoffs have decreased. As be seen, is misleading

it on a fixed level of m (and if L is decreasing in e, then M is in

us now to the of the 6. Since 6 appears nowhere in (1 l), it = aw/&Y 0. is again a conventional result. It be seen to different

to the of free in the it to note of a firm a fixed number of

as the of the UI scheme To see by EII(e,&m) by use of the

S,

& -(l--J) (m-l)n$+(N-n)h ~0,

CSt

aEII(e, 6, m) a6

= -N<O. lll=CSt

Consequently, and since the entry decision of a firm is made on the basis of the expected profits, the number of firms that will enter the industry will vary as the tax parameters are changed. This is a motivation for the exercise performed in the following section.

4. Free entry

If there is free entry in the industry, the number of firms m will be endogenously determined so that the expected profits of entering firms are zero:i6

16Note that this assumes a continuous number of firms. If the number of firms is a discrete number, the so-called ‘integer problem’ may arise. This problem has been dealt with, for the case of Cournot-Nash equilbria, by Novshek (1980) and Mankiw and Whinston (1986). In this case, the equilibrium number of firms m* will be given by the following two conditions rather than eq. (12): En(m and EL’(m*+ 1)cO.


EH=A[N(k, -mN)-NW]

+(l-A)[n(k,-mn)-nw--(N-n)eb]-6N-c=O. (12)

Eq. (12), along with eqs. (10) and (1 l), now determine the endogenous variables {n,m, w}. By differentiating those equations, the impact of a change in the experience-rating parameter on the endogenous variables can be obtained:

an HZNb,O

z=-w ’

de

(1 -I)HNbZ,O

IEI ”

- n)rZ2 + H(N - + 1) + - l)] <

as ZGO,

as in no entry case, is obtained. a free entry effect, is also present.” Thus, increase in

of layoffs of firms. This last is understood to be

consequence of in profits associated with the increase in experience rating. It can be seen that, once of layoffs in L, will decrease as result of a of experience rating:

‘:=(I-i)(N-n) 2 -(i-L)m$<O.

on average employment A4 is ambiguous:

dM (1-I)Hb -=-------- - [-(l-A)(N-n)rZ2-HN+2Hn]><O. de IEI

Moreover, a weak sufficient condition for aM/de <O is simply that n is

“Note that the free entry is also present in the case firms in a in this case, a on prices, to the fact

as given, could also present it would mitigate of monopolistically competitive industry was thus made for heuristic reasons.


sufficiently small, i.e. n< N/2. This sufficient condition will be satisfied if k2 is itself small enough. To see this, simply note that, from eqs. (10)-(12):

.u-I+(I-~)H~~,~, -=_-1El dk2

Thus, for smaller and smaller k,, the chances are that the sufficient condition will be satisfied. Obviously, as long as k2 is not bounded from below, there exists a k2 such that the sufficient condition is satisfied since ultimately, n goes to 0 as k, goes to 0.

It has thus been demonstrated that because of the free entry effect, increasing the experience-rating parameter can be harmful to employment. This result is in the same vein as the one obtained by BW when they consider the firm size effect. Note that the fact that there is exit from the industry when the experience rating increases means that, at least in the short run, the newly unattached workers will join the permanently unemployed. In the short run, therefore, the unemployment rate will increase. In the long run, those workers will reallocate themselves in other industries so that the adverse effects of the experience rating, described above, will vanish.

Now consider the impact of a change in the payroll tax on the endogenous variables:

am a6=

-N[(m+1)H+(l-i)rZ2]<0

IEl ____ ’

aw (1-A)NnZ

as=- JEJ 50, as ZSO.

The first result obtained is that &/&3>0. This is explained by the fact that, in this framework, the size of the firm is identified with its capacity and it becomes more and more costly to have unused capacity when the payroll tax increases. Consequently, layoffs will decrease in bad times. A second result obtained here is that, as for the experience-rating parameter, the number of firms decreases as the payroll tax is increased: am/a6 < 0. Consequently, even if average layoffs decrease, i.e. iYL/&Y < 0, average industrial employment falls, i.e. aM/aS ~0. Note that these results are in contrast to the previous literature. The payroll taxes here have an effect that could not be obtained with an exogenous labor force, N, and a fixed number of lirms, m.

As was pointed out by an anonymous referee, the fact that the UI system is not self-financed is important. If the UI system was self-financed at the


industry level, a decrease in experience rating would have to be compensated by, say, an increase in lump-sum taxes on firms. If the increase in lump-sum taxes turns out to decrease the profits by more than the increase associated with the decrease in experience rating, then the above results are reversed. It seems, however, to be the case that most UI schemes are not self-financed at the industry level. Deere (1991) reports that in the United States there is redistribution from the relatively more volatile industries to the relatively more stable ones. A complete analysis would therefore also have to include the shifts in resources due to the redistribution and this would require a general equilibrium model.

Finally, note that the variations in the number of workers reported to be important in North America by Burdett and Wright (1989a, table 1) can be viewed as evidence of the claim made here. Indeed, variations in the number of workers can be explained by changes in the size of the firms, but also by changes in the number of firms.

5. Conclusion

This paper has examined the impact of UI on employment and unemployment. The main contribution of this paper has been to consider the case where the prices in the economy can vary.

It has been shown that under Cournot competition and free entry, increasing the taxes used to finance the UI scheme would decrease average industrial employment under a weak sufficient condition. This result is in the same spirit as the one obtained by BW when they considered the firm size effect. In fact, combining the results of BW’s paper with those described here, it can be said that if the experience rating or the payroll tax is increased, the number as well as the size of the firms might be decreased. There are thus mechanisms through which employment can fall if the firms have to bear a heavier fraction of their unemployment costs. This conclusion contradicts the conventional view in that a decrease in unemployment is not necessarily associated with an increase in employment.

A more general conclusion is that for industries or economies with different degrees of market power, the same UI scheme may well have drastically different impacts.

References

Azariadis, C., 1975, Implicit contracts and underemployment equilibria, Journal of Political Economy 83, 1183-1202.

Bailv, M.N., 1974, Wages and employment under uncertain demand, Review of Economic Studies 41, 35-50. -

_ .

Baily, M.N., 1977, On the theory of layoffs and unemployment, Econometrica 45, 1043-1063.


Burdett, K. and B. Hool, 1983, Layoffs, wages, and unemployment insurance, Journal of Public Economics 21, 325-357.

Burdett, K. and R. Wright, 1989a, Unemployment insurance and short-time compensation: The effects on layoffs, hours per worker, and wages, Journal of Political Economy 97, 1479-1496.

Burdett, K. and R. Wright, 1989b, Optimal firm size, taxes, and unemployment, Journal of Public Economics 39, 275-287.

Chari, V.V., L.E. Jones and R.E. Manuelli, 1989, Labor contracts in a model of imperfect competition, American Economic Review: Papers and Proceedings 79, 358-363.

Cooper, R., 1990, Optimal labour contracts and imperfect competition: A framework for analysis, Canadian Journal of Economics 23, 509-522.

Deere, D.R., 1991, Unemployment insurance and employment, Journal of Labor Economics 9, 307-324.

Feldstein, M., 1976, Temporary layoffs in the theory of unemployment, Journal of Political Economy 84,937-957.

Gordon, D.F., 1974, A neoclassical theory of Keynesian unemployment, Economic Inquiry 12, 431459.

Mankiw, N.G. and M.D. Whinston, 1986, Free entry and social inefficiency, Rand Journal of Economics 17,48858.

Mortensen, D.T., 1983, A welfare analysis of unemployment insurance: Variations on second- best themes, Carnegie-Rochester Series on Public Policy 19, 67-98.

Novshek, W., 1980, Cournot equilibrium with free entry, Review of Economic Studies 47, 4733486.

Oswald, A.J., 1986, Unemployment insurance and labor contracts under assymetric information: Theory and facts, American Economic Review 79, 365-377.

Statistics Canada, 1991, Labour force annual averages, 1991, Catalogue 71-220 Annual, Canada. Topel, R. and F. Welch, 1980, Unemployment insurance: Survey and extension, Economica 47,

351-379.

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Unemployment insurance and market structure

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