Optimal firm size, taxes, and unemployment

Journal

of Public

Economics

39 (1989) 275-287.

North-Holland

OPTIMAL FIRM SIZE, TAXES, AND UNEMPLOYMENT Kenneth

BURDETT

Cornell University, Ithaca, NY 14853, USA

Randall

WRIGHT*

University of Pennsylvania, Philadelphia, PA 19104, USA Received

February

1988, revised version

received

May 1989

We analyze a model similar to the standard implicit contracting framework, but assume that the size of the firm (the number of workers under contract) is endogenous. Some well-known predictions from contract theory with firm size fixed exogenously are reversed. In particular, a result obtained by Feldstein concerning unemployment insurance does not hold when firm size is chosen optimally: he concludes an increase in experience rating (the extent to which firms pay for unemployment benefits through their taxes) reduces unemployment, while we show that it increases uemployment under reasonable conditions.

1. Introduction In his more than useful survey, Rosen (1985) suggests that ‘Contract theory adds no insights into the determination of firm size.. . ‘. By ‘firm size’ he means the total number of workers attached, or under contract, to a given firm (this is not the same as the number of workers employed at the firm, since some of the attached workers may be temporarily laid off). His claim is certainly correct in that the vast majority of studies takes the number of attached workers to be exogenous, even though it was demonstrated how it might be determined in the original Azariadis (1975) contract paper, among other places (see below). In this study, we argue that not only is the choice of firm size a well-defined problem, but by ignoring it, previous analysts have come to conclusions that are incorrect. To illustrate this point, we show that some results from Feldstein’s (1976) classic work on unemployment insurance (UI) do not hold when firm size is endogenous. Feldstein and many others since predicted that an increase in ‘experience rating’ reduces unemployment, *We thank Costas Azariadis, John Haltiwanger and Bertil Holmlund, as well as participants in seminars and two anonymous referees, for their insightful comments. Of course, the usual disclaimer applies. Burdett also thanks the IUI, Stockholm, for research support. 0047%2727/89/%3.50

0

1989, Elsevier Science Publishers

B.V. (North-Holland)

216

K. Burdett and R. Wright, Optimal firm size

given a fixed number of workers under contract. But when firm size is endogenous, we show that the same policy actually increases unemployment under reasonable conditions. We consider a simple model in which an expected profit-maximizing firm enters into contracts with an endogenously determined number of risk-averse workers. These contracts specify, in each state, how many of the attached workers are to be employed and at what wage. An attached worker who is not employed is considered to be on temporary layoff, and receives a government UI benefit of b while his employer suffers an increase in his UI tax bill of e. b, where e is the experience rating factor (typically, 0 se 5 1). Feldstein’s insight was that an increase in e raises the marginal cost of laying off a worker, and so greater experience rating should reduce unemployment. But when firm size is chosen optimally, although an increase in e still reduces layoffs, it also reduces the number of workers under contract as the firm will be more reluctant to hire them in the first place. Under reasonable conditions we verify the net effect of an increase in e is to increase total (layoff plus unattached) unemployment.’ The nature of our argument is really quite general - a change in any exogenous variable can affect the number of workers under contract, as well as layoffs and wages. Therefore we also derive the effects on optimal firm size and the equilibrium contract of changes in the payroll tax rate and the UT benefit level, and contrast our predictions with those that arise when firm size is tixed.2 2. The basic model Consider a firm that is a price-taker in the market for its output, but does not know with certainty what the price p will be. It is known, however, that it will face price p1 with probability AE(O,1) and price p2 with probability (1 -A), where p1 2 p2 > 0 with p1 > p2 unless explicitly indicated otherwise. Let Rj(n)=pif(n) denote revenue in state j when n units of labor are employed, where the production function f( .) satisfies f’ >O and f” ~0. It is equivalent to reinterpret pj as a productivity shock, instead of a relative price ‘This is true at least in the short run; what happens in the long run depends on unattached workers’ opportunities outside of the firm under consideration. Note that although we reverse the main positive prediction by endogenizing firm size, we do not necessarily quarrel here with Feldstein’s normative prescriptions, since there may well have been overemployment in the particular firm to begin with. 2Feldstein’s (1976) model is different in some respects from the typical implicit contract approach, including the fact that he assumes risk-neutral workers. The set-up here, where workers have general concave preferences, is closest to the version of his model in Burdett and Ho01 (1983); there, however, firm size remains exogenous. Baily’s (1977) model determines firm size, although he also assumes risk neutrality. Miyazaki (1984) considers firm size in a model with risk aversion, but assumes leisure does not enter the utility function (or, at best, enters only in a very restrictive way); see also Miyazaki and Neary (1985). These authors did not analyze the impact of experience rating, however, the main application of the present analysis.

K. Burdett and R. Wright, Optima/firm

size

277

shock; absolutely nothing hinges on this. The restriction to a two-state model is made to simplify the presentation. The firm, or the employer, enters into price contingent contracts with N homogeneous workers. These workers are said to be attached and face no other employment opportunities during the period under consideration. We assume that hours per worker are technologically indivisible: each attached agent either works one unit of time during the period or not at all. Given that the contract specifies the employment of n < N of the attached workers in some state, the employer chooses those to lay off at random and therefore (N -n)/N is the probability that any one of them is unemployed. Workers have the von Neuman-Morgenstern utility function u(y, h), where y denotes income and h denotes hours of work, satisfying ui >O, u2 ~0, uli O. Any contract that provides an expected utility of less than the ‘reservation level’ W will not be accepted, as the workers are assumed capable of obtaining W elsewhere before they become attached. Some factors that influence W will be discussed below. Each laid off worker receives a UI benefit b from the government. To finance these benefits taxes are levied on the employer that depend on the number of attached workers as well as the number of layoffs. Let t=eb(N-n)+6N+T

(1)

be the tax bill when II of N attached workers are employed. The experience rating factor, ez 0, is thus the marginal tax cost of laying off a worker. The second term, 6N, is a payroll tax (or subsidy if 6<0), and the final term is a lump-sum levy.3 This is a reasonable stylized description of the UI tax in most countries (although outside of the United States we typically observe e=O) and essentially the same as in the previous literature except that the payroll tax was not included there since N was assumed to be fixed. The decision variables of the employer are firm size N and the contract C=(ni, n,, y,, y,), where nj is the number of employed workers and yj is the wage income each employed worker receives when p=~~.~ Expected profit for a firm with N workers under the contract C is given by: The tax T could always be set to balance this firm’s UI budget; but even if the budget is balanced, UI is not neutral (since e and b are distorting while T is lump sum). In an explicit multi-firm model, of course, taxes on one firm could subsidize the UI account of another. 41t should be emphasized that we assume the firm does not pay its laid-08 workers directly, i.e. we have ruled out what are sometimes called ‘severance payments’ or private UI. This is done often in the literature [including Feldstein’s (1976) model, Burdett and HOOTS (1983) version, and Azariadis’ (1975) original contracting model]. Allowing firms to pay laid-off workers, however, may well be more reasonable in many contexts, and in fact we do allow this in Burdett and Wright (1989). For the purpose of making our point in this paper, it simplifies things considerably to exclude them. At a purely logical level, if we assume the government reduces public UI benefits dollar for dollar with private benefits, then optimal contracts will clearly set the latter equal to zero endogenously [an idea used earlier by Grossman (1981)]. Private UI payments will also be set to zero endogenously if the public benefits are set at exactly the ‘correct’ level by the government.

K. Burdett and R. Wright, Optimal firm size

278

ZI(N,C)=qR,(n,)-y~n,-eb(N-n,)-6N-T]

+(l-1)[R,(n,)-y,n,-eb(N-n,)-6N-T].

(2)

Similarly, the expected utility of a worker in such a firm is:

+

1-A 7

Cn,u(y,,1)+v

- n,)u@,on

In what follows we assume f’(0) =ul(O, 1) = co; this guarantees that both employment and income are strictly positive. Then the employer maximizes U(N, C) subject to U(N, C) >=W and njs N for j= 1,2. A solution (N, C) to this problem is referred to as an optimal firm size-contract pair.5 The Lagrangian for the firm’s maximization problem is:

L=n(N,C)+~[U(N,C)-Wl+P,(N-n,)+Bz(N-n,),

(4)

where p, fll and flZ are non-negative multipliers. As the expected utility constraint will be binding, the first-order conditions are: l)-t~(b,O)]pln,/N~

aL/aN = -eb-&[u(y,,

a,!@,=(1

-1){R;(n,)-y,+eb+

C4y2, 1)-4hWLIN}

-82=0,

(5~)

(54

aLlap = U(N,c) - w = 0, dL/afij=N-njLd,

pj20,

(5f) /-IAN-nj)=O,

j=l,2.

(5g)

‘It can matter whether we solve this problem, or its dual, max U s.t. II 1 II,. Although both trace out exactly the same ‘contract curve’ as we vary W or II,, changes in the policy parameters involve a shift to a new ‘contract curve’ [see Burdett and Ho01 (1983) or Wright and Hotchkiss (1987)]. The problem in the text of maximizing II seems more natural here.

K. Burdett and R. Wright, Optimalfirm

size

279

One can also verify that the second-order conditions will always hold, given the restrictions made here. With the exception of (5a), which determines optimal firm size, these are fairly standard. For instance, (5d) and (5e) imply: U,(Y,,

l)=Nl/J==l(Y2>

11,

(6)

and hence y1 =y, -y (state independent income). Also, as long as the constraint nj< N is not binding, (5b) and (5~) imply: RJ(nj)=y-eb-z,

(7)

where ZE

a(~, 1) - u(b, 0) U,(Y,

1)

.

Eq. (7) guarantees n, &nz with strict inequality unless n, = n2 = N. If we let a = [ln, + (1 - L)n,]/N = E(n/N) be the unconditional probability of employment, (3) can be rearranged to express expected utility as a function of only CI(the reduction of compound lotteries): U(N, C) = w(y, 1) + (I-

cr)u(b, 0).

Now by inserting /?r and p2 from (5b) and (5c), we can write (5a) as nR;(n,)+(l-2)R;(n,)=y+6--(1

--a)~.

(8)

Thus the expected marginal revenue product, ERJ, equals the cost of the Nth employee, given by wage income, plus the payroll tax rate, minus the average ‘employment premium’, z. The employment premium z measures how much an attached worker enjoys working relative to temporary layoff, and can be either positive (if agents prefer employment) or negative (if they would rather be laid off). Two parameters, the UI benefit b and the reservation utility K plus the utility constraint, ctu(y, 1) +(l -a)u(b,O) = W determine the sign of z. For instance, if b and W are such that W Iu(b,O) (if, for example, the UI benefit b is available to unattached as well as laid-off workers), any acceptable contract must entail u(y, 1) 2 K and therefore ~20. On the other hand, if b and W are such that u(b,O) > W (say, because unattached workers have no alternative opportunities and are ineligible for UI), then u(y, 1) < W and z < 0. Contracts for which ~20 will be called ‘labor contracts’ (since employees prefer h = l), while those for which z ~0 will be called ‘leisure contracts’ (since they prefer h=O). An optimal contract can be of either type, in theory,

280

K. Burdett and R. Wright, Optimalfirm

size

depending on W and b. On he surface it may appear the empirically relevant case involves ‘labor contracts’; but the net reduction in income during a temporary layoff can be rather small, and potentially compensated by leisure, at least for some workers [e.g. see Feldstein (1974)]. We see no reason to take a stand on this issue here, and consider both ‘labor contracts’ and ‘leisure contracts’ below. 3. Changes in policy We have argued above that n, 2 n,, with strict inequality unless n, =nz = N, in any optimal contract. It may be shown that, given pi, there is a fi such that p2 n, 2 n2 implies that the multipliers /I1 and flz vanish in (5a), which implies z < 0.1 The intuition is that whenever workers prefer not to be laid off, it could not pay the firm to have more of them under contract than will be employed in the best possible state. Having fewer attached workers lowers costs and at the same time makes each attached worker happier by reducing layoffs. On the other hand, although n, = N in all ‘labor contracts’, n,
l)-u(b,O)]/N’=O,

(9a)

R; - y + eb + p[u(y, 1) - u(b, O)]/N = 0,

(9’4

PI(Y,

(9c)

1)-N=&

W-u(y,l)[AN+(l-A)n]/N-u(b,O)(l-I)(N-n)/N=O.

(9d)

Totally differentiating and simplifying this system yields: (l-A)bde+da+(l-A)(e--pn/N)db -bde-(e-p)db 0 (l-a)pNdb where p-u,(b,O)/u,(y,

l), and the matrix L is given by

(10)

K. Burdett and R. Wright, Optimal firm

+22(1 -A)n/N’ L=

-z(l-1)/N

- z/N

R’;

-1

0

z( 1- J)n/N

-z(l-2)

size

281

--CI

- z( 1 - I)n/pN

0

ZIP

Pll

NIP

-aN

0

The determinant of L simplifies to: ILI=z*(l -1)N-2

u,,[AN2R;+(1-i)n2R’;]+allN2p-‘R’;R;>O.

Letting D = L - ‘, the effects of a change in the exogenous experience rating factor e on n, N and y are calculated as follows: (114 (lib)

8y/3e=zDb(l

-;i)p-‘[ANR;‘+(l

-A)nRi]

$0,

as

~20.

(llc)

Greater experience rating decreases optimal firm size, N, as potential layoffs are now more costly and so the firm will be more reluctant to have extra workers under contract. The effect on employment in the p2 state, n, cannot generally be signed. This differs from a version of the same model where N is fixed exogenously, where n unambiguously rises with e,6 The average number of layoffs in this firm is 1= /Z(N-n). Differentiating and using (1 la) and (11 b), we find: (114

With N fixed exogenously we also have al/& < 0, and so allowing firm size to react optimally in response to policy changes does not alter the basic qualitative prediction concerning layoffs. However, observing that average employment is M = Enj= ;IN +( 1 - A)n, the model with N fixed implies dM/a’e = (1 - I.) &t/de > 0, while here we have: aM/ae=Dab(l

-n)[z’(l

-a)ull-AN’p-‘(R;-Ri)].

(114

Although (1 le) is not determinate in general, a sufficient condition for it to be negative is R; > R’;, which is certainly true if f”(n) is increasing [as it is, for example, for f(n) = A.ne, 0~8~ 11. Under some reasonable conditions, then, a major prediction is reversed: the fixed N model implies that a greater 6A11 of the results and 2.

for this model

and for a fixed N model

are summarized

below in tables

1

282

K. Burdett and R. Wright, Optimal$rm size

experience rating will increase average employment, while our more general model implies that this same policy will reduce average employment, because the desire to reduce layoffs is partially realized via fewer hires. What about total unemployment? We have concentrated on a single firm here, without describing in any detail the market structure in which it exists. However, it seems reasonable to suggest that when the firm reduces the number of workers under contract, those who are let go become, at least in the short run, unattached unemployed. Then the change in the average level of total (layoff plus unattached) unemployment is simply the negative of the change in M. Under the assumption f”(.) is increasing, a greater experience rating increases the average level of total unemployment in the short run, as the increase in unattached unemployment is greater than the reduction in layoff unemployment. This contrasts sharply with a fixed N model, where an increase in e unambiguously decreases total unemployment. Of course, the increase in unattached unemployment could disappear quickly if these workers soon find acceptable contracts elsewhere; serious analysis of these effects would require a framework with some notion of job search. Furthermore, the rise in unattached unemployment may or may not be a bad thing, as there could have been too many workers attached to this firm to begin with. We do not pursue either of these issues further in this paper.7 There is another way to think about total unemployment in this model which, although less interesting than analyzing the dynamic implications of a multi-firm economy, does have the advantage of simplicity. Assume there is a continuum of homogeneous workers in the economy, normalized to the unit interval. When all workers have the same reservation expected utility that they require to sign a contract, say W*, we have the ‘supply curve’ for workers depicted in fig. 1. A representative aggregate firm will choose N = N(W), as above, taking W parametrically. This generates the ‘demand curve’ for workers shown in the figure.’ Assuming ‘demand’ intersects ‘supply’ to the left of N = 1, equilibrium firm size is N( W*), while 1 - N( W*) workers are voluntarily unattached. A change in e now shifts the ‘demand curve’ and the effects of policy changes can be re-interpreted as aggregate general equilibrium effects, where a change in firm size constitutes a change in long-run voluntary unattached unemployment as opposed to a change in short-run frictional unemployment. This simple way of closing the model allows us to make statements about general equilibrium effects without tackling the dynamic multi-firm problem. ‘An analysis of the effect of UI on the sectoral allocation of workers (say, between more and less risky occupations or firms) clearly requires determining the size of the firm endogenously. It might be interesting to examine such issues in an explicit multi-firm version of the model here. ‘We have drawn the ‘demand curve’, N(W), as downward-sloping in fig. 1. In the case of a ‘labor contract’ N’(W) < 0 is unambiguous - but, perhaps surprisingly, for a ‘leisure contract’ this cannot be guaranteed, and N(W) may slope upward over some range.

K. Burdett and R. Wright, Optimalfirm

N(W*) Fig. 1. Labor

1

market

size

283

N

equilibrium.

The consequences of changes in the policy parameters 6 and b can also be derived (a change in T has no effect, of course, unless it causes the firm to stop producing altogether). Considering the payroll tax 6 first, some of the more interesting results are: 13N/X5=D[z’(l -/z)u,, +crN’~~‘R’;]
(12a) (12b) (12c)

ah4las = 2 alvjas + (1 -n)

ih/i% <

0.

(124

An increase in 6 unambiguously reduces N as well as n. It turns out that N falls by more than n, since layoffs, 1, also decline. But although there are fewer layoffs, average total employment, M, is lower. These effects all differ from a model with firm size fixed, obviously, since in such a model 6 is equivalent to a lump-sum tax. The impact of the UI benefit level b is more complicated. Not much can be said, in general, unless we restrict attention to changes in the neighborhood of b*, the value of benefits that the firm chooses if it has control over b. First-order conditions for the problem of choosing (N, C) and b to maximize Zl subject to IJz W are eqs. (9a)+9d), plus dL/db= -(l

-cr)eN+(l

-cc)pul(b,O)=O.

(94

This reduces to e = u,(b, O)p/N =p. Imposing e= p greatly simplifies the coefficients on db in eq. (10) and allows us to compute, for example,

K. Burdett

284

and R. Wright,

Optimalfirm size

aMjab = - zDe( 1 - c@( 1 - A)u, ,(NR; - nR;).

(13)

Now dM/db takes the same sign as z if NR’; > nR;, a sufficient condition for which is again f” increasing. In this case, an increase in b raises total employment in ‘labor contracts’ and lowers it in ‘leisure contracts’ - just the opposite of the model with N fixed exogenously. Table N determined

de d6 db

1

endogenously.

dN

dn

dy

dl

dM

_

1 --z

--z --z _

_ _

_ _

+z

+2

dy

dl

dM

--z

_

0 _

0 +z

+Z

Table 2 N fixed exogenously. dN de

0

da db

0 0

dn 0’ -z

0’ -Z

All results for the model are summarized in table 1. The plus or minus signs mean the relationships between the policy variables and the endogenous variables are positive or negative, respectively. A plus or minus z means the relationships take the same or the opposite sign of z, respectively (e.g. +z in the lower left corner of table 1 means dN/db is equal in sign to z); in these cases, the results can be pinned down once we know whether we have a ‘labor’ or ‘leisure’ contract. Two restrictions mentioned above have been imposed; f”( .) is assumed to be increasing in order to sign aM,& and aMlab, and b is assumed to be in a neighborhood of b* in order to sign the effects of a change in benefits. For comparison, table 2 presents analogous results for this model with firm size fixed exogenously. Two key differences are that (i) an increase in e raises n when firm size is exogenous but has an ambiguous effect in the general model, and (ii) the effects of e and b on total employment are reversed. In particular, our model predicts that greater experience rating reduces total employment. This is not the conventional wisdom, and could not have been discovered in a model where firm size was not allowed to respond optimally to policy changes.

4. Extensions We briefly discuss two extensions. First, consider the case where n2
K. Burdett and R. Wright, Optimalfirm

size

285

N.9 The effects of changes in policy for this case are reported in table 3, where because n, O. As in section 3, the sign of dM/de is reversed when N becomes endogenous: although greater experience rating again reduces layoffs, it also reduces firm size by enough to generate a net decline in employed workers. Another interesting result is that an increase in b now reduces N but has no impact on nj. More generous benefits result in fewer layoffs, perhaps surprisingly; but this is exclusively due to a decline in the number of attached workers, and total unemployment does not change. Table 3 N > n, > nz. N endogenous.

de d6 db

dN

dni

dy

dl

dM

-

0

+

-

_ -

0’

-

0

Finally, we mention what happens when hours per worker are perfectly divisible, and the UI system pays ‘short-time compensation’ - i.e. partial benefits to employed workers whenever their hours fall below some policy determined ‘normal’ level.” With certain assumptions, one can show that under this regime optimal contracts always specify the same hours for all attached workers, using worksharing rather than layoffs when p is low. A 9We have shown this situation can never arise in a ‘labor contract’; but it can in a ‘leisure contract’. Since it suffices to construct an example, assume pl =p2, and write R(.) for Rd.), n for nj, etc. Now, consider an arbitrary contract with n=N, and think about what happens if we increase N, holding n fixed. To keep U(N, C) = w Y must change according to: dY_~~(~,1)-u(b,O)=W-u(b,O)<~, dN N~,(Y> 1) “U,(Y. 1) The change

in expected dIl -= dN

protit is now

-n$-(eb+d)=

- wu~(~~~o)-(eb+6)

For small eb + 6, this is positive, so an optimal contract “Since dn, and dn, always take the same sign, table case of N>n,>n,, average employment and layoffs l=N-In,-(l-i)n,. “Short-time compensation has been used for years been introduced recently in North America as well. We in Burdett and Wright (1989).

entails N > n. 3 simply reports dnj. Note that for the are given by M =In, +( 1 -I)n, and in several European countries, and has analyze this policy in considerable detail

286

K. Burdett and R. Wright, Optimal firm size

contract now must specify hours per worker in each state, and the effects of policy changes on firm size, hours per worker and total manhours may be derived [see Burdett and Wright (1988) for details]. One result is that greater experience rating reduces firm size and raises hours per worker, resulting in a net reduction in total manhours. This contrasts with the model with the number of workers under contract fixed, where an increase in experience rating raises total manhours. Thus, our basic message concerning the importance of endogenous firm size carries over to models with divisible hours. 5. Conclusion

We have studied a contracting model in which the size of the firm is a choice variable. Some well-known results concerning unemployment insurance derived in models where firm size is fixed exogenously continue to hold, but others are reversed, and several of our predictions conflict with conventional wisdom. Some new testable implications surface. While much of the empirical work motivated by Feldstein’s (1976) original paper has concentrated on the impact of UI on temporary layoffs [e.g. Feldstein (1978), Brechling (1981), Topel (1983)], this analysis suggests looking at the impact on unattached unemployment and on the number of workers under contract. The model pretty clearly predicts that a UI system with a lower value of e will lead to larger firms - that is, to employers with greater numbers of workers under contract.12 The implications for policy of endogenizing firm size go beyond the analysis of UI, and we also discussed effects of changes in the payroll tax or subsidy rate, for instance. As a related example, in Europe, policy-makers have imposed severe severance penalties on employers, which might be expected to reduce unemployment by making layoffs more costly. Similarly, forcing employers to provide extended advanced notice prior to layoffs (a policy currently under debate) might be expected to lower unemployment. Such expectations could be confirmed in a model with firm size N fixed exogenously; but if N is made endogenous, employers will not only be more reluctant to layoff the marginal worker, they will also be more reluctant to hire him in the first place. Imposing severance penalties can therefore actually increase total unemployment. l3 In any case, economists and policy “Although we. have different degrees of experience rating in the United States and Europe, a test based on such a comparison would be difficult because there are many differences other than experience rating across these economies - including the use of short-time compensation. It might be better to examine U.S. firms across states with different experience rating practices. 13Another example concerns the marriage market. Imposing a tax or some other cost on divorce could reduce the number of separations, but it could also reduce the number of marriages as people would be more reluctant to become attached in the first place. The net result could well be more unattached individuals.

K. Burdett

and R. Wright, Optimalfirm

size

287

analysts ought to be aware of the fact that just because a policy reduces layoffs, it need not lead to a lower unemployment rate. References Azariadis, Costas, 1975, Implicit contracts and underemployment equilibria, Journal of Political Economy 83, 1183-1202. Baily, Martin N., 1977, On the theory of layoffs and unemployment, Econometrica 45, 1043-1064. Burdett, Kenneth and Bryce Hool, 1983, Layoffs, wages, and unemployment insurance, Journal of Public Economics 21, 325-357. Burdett, Kenneth and Randall Wright, 1988, Optimal firm size, taxes, and unemployment, University of Pennsylvania Center for Analytic Research in Economics and the Social Sciences working paper no. 88-05. Burdett, Kenneth and Randall Wright, 1989, Unemployment insurance and short-time compensation: The effects on layoffs, hours per worker, and wages, Journal of Political Economy, in press. Brechling, Frank, 1981, Unemployment insurance and layoffs, Manuscript. Feldstein, Martin, 1974, Unemployment compensation: Adverse incentives and distributional anomalies, National Tax Journal 27, 231-244. Feldstein, Martin, 1976, Temporary layoffs and the theory of unemployment, Journal of Political Economy 84,937-957. Feldstein, Martin, 1978, The effect of unemployment insurance on temporary layoff unemployment, American Economic Review 68, 834-846. Grossman, Herschel I., 1981, Risk shifting, unemployment insurance and layoffs, in: Zmira Hornstein, Joseph Grice and Alfred Webb, eds., The economics of the labor market (HMSO, London). Miyazaki, Hajime, 1984, Internal bargaining, labor contracts, and a Marshallian theory of the firm, American Economic Review, 381-393. Miyazaki, Hajime and Hugh Neary, 1985, Output, work hours and employment in the short run of a labor-managed lirm, Economic Journal 95, 1035-1048. Rosen, Sherwin, 1985, Implicit contracts: A survey, Journal of Economic Literature 23, 1144-1175. Topel, Robert H., 1983, On layoffs and unemployment insurance, American Economic Review 73, 541-559. Wright, Randall and Julie Hotchkiss, 1987, A general model of unemployment insurance with and without short-time compensation, in: Ronald G. Ehrenberg, ed., Research in labor economics 9 (JAI Press, Greenwich, CT).