It is commonly believed that firms prefer layoffs to worksharing, in part, because layoffs economize on fringe benefit costs. We find that when labor markets are characterized by optimal implicit contracts, layoffs will never occur in equilibrium, regardless of the level of fringe benefits

Jehle, Geoffrey A.

Lieberman, Marc O.

English

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Vassar CollegeDigital Window @ VassarFaculty Research and Reports10-1990Do fringe benefits cause layoffs?Geoffrey A. JehleVassar CollegeMarc O. LiebermanVassar CollegeFollow this and additional works at: https://digitalwindow.vassar.edu/faculty_research_reportsThis Working Paper is brought to you for free and open access by Digital Window @ Vassar. It has been accepted for inclusion in Faculty Research andReports by an authorized administrator of Digital Window @ Vassar. For more information, please contact library_thesis@vassar.edu.Citation InformationJehle, Geoffrey A. and Lieberman, Marc O., "Do fringe benefits cause layoffs?" (1990). Faculty Research and Reports. 20.https://digitalwindow.vassar.edu/faculty_research_reports/20DO FRINGE BENEFITS CAUSE LAYOFFS?GeoÆrey A. Jehle§Marc O. Lieberman§Working Paper No: 12October 1990§ Vassar College, Poughkeepsie, NY 12601Vassar College Economics Working Paper # 12DO FRINGE BENEFITS CAUSE LAYOFFS?ABSTRACTWe examine the role of fringe benefits in the firm’s choice between layoÆs and work-sharing. We find that when labor markets are characterized by forward-lookingimplicit contracts, the equilibrium contract will never call for layoÆs, regardless ofthe level of fringe benefits.1I. IntroductionWorksharing—the practice of reducing hours for all employees to avoid layoÆs for someduring downturns—is still very rare in the United States by comparison to Western Europe.Yet well-known arguments due to Mortensen (1978) and Akerlof and Miyazaki (1980) suggestthat, in the absence of complicating factors, an optimal implicit labor contract will alwayscall for worksharing, and never call for layoÆs. Three of these complicating factors arecommonly cited as the principal explanations for layoÆs in the United States. They are:(1) the presence of tax distortions in the US unemployment insurance system which tendto create a “layoÆ subsidy,” (2) an hours-elasticity in production that typically exceeds theemployment-elasticity, allowing firms greater savings through layoÆs during downturns, and(3) the savings firms can achieve during downturns on fringe benefits and other fixed costsof employment by the use of layoÆs.The first two pillars of this conventional wisdom have been carefully and rigorously in-vestigated. Support for the first can be found in Burdett and Wright (1989) and in Feldstein(1976). Some empirical support for the second can also be found in Feldstein (1967). How-ever, the role of fringe benefits in discouraging worksharing and encouraging the use of layoÆshas so far escaped careful scrutiny. Instead, it owes its continued life in the literature to aseries of assertions and conjectures, such as those to be found in Bednarzik (1980), Best andMattesich (1980), Best (1978), Clark (1977) and Baily (1976), among others.In this note we demonstrate that when the labor market is characterized by forward-looking implicit contracts, fringe benefits are a wholly invalid explanation for the prevalenceof layoÆs. Our findings thus refute an important lingering part of the conventional wisdomon layoÆs and serve to extend the results of Burdett and Wright (1989), Mortensen (1978),and Akerlof and Miyazaki (1980).In Section II we construct a simple but general model of equilibrium in the labor marketwhere firms oÆer workers implicit employment contracts which may specify either layoÆs orworksharing, or both, during downturns. Then we demonstrate that the optimal contractwill call for worksharing—and never call for layoÆs—regardless of the level of fringe benefits.Section III oÆers some concluding remarks.2II. Market EquilibriumConsider a set of firms producing a perishable good. Since our results do not depend onany particular structure to competition in the product market, the set of firms concerned maybe thought of quite broadly to encompass anything from monopoly to perfect competition.We let both demand and supply conditions be state dependent, and states x may have anydistribution function, F (x). Firm output in state x is produced from labor according tothe production function f(hxLx, x), where Lx is the number of employees and hx is normalhours per employee.1 Workers join a firm’s labor pool before the state of the world is known,and cannot move to another firm ex post. The normal pool of workers available to the firmis bounded above, and we choose units so that 0 ∑ Lx ∑ 1. Thus, Lx can be interpretedas the share of the firm’s labor pool which it employs in state x. In what follows, we willassume that when firms resort to layoÆs, those laid oÆ are chosen by random draw. Fromthe worker’s point of view, then, Lx can also be interpreted as the probability that he or shewill be employed in state x.Each firm oÆers an implicit contract to its workers which specifies, for each state x, theprobability of employment Lx, normal hours hx, and the wage rate wx, together with anyseverance pay bx, and the cash equivalent of any fringe benefits c.2Facing a contract which specifies the terms {Lx, hx, wx, bx, c}, firm profits in state x willbeº(x) ¥ pxf (hxLx, x)° hxLxwx ° (1° Lx) bx ° cLx, (1)where the px is the market price of firm output.1The assumption that output depends only on one factor is not critical to our findings, and is only madefor simplicity. We also make the standard assumption of equal hours and employment elasticities of output.This can be relaxed, slightly, to correspond with Burdett and Wright’s (1989) Assumption L.2Fringe benefits, provided by the firm to all employed workers, may include such things as medicalinsurance, life insurance, some types of paid vacations and pension fund contributions. We use the cashequivalent of fringe benefits in order to focus on their salient feature in explaining layoÆs, i.e., that theseare costs to the firm which do not depend on the hours a person works, but only depend on the person’semployment status. Usually, fringe benefits are state-independent as well, and our choice of notation reflectsthis. However, our results and arguments are unchanged if we allow fringes to be state-dependent and writecx.Severance payments, bx, can be interpreted to include unemployment insurance taxes paid by firms andreceived by workers as unemployment benefits, as long as the tax rate is “perfectly experience rated.” Wethus rule out any layoÆ subsidy due to imperfect experience rating. On the role of imperfect experiencerating, see Burdett and Wright (1989) and Feldstein (1976).3Workers are assumed to have identical increasing and strictly concave utility functionsover income and leisure. Setting total time per period equal to unity, we write utility interms of income and hours worked, U(Y, 1 ° hx). The expected utility of a representativeworker in state x, facing the contract specifying {Lx, hx, wx, bx, c}, will bev(x) ¥ Lx · U (wxhx + c, 1° hx) + (1° Lx) · U (bx, 1) . (2)Firms compete for workers by oÆering implicit labor contracts that provide competinglevels of expected utility to their workers. Each firm f seeks to maximize the expectationof some increasing function, √f (·), of state dependent profits. We thus impose neither riskneutrality nor risk aversion on the part of firms, nor do we require that the functions √f (·)be identical across firms.The equilibrium contract oÆered by any individual firm must maximize the expectation,Z +1°1√f (º(x))dF (x), (3)subject to a constraint of the form,Z +1°1v(x)dF (x) = v§. (4)Here, v§ can be interpreted as a “reservation” level of expected utility which makes themarginal worker indiÆerent between joining the firm’s labor pool and accepting some nextbest alternative.In the following theorem, we show that the equilibrium contract will never call for layoÆs,regardless of the level of fringe benefits paid to workers. Instead, the firm will always employits entire labor pool.Theorem 1 Regardless of the level of fringe benefits, c, the equilibrium contract mustspecify Lx = 1 for all x.We adapt an argument used by Burdett and Wright (1989, p. 1488) to show that,regardless of the level of fringe benefits, any contract calling for layoÆs in some state can beimproved upon by a diÆerent contract that instead calls for worksharing in that state.4Proof: Suppose a contract specifies {Lz, hz, wz, bz, c}, where Lz < 1, so that layoÆs arecalled for in state z. First note that any other contract that precludes layoÆs in z byspecifying L0z = 1 and h0z = hzLz, produces the same output in z since L0zh0z = hzLz. If, inaddition, the wage is reset to w0z = wz + (1° Lz)(bz ° c)/hzLz, the terms {L0z, h0z, w0z, bz, c}will give the same level of firm profits in state z as the contract calling for {Lz, hz, wz, bz, c}.This is easy to verify by forming (1) in the two cases. However, the contract calling for{L0z, h0z, w0z, bz, c} must provide a higher expected utility in state z than the one which callsfor {Lz, hz, wz, bz, c}. To see this, compare (2) under the two alternatives. Substituting andrearranging, then invoking Jensen’s inequality, we have:U (w0zh0z + c, 1° h0z) = U (Lz · (wzhz + c) + (1° Lz) · bz , Lz · (1° hz) + (1° Lz) · 1)> Lz · U (wzhz + c, 1° hz) + (1° Lz) · U (bz, 1) , (P.1)so workers would be strictly better oÆ with the terms {L0z, h0z, w0z, bz, c}.In view of (P.1), there must exist some reduction in wages to w§z < w0z satisfyingU (w§zh0z + c, 1° h0z) = Lz · U (wzhz + c, 1° hz) + (1° Lz) · U (bz, 1) ,because utility is increasing in income. But then any contract calling for {L0z, h0z, w§z , bz, c}must give workers the same level of expected utility in state z, produce the same firmoutput in z, and give strictly greater firm profits in z compared to the contract calling for{Lz, hz, wz, bz, c}. From this we conclude that no contract which calls for layoÆs in anystate can maximize (3) subject to (4), and thus the equilibrium contract must call for fullemployment in every state.III. ConclusionThe intuition for the preceding theorem is simple enough. In any state of the world,when output depends only on total labor hours, the firm is indiÆerent between oÆering theworker a gamble over income and leisure and guaranteeing the worker the expected value ofthat gamble. Its revenue and costs will be the same in either case. However, with strictlyconvex preferences, workers will always prefer the expected value of any gamble in income5and leisure to the gamble itself. There is thus a gain to be realized by preventing layoÆs inimplicit labor contracts. How this gain is distributed between the firm and its workers willdepend on the competitive structure of product and labor markets.The view that fringe benefits cause layoÆs can only be supported in a world where thefirm’s ex post behavior is unrestricted by an implicit contract with workers. Only then canthe firm take advantage of the asymmetrical cost savings that come with layoÆs. Whenthe labor market is characterized by forward-looking implicit contracts, such ex post firmbehavior will be ruled out in equilibrium.ReferencesAkerlof, George and Miyazaki, Hajime. “The Implicit Contract Theory of Unemploymentmeets the Wage Bill Argument.” Review of Economic Studies 47, (January 1980): 321-338.Baily, Martin M. “Contract Theory and the Moderation of Inflation by Recession and byControls.” Brookings Papers on Economic Activity 3, (1976): 585-633.Bednarzik, R. “Worksharing in the U.S.: Its Prevalence and Duration.” Monthly LaborReview 103, (July 1980) 3-12.Best, Fred and Mattesich, James. “Short-Time Compensation Systems in California andEurope.” Monthly Labor Review 103 (July 1980): 13-22.Best, Fred. “Comment.” National Commission for Manpower Policy, Work Time andEmployment 28 (1978): 213-228.Burdett, Kenneth and Wright, Randall. “Unemployment Insurance and Short-Time Com-pensation: The EÆects on LayoÆs, Hours per Worker, and Wages.” Journal of PoliticalEconomy 97 (December 1989): 1479-1496.Clark, R. Adjusting Hours to Increase Jobs. Washington: National Commission For Man-power Policy 1977.Feldstein, Martin. “Specification of the Labour Input in the Aggregate Production Func-tion.” Review of Economic Studies 34 (October 1967): 375-386.Feldstein, Martin. “Temporary LayoÆs in the Theory of Unemployment.” Journal of Polit-ical Economy 84 (October 1976): 937-957.Mortensen, Dale T. “On the Theory of LayoÆs.” Discussion Paper No. 322. Evanston, Ill.:Northwestern University, Center for Mathematical Studies in Economics and Manage-ment Science, March 1978.

Do fringe benefits cause layoffs?

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Do fringe benefits cause layoffs?

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