“BUMPING”, LAYOFFS, AND WORKSHARING

“BUMPING”, LAYOFFS, AND WORKSHARING

TAKA0 KATO’

This paper deals with an interesting but often-neglected labor practice prevalent in large North American firms with well- deuelo ped internal labor markets. Large North American firms typically respond to a decline in demand for their products b y first reducing the number of hours worked (or worksharing). As the demand continues to fall, however, they begin to make skilled workers “bump onto” unskilled iobs, displacing unskilled workers. Skilled workers are laid off only after a considerable number have bumped. Z deuelop an implicit contract model and explain the practice.

I. INTRODUCTION

Large North American firms with well-developed internal labor markets typically respond to a decline in demand for their products by first reducing the number of hours worked (or worksharing). As the demand continues to fall, however, they begin to make skilled workers “bump onto” unskilled jobs, displacing unskilled workers. Skilled workers are laid off only after a considerable number have bumped.’ The aim of this paper is to explain these stylized facts.

Previous papers which have discussed firms’ responses to a decline in demand have focused on the issue of worksharing versus layoffs, and have ignored bumping. In the implicit contract literature, worksharing versus layoffs was first discussed by Feldstein [1977], Baily [1977], and Mortensen [1978]. In their models, workers are assumed to be homogeneous, and hence there is no room for bumping.2 Lowenstein [1984] allowed workers to differ in their productivity and showed in the case of a risk-neutral firm and workers that unskilled workers are laid off before skilled workers. In contrast to its realistic prediction concerning who is laid off first, his model yields a

“Assistant Professor, Colgate University. This paper is a revised version of Chapter 3 of my doctoral dissertation submitted to Queen’s University, Kingston. I owe much to my supervisors Richard Arnott, Lorne Carmichael, Steve Kaliski (Queen’s University), Kazuo Koike (Kyoto University), and Tsuneo Iida (Nagoya University). I wish to thank Doug Purvis, Simon Ander- son, Kevin Hebner (Queen’s University), Leslie Rob (MacMaster University), and an anonymous referee for numerous useful comments. I am also grateful to the editor for directing me to a useful article concerning economical writing. Any errors which may remain in this paper are mine.

1. Doeringer and Piore [1971, 55, 791 and Koike [1984, 50-521 report the prevalence of bumping in large North American firms with well-developed internal labor markets. Koike [1977,213-15; 1978,4245; 1983,46-50; 1984,851 also reports that the practice does not prevail in large Japanese firms. I foilow Doeringer and Piore’s usage of the term “bumping”.

2. Recently Miyazaki and Neary [1985] investigated the issue of worksharing versus layoffs in labour-managed firms while Brown and Wolfstetter [1984] studied the issue in an implicit contract model with private information. They all assumed that workers are homogeneous.

Economic Inquiry Vol. XXIV, October 1986

857

658 ECONOMIC INQUIRY

rather disturbing prediction about the issue of worksharing versus layoffs: worksharing occurs only after all unskilled workers are laid off. Moreover, it does not deal with the possibility of bumping.

In this paper, I develop an implicit contract model which allows skilled workers to bump onto unskilled jobs, and study how firms use bumping along with worksharing and layoffs as alternative ways of responding to a decline in demand for their products.

II. EFFICIENT CONTRACTS WITH BUMPING

Consider a risk-neutral firm producing output, Q, which is sold compe- titively. There are two types of jobs required to produce Q, skilled and unskilled. The price of output, P, is the only uncertain variable and is dis- tributed according to the probability density function, f ( P ) . Before the price is known, the firm and each of M risk-neutral skilled workers agree upon a contract describing how production will take place after the price is known. Likewise, the firm and each of m risk-neutral unskilled workers agree upon a ~on t rac t .~ (From now on, all variables denoted by upper-case Roman letters refer to skilled jobs and lower-case Roman letters to unskilled. If a variable is common to both, then an upper-case letter is used).

This paper focuses on state-contingent contracts, in which the state is revealed through the publicly observed output price, P.4 The contract for each skilled worker takes the following form. If the revealed price is P, then the number of layoffs of skilled workers will be Z ( P ) . Similarly, the number of bumps, X; the number of hours worked on skilled and unskilled jobs, H and h; and the wage rate paid on skilled and unskilled jobs, W and w, are specified as functions of P. Each skilled worker cares about the number of hours worked on unskilled jobs and the wage rate paid on unskilled jobs because he may bump onto unskilled jobs. Formally, the skilled contract is [ Z ( P ) , X ( P ) , H ( P ) , h(P) , W(P), w(P)]. Likewise, the unskilled contract may be expressed as [ z ( P ) , h (P) , w(P)].

Assuming that the firm uses only labor as an input,5 measuring labor in man-hours, and denoting the number of workers employed in skilled and unskilled jobs by N and n, I write the production function as

3. Assuming workers are risk-neutral allows us to abstract from the risk-shifting aspect of contracts, which was the major feature of the original implicit contract literature such as Azaria- dis [1975], Baily [1974], and Gordon [1974].

4. In recent years, a growing number of scholars have investigated contracts with private information. See, for example, Hall and Lilien [1!379], Green and Kahn [1983], Grossman and Hart [1983], Hart [1983], and Brown and Wolfstetter [1984] for one-sided private information models, and also Hashimoto [laSl], Carmichael [laSl], and Hall and Lazear [lW] for two- sided private information models dealing with specific human capital. For an up-to-date survey of the literature, see Rosen [1985]. Though I do not deny that my results could be enriched by introducing private information, I st i l l believe that the simple public information model pro- vides insight into bumping.

5. The implicit contract literature usually ignores capital because of its interest in short-run fluctuations of wages and employment.

KATO: “BUMPING” 659

(1) Q = Q ( H N , hn).

Assume also that the function is concave and that skilled and unskilled man- hours are complements in production (a2Q/a(HN)d(hn) = Qi2 > 0).

Workers employed in skilled jobs are skilled workers who are neither laid off nor made to bump:

(2) Workers employed in unskilled jobs consist of unskilled workers who are not laid off and skilled workers who are forced to bump:

(3) n = m - z + X. Layoffs impose several costs on the firm. Costly reorganization of job

assignments is required. Also, because of team work, the workplace is a community where workers are tied to each other and behave according to a code of community or custom. An attempt by the firm to lay off some of its members will generate friction within the community, which will be mani- fest in lower productivity.e

The unskilled workplace typically has a simpler job structure than the skilled workplace, and hence layoffs there will demand less costly reorganization. Moreover, since the unskilled workplace tends to need less team- work, layoffs will cause less costly friction. To highlight this difference between the two types of jobs, the adjustment costs involved in laying off skilled and unskilled workers are assumed to be A and zero respectively, where A > 0.7

Bumping will also require costly reorganization of the job structure and cause costly friction. However, since bumping involves mobility within the firm, it may be considered a less serious threat to the community than layoffs, especially if it is perceived as temporary. Denote the adjustment costs involved in bumping by B, where B 3 0.

As the number of layoffs and bumps increase, their associated costs rise at an increasing rate. The relationships are specified by

(4) A(2) =AoZ + A I Z * and

N = M - 2 - X .

(5) B(X) = BOX + B , X 2 ,

where Ao, Al , B, , B , X . I also assume that A, > B o and A , 2 B , . 8 The marginal adjustment cost curve for layoffs of skilled workers therefore al- ways lies above the one for bumping.

6. These features are emphasized by the internal labor market literature. See, for instance, Doeringer and Piore [1971] and Koike [1977].

7. Introducing adjustment costs for layoffs of unskilled workers will not change the major results provided they are less than the adjustment costs for layoffs of skilled workers.

8. In the previous version of this paper, I assumed a linear adjustment cost function, as did Baily [1977]. Following the suggestion of an anonymous referee, I have introduced a non-linear adjustment cost function. I am grateful to the rieferee for the insightful suggestion.


Layoffs are costly not only to the firm but also to its workers. When he loses his job, a worker loses his workplace community and friends, and per- haps his social status, self-confidence and self-esteem as well.9 As mentioned above, in the skilled workplace, workers tend to develop a stronger sense of community than in the unskilled workplace. Furthermore, skilled jobs are likely to have a higher social status and yield more self-confidence and self- esteem than unskilled jobs. Therefore, layoffs will probably inflict more psychological costs on skilled workers than on unskilled workers. To contrast this difference between the two classes of workers, I assume that the psychological costs involved in laying off a skilled and an unskilled worker are RZ and zero respectively, where RZ > 0.

Bumping will also entail psychological costs but to a lesser extent than layoffs because it involves mobility within the firm. The psychological costs of bumping are denoted by R X , where RZ > R X > 0.

One can now investigate the efficient skilled and unskilled contracts. The firm maximizes expected profits, IT, which are given by subtracting the wage bill and adjustment costs from total revenue:

ll= ( P Q - W H N - whn - A - B ) f ( P ) d P . (6) i-

Workers maximize their expected utility. Workers are not allowed to differ in their tastes, even though they differ in their exogenously determined skill levels.’* Each skilled worker will experience one of the following three mu- tually exclusive events: (1) being employed in a skilled job, (2) being laid off, and (3) bumping onto an unskilled job. If he is employed in a skilled job, he receives a net income of W H - D(H) . D ( H ) is the disutility of work function in income-equivalent units, assumed to be quadratic with D(0) = 0, D’ > 0, and D” > 0. If laid off, the skilled worker receives an alternative income net of the psychological costs of being laid off, Y - RZ. If he bumps, he receives the corresponding net income less the psychological costs associated with bumping, wh - D(h) - R X . Consequently, the expected net income of each skilled worker, U , is written as1’

(7) U = [ ; ( N / M ) [ W H - D ( H ) ] + (Z/M)(Y - Rz) JO

+ ( X / M ) [wh - D(h) - RX}) f (P)dP .

9. A large-scale telephone survey of the metropolitan work force conducted in 1976 shows that 41% of those who lost their jobs expressed their dissatisfaction with what they are doing in life, while only 21% of those who have maintained their jobs did. See Schlozman and Verba “ 7 8 , 3501.

10. In contrast to my approach, Samuelson “8.51 developed an implicit contract model in which workers differ only in their tastes, and derived a positive correlation between wages and employment stability.

11. The form of this expression implies that the utility function is additively separable in income and leisure. Baily [1977] used the same utility function.

KATO: “BUMPING” 661

By a similar argument, an unskilled worker’s expected net income, u, is expressed as

(8)

Note that both expressions involve integration over the price of output because N, n, Z , z, X , H , h, W, and w are functions of P.

I characterize the efficient skilled and unskilled contracts by solving the following problem: choose N ( P ) , n ( P ) , Z ( P ) , z ( P ) , X ( P ) , H ( P ) , h(P) , W(P) , and w(p) to maximize the firm’s expected profits, r, subject to the condition that the firm’s employees are provided with an expected utility at least as large as that available from other firms:

u = i l [ ( n - X ) / r n ] [ w h - D ( h ) ] + ( z / rn )y ) f (P)dP .

where U , , uo denote the expected net incomes available from other firms, and are assumed to be exogenously determined.12

111. BUMPING, LAYOFFS, AND WORKSHARING

It is a relatively easy matter to derive the first-order conditions for the efficient contracts. The conditions are listed be10w.l~ First, there is a pair of conditions requiring equality between the value of marginal product and the marginal disutility of work:

P Q , ( H N , hn) = D’(H), and

P Q , ( H N , hn) = D’(h).

Second, in order to avoid the unrealistic and uninteresting case in which the bumping skilled workers do not displace unskilled workers, the possibility of a corner solution is assumed away; i.e., I set z > 0. Under this assumption the following condition determines the number of hours worked on unskilled jobs (h):

( 13) y - [D’(h)h - D ( h ) ] = 0.

Whether skilled workers are laid off depends upon the condition

(14) L z - = Y - R Z - (Ao + 2A1Z) - [D‘(H)H - D ( H ) ] 50; 2 2 0 ; L z Z = O .

12. The solution to this problem is efficient in the usual Pareto sense. No one can be made better off without making someone worse off, Put differently, the efficient contracts lie on the contract curve. As in most implicit contract models, I regard the number of skilled and unskilled workers as exogenous. Miyazaki “841 investigated how they may be endogenized.

13. See Appendix A for the derivation of the conditions.


Finally there is a condition which determines whether skilled workers bump:

(15) Lx y - R X - (B, + 2&X) - [D ' (H)H - D ( H ) ] 5 0;

x 2-0; LXX = 0.

One can now explain how bumping, layoffs, and worksharing occur as the price of output declines. In the upper panel of Figure 1 is a graph of D ' ( H ) H - D ( H ) . It is an upward-sloping curve passing through the origin because D( H ) is quadratic.

D' [HI H-D[H]

d[H] H-D[H]

X y-R -8,

Y - R ~ - A ,

0 H

X y-R -8,

Y - R ~ -A.

P H =H[P]

FIGURE 1

The middle panel illustrates the relationships between H and X , X = G ( H ) , and between H and 2, 2 = K ( H ) . From (15), we know that as long as D'(H)H - D(H) exceeds y - R X - Bo, X is equal to 0. Denoting the value of H where the two lines in the upper panel intersect as H", one can say that as long as H exceeds H', X is equal to 0. However, when His less than HO, X becomes positive, and the relationship between H and X is then determined by

(16)

From (16), we know that the slope of X = G ( H ) , G , is equal to ( - D " H / 2 B , )

- R X - ( B o + 2 B 1 X ) - [D ' (H)H - D ( H ) ] =O.

< 0.14

14. We also know that G" = ( -D"/2B1) < 0.

KATO: "HUMPING" 663

I will now provide intuition for the result that no skilled worker will bump as long as D'(H)H - D ( H ) > y - R X - B, . Substituting (11) and X = 0 into (15) and rearranging yields the no bumping condition:

(17)

PQIH - D ( H ) represents the value of the marginal skilled worker if employed in a skilled job; PQzh - D(h.) represents the value of the marginal skilled worker if forced to bump and work in an unskilled job; and B, + R X depicts the marginal adjustment and psychological costs involved in bumping, as evaluated when bumping is just beginning to occur. Therefore the no bumping condition may be interpreted as saying that bumping will not occur as long as the value of the marginal skilled worker if employed in a skilled job exceeds his net value if forced to bump.

The same considerations apply to layoffs of skilled workers. From (14), as long as D ' ( H ) H - D ( H ) exceeds Y - R" - A,, and therefore H exceeds H" ', as shown in the upper and middle panels of Figure 1, no skilled worker will be laid off. If H falls short of H O " , then some skilled workers will be laid off, and the relationship between H and 2 is negative, as is illustrated by Z = K ( H ) in Figure 1. The slope of the curve is given by K' = ( -D"H/2A,) < 0. This implies that no layoffs of skilled workers will occur as long as the marginal skilled worker is worth more if employed in a skilled job than if laid off.

In drawing the graphs of X = G(H) and 2 = K ( H ) in Figure 1, it has been assumed that y - R X - B , is larger than Y - R Z - A,. Whether bumping will occur prior to layoffs as the price of output falls hinges upon this assumption, as will be seen shortly. The assumption implies that (A, - B , ) + (Rz - R x ) > (Y - y). (A, - B , ) tells how much more in adjustment costs layoffs entail for the firm than bumping, as evaluated at zero layoffs and zero bumps; ( R z - R X ) how much more psychological costs layoffs inflict on each skilled worker than bumping; and ( Y - y) how much more each skilled worker can earn than each unskilled worker if laid off.

As Doeringer and Piore [1971] suggest, in large firms with well-developed internal labor markets, skills are typically firm-specific, and each firm tends to be a community into which workers are integrated. As skills become more firm-specific, the edge that skilled workers have over unskilled workers when laid off will diminish, and (Y -- y) will become smaller. In the limit where all skills possessed by a worker are firm-specific, (Y - y) equals zero. Also, the sense of community developed in the firm magnifies the adjustment and psychological costs of layoff s relative to bumping. It follows then that in the firms with well-developed internal labor markets, (Y - y) tends to be small whereas (A, - B , ) and (Rz - R x ) tend to be large. Therefore, I believe that the assumption, y - R X -- B , > Y - RZ - A,, is valid for firms with well-developed internal labor markets which are under consideration in the paper.

The lower panel of Figure 1 shows the relationship between H and P under efficient contracts. Po and Po* correspond to H' and H u e . When Pis

PQlH - D ( H ) > PQZh - D(h) - ( B , + R').


higher than Po, we know that X = 2 = 0. Equation (13) alone determines h, therefore equations (11) and (12) determine H(P) and z(P). A routine comparative statics exercise on H of P shows that dH/dP > 0 when P exceeds Po. Likewise, dH/dP > 0 when P is between Po ' and Po, as well as when P is less than Po0.ls

I now describe how bumping, layoffs, and worksharing will occur under efficient contracts as the price of output decreases. At early stages of the price decrease (when P > Po), the efficient skilled contract will dictate worksharing to be the sole device for labor utilization adjustment, and neither bumping nor layoffs will be used. Worksharing is chosen over bumping and layoff s because worksharing does not entail the adjustment and psychological costs that bumping and layoffs do. Bumping and layoffs will not be used at all when P > Po because the value of the marginal skilled worker if employed in a skilled job exceeds his net value if forced to bump or laid off.

As the price continues to fall toward Po, more worksharing will take place, which will cause D'(H)H - D(H) to decline, and therefore the value of the marginal skilled worker if employed in a skilled job falls. Also it can be easily shown from (12) and (13) that the net value of the marginal skilled worker if forced to bump, as evaluated at zero bumps, is given by y - R X - Bo, which does not depend on H. As a result, as more worksharing occurs, the gap between the value of the marginal skilled worker if employed in a skilled job and his net value if forced to bump will diminish. When Preaches Po, the gap will disappear, and the efficient skilled contract will start to require bumping to be used along with worksharing.

In response to a further decline in P below Po, more bumping and worksharing will occur. When P reaches Po ', and therefore X reaches X'' in the middle panel of Figure 1, the efficient skilled contract will entail the use of layoffs along with worksharing and bumping.

Intuition can be provided for the result that layoffs will commence when the number of bumps reaches X". Substituting 2 = 0 into (14) and combining the result with (16) yields the relevant no-layoff condition:

(18) PQ2h - D(h) - R X - (Bo i- 2BlX) > Y - RZ - Ao. As explained above, the left-hand side of (18) represents the value of the marginal skilled worker if forced to bump, less the marginal adjustment and psychological costs involved in bumping; and the right-hand side the value of the marginal skilled worker if laid off, less the corresponding marginal adjustment and psychological costs, as evaluated at zero layoffs. Clearly, as more bumping occurs, the marginal adjustment costs of bumping, (73, + 2B1X), increase and therefore the net value of the marginal skilled worker if forced to bump, the left-hand side of (18), falls. When X finally reaches

15. It can also be shown that H = H ( P ) has kink points at both P = Po and P = P O o , as illustrated in the lower panel of Figure 1.

KATO: "BUMPING 665

X"", the net value of the marginal skilled worker if forced to bump will become equal to his net value if laid off, and hence layoffs will start to occur.

As P falls still further, then more worksharing, bumping, and layoffs will occur.16 Obviously the order in which bumping and layoffs take place would be reversed if the assumption that y - RX - Bo > Y - RZ - A,, were reversed.

Two results are notable concerning how the critical values of P , P o and P O 0 will be influenced by changes in some exogenous variables. First, an increase in the alternative net income of unskilled workers together with a decrease in the marginal psychological and adjustment costs of bumping, as evaluated at zero bumping, will lead to an increase in Po and a decrease in Po *, This implies that bumping will be initiated after a smaller price reduction and that layoffs will commence after a larger reduction. Second, an increase in the alternative net income of skilled workers together with a decrease in the psychological and marginal adjustment costs of layoffs, as evaluated at zero layoffs, will lead to a rise in P"", which means that layoffs will begin following a smaller price redu~ti0n.l~

IV. CONCLUDING REMARKS

This paper has dealt with the practice prevalent in large North American firms with well-developed internal labor markets whereby a firm, faced with a declining demand for its output, uses three alternative methods of labor utilization adjustment conducted in the following order: (1) worksharing, (2) bumping, and (3) layoffs.

I have developed a simple implicit contract model with bumping, and have shown that the practice may have evolved as a rational response by the firm and its workers to what the internal labor market literature calls the "internalization of the firm". According to the literature, a firm with well- developed internal labor markets is not just a place where workers supply their labor services to the firm at the market wage, but is a community in which workers are strongly tied to each other. Layoffs disturb the community and therefore entail various adjustment and psychological costs. Since bumping, as an alternative to layoffs, can reduce some of these costs, it will be used before layoffs when reductions in labor are required. The adjustment costs of bumping will rise rapidly, however, as more of it takes place. Eventually, bumping will become as costly as layoffs, and layoffs will begin to be used in conjunction with bumping. Worksharing does not entail any adjustment and psychological costs, and therefore will be used prior to bumping and layoffs. Worksharing does not completely dominate bumping

16. It can be shown that the slope of H ( P ) falls discretely at P o and Po'. This implies that worksharing will be used less intensively as the price of output falls.

17. See Appendix B for the derivation of these two results. The effect on Pro of the increase in the alternative net income of unskilled workers is ambiguous. The remaining results are all unambiguous.


and layoffs, however, since the net value of the marginal skilled worker if forced to bump or if laid off will eventually become equal to his value if employed in a skilled job as more worksharing occurs.

Though worker heterogeneity has been introduced into the implicit contract model by creating two types of workers, skilled and unskilled, all workers within each category have been treated as homogeneous. Therefore I could not investigate a related practice in which, among skilled workers, the least senior worker will bump first. In order to shed light on that practice, the single-period model would have to be extended to a multi-period one in which the firm hires new workers every period. Workers stay with the firm for a number of periods and therefore differ in seniority. The extension would be important but challenging.18

APPENDICES

A. Derivation of the Conditions for Efficient Contracts In this appendix the conditions for the efficient contracts are derived.

Denoting the multipliers for constraints (9) and (10) by A and p, I form the Lagrangean, L:

(19) 1: = Il 4- A(U - Vo) + / L ( U - ~ 0 ) .

Partially differentiating 1: with respect to W(P) and w(P) yields

(20) A = N , and

(21) /L = n.

Since N , n > 0, then A, p > 0, and therefore conditions (9) and (10) are binding

(22) U = U,,, and

(233) 11 = 240.

Partially differentiating L with respect to H ( P ) and h(P) and combining the results with equations (20) and (21) produces conditions (11) and (12). Simi- larly, partially differentiating 1: with respect to z(P) , Z ( P ) , and X ( P ) and combining the results with equations (20) and (21), conditions (11) and (12), and the assumption that z > 0, yields conditions (13), (14), and (15).

Note that conditions (11)-(15) determine a solution for H ( P ) , h(P), z (P) , Z ( P ) , and X ( P ) . Given the above solution, equations (22) and (23) determine a solution for W(P) and w(P).

18. Carmichael [1983] developed a Becker-type specific human capital model with two- sided private information, and explained seniority-based promotion as a feasible solution to a moral hazard problem.

KATO: “BUMPING 667

B. Determination of Po and Po* When P = Po, we know that X = Z = 0; condition (13) determines h, and

condition (15) determines H = H ” . It follows that conditions (11) and (12) jointly determine Po and z. Likewise, when P = Po* , we know that 2 = 0 and X > 0; condition (13) again determines h; and condition (14) determines H = H**. Given H = H o e , from above, condition (15) determines X. Fi- nally, conditions (11) and (12) jointly determine Po* and z.

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“BUMPING”, LAYOFFS, AND WORKSHARING