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Another possible source of wage stickiness
ROBERT M. SOLOW Massachusetts
Institute
of Technology
Another Possible Stickiness
Source of Wage
A number of hypotheses have been advanced to explain wage stickiness. This article explores another reason why wage stickiness might be in an employer’s interest: the relationship between productivity and the wage rate. If the wage enters the short-run production function, a cost-minimizing firm will leave its wage offer unchanged, no matter how its output varies, if and only if the wage enters the production function in a labor-augmenting way.
One could argue-and I would argue-that the most interesting and important line of work in current macro theory is the attempt to reconstruct plausible microeconomic underpinnings for a recognizably Keynesian macroeconomics. The best developed approach to this task, which has just achieved at least a local maximum in Malinvaud (1977), starts from the presumption that the nominal wage, or some other equally important price, is sticky.’ I say “sticky” rather than “rigid’ because the wage is allowed to move; the presumption is only that it does not move quickly enough to clear the labor market in a reasonable time. A theory that rests on sticky wages owes itself an explanation of wage stickiness. Why does the wage not move flexibly to clear the labor market? The literature has produced several answers to that question, generally not mutually exclusive. Keynes gave one answer in the Gene& Theory: in a decentralized labor market, every change in a nominal wage is also a change in relative wages; workers can and do resist reductions in their relative wages in the only way the institutions allow-by resisting wage cuts even in soft labor markets. 2 The recent revival of interest in macro theory has produced alternative accounts. Hahn (1976) and Negishi (1974) suggest a sort of kinked perceived demand curve, both for labor and for produced commodities. The current favorite seems to be the implicit contract: wage stickiness is a rational market response to the fact that employers are less risk averse than workers, combined with the
‘See also Barre and Grossman (1976). 2For a recent discussion of this idea, see Trevithick Journal of Macroeconomics, @ Wayne State Unioersity
Winter 1979, Press, 1979.
(1976).
Vol. 1, No. 1, pp. 79-82
79
Robert M. Solow existence of some sources of income for unemployed workers.3 There are undoubtedly other possibilities. One of the attractive features of the implicit contract approach is that it brings the employer into the act. Whether or not it is surprising that unemployed workers do not try to undercut the still-employed by offering to work for less than the going wage, it requires explanation that employers do not typically solicit wage-cutting behavior. In the implicit contract model, the employer has tacitly given up that ploy in return for a lower going, wage than would otherwise prevail. I want to suggest yet another reason why wage stickiness might be in the employer’s interest. Part of the folklore of the labor market is that “you get what you pay for.” An employer who did try to induce wage-cutting in a buyer’s market might find that the short-run gain was more than offset by hidden longerrun costs. Bad morale may lead to lower productivity or even to carelessness verging on sabotage. A reputation as a lousy employer will carry over to tighter labor market conditions and lead to adverse selection in recruiting and perhaps even worse productivity performance. Suppose we try to formalize this piece of home-made sociology. Consider an employer who is sales-constrained in the market for output, 9. Labor, n, is the only variable input in the short run, and the labor market is imperfect enough so that the employer has some choice of the wage, w, to be offered. (Since I will not be considering price changes, w can do duty both as nominal and real wage.) However, the employer knows that realized productivity will depend on the wage quoted, with the two rising or falling together. This may come about either by selectivity in recruiting or behavior on the job. Let 9 = f(n,w) be the short-run production function, giving output as an increasing function of employment and the wage. The partial inverse n = n(9.w) will exist and exhibit labor requirements as an increasing function of the rate of output and a decreasing function of the wage. Prime cost is then w *n(9,w). For given 9, the firm naturally chooses the wage that minimizes cost. The first-order condition is n(9,w)
+ wh,(9,w)
= 0 ,
(1)
and I will suppose that this represents a unique interior minimum. For each rate of output given by the market there is a best wage for the firm to quote, obtained by solving (1). Thus (1) defines w as a function of 9. The sensitivity of the quoted wage to business cycle variations in output is measured by dwldq, obtained by implicit differentiation of (I). 3For 80
a summary
and references
see Gordon
(1977).
Wage Stickiness For the ultimate in wage stickiness, we can ask when dwldq = 0. The answer is: when and only when n, + wh, = 0, for (q,w) satisfying (I). Use (1) to substitute for the explicit w, and we find a partial differential equation for wage-stickiness-at-all-levels-of-output:
It iseasilychecked that 8’ lognlaq dw = nd(n en, -n,, an,), so (2) isequivalent to a* log n/aq aw = 0. The general solution of (2) is therefore log n = A(q) + B(w) ,
(3)
where A and B are arbitrary functions (increasing and decreasing, respectively). Now, setting e* = a and eeB = b, we have n = a(q)/b(w) or, finally,
q = g[Wwhl ,
(4
where g (the inverse function ofa) and b are arbitrary increasing functions. The upshot is: if the wage enters the short-run production function, a cost minimizing firm will leave its wage offer unchanged no matter how its output varies if and only if the wage enters the production function in a labor augmenting way. And in that case, the cost minimizing wage is the one that minimizes the cost of a unit of effort or effective labor, while employment is varied to meet output needs. Now this condition may be special, but it is not implausible. It requires simply that higher morale or higher quality of personnel aifect production like an increase in effort. And in any case it would be enough for macro theory if the condition were only approximately met and the wage only nearly invariant. I find this story fairly easy to believe. It can not be the whole story .of wage stickiness, however. For one thing, although wage stability may be good for morale, presumably instability of employment is not. Why is it better for firms to offer stable wages than to offer stable employment? Perhaps because, except in the worst of times, the number laid off is only a small fraction of the number of workers attached to a typical firm, and everyone knows that. Wage cutting might therefore have far more drastic effects on morale than would layoffs. In any case, the factor emphasized here does not exclude any of the other factors mentioned in the literature, nor is it excluded by them. The underlying point of this paper must be as old as the hills. This particular formulation began life as an exam question in the graduate macro course at M.I.T. At about the same time, I came across an unpub81
Robert M. Solow lished paper, by Negishi (1976), which states the easier sufficiency half of the theorem proved above. Negjshi also gives a reference to Rees (1973, p. 226). This is especially nice, although Rees merely mentions the phenomenon, because at last we come to someone who actually knows something about real labor markets. Received:
June
10, 1977
References Barr-o, R.J. and H.I. Grossman. Money, Employment and Inflation. Cambridge and New York: Cambridge University Press, 1976. Gordon, R. J. “The Theory of Domestic Inflation.” American Economic Review 67 (February 1977): 126-134. Hahn, F.H. “On Non-Wah-asian Equilibria.” Institute for Mathematical Studies in the Social Sciences, Stanford University, Technical Report No. 203, 1976. Malinvaud, Edmond. The Theory of Unemployment Reconsidered. Yrijo Jahnsson Lectures, Oxford: Basil Blackwell, 1977. Negishi, Takaski. “Involuntary Unemployment and Market Imperfection.” Economic Studies Quarterly 25 (April 1974): 3241. -. “Microeconomic Foundations of Keynesian Macroeconomics.” Mimeographed, Summer 1976. Rees, Albert. The Economics of Work and Pay. New York: Harper and Row, 1973. Trevithick, G.A. “Money Wage Inflexibility and the Keynesian Labour Supply Function.” Economic Journal 86 (June 1976): 32732.
82
Institute
of Technology
Another Possible Stickiness
Source of Wage
A number of hypotheses have been advanced to explain wage stickiness. This article explores another reason why wage stickiness might be in an employer’s interest: the relationship between productivity and the wage rate. If the wage enters the short-run production function, a cost-minimizing firm will leave its wage offer unchanged, no matter how its output varies, if and only if the wage enters the production function in a labor-augmenting way.
One could argue-and I would argue-that the most interesting and important line of work in current macro theory is the attempt to reconstruct plausible microeconomic underpinnings for a recognizably Keynesian macroeconomics. The best developed approach to this task, which has just achieved at least a local maximum in Malinvaud (1977), starts from the presumption that the nominal wage, or some other equally important price, is sticky.’ I say “sticky” rather than “rigid’ because the wage is allowed to move; the presumption is only that it does not move quickly enough to clear the labor market in a reasonable time. A theory that rests on sticky wages owes itself an explanation of wage stickiness. Why does the wage not move flexibly to clear the labor market? The literature has produced several answers to that question, generally not mutually exclusive. Keynes gave one answer in the Gene& Theory: in a decentralized labor market, every change in a nominal wage is also a change in relative wages; workers can and do resist reductions in their relative wages in the only way the institutions allow-by resisting wage cuts even in soft labor markets. 2 The recent revival of interest in macro theory has produced alternative accounts. Hahn (1976) and Negishi (1974) suggest a sort of kinked perceived demand curve, both for labor and for produced commodities. The current favorite seems to be the implicit contract: wage stickiness is a rational market response to the fact that employers are less risk averse than workers, combined with the
‘See also Barre and Grossman (1976). 2For a recent discussion of this idea, see Trevithick Journal of Macroeconomics, @ Wayne State Unioersity
Winter 1979, Press, 1979.
(1976).
Vol. 1, No. 1, pp. 79-82
79
Robert M. Solow existence of some sources of income for unemployed workers.3 There are undoubtedly other possibilities. One of the attractive features of the implicit contract approach is that it brings the employer into the act. Whether or not it is surprising that unemployed workers do not try to undercut the still-employed by offering to work for less than the going wage, it requires explanation that employers do not typically solicit wage-cutting behavior. In the implicit contract model, the employer has tacitly given up that ploy in return for a lower going, wage than would otherwise prevail. I want to suggest yet another reason why wage stickiness might be in the employer’s interest. Part of the folklore of the labor market is that “you get what you pay for.” An employer who did try to induce wage-cutting in a buyer’s market might find that the short-run gain was more than offset by hidden longerrun costs. Bad morale may lead to lower productivity or even to carelessness verging on sabotage. A reputation as a lousy employer will carry over to tighter labor market conditions and lead to adverse selection in recruiting and perhaps even worse productivity performance. Suppose we try to formalize this piece of home-made sociology. Consider an employer who is sales-constrained in the market for output, 9. Labor, n, is the only variable input in the short run, and the labor market is imperfect enough so that the employer has some choice of the wage, w, to be offered. (Since I will not be considering price changes, w can do duty both as nominal and real wage.) However, the employer knows that realized productivity will depend on the wage quoted, with the two rising or falling together. This may come about either by selectivity in recruiting or behavior on the job. Let 9 = f(n,w) be the short-run production function, giving output as an increasing function of employment and the wage. The partial inverse n = n(9.w) will exist and exhibit labor requirements as an increasing function of the rate of output and a decreasing function of the wage. Prime cost is then w *n(9,w). For given 9, the firm naturally chooses the wage that minimizes cost. The first-order condition is n(9,w)
+ wh,(9,w)
= 0 ,
(1)
and I will suppose that this represents a unique interior minimum. For each rate of output given by the market there is a best wage for the firm to quote, obtained by solving (1). Thus (1) defines w as a function of 9. The sensitivity of the quoted wage to business cycle variations in output is measured by dwldq, obtained by implicit differentiation of (I). 3For 80
a summary
and references
see Gordon
(1977).
Wage Stickiness For the ultimate in wage stickiness, we can ask when dwldq = 0. The answer is: when and only when n, + wh, = 0, for (q,w) satisfying (I). Use (1) to substitute for the explicit w, and we find a partial differential equation for wage-stickiness-at-all-levels-of-output:
It iseasilychecked that 8’ lognlaq dw = nd(n en, -n,, an,), so (2) isequivalent to a* log n/aq aw = 0. The general solution of (2) is therefore log n = A(q) + B(w) ,
(3)
where A and B are arbitrary functions (increasing and decreasing, respectively). Now, setting e* = a and eeB = b, we have n = a(q)/b(w) or, finally,
q = g[Wwhl ,
(4
where g (the inverse function ofa) and b are arbitrary increasing functions. The upshot is: if the wage enters the short-run production function, a cost minimizing firm will leave its wage offer unchanged no matter how its output varies if and only if the wage enters the production function in a labor augmenting way. And in that case, the cost minimizing wage is the one that minimizes the cost of a unit of effort or effective labor, while employment is varied to meet output needs. Now this condition may be special, but it is not implausible. It requires simply that higher morale or higher quality of personnel aifect production like an increase in effort. And in any case it would be enough for macro theory if the condition were only approximately met and the wage only nearly invariant. I find this story fairly easy to believe. It can not be the whole story .of wage stickiness, however. For one thing, although wage stability may be good for morale, presumably instability of employment is not. Why is it better for firms to offer stable wages than to offer stable employment? Perhaps because, except in the worst of times, the number laid off is only a small fraction of the number of workers attached to a typical firm, and everyone knows that. Wage cutting might therefore have far more drastic effects on morale than would layoffs. In any case, the factor emphasized here does not exclude any of the other factors mentioned in the literature, nor is it excluded by them. The underlying point of this paper must be as old as the hills. This particular formulation began life as an exam question in the graduate macro course at M.I.T. At about the same time, I came across an unpub81
Robert M. Solow lished paper, by Negishi (1976), which states the easier sufficiency half of the theorem proved above. Negjshi also gives a reference to Rees (1973, p. 226). This is especially nice, although Rees merely mentions the phenomenon, because at last we come to someone who actually knows something about real labor markets. Received:
June
10, 1977
References Barr-o, R.J. and H.I. Grossman. Money, Employment and Inflation. Cambridge and New York: Cambridge University Press, 1976. Gordon, R. J. “The Theory of Domestic Inflation.” American Economic Review 67 (February 1977): 126-134. Hahn, F.H. “On Non-Wah-asian Equilibria.” Institute for Mathematical Studies in the Social Sciences, Stanford University, Technical Report No. 203, 1976. Malinvaud, Edmond. The Theory of Unemployment Reconsidered. Yrijo Jahnsson Lectures, Oxford: Basil Blackwell, 1977. Negishi, Takaski. “Involuntary Unemployment and Market Imperfection.” Economic Studies Quarterly 25 (April 1974): 3241. -. “Microeconomic Foundations of Keynesian Macroeconomics.” Mimeographed, Summer 1976. Rees, Albert. The Economics of Work and Pay. New York: Harper and Row, 1973. Trevithick, G.A. “Money Wage Inflexibility and the Keynesian Labour Supply Function.” Economic Journal 86 (June 1976): 32732.
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