《宏观经济学 Macroeconomics》课外读物：Money-Wage Dynamics and Labor-Market Equilibrium

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Money-Wage Dynamics and Labor-Market Equilibrum* Edmund S. Phelps University of Pennsylvania If the economy were always in macroeconomic equilibrium then perhaps the full-employment money-and-growth models of recent vintage would suffice to explain the time paths of the money wage and the price level. But since any actual economy is almost continuously out of equilibrium we need also to study wage and price dynamics under arbitrary conditions. The numerous Phillips-curve studies of the past ten years have done this with a vengeance in offering countless independent variables in numerous combinations to explain wage movements. But it is difficult to choose among these econometric models, and rarely is there a clear rationale for the model used. This paper presents a modest start toward a unified and empirically applicable theory of money-wage dynamics. At the same time it tries to capture the role of expectations and thus to work into the theory the notion of labor-market equilibrium. I. Evolution of the Phillips Curve and its Opposition Keynes' General Theory (1936) and virtually all formal macroeconomic models of the postwar era postulated a minimum unemployment level-a full-employment level of unemployment-which could be maintained with either stable prices or rising prices. In this happy state, additional aggregate demand would produce rising prices and wages but no reduction of unemployment. The full-employment quantity of unemployment was identified as "frictional " and "voluntary "; and frictional unemployment was (mistakenly) assumed to be unresponsive to demand.l Hence there was no need to choose between low unemployment and price stability. * This study was supported by a grant from the National Science Foundation. A monetary economy can choose among different levels of frictional unemployment that correspond to different levels of aggregate demand and job vacancies. In fact, therefore, there is no unique full-employment quantity of frictional unemployment

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM This doctrine depended on Keynes' notions of money-wage behavior At more than minimum unemployment, a rise(fall) of demand and em- ployment would produce a once-for-all rise(fall) of the money wage prices constant; a rise(fall) of the price level would cause a rise(fall)of th money wage in smaller proportion. Hence, in a stationary economy at least, his theory did not predict the possibility of a secular rise of money wage rates at normal unemployment rates-let alone wage rises exceeding productivity growth-only the one-time"semi-inflation"(Keynes, 1936, p. 301)of prices and wages during the transition to minimum unem- ployment. This doctrine was quickly disputed by robinson(1937, pp 30-31) wrote of a conflict between moderately high employment and stability. Dunlop(1938)suggested that the rate of change of the money wage depends more on the level of unemployment than upon the rate of change of unemployment, as Keynes had it. After the war, Singer(1947) Bronfenbrenner(1948), Haberler (1948), Brown( 1955), Lerner(1958), and many others wrote that at low albeit above-minimum unemployment levels there occurs a process of“ cost inflation,”"“wage- push infation,” ¨ income inflation,”“ creeping inflation,”“ sellers' inflation,”“ dilemma inflation,” or the‘ new infation”- a phenomenon which was attributed to the discretionary power of unions or oligopolies or both to raise wages or prices or both without"excess demand I believe this customary attribution of cost infation to the existence of such large economic units to be unnecessary and insufficient. Like the theory of unemployment, the theory of cost inflation requires a nor Walrasian model in which there is no auctioneer continuously clearin commodity and labor markets. Beyond that, it is not clear to me what monopoly power contributes. An increase of monopoly power-due, say, to increased concentration -will raise prices relative to wages at any given unemployment rate and productivity level; but employment rate, the real wage has fallen (relative to productivity) continuation of inflation will depend on other sources will stop and any enough to accommodate the higher markup this process ush theorists like Weintraub (1959) to treat innatic almost spontaneous, virtually independent of the unemployment rate over any rele vant range, and hence not induced by aggregate demand I once tested the hypothesis that the 1955-57 inflation was more of this character than were the two earlier post ar infla making the push"would be uneven in its sectoral incidence, so that the coefficient of correlation between sector price changes and sector output changes would (if the hypothesis were true) be algebraically smaller in the 1955-57 period than it was earlier(1961). It was stical significance of the decline was impossible to determine. Incidentally, Selden,s correlation test ( 1959) wrongly attributes significance to the positivity of the coef n 1955-57 instead of to the magnitude of tl 3 The answer of Ackley (1966)and Lerner(1967) that correspondin mployment rate and productivity level there is a natural real wage that is irreducible

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM 679 This doctrine depended on Keynes' notions of money-wage behavior. At more than minimum unemployment, a rise (fall) of demand and employment would produce a once-for-all rise (fall) of the money wage, prices constant; a rise (fall) of the price level would cause a rise (fall) of the money wage in smaller proportion. Hence, in a stationary economy at least, his theory did not predict the possibility of a secular rise of moneywage rates at normal unemployment rates-let alone wage rises exceeding productivity growth-only the one-time "semi-inflation" (Keynes, 1936, p. 301) of prices and wages during the transition to minimum unemployment. This doctrine was quickly disputed by Robinson (1937, pp. 30-31), who wrote of a conflict between moderately high employment and price stability. Dunlop (1938) suggested that the rate of change of the money wage depends more on the level of unemployment than upon the rate of change of unemployment, as Keynes had it. After the war, Singer (1947), Bronfenbrenner (1948), Haberler (1948), Brown (1955), Lerner (1958), and many others wrote that at low albeit above-minimum unemployment levels there occurs a process of "cost inflation," "wage-push inflation," "income inflation," "creeping inflation," "sellers' inflation," "dilemma inflation," or the "new inflationu-a phenomenon which was attributed to the discretionary power of unions or oligopolies or both to raise wages or prices or both without "excess demand."2 I believe this customary attribution of cost inflation to the existence of such large economic units to be unnecessary and insufficient. Like the theory of unemployment, the theory of cost inflation requires a nonWalrasian model in which there is no auctioneer continuously clearing commodity and labor markets. Beyond that, it is not clear to me what monopoly power contributes. An increase of monopoly power-due, say, to increased concentration-will raise prices relative to wages at any given unemployment rate and productivity level; but once, at the prevailing unemployment rate, the real wage has fallen (relative to productivity) enough to accommodate the higher markup, this process will stop and any continuation of inflation will depend on other ~ources.~ Some wage-push theorists like Weintraub (1959) appear to treat inflation as almost spontaneous, virtually independent of the unemployment rate over any relevant range, and hence not induced by aggregate demand. I once tested the hypothesis that the 1955-57 inflation was more of this character than were the two earlier postwar inflations, making the assumption that autonomous "wage push" or "profit push" would be uneven in its sectoral incidence, so that the coefficient of correlation between sector price changes and sector output changes would (if the hypothesis were true) be algebraically smaller in the 1955-57 period than it was earlier (1961). It was algebraically smaller, but the statistical significance of the decline was impossible to determine. Incidentally, Selden's correlation test (1959) wrongly attributes significance to the positivity of the coefficient in 1955-57 instead of to the magnitude of the decline. The answer of Ackley (1966) and Lerner (1967) that corresponding to every unemployment rate and productivity level there is a natural real wage that is irreducible

JOURNAL OF POLITICAL ECONOMY Similarly, I doubt that the existence of labor unions is remotely sufficient to explain the cost inflation phenomenon. whether the unions significantly exacerbate the problem-whether they increase that unemployment rate which is consistent with price stability-is, however, a difficult question The affirmative answer frequently starts from the theory, set forth by Dunlop(1950), that a union, to maximize its utility, seeks to "trade off the real wage rate against the unemployment of its members, raising the former (relative to productivity) until the gain from a further real wage increase is offset by the utility loss from the increase in unemployment expected to result from it. At an unemployment level below the unions the unions then push up wage rates faster than productivit But firms pass these higher costs on to consumers, so the real wage gains are frustrated, and as long as the government maintains the low unem- ployment level the rounds of inflation will continue I have trouble applying such a model to the American economy. Almost three-quarters of the civilian labor force do not belong to unions. This fact ts doubt on the quantitati ive importance of the model. And perhaps the fact goes much deeper. If the union members whom the unions make unemployed have no good prospect of future union employment, they will be inclined to seek employment elsewhere. If, at the other extreme, the union unemployment is shared in the form of a short workweek, this un- employment-while real enough to the extent that members do not moonlight"-does not add to the official unemployment rate as it is measured. Certainly the unions participate in the cost inflation process, and they may even increase a little the volume of unemployment consistent with price stability, But I should think that a union must offer its member ship a frequency of employment opportunities that is roughly comparable to that elsewhere in order to thrive and that appreciably reduced employ ment opportunities require a greater wage differential between union and other employment than is commonly observed. 4 Phillip: sful fitting of what to a scatter diagram of historical British data deprived the discussions of some of their institutional color, but epitomized the new concept of cost inflation---if by that term we mean(as i think most of the aforementioned writers intended) that kind of inflation which can be stopped only by a reduc- tion of the employment rate through lower aggregate demand and which structural changes, so that money wages will keep pace with prices until to increase, seems to me to be terribly implausible. In any IIs paper monopoly"argument 4 It is certainly likely, however, that an increase of union power, even if localized

680 JOURNAL OF POLITICAL ECONOMY Similarly, I doubt that the existence of labor unions is remotely sufficient to explain the cost inflation phenomenon. Whether the unions significantly exacerbate the problem-whether they increase that unemployment rate which is consistent with price stability-is, however, a difficult question. The affirmative answer frequently starts from the theory, set forth by Dunlop (1950), that a union, to maximize its utility, seeks to "trade off" the real wage rate against the unemployment of its members, raising the former (relative to productivity) until the gain from a further real wage increase is offset by the utility loss from the increase in unemployment expected to result from it. At an unemployment level below the unions' optimum, the unions then push up wage rates faster than productivity. But firms pass these higher costs on to consumers, so the real wage gains are frustrated, and as long as the government maintains the low unemployment level the rounds of inflation will continue. I have trouble applying such a model to the American economy. Almost three-quarters of the civilian labor force do not belong to unions. This fact casts doubt on the quantitative importance of the model. And perhaps the fact goes much deeper. If the union members whom the unions make unemployed have no good prospect of future union employment, they will be inclined to seek employment elsewhere. If, at the other extreme, the union unemployment is shared in the form of a short workweek, this unemployment-while real enough to the extent that members do not "moonlightM-does not add to the official unemployment rate as it is measured. Certainly the unionsparticipate in the cost inflation process, and they may even increase a little the volume of unemployment consistent with price stability. But I should think that a union must offer its membership a frequency of employment opportunities that is roughly comparable to that elsewhere in order to thrive and that appreciably reduced employment opportunities require a greater wage differential between union and other employment than is commonly observed.* Phillips' successful fitting of what we now call the Phillips curve (1958) to a scatter diagram of historical British data deprived the discussions of some of their institutional color, but epitomized the new concept of cost inflation-if by that term we mean (as I think most of the aforementioned writers intended) that kind of inflation which can be stopped only by a reduction of the employment rate through lower aggregate demand and which despite structural changes, so that money wages will keep pace with prices until unemployment is allowed to increase, seems to me to be terribly implausible. In any case, if this paper is right, cost inflation theory does not require any such "double monopoly" argument. It is certainly likely, however, that an increase of union power, even if localized, will raise the average money-wage level at any constant unemployment rate (see Hines, 1964)

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM thus raises a cruel dilemma for fiscal and monetary policy. The Phillips curve portrayed the rate of wage change as a continuous and decreasing function of the unemployment rate, with wage increases exceeding typical productivity growth at sufficiently low albeit above-minimum unemploy ment rates. Hence, if prices are tied to marginal or average costs, the smaller the level at which aggregate demand sets the unemployment rate the greater is the continuing rate of infiation Strikingly, Phillips found that the nineteenth-century data pointed to a trade-off between wage increases and unemployment in the same way as contemporary data. Lipsey's sequel(1960) showed a statistically significant Phillips-curve relation for the subperiod 1861-1913. In fact, this early Phillips curve was higher(by about one percentage point) than the Phillips curve he fitted to the period 1929-57. 6 Apparently the cost inflation ten dency, if real, is not""in history; in Britain anyway it may be no worse than it used to be But is the Phillips trade-off real, serious, and not misleading? I shall discuss briefly two challenges to the Phillips curve to which this paper is relevant. The first is the question of whether the slope of the wage increase- unemployment relation is great enough to pose a serious dilemma for ggregate demand policy. Though proponents of an American Phillips curve had tough sledding at first--numerous other variables were held to be important(Bowen, 1960; Bhatia, 1962; Eckstein and Wilson, 1962)- Perry's synthesis (1964)of much of this early work left a quantitatively important role for the unemployment rate(as well as for the profit rate and the rate of change of prices)in explaini nts in U.S. manufacturing. But in 1963 Bowen and Berry(1963)found that the decrease of the unemployment rate was far more important than the level of the unemployment rate in contributing to wage increases. The recent study of annual long-term wage data by Rees and Hamilton (1967)also showed a negligible (and statistically insignificant) relation between the eady-state unemployment rate and the rate of wage increase(though s By contrast, in the pure"demand inflation"of Keynes and the classics, a reduc ion of the price trend could be achieved without cost to output and employment since aggregate demand is necessarily superfluous to begin with "Demand inflatio ay be worth preserving, since a regime of mixed inflation"is conceivable My earlier paper(1961)contains a fairly complete taxonomy of inflations(see also Fellner, 1959). Incidentally, the occasional definition of cost inflation as an autono mous upward shift of the Phillips curve is very awkward and does not imply the policy dilemma"with which inflation analysts were concerned in the fifties 1862-1913 regression(his equation [10]) predicts a 2.58 per cent wage increase an nually, while the 1929-57 regression (his equation [13])predicts a 1.65 per cent 四 the same 3 per cent productivity growth in both periods, for bility would have permitted smaller unemployment in the latter s Table 2(p. 30)is evidence of the early Phillips curves under age increases after World War II

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM 681 thus raises a cruel dilemma for fiscal and monetary p01icy.~ The Phillips curve portrayed the rate of wage change as a continuous and decreasing function of the unemployment rate, with wage increases exceeding typical productivity growth at sufficiently low albeit above-minimum unemployment rates. Hence, if prices are tied to marginal or average costs, the smaller the level at which aggregate demand sets the unemployment rate the greater is the continuing rate of inflation. Strikingly, Phillips found that the nineteenth-century data pointed to a trade-off between wage increases and unemployment in the same way as contemporary data. Lipsey's sequel (1960) showed a statistically significant Phillips-curve relation for the subperiod 1861-1913. In fact, this early Phillips curve was higher (by about one percentage point) than the Phillips curve he fitted to the period 1929-57.6 Apparently the cost inflation tendency, if real, is not "new" in history; in Britain anyway it may be no worse than it used to be. But is the Phillips trade-off real, serious, and not misleading? I shall discuss briefly two challenges to the Phillips curve to which this paper is relevant. The first is the question of whether the slope of the wage increaseunemployment relation is great enough to pose a serious dilemma for aggregate demand policy. Though proponents of an American Phillips curve had tough sledding at first-numerous other variables were held to be important (Bowen, 1960; Bhatia, 1962; Eckstein and Wilson, 1962)- Perry's synthesis (1964) of much of this early work left a quantitatively important role for the unemployment rate (as well as for the profit rate and the rate of change of prices) in explaining money-wage movements in U.S. manufacturing. But in 1963 Bowen and Berry (1963) found that the decrease of the unemployment rate was far more important than the level of the unemployment rate in contributing to wage increases. The recent study of annual long-term wage data by Rees and Hamilton (1967) also showed a negligible (and statistically insignificant) relation between the steady-state unemployment rate and the rate of wage increase (though By contrast, in the pure "demand inflation" of Keynes and the classics, a reduction of the price trend could be achieved without cost to output and employment, since aggregate demand is necessarily superfluous to begin with. "Demand inflation" may be worth preserving, since a regime of "mixed inflation" is conceivable. My earlier paper (1961) contains a fairly complete taxonomy of inflations (see also Fellner, 1959). Incidentally, the occasional definition of cost inflation as an autonomous upward shift of the Phillips curve is very awkward and does not imply the "policy dilemma" with which inflation analysts were concerned in the fifties. At a constant price level and an unemployment rate of 2 per cent, Lipsey's (1960) 1862-1913 regression (his equation [lo]) predicts a 2.58 per cent wage increase annually, while the 1929-57 regression (his equation [13]) predicts a 1.65 per cent annual increase. At the same 3 per cent productivity growth in both periods, for example, price stability would have permitted smaller unemployment in the latter period. But Lipsey's Table 2 (p. 30) is evidence of the early Phillips curve's underestimation of the wage increases after World War 11

682 JOURNAL OF POLITICAL ECONOMY wage-change effects on prices feed back strongly on wages in their ee tion). This evidence strongly supports the neo-Keynesian revival led Sargan(1964)and Kuh(1967)who make the level of the unemployment rate, together with productivity and the price level, determine the level of the money wage. The underlying theory is apparently that a rise of aggre gate demand creates"bottlenecks"and hence a rise of wage rates in certain areas and skills at the same time that it increases employment once these bottlenecks have melted away and employment has reached its new and higher level there is no longer upward wage pressure. On this heory, money-wage increases go hand in hand with employment growth and not intrinsically with a high level of the employment rate Less frontal in a way but having equally profound policy implications is the second issue of the so-called stability of the Phillips curve. Conti nental economists like von Mises(1953, pp. 418-20)always emphasized the role of expectations in the inflationary process In our own day, william Fellner and Henry Wallich are most closely associated with the proposition that the maintenance of too low an unemployment rate and the resulting continued revision of disappointed expectations will cause a runaway infation. These ideas are reflected in the modern-day models of steady, anticipated"inflation, begun by Lerner (1949), which imply(or assume) that high inflation confers no benefits in the form of higher employment if (or as soon as)the inflation rate is fully anticipated by firms and workers. Recently, Friedman (1966)and I (1967) have sought to reconcile the Phillips hypothesis with the aforementioned axiom of anticipated inflation theory. I postulated that the Phillips curve, in terms of percentage price increase (or wage increase), shifts uniformly upward by one point with every one point increase of the expected percentage price increase (or xpected wage increase). Then the equilibrium unemployment rate-the rate at which the actual and expected price increases(or wage increases) are equal-is independent of the rate of inflation. If one further postulates as Friedman and i did,an" adaptive”or“eror- correcting"” theory of expectations, then the persistent underestimation of price or wage in creases which would result from an unemployment level consistently below the equilibrium rate would cause expectations continually to be revised upward so that the rate of inflation would gradually increase without limit; and, similarly, a very high, constant rate of infation, while buying"a very low unemployment rate at first, would require a gradual rise of the unemployment rate toward the equilibrium rate as expectations ? If the real wage rate were made a rapidly increasing function of the employment ate,the Kuh-Sargan model could then produce (cost) inflation at low, yet above ployment rate recants. a paper of mine(1965)on anticipated Two recent money-an models which study the consequences of alternative anticipated price trends are those by tobin (1965) and

682 JOURNAL OF POLITICAL ECONOMY wage-change effects on prices feed back strongly on wages in their equation). This evidence strongly supports the neo-Keynesian revival led by Sargan (1964) and Kuh (1967) who make the level of the unemployment rate, together with productivity and the price level, determine the level of the money wage.7 The underlying theory is apparently that a rise of aggregate demand creates "bottlenecks" and hence a rise of wage rates in certain areas and skills at the same time that it increases employment; once these bottlenecks have melted away and employment has reached its new and higher level there is no longer upward wage pressure. On this theory, money-wage increases go hand in hand with employment growth and not intrinsically with a high level of the employment rate. Less frontal in a way but having equally profound policy implications is the second issue of the so-called stability of the Phillips curve. Continental economists like von Mises (1953, pp. 418-20) always emphasized the role of expectations in the inflationary process. In our own day, William Fellner and Henry Wallich are most closely associated with the proposition that the maintenance of too low an unemployment rate and the resulting continued revision of disappointed expectations will cause a runaway inflation. These ideas are reflected in the modern-day models of steady, "anticipated" inflation, begun by Lerner (1949), which imply (or assume) that high inflation confers no benefits in the form of higher employment if (or as soon as) the inflation rate is fully anticipated by firms and workem8 Recently, Friedman (1966) and I (1967) have sought to reconcile the Phillips hypothesis with the aforementioned axiom of anticipated inflation theory. I postulated that the Phillips curve, in terms of percentage price increase (or wage increase), shifts uniformly upward by one point with every one point increase of the expected percentage price increase (or expected wage increase). Then the equilibrium unemployment rate-the rate at which the actual and expected price increases (or wage increases) are equal-is independent of the rate of inflation. If one further postulates, as Friedman and I did, an "adaptive" or "error-correcting" theory of expectations, then the persistent underestimation of price or wage increases which would result from an unemployment level consistently below the equilibrium rate would cause expectations continually to be revised upward so that the rate of inflation would gradually increase without limit; and, similarly, a very high, constant rate of inflation, while "buying" a very low unemployment rate at first, would require a gradual rise of the unemployment rate toward the equilibrium rate as expectations If the real wage rate were made a rapidly increasing function of the employment rate, the Kuh-Sargan model could then produce (cost) inflation at low, yet aboveminimum, unemploymellt rates. Lerner (1967) now recants. A paper of mine (1965) on anticipated inflation contains many of the references. Two recent money-and-growth models which study the consequences of alternative anticipated price trends are those by Tobin (1965) and Sidrauski (1967)

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM of that inflation developed. Therefore, society cannot trade between steady unemployment and steady inflation, on this theory. Society must eventually drive (or allow) the unemployment rate toward the equilibrium level or force it to oscillate around that equilibrium level. 9 This paper is addressed primarily to these two issues. The next section offers a theory of why, given expectations, both the level of unemploymer and the rate of change of employment should be expected to explain money-wage movements. The following section presents a theory of the influence of expected wage changes upon the Phillips curve. Some econo- metric tests of the predictions of these theories are reported in a statistical I.“ Turnover”’and“ Generalized excess demand For most of this section, until I try to accommodate other factors, I shal deal only with a more or less"atomistic "labor market in which there is no collective bargaining between unions and firms. But I exclude any Wal- rasian auctioneer to clear the labor market -the labor market is never properly cleared in this model-and I do not require that commodity markets be cleared. Firms may be said to have some dynamic monopsony power in that they need to pay a higher wage the faster they wish to attract labor. other recruitment activities held constan The model postulates considerable variety in the kinds of jobs and workers and postulates imperfect information about their availabilities. 10 Firms must inc ch costs" to find round pegs to fill round holes, and unemployed workers must aiso expend money and energy to find suitable mployment. As a consequence, positive unemployment and positive job vacancies tend to persist in a growing labor market and even under stationary labor supply because of the turnover or attrition of firms' employment rolls. Total vacancies can be positive for every kind of job and total unemployment can be positive for every type of worker because On certain assumptions regarding preferences and other matters, I showed that society(or the world)would choose between an"overemployment"route down to the equilibrium employment rate(thus leaving a heritage of a high Phillips curve corre- sponding to inflationary expectations)and an"underemployment"ror to the quilibrium employment rate on the basis of time preference. "The role of time preference is illuminated by Friedman's (1966) characterization of the true trade off"(p. 59)as one between" unemployment today and unemployment at a later date", there is such an intertemporal trade-off in the model under discussion if one holds eventual inflation rates constant, in the same way that the Fisherian trade-off between consumption today and consumption tomorrow holds subs wealth or pital constant. but there remains at any moment of time a statical unemployment and inflation(with the expected infation rate a parameter), analogous to the statical trade-off between consumption and capital formation (with initial capital stock a parameter) which lies at the roots of the intertemporal trade-off. ks by Stigler(1962), by Alchian and Allen (1964, xxxi), and by Holt and David (1966)contain some economics of such labor markets

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM 683 of that inflation developed. Therefore, society cannot trade between steady unemployment and steady inflation, on this theory. Society must eventually drive (or allow) the unemployment rate toward the equilibrium level or force it to oscillate around that equilibrium level.g This paper is addressed primarily to these two issues. The next section offers a theory of why, given expectations, both the level of unemployment and the rate of change of employment should be expected to explain money-wage movements. The following section presents a theory of the influence of expected wage changes upon the Phillips curve. Some econometric tests of the predictions of these theories are reported in a statistical appendix. 11. "Turnover" and "Generalized Excess Demand" For most of this section, until I try to accommodate other factors, I shall deal only with a more or less "atomistic" labor market in which there is no collective bargaining between unions and firms. But I exclude any Walrasian auctioneer to clear the labor market-the labor market is never properly cleared in this model-and I do not require that commodity markets be cleared. Firms may be said to have some dynamic monopsony power in that they need to pay a higher wage the faster they wish to attract labor, other recruitment activities held constant. The model postulates considerable variety in the kinds of jobs and workers and postulates imperfect information about their a~ailabilities.~~ Firms must incur "search costs" to find round pegs to fill round holes, and unemployed workers must also expend money and energy to find suitable employment. As a consequence, positive unemployment and positive job vacancies tend to persist in a growing labor market and even under stationary labor supply because of the turnover or attrition of firms' employment rolls. Total vacancies can be positive for every kind of job and total unemployment can be positive for every type of worker because O On certain assumptions regarding preferences and other matters, I showed that society (or the world) would choose between an "overemployment" route down to the equilibrium employment rate (thus leaving a heritage of a high Phillips curve corresponding to inflationary expectations) and an "underemployment" route up to the equilibrium employment rate on the basis of "time preference." The role of time preference is illuminated by Friedman's (1966) characterization of "the true tradeoff" (p. 59) as one between "unemployment today and unemployment at a later date"; there is such an intertemporal trade-off in the model under discussion if one holds eventual inflation rates constant, in the same way that the Fisherian trade-off between consumption today and consumption tomorrow holds subsequent wealth or capital constant. But there remains at any moment of time a statical trade-off between unemployment and inflation (with the expected inflation rate a parameter), analogous to the statical trade-off between consumption and capital formation (with initial capital stock a parameter) which lies at the roots of the intertemporal trade-off. loWorks by Stigler (1962), by Alchian and Allen (1964, xxxi), and by Holt and David (1966) contain some economics of such labor markets

JOURNAL OF POLITICAL ECONOMY of spatial mismatching among jobs and people. In the formal model I shall exclude serious bottlenecks in one or more kinds of labor in order to speak vacancy rate as if they were pretty much uniform over the spectrum of workers and jobs As defined here aggregate unemployment, "denoted U, consists of both those individuals without employment who are actively seeking a job (at going real wage rates) and the more passive without work who would accept a job opportunity (at the going rate) were it known to them Aggregate job vacancies, "denoted V, consist both of those jobs which employers are actively seeking at a cost to fill and of the quantity of un filled jobs that would be filled if and only if workers presented themselves without recruitment cost to the firm. Though it is doubtful that"active unemployment and vacancies are equivalent, respectively, to"passive unemployment and vacancies in their consequences for wage rates, I merge these active and passive components for simplicity. I Letting n denote the number of persons employed we have as a defini tion of labor supply, L, the relation L=N+U (1) Labor demand, Np, is defined by L may depend upon the usual factors like the real wage rate, income, wealth, and demographic factors; Np may depend on the technology, the product wage(net of interest and"depreciation"on the investment out- lays to process and train a new employee), the degree of monopoly power, and, if prices do not clear the commodity markets, upon aggregate demand o The concept of"excess demand"for labor, denoted x, is usually fined (3) The usual excess-demand theory of money-wage dynamics states that the proportionate rate of change of the money wage is proportional to the excess demand rate, denoted x. The latter is excess demand per unit of labor supply, and hence equal to the excess of the vacancy rate, v, over the x=U-u, x=XL, U=VL, u=UL e. I1 Econometric analysis by Simler and Tella(1967)shows total unemployment to plain wage movements than active or"measured"unemployment alone

684 JOURNAL OF POLITICAL ECONOMY of spatial mismatching among jobs and people. In the formal model I shall exclude serious bottlenecks in one or more kinds of labor in order to speak aggregatively of "the" wage rate, "the " unemployment rate, and "the" vacancy rate as if they were pretty much uniform over the spectrum of workers and jobs. As defined here, "aggregate unemployment," denoted U, consists of both those individuals without employment who are actively seeking a job (at going real wage rates) and the more passive without work who would accept a job opportunity (at the going rate) were it known to them. "Aggregate job vacancies," denoted V, consist both of those jobs which employers are actively seeking at a cost to fill and of the quantity of unfilled jobs that would be filled if and only if workers presented themselves without recruitment cost to the firm. Though it is doubtful that "active" unemployment and vacancies are equivalent, respectively, to "passive" unemployment and vacancies in their consequences for wage rates, I merge these active and passive components for simplicity.ll Letting N denote the number of persons employed, we have as a definition of labor supply, L, the relation Labor demand, ND,is defined by L may depend upon the usual factors like the real wage rate, income, wealth, and demographic factors; ND may depend on the technology, the product wage (net of interest and "depreciation" on the investment outlays to process and train a new employee), the degree of monopoly power, and, if prices do not clear the commodity markets, upon aggregate demand as well. The concept of "excess demand" for labor, denoted X, is usually defined as when The usual excess-demand theory of money-wage dynamics states that the proportionate rate of change of the money wage is proportional to the excess demand rate, denoted x. The latter is excess demand per unit of labor supply, and hence equal to the excess of the vacancy rate, v , over the unemployment rate, u: " Econometric analysis by Simler and Tella (1967) shows total unemployment to explain wage movements better than active or "measured" unemployment alone

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM The modal rationale for the simple Phillips-curve relation between wag change and the unemployment rate is that, at least in sectors or economies with little or no unionization, the unemployment rate is a good proxy for the excess-demand rate and that the latter largely explains wage move ments(apart from aggregation phenomena like changes in the employment mix).2 Even if excess demand were the sole determinant of wage changes this paper seeks to generalize that theory and to make it accommodate the infuence of expectations--it is not obvious that the unemployment rate is a good proxy for it. What if, at times, the vacancy rate in()enjoys a life of its own, moving independently of the unemployment rate?( I shall later discuss the evidence on this. Lipsey's paper (1960) brilliantly deduces from a model of employment dynamics a well-behaved relationship be- tween the vacancy rate(hence the excess-demand rate)and the steady unemployment rate. I shall show, however, using a similar model, that in the non-steady-state case the unemployment rate is an inadequate indicator of the excess-demand rate and that the rate of change of employment constitutes an essential additional indicator for inferring the excess-demand rate. 13 The excess-demand explanation of wage movements is unlike the law of ravity in that this explanation itself calls for an underlying explanation When we try to rationalize it, however, its restrictiveness becomes clear. It implies that a one-unit increase of the vacancy rate always has the same 12 The most extensive exposition is Lipsey' s (1960). In criticizing the reliance rate which this rationale promotes, Perry (1966) If the rate of wage change is proportional to the amount of excess demand which in turn is measured by unemployment, there is no room for other variables"(p. 22) believe his abandonment of the excess-demand theory on this ground was mistaken This paper adduces three explanatory variables from what is essentially an excess- demand theory. These two poi wing exercise Draw a non-negatively sloped labor supply curve and a non-positively sloped lat demand curve in the customary real wage-employment plane. Consider now the locus of points corresponding to a given unemployment rate; this iso-unemployment rate curve will lie to the left of the supply curve and will also be non- negatively sloped It is immediately obvious that if the demand curve is negatively sloped, or the supply positively sloped, then not all points on the locus represent equal algebra the demand curve, vacancies and excess demand increase despite constancy of the unemployment rate, Thus the latter is not - ssarily a sufficient proxy for excess rate constant, excess demand is decreasing in unemployment. The zero-vacancy, on-the-demand- curve case is a familiar example. This paper tries to get away from the supposition that we are always "on the demand curve, even t urve arising from excess supply in commodity markets. However, as we consider situations of higher vacancies, the unemployment rate unchanged we should expect the rate of increase of employment likewise to be nployers seek to reduce vacancies through grea tment. The t pieces of information-the unemployment rate he rate of increase of employ- ment--may together constitute a satisfactory proxy, or a better proxy, for excess

MONEY-WAGE DYNAMICS AND LABOR-MARKET EQUILIBRIUM 685 The modal rationale for the simple Phillips-curve relation between wage change and the unemployment rate is that, at least in sectors or economies with little or no unionization, the unemployment rate is a good proxy for the excess-demand rate and that the latter largely explains wage movements (apart from aggregation phenomena like changes in the employment mix).12 Even if excess demand were the sole determinant of wage changesthis paper seeks to generalize that theory and to make it accommodate the influence of expectations-it is not obvious that the unemployment rate is a good proxy for it. What if, at times, the vacancy rate in (5) enjoys a life of its own, moving independently of the unemployment rate? (I shall later discuss the evidence on this.) Lipsey's paper (1960) brilliantly deduces from a model of employment dynamics a well-behaved relationship between the vacancy rate (hence the excess-demand rate) and the steady unemployment rate. I shall show, however, using a similar model, that in the non-steady-state case the unemployment rate is an inadequate indicator of the excess-demand rate and that the rate of change of employment constitutes an essential additional indicator for inferring the excess-demand rate.13 The excess-demand explanation of wage movements is unlike the law of gravity in that this explanation itself calls for an underlying explanation. When we try to rationalize it, however, its restrictiveness becomes clear. It implies that a one-unit increase of the vacancy rate always has the same The most extensive exposition is Lipsey's (1960). In criticizing the reliance solely on the unemployment rate which this rationale promotes, Perry (1966) wrote, "If the rate of wage change is proportional to the amount of excess demand which in turn is measured by unemployment, there is no room for other variables" (p 22). I believe his abandonment of the excess-demand theory on thisground was mistaken. This paper adduces three explanatory variables from what is essentially an excessdemand theory. l3 These two points can perhaps be understood simply from the following exercise: Draw a non-negatively sloped labor supply curve and a non-positively sloped labor demand curve in the customary real wage-employment plane. Consider now the locus of points corresponding to a given unemployment rate; this iso-unemploymentrate curve will lie to the left of the supply curve and will also be non-negatively sloped. It is immediately obvious that if the demand curve is negatively sloped, or the supply curve positively sloped, then not all points on the locus represent equal algebraic excess demand; in particular, as we move down this locus from its intersection with the demand curve, vacancies and excess demand increase despite constancy of the unemployment rate. Thus the latter is not necessarily a sufficient proxy for excess demand. (This demonstration in no way contradicts the proposition that, vacancy rate constant, excess demand is decreasing in unemployment. The zero-vacancy, on-the-demand-curve case is a familiar example. This paper tries to get away from the supposition that we are always "on the demand curve," even the Keynesian demand curve arising from excess supply in commodity markets.) However, as we consider situations of higher vacancies, the unemployment rate unchanged, we should expect the rate of increase of employment likewise to be higher as employers seek to reduce vacancies through greater recruitment. The two pieces of information-the unemployment rate, and the rate of increase of employment-may together constitute a satisfactory proxy, or a better proxy, for excess demand

JOURNAL OF POLITICAL ECONOMY wage effect as a one-unit decrease of the unemployment rate. Second, the excess-demand theory implies that most of the time, in the neighborhood of"equilibrium"(see Part IID), vacancies will equal unemployment and that a disequilibrium rise of wage rates red employment. That vacancies almost never exceed unemployment may be due in part to the behavior of unions, as conceded earlier, and in part to the existence of"unemployables"and the resistence to money-wage cuts in sectors and trades where the market calls for them. But I suspect that a part of the reason is the of the theory of money-wage movements, one which is less restrictive than the simple excess-demand theory but which admits it as a special case. Ele- ments of this approach have previously been discussed by James duesen- berrys(1958, pp. 300-9). Until Part lll, where expectatic I hold constant the rate at which each firm expects other firms to change over time the wage they pay their labor. For ease of exposition, it is as- sumed simply that each firm expects the wage paid elsewhere to be constan for the near future An important element of this theory is the cost to the firm of its"turn- over rate. Given a constant differential between the firms wage rate and the wage rates paid by other firms, a fall of the unemployment rate will tend to increase the quit rate experienced by the firm. Unless the firms employment was excessive to begin with, the increase of its quit rate will impose costs: The firm must either allow its output to decrease, thus losing profits, or incur the recruitment, processing, and training costs of replacing the departing workers (or choose some combination of these two losses) At a sufficiently high quit rate corresponding to a low unemployment rate, the firm will want to increase the differential between the wage it pays and the average wage paid elsewhere, on the ground that the savings from lower turnover costs will more than pay for the extra wage bill. As all firms attempt to raise this differential, the general wage index rises. 16(The theory will Is well: There presumably exists a sufficiently high un- employment rate such that the quit rate is low enough to induce the firm to unemployment in this theory stems from its effect upon quit rates rather than from any supposed underbidding for jobs by unemployed workers loubtedly job vacancies also play a part. First of all, the qu may depend upon both the unemployment rate and the vacancy rate since A ROss(1966, p. 98) reports American eider yment versation on ubject with Professor Duesen berry, but he is not iations and on my part. 6 For impressive of this part of the theory, see Eagly (1965)

686 JOURNAL OF POLITICAL ECONOMY wage effect as a one-unit decrease of the unemployment rate. Second, the excess-demand theory implies that most of the time, in the neighborhood of "equilibrium" (see Part III), vacancies will equal unemployment and that a disequilibrium rise of wage rates requires vacancies to exceed unemployment. That vacancies almost never exceed unemployment14 may be due in part to the behavior of unions, as conceded earlier, and in part to the existence of "unemployables" and the resistence to money-wage cuts in sectors and trades where the market calls for them. But I suspect that a part of the reason is the inaccuracy of the excess-demand theory on its own terms. I shall now describe and try to rationalize a generalized excess-demand theory of money-wage movements, one which is less restrictive than the simple excess-demand theory but which admits it as a special case. Elements of this approach have previously been discussed by James Duesenberry15 (1958, pp. 300-9). Until Part 111, where expectations are introduced, I hold constant the rate at which each firm expects other firms to change over time the wage they pay their labor. For ease of exposition, it is assumed simply that each firm expects the wage paid elsewhere to be constant for the near future. An important element of this theory is the cost to the firm of its "turnover rate." Given a constant differential between the firm's wage rate and the wage rates paid by other firms, a fall of the unemployment rate will tend to increase the quit rate experienced by the firm. Unless the firm's employment was excessive to begin with, the increase of its quit rate will impose costs : The firm must either allow its output to decrease, thus losing profits, or incur the recruitment, processing, and training costs of replacing the departing workers (or choose some combination of these two losses). At a sufficiently high quit rate corresponding to a low unemployment rate, the firm will want to increase the differential between the wage it pays and the average wage paid elsewhere, on the ground that the savings from lower turnover costs will more than pay for the extra wage bill. As all firms attempt to raise this differential, the general wage index rises.16 (The theory will work in reverse as well: There presumably exists a sufficiently high unemployment rate such that the quit rate is low enough to induce the firm to want to pay a wage below that paid by others on the ground that the wage savings will more than pay for the extra turnover costs.) Thus one role of unemployment in this theory stems from its effect upon quit rates rather than from any supposed underbidding for jobs by unemployed workers. Undoubtedly job vacancies also play a part. First of all, the quit rate may depend upon both the unemployment rate and the vacancy rate since l4 ROSS (1966, p. 98) reports American evidence that only at an unemployment rate as low as 2.5 per cent does the vacancy rate equal the unemployment rate. l5 I have also benefited from a conversation on this subject with Professor Duesenberry, but he is not responsible for deviations and errors on my part. '"or impressive empirical support of this part of the theory, see Eagly (1965)

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