Journal of Monetary Economics 46 (2000) 143}171

Wages, business cycles, and comparative advantage夽 Yongsung Chang* Department of Economics, University of Pennsylvania, Philadelphia, PA 19104, USA Received 13 July 1998; received in revised form 8 September 1999; accepted 1 October 1999

Abstract The standard equilibrium models of business cycles face a puzzling fact that total hours vary greatly over the business cycle without much variation in aggregate wages. The model augments the standard RBC model to include Lucas span of control. Distinction between market and non-market and managerial and non-managerial work makes aggregate wages far less cyclical than individual wages. Cross-sectional comparative advantage between market and non-market sector in the workforce substantially increases the response of aggregate hours to shifts in relative productivity. As a result, the model provides a reconciliation between data and equilibrium macroeconomics.  2000 Elsevier Science B.V. All rights reserved. JEL classixcation: E32; J31; J62 Keywords: Wages; Business cycles; Comparative advantage

夽

The previous version of the paper has been circulated under the title &Cyclical Behavior of Occupational Choices and Wages'. I thank Mark Bils for advice and encouragement. I also thank Je! Campbell, Pat Kehoe, Bob King, Monika Merz, Sergio Rebelo, Richard Rogerson, Alan Stockman, Randy Wright, an anonymous referee, and workshop participants at Chicago, Penn, Penn State, Rice, Rochester, and Texas A & M for helpful comments. All remaining errors are mine. * Tel.: 215-898-6691; fax: 215-573-2057. E-mail address: [email protected] (Y. Chang). 0304-3932/00/$ - see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 3 2 ( 0 0 ) 0 0 0 1 5 - 5

144

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

1. Introduction One of the big puzzles in macroeconomics has been that total hours vary greatly over the business cycle without much variation in wages. The equilibrium approach to economic #uctuation pioneered by Lucas and Rapping (1969) and put forward by Kydland and Prescott (1982) and Long and Plosser (1983), views the variation of total hours of work as people's willingness to intertemporally substitute leisure and work over the business cycle. As Barro and King (1984) illustrate, under standard preferences the equilibrium business-cycle models require a strongly pro-cyclical real wages to be consistent with the movement in hours and consumption in the data. The model in this paper augments the standard real-business-cycle (RBC) model to include Lucas' (1978) span of control and Rosen's (1982) hierarchy, where workers are assigned to managerial, production, and non-market tasks based on comparative advantage. It provides a partial resolution to puzzling observation on hours and wages in the data. It shows that heterogeneity of workers signi"cantly decreases the movement of aggregate wages over the business cycle and that the comparative advantage between market and nonmarket activities may substantially increase the response of aggregate hours to shifts in relative productivity. Previous studies have shown that entry and exit of low-wage workers create a counter-cyclical composition bias in aggregate wages (e.g., Stockman, 1983; Bils, 1985; Solon et al., 1994). Aggregate wages constructed by the Bureau of Labor Statistics (BLS) are based on the wages of non-supervisory workers at a point in time. The transition matrix of the occupational change constructed from the Panel Study of Income Dynamics (PSID) for 1971}1992 indicates that there is a signi"cant cyclical movement between non-supervisory and supervisory occupations (managers and self-employed). For example, the likelihood of moving from non-supervisory workers to managers and self-employed increases by 16.2% during expansions relative to recession. On the other hand, the likelihood of moving from managers and self-employed to workers decreases by 26.9% during expansions. This implies that aggregate wages are subject to compositional e!ect in both ends of the wage distribution. Not only do lessskilled workers enter the workforce, biasing down wages and productivity in expansion, but higher-wage earners become managers and self-employed, lowering aggregate wages further. In fact, when the cyclicality is measured as a percentage response to output growth, the compositional e!ect reduces the  The implicit labor contract can generate acyclical wages (e.g., Azariadis, 1974; Gomme and Greenwood, 1995; Boldrin and Horvarth, 1995). Yet it is still incapable of explaining why labor productivity is not highly correlated with hours over the business cycle.  See also Kydland (1984), Cho and Rogerson (1988), and Cho (1995) for business-cycle models that incorporate the "rst composition bias.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

145

cyclicality of aggregate wages by one-third relative to individual wages both in the model and data. In order to match the observed movement in total hours worked in the data, the representative-agent models often rely on labor-supply elasticity that is beyond the admissible estimates based on micro data. The model in this paper explores the relationship between the cross-sectional comparative advantage and aggregate labor-supply elasticity. A worker who has a very strong and clear comparative advantage would not exhibit frequent movement between sectors in response to shifts in relative productivity. On the other hand, a weak comparative advantage implies frequent movement between sectors. Home production is introduced to represent the activity in the non-market sector, and the notion of comparative advantage is formalized by the cross-sectional correlation of productivity between the market and home production in the workforce. The quantitative analysis shows that it is capable of generating a realistic movement of aggregate hours in response to shifts in total factor productivity (TFP) under the cross-sectional comparative advantage observed in the PSID. When the skill distribution is calibrated by the wage distribution of the PSID, the model is very successful in matching the cyclical behavior of aggregate wages, labor productivity, and employment in the data. The employment in the model is nearly as volatile as that in the data, and yet it is not highly correlated with labor productivity. Aggregate wages and labor productivity are mildly pro-cyclical, as in the data. The model produces interesting dynamics for relative wages and employment in the data. The skill-premium is known to be counter-cyclical. Based on the occupational classi"cation, the PSID data are in accord with this view in general } wages of workers in low-grade occupations are more pro-cyclical. However, contrary to the conventional wisdom, I "nd that wages of workers in managerial task, who are among the highest paid, show the most pro-cyclical pattern over the business cycle. According to the model, the managerial wage depends on the span of control, and the span of control exhibits a strongly pro-cyclical pattern. Under capital-skill complementarity the demand for production labor increases sharply in the beginning of an expansion before capital is accumulated. This is  For empirical estimate of labor-supply elasticity, see Ghez and Becker (1975), MaCurdy (1981), or Altonji (1986).  Lottery economy such as Rogerson (1988) and Hansen (1985) generates a high aggregate labor-supply elasticity as well. However, a lottery economy has a counter-intuitive implication that people who &unfortunately' draw bad lots are hired. Yet job assignment including market participation is determined based on comparative advantage in our model.  Alternatively, one can reduce this correlation by introducing an additional disturbance that shifts labor supply curve (e.g., Benhabib et al., 1991; Greenwood and Hercowitz, 1991; Bencivenga, 1992; Christiano and Eichenbaum, 1992).

146

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

consistent with the empirical observation in the U.S. quarterly data, as the employment of production workers tends to lead that of non-production workers over the business cycle. This paper is organized as follows. Section 2 provides empirical evidence of the hierarchical structure of occupations and the cyclical movement of labor and wages that are consistent with the prediction of the model. Section 3 develops the general-equilibrium model with job assignment. Section 4 presents the static model to illustrate its important features. In Section 5, the dynamic model is calibrated, and its response to stochastic variations in TFP is analyzed. Section 6 is the conclusion.

2. Some evidence of labor-market 6uctuations The model in this paper assumes three occupations: managers, production workers, and home workers. These occupations are hierarchically ordered in terms of required skill. The model predicts a cyclical movement of workers between low- and high-grade occupations in response to wage di!erentials over the business cycle. For example, workers move from non-market to market sectors and non-managerial to managerial positions in expansions in response to pro-cyclical wages and managerial-wage premium. Thus, the aggregate wage based on non-supervisory workers is far less cyclical than individual wages due to the composition e!ect in both ends of the wage distribution. To see the empirical relevance of these features, based on the annual PSID data for 1971}1992, the following aspects of the labor-market #uctuation are examined. First, evidence on the hierarchical structure and comparative advantage among the three occupations is presented. Second, the wage response over the business cycle is estimated across occupations. Third, based on the transition matrix, the cyclical movement of workers among the three occupations is examined. Finally, the composition e!ects in aggregate wages are measured. Table 1 shows the summary statistics, and the Appendix explains the data in detail. Table 1 Summary statistics of the PSID 1971}1992 Variables

Mean

Standard deviation

Observations

Age Years of schooling Head Female dummy Real wages Annual working hours Annual labor income

36.87 12.89 0.66 0.44 10.88 2044.83 22499.42

10.96 2.53 0.47 0.49 7.24 649.23 17222.97

89,867 89,032 89,867 89,867 59,827 59,827 59,827

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

147

2.1. Hierarchical structure If occupations are ordered hierarchically in terms of required skill, and if workers are assigned to these occupations according to their comparative advantage, workers who change their occupations from lower-grade jobs to higher-grade jobs must be relatively more-skilled and high-wage workers in their former occupations. At the same time, these workers must be less-skilled and lower-wage workers in their new occupations. In other words, new managers are relatively poor managers compared to existing ones, but they were originally relatively good workers. Table 2A summarizes average wages at time t in each cell of the transition matrix among &managers' (self-employed#not self-employed managers), &workers' (not self-employed and non-managerial workers), and &home workers' (not employed). The numbers in parentheses are average wages relative to existing workers in the target occupation. For example, the number &7.71 (!3.12)' in the (1,2)th cell in Table 2A implies that the average wage of new workers from the home sector in time t is $7.71 (in 1984 dollars), and it is lower than the average wage of existing workers by $3.12. Hierarchy structure in occupations and assignment of workers according to comparative advantage implies that the numbers in parentheses in the upper diagonal terms must be negative, and the lower diagonal terms must be positive. Table 2B compares the wages of movers and stayers at time t!1. The numbers in parentheses are those relative to the stayers in the previous occupation. By the same reason, the upper diagonal terms must be positive, and the lower-diagonal terms must be negative. There is no exception in the signs of these relative wages of movers and stayers. Table 2 (A) Comparison of wages of movers and stayers: wages at time t

(Non-market) R\ (Non-managers) R\ (Managers) R\

(Non-market) R

(Non-managers) R

(Managers) R

NA NA NA

7.71 (!3.12) 10.83 (0) 11.94 (1.11)

9.10 (!4.53) 11.66 (!2.97) 14.63 (0)

(B) Comparison of wages of movers and stayers: wages at time t!1


(Non-market) R\ (Non-managers) R\ (Managers) R\

(Non-market) R

(Non-managers) R

(Managers) R

NA 8.48 (!2.14) 10.07 (!4.35)

NA 10.62 (0) 11.51 (!2.91)

NA 11.59 (0.97) 14.42 (0)

Note: Numbers in parentheses are average wages relative to the stayers in the new occupation.
Note: Numbers in parentheses are average wages relative to the stayers in the old occupation.

148

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

2.2. Cyclical behavior of wages across occupations Table 3 shows the cyclicality of wages, hours, and incomes across occupations. The cyclicality is measured as the percentage response to real GDP growth, the coe$cient b of the regression  Dlog(X )"b #b Dlog(real GDP )#e . (1) GR   R GR Consistent with previous studies by Bils and Solon et al., individual wages have been quite pro-cyclical during the sample period. However, impacts of business cycles are not uniform across occupations. To avoid the compositional e!ect due to changes of occupation, the sample consists of workers who were in the same occupation during two consecutive periods. According to the previous studies on skill-premium, workers with low skill tend to show more cyclical wages (e.g., Dunlop, 1939; Reder, 1955), and this view seems to apply to occupational categories as well. Table 3 shows that the workers in the relatively low-wage group, such as operatives and laborers, show more cyclical wages and hours than do others. However, managerial workers exhibit most cyclical wages, although they are the most-skilled workers in terms of average wages. Selfemployed workers, who are also involved in managerial tasks, show highly cyclical hourly earnings as well. In sum, both individual wages and managerialwage premium are pro-cyclical during 1971}1992, which provides incentive for workers to move from non-market to market and non-managerial to managerial positions during expansions. 2.3. Transition matrix of occupations In order to examine the cyclical movement of workers among three occupations, the transition matrix is constructed from the same PSID data. The sample periods are divided into expansion, normal, and recession periods based on the real GDP growth rates. The expansion period is de"ned as the period of GDP growth rate above 4% (Table 4A), and the recession period is de"ned as the period of GDP growth rate less than 1% (Table 4B). For instance, the likelihood of moving from the non-market sector to non-managerial positions in the  The advantage of "rst-di!erence estimation is twofold. It ensures stationarity and eliminates any "xed e!ects in the panel data.  The conventional wisdom of counter-cyclical skill-premium is mostly based on educational attachment and labor-market experience. Raisian (1983) and Keane and Prasad (1993) challenged this view by reporting that they did not "nd a signi"cant cyclical pattern in such skill-premium in the PSID.  One might view this procyclical managerial premium in favor of the quasi-"xed labor theory, such as Oi (1962). This theory predicts a higher utilization of skilled workers during booms. However, according to Table 3, less-skilled workers show more procyclical hours.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

149

Table 3 Cyclical behavior of wages, hours, and labor income: occupational categories are only for the non-self-employed Occupation

Wage

Hour

Income

Obs.

Average wage

All

0.542 (0.063)
0.747 (0.337)
0.828 (0.237)
0.453 (0.136)
0.373 (0.126)
0.582 (0.150)
0.637 (0.131)


0.523 (0.064)
0.565 (0.206)
0.179 (0.198) 0.316 (0.150)
0.234 (0.141) 0.505 (0.150)
1.014 (0.162)


1.065 (0.071)
1.312 (0.332)
1.007 (0.212)
0.770 (0.151)
0.607 (0.152)
1.087 (0.160)
1.652 (0.112)


48456

11.46

4353

13.58

2273

14.77

8438

14.05

9359

10.39

5384

11.92

8931

8.37

Self-employed Managerial Professional/technical Clerical/sales Craftsmen Operatives/laborer

Note: Numbers in parentheses are standard deviations.
Signi"cant at 5%

market is 0.261 during expansions. This likelihood drops to 0.193 during recessions. The likelihood of moving from workers to managers during expansions is 0.059, and this likelihood drops to 0.049 during recessions. Table 4C shows the di!erence of transition matrix between expansion and recession in terms of percentage: 50;(Table 4A!Table 4B)/(Table 4A#Table 4B). The likelihood of moving from workers to managers increases by 16.2% in expansions. On the other hand, the likelihood of moving from managers to workers decreases by 26.9%. Overall, the movement of labor from the lowergrade occupations to the higher-grade occupations seems much stronger in booms, and vice versa in recessions. In fact, in Table 4C all upper-diagonal terms are positive and all lower diagonal terms are negative. 2.4. Composition ewects in wages Finally, I examine the composition e!ects of wages in the data. Since the aggregate wage constructed by the BLS is based on non-supervisory workers only, aggregate wages are subject to composition e!ects in both ends of wage  There exists a signi"cant movement of workers between non-market sector and managerial positions as well. For example, movement from non-market to managers is 0.053 in expansions and 0.038 in recessions. Yet the model in this paper does not allow such jumps due to its strict hierarchy structure.

150

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

Table 4 (A) Transition matrix of occupational changes: expansions

(Non-market) R\ (Non-managers) R\ (Managers) R\ Total

(Non-market) R

(Non-managers) R

(Managers) R

0.686 0.061 0.040 0.16

0.261 0.881 0.176 0.65

0.053 0.059 0.783 0.19

(B) Transition matrix of occupational change: recessions

(Non-market) R\ (Non-managers) R\ (Managers) R\ Total

(Non-market) R

(Non-managers) R

(Managers) R

0.768 0.085 0.066 0.24

0.193 0.865 0.231 0.613

0.038 0.049 0.704 0.148

(C) The di!erence between expansions and recessions in percentage: 50;(Table 4A!Table 4B)/(Table 4A#Table 4B))

(Non-market) R\ (Non-managers) R\ (Managers) R\

(Non-market) R

(Non-managers) R

(Managers) R

11.4 !33.8 !47.8

29.9 1.8 !26.9

31.8 16.2 10.8

distribution during expansions: the entry of low-wage workers from the nonmarket sector and the exit of high-wage workers to self-employed and managers. To distinguish these two e!ects, I construct both average wages (average wages of the entire workforce) and aggregate wages (average wages of non-supervisory workers) from the PSID, and the cyclicality of these wages is compared to that of individual wages. Table 5 shows the cyclicality, the estimate of b in Eq. (1), of individual wages,  the average wage of all workers, the aggregate wage based on non-supervisory workers, and "nally, the BLS aggregate wage, respectively. The di!erence in the cyclicality between individual wages and the average wage represents the compositional e!ect due to entry and exit of less-skilled workers only. This reduces the cyclicality of wages by 16% (0.597 for non-supervisory workers  Wages of spouses are available since 1979 survey. For the empirical analysis on this compositional e!ect, I use the wages of households' heads only in order to generate a consistent time series for average wages.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

151

Table 5 Two composition e!ects in aggregate wages from the PSID Wages

Data

Supervisory workers Non-supervisory workers Average wage of all Aggregate wage based on non-supervisory workers BLS aggregate wage

0.873 0.597 0.501 0.396 0.434

Obs. (0.244) (0.071) (0.179) (0.188) (0.158)

5952 27667 20 20 20

to 0.501). When aggregate wage is constructed based on non-supervisory workers (not self-employed and non-managers), the cyclicality of wage is reduced by 33% (from 0.597 to 0.396). This re#ects the e!ect of both types of composition bias. The cyclicality of our aggregate-wage measure is similar to that of the BLS aggregate wage (0.434). In sum, the PSID data does show the signi"cant role of both composition biases in aggregate wages. Furthermore, the cyclical behavior of wages and occupational changes in the PSID data seems consistent with the prediction of the model.

3. The model There are identical families consist of continuum of family members with talent or skill z3[z, z ]. The measure k(z) describes the number of members of the family of type z. The family maximizes lifetime utility de"ned over consumption of goods produced in the market, C "X c (z)k(z) dz, R X R and goods produced from non-market activity, namely, home-produced  This is consistent with the "ndings in Bils and Solon et al. The compositional e!ect reduces the cyclicality of aggregate wages by about 20% in Bils and more than 50% in Solon et al. The di!erences can be explained as follows. Bils uses the NLSY data, which has less heterogeneity than the PSID. The average wages of new workers are lower than those of existing workers by 19% in his data, as opposed to 30% in the PSID. Solon et al. also use the PSID data, but their aggregate wage measure is di!erent from the one used here. They weight wages by hours as in the BLS aggregate wage. This generates another composition e!ect in aggregate wages by giving higher weights to low-wage workers in booms because low-wage workers work longer hours in booms. Since the model has an extensive margin only, I do not weight the wages by hours here.  The family assumption simpli"es the analysis greatly because the allocation of the economy is independent of income distribution, and the occupational choice depends on workers' talent only.

152

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

goods, H "X h (z)k(z) dz, R X R  max E oR[log C #B log H ] (2)  R R + !R 'R JR X,R R X s.t. [X (z)l (z)]k(z) dz!C "u K !I , (3) R R R R R R X K "I #(1!d)K , (4) R> R R where o is the discount factor, and l (z) is market labor-supply of family R member z. There are two occupations in the market: manager and production worker. A worker can earn w (z) as a production worker, n (z) as a manager. R R There is no &learning by doing' on the job so that the agent chooses the job that o!ers the highest current wage. Thus, the market earnings X (z) are R max[w (z), n (z)]. The family owns the capital stock K and rents it at rental rate R R R u . Capital depreciates at rate d, and the investment by the family is I . Each R R agent has a time endowment 1#h. The agent can either supply one unit of labor inelastically to the market or spend it on non-market activity } l (z) is 1 if he R works in the market and 0 otherwise. The other h units of time are always used for non-market activity that includes home production such as cleaning and child care,



h (z)"a(z)(h#1!l (z)), (5) R R a(z)"a z? , 0(a , 04a (1. (6)    Productivity in home production may depend on the worker's skill level as well. The important parameter regarding the comparative advantage between market and non-market activity is returns to skill in home production, a . According to  the market-production technology below, the wage of non-managerial worker is proportional to his skill. This implies that a represents the cross-sectional  correlation of productivity between market and home production. For example, if a "0, workers have the same home-production productivity regardless of earn ing ability in the market. However, if a is positive, for instance with a "1/2,   a worker A who is four times as productive as a worker B in the market, is twice as productive as B in home production. When a is close to 1 the worker A is equally  more productive than B in the market and at home. A higher value of a implies  weaker comparative advantage between market and non-market work across workers. The value of a should depend on speci"c non-market activity. Yet given  that our measure z represents general ability, including education, organizational skill, health, and so on, it seems natural to assume there exists a fairly signi"cant correlation between productivity in the market and home production. For instance, it is more likely that parents with better educational backgrounds do better in raising children. I will also provide evidence in Section 5 of positive a based on relative returns to skill in occupations that are comparable to home 

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

153

production activities to those in other occupations. Speci"cally, I estimate the returns to schooling and labor market experience of private household workers (baby sitters and housekeepers, etc.) and compare them to those of other unskilled workers in the PSID. The quantitative analysis in Section 5 below shows that a high value of a substantially increases the response of aggregate  hours to shifts in TFP. The intuition behind this result is that weak comparative advantage (high cross-sectional correlation in productivity) allows frequent movement between market and non-market sectors. The production process in the market has a hierarchical structure so that the manager commands production labor and capital. If the agent decides to be a worker, his talent z is transformed into e$ciency unit of production labor linearly so that his wage as a production worker is w z, where w is the wage rate R R for e$ciency unit of production labor. If an agent with skill z becomes a manager, he rents capital k , hires production labor n , and produces the output R R according to production technology: y (z)"F(z, k , n )"A zR[g(k , n )]@, t"1!b#i, 0(b(1, i'0. (7) R R R R R R where g(k , n )"[sk\C#(1!s)n\C]CC\, 0(s(1, e'0. (8) R R R R The substitution elasticity between capital and production labor is e, and that between capital and manager is 1 given the multiplicative speci"cation. Production workers are perfect substitutes for each other so that n is measured in R e$ciency units. However, managerial labor is assumed to be indivisible and uncombinable; two mediocre managers are not comparable to one superior manager. Managerial work consists of managerial decision making and monitoring/supervising. There are economies of scale in managerial decisions because improvements in upper-level decisions have an enormous in#uence on the organization by a!ecting productivity of all lesser-ranking workers. A supervisory activity congests this scale economy and determines the optimal span of control for each manager. (See Rosen, 1982, for a detailed discussion on this feature.) These considerations are re#ected in the production technology F( ):F(z, n, k) is increasing returns to scale in z, n, and k, and strictly concave in n and k. Given the wage rate for production labor in e$ciency unit w and the rental R rate of the capital u , the manager receives the residual R n (z)"F(z, k , n )!u k !w n . (9) R R R R R R R The "rst-order conditions for this maximum problem includes F (z, k , n )"u , I R R R F (z, k , n )"w . L R R R

(10) (11)

154

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

Demand for production labor n(z, w , u ) and capital k(z, w , u ) by the manager R R R R z can be obtained from (10) and (11). Economies of scale imply managerial wage convex in z : n(z)'0, n(z)'0. For ezcient allocation, only the most talented will become managers and the least talented become home production workers given the one-dimensional speci"cation of talent. Critical levels of talent, z , z '0, exist such that if KR UR z5z , then the agent is a manager. If z 'z5z , the agent is a production KR KR UR worker. If z(z , the agent works at home. An allocation in this economy UR means two critical values of talent z , z , and the demand functions for labor KR UR and capital by a manager with talent z, n(z, w , u ), k(z, w , u ). In equilibrium, the R R R R demands for factors are equal to their supplies:

 

X

XKR X XKR



n(z, w , u )k(z) dz" R R

XKR

zk(z) dz,

(12)

XUR

k(z, w , u )k(z) dz"K . R R R

(13)

4. Qualitative analysis This section presents the static version of the model to illustrate its key elements. Utility is linear and capital is dismissed. The manager with talent z receives n(z, w)"max F(z, n)!wn. The "rst-order condition, F (z, n)"w, L L provides the implicit demand function for production labor n(z; w). Because l(z)"0 for z(z , the total consumption is U X X c(z)k(z) dz# [a(z)(h#1!l(z))]k(z) dz X X X XU " F(z, n(z))k(z) dz# a(z)k(z) dz. XK X Without loss of generality, the constant is dropped after the equality. The maximization problem is now to choose the two critical skill levels for job assignment, z and z , given the labor-market constraint (12). In the Lagrangian K U with w as the multiplier associated with the labor-market constraint, this allocation is the competitive equilibrium with w being the wage rate of production labor:













X XU max F(z, n(z))k(z) dz# a(z)k(z) dz X XK XU XK XK X #w zk(z) dz! n(z)k(z) dz . XU XK







Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

155

The "rst-order conditions for critical level z and z are K U F(z , n(z ))!wn(z )"wz , (14) K K K K wz "a(z ). (15) U U Equation (14) states that the marginal manager, whose talent is z , faces K a break-even point. The marginal manager's income will be the same as his wage as a production worker. The second condition states that the marginal market participant's wage is the same as the value of his home production. Fig. 1 illustrates the labor-market equilibrium when a "0.  With market technology F(z, n)"AzRn@, the optimal span of control, the employment of production labor under the manager z, is




n(z, w)"

bA \@ zR\@. w

Fig. 1. Equilibrium in the labor market.

(16)

156

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

The optimal span of control is more than proportional to the skill of the manager; d ln(n(z))/d ln(z)"1#i/(1!b)'1 as i captures economies of scale in managerial labor. Except for the marginal manager, managers receive more than proportional economic rent for their superior talent. This skews the wage distribution to the right, relative to the underlying skill distribution. Inserting (16) into the labor-market equilibrium condition (12) reveals the wage rate of production labor as a function of critical levels z , and z : K U X K zR\@k(z) dz \@ w(z , z )"bA X . (17) K U XKU zk(z) dz X It is very useful to de"ne the aggregate index of managerial labor and production labor in e$ciency units as follows:






Z"

X

zR\@k(z) dz





\@



XK

zk(z) dz. (18) XK XU With these aggregate indices one can recover the aggregate market-production function as



>(z , z )" K U

and N"

X

AzRn(z)@k(z) dz"AZN@. (19) XK The wage rate of production labor in (17) is equivalent to the marginal product of production labor in the aggregate production function in (19), bAZN@\. The aggregate home production is



XU

a k(z) dz.  X Using aggregate production functions (19) and (20), the problem is H(z )" U

(20)

max >(z , z )#H(z ). K U U XK XU The "rst-order conditions for z and z are equivalent to (14) and (15). K U I examine the response of economy to shifts in TFP in the market. Suppose that working in the market becomes more pro"table due to an increase in A. Critical level of skill that determines market participation z is, U from (6) and (14), z "(a /w)\? . As an increase in TFP increases the wage rate U  in the market, more people are drawn to the market sector. Fig. 2 illustrates this. From (16), the span of control n(z) increases as production wage (w) increase is smaller than the TFP increase. An increase in the span of control  The supply curve of production labor is upward sloping because of the existence of the non-market sector, and the demand curve is downward sloping because b(1. This implies that the increase of production wage rate will be smaller than the increase of TFP.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

157

Fig. 2. Productivity increase in the market.

makes the employment of managers less cyclical than that of production workers because existing managers can absorb new production workers. Since the managerial wage for agent z is n(z)"(!1)wn(z), the relative @ wage of manager to production worker also increases as the span of control increases: n(z)/w(z)"(!1)(@)\@zG\@. @ U The cross-sectional comparative advantage between the market and home in the labor force has an interesting implication on the aggregate labor-supply elasticity as weak comparative advantage implies frequent movement of workers between sectors. As Fig. 3 illustrates, when a '0, the same increase in  TFP draws more people to the market. The output from home production represents the opportunity cost of labor market participation. When productivity between market and home is correlated, it is less costly to draw less-skilled workers into the market because they have a lower opportunity cost as well.

158

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

Fig. 3. Productivity increase in the market when a(z)'0 and a(z)"0.

5. Quantitative analysis The family assumption greatly simpli"es the analysis of the model economy. It separates the static problem of resource allocation at time t from the dynamic capital-accumulation problem over time so that the model can be solved recursively. First, the allocation of capital and production labor across managers at time t is solved, given K , z , and z . Second, the paths of investment, R KR UR I , consumption, C , and labor-supply decisions, z and z , are determined by R R KR UR the intertemporal consumption theory. Given the constant returns to scale in g(k, n), it is useful to write the output under manager z as y (z)"A zR(n f (r ))@, where r "k /n is capital}labor ratio. R R R R R R R The CRS of g( ) also implies that the capital}labor ratio is common across managers so that r "K /N . The "rst order conditions (10) and (11) imply R R R f (r )!r f (r ) w R R R " R. (21) f (r ) u R R From (10) and (7), the demand for production labor by the manager z is




n(z, w , u )" R R



bA zRf (r ) \@ 1 R R . u f (r ) R R

(22)

 The family assumption dismisses possible income e!ects on labor supply across agents. However, relaxing the family assumption along with allowing divisible labor will not a!ect the result on the cyclical behavior of relative wages. Given that wages are measured by total earnings divided by hours, income e!ect on hours will strengthen the result of this paper by reinforcing the procyclical managerial wage because it will reduce the hours of high-wage earners who are managers here.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

159

Inserting (22) into the labor}market-equilibrium condition (12) and using the aggregate index in (18), one can write the rental rate as u "bA Z (N f (r ))@\f (r ). R R R R R R Using (21) and (23) the wage rate for production labor is

(23)

w "bA Z (N f (r ))@\( f (r )!r f (r )). R R R R R R R R The wage of manager z is, from (9), (21), and (22),

(24)

n (z)"(1!b)A Z (N f (r ))@\f (r )n(z). (25) R R R R R R Then, the growth rate of the relative wage of managers to production labor is




n (z ) w (z ) n (z ) 1 r R ! R " R #s 1! R, (26) n (z) w (z) n (z) e r R R R R where x "dx(t)/dt. The relative wage depends on the span of control, substituR tion elasticity, and capital}labor ratio. For instance, under capital-skill complementarity (e'1), an increase in capital}labor ratio favors managers relative to workers. Again, using the aggregate index in (18), the aggregate market-production function is



>(z , z , K )" KR UR R

X

[A zR(n (z)f (r ))@]k(z) dz"A Z ( f (r )N )@. R R R R R R R

(27)

X The aggregate home-production function is



KR



X XUR a z? k(z) dz# a z? k(z) dz.   X X Using (27) and (28) one can rewrite the maximization problem as H(z )"h UR

max !R XKR XUR )R> ,

+



E  oR[log C #log H(z ) R UR  R

(28)



>(z , z , K )!C !K #(1!d)K . KR UR R R R> R With Lagrange multiplier j for the resource constraint, the "rst-order condiR tions are s.t.

C\"j , R R (1!b)A Z\@\@(N f (r ))@zR\@ R R R R KR "bA Z (N f (r ))@\( f (r )!r f (r ))z , R R R R R R R KR Ba z? H (z )\"j bA Z (N f (r ))@\( f (r )!r f (r ))z ,  UR R UR R R R R R R R R UR j "oE [j (bA Z (N f (r ))@\f(r )#1!d)], R R R> R> R> R> R> R> A Z (N f (r ))@"C #K !(1!d)K . R R R R R R> R

(29)

(30) (31) (32) (33)

160

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

Eq. (30) states that, for the marginal manager, the marginal product as a manager is equal to the marginal product as a production worker. Eq. (31) states that, for the marginal market participant, the marginal product of labor is the same as the value of marginal product in home production. Eq. (32) is the Euler equation. Eq. (33) is the resource constraint. 5.1. Calibration of the model According to the model, the wage of a non-supervisory worker is linear in worker's talent z. This allows us to calibrate the talent distribution k(z) directly from the cross-sectional wage distribution of the non-supervisory workers from PSID (wages of heads of households and wives). I use the wage distribution of 1983 and 1984 because it is the mid-point of the sample period and the base year of the de#ator for nominal earnings. The mean and the standard deviation of the wage distribution are 2.17 and 0.53, respectively. This wage distribution is a doubly truncated representation of skill distribution k(z) for two reasons. First, workers in the non-market sector are not included. Second, as usual in micro data, to avoid outliers due to measurement error in reported hours and income, wages below $3 or above $100 are eliminated. This is consistent with the top-coding practice at wage $100 in the PSID. Then, the mean k and variance X p of the underlying skill distribution k(z) are searched among log-normal X distributions to match the mean and standard deviation of the truncated wage distribution. Speci"cally, when U( ) is the cumulative standard normal distribution, k and p are chosen to satisfy the following two conditions (see Maddala, X X 1983): U[c ]!U[c ] 2.17!k   " X, E[ln(w)"34w4100)" p U[c ]!U[c ]   X c U[c ]!c U[c ]    <[ln(w)"34w4100]"1!E[ln(w)"34w4100]#  U[c ]!U[c ]   (0.53) " , p X where ln(3)!k ln(100)!k X and c " X. c "   p p X X The calibrated values are k "2.11 and p "0.58. Fig. 4 shows the actual wage X X distribution and the calibrated skill distribution k(z). Given the calibrated skill distribution k(z), the steady-state critical values are chosen to match the occupational breakdown of the PSID: 12% managers, 63% non-managerial workers, and 25% non-market workers: z "16.4 and z "5.5. K U

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

161

Fig. 4. Wage distribution of the PSID (*) and the lognormal distribution (} }).

For production technology in the market we need to specify e, s, b, and i. As a benchmark, the elasticity of substitution between production labor and capital: e"1. Given the steady-state values of z and z , the "rst-order condiK U tion (30) imposes one constraint among s, b, and i. I calibrate s and b based on disaggregate manufacturing-industry data, and equation (30) will provide i. Using the four-digit NBER productivity data constructed by Bartelsman and Gray (1996) from the Annual Survey of Manufacturing for 1954}1996, the shares of payment to employed labor in value-added output are calculated. The average of this share is 0.45. Since their data do not include some fringe bene"t payment, I use a slightly higher value: (1!s)"0.5. Based on 3-digit industry data, Burnside, Eichenbaum, and Rebelo (1995) report the returns to scale between 0.8 and 0.92. (See Table 5 of their paper.) According to Basu and Fernald (1996), aggregation tends to produce a higher estimate for the returns to scale. Since b represents the "rm or plant-level decreasing returns to scale in our model, I use the smallest value of the estimates in Burnside et al.: b"0.8. The parameter i is set to 0.075 to satisfy Eq. (30). This leads to this production function for the benchmark case: y (z)"A z (k n ) . The capital share R R R R in total output is 0.372, which is close to the values commonly used in the literature. In addition, the calibrated values of i and b imply a relative standard

 In fact, when the shares are adjusted for fringe bene"ts at 2-digit level the averages of shares are 0.474 (value-added weighted) and 0.525 (non-weighted).

162

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

deviation of log wages of managers to workers of 1.375, which is very close to that of self-employed workers to non-self-employed workers in the PSID (1.39). According to the model, the returns to skill is 1 for non-managerial workers. Since a represents the returns to skill in home production, the relative returns  to skill in occupations that are comparable to home production to those of other unskilled workers would provide some information on the size of a . In the  PSID, for female workers the relative returns to skill of private household workers such as baby sitters and housekeepers to those of other female unskilled workers are 0.62 and 0.70 when the skill is measured by the years of schooling and the labor market experience (age-schooling-4), respectively. For male workers, they are 0.29 and 0.45, respectively, for schooling and labor market experience. As a benchmark case, the returns to skill in home production is zero (a "0). I use other values such as  and  in the quantitative analysis as    well. Values of other parameters are fairly standard. The discount factor is chosen to match the steady state real interest rate of 6.5% annual. The depreciation rate of capital is 10% annual. The ratio of non-working time to working time is 3 : h"3. Temporary shifts in productivity A follow the "rst-order autocorrelaR tion in logs as in King et al.: lnA "(1!o )lnAM #0.9lnA #e . The stanR  R\ R dard deviation of e is set to match the standard deviation of real GDP in the R data in the benchmark case. The values of the integrals are approximated by a linear quadrature. Skill levels are con"ned within the range z3[0.5, 300]. This range covers almost 100% of the calibrated skill distribution k(z). B and a are  free parameters. Table 6 summarizes the parameter values for the benchmark case. The model is solved numerically by a log-linear approximation of the "rstorder conditions (29)}(33) around the steady states of the economy with a deterministic trend as in King et al. (1988). 5.2. Cross-sectional comparative advantage and aggregate labor supply Fig. 5 shows the impulse responses of the benchmark economy to a one percent increase in TFP, A . All variables are percentage deviations from the R  Speci"cally, for female unskilled workers, the returns to schooling and labor market experience are 4.24 and 0.55 respectively. For female private household workers, they are 2.64 and 0.38. For male unskilled workers, they are 5.43 and 1.63. For male private household workers, they are 1.56 and 0.73.  As is common in the literature, a deterministic trend in productivity is incorporated to allow the output, consumption, investment, and capital grow over time as in the data. When the productivity of production labor in g(k, n), home production a(z), and managerial labor grow at rates c, c, and c\@\@>G, respectively, the model has a balanced growth path where output, capital, investment, and consumption of both market goods and home produced goods grow at a common growth rate c. See King et al. (1987) for a detailed discussion on how to obtain a stationary economy from one with balanced growth.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171 Table 6 Parameter values for the benchmark case Parameters

Description

k "2.11 X p "0.58 X z "16.4 K z "5.5 U b"0.8 e"1 s"0.5 i"0.075 d"0.025 h"3 o"0.988 a "0  o "0.9 

Mean of lognormal skill distribution k(z) Standard deviation of lognormal skill distribution k(z) Steady-state critical-skill level for z KR Steady-state critical-skill level for z UR Curvature in production function y"Az\@>G[g(n, k)]@ Substitution elasticity between n and k Capital share in g(n, k) Economies of scale parameter Quarterly depreciation rate Ratio of non-working time to working time Quarterly discount factor Home production technology a(z)"a z?  Autocorrelation of productivity shock A R

Fig. 5. Impulse responses of the economy when a "0 and e"1. 

163

164

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

steady state. Panel (1) shows the exogenous TFP shock and the capital stock. Panel (2) shows aggregate employment and average labor productivity. Aggregate employment and labor-productivity increase about 0.4% and 0.7% respectively in the "rst period. Panel (3) shows aggregate consumption, investment, and output. The responses are similar to those from the standard RBC model. Panel (4) shows the employment of production workers and managers. Employment of production workers is more volatile because of the procyclical span of control. Panel (5) shows the average span of control, i.e., the average employment of production labor per managers. Span of control increases initially, and then goes below the steady state in the later stage of an expansion as market participation decreases. In the later stage of expansion, the demand for home-produced goods increases along with the consumption of market goods. Panel (6) shows the wages of production workers and managers. Since capital accumulation is neutral (e"1), the wage gap between managers and workers represents the span of control e!ect only. Table 7 reports the population moments of the model economy. The "rst column is the benchmark case. Like other RBC models with productivity shocks, labor productivity is too procyclical (0.98 relative to 0.753 in the data) and the employment is not so volatile as in the data (0.246 relative to 0.7 in the data). As is explained in the static case, the response of aggregate employment depends on the cross-sectional comparative advantage. As the cross-sectional correlation of productivity in the market and at home increases, employment becomes more volatile. For instance, when a "1/2, the relative volatility of  employment increases from 0.246 to 0.387. When a "3/4, the relative  volatility of employment increases to 78% of the data (0.544 relative to 0.7). Table 7 Population moments of the models

Statistics

a "0  e"1

a "1/2  e"1

a "3/4  e"1

a "3/4  e"3/2

Data

p 7 p /p ! 7 p /p ' 7 p /p #  7 p /p #  7#  cor(Y, Emp) cor(Y, Y/Emp) cor(Emp, Y/Emp)

3.98 0.703 2.369 0.246 0.295 0.745 0.98 0.599

4.167 0.694 2.43 0.387 0.514 0.752 0.94 0.484

4.388 0.685 2.5 0.544 0.796 0.760 0.855 0.314

4.591 0.627 2.666 0.618 0.819 0.652 0.786 0.052

3.98 0.812 2.07 0.7 1.062 0.753 0.715 0.079

Note: Data are linearly detrended. p /p : standard deviation of consumption relative to >. Emp: ! 7 total employment in the model, total employed hours in the data. cor(C, >): correlation of C and >.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

165

Fig. 6. Impulse responses of the economy when a "3/4 and e"1. 

As employment becomes more volatile, the composition e!ect due to entry and exit of less-skilled workers reduces the labor productivity-employment correlation signi"cantly (0.314 when a "3/4). As a result, the volatility of output  increases as well. Fig. 6 shows the impulse response for the case of a "3/4.  Aggregate employment is much more volatile relative to labor productivity as it increases almost 1% initially, yet labor-productivity increases 0.3% only. While the relative volatility of employment to labor-productivity in the benchmark case (0.295) is far short of that in the data (1.062), it is now quite close to data (0.796). 5.3. Capital-skill complementarity Capital-skill complementarity has been emphasized as it creates an interesting short-run dynamics for relative employment (e.g., Rosen, 1968; Griliches, 1969). In this case, the short-run production function is not homothetic, and the relative demand for labor depends on the stage of business cycles. The relative demand for unskilled labor increases in the beginning of an

166

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

expansion when capital is not yet accumulated. But subsequent capital accumulation will substitute for the unskilled labor and will favor the skilled labor. Fig. 7 shows the impulse response when production labor is a better substitute for capital than managerial labor (e"3/2). At the outset of an expansion, the employment of production workers increases sharply. This is re#ected in the impulse response of the span of control. It sharply increases in the beginning and retreats as capital accumulates. In fact, employment of production workers tends to lead that of non-production labor in the U.S. quarterly data for 1954}1996. The relative wage of managers to workers increases in the beginning because of the spike in span of control. It is sustained even after the span of control falls below the steady-state level because capital accumulation favors managerial labor, which is relatively complementary to capital } recall Eq. (6). Due to the higher substitution between capital and production labor, employment becomes more volatile and its volatility (0.618) is now quite close to that of data (0.7). A higher volatility of employment reinforces the compositional bias

Fig. 7. Impulse responses of the economy when a "3/4 and e"3/2. 

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

167

Fig. 8. Impulse responses of the economy when a "3/4 and e"2/3. 

and the labor productivity-employment correlation is close to zero (0.052) as in the data. 5.3.1. Two compositional ewects in aggregate wages The model generates less cyclical aggregate wages and labor productivity than those in the standard RBC models. This is due to the changes in skill mix of the workforce over the business cycle. Since the aggregate wage constructed by the BLS is based on non-supervisory workers only, there are two compositional e!ects in aggregate wages during expansions: the entry of low-wage workers  For comparison, Fig. 8 shows the impulse responses for the case of e"2/3, the opposite case to the capital-skill complementarity. The span of control is relatively #at over the business cycle because the relative demand for production labor does not sharply increase in the beginning, and capital accumulation complements production workers in the later stage of the business cycle. The wage growth is reversed in the early stage of the business cycle, even though the span of control stays above the steady state.  The results based on the Hodrick}Prescott "lter show a similar pattern to those in Table 7 except for labor productivity-employment correlations. They exhibit slightly higher correlation in the model and lower correlation in the data than in Table 7.

168

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

Table 8 Composition e!ect in wages from the model

Statistics cov(= , >)/Var(>)

 cov(= , >)/Var(>)  cov(= , >)/Var(>)   cov(= , >)/Var(>)  

a "0  e"1

a "3/4  e"1

a "3/4  e"3/2

Data

0.926 0.911 0.816 0.804

0.834 0.800 0.585 0.557

0.779 0.734 0.593 0.483

0.873 0.597 0.501 0.396

Note: = : wages of managers including self-employed. = : wages of non-managerial workers.

  = : average wage of workers in the market sector. = : average wage of non-managerial     workers.

from the non-market sector and the exit of high-wage workers to self-employed and managers. Parallel to the empirical analysis in Section 2, I construct the average wages (average wages of the entire workforce) and the aggregate wages (average wages of production workers) from the model. The last column of Table 8 shows the cyclicality of these wages based on the PSID data in Section 2. To compare the performance of the model, implied regression coe$cient the ratio of the covariance between the output and wage measure to the variance of output, is calculated. In the benchmark case, the composition e!ect reduces the cyclicality of average wages and aggregate wages by 10% (from 0.911 to 0.816) and 12% (from 0.911 to 0.804), respectively. Because employment is not so volatile as in the data, the composition e!ect is not so big as in the data. When the employment is nearly as volatile as in the data (the model with a "3/4, e"3/2), the cyclicality of average wage  decreases by 19% (from 0.734 to 0.593), and that of aggregate wage decreases by 34% (from 0.734 to 0.483). The compositional e!ect predicted by the model is very close to what we "nd from the PSID data in Section 2. They are 16% and 33%, respectively. In sum, both in the data and the model, not only the "rst bias due to entry and exit of low-wage workers between market and home, but also the second bias due to the movement between non-supervisory workers and managerial workers signi"cantly reduces the cyclicality of wages.

6. Concluding remarks Equilibrium models of the business cycle that emphasize shifts in TFP as a major source of economic #uctuation faces a puzzling fact that aggregate

 Due to di!erences in detrending method and frequency between the panel data and the model, I compare the relative size of compositional e!ects instead of comparing the numbers directly.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

169

hours vary greatly over the business cycle without much variation in aggregate wages. This paper explores a resolution to this puzzle by recognizing the heterogeneity of skill possessed by workers. The model augments the standard RBC model to include distinction between managerial and non-managerial and home and market production. Business cycles are associated with the systematic movement of workers that makes aggregate wages and labor productivity less cyclical than individual wages. Not only do less-skilled workers enter the workforce, biasing down wages and productivity in expansion, but higher wage earners become managers and self-employed, lowering aggregate wages further. Weak comparative advantage between market and non-market work implies frequent movement between sectors in response to relative productivity shifts. Under a comparative advantage that is consistent with PSID, this model is capable of matching the key moments in the aggregate labor market. Aggregate hour is nearly as volatile as in the data, and yet it is not highly correlated with labor productivity. Aggregate wage and labor productivity exhibit mildly procyclical behavior. The model produces an interesting dynamics for relative wages and employment as well. Wages of managerial workers are highly pro-cyclical as in the PSID data. As the employment of production labor tends to lead that of non-production labor in the data, under capital-skill complementarity, the relative demand for production labor sharply increases at the beginning of an expansion. The model abstracts from any friction in the labor market. For instance, in an economy with rigid labor market, the response of the economy may look quite di!erent from those predicted by the model presented here. Examples of such friction include search friction, speci"c human capital, hiring costs, and "ring costs. While the model assumes a "xed one-dimensional talent distribution in the economy, allowing multi-dimensional talent or endogenous evolution of job-speci"c skills such as learning-by-doing will enrich the employment dynamics across occupations.

Appendix. Data The PSID data consist of a random sample and a poverty sample. Only the random sample is used to represent the skill distribution of the aggregate economy. The sample period is 1971}1992. The sample consists of heads of households and wives who are 18}60 years old. Wage data for wives are available only since 1979. Wage data are annual hourly earnings (annual labor incomes divided by annual hours). The wages are for those workers who were working in the private and non-agricultural sectors for at least 100 hours per year, and whose hourly wage rate was above $3 in 1983 dollars. Wages are de#ated by the Consumer Price Index. The base year is 1983. The descriptive statistics for workers in the market sector are given in Table 1. In the estimation

170

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

of the cyclicality of wages in di!erent occupations in Table 3, the sample consists of workers who were in the same occupation in two consecutive periods to capture the pure price changes of labor in the corresponding category. In Table 7, because wives' wages are available only since 1979, data of heads are used here in order to generate a consistent time series of average wages. Aggregate data are quarterly for 1955:I}1994:IV from the Citibase. Output is real GDP (in 1987 constant dollars). Consumption is non-durables and services. Investment is gross "xed investment. Employment is employed man-hours based on the BLS establishment survey.

References Altonji, J., 1986. Intertemporal substitution in labor supply: evidence from micro data. Journal of Political Economy 94, s176}s215. Azariadis, C., 1974. Implicit contracts and underemployment equilibria. Journal of Political Economy 83, 1183}1202. Barro, R., King, B., 1984. Time separable preferences and intertemporal-substitution models of business cycles. Quarterly Journal of Economics 99, 817}839. Basu, S., Fernald, J., 1996. Returns to scale in U.S. production: estimates and implications. Internal Finance Working Papers No. 546, Board of Governors of the Federal Reserve System. Bartelsman, E. J., Gray, W., 1996. The NBER manufacturing productivity database. NBER Technical Working Paper No. 205. Bencivenga, V., 1992. An econometric study of hours and output variation with preference shocks. International Economic Review 33, 449}471. Benhabib, J., Rogerson, R., Wright, R., 1991. Homework in macroeconomics: household production and aggregate #uctuations. Journal of Political Economy 6, 1166}1181. Bils, M., 1985. Real wages over the business cycles: evidence from panel data. Journal of Political Economy 93, 666}689. Boldrin, M., Horvarth, M., 1995. Labor contracts and business cycles. Journal of Political Economy 103, 972}1004. Burnside, C., Eichenbaum, M., Rebelo, S., 1995. Capital utilization and returns to scale. NBER Macroeconomic Annual 10, 67}109. Cho, J., 1995. Ex-post heterogeneity and the business cycle. Journal of Economic Dynamics and Control 19, 533}551. Cho, J., Rogerson, R., 1988. Family labor supply and aggregate #uctuations. Journal of Monetary Economics 21, 233}246. Christiano, L., Eichenbaum, M., 1992. Current real-business-cycle theories and aggregate labormarket #uctuations. American Economic Review 82, 430}450. Dunlop, J., 1939. Cyclical variations in wage structure. Review of Economics and Statistics 21, 30}39. Ghez, G.R., Becker, G., 1975. The Allocation of Time and Goods over the Life Cycle. National Bureau of Economic Research, Columbia University Press, New York. Gomme, P., Greenwood, J., 1995. Cyclical allocation of risk. Journal of Economic Dynamics and Control 19, 91}124. Greenwood, J., Hercowitz, Z., 1991. The allocation of capital and time over the business cycle. Journal of Political Economy 99, 1188}1214. Griliches, Z., 1969. Capital-skill complementarity. Review of Economics and Statistics 51, 465}468.

Y. Chang / Journal of Monetary Economics 46 (2000) 143}171

171

Hansen, G., 1985. Indivisible labor and the business cycle. Journal of Monetary Economics 16, 309}327. Keane, M., Prasad, E., 1993. Skill levels and the cyclical variability of employment, hours, and wages. IMF Sta! Papers 40, No. 4, pp. 711}743. King, R., Plosser, C., Rebelo, S., 1987. Production, growth and business cycles: technical appendix. Manuscript, University of Rochester. King, R., Plosser, C., Rebelo, S., 1988. Production, growth and business cycles: I. The basic neoclassical model. Journal of Monetary Economics 21, 195}232. Kydland, F., 1984. Heterogeneity in labor market and business cycles. Carnegie-Rochester Conference Series on Public Policy 21, 173}208. Kydland, F., Prescott, E., 1982. Time to build and aggregate #uctuations. Econometrica 50, 1345}1370. Long, J., Plosser, C., 1983. Real business cycles. Journal of Political Economy 91, 30}69. Lucas, R., 1978. On the size distribution of business "rms. Bell Journal of Economics 9, 508}523. Lucas, R., Rapping, L., 1969. Real wages, employment, and in#ation. Journal of Political Economy 77, 721}754. Maddala, G.S., 1983. Limited-Dependent and Qualitative Variables in Economics. Cambridge University Press, Cambridge. MaCurdy, T., 1981. An empirical model of labor supply in a life-cycle setting. Journal of Political Economy 89, 1059}1085. Oi, W., 1962. Labor as a quasi-"xed factor. Journal of Political Economy 70, 538}555. Raisian, J., 1983. Contracts, job experience, and cyclical labor market adjustments. Journal of Labor Economics 1, 152}170. Reder, M., 1955. The theory of occupational wage di!erentials. American Economic Review 45, 833}852. Rogerson, R., 1988. Indivisible labor, lotteries and equilibrium. Journal of Monetary Economics 21, 3}16. Rosen, S., 1968. Short-run employment variation on class-I railroads in the U.S., 1947-1963. Econometrica 36, 511}529. Rosen, S., 1982. Authority, control, and the distribution of earnings. Bell Journal of Economics 13, 311}323. Solon, G., Barsky, R., Parker, J., 1994. Measuring the cyclicality of real wages: how important is compositional bias? Quarterly Journal of Economics 106, 587}616. Stockman, A., 1983. Aggregation bias and the cyclical behavior of real wages. Manuscript, University of Rochester.