Decomposition of hours based on extensive and intensive margins of labor

Economics Letters 72 (2001) 361–367 www.elsevier.com / locate / econbase

Decomposition of hours based on extensive and intensive margins of labor Yongsung Chang a , *, Noh-Sun Kwark b a

Department of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104, USA b Department of Economics, Dongguk University, Dongguk, South Korea Received 19 November 2000; accepted 13 March 2001

Abstract We decompose the underlying disturbances in total hours into three kinds: disturbances that shift the level of employment in the long run, those that change the sectoral composition of employment in the long run, and those that cause temporary movement of hours. Our identifying restriction exploits the distinctive nature of the two margins of labor: employment and hours per worker. Based on the postwar U.S. data, we find that aggregate and sectoral disturbances are roughly equally important for the cyclical fluctuations of aggregate hours.  2001 Elsevier Science B.V. All rights reserved. Keywords: Decomposition of hours; Sectoral reallocation; Extensive margins; Intensive margin JEL classification: E32; E24; J2

1. Introduction The sectoral-shift hypothesis that a change in the composition of employment across sectors is a significant contributor to the fluctuations in the aggregate labor market has been debated since David Lilien’s (1982) seminal paper. While many researchers (e.g., Davis, 1987; Rogerson, 1987 and Phelan and Trejos, 2000) investigate various economic mechanisms through which sectoral disturbances manifest themselves as an aggregate recession, its empirical importance seems far from a sensible consensus. For instance, Abraham and Katz (1986) argue that the statistical finding of a positive correlation between the dispersion index and aggregate unemployment rates by Lilien (1982) does not even require workers to be changing sectors. Murphy and Topel (1987), based on the March Current Population Survey on prime-age males, report that only 24% of the total incidence of unemployment * Tel.: 11-215-898-6691; fax: 11-215-573-2057. E-mail address: [email protected] (Y. Chang). 0165-1765 / 01 / $ – see front matter PII: S0165-1765( 01 )00453-0

 2001 Elsevier Science B.V. All rights reserved.

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is explained by sectoral shifts. Loungani and Rogerson (1989), based on the Panel Study of Income Dynamics, report that permanent job switchers may account for about 40% of the total weeks of unemployment during recessions. Campbell and Kuttner (1996) report that more than 50% of cyclical fluctuation in aggregate employment may be explained by sectoral reallocation. In this paper, we propose a simple way of decomposing the underlying disturbances of total hours into three types of shocks: disturbances that shift the aggregate employment rate in the long run (aggregate permanent shocks), disturbances that change the sectoral composition of employment in the long run (sectoral reallocation shocks), and disturbances that cause temporary movement of hours around the steady state (temporary shocks). Our identifying restriction relies on the distinctive nature of the two margins of labor: employment (the extensive margin) and hours per worker (the intensive margin). Time series of employment possesses a non-stationary unit root component, whereas hours per worker tends to exhibit a stationary process around a deterministic trend. This statistical property conforms to our economic intuition. In need of a permanent increase in labor input, firms find it optimal to increase employment, rather than hours per worker, in the long run, as they face an upward sloping marginal cost along the intensive margin due to the overtime wage premium (e.g., Bils, 1987). At the same time, firms also find it optimal to adjust hours per worker in response to very short-lived disturbances because of adjustment costs in employment, possibly due to hiring and firing costs (e.g., Oi, 1962). This justifies our first identifying restriction that temporary disturbances do not affect the employment levels in the long run. Similarly, a permanent increase in the demand for labor in one sector relative to the others will show up as a change in the relative employment in the long run. This allows us to distinguish the aggregate from the sectoral reallocation shocks. We apply this identification scheme to a tri-variate just-identified vector autoregression (VAR) consisting of aggregate employment, aggregate hours per worker, and the measure of employment distribution across sectors.

2. Empirical analysis

2.1. Employment, hours, and sectoral reallocation First, we investigate the distinctive statistical properties inherent in employment and hours per worker in the monthly U.S. data for 1947:01–1997:07.1 Conforming to our economic intuition, according to Table 1, we cannot reject the existence of a unit root in the employment, employment rates to be precise as we normalize them by the population, both at aggregate and at one-digit industry levels. The only exception is the construction industry. In contrast, unit roots in average hours per worker are strongly rejected except for two industries: the wholesale and retail trade industry and the service industry. The employment ratios, sectoral employment relative to aggregate, also exhibit non-stationary processes, again, except for the construction industry, suggesting the existence of permanent shifts in the employment distribution across sectors. 1

Employment series, both aggregate and sectoral, are divided by the civilian noninstitutional population of 16 years and over, whose seasonality is adjusted by the X-11 procedure in the SAS.

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Table 1 Unit root tests a,b Variables

Employment

Aggregate Durable goods Nondurable goods Construction Transportation and utilities Wholesale and retail trade Finance and insurance Services

22.63 22.24 22.17 23.54* 21.51 22.06 0.03 22.11

Employment ratio

Hours per worker

21.84 21.62 24.10* 21.20 21.76 20.49 22.40

24.40* 24.53* 25.33* 211.91* 24.57* c 20.17 c 214.20* c 22.16 d

* indicates a rejection of a unit root at the 5 percent significance level (the critical value: 2 3.42). a Data are from the DRI database, and all employment variables are divided by population over 16. Mnemonics of the aggregate employment is LPNAG, and average hours per worker is LPMHU / LPNAG. The sample period is from 1947:1 to 1997:08, unless otherwise specified. b Each test is based on the Phillips–Perron Test (5 truncation lags suggested by Newey–West) with a linear trend. c 1964:1–1997:8. d 1964:1–1996:2.

Suppose Nt and Nj,t represent aggregate employment and sector j’s employment, respectively. The employment share of sector j at time t is denoted by vj,t 5 Nj,t /Nt . We define the measure that reflects changes in the employment distribution across industries over time as follows.

FO J

Mt 5

j51

(vj,t 2 vj,0 )

G

2

1/2

,

where J is the number of sectors. Mt measures how far the employment distribution of the economy has deviated since period 0. Mt is non-stationary as employment shares vj,t ’s are non-stationary. The unit-root test statistic of Mt is 2 1.17, suggesting the permanent shifts in the distribution of sectoral employment. In the VAR analysis below, consistent with the results from the unit-root tests, we assume that employment and sectoral-shift measures are nonstationary, while the average hours per worker are stationary.

2.2. Identifying restrictions Consider a structural VAR model with three stationary variables: DMt , D ln Nt , and ln Ht where H denotes the average hours per worker.2 Suppose there are three types of structural shocks in the labor market. Innovations to structural shocks are assumed to be orthogonal and serially uncorrelated. We use the following identifying restrictions: IR-1 and IR-2. IR-1: Temporary shocks have no effect on employment, both aggregate level and sectoral composition, in the long run. 2

To control for a strike by the Communications Workers and Telecommunications International Union against AT&T (a drop of 640 000 in the employment) in August 1983, we included a dummy variable but found no difference in the result.

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IR-2: Pure aggregate shocks, as opposed to sectoral reallocation shocks, do not affect employment composition across sectors in the long run. That is, aggregate shocks have no effect on M in the long run. It is straightforward to show that one can identify the three structural shocks based on IR-1, IR-2, and the covariance matrix of the reduced-form residuals from the VAR. (See Stock and Watson, 1988.) IR-1 identifies the temporary disturbances. IR-2 identifies the pure aggregate disturbances. Sectoral reallocation shocks are identified by the orthogonality.

2.3. Results Our primary interest is the relative importance of the three structural shocks for the cyclical fluctuations of total hours employed. Table 2 shows the k-month ahead forecast-error variance decomposition (k51, 6, 12, 24, 60, 120) for aggregate employment, sectoral-shift measure, aggregate hours per worker, and finally total hours worked. Looking at the last three rows of Table 2, at 6- to 24-month horizons, aggregate permanent shocks account for 26–40% of variation in total hours. Sectoral reallocation shocks explain 45–50% of variation of total hours. In contrast, the role of temporary shocks is modest except for a very short run. At a 1-month horizon temporary shocks are responsible for 77% of variation. However, as the horizon increases, its contribution decays quickly. At a 2-year horizon, it contributes only 15% of variation in total hours. To better understand the cyclical properties of structural shocks identified from the VAR, we compute their correlations with the growth rate of monthly output measure, industrial production. Table 3 presents these correlations for various leads and lags. Total hours co-move with the business cycle, as the contemporaneous correlation of growth rate of hours with output growth is 0.54. Aggregate disturbances, both permanent and temporary, are mildly procyclical as their contempora-

Table 2 Forecast-error variance decomposition Variable

Shock

1

6

12

24

60

120

Aggregate employment

A S T A S T A S T A S T

0.43 0.49 0.09 0.01 0.98 0.00 0.01 0.02 0.98 0.06 0.18 0.77

0.39 0.52 0.09 0.01 0.97 0.02 0.03 0.14 0.83 0.26 0.45 0.29

0.39 0.53 0.08 0.02 0.95 0.03 0.05 0.23 0.72 0.31 0.50 0.18

0.43 0.50 0.07 0.02 0.96 0.03 0.04 0.22 0.74 0.35 0.49 0.15

0.47 0.47 0.05 0.01 0.98 0.02 0.03 0.20 0.77 0.40 0.48 0.12

0.51 0.46 0.04 0.00 0.98 0.01 0.03 0.19 0.78 0.44 0.47 0.09

Sectoral shift

Average hours

Total hours

A: Aggregate permanent shock S: Sectoral reallocation shock T : Temporary shock

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Table 3 Cross-correlation with growth rates of industrial production cor(Dy t , x t 2j ) Variable for x

x t 23

x t 22

x t 21

xt

x t 11

x t 12

x t 13

Industrial production Total hours Aggregate shock Sectoral shock Temporary shock

0.18 0.08 2 0.01 2 0.02 0.02

0.25 0.15 0.08 2 0.04 0.00

0.40 0.21 0.08 2 0.15 0.11

1.00 0.54 0.27 2 0.51 0.27

0.40 0.24 0.16 2 0.16 0.09

0.25 0.19 0.05 2 0.07 0.05

0.18 0.23 0.10 2 0.08 2 0.03

neous correlations with output growth are 0.27. In contrast, sectoral reallocation shocks exhibit a strong counter-cyclicality. Its contemporaneous correlation with output growth is 20.51, suggesting acceleration of the reallocation process of labor during recession. This finding is clearly consistent with the economic mechanism put forward by the sectoral-shift hypothesis: Sectoral disturbances manifest themselves as an aggregate recession. This finding also sharply distinguishes the sectoralshift hypothesis from the normal-business-cycle hypothesis which views economic fluctuations driven mostly by aggregate shocks. This property can also be observed from the impulse response functions. Fig. 1 shows the impulse responses of aggregate employment, sectoral-shift measures, and

Fig. 1. Impulse responses: aggregate (—), sectoral (– ?

–), temporary (– – –).

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aggregate hours per worker to one-standard-deviation innovations to aggregate, sectoral, and temporary shocks, respectively. Looking at the first graph, in response to a permanent aggregate disturbance, employment approaches the new steady state in about a year. Consistent with the sectoral-shift hypothesis, aggregate employment clearly decreases in response to a sectoral reallocation shock. It responds only slightly to temporary shocks. In the second graph, sectoral-shift measure decreases initially in response to aggregate permanent and temporary disturbances. Finally, in the last graph, hours per worker respond very strongly to temporary shocks as our economic intuition predicts, whereas they respond slightly to permanent shock, both aggregate and sectoral.

3. Summary We exploit the distinctive nature between extensive and intensive margins of labor to identify the underlying forces that cause the cyclical fluctuations of total hours. According to the variance decomposition from a VAR model based on monthly data for 1947:1–1997:07 at one-digit industries in the U.S., we find that pure aggregate disturbances, those that do not cause any changes in the employment distribution in the long run, account for 26–40% of cyclical fluctuations of aggregate total hours worked. Purely temporary shocks, those that cause neither aggregate nor sectoral employment in the long run, account for 15–29% of cyclical variation of total hours. Sectoral reallocation shocks, defined by the disturbances that shift the distribution of the employment across sectors in the long run, account for about half the cyclical variation in hours. Further, we find the sectoral reallocation shocks counter-cyclical, which is consistent with the economic mechanism put forward by the sectoral-shift hypothesis: Sectoral disturbances manifest themselves as an aggregate recession.

Acknowledgements We thank Mark Bils, Bill Dupor, Frank Schorfheide, and participants at the Wharton Macro Lunch and the Econometrics Society Meeting in Seattle for suggestions and comments. Noh-Sun Kwark gratefully acknowledges the financial support of the Dongguk University Research Fund.

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