Trend employment growth and the bunching of job creation and destruction.

I. INTRODUCTION

Research on labor market dynamics has begun to focus on the two separate components of aggregate employment growth: the number of jobs created at expanding and newly born establishments (job creation) and the number of jobs lost at declining and dying establishments (job destruction). A key stylized fact in this literature is that job destruction varies more over time than job creation. This finding has already informed a number of theoretical models, but because of data limitations, most of the direct evidence on gross job flows has come from manufacturing data alone.(1) This limitation arises because the separation of net employment growth into the two gross flows requires employment data on individual firms or plants, and such data are difficult to assemble and link from period to period. The best known source of panel data on micro-level employment is the Longitudinal Research Database of manufacturing establishments (LRD),(2) which was the first to suggest the dominance of fluctuations in job destruction over the business cycle. Because results from the manufacturing sector have become so important to theoretical research, it is worth asking how representative of the economy manufacturing is likely to be.

This paper uses new data with nonmanufacturing and manufacturing firms to investigate this question. The data consist of annual employment reports from firms in Michigan from 19781988, collected by the state's unemployment insurance (UI) system. Simple analysis of these data indicate that while job destruction in Michigan's manufacturing sector is relatively volatile over the sample period, this is not the case in most other sectors, where job creation varies more.(3)

What explains the difference between manufacturing and other sectors? Empirically, it appears that one-digit sectors that are declining have high variances of job destruction, while growing sectors display high variances of job creation. One model that delivers an inverse relationship between trend growth and the relative volatility of job destruction is an (S,s) model of micro-level employment adjustment. An (S,s) model is a good starting point from which to think about gross job flows, because a number of empirical studies suggest that microeconomic employment adjustment looks "lumpy," suggesting (S,s)-type behavior [Caballero, Engel, and Haltiwanger 1997]. This paper explains how a low-frequency trend can interact with an (S,s) rule to make job destruction a more important margin of adjustment in a declining industry, and thereby inflate the variance of job destruction relative to that of creation. The simple model developed here can be therefore be placed in a larger literature on the relationship between a low-frequency trend in the desired value of a state variable and aggregate dynamics when individual agents follow (S,s) rules.(4) Taking a cue from this work, I use a simple (S,s) model to derive a regression equation that links the relative standard deviations of creation and destruction in an industry to the relative means of an industry's gross job flows. It turns out that the (S,s) model has two sharp predictions for the relationship between trend growth and the relative volatility of gross job flows. The first prediction is that job creation in a sector with a zero employment trend should be just as volatile as job destruction. The second prediction derived and tested below is that the log difference between the means of job creation and destruction should be larger in absolute value than the log difference between the standard deviations of these gross flows.

Confronting these predictions with the data gives mixed results. Looking across one-digit Michigan industries, the positive empirical relationship between trend employment growth and the volatility of creation relative to destruction is too strong for the model to explain. Log differences between standard deviations of the two gross flows within an industry are typically larger, not smaller, than log differences between gross-flow means. Model performance generally improves when UI data from two-digit sectors is used, but destruction still appears excessively volatile in manufacturing. A corollary to this finding, however, is that the model finds it hard to explain the high volatility of job creation in services, the fastest growing sector in the Michigan data. Using two-digit and four-digit data from the LRD tells much the same story, as accounting for trend employment growth removes some, but not all, of the excess volatility of job destruction in manufacturing. The bottom line is that the empirical relationship between trend growth and relative gross-flow volatility should take its place as a stylized fact that future research should address, and the modeling approach advanced here may prove useful in this work. But a simple (S,s) model interacting with trend growth alone is probably. not sufficient to explain why job destruction in manufacturing varies so much.

The paper proceeds as follows. Section II presents the basic empirical relationship between employment trends and the relative variances of gross job flows in the Michigan data. Section III adapts a canonical (S,s) model into a regression equation appropriate for the examination of gross job flows. Section IV presents the empirical results, and Section V concludes. The Data Appendix describes the Michigan data in detail.

II. IS MANUFACTURING UNIQUE?

Comparison of manufacturing and nonmanufacturing behavior is possible in this paper because it uses administrative data from the UI system, as did one of the first papers to investigate gross job flows [Leonard 1987]. By contrast, the LRD is generated by survey data from manufacturing plants. Firm-level employment data used below were originally collected by the Michigan Employment Security Commission (MESC) from 1978 through 1988 in order to levy UI taxes on firms. Firm-level records were linked across years by researchers at the University of Michigan in 1991. The resulting longitudinal data set is described in detail in the Data Appendix, but the main differences between the Michigan data and the LRD should be noted here. First, the Michigan data are on the firm level, while the LRD are on the plant level.(5) Second, the data are annual averages, while the LRD's annual sample is measured at a point-in-time (the middle of March). Third, the LRD uses a plant-level identifying number to longitudinalize employment records, while researchers creating the Michigan data worked with firm-level tax ID numbers, linked across changes in legal ownership with special records supplied by the MESC. Firms that merge at any point in the sample are treated as a single firm throughout the sample, as are firms that spin off from one other at some point. In a small percentage of cases, records linked across changes in ownership resulted in spurious "spikes" in the year of the transfer, as employment at the firm was double counted in that year. A filter was written to detect and correct these occurrences (to the greatest degree possible). The use of this filter did not appear to affect results presented below, although it did bring the yearly aggregates constructed from the panel data closer to aggregates published by the Bureau of Labor Statistics.(6) Finally, some sectors were excluded from the Michigan data because of questions regarding the quality of the data there, or because they are dominated by public sector employers. The main examples are the U. S. Post Office (SIC 43) and Health Services (SIC 80).

With these basic features of the Michigan data in mind, job creation and destruction rates are defined in the now-standard way originally proposed by Davis and Haltiwanger:

(1) [POS.sub.jt] = 1/[X.sub.jt] [summation over i] [([E.sub.ijt] - [E.sub.ij,t-1]).sup.+]

(2) [NEG.sub.jt] = 1/[X.sub.jt] [summation over i] [[absolute value of ([E.sub.ijt] - [E.sub.ij,t-1]].sup.-],

where [([E.sub.ijt]- [E.sub.ij,t-1]).sup.+] is firm i's positive change in employment (equal to zero if the firm does not increase employment), [[absolute value of ([E.sub.ijt] - [E.sub.ij,t-1]).sup.-]] is the absolute value of a firm's negative change, and [X.sub.jt] is the size of the sector, defined as the average employment in sector j in t - 1 and t. The sum and difference of these gross job flows are

[SUM.sub.jt] = …