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The short-run relationship between sectoral shifts and U.S. labor market fluctuations.

1. Introduction

An explicit policy goal of the U.S. government since the passage of the Employment Act of 1946 has been to maintain full employment by acting to reverse any significant increases in cyclical unemployment. Beginning with the work of Lilien (1982), the view that reductions in aggregate demand or shocks to aggregate supply are responsible for the onset of recessions and increases in unemployment has been challenged. Instead, shifts in labor demand among various sectors of the economy, caused by either changes in production technology or the emergence of new products or sources of supply for existing products, are assigned primary importance as a cause of cyclical increases in aggregate unemployment. One implication of this view is that demand management policies are ineffective against unemployment because the natural rate of unemployment fluctuates with shifts in the demand for labor across sectors of the economy. Thus, implementation of the Employment Act to address short-run macroeconomic fluctuations is not possible on a practical level.

Recent work reviewed below calls into question the strength and causal direction of the sectoral shift effect. One line of research critical of the Lilien model yields results showing that aggregate disturbances account for much of the movement in unemployment previously attributed to sectoral shifts. Another line has found that variation in the rate of job destruction over the business cycle explains most of the cyclical fluctuation in unemployment. Aggregate downturns trigger employment adjustments which result in a changed mix of employment across industries. A third line, relying on microdata, shows that there is little difference in the pace of long-term sectoral shifts between recessions and expansions, with most workers ultimately returning to the same sector following a spell of unemployment. Thus, short-term sectoral shifts may reflect differences in industry patterns of cyclical layoffs and recalls. In each case, these previous findings suggest that short-run movements in aggregate output and unemployment may cause, rather than be caused by, sectoral shifts in employment.

Using commonly applied measures of sectoral shifts in employment, this paper presents new evidence on labor market processes related to the sectoral shifts hypothesis. It extends previous criticisms of the hypothesis to show that there is causality from changes in unemployment to sectoral shifts, with an asymmetry to the relationship and a significant structural change after 1973. Another innovation is to test conditions under which an increase in sectoral shifts can lead to reductions in unemployment. Also new is the use of monthly data for the entire postwar period, with adjustments for major work stoppages during that time. The monthly analysis enables detection of dynamic adjustments that have not been captured by those using quarterly or annual time series. It is shown that work stoppages such as strikes have a major impact on the construction of a time series for sectoral shifts, an impact that can significantly influence the estimated unemployment-sectoral shifts relationship when using monthly or quarterly data.

The next section briefly outlines the sectoral shifts hypothesis of labor market adjustment and the empirical evidence to date. It reviews recent work involving employment fluctuations over the business cycle and alternative hypotheses on the short-run relationship between sectoral shifts and fluctuations in unemployment. Section 3 contains a description of the data and a set of empirical results which support three different hypotheses concerning this relationship. The paper's main conclusions are summarized in section 4.

2. Sectoral Shifts and the Macroeconomy

Most previous analyses have used Lilien's dispersion measure for relative sectoral growth rates as the initial specification of sectoral shifts in the allocation of labor. For consecutive time periods, it is calculated as:

[[Sigma].sub.t] = [{[summation of] i=1 to N ([e.sub.it]/[E.sub.t]) [[ln [e.sub.it] - ln[e.sub.it-1]) - (ln [E.sub.t] - ln [E.sub.t-1])].sup.2]}.sup.1/2] (1)

where [e.sub.it] is employment in industry i at time t, and [E.sub.t] is the sum of [e.sub.it] across industries. As summarized in Davis (1987), the sectoral shifts hypothesis maintains that increases in employment growth dispersion reflect greater mismatch between existing and optimal allocations of labor across industries. This mismatch is due to changes in patterns of industry labor demand related to changing consumer tastes and production technologies. Information costs and the time and money costs of changing sectors combine to cause labor supplies to adjust slowly to the new set of industry demands. Thus, periods with greater dispersion are expected to have higher rates of unemployment. Lilien obtained such a result with annual data for 1948-1980, with [[Sigma].sub.t] and [[Sigma].sub.t-1] having positive coefficients in a regression model relating the unemployment rate to sectoral shifts, unexpected monetary growth, the lagged unemployment rate, and a time trend.

Abraham and Katz (1986) maintained that fluctuations in aggregate demand rather than sectoral shifts in the allocation of labor are the primary explanation for a positive correlation between changes in the unemployment rate, U[R.sub.t], and [[Sigma].sub.t]. This is the case when (i) more cyclically sensitive industries have the slowest employment trend growth rates or (ii) there are interindustry differences in cyclical sensitivity, and hiring costs exceed termination costs on a per worker basis. Because U[R.sub.t] is positively correlated with AU[R.sub.t], a positive relationship between U[R.sub.t] and [[Sigma].sub.t] can occur due to changes in either aggregate demand or the rate of sectoral shifts in labor demand. Their finding of a negative relationship between [[Sigma].sub.t], and an index of help-wanted advertising implied that changes in aggregate demand were responsible for fluctuations in the unemployment rate. However, the importance of their result has been questioned by Hosios (1994), who showed that sectoral shifts may also lead to a negative relationship between unemployment and the number of job vacancies.

Although the Abraham and Katz view implies that [[Sigma].sub.t], is smaller at lower rates of unemployment, during economic expansions [[Sigma].sub.t] will be larger when U[R.sub.t] declines more rapidly than when U[R.sub.t] declines slowly. This is the case because employment growth in cyclical (noncyclical) industries will exceed (lag) total employment growth by a greater amount when declines in U[R.sub.t] are steeper, thereby implying larger values of [[Sigma].sub.t]. Thus, when [[Sigma].sub.t] is related to [Delta]U[R.sub.t] in the empirical work below, a positive relation is expected when unemployment is rising and a negative relation is expected when unemployment is falling. This result is referred to here as the business cycle sensitivity hypothesis.

Davis (1987) provided two important extensions to the labor reallocation model of unemployment fluctuations. Theoretically, because the value of lost output increases during periods of above-normal growth, structural adjustments to interindustry changes in output demands and production methods are more prevalent during recessions. This reallocation-timing hypothesis also implies a positive relationship between unemployment and sectoral shifts, even if fluctuations in output and unemployment are caused by changes in aggregate demand or supply. Empirically, Davis found the positive relationship is stronger during recessions (his stage-of-business cycle effect). This occurs because the unemployed conduct longer searches during recessions when forgone earnings tend to be lower, especially if unemployment insurance is available. The unemployment pool also tends to shift during recessions toward individuals who are less likely to exit from the labor force.

Early empirical work testing the Lilien model for the postwar U.S. economy did not provide strong support for the sectoral shifts hypothesis (Loungani 1986; McCallum 1987; Samson 1990). Either monetary variables or oil shocks proved to be the main determinants of unemployment fluctuations over the business cycle. Inconclusive results emerge from more recent studies. Based on quarterly data for the U.S. from 1948:3-1988:2, Palley (1992) found that cyclical movements in unemployment were explained almost completely by aggregate fluctuations as opposed to sector-specific effects. Using annual data from 1956-1987, Parker (1992) estimated a contemporaneous positive effect on U.S. unemployment for sectoral shifts, but only an aggregate demand variable measured as unanticipated money growth had significant lagged effects. For state and local labor markets, Holzer (1991) and Partridge and Rickman (1995) found that within market variances of industry employment, growth rates were not significantly related to local rates of unemployment.

Conversely, Mills, Pelloni, and Zervoyianni (1995) used quarterly U.S. data for 1960-1991 and found that the current value and two lags of Lilien's measure of employment growth dispersion were significant positive determinants of changes in the rate of unemployment. A contemporaneous positive effect remained significant after the dispersion index was purged of monetary effects, but the same variable lagged four quarters was negative and significant. As in Davis (1987), they found a stronger positive effect when real GNP was increasing at a rate slower than its long-term trend growth rate. Brainard and Cutler (1993) measured quarterly sectoral shocks as the variance of industry excess returns in the stock market from 1948 to 1991. It had a significant, but modest, positive impact on aggregate U.S. unemployment 8 to 12 quarters in the future, even when a significant employment growth dispersion index was included in the model.

Gross Labor Adjustments and the Business Cycle

Empirical assessments of the sectoral shifts hypothesis have relied on interindustry comparisons of net employment flows. Recent analyses of gross worker flows and job creation and destruction over the business cycle do not yield patterns of adjustment consistent with a primary role for sectoral shifts as a cause of fluctuations in unemployment. Starr-McCluer (1993) estimated that the fraction of unemployed who moved to significantly different jobs during 19801982 was only five percentage points higher during the recession than the expansion for both the goods and service sectors of the economy. Murphy and Topel (1987) concluded from Current Population Survey data for 1970-1985 that less than 25 percent of unemployed workers switched industries at the two-digit level, with neither a cyclical pattern nor secular increase in such moves over time. In addition, intersectoral mobility declined as unemployment rose.

In contrast, rates of job destruction have distinctive countercyclical patterns in industry surveys. Data on Wisconsin firms gathered by Leonard (1987) revealed that although job creation was not related to cyclical fluctuations, the rate of job destruction moved inversely with the business cycle, especially for the manufacturing sector. Based upon CPS data for 19681986 and manufacturing data developed by Davis and Haltiwanger (1990), Blanchard and Diamond (1990) observed the same cyclical patterns as Leonard and concluded that fluctuations in unemployment were largely due to fluctuations in aggregate demand and supply. They theorized that recessions are a time of economic "cleaning up" when marginally viable operations fail to remain profitable and therefore must scale back variable costs or shut down.(1)

Working with annual and quarterly surveys of manufacturing establishments from 1972-1986, Davis and Haltiwanger (1990, 1992) found that most countercyclical job destruction was idiosyncratic in that there was no pattern of different cyclical responses by the industry groups involved. There was support for the reallocation-timing hypothesis of unemployment fluctuations as aggregate shocks appeared to initiate increased rates of job destruction and sectoral shifts in employment as less efficient plants suffered employment losses. Although less important, allocative shocks such as large reductions in defense spending also had a positive effect on unemployment and job destruction. The latter can lead to job creation after resources have time to shift to new uses and uncertainties involving the extent of changes in technology and consumer demand are resolved.

Overall, there is evidence to support three hypotheses concerning the relationship between sectoral shifts in employment and fluctuations in the aggregate rate of unemployment: (i) adverse aggregate shocks cause increases in unemployment, with sectoral shifts reflecting industry differences in cyclical sensitivity to the business cycle, (ii) sectoral shifts in employment caused by allocative shocks lead to higher unemployment in the short run, but perhaps greater employment in the long run, and (iii) sectoral shifts reflect a reallocation-timing effect which causes job destruction to increase greatly during recessions. The empirical work in the next section reveals conditions under which each of these views is correct.

3. Data, Models, and Estimation Results

Data

This analysis uses the monthly data from which the quarterly and annual time series used in many previous studies were constructed. Estimates of sectoral shifts using monthly data yield means and variances (see Table 1) much lower than those reported using quarterly or annual data. The chief advantage is that the data will include short-term fluctuations in sectoral reallocations, unemployment, and related macroeconomic variables not captured by temporally aggregated time series (Rossana and Seater 1995). Thus, statistical models may capture relationships between [Delta]U[R.sub.t] [[Sigma].sub.t] not observable with more aggregate data. For example, there will be richer content with respect to short-term layoffs and recalls, increasing the likelihood that sectoral shifts are a consequence of cyclical fluctuations. Adjustments for work stoppages are also possible with monthly data. A possible disadvantage is that with less variation in [[Sigma].sub.t] and greater influence for layoffs and recalls, relatively less of measured labor reallocation will be associated with long-term sectoral shifts. However, if there is still support for the sectoral shifts or reallocation-timing hypotheses using monthly data, the relevance of these hypotheses in the short run would reinforce their importance in explaining cyclical fluctuations as well as longer term patterns of economic growth.

The Appendix contains sources and definitions for the time series used to construct variables included in the regressions models estimated below. The full sample contains seasonally adjusted monthly data for 1948-1994. Total nonagricultural employment is divided into ten sectors for the calculation of [[Sigma].sub.t]. Although many previous studies have used similar disaggregation, some have disaggregated to the two-digit level for manufacturing. Even though sectoral shifts within the durable and nondurable manufacturing sectors are not included in this study, less disaggregation is favored for several reasons.

First, periodic changes to the standard industrial classification system are less likely to cause large increases in [[Sigma].sub.t] when fewer sectors are used, because reclassifications usually occur on an intrasectoral basis for these ten sectors. Second, disaggregation by product durability captures significant differences in the cyclical sensitivity of employment within the manufacturing sector. Parker (1992) obtained better fits relating unemployment to the sectoral dispersion index when using only 13 rather than 65 sectors. He hypothesized that mobility costs within broadly defined sectors are much lower than between them. Also, 80% of the variation in annual gross job reallocation (i.e., job creation and job destruction) within manufacturing has been found to involve idiosyncratic plant-level changes rather than aggregate or sector-specific fluctuations (Davis and Haltiwanger 1990). Thus, further disaggregation to capture intrasectoral labor reallocations is not likely to be useful.

[TABULAR DATA FOR TABLE 1 OMITTED]

Finally, the assignment of work-stoppage adjustments to manufacturing industries at the two-digit level is not possible with Bureau of Labor Statistics (BLS) work stoppage data. Employer and union names are sufficient to assign workers affected by strikes to broad industry classifications such as durable versus nondurable manufacturing or transportation, communications, and public utilities versus services, but not always at the two-digit level for manufacturing. An important data adjustment would not be possible with a finer degree of disaggregation.

Adjustment for Work Stoppages

Previous work using measures of sectoral dispersion in quarterly employment growth rates has not considered the impact of major work stoppages on employment time series. Because striking workers are not counted as unemployed, major stoppages can generate large values of the dispersion index which are unrelated to observed values of unemployment. Even if viewed as allocative shocks, most employment declines due to strikes are eventually reversed and have no substantive impact on desired resource demands across sectors.

For each major work stoppage, an adjustment equal to the number of workers affected is added to the employment figures for the months and industries involved. This process, which is described in a technical appendix available on request from the author, removes the impact of major work stoppages from the employment data. Only stoppages affecting a minimum of 10,000 workers and clearly determined to affect the monthly BLS employment report are included in the adjustment. This yields the minimum changes which could result from taking stoppages into account when calculating monthly employment growth rates by industry. The entries for [Sigma] and [[Sigma].sub.w] (for expositional ease, the time subscript has been dropped) in Table 1 show a decline in the mean value of the dispersion index of greater than 20% for the full sample period when the adjustment is made. The standard deviation is reduced by more than half of that of the unadjusted value. Greater reductions resulted for the 1948-1973.10 period, when strikes were more prevalent in the U.S. economy.

Because long strikes involving many thousands of workers can have a large impact on quarterly averages of monthly data, omission of the adjustment in earlier work may have permitted observations with large values of [Sigma] to become influential outliers in statistical models. The adjustment removes from the data a major cause of dispersion in sectoral growth rates and enables a clearer focus on the relationship between sectoral shifts and fluctuations in the rate of unemployment.

Sample Statistics and Sectoral Shifts over the Business Cycle

Table 1 provides the definitions, means, and standard deviations for the variables included in the empirical analysis for the five samples used. Several items support dividing the post-war data series at the time of the 1973 oil crisis and the onset of slower aggregate productivity growth. First, at nearly 7%, the average unemployment rate (UR) was more than two percentage points lower during the 1948-1973.10 period as compared to 1973.11-1994. Second, the annual inflation rate increased from an average of 2.5% during the earlier period to 5.8% in the later period, while the mean rate of interest (RATE) more than doubled from 4.8% to 10.4%. Finally, the increase in the index of coincident economic indicators (CYCLE) averaged 3.3% on an annual basis during the early period, and dropped to 2.1% during the later period. Except for the mean value of CYCLE, there is little difference in these variables between below average and above average growth periods.

Three measures of sectoral dispersion in employment growth are also shown in Table 1: [Sigma], unadjusted dispersion; [[Sigma].sub.w], [Sigma] adjusted for work stoppages; and [[Sigma].sub.R], [[Sigma].sub.w] adjusted for aggregate fluctuations in the macroeconomy. [[Sigma].sub.R] has been purged of cyclical effects in a manner analogous to the technique of Mills, Pelloni, and Zervoyianni (1995), who removed from their measure of dispersion any aggregate demand disturbances related to changes in money supply growth. For each sector i, the relative employment growth rate (ln [e.sub.it], - ln [e.sub.i,t-1]) - (ln [E.sub.t] - ln [E.sub.t-1]) was regressed on the current value and six lagged values of CYCLE. Denoting the residuals for the sector i regression model as [x.sub.i], cyclically adjusted dispersion was then calculated as

[Mathematical Expression Omitted].

[R.sup.2] values for the relative employment growth regressions ranged from 0.02 for the mining sector and transportation, communications, and public utilities to 0.43 for services, 0.47 for finance, insurance, and real estate; and 0.61 for durable manufacturing. As expected, durable manufacturing's relative growth was procyclical, while for services and the financial sector relative growth was countercyclical. [[Sigma].sub.R] provides a time series for employment growth dispersion purged of past and present aggregate cyclical fluctuations, unlike previous adjustments that purged only monetary fluctuations.(2)

For each sample in Table 1, calculation of [[Sigma].sub.R] results in a further reduction in sectoral shifts. For the full sample, one-third of the unadjusted mean and nearly two-thirds of the unadjusted standard deviation of [Sigma] are eliminated when both the work stoppage and cyclical effects are removed. Both the mean and standard deviation of sectoral shifts are smaller during the later period than the earlier period for all measures of dispersion used; and although the differences are smaller in magnitude, slower growth periods exhibit greater dispersion in employment growth than faster growth periods as suggested by the sectoral shifts hypothesis.(3)

Table 2 characterizes the typical behavior of the unemployment rate and sectoral shifts during postwar expansions and recessions defined according to official National Bureau of Economic Research dates. The net change in the unemployment rate is comparable for expansions and recessions, but the average duration of expansions is nearly five times that of recessions. The magnitude of sectoral shifts during the typical expansion is 40% greater than during the typical recession. Although this implies significant labor reallocation over the long run, shifts are more than three times greater on a per-month basis during recessions than expansions (row 4 of Table 2). Durable manufacturing, a secularly declining employment sector, lost more [TABULAR DATA FOR TABLE 2 OMITTED] than 1.25 percentage points in its employment share during the typical recession, while service employment, the largest source of secular employment growth, gained more than one percentage point during expansions. Combined with the greater cyclical sensitivity of relative employment growth in these sectors, these facts support the view that aggregate shocks may still be the main cause of unemployment fluctuations.

Models and Estimation Results

The business cycle sensitivity and reallocation-timing hypotheses view fluctuations in the aggregate demand for labor as the cause of sectoral employment shifts. Conversely, changes in the pace of labor reallocation across industries cause fluctuations in unemployment under the sectoral shifts hypothesis. Empirically, the causal forces are likely to operate both contemporaneously and with lagged effects, yielding a dynamic simultaneous equations model.(4) Previous analyses of the sectoral shifts hypothesis have assumed that labor reallocations are exogenous and have not attempted to estimate the impact of changes in the unemployment rate on sectoral shifts. As demonstrated by Pierce and Haugh (1977), a significant contemporaneous effect operates in both directions and does not provide information regarding the acceptance or rejection of alternative hypotheses concerning temporal causality. Thus, earlier results having only a significant contemporaneous effect for the impact of sectoral shifts on unemployment could have captured the effects of any or all of the three competing hypotheses.

A pure vector autoregressive (VAR) model without contemporaneous variables is not used in this study because current period effects are contained in both empirical models. Their inclusion avoids omitted-variable bias, at the expense of the possibility of some bias in the estimates of contemporaneous effects as discussed below for each model. However, the causality framework permits an assessment of the various hypotheses based upon the significance of lagged variables.

Model One

The reallocation-timing and business cycle sensitivity hypotheses imply that fluctuations in the aggregate economy lead to sectoral reallocations of labor as measured by sectoral dispersion in employment growth adjusted for work stoppages, [Sigma].sub.w]. The initial specification to test these hypotheses for the entire sample is:

[[Sigma].sub.w,t] = [[Alpha].sub.1] + [summation of] [[Beta].sub.i][[Sigma].sub.w,t-i] where i=1 to N + [summation of] [[Gamma].sub.j]PDU[R.sub.t-j] where j=0 to M + [summation of] [[Delta].sub.j]NDU[R.sub.t-j] where j=0 to M + [summation of][[Rho].sub.k][MONTH.sub.k] + [epsilon.sub.t] (2)

where PDUR = [Delta]UR if [Delta]UR [greater than] 0, 0 otherwise; NDUR = [Delta]UR if [Delta]UR [less than or equal to] 0, 0 otherwise; MONTH is a vector of 11 monthly dummies; [[Alpha].sub.1], [[Beta].sub.i], [[Gamma].sub.j], [[Delta].sub.j], and [[Rho].sub.k] are parameters to be estimated by ordinary least squares; and [[Epsilon].sub.t] is a random error term.(5)

According to the business cycle sensitivity hypothesis, [[Sigma].sub.w] should be greater when there are large increases or decreases in the aggregate unemployment rate. This implies [[Gamma].sub.j] [greater than] 0 and [[Delta].sub.j] [less than] 0. This result is due to an increase in layoffs (recalls) when aggregate unemployment rises (falls) sharply and to large intersectoral differences in the responsiveness of employment to aggregate fluctuations. The reallocation-timing hypothesis views recessions as more efficient periods for finn contractions and closures. This implies [[Gamma].sub.j] [greater than] 0 for months with rising unemployment. Because job creation across sectors is less sensitive to cyclical fluctuations, there may be no relationship between NDU[R.sub.t-j.] and [[Sigma].sub.w]. When these hypotheses are combined with the business cycle sensitivity hypothesis, it is expected that [Sigma] [[Gamma].sub.j] [greater than] [absolute value of [Sigma][[Delta].sub.j]].(6) An F-test at the 0.01 level of significance confirmed an increase in explanatory power when allowing separate effects for increases and decreases in unemployment (the unrestricted model).(7) Based on the optimal lag lengths for this model, a Chow test at the 0.01 level of significance indicated a change in model structure coinciding with the oil shock in October 1973.

Results using [[Sigma].sub.w] as the dependent variable for two periods, 1948-1973.10 and 1973.11-1994, are shown in the first and third columns of Table 3. In both periods, F-tests supported the unrestricted specification, with estimates for the lagged dependent variable revealing persistence in the sectoral reallocation of labor. For 1948-1973.10, increases in UR generated quicker and larger sectoral reallocations of employment compared to the corresponding effect for decreases in UR. The latter were significant after a one-month delay and are smaller in absolute value. The signs of the coefficients on lagged changes in UR are consistent with the business cycle sensitivity hypothesis, with large changes in unemployment in either direction leading to increases in [[Sigma].sub.w]. The smaller impacts of the NDU[R.sub.t-j] reflect the slower responses of recalls and job creation to economic upturns compared to layoffs and job destruction during downturns.

For 1973.11-1994, increases in [[Sigma].sub.w] occurred when the unemployment rate rose more sharply, but there was no significant relationship between reductions in unemployment and labor reallocation. This suggests a greater role for the reallocation-timing hypothesis, with downturns being opportunities for permanent job destruction. The difference in results for NDU[R.sub.t-j] between [TABULAR DATA FOR TABLE 3 OMITTED] the two time periods also suggests that job creation in cyclically sensitive sectors declined in cyclical responsiveness after 1973. This is consistent with the work of Davis, Haltiwanger, and Schuh (1996), who found that manufacturing job creation rates increased after recessions in the 1950s and 1960s, but not in later recoveries. If there were fewer recalls and less job creation after downturns in the later period, then the negative relationship between [[Sigma].sub.w] and NDU[R.sub.t-j] during expansions would not occur, in contrast to the results for 1948-1973.10.

Estimates shown in columns 2 and 4 of Table 3 use [[Sigma].sub.R] in place of [[Sigma].sub.w] in order to focus on sectoral reallocations unrelated to the business cycle.(8) Support for the restricted model during the earlier period implies that the results for [[Sigma].sub.w] were strongly influenced by the business cycle sensitivity effect. This is reinforced by the diminished size of the positive, contemporaneous relationship between [Delta]UR and [[Sigma].sub.R]. Because the lags on [Delta]UR are not significant, the results do not distinguish between the reallocation-timing hypothesis and the sectoral shifts hypothesis, the latter of which implies causation in the reverse direction. Results for the 1973.11-1994 period also reject the unrestricted model and provide additional support for the reallocation-timing hypothesis. Lagged increases in the unemployment rate lead to greater sectoral shifts as reallocations are timed to occur when the labor market is weakening rather than strengthening.

Taken together, the results for model one indicate that the business cycle sensitivity hypothesis has more support during the earlier period while the reallocation-timing hypothesis appears more relevant to the later period. For 1948-1973.10, larger sectoral shifts took place when there were large changes in the unemployment rate in either direction, with the effect being greater for increases in unemployment. Since 1973.11, the results indicate that larger employment shifts occurred during and after large increases in unemployment. Reductions in unemployment generated either no change or reductions in the pace of sectoral shifts.(9)

Model Two

In this section, the direction of causality is reversed in order to assess the impact of sectoral employment shifts on the aggregate rate of unemployment as in previous work. The initial model for the full sample is specified as:

[Delta]U[R.sub.t] = [a.sub.1] + [summation of] [b.sub.i][Delta]U[R.sub.t-1] where i=1 to N + [summation of] [c.sub.j][[Sigma].sub.w,t-j] where j=0 to M + [summation of] [d.sub.k][Delta]INF[L.sub.t-k] where k=1 to L + [summation of] [e.sub.h][Delta]RAT[E.sub.t-h] where h=1 to G + [[Eta.sub.t]

where [Delta] represents the first difference operator and [a.sub.1], [b.sub.i], [c.sub.j], [d.sub.k], and [e.sub.h] are parameters to be estimated by ordinary least squares and [[Eta].sub.t], is a random error term.(10)

Changes in inflation and interest rates are included to control for changes in aggregate demand and financial shocks, which can affect the unemployment rate. Traditional Phillips Curve models hypothesize that past increases in inflation lead to lower unemployment. However, if caused by an adverse supply shock, increases in inflation may accompany increases in unemployment. Because higher interest rates raise the cost of borrowing, past increases are expected to be positively related to changes in the unemployment rate. To avoid simultaneity bias [TABULAR DATA FOR TABLE 4 OMITTED] and because changes in unemployment typically trail changes in aggregate demand and financial variables, only past values of [Delta]INFL and [Delta]RATE are included.

Based on the original sectoral shifts hypothesis, current and past values of [[Sigma].sub.w] should be positively related to [Delta]UR. The reallocation-timing hypothesis also implies that the contemporaneous relationship should be positive. The impact of [[Sigma].sub.w] on [Delta]UR under the business cycle sensitivity hypothesis depends on the state of the macroeconomy. As economic growth weakens, the pace of layoffs increases, and greater sectoral dispersion in employment growth will be associated with higher unemployment. Conversely, if strong growth causes the pace of recalls of laid off workers to be brisk, the resulting increase in sectoral growth dispersion may lead to reductions in unemployment.(11) This would involve the restoration of intersectoral demand and supply linkages that work with a multiplier process to generate lower aggregate unemployment. Thus, the business cycle sensitivity hypothesis yields a negative relationship between sectoral shifts and changes in unemployment when economic growth is strong.

Column one of Table 4 presents results for a traditional sectoral shifts regression model for the entire sample period. Although only the current period is significant, the expected sectoral shift effect is observed. An increase in employment growth dispersion leads to larger increases in the unemployment rate. This result is consistent with Lilien's original empirical findings which have been interpreted to represent either a sectoral shifts or reallocation-timing effect. As expected, increases in inflation lead to reductions in [Delta]UR and increases in interest rates to increases in [Delta]UR.

A Chow test was insignificant for a structural break at 1973.10, but was significant at the 0.01 level when the sample was split at the mean monthly growth rate of CYCLE.(12) This permits an assessment of the business cycle sensitivity hypothesis. As expected, during slow growth months, larger sectoral shifts are associated with greater unemployment. The coefficient is more than double that of the full sample coefficient, implying that during periods of above-average growth, current-period sectoral shifts are associated with reductions in unemployment. In fact, although insignificant after its lagged values are included, larger current values of [[Sigma].sub.w] are negatively related to changes in the unemployment rate for the above-average growth sample.

Past increases in sectoral shifts lead to lower unemployment rates during above-average growth periods. This supports the hypothesis that large sectoral shifts during expansions contribute to lower unemployment by restoring intersectoral linkages and greater efficiency in the allocation of labor. The smaller impact of sectoral shifts when growth is strong reflects the cyclical phenomenon of slower recovery from recessions and periods of weak growth compared to the sharper pace of downturns. The pool of unemployed workers during recessions also has relatively more members who are less likely to exit from the labor force. Taken together, estimates for the below-average and above-average growth periods show that the impact on unemployment of conventional measures of sectoral shifts is significantly affected by the aggregate business cycle. Increases in inflation lead to lower unemployment rates when the economy is growing slowly and to higher unemployment rates when economic growth is faster. The latter result is likely due to the association between higher inflation and the peak of an economic cycle, after which unemployment typically begins to rise. A positive interest rate effect is observed only for below-average growth months.

In order to assess the sectoral shifts hypothesis without cyclical fluctuations, [[Sigma].sub.w] is replaced by [[Sigma].sub.R]. A Chow test for a structural break at 1973.10 was not significant at the 0.05 level. The estimates in the last column of Table 4 show that current-period sectoral shifts are still positively related to changes in the unemployment rate. This is strong evidence that sectoral variation in sensitivity to the business cycle is not a full explanation of the positive relationship between sectoral shifts and unemployment. However, when variation in cyclical sensitivity is removed, the positive relationship between current-period sectoral shifts and [Delta]UR is reduced by nearly half compared to the estimate for months with below-average growth. Because much of the endogeneity may be purged from [[Sigma].sub.w] when [[Sigma].sub.R] is used, this latter result implies that previous analyses not correcting for the positive impact on [Sigma] of adverse shocks to unemployment are likely to have overestimated the strength of the contemporaneous sectoral shifts effect.

Conversely, purged shifts from one month earlier are negatively related to [Sigma]UR. This could reflect either renewed employment growth following sectoral reallocations or exit from the labor force in response to structural shifts in the economy. A simple correlation of -0.35 (significant at the 0.01 level) between [[Sigma].sub.R,t-1] and current-period labor force participation rates, and an insignificant correlation between [[Sigma].sub.R,t-1] and employment growth, confirms the exit from the labor force explanation. This outcome supports the view that recent shifts in the sectoral allocation of labor lead to lower aggregate output in the short run as in the sectoral shifts hypothesis. For the above-average growth sample, there is a significant positive correlation between [[Sigma].sub.R,t-1] and employment growth, implying there can be positive benefits to past reallocations of labor as suggested by Davis and Haltiwanger (1990). The results for changes in inflation and interest rates are similar to those obtained for the full sample when [[Sigma].sub.w] was used.(13)

4. Conclusions

Monthly data for the U.S. economy have been used to assess competing hypotheses concerning the short-run relationship between sectoral shifts in labor allocation and fluctuations in the rate of unemployment. Four factors affecting the pace of sectoral shifts have been identified: the incidence of major work stoppages, cyclical fluctuations in the aggregate economy, the reallocation-timing effect which causes more employment adjustments to occur during recessions, and a residual effect comprising allocative shocks at the sectoral level. The impacts of work stoppages and cyclical fluctuations were greater during the 1948-1973:10 period, when large reductions and increases in unemployment led to increases in labor reallocation. Since 1973, higher rates of reallocation have resulted from past increases in the unemployment rate, a result consistent with the reallocation timing hypothesis.

The impact of sectoral shifts on unemployment, as measured by [[Sigma].sub.w], depends on the state of the macroeconomy. Larger shifts are associated with higher unemployment rates when the economy experiences below-average growth and with lower unemployment rates during above-average growth. The magnitude of the relationship is smaller during the above-average period and operates only with a lag from employment shifts to lower unemployment, as prior patterns of production and exchange are restored. These results are consistent with business cycle facts concerning employment adjustments during recessions and expansions. However, there is still empirical support for the sectoral shifts hypothesis: shifts not caused by cyclical forces result in higher rates of unemployment during the current period and lower rates in the next period, the latter due to lower rates of labor force participation.

Because cyclical fluctuations create sectoral shifts and sectoral shifts in turn affect the macroeconomy, implications for antirecession policy are contingent on an accurate identification of the cause and extent of a slowdown. Demand management policies designed to restore growth and reduce unemployment may be appropriate when many cyclical industries experience employment losses due to aggregate shocks or adjustments to higher interest rates at the end of expansions. The same policies may be inflationary if the natural rate of unemployment has risen during a period of large sectoral shifts, and they may inhibit the cleansing effect of slowdowns which promote the permanent reallocation of labor to new sectors. Policies that facilitate labor mobility are more appropriate in this case. The dependence of empirical results and policy implications on the economic circumstances at hand is an outcome that helps to reconcile past differences in the sectoral shifts debate.

Appendix

A. With the exception of the work stoppage information, all variables used in this study are derived from variables contained in the FAME Economics data file (formerly CITIBASE) maintained by FAME Information Services, Inc. All variables are monthly (1948-1994) and have been seasonally adjusted. The original variables (with FAME Economics labels) are:

1. National employment by sector (BLS establishment survey)

LPMI mining LPCC construction LPED durable goods LPEN nondurable goods LPTU transportation, communications, public utilities LPTW wholesale trade LPTR retail trade LPFR finance, insurance, real estate LPGOV government

2. LHUR civilian unemployment rate (BLS household survey)

3. DCOINC BEA composite index of four coincident indicators, 1982 = 100

4. PUNEW BLS consumer price index, all items, urban consumers

5. FYAVG average yield on corporate bonds (Department of Treasury)

B. Work stoppage records

1. 1948-1972: Analysis of work stoppages, Bureau of Labor Statistics, Bulletins 963, 1003, 1035, 1090, 1136, 1163, 1184, 1196, 1218, 1234, 1258, 1278, 1302, 1339, 1381, 1420, 1460, 1525, 1573, 1611, 1646, 1687, 1727, 1777, 1813.

2. 1973-1981: Labor relations yearbook. Washington, D.C.: Bureau of National Affairs, 1974-1982.

3. 1982-1984, 1987: Current wage developments, Bureau of Labor Statistics.

4. 1985-1986, 1988-1994: Major work stoppages, Bureau of Labor Statistics.

The author is grateful to an anonymous reviewer for comments which led to substantive improvements in earlier versions of the paper and to the Division of Labor-Management Relations at the Bureau of Labor Statistics for its assistance in identifying sources of information on major work stoppages. Of course, the author is responsible for decisions regarding the use of these data.

1 Cabellero and Hammour (1994) developed a vintage model of creative destruction in which heterogeneous firms vary according to their states of technology and rates of product innovation. Their model accounted for the fluctuations in job creation and destruction contained in the manufacturing data assembled by Davis and Haltiwanger (1990). Davis, Haltiwanger, and Schuh (1996) maintained that restructurings are less costly during downturns since the value of forgone production moves procyclically and there may be positive information externalities as agents observe the profit-improving reallocations of resources undertaken by others. They also argued that marginal operations have less access to credit, which may increase their rate of job contraction.

2 This approach assumes that there are aggregate disturbances other than monetary ones that affect industry employment growth rates. Instead of trying to identify monthly time series for the entire postwar period that would measure changes in aggregate demand and supply, empirically it is more straightforward to remove all cyclical changes from the employment growth series. Even though this could hypothetically remove some sectoral shift effects, the finding of support for the sectoral shifts hypothesis in the empirical work indicates it is not a serious problem. As with the use of monthly data, this constitutes a more difficult test for acceptance of this hypothesis relative to the others being considered. The components of the index of coincident indicators are total nonagricultural employment, an index of industrial production, personal income less transfer payments, and sales in manufacturing and trade.

3 Unit root tests using the augmented Dickey-Fuller test statistic were conducted for the variables used in the statistical models estimated in the next section. Each of the growth rate dispersion variables is an I(0) variable, meaning there was no evidence of a unit root. INFL and RATE had unit roots and are I(1) variables, and therefore are entered in first difference form in regression models. The evidence is mixed for UR, with some specifications yielding an I(0) result and others an I(1) result. For consistency with the dynamic specifications of the other variables, UR is also entered in first-difference form.

4 Such a model is not estimated here because suitable exogenous instruments are not available on a monthly basis. Also, the empirical work presented later shows that the appropriate samples for the two models are different. Chow tests reveal that the impact of AUR on sectoral shifts changed after 1973.10 and that the impact of sectoral shifts upon AUR depends upon whether the aggregate economy is growing at an above-average or below-average rate.

5 Lag lengths are determined according to the Akaike Information Criterion (AIC). Lags are added until AIC is higher for two consecutive additional lags, which are not included in the final model. In this and all subsequent models, the lag length for the lagged dependent variable is determined first. The monthly dummies proved to be jointly significant in each of the models estimated for Equation 2 and shown in Table 3.

6 According to the sectoral shifts hypothesis, increases in the pace of labor reallocation result in higher rates of unemployment. For months with increases in unemployment (PDUR [greater than] 0), this may increase the positive association between PDU[R.sub.t] and [[Sigma].sub.w.t], imparting a positive bias to the estimate of [[Sigma].sub.0]. Estimates of [[Sigma].sub.0] may also be biased upwards if the sectoral shifts effect partially offsets the negative impact hypothesized for [[Sigma].sub.0] during times of declining unemployment.

7 The estimation sequence was to first find optimal lag lengths for the full sample assuming no difference in the coefficients for positive and negative changes in UR (the restricted model). Using the same lag lengths, Equation 2 was estimated in order to carry out an F-test for the unrestricted versus restricted model.

8 An F-test favored the unrestricted specification for the full sample, but a Chow test supported splitting the sample as before. Both tests were significant at the 0.01 level. After splitting the sample, the restricted specification was appropriate for both periods.

9 Use of [Sigma], the unadjusted measure of employment growth dispersion, resulted in two subsamples with unrestricted specifications for AUR in each case. For 1948-1973.10, the total positive impact of increases in unemployment was estimated to be more than three times greater than when using [[Sigma].sub.w]. For reductions in unemployment, the negative impact was more than four times that estimated for [[Sigma].sub.w]. It occurred contemporaneously rather than with a lag. Failure to adjust for work stoppages increased the apparent strength of cyclical effects because much larger values of [Sigma] were used. For the later period, the coefficient magnitudes were also much greater when using , in place of [[Sigma].sub.w]. More importantly, periods with larger reductions in current and prior-month unemployment had significantly greater sectoral shifts. This business cycle effect did not exist when adjustments for work stoppages were made. Although others have not estimated the impact of unemployment rate fluctuations on sectoral shifts, these results indicate that the effect of work stoppages, a significant source of short-run movements in [Sigma] but not part of the sectoral shifts hypothesis, should be removed from the data.

10 Monthly dummies were not jointly significant in any of the unemployment rate equations and therefore have been omitted from these models. Lag lengths were chosen as described above for model one. The order of inclusion for [[Sigma].sub.w.t-j], AINF[L.sub.t-k], and ARAT[E.sub.t-h] was determined according to which variable contributed the largest incremental reduction in AIC after N was determined for [Delta]U[R.sub.t-i]. Lag lengths were selected first for that variable contributing the greatest reduction in AIC and last for the variable contributing the smallest reduction. Only significant lags for [[Sigma].sub.w], [Delta]INFL, and [Delta]RATE are included in the final specifications. The coefficients reported in Table 4 for [[Sigma].sub.w,t-j], [Delta]INF[L.sub.t-k], and [Delta]RAT[E.sub.t-h] represent the sums of significant coefficients for each variable, with standard errors calculated from the covariance matrix.

11 In this case, past increases in the pace of sectoral shifts may yield an outcome closer to the optimal allocation of labor across sectors. Davis (1987) discussed the relationship between unemployment and the distance between actual and optimal labor allocations.

12 Variable lags were constructed in the computer program before the subsamples were formed, so the lags are specified correctly for temporally consecutive time periods. Chow tests on the below- and above-average growth subsamples rejected a structural break at 1973.10.

13 Significantly different results were obtained using unadjusted sectoral shifts. During below-average growth periods, current and lagged values of [Sigma] were positively related to [Delta]UR. The current period coefficient was lower by more than half of the [[Sigma].sub.w] coefficient because much of the variation in [Sigma] was due to work stoppages rather than the aggregate economy. The significant lagged effect would have provided support for the sectoral shifts hypothesis. For above-average growth periods, current and lagged values of [Sigma] were negatively related to [Delta]UR. Unlike the results for [[Sigma].sub.w], most of the impact was contemporaneous and much smaller in magnitude. In both cases, the work stoppage adjustment significantly increases the contemporaneous impact of sectoral shifts on unemployment. It is possible that earlier studies using quarterly observations would have obtained much stronger relationships between sectoral shifts and changes in unemployment if the short-term employment effects of work stoppages had been removed from the data.

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