# Sectoral shifts and cyclical unemployment: a reconsideration.

SECTORAL SHIFTS AND CYCLICAL UNEMPLOYMENT: A RECONSIDERATION

The debate over the relative importance of sectoral and aggregate shocks in

explaining fluctuations in the aggregate unemployment rate has centered on the relationship

between unemployment, job vacancies, and the dispersion of sectoral employment

growth rates (which proxies for sectoral shocks). This paper examines some possible

theoretical relationships between these variables, and, after decomposing

unemployment into components attributable to sectoral and aggregate shocks, estimates the

importance of each. If finds that fluctuations in unemployment are principally caused

by aggregate shocks, but sectoral shifts explain a significant, albeit steady, amount of

unemployment.

I. INTRODUCTION

In a controversial paper Lillien [1982] argued that much of the rise in aggregate unemployment experienced in the 1970s and 1980s was attributable to increases in the natural rate of unemployment. These increases, he said, arose from shifts of demand between the different sectors of the national economy. These demand shifts increased unemployment because labor market frictions prevented the immediate reallocation of workers from declining sectors to expanding sectors. Lillien used a dispersion index of sectoral employment growth rates as a proxy for the extent of sectoral shifts and found that aggregate unemployment could be explained by this dispersion with a positive distributed lag.

Given the much discussed changing composition of output and employment in the U.S., this interpretation of unemployment quickly won adherents, such as Barro [1984]. More recent work by Abraham and Katz [1986] challenges this view. They argue that the rise in aggregate unemployment was attributable to aggregate demand disturbances. They showed that if sectors had different cyclical sensitivities, aggregate demand disturbances (such as those resulting from monetary policy or fluctuations in "animal spirits") could produce counter-cyclical fluctuations in the dispersion of sectoral employment growth rates. The finding that unemployment was a distributed lag of this dispersion did not, therefore, distinguish between the two hypotheses. Instead, Abraham and Katz found vacancy rates to be negatively related to dispersion with a distributed lag. They interpreted this result as confirmation of the aggregate demand hypothesis since it was consistent with a movement along the Beveridge curve.(1)

My paper further explores the relationships between sectoral shifts, aggregate unemployment and aggregate vacancies. The theoretical section demonstrates that sectoral shifts are also consistent with a movement along the Beveridge curve and a negative relation between vacancies and the dispersion of sectoral employment growth rates. This result potentially invalidates Abraham and Katz's claim, and at the same time provides a novel explanation of the Beveridge curve. In the empirical section I use the implications of the two hypotheses to decompose the dispersion of sectoral employment growth rates into parts attributable to sectoral shifts and aggregate shocks respectively. These new measures are then used to estimate the relative contributions of sectoral shifts and aggregate disturbances to aggregate unemployment.

This paper is linked to an emerging literature on the sources of macroeconomic fluctuations. The seminal paper by Long and Plosser [1983] showed how real business cycle models could explain comovements of output across sectors on the basis of sector-specific shocks. In a subsequent paper Long and Plosser [1987] sought to identify the relative importance of aggregate versus sector specific shocks. Using a single-factor model of output growth, they found that aggregate shocks explained only a relatively small amount of the convariation of output across sectors, and concluded that sectoral shocks are largely responsible for cyclical fluctuations. Norrbin and Schlagenhauf [1988; 1991] continued this line of research, but allowed for multiple factors. In addition, they sought to quantify the relative significance of sectoral versus aggregate shocks by decomposing the forecast error variance for individual industries into components explained by the aggregate and sectoral factors. My current paper is distinguished from previous research in both focus and methodology. First, I focus on the evolution of the aggregate rate of unemployment rather than the rate of output growth. Second, rather than adopting a VAR approach and decomposing forecast error variances, I attempt to explain the evolution of aggregate unemployment using a summary measure of sectoral shifts introduced by Lillien [1982], but with important innovations in the measure's construction.

Finally, the empirical decomposition of unemployment into parts attributable to sectoral and aggregate shocks is of considerable significance from a policy standpoint. If cyclical fluctuations in unemployment are largely attributable to sectoral shocks, this implies that increases in the unemployment rate represent increases in the non-accelerating inflation rate of unemployment (NAIRU), with depressed sectors characterized by high unemployment and booming sectors characterized by bottlenecks. In this case, attempts to reduce unemployment with macroeconomic measures are likely to have significant inflation costs. In contrast, if aggregate shocks explain cyclical fluctuations in the unemployment rate, this leaves open the possibility of a non-inflationary stabilization policy.

II. THE COMPETING THEORETICAL MODELS

The sectoral shift hypothesis

Lillien's model is derived from an earlier paper by Lucas and Prescott [1974] in which imperfect information concerning the location of new jobs gives rise to search unemployment. The logic of the model is easily illustrated. Aggregate unemployment, [U.sub.t], evolves according to (1) [U.sub.t] = [U.sub.t-1] + [S.sub.t] - [H.sub.t], where [S.sub.t] = current period separations,

[H.sub.t] = current period hires. Separations are assumed to depend on the extent of demand shifts between sectors. These shifts may be summarized by the statistic [[Sigma].sub.t] which measures the dispersion of sectoral demand shocks. Thus (2) [S.sub.t] = S([[Sigma].sub.t]), S'> O. Finally, new hires are assumed to be a constant proportion (k > 0) of last period's unemployment so that (3) [H.sub.t] = k [U.sub.t-1]. Solving the model given by equations (1)-(3) yields expecting equilibrium unemployment of (4) U* = S([Bar] [Sigma])/k, where [Bar] [Sigma] equals the expected dispersion of sectoral demand shocks. Temporary increases in the dispersion of sectoral demand disturbances ([Sigma.sub.t] > [Bar] [Sigma]) resulting from adverse random sectoral demand shocks can cause temporary increases in unemployment above [U.sup.*]. If the increase in dispersion is permanent, owing to a change in the probability distribution governing sectoral demand shocks, this will cause a permanent increase in [U.sup.*].

In order to test for the effect of sectoral shifts on aggregate unemployment, Lillien created a proxy statistic for [[Sigma].sub.t] given by (5) [Mathematical Expression Omitted] where n = the number of sectors

[s.sub.i,t] = share of ith sector

[g.sub.i,t] = rate of growth of

Lillien then used [Mathematical Expression Omitted] as an explanatory variable in regressions of the aggregate rate of unemployment and found it to have considerable explanatory power.

For current empirical purposes, the significant implication is that employment growth in an individual sector is determined mainly by the underlying sector trend combined with a random sector disturbance. Additionally, if there are convex firm-level costs of adjusting employment, past sector employment growth will help predict current sector employment growth since firms will smooth expansions and contractions of their workforces.

The aggregate disturbance hypothesis

Abraham and Katz [1986] challenge this explanation of dispersion in sectoral employment growth rates. They argue that the observed values of [[Sigma].sub.t] can also be explained by aggregate disturbances (they emphasize aggregate demand disturbances) if sectors differ in their sensitivity to aggregate disturbances. In this model employment in each sector is determined according to (6) [Mathematical Expression Omitted] where [N.sub.i,t] = the level of employment

[Mathematical Expression Omitted] = trend GNP,

In = natural log.

Then, for a two-sector model (i = 1,2) in which [[Alpha].sub.0,1] = [[Alpha].sub.0,2], employment growth dispersion is defined as (7) [Mathematical Expression Omitted] Assuming the two sectors are initially equal in size, [N.sub.1,t] = [N.sub.2,t], this is approximately equal to (8) [Mathematical Expression Omitted] In this case if ([[Alpha].sub.2,1] - [[Alpha].sub.2,2]) < 0, which implies that industry 2 is cyclically more sensitive than industry 1, the second term is positive when actual GNP is below trend and negative when it is above. The variable [[Sigma].sub.t] can therefore exhibit counter-cyclical variation.

The Abraham-Katz hypothesis is illustrated in Figure 1, which shows employment growth plotted against output growth. Point [gy.sup.*] represents the underlying growth of potential output. If output growth is greater than [gy.sup.*], the dispersion of employment growth across sectors narrows. Conversely, if output growth is less than [gy.sup.*], the dispersion widens. Putting the pieces together, the evolution of unemployment is explained as follows. As the economy enters recession, output growth drops below potential, dispersion widens, and unemployment starts to rise. As the economy exits recession, output growth increases above potential, dispersion narrows, and unemployment starts to fall. Finally, for the purposes of this paper, the significant implication of the aggregate demand hypothesis is that employment growth in an individual sector is explained by its own trend and its sensitivity to aggregate demand shocks. Essentially, the model is a single-factor model, and this factor affects all sectors in differing degrees. Thus contemporaneous employment growth in the rest of the economy will predict employment growth in an individual sector, and can therefore serve to proxy for the unobserved aggregate demand shock. Lastly, if there are convex costs of adjusting employment, firms will smooth changes in their workforces and aggregate disturbances will have a lagged effect on unemployment.

To test between these competing hypotheses concerning the determination of [[Sigma].sub.t], Abraham and Katz turned to the relationship between unemployment and vacancies (proxied by the help wanted index). Under the sectoral shift hypothesis, they argued, there should be a positive relationship between unemployment and vacancies, and [[Sigma].sub.t] should have a positive coefficient when used as an explanatory variable in regressions explaining vacancies. This is because shifts of demand cause increased job opportunities in sectors receiving positive shocks, which remain unfilled because of worker ignorance about the location of jobs or other labor market imperfections. In contrast the aggregate disturbance approach implies that unemployment and vacancies should be negatively correlated, and [[Sigma].sub.t] should have a negative coefficient in vacancy regressions since increases in [[Sigma].sub.t] are associated with aggregate output being below trend. Abraham and Katz found the latter to be the case in their vacancy regressions for both U.S. and British data, and they interpreted this finding as a rejection of the sectoral shift hypothesis.

Critique of the Abraham-Katz Hypothesis

The central piece of evidence which Abraham and Katz used to reject the sectoral shift hypothesis was that job vacancies (proxied by the ratio of the help wanted index to total non-agricultural employment) were negatively correlated with the dispersion of sectoral employment growth rates. Abraham and Katz interpreted this negative correlation as indicative of a movement along the Beveridge curve, which they claimed was consistent with the aggregate demand hypothesis. In contrast, they state, the sectoral shift hypothesis implies a positive correlation between vacancies and unemployment reflecting an outward expansion of the Beveridge curve. However, I argue below that a negative correlation between vacancies and unemployment is also consistent with the sectoral shift hypothesis if it is costly to hire new workers. This possibility undermines Abraham and Katz's claim to have unambiguously disproved the sectoral shift hypothesis.

To see this, consider the following simple model.(2) The model is not intended to be a full general equilibrium model, and it ignores the role of price adjustment in smoothing quantity fluctuations. Instead it is merely intended to convey the general reason why vacancies and unemployment may be negatively correlated in the presence of sectoral demand shifts. Aggregate unemployment, [U.sub.t], evolves according to (9) [U.sub.t] = [U.sub.t-1] + [S.sub.t] - [H.sub.t], where [S.sub.t] represents aggregate separations, which are given by (10) [Mathematical Expression Omitted] [H.sub.t] represents aggregate hires, which are given by (11) [Mathematical Expression Omitted] and n is the number of sectors. Separations at the sectoral level are given by (12) [Mathematical Expression Omitted] where [L.sub.i,t-1] = last period's employment,

[Mathematical Expression Omitted] = current period desired

When it comes to lay-offs, firms are assumed to adjust immediately to their desired workforce.(3) Total separations consist of quits and lay-offs (if positive). Hires at the sectoral level are given by (13) [H.sub.i,t] = Min [[Mathematica Expression Omitted], where [A.sub.i,t] = current period job

applicants,

[V.sub.i,t] = current period vacancies. Current period applicants are given by (14) [A.sub.i,t] = [U.sub.t-1]/n. Thus last period's unemployed are evenly spread across all sectors of the economy to become this period's job applicants. This is the same labor allocation mechanism as in Lucas and Prescott [1974]. Job vacancies are given by (15) [Mathematical Expression Omitted] The logic of this rule is as follows. Vacancies are zero if this period's desired labor force, [Mathematical Expression Omitted], is less than the existing labor force (1-q)[L.sub.t-1]. If the desired labor force exceeds the existing labor force, firms replace current period quits and there is an additional partial adjustment. The partial adjustment term reflects the fact that it is costly to add new workers, and these costs increase with the size of the addition.(4) The condition 0 < a < 1 ensures that vacancies are non-negative and that vacancies are less than the gap between desired and existing employment, i.e., the firm does not overshoot in its hiring. From (15) it then follows that if desired employment expands, firms increase their advertised vacancies. However, the actual adjustment to the desired level of employment is smoothed over a number of periods so that vacancies only increase a little initially.

Now let desired employment in each sector evolve according to (16) [Mathematical Expression Omitted] where [e.sub.e,t] is a random sectoral demand shock distributed in some unspecified way and has a zero mean. In this case, should a sector receive a negative demand shock, vacancies in that sector may drop to zero, and there is no need even to advertise to replace normal quits. At the same time other sectors hit with positive demand shocks will increase the level of their advertised vacancies. However, because of the partial adjustment mechanism governing additions to employment, this increase may not offset the decline in vacancies elsewhere. As a result, aggregate vacancies fall. The net effect is that aggregate unemployment rises while aggregate vacancies fall. Sectoral shifts in the presence of asymmetric hiring and firing costs can, therefore, trace out a Beveridge curve and explain movements along it.(5)

The relative size of industries may also matter. Suppose costs of hiring are a decreasing function of existing size.(6) Then, if sectors receiving negative shocks are large mature industries, while sectors receiving positive shocks are small emerging industries, the drop in vacancies may be substantial in absolute size in the mature sector and outweigh the smaller absolute gain in the emergent sector.

Lastly, if firms receiving negative demand shocks hoard labor because they know they will have to replace future costly quits, then vacancies at these firms will be zero for some time after. This means that sectoral shifts may have a negative influence on vacancies for a number of periods.

Given the above description of hiring and firing behavior, a shift of demand between sectors instantaneously raises aggregate unemployment and depresses aggregate vacancies. Vacancies remain low for a number of periods, while unemployment is high for a number of periods as growing industries gradually absorb the laid-off workers. There is some empirical support for this asymmetric pattern of employment adjustment. Neftci [1984] shows that increases in unemployment tend to be characterized by sudden jumps, while decreases involve gradual drops spread over a longer duration. This pattern is consistent with underlying firm behavior involving immediate layoffs and smoothed hiring.

III. THE RELATIVE IMPACT OF SECTORAL SHIFTS AND AGGREGATE DISTURBANCES: AN ECONOMETRIC MODEL

The above discussion shows that the correlation between vacancies and the dispersion of employment growth cannot be used to distinguish between the sectoral shifts and aggregate disturbance hypotheses. This is because both the sectoral shifts hypothesis and the aggregate disturbance hypothesis can predict a negative relationship between vacancies and the dispersion of sectoral employment growth. Therefore, the method adopted in the current paper is to decompose the dispersion of sectoral employment growth into a part attributable to sectoral factors and a part attributable to aggregate factors. I then use these separate measures to identify the relative contributions of sectoral and aggregate disturbances in explaining the rate of aggregate unemployment.

I used the following procedure for constructing the decomposed measures of employment growth dispersion. First, a regression was run determining the evolution of employment growth in each individual sector: (17) [Mathematical Expression Omitted] where [g.sub.i,t] = rate of employment growth

in the ith sector,

[g.sub.-i,t] = rate of aggregate

[e.sub.i,t] = residual. All growth rates were computed using the first difference of the natural log. The variable [g.sub.-i,t] was defined as follows: (18) [g.sub.-i,t] = 1n ([[N.sub.t] - [N.sub.i,t]]) - 1n ([[N.sub.t-1] - [N.sub.i,t-1]]), where [N.sub.t] = aggregate employment,

[N.sub.i,t] = employment in the ith

sector.

Equation (17) is a critical building block of the empirical model. Its purpose is to identify that part of a sector's employment growth which is attributable to sector-specific factors, and that part attributable to aggregate factors. The logic of this procedure is based on the inferential assumptions that underlie the Granger-causality literature. Thus aggregate influences were accounted for by looking at employment growth in the rest of the economy: to the extent that employment growth in an individual sector was Granger-caused by growth in the rest of the economy this suggests the influence of aggregate forces. The effects of contemporaneous aggregate disturbances were accounted for by including the current rate of employment growth in the rest of the economy as an independent variable.

Analogously, to capture sector-specific factors I looked at the extent to which lagged sectoral employment growth Granger-caused current sectoral employment growth. Additionally, the effect of contemporaneous sector-specific disturbances were accounted for by treating the residual as part of the sector-specific component. Finally, note that the definition of the aggregate rate of employment growth given by (18) ensures the removal of any direct influence of the dependent variable in (17) on the rate of aggregate employment growth.

One caveat regarding the above methodology relates to the possibility of incorrectly attributing causality if there are contemporaneous spill-overs between sectors. In the current application, if there are strong within-quarter inter-sectoral multipliers, sector specific shocks could have an immediate effect on output and employment in the rest of the economy. In this case, given the specification of equation (17), such shocks might be incorrectly counted as part of the aggregate factor, [g.sub.-i,t]. In effect, there is a possible problem of simultaneity bias with the left-hand-side variable impacting the right-hand-side regressor. To address this problem, equation (17) was estimated using the Fair[1970] two-stage least squares estimator. The instruments for [g.sub.-i,t], were the current and four lagged values of the three-month treasury bill, and four lagged values of aggregate output growth. The use of the treasury bill rate as an instrument reflects the belief that monetary policy targets short-term interest rates, so that they are therefore exogenous. Aggregate output growth was computed in a manner analogous to equation (18).

Having estimated (17) for each sector, the next step involved decomposing the rate of employment growth in each sector into a part attributable to sector specific and sectoral shift factors, and that part attributable to aggregate factors. The component attributable to sectoral influences was defined as (19) [Mathematical Expression Omitted] while the component attributable to aggregate influences was given by (20) [Mathematical Expression Omitted] Using equation (19) the dispersion in sectoral employment growth rates attributable to sectoral influences was calculated as (21) [Mathematical Expression Omitted] where [s.sub.i,t] = share of ith sector

[[Bar] Z.sub.t] = average employment growth

(22) [Mathematical Expression Omitted] The dispersion in sectoral employment growth rates attributable to aggregate influences was calculated as (23) [Mathematical Expression Omitted] where [[Bar] X.sub.t] = average employment growth attributable to aggregate influences. [X.sub.t] was computed as (24) [Mathematical Expression Omitted] The variables [[Sigma].sub.Z,t] and [[Sigma].sub.X,t] bear the following interpretations. [[Sigma].sub.Z,t] captures the dispersion in employment growth rates arising from pure sectoral influences which were relevant for the sectoral shift hypothesis. [[Sigma].sub.X,t] captures the influence of aggregate disturbances on sectoral employment growth rates which were relevant to the aggregate disturbance hypothesis.

The variables [[Sigma].sub.Z,t] and [[Sigma].sub.X,t] were then used in regressions of aggregate unemployment given by (25) [Mathematical Expression Omitted] The coefficients attaching to [[Sigma].sub.Z] and [[Sigma].sub.X] reveal the relative sensitivity of aggregate unemployment to sectoral shifts and aggregate disturbances.(7)

IV. THE DATA AND RESULTS

The data used for estimating the model are form the Citibase Data Bank and were quarterly and seasonally adjusted. The sample period was 1948:III-1988:II. Two-stage least squares regressions of equation (17) were run for the eleven different sectors into which aggregate non-agricultural employment is decomposed: the results are shown in Table I. These results were then used to compute values of [[Sigma].sub.X] and [[Sigma].sub.Z] per the formulae in (21)-(24). These constructed variables were, in turn, used in estimating equation (25) to estimate the effect of dispersion in sectoral employment growth rates on aggregate unemployment.

The results of these further regressions are shown in Table II. A number of different functional specifications, including log and semi-log transformations, were estimated to test for any non-linearities in the relationship, but only the simple linear form is reported. All regressions were estimated using a maximum likelihood procedure with a correction for second-order serial correlation. The coefficients of [[Sigma].sub.X] are negative. This suggests, contrary to Abraham and Katz, that positive aggregate disturbances cause the dispersion of sectoral employment growth to widen. Three out of four coefficients for [[Sigma].sub.Z] are positive, with the current and once lagged values having large and statistically significant coefficients. This pattern of signing confirms the hypothesis that sectoral shifts raise unemployment.

The dispersion variables, [[Sigma].sub.X] and [[Sigma].sub.Z] are generated regressors. Pagan [1984] explains why the standard errors obtained from single-stage estimates using such regressors may be inconsistent. In the current application, the generation of [[Sigma].sub.x] per equation (17) involves the contemporaneous rate of growth of aggregate employment, and this variable may be correlated with the error term in equation (25). To correct for this problem, equation (25) was re-estimated using the Fair [1970] two-stage least squares estimator with a correction for second-order serial correlation.(8) The estimates obtained from this procedure are shown in the right-hand column of table (2). The results from these two-stage estimates are fully consistent with the earlier single-stage estimates with the sums of the regression coefficients of [[Sigma].sub.z] being positive. To test for specification bias, I applied Hausman [1978] t-tests. The tests revealed no indication of specification bias at the 95 percent confidence interval.

Further diagnostic tests were then applied to test for the appropriateness of the functional form and higher-order autocorrelation in the errors. Following Pagan [1984] the correctness of the specified functional form was tested by regressing the residuals from equation (25) against transformed values of the right-hand-side variables. No correlations between the residuals and the transformed variables were found. To test for higher-order autocorrelation, the residuals of the without instruments estimate in Table II were examined for fourth-order serial correlation using the procedure developed by Godfrey [1978]. No evidence of the problem was found.(9)

Following Abraham and Katz, regressions showing the relationship between vacancies and the dispersion of sectoral employment growth rates were also estimated. Aggregate vacancies were proxied by a normalized help wanted index (VAC) which was defined as the ratio of the help wanted index to total non-agricultural employment. The estimated equation was of the form (26) [Mathematical Expression Omitted] Results of this regression for the sample period 1952:I-1988:II are shown in columns one and two of Table III. The regression was again estimated using a maximum likelihood procedure with correction for second-order serial correlation. I also estimated the equation in semi-log form to check for any non-linearities, though only the simple linear form is reported. The results shown in Table III are consistent with the earlier theoretical model which explained why sectoral shifts could cause a reduction in vacancies. This is seen by the negative coefficients of [[Sigma].sub.Z]

The diagnostic procedures used above on the unemployment equation were also applied to the vacancy equation. To address the problem of generated regressors, I re-estimated equation (26) using two-stage least squares with a correction for second-order serial correlation. The instruments for [[Sigma].sub.X,t] were the same as above. These estimates are shown in the right-hand-side righthand column of Table III. Once again, Hausman t-tests were applied to the coefficients to test for specification errors, and again there was no evidence for specification bias.

Finally, the same tests regarding functional form and higher-order autocorrelation which were applied to the unemployment equation were also applied to the vacancy equation. No problems in connection with these tests were found.(10) In sum, the evidence is consistent with sectoral shifts having a small negative effect on aggregate vacancies.

V. THE CONTRIBUTION OF SECTORAL SHIFTS TO AGGREGATE UNEMPLOYMENT

The model estimated in the previous section was then used to compute the contribution of sectoral shifts to aggregate unemployment. This was computed using the estimates of equation (25) contained in the first column of Table II, as follows: (27) [Mathematical Expression Omitted] (28) [Mathematical Expression Omitted] Technically [Mathematical Expression Omitted] is a function of the entire history of [Mathematical Expression Omitted] but for computational purposes i was restricted to thirty lags. The series [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are shown in Table IV. The evidence from these series rejects the hypothesis that cyclical fluctuations in the aggregate unemployment rate can be explained by sectoral shifts. Instead, aggregate disturbances explain almost all of the fluctuation. Across the sample period the rate of sectoral shift unemployment is relatively stable as evidenced in Table V. For the sample period, 1957:I-1973:IV the mean rate is 4.51 percent, while for the sample period 1974:I-1988:IV it is 4.62 percent. Lillien's claim to have explained fluctuations in the aggregate rate of unemployment as arising from sectoral shifts of employment demand therefore stands rejected according to the current evidence. That said, however, the evidence also reveals that sectoral shifts account for a substantial, albeit stable, component of aggregate unemployment. If we interpret this component as the natural rate of unemployment, this suggests that full-employment for the U.S. economy currently involves an unemployment rate between 4.5 percent and 5 percent.

VI. CONCLUSION

Abraham and Katz [1986] challenged Lillien's [1982] claim that sectoral shifts are important for explaining the aggregate rate of unemployment. They claimed that the sectoral shift hypothesis implied a positive relationship between aggregate unemployment and aggregate vacancies reflecting a radial expansion outward of the Beveridge curve. In regressions using a proxy for vacancies against a proxy for sectoral shifts they found a negative relationship, and they therefore concluded that the sectoral shift hypothesis was inconsistent with the empirical evidence. The current paper has provided theoretical arguments explaining why Abraham and Katz's conclusion is unjustified. This is because sectoral shifts can generate a negative relationship between unemployment and vacancies if there are asymmetric costs of adjusting labor inputs--specifically, if costs of hiring exceed costs of layoffs. In this case, sectors that receive negative shocks immediately lay off workers, while sectors that receive positive demand shocks expand their workforces only gradually. To test for this effect, I decomposed the dispersion of sectoral employment growth into components attributable to aggregate disturbances and sector-specific influences respectively. The regression results revealed a positive relationship between aggregate unemployment and the proxy for sectoral shifts, and a negative relationship between the vacancy proxy and the sectoral shift proxy. These results are consistent with the theoretical model describing the impact of sectoral shifts on unemployment and vacancies. However, although sectoral shifts do contribute positively to aggregate unemployment, the model and the data reveal that they are unable to account for the large cyclical variation in unemployment, which is better explained by aggregate disturbances.

TABLE II

Estimates of the aggregate unemployment rate per equation (25)

Note: The sample period was 1951:II-1988:II, and figures in parentheses are t-statistics.

TABLE IV

Shows the series for aggregate unemployment, unemployment atrributable to sectoral

TABLE V

Shows the mean values of U U*, and U - U* for various sample

[Table I & III Omitted] [Figure 1 Omitted]

(1)The Beveridge Curve describes the relationship between vacancies and the rate of unemployment. (2)The model developed here is similar to a model by Weiss (1984) that is described by Abraham and Katz. However, the model is extended to include vacancies and therefore provides an explanation of the unemployment-vacancy relationship. (3)The assumption of costless layoffs is extreme. If there are some convex costs to layoffs, they will be smoothed. For purposes of the current argument all that is required is that layoff adjustments be more rapid than new hires. This is most easily managed by assuming instant layoffs. (4)The vacancy rule given by equation (15) may be interpreted as an approximation to an optimal adjustment rule in the presence of zero firing costs and convex hiring costs. The one complication which is not accounted for is that if the current labor force were greater than the desired labor force the firm might still hire additional (temporarily surplus) workers so as to save a little next period when it anticipates replacing quits. (5)Asymmetric hiring and firing costs therefore provide a novel explanation complements a recent search theoretic explanation advanced by Blanchard and Diamond [1989]. (6)This is a standard argument in the investment literature. (7)The regression given by equation (25) differs from that used by Lillien and by Abraham and Katz not only in its decomposition of the dispersion variable, but also in its exclusion of an unanticipated monetary policy variable. The inclusion of this variable would be important if one were interested in constructing a series for the natural rate and subscribed to the anticipated policy ineffectiveness proposition. (8)The instruments used to proxy for [Sigma] [.sub.x] (0) were four lagged values of the unemployment rate and two lagged values of aggregate employment growth. (9)The Godfrey statistic was 2.03 while the critical value under the Chi-square distribution with fifteen degrees of freedom at the 95 percent confidence level was 7.26. (10)The Godfrey statistic was 6.10 while the critical Chi with 15 degrees of freedom at the 95 percent confidence level was 7.26.

REFERENCES

Abraham, K. G., and L. F. Katz. "Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances." Journal of Political Economy, June 1986, 507-22. Barro, R. J. "Rational Expectations and Macroeconomics in 1984." American Economic Review, Papers and Proceedings, May 1984, 179-82. Blanchard, O. J., and P. Diamond. "The Beveridge Curve." Brookings Papers on Economic Activity 1, 1989, 1-60. Fair, R.C. "The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Correlated Errors." Econometria, May 1970, 507-16. Godfrey, L. G. "Testing for Higher Order Serial Correlation in Regression Equations when the Regressors include Lagged Dependent Variables." Econometrica, November 1978, 1303-10. Hausman, J. A. "Specification Tests in Econometrics." Econometrica, November 1978, 1251-71. Lillien, D. M. "Sectoral Shifts and Cyclical Unemployment." Journal of Political Economy, August 1982, 777-93. Long, J. B., and C. I. Plosser. "Real Business Cycles." Journal of Political Economy, 91(1), 1983, 39-69. __. "Sectoral Versus Aggregate Shocks in the Business Cycle." American Economic Review, Papers and Proceedings, May 1987, 333-36. Lucas, R. E., Jr., and E. C. Prescott. "Equilibrium Search and Unemployment." Journal of Economic Theory, February 1974, 188-209. Neftci, S. N. "Are Economic Time Series Asymmetric over the Business Cycle?" Journal of Political Economy, February 1984, 307-28. Norrbin, S. C., and D. E. Schlagenhauf. "An Inquiry into the Sources of Macroeconomic Fluctuations." Journal of Monetary Economics, 1988, 22(1), 43-70. __. "The Importance of Sectoral and Aggregate Shocks in Business Cycles." Economic Inquiry, April 1991, 317-35. Pagan, A. "Econometric Issues in the Analysis of Regressions with Generated Regressors." International Economic Review, February 1984, 221-47. __. "Model Evaluation by Variable Addition," in Econometrics and Quantitative Economics, edited by D. F. Hendry and K. F. Wallis. Oxford: Basic Blackwell, 1984, 103-33. Weiss, L. "Asymmetric Adjustment Costs and Sectoral Shifts." Mimeo, University of Chicago, Department of Economics, 1984.

THOMAS I. PALLEY, Assistant Professor, New School for Social Research, New York.

The debate over the relative importance of sectoral and aggregate shocks in

explaining fluctuations in the aggregate unemployment rate has centered on the relationship

between unemployment, job vacancies, and the dispersion of sectoral employment

growth rates (which proxies for sectoral shocks). This paper examines some possible

theoretical relationships between these variables, and, after decomposing

unemployment into components attributable to sectoral and aggregate shocks, estimates the

importance of each. If finds that fluctuations in unemployment are principally caused

by aggregate shocks, but sectoral shifts explain a significant, albeit steady, amount of

unemployment.

I. INTRODUCTION

In a controversial paper Lillien [1982] argued that much of the rise in aggregate unemployment experienced in the 1970s and 1980s was attributable to increases in the natural rate of unemployment. These increases, he said, arose from shifts of demand between the different sectors of the national economy. These demand shifts increased unemployment because labor market frictions prevented the immediate reallocation of workers from declining sectors to expanding sectors. Lillien used a dispersion index of sectoral employment growth rates as a proxy for the extent of sectoral shifts and found that aggregate unemployment could be explained by this dispersion with a positive distributed lag.

Given the much discussed changing composition of output and employment in the U.S., this interpretation of unemployment quickly won adherents, such as Barro [1984]. More recent work by Abraham and Katz [1986] challenges this view. They argue that the rise in aggregate unemployment was attributable to aggregate demand disturbances. They showed that if sectors had different cyclical sensitivities, aggregate demand disturbances (such as those resulting from monetary policy or fluctuations in "animal spirits") could produce counter-cyclical fluctuations in the dispersion of sectoral employment growth rates. The finding that unemployment was a distributed lag of this dispersion did not, therefore, distinguish between the two hypotheses. Instead, Abraham and Katz found vacancy rates to be negatively related to dispersion with a distributed lag. They interpreted this result as confirmation of the aggregate demand hypothesis since it was consistent with a movement along the Beveridge curve.(1)

My paper further explores the relationships between sectoral shifts, aggregate unemployment and aggregate vacancies. The theoretical section demonstrates that sectoral shifts are also consistent with a movement along the Beveridge curve and a negative relation between vacancies and the dispersion of sectoral employment growth rates. This result potentially invalidates Abraham and Katz's claim, and at the same time provides a novel explanation of the Beveridge curve. In the empirical section I use the implications of the two hypotheses to decompose the dispersion of sectoral employment growth rates into parts attributable to sectoral shifts and aggregate shocks respectively. These new measures are then used to estimate the relative contributions of sectoral shifts and aggregate disturbances to aggregate unemployment.

This paper is linked to an emerging literature on the sources of macroeconomic fluctuations. The seminal paper by Long and Plosser [1983] showed how real business cycle models could explain comovements of output across sectors on the basis of sector-specific shocks. In a subsequent paper Long and Plosser [1987] sought to identify the relative importance of aggregate versus sector specific shocks. Using a single-factor model of output growth, they found that aggregate shocks explained only a relatively small amount of the convariation of output across sectors, and concluded that sectoral shocks are largely responsible for cyclical fluctuations. Norrbin and Schlagenhauf [1988; 1991] continued this line of research, but allowed for multiple factors. In addition, they sought to quantify the relative significance of sectoral versus aggregate shocks by decomposing the forecast error variance for individual industries into components explained by the aggregate and sectoral factors. My current paper is distinguished from previous research in both focus and methodology. First, I focus on the evolution of the aggregate rate of unemployment rather than the rate of output growth. Second, rather than adopting a VAR approach and decomposing forecast error variances, I attempt to explain the evolution of aggregate unemployment using a summary measure of sectoral shifts introduced by Lillien [1982], but with important innovations in the measure's construction.

Finally, the empirical decomposition of unemployment into parts attributable to sectoral and aggregate shocks is of considerable significance from a policy standpoint. If cyclical fluctuations in unemployment are largely attributable to sectoral shocks, this implies that increases in the unemployment rate represent increases in the non-accelerating inflation rate of unemployment (NAIRU), with depressed sectors characterized by high unemployment and booming sectors characterized by bottlenecks. In this case, attempts to reduce unemployment with macroeconomic measures are likely to have significant inflation costs. In contrast, if aggregate shocks explain cyclical fluctuations in the unemployment rate, this leaves open the possibility of a non-inflationary stabilization policy.

II. THE COMPETING THEORETICAL MODELS

The sectoral shift hypothesis

Lillien's model is derived from an earlier paper by Lucas and Prescott [1974] in which imperfect information concerning the location of new jobs gives rise to search unemployment. The logic of the model is easily illustrated. Aggregate unemployment, [U.sub.t], evolves according to (1) [U.sub.t] = [U.sub.t-1] + [S.sub.t] - [H.sub.t], where [S.sub.t] = current period separations,

[H.sub.t] = current period hires. Separations are assumed to depend on the extent of demand shifts between sectors. These shifts may be summarized by the statistic [[Sigma].sub.t] which measures the dispersion of sectoral demand shocks. Thus (2) [S.sub.t] = S([[Sigma].sub.t]), S'> O. Finally, new hires are assumed to be a constant proportion (k > 0) of last period's unemployment so that (3) [H.sub.t] = k [U.sub.t-1]. Solving the model given by equations (1)-(3) yields expecting equilibrium unemployment of (4) U* = S([Bar] [Sigma])/k, where [Bar] [Sigma] equals the expected dispersion of sectoral demand shocks. Temporary increases in the dispersion of sectoral demand disturbances ([Sigma.sub.t] > [Bar] [Sigma]) resulting from adverse random sectoral demand shocks can cause temporary increases in unemployment above [U.sup.*]. If the increase in dispersion is permanent, owing to a change in the probability distribution governing sectoral demand shocks, this will cause a permanent increase in [U.sup.*].

In order to test for the effect of sectoral shifts on aggregate unemployment, Lillien created a proxy statistic for [[Sigma].sub.t] given by (5) [Mathematical Expression Omitted] where n = the number of sectors

[s.sub.i,t] = share of ith sector

employment in total employment,

[g.sub.i,t] = rate of growth of

employment the ith sector, [g.sub.t] = rate of growth of aggregate employment.

Lillien then used [Mathematical Expression Omitted] as an explanatory variable in regressions of the aggregate rate of unemployment and found it to have considerable explanatory power.

For current empirical purposes, the significant implication is that employment growth in an individual sector is determined mainly by the underlying sector trend combined with a random sector disturbance. Additionally, if there are convex firm-level costs of adjusting employment, past sector employment growth will help predict current sector employment growth since firms will smooth expansions and contractions of their workforces.

The aggregate disturbance hypothesis

Abraham and Katz [1986] challenge this explanation of dispersion in sectoral employment growth rates. They argue that the observed values of [[Sigma].sub.t] can also be explained by aggregate disturbances (they emphasize aggregate demand disturbances) if sectors differ in their sensitivity to aggregate disturbances. In this model employment in each sector is determined according to (6) [Mathematical Expression Omitted] where [N.sub.i,t] = the level of employment

in the ith sector, T = time trend, [Y.sub.t] = actual GNP,

[Mathematical Expression Omitted] = trend GNP,

In = natural log.

Then, for a two-sector model (i = 1,2) in which [[Alpha].sub.0,1] = [[Alpha].sub.0,2], employment growth dispersion is defined as (7) [Mathematical Expression Omitted] Assuming the two sectors are initially equal in size, [N.sub.1,t] = [N.sub.2,t], this is approximately equal to (8) [Mathematical Expression Omitted] In this case if ([[Alpha].sub.2,1] - [[Alpha].sub.2,2]) < 0, which implies that industry 2 is cyclically more sensitive than industry 1, the second term is positive when actual GNP is below trend and negative when it is above. The variable [[Sigma].sub.t] can therefore exhibit counter-cyclical variation.

The Abraham-Katz hypothesis is illustrated in Figure 1, which shows employment growth plotted against output growth. Point [gy.sup.*] represents the underlying growth of potential output. If output growth is greater than [gy.sup.*], the dispersion of employment growth across sectors narrows. Conversely, if output growth is less than [gy.sup.*], the dispersion widens. Putting the pieces together, the evolution of unemployment is explained as follows. As the economy enters recession, output growth drops below potential, dispersion widens, and unemployment starts to rise. As the economy exits recession, output growth increases above potential, dispersion narrows, and unemployment starts to fall. Finally, for the purposes of this paper, the significant implication of the aggregate demand hypothesis is that employment growth in an individual sector is explained by its own trend and its sensitivity to aggregate demand shocks. Essentially, the model is a single-factor model, and this factor affects all sectors in differing degrees. Thus contemporaneous employment growth in the rest of the economy will predict employment growth in an individual sector, and can therefore serve to proxy for the unobserved aggregate demand shock. Lastly, if there are convex costs of adjusting employment, firms will smooth changes in their workforces and aggregate disturbances will have a lagged effect on unemployment.

To test between these competing hypotheses concerning the determination of [[Sigma].sub.t], Abraham and Katz turned to the relationship between unemployment and vacancies (proxied by the help wanted index). Under the sectoral shift hypothesis, they argued, there should be a positive relationship between unemployment and vacancies, and [[Sigma].sub.t] should have a positive coefficient when used as an explanatory variable in regressions explaining vacancies. This is because shifts of demand cause increased job opportunities in sectors receiving positive shocks, which remain unfilled because of worker ignorance about the location of jobs or other labor market imperfections. In contrast the aggregate disturbance approach implies that unemployment and vacancies should be negatively correlated, and [[Sigma].sub.t] should have a negative coefficient in vacancy regressions since increases in [[Sigma].sub.t] are associated with aggregate output being below trend. Abraham and Katz found the latter to be the case in their vacancy regressions for both U.S. and British data, and they interpreted this finding as a rejection of the sectoral shift hypothesis.

Critique of the Abraham-Katz Hypothesis

The central piece of evidence which Abraham and Katz used to reject the sectoral shift hypothesis was that job vacancies (proxied by the ratio of the help wanted index to total non-agricultural employment) were negatively correlated with the dispersion of sectoral employment growth rates. Abraham and Katz interpreted this negative correlation as indicative of a movement along the Beveridge curve, which they claimed was consistent with the aggregate demand hypothesis. In contrast, they state, the sectoral shift hypothesis implies a positive correlation between vacancies and unemployment reflecting an outward expansion of the Beveridge curve. However, I argue below that a negative correlation between vacancies and unemployment is also consistent with the sectoral shift hypothesis if it is costly to hire new workers. This possibility undermines Abraham and Katz's claim to have unambiguously disproved the sectoral shift hypothesis.

To see this, consider the following simple model.(2) The model is not intended to be a full general equilibrium model, and it ignores the role of price adjustment in smoothing quantity fluctuations. Instead it is merely intended to convey the general reason why vacancies and unemployment may be negatively correlated in the presence of sectoral demand shifts. Aggregate unemployment, [U.sub.t], evolves according to (9) [U.sub.t] = [U.sub.t-1] + [S.sub.t] - [H.sub.t], where [S.sub.t] represents aggregate separations, which are given by (10) [Mathematical Expression Omitted] [H.sub.t] represents aggregate hires, which are given by (11) [Mathematical Expression Omitted] and n is the number of sectors. Separations at the sectoral level are given by (12) [Mathematical Expression Omitted] where [L.sub.i,t-1] = last period's employment,

[Mathematical Expression Omitted] = current period desired

employment, q = fixed quit rate.

When it comes to lay-offs, firms are assumed to adjust immediately to their desired workforce.(3) Total separations consist of quits and lay-offs (if positive). Hires at the sectoral level are given by (13) [H.sub.i,t] = Min [[Mathematica Expression Omitted], where [A.sub.i,t] = current period job

applicants,

[V.sub.i,t] = current period vacancies. Current period applicants are given by (14) [A.sub.i,t] = [U.sub.t-1]/n. Thus last period's unemployed are evenly spread across all sectors of the economy to become this period's job applicants. This is the same labor allocation mechanism as in Lucas and Prescott [1974]. Job vacancies are given by (15) [Mathematical Expression Omitted] The logic of this rule is as follows. Vacancies are zero if this period's desired labor force, [Mathematical Expression Omitted], is less than the existing labor force (1-q)[L.sub.t-1]. If the desired labor force exceeds the existing labor force, firms replace current period quits and there is an additional partial adjustment. The partial adjustment term reflects the fact that it is costly to add new workers, and these costs increase with the size of the addition.(4) The condition 0 < a < 1 ensures that vacancies are non-negative and that vacancies are less than the gap between desired and existing employment, i.e., the firm does not overshoot in its hiring. From (15) it then follows that if desired employment expands, firms increase their advertised vacancies. However, the actual adjustment to the desired level of employment is smoothed over a number of periods so that vacancies only increase a little initially.

Now let desired employment in each sector evolve according to (16) [Mathematical Expression Omitted] where [e.sub.e,t] is a random sectoral demand shock distributed in some unspecified way and has a zero mean. In this case, should a sector receive a negative demand shock, vacancies in that sector may drop to zero, and there is no need even to advertise to replace normal quits. At the same time other sectors hit with positive demand shocks will increase the level of their advertised vacancies. However, because of the partial adjustment mechanism governing additions to employment, this increase may not offset the decline in vacancies elsewhere. As a result, aggregate vacancies fall. The net effect is that aggregate unemployment rises while aggregate vacancies fall. Sectoral shifts in the presence of asymmetric hiring and firing costs can, therefore, trace out a Beveridge curve and explain movements along it.(5)

The relative size of industries may also matter. Suppose costs of hiring are a decreasing function of existing size.(6) Then, if sectors receiving negative shocks are large mature industries, while sectors receiving positive shocks are small emerging industries, the drop in vacancies may be substantial in absolute size in the mature sector and outweigh the smaller absolute gain in the emergent sector.

Lastly, if firms receiving negative demand shocks hoard labor because they know they will have to replace future costly quits, then vacancies at these firms will be zero for some time after. This means that sectoral shifts may have a negative influence on vacancies for a number of periods.

Given the above description of hiring and firing behavior, a shift of demand between sectors instantaneously raises aggregate unemployment and depresses aggregate vacancies. Vacancies remain low for a number of periods, while unemployment is high for a number of periods as growing industries gradually absorb the laid-off workers. There is some empirical support for this asymmetric pattern of employment adjustment. Neftci [1984] shows that increases in unemployment tend to be characterized by sudden jumps, while decreases involve gradual drops spread over a longer duration. This pattern is consistent with underlying firm behavior involving immediate layoffs and smoothed hiring.

III. THE RELATIVE IMPACT OF SECTORAL SHIFTS AND AGGREGATE DISTURBANCES: AN ECONOMETRIC MODEL

The above discussion shows that the correlation between vacancies and the dispersion of employment growth cannot be used to distinguish between the sectoral shifts and aggregate disturbance hypotheses. This is because both the sectoral shifts hypothesis and the aggregate disturbance hypothesis can predict a negative relationship between vacancies and the dispersion of sectoral employment growth. Therefore, the method adopted in the current paper is to decompose the dispersion of sectoral employment growth into a part attributable to sectoral factors and a part attributable to aggregate factors. I then use these separate measures to identify the relative contributions of sectoral and aggregate disturbances in explaining the rate of aggregate unemployment.

I used the following procedure for constructing the decomposed measures of employment growth dispersion. First, a regression was run determining the evolution of employment growth in each individual sector: (17) [Mathematical Expression Omitted] where [g.sub.i,t] = rate of employment growth

in the ith sector,

[g.sub.-i,t] = rate of aggregate

employment growth excluding sector i, T = time trend,

[e.sub.i,t] = residual. All growth rates were computed using the first difference of the natural log. The variable [g.sub.-i,t] was defined as follows: (18) [g.sub.-i,t] = 1n ([[N.sub.t] - [N.sub.i,t]]) - 1n ([[N.sub.t-1] - [N.sub.i,t-1]]), where [N.sub.t] = aggregate employment,

[N.sub.i,t] = employment in the ith

sector.

Equation (17) is a critical building block of the empirical model. Its purpose is to identify that part of a sector's employment growth which is attributable to sector-specific factors, and that part attributable to aggregate factors. The logic of this procedure is based on the inferential assumptions that underlie the Granger-causality literature. Thus aggregate influences were accounted for by looking at employment growth in the rest of the economy: to the extent that employment growth in an individual sector was Granger-caused by growth in the rest of the economy this suggests the influence of aggregate forces. The effects of contemporaneous aggregate disturbances were accounted for by including the current rate of employment growth in the rest of the economy as an independent variable.

Analogously, to capture sector-specific factors I looked at the extent to which lagged sectoral employment growth Granger-caused current sectoral employment growth. Additionally, the effect of contemporaneous sector-specific disturbances were accounted for by treating the residual as part of the sector-specific component. Finally, note that the definition of the aggregate rate of employment growth given by (18) ensures the removal of any direct influence of the dependent variable in (17) on the rate of aggregate employment growth.

One caveat regarding the above methodology relates to the possibility of incorrectly attributing causality if there are contemporaneous spill-overs between sectors. In the current application, if there are strong within-quarter inter-sectoral multipliers, sector specific shocks could have an immediate effect on output and employment in the rest of the economy. In this case, given the specification of equation (17), such shocks might be incorrectly counted as part of the aggregate factor, [g.sub.-i,t]. In effect, there is a possible problem of simultaneity bias with the left-hand-side variable impacting the right-hand-side regressor. To address this problem, equation (17) was estimated using the Fair[1970] two-stage least squares estimator. The instruments for [g.sub.-i,t], were the current and four lagged values of the three-month treasury bill, and four lagged values of aggregate output growth. The use of the treasury bill rate as an instrument reflects the belief that monetary policy targets short-term interest rates, so that they are therefore exogenous. Aggregate output growth was computed in a manner analogous to equation (18).

Having estimated (17) for each sector, the next step involved decomposing the rate of employment growth in each sector into a part attributable to sector specific and sectoral shift factors, and that part attributable to aggregate factors. The component attributable to sectoral influences was defined as (19) [Mathematical Expression Omitted] while the component attributable to aggregate influences was given by (20) [Mathematical Expression Omitted] Using equation (19) the dispersion in sectoral employment growth rates attributable to sectoral influences was calculated as (21) [Mathematical Expression Omitted] where [s.sub.i,t] = share of ith sector

employment in total employment,

[[Bar] Z.sub.t] = average employment growth

attributable to sectoral influences. [[Bar] Z.sub.t] was computed as

(22) [Mathematical Expression Omitted] The dispersion in sectoral employment growth rates attributable to aggregate influences was calculated as (23) [Mathematical Expression Omitted] where [[Bar] X.sub.t] = average employment growth attributable to aggregate influences. [X.sub.t] was computed as (24) [Mathematical Expression Omitted] The variables [[Sigma].sub.Z,t] and [[Sigma].sub.X,t] bear the following interpretations. [[Sigma].sub.Z,t] captures the dispersion in employment growth rates arising from pure sectoral influences which were relevant for the sectoral shift hypothesis. [[Sigma].sub.X,t] captures the influence of aggregate disturbances on sectoral employment growth rates which were relevant to the aggregate disturbance hypothesis.

The variables [[Sigma].sub.Z,t] and [[Sigma].sub.X,t] were then used in regressions of aggregate unemployment given by (25) [Mathematical Expression Omitted] The coefficients attaching to [[Sigma].sub.Z] and [[Sigma].sub.X] reveal the relative sensitivity of aggregate unemployment to sectoral shifts and aggregate disturbances.(7)

IV. THE DATA AND RESULTS

The data used for estimating the model are form the Citibase Data Bank and were quarterly and seasonally adjusted. The sample period was 1948:III-1988:II. Two-stage least squares regressions of equation (17) were run for the eleven different sectors into which aggregate non-agricultural employment is decomposed: the results are shown in Table I. These results were then used to compute values of [[Sigma].sub.X] and [[Sigma].sub.Z] per the formulae in (21)-(24). These constructed variables were, in turn, used in estimating equation (25) to estimate the effect of dispersion in sectoral employment growth rates on aggregate unemployment.

The results of these further regressions are shown in Table II. A number of different functional specifications, including log and semi-log transformations, were estimated to test for any non-linearities in the relationship, but only the simple linear form is reported. All regressions were estimated using a maximum likelihood procedure with a correction for second-order serial correlation. The coefficients of [[Sigma].sub.X] are negative. This suggests, contrary to Abraham and Katz, that positive aggregate disturbances cause the dispersion of sectoral employment growth to widen. Three out of four coefficients for [[Sigma].sub.Z] are positive, with the current and once lagged values having large and statistically significant coefficients. This pattern of signing confirms the hypothesis that sectoral shifts raise unemployment.

The dispersion variables, [[Sigma].sub.X] and [[Sigma].sub.Z] are generated regressors. Pagan [1984] explains why the standard errors obtained from single-stage estimates using such regressors may be inconsistent. In the current application, the generation of [[Sigma].sub.x] per equation (17) involves the contemporaneous rate of growth of aggregate employment, and this variable may be correlated with the error term in equation (25). To correct for this problem, equation (25) was re-estimated using the Fair [1970] two-stage least squares estimator with a correction for second-order serial correlation.(8) The estimates obtained from this procedure are shown in the right-hand column of table (2). The results from these two-stage estimates are fully consistent with the earlier single-stage estimates with the sums of the regression coefficients of [[Sigma].sub.z] being positive. To test for specification bias, I applied Hausman [1978] t-tests. The tests revealed no indication of specification bias at the 95 percent confidence interval.

Further diagnostic tests were then applied to test for the appropriateness of the functional form and higher-order autocorrelation in the errors. Following Pagan [1984] the correctness of the specified functional form was tested by regressing the residuals from equation (25) against transformed values of the right-hand-side variables. No correlations between the residuals and the transformed variables were found. To test for higher-order autocorrelation, the residuals of the without instruments estimate in Table II were examined for fourth-order serial correlation using the procedure developed by Godfrey [1978]. No evidence of the problem was found.(9)

Following Abraham and Katz, regressions showing the relationship between vacancies and the dispersion of sectoral employment growth rates were also estimated. Aggregate vacancies were proxied by a normalized help wanted index (VAC) which was defined as the ratio of the help wanted index to total non-agricultural employment. The estimated equation was of the form (26) [Mathematical Expression Omitted] Results of this regression for the sample period 1952:I-1988:II are shown in columns one and two of Table III. The regression was again estimated using a maximum likelihood procedure with correction for second-order serial correlation. I also estimated the equation in semi-log form to check for any non-linearities, though only the simple linear form is reported. The results shown in Table III are consistent with the earlier theoretical model which explained why sectoral shifts could cause a reduction in vacancies. This is seen by the negative coefficients of [[Sigma].sub.Z]

The diagnostic procedures used above on the unemployment equation were also applied to the vacancy equation. To address the problem of generated regressors, I re-estimated equation (26) using two-stage least squares with a correction for second-order serial correlation. The instruments for [[Sigma].sub.X,t] were the same as above. These estimates are shown in the right-hand-side righthand column of Table III. Once again, Hausman t-tests were applied to the coefficients to test for specification errors, and again there was no evidence for specification bias.

Finally, the same tests regarding functional form and higher-order autocorrelation which were applied to the unemployment equation were also applied to the vacancy equation. No problems in connection with these tests were found.(10) In sum, the evidence is consistent with sectoral shifts having a small negative effect on aggregate vacancies.

V. THE CONTRIBUTION OF SECTORAL SHIFTS TO AGGREGATE UNEMPLOYMENT

The model estimated in the previous section was then used to compute the contribution of sectoral shifts to aggregate unemployment. This was computed using the estimates of equation (25) contained in the first column of Table II, as follows: (27) [Mathematical Expression Omitted] (28) [Mathematical Expression Omitted] Technically [Mathematical Expression Omitted] is a function of the entire history of [Mathematical Expression Omitted] but for computational purposes i was restricted to thirty lags. The series [Mathematical Expression Omitted] and [Mathematical Expression Omitted] are shown in Table IV. The evidence from these series rejects the hypothesis that cyclical fluctuations in the aggregate unemployment rate can be explained by sectoral shifts. Instead, aggregate disturbances explain almost all of the fluctuation. Across the sample period the rate of sectoral shift unemployment is relatively stable as evidenced in Table V. For the sample period, 1957:I-1973:IV the mean rate is 4.51 percent, while for the sample period 1974:I-1988:IV it is 4.62 percent. Lillien's claim to have explained fluctuations in the aggregate rate of unemployment as arising from sectoral shifts of employment demand therefore stands rejected according to the current evidence. That said, however, the evidence also reveals that sectoral shifts account for a substantial, albeit stable, component of aggregate unemployment. If we interpret this component as the natural rate of unemployment, this suggests that full-employment for the U.S. economy currently involves an unemployment rate between 4.5 percent and 5 percent.

VI. CONCLUSION

Abraham and Katz [1986] challenged Lillien's [1982] claim that sectoral shifts are important for explaining the aggregate rate of unemployment. They claimed that the sectoral shift hypothesis implied a positive relationship between aggregate unemployment and aggregate vacancies reflecting a radial expansion outward of the Beveridge curve. In regressions using a proxy for vacancies against a proxy for sectoral shifts they found a negative relationship, and they therefore concluded that the sectoral shift hypothesis was inconsistent with the empirical evidence. The current paper has provided theoretical arguments explaining why Abraham and Katz's conclusion is unjustified. This is because sectoral shifts can generate a negative relationship between unemployment and vacancies if there are asymmetric costs of adjusting labor inputs--specifically, if costs of hiring exceed costs of layoffs. In this case, sectors that receive negative shocks immediately lay off workers, while sectors that receive positive demand shocks expand their workforces only gradually. To test for this effect, I decomposed the dispersion of sectoral employment growth into components attributable to aggregate disturbances and sector-specific influences respectively. The regression results revealed a positive relationship between aggregate unemployment and the proxy for sectoral shifts, and a negative relationship between the vacancy proxy and the sectoral shift proxy. These results are consistent with the theoretical model describing the impact of sectoral shifts on unemployment and vacancies. However, although sectoral shifts do contribute positively to aggregate unemployment, the model and the data reveal that they are unable to account for the large cyclical variation in unemployment, which is better explained by aggregate disturbances.

TABLE II

Estimates of the aggregate unemployment rate per equation (25)

Without Instruments With Instruments C .561 .622 (1.05) (2.19) Time .001 -.001 (.21) (-.55) U(t-1) .926 .956 (26.37) (26.78) [Sigma] x(t) -22.07 -47.42 (-2.33) (-2.05) [Sigma] x(t-1) -21.19 -25.44 (-2.24) (-2.56) [Sigma] x(t-2) -19.00 -14.40 (-2.04) (-1.41) [Sigma] x(t-3) -15.89 -13.63 (-1.90) (-1.55) [Sigma] z(t) 18.00 24.15 (2.42) (2.70) [Sigma] z(t-1) 15.24 14.72 (1.86) (1.80) [Sigma] z(t-2) -5.99 -7.61 7.91 6.19 (1.08) (.82) Adj. [R.sup.2] .91 .91 S.E.E. .29 .30 [Rho] 1 .71 .64 [Rho] 2 -.27 -.25 Durbin-H -.23 -.15

Note: The sample period was 1951:II-1988:II, and figures in parentheses are t-statistics.

TABLE IV

Shows the series for aggregate unemployment, unemployment atrributable to sectoral

shifts, and unemployment attributable to aggregate factors. U U* U-U* 1957:I 3.83 5.23 -1.40 II 3.93 5.13 -1.19 III 4.10 5.01 -0.91 IV 4.80 4.86 -0.06 1958:I 6.10 4.77 1.33 II 7.17 4.76 2.41 III 7.13 4.74 2.40 IV 6.17 4.64 1.53 1959:I 5.63 4.59 1.04 II 5.00 4.56 0.44 III 5.17 4.65 0.52 IV 5.47 4.73 0.73 1960:I 5.03 4.76 0.27 II 5.10 4.98 0.12 III 5.43 4.93 0.50 IV 6.10 4.86 1.24 1961:I 6.63 4.77 1.87 II 6.80 4.65 2.15 III 6.60 4.57 2.03 IV 6.00 4.49 1.51 1962:I 5.43 4.35 1.08 II 5.33 4.33 1.00 III 5.40 4.33 1.07 IV 5.37 4.24 1.13 1963:I 5.63 4.17 1.47 II 5.53 4.15 1.39 III 5.37 4.11 1.26 IV 5.47 4.12 1.34 1964:I 5.33 4.14 1.19 II 5.10 4.13 0.97 III 4.87 4.09 0.78 IV 4.80 4.12 0.68 1965:I 4.73 4.12 0.61 II 4.53 4.07 0.46 III 4.27 4.11 0.16 IV 4.00 4.09 -0.09 1966:I 3.77 4.08 -0.31 II 3.73 4.10 -0.37 III 3.67 4.17 -0.50 IV 3.60 4.14 -0.54 U U* U-U* 1973:I 4.83 4.57 0.27 II 4.83 4.44 0.40 III 4.70 4.31 0.39 IV 4.70 4.25 0.45 1974:I 5.03 4.21 0.82 II 5.10 4.21 0.89 III 5.53 4.25 1.28 IV 6.47 4.34 2.13 1975:I 8.10 4.52 3.58 II 8.67 4.73 3.94 III 8.37 4.86 3.50 IV 8.13 4.95 3.19 1976:I 7.63 4.92 2.72 II 7.40 4.89 2.51 III 7.57 4.72 2.85 IV 7.63 4.56 3.08 1977:I 7.40 4.41 2.99 II 7.03 4.39 2.65 III 6.80 4.46 2.34 IV 6.57 4.50 2.06 1978:I 6.23 4.63 1.61 II 5.90 5.03 0.87 III 5.93 5.20 0.73 IV 5.80 4.95 0.85 1979:I 5.80 4.93 0.87 II 5.60 4.80 0.80 III 5.77 4.72 1.05 IV 5.87 4.64 1.23 1980:I 6.20 4.59 1.61 II 7.23 4.70 2.54 III 7.57 4.82 2.74 IV 7.27 4.71 2.56 1981:I 7.30 4.65 2.65 II 7.30 4.64 2.66 III 7.30 4.68 2.62 IV 8.10 4.69 3.41 1982:I 8.70 4.55 4.15 II 9.27 4.55 4.72 III 9.80 4.53 5.27 IV 10.53 4.56 5.97 U U* U-U* 1967:I 3.73 4.19 -0.46 II 3.73 4.26 -0.53 III 3.70 4.34 -0.64 IV 3.80 4.38 -0.58 1968:I 3.63 4.32 -0.69 II 3.47 4.37 -0.90 III 3.40 4.44 -1.04 IV 3.30 4.49 -1.18 1969:I 3.30 4.51 -1.21 II 3.33 4.52 -1.18 III 3.50 4.48 -0.98 IV 3.47 4.48 -1.01 1970:I 4.07 4.57 -0.51 II 4.63 4.53 0.01 III 5.03 4.57 0.47 IV 5.67 4.62 0.85 1971:I 5.77 4.93 0.83 II 5.80 4.82 0.98 III 5.83 4.90 0.94 IV 5.83 4.84 0.99 1972:I 5.77 4.91 0.77 II 5.57 4.86 0.70 III 5.47 4.78 0.69 IV 5.23 4.70 0.54 U U* U-U* 1983:I 10.27 4.56 571 II 9.93 4.51 5.43 III 9.20 4.61 4.59 IV 8.40 4.67 3.73 1984:I 7.73 4.60 3.14 II 7.33 4.59 2.75 III 7.33 4.53 2.81 IV 7.17 4.55 2.61 1985:I 7.13 4.86 2.55 II 7.20 4.60 2.60 III 7.10 4.67 2.43 IV 6.93 4.67 2.26 1986:I 6.90 4.61 2.29 II 7.07 4.60 2.47 III 6.87 4.69 2.17 IV 6.77 4.69 2.07 1987:I 6.50 4.69 1.81 II 6.20 4.65 1.55 III 5.93 4.60 1.33 IV 5.77 4.50 1.27 1988:I 5.60 4.45 1.15 II 5.43 4.39 1.04 III 5.40 4.35 1.05 IV 5.23 4.33 0.90

TABLE V

Shows the mean values of U U*, and U - U* for various sample

periods. U U* U - U* 1957:I-1988:IV 5.94 4.56 1.38 1957:I-1973:IV 4.91 4.51 .40 1974:I-1988:IV 7.10 4.62 2.48

[Table I & III Omitted] [Figure 1 Omitted]

(1)The Beveridge Curve describes the relationship between vacancies and the rate of unemployment. (2)The model developed here is similar to a model by Weiss (1984) that is described by Abraham and Katz. However, the model is extended to include vacancies and therefore provides an explanation of the unemployment-vacancy relationship. (3)The assumption of costless layoffs is extreme. If there are some convex costs to layoffs, they will be smoothed. For purposes of the current argument all that is required is that layoff adjustments be more rapid than new hires. This is most easily managed by assuming instant layoffs. (4)The vacancy rule given by equation (15) may be interpreted as an approximation to an optimal adjustment rule in the presence of zero firing costs and convex hiring costs. The one complication which is not accounted for is that if the current labor force were greater than the desired labor force the firm might still hire additional (temporarily surplus) workers so as to save a little next period when it anticipates replacing quits. (5)Asymmetric hiring and firing costs therefore provide a novel explanation complements a recent search theoretic explanation advanced by Blanchard and Diamond [1989]. (6)This is a standard argument in the investment literature. (7)The regression given by equation (25) differs from that used by Lillien and by Abraham and Katz not only in its decomposition of the dispersion variable, but also in its exclusion of an unanticipated monetary policy variable. The inclusion of this variable would be important if one were interested in constructing a series for the natural rate and subscribed to the anticipated policy ineffectiveness proposition. (8)The instruments used to proxy for [Sigma] [.sub.x] (0) were four lagged values of the unemployment rate and two lagged values of aggregate employment growth. (9)The Godfrey statistic was 2.03 while the critical value under the Chi-square distribution with fifteen degrees of freedom at the 95 percent confidence level was 7.26. (10)The Godfrey statistic was 6.10 while the critical Chi with 15 degrees of freedom at the 95 percent confidence level was 7.26.

REFERENCES

Abraham, K. G., and L. F. Katz. "Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances." Journal of Political Economy, June 1986, 507-22. Barro, R. J. "Rational Expectations and Macroeconomics in 1984." American Economic Review, Papers and Proceedings, May 1984, 179-82. Blanchard, O. J., and P. Diamond. "The Beveridge Curve." Brookings Papers on Economic Activity 1, 1989, 1-60. Fair, R.C. "The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Correlated Errors." Econometria, May 1970, 507-16. Godfrey, L. G. "Testing for Higher Order Serial Correlation in Regression Equations when the Regressors include Lagged Dependent Variables." Econometrica, November 1978, 1303-10. Hausman, J. A. "Specification Tests in Econometrics." Econometrica, November 1978, 1251-71. Lillien, D. M. "Sectoral Shifts and Cyclical Unemployment." Journal of Political Economy, August 1982, 777-93. Long, J. B., and C. I. Plosser. "Real Business Cycles." Journal of Political Economy, 91(1), 1983, 39-69. __. "Sectoral Versus Aggregate Shocks in the Business Cycle." American Economic Review, Papers and Proceedings, May 1987, 333-36. Lucas, R. E., Jr., and E. C. Prescott. "Equilibrium Search and Unemployment." Journal of Economic Theory, February 1974, 188-209. Neftci, S. N. "Are Economic Time Series Asymmetric over the Business Cycle?" Journal of Political Economy, February 1984, 307-28. Norrbin, S. C., and D. E. Schlagenhauf. "An Inquiry into the Sources of Macroeconomic Fluctuations." Journal of Monetary Economics, 1988, 22(1), 43-70. __. "The Importance of Sectoral and Aggregate Shocks in Business Cycles." Economic Inquiry, April 1991, 317-35. Pagan, A. "Econometric Issues in the Analysis of Regressions with Generated Regressors." International Economic Review, February 1984, 221-47. __. "Model Evaluation by Variable Addition," in Econometrics and Quantitative Economics, edited by D. F. Hendry and K. F. Wallis. Oxford: Basic Blackwell, 1984, 103-33. Weiss, L. "Asymmetric Adjustment Costs and Sectoral Shifts." Mimeo, University of Chicago, Department of Economics, 1984.

THOMAS I. PALLEY, Assistant Professor, New School for Social Research, New York.

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Author: | Palley, Thomas I. |
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Publication: | Economic Inquiry |

Date: | Jan 1, 1992 |

Words: | 6655 |

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