Sectoral shocks and unemployment rate fluctuations.

Elias, Carlos G.

I - Introduction

One of the basic problems in macroeconomics has been to provide explanations for aggregate business fluctuations. In the classical model the level of production is determined by exogenous tastes and technology. The basic assumption is that the economy is populated by self-interest agents who leave no opportunity for mutual gain unexploited. Price and wage flexibility is the outcome of such an economy. If aggregate demand falls and output falls below the potential GNP, firms with excess capacity will reduce prices to stimulate sales. If demand rises and output increases above the potential GNP, prices will increase thereby reducing sales and consequently output. In this economy any deviation of output from potential GNP will be temporary. Furthermore, fiscal and monetary policies are completely unnecessary to restore the long run equilibrium.

In the Keynesian model, wage and price rigidity could cause the economy to operate in a suboptimal position. In this case, government intervention in the economy is necessary to restore long term equilibrium whenever the economy is trapped in a low output, high unemployment situation.

The basic line of research for classical economists was to explain how business fluctuations were possible in a world with flexible prices and full employment. The rational expectations school assumed as valid the classical assumption of price-wage flexibility. However, they assumed also that expectations are formed rationally (i.e., using all available information). In this case, expected monetary shocks will have no effect on output but an unexpected shock may cause output to deviate from the potential GNP. This, of course, could be used to explain business cycles. One problem remains; given that only unexpected shocks could cause deviations from potential GNP, and unexpected shocks are completely random, the deviations should be random with an expected value equal to zero. Thus no persistent cycles should be observable. In reality, business cycles do not behave like that. Business cycle research has found a high degree of persistence in GNP data.(1)

The research also suggests that there is comovement (a tendency to move together) among different sectors in the economy. Comovement was a major problem in the original formulation of the classical model. In the original classical formulation the result of a decline in consumption was an increase in the total amount of savings in the economy. This additional savings will reduce interest rates and, keeping everything else constant, stimulate investment. In this case a recession will be avoided but no comovement is observed, and consumption and investment will move in different directions. Keynes suggested that it is contradictory for firms to increase investment expenditure if they observe consumption falling. An increase in investment implies increasing production capacity but consumers are buying less not more; therefore less capacity is needed.

Real Business Cycle (RBC) models try to explain comovement and persistence within the classical framework by arguing that business cycles are mainly caused by technological shocks.(2) Long and Plosser(3) have shown that even with sector specific technological disturbances it is possible to have comovement in output.

A major drawback of RBC models is they fail to explain the role of unemployment fluctuations in the economy. An important assumption in RBC is intertemporal substitution. That is, how responsive in terms of hours worked are employees to changes in wages. An adverse technological shock will decrease demand for labor and reduce both real wages and employment, but due to wage flexibility labor demand and supply will equilibrate. Thus the unemployment rate does not have to change in the presence of sectoral shocks.

Cooper and Haltiwanger (1990) found that sectoral shocks with RBC assumptions do not lead to comovement among employment in different sectors. However, if sectoral shocks occur in the presence of imperfect competition, employments in different sectors will tend to move together. The data examined by Cooper and Haltiwanger suggests that there is comovement in employment among sectors. Therefore they imply that some imperfection or rigidity is present in the labor market.

The main topic of this paper is to analyze the relative importance of productivity shocks on unemployment rate fluctuations. Sectoral shocks can cause comovement if there are spillover effects to other sectors. It is clear that an adverse shock will reduce employment in the sector where the shock occurs. An adverse technological shock will reduce the demand for labor. Employment will be reduced in the presence of the Keynesian assumption of wage rigidity and also in the presence of the RBC assumption of wage flexibility with a fiat labor supply. The response of the unemployment rate will be very different. In the presence of wage rigidity the unemployment rate will increase; while under the RBC assumption, the unemployment rate will be mostly unaffected. For this reason, if sectoral shocks are important in the fluctuations of the unemployment rate, this would give support to the Cooper and Haltiwanger hypothesis that some type of imperfection is present in the market.

The reduction in employment will have two effects on the other sectors: on the one hand it will increase the relative price of the good in question, increasing the demand for products of other sectors; on the other hand the consequent reduction in income will tend to reduce production and employment in other sectors. If the income effect is sufficiently big we will see comovement of employment in different sectors. If the substitution effect is bigger than the income effect, comovement will not be observed.

In this paper, a vector autoregressive model (VAR) for unemployment in different sectors and for the unemployment rate is estimated. From the assumptions made, it will be possible to identify the shocks and measure the importance of sectoral shocks using variance decomposition. In Section II a simple theoretical model will be developed, In Section III the model will be estimated to measure the relative importance of sectoral shocks on the unemployment rate. Section IV summarizes major findings and conclusions.

II - The Model

A major recent feature of employment in industrialized nations has been the secular shift from manufacturing to services. Although employment is growing over time, on average, in all sectors, the share of employment in manufacturing has been declining over time. In general this shift in employment is due to the fact that productivity grows faster in the manufacturing sector while the demand for services is growing faster that the demand for manufactured goods.(4) Abraham and Katz (1986) show that employment in the manufacturing sector responds more to the business cycle than does employment in the services sector. In this model there will be a sectoral shock and a labor supply shock affecting the manufacturing sector. It will be assumed that service sector employment will not be subject to a sectoral shock.

The first assumption that will be made is that sectoral shocks will have a permanent effect of the level of employment in a given sector. Aggregate monetary shocks will have a temporary effect on the level of employment. None of the shocks will have a permanent effect on the unemployment rate.(5) This assumption, together with the trend explained in the previous paragraph, will be enough to identify the shocks.

The economy will be divided into two sectors, manufacturing (m) and services (s). The long run level of employment in manufacturing will be determined by sector specific technological shocks, labor supply and product demand. The long run level of employment in the manufacturing sector evolves according to the following equation:(6)

[Mathematical Expression Omitted] (1)

Where [Mathematical Expression Omitted] is the long rum level of employment in manufacturing, [[Phi].sup.m](L) is an infinite lag polynomial(7) and [[Epsilon].sup.m] is the productivity shock in the manufacturing sector. It is expected that an adverse productivity shock will depress the employment in the manufacturing sector.

The long run evolution of the labor supply will be determined by the following equation:

[Mathematical Expression Omitted] (2)

A positive labor supply shock is expected to increase the labor supply.

In the short run the level of employment in each sector can deviate from the long run level (equation 1) because of the transitory adjustment of productivity shocks and aggregate monetary shocks.

[Mathematical Expression Omitted] (4)

Taking first differences of equation (4) and using (1) will produce:

[Mathematical Expression Omitted] (5)

[Mathematical Expression Omitted]. (6)

For the services sector:

[Mathematical Expression Omitted] (7)

Taking first differences of equation (7) and using (1), (2) and (4) we find:

[Mathematical Expression Omitted] (8)

[Mathematical Expression Omitted] (9)

It will be assumed that the unemployment rate will be affected by three types of shocks: A monetary aggregate demand shock ([[Mu].sub.t]), a productivity shock from manufacturing [Mathematical Expression Omitted] and a labor supply shock [Mathematical Expression Omitted]. None of the shocks have permanent effects on the unemployment rate.

[Mathematical Expression Omitted] (10)

The system will consist of the following equations:

[Y.sub.t] = [summation of] A([Tau])[e.sub.t-[Tau]] where [Tau] = 0 to [infinity] (11)

Where:(8)

[Mathematical Expression Omitted] and [Mathematical Expression Omitted]

or:

[Y.sub.t] = A(L)[e.sub.t] (12)

A(L) is a matrix that is derived from the lag polynomials [[Phi].sup.m](L), [[Phi].sup.l](L). Following Shapiro and Watson (1988), I will identify the shocks by using the long run multipliers matrix A(1). It is clear from equations (6), (9) and (10) that A(1) will be a lower triangular.

[Mathematical Expression Omitted]

III-Estimation Procedure and Results

One of the main assumptions of this paper is that variables follow a random walk. It is then necessary to test the hypothesis of unit root to the variables.[9] We test the hypothesis that [Gamma] = 0 in equation (13) below.

[Delta][X.sub.t] = [Alpha] + [Beta]t + [Gamma][X.sub.t-1] + [summation of] [[Delta].sub.i][Delta][X.sub.t-i] where i = 1 to p + [u.sub.t] (13)

Where t is a trend and [u.sub.t] is white noise.

The results of the estimation of the equation (13) are shown in Tables 1-3. This is done for the employment series in the manufacturing and services sectors and for the seasonally adjusted unemployment rate. The null hypothesis is that [Gamma] = 0; the alternative is that [Gamma] [less than] 0.(10)

The t statistic in Tables 1-3 can be used to test [H.sub.0]:[Gamma] = 0 vs. [H.sub.1]: [Gamma] [less than] 0.(11) The critical value of t at the 5% confidence level is -2.87. (See Fuller (1979) pp. 373.) Using this test, we can accept the null hypothesis of unit root.

TABLE 1

Estimated equation (13) for employment in manufacturing

 Estimated equation with
 dependent variable [Delta]Manuf

Variable
or
Statistic (1) (2)

Constant .148 .096
 (1.9) (1.65)
Manuf(-1) -.02 -.010
 (-1.9) (-1.64)
[Delta]Manuf(-1) .397 .490
 (8.66) (0)
[Delta]Manuf(-2) .209
 (4.58)
[R.sup.-2] .27 .24
DW 2.03 2.19

The t statistics are shown in parentheses.
TABLE 2

Estimated equation (13) for employment in services

 Estimated equation with
 dependent variable [Delta]Serv

Variable
or
Statistic (1) (2)

Constant -.005 -.005
 (-.93) (-1.19)
Serv(-1) .001 .0006
 (1.40) (1.75)
[Delta]Serv(-1) .186 .222
 (4.11) (4.98)
[Delta]Serv(-2) .164
 (3.63)
[R.sup.-2] .079 .055
DW 2.07 2.07
TABLE 3

Estimated equation (13) for unemployment

 Estimated equation with
 dependent variable [Delta]Unemplsa

Variable
or
Statistic (1) (2)

Constant .048 .036
 (2.42) (2.24)
Un(-1) -.028 -.021
 (-2.42) (-2.23)
[Delta]Un(-1) .060 .062
 (1.28) (1.33)
[Delta]Un(-2) .147
 (3.13)
[R.sup.-2] .027 .009
DW 2.01 2.02

Given our assumptions, equation can be rewritten:

[B.sub.p](L)[Y.sub.t] = [e.sub.t] (14)

Where [B.sub.p](L) is a finite lag polynomial of order p and A(L) = [[[B.sub.p](L)].sup.-1].

The objective will be to estimate the VAR coefficients of (14) and then estimate the contribution of the different shocks to the unemployment rate.(12) One problem mentioned by Blanchard and Quah is that the unemployment rate is not stationary. The answer to this problem is not trivial. If the unemployment rate is subject to hysteresis, an aggregate monetary shock can have permanent effects.(13) Because this does not seem to be very important to U.S. data, a trend variable is included in the VAR estimation to account for it. However, the results are similar with or without the trend.

The data used to estimate the model is employment in the manufacturing(14) and services(15) sectors, monthly and seasonally adjusted. The sample period is from January 1948 to December 1987.(16) (The level of employment is measured in number of workers. This is the appropriate measure if we want to analyze the effects of sectoral shocks on unemployment rate fluctuations.)

Figures 1-2 show the impulse response function of shocks in manufacturing, and on the unemployment rate.(17) Figure 1 shows the effect of sectoral manufacturing shock on the three endogenous variables in equation (10) (employment in manufacturing, employment in services and unemployment rate). Figure 2 shows the effect of a monetary shock on the same three endogenous variables. I am going to concentrate on the effect on the aggregate unemployment rate (UNEMPLSA).

In Figure 1 it is observed that a sectoral manufacturing shock will have a perceptible impact on the unemployment rate. This effect is small initially but increases steadily until the ninth month. After the ninth month the effect of the sectoral manufacturing shock decreases and is almost completely eliminated by the thirty-fifth month. This result suggests that sectoral shocks are important on aggregate unemployment. The impact tends to completely disappear three years after the initial shock.

Figure 2 shows the effect of the aggregate monetary shock.(18) The effect of this shock on unemployment is large initially but decreases steadily over the sample and is almost completely eliminated by the thirtieth month. This suggests that a monetary shock has an important effect on the unemployment rate in the first months, but it loses importance until it is completely eliminated two and a half years after the initial shock.

TABLE 4

Estimation results

Dependent variable

 Manuf1 Serv1 Unemplsa
Ind. Coefficient Coefficient Coefficient
Variable (t stat.) (t stat.) (t stat.)

Manuf1(-1) .31 .07 -1.54
 (6.15) (3.9) (-3.27)
Manuf1(-2) .10 .04 -1.28
 (1.88) (2.4) (-2.7)
Manuf1(-3) .02 .01 -.51
 (.30) (.4) (-1.1)
Manuf1(-4) .07 .002 -.30
 (1.34) (.2) (-.7)
Serv1(-1) .08 -.01 -1.24
 (.61) (-.15) (-1.0)
Serv1 (-2) .12 .003 -2.13
 (.89) (-.06) (-1.7)
Serv1(-3) .10 .115 1.09
 (.72) (.237) (.9)
Serv1(-4) .10 .10 -3.08
 (.73) (2.14) (-2.4)
Unemplsa(-1) -.01 -.001 .88
 (-1.72) (-.46) (18.5)
Unemplsa(-2) -.002 -.001 -.06
 (-.35) (-.47) (1.02)
Unemplsa(-3) .01 .001 -.08
 (1.65) (.25) (-1.36)
Unemplsa(-4) .003 .001 .08
 (.72) (.70) (1.8)
Trend 0 0 0
Constant -.005 .002 .09
 (-2.4) (2.21) (5.03)
[R.sup.-2] .29 .19 .97
DW 2.00 1.99 2.02
F 16.0 9.9 1154.2

Table 5 and Figure 3 show the variance decomposition of a shock to the unemployment rate. The aggregate shock will drop from 93% in the first month to 43% a year later to stabilize at 34% after five years. The sectoral manufacturing shock on the other hand will increase from 7% in the first month to 52% after a year to stabilize at 59% after five years.

The impulse function suggests that both sectoral shocks and aggregate monetary shocks play an important role in the fluctuations of the unemployment rate. The aggregate monetary shock is especially important in the first year and its importance diminishes over time. The sectoral manufacturing shock increases over time until the ninth month after the initial shock and its importance diminishes thereafter.

TABLE 5

Decomposition of Variance

Fraction of unemployment rate explained by shock to:

Month MANUF1 SERV1 UNEMPLSA S.E.

1 6.5 .56 92.9 .05
2 12.0 .95 87.0 .07
3 19.8 1.77 78.5 .09
4 26.5 1.80 71.7 .10
12 51.9 5.65 42.5 .20
24 58.5 6.87 34.7 .24
36 58.7 6.95 34.3 .24
48 58.8 6.95 34.3 .24
60 58.8 6.95 34.3 .24

The analysis of variance suggests most of the variance on the unemployment rate is explained by aggregate shock. The manufacturing sectoral shock initially explains less than 7% of the variance of the unemployment rate in the first months but this effect increases over time to explain almost 60% five years after the shock.

In order for a sectoral shock to affect the unemployment rate it needs to propagate to other sectors. This explains the delay of the shock on manufacturing in our analysis of variance.

IV - Conclusion

In this paper a simple vector autoregression model is estimated to measure the importance of sectoral shocks on the unemployment rate for the U.S. for the period 1948-1987. The main finding of the variance decomposition suggests that shocks to the manufacturing sector are an important source of fluctuations to the unemployment rate. This does not imply that aggregate shocks are not important. Five years after the shock, the aggregate shock contributes to approximately 34% of the variance in the unemployment rate, while the manufacturing shock contributes 59%. This last shock increases its contribution over time. That is consistent with the theory of spillover effects.

I would like to express my appreciation for the helpful comments ana suggestions by Mitch Charkiewicz, the faculty of Manhattan College, and an anonymous referee. Any opinion expressed is my own and does not necessarily reflect the opinion of the Business Market Division at AT&T.

Notes

1. Persistence is a situation where the next period GNP is not very different from this period value. If a variable follows a first order autoregressive process, [y.sub.t] = [Alpha][y.sub.t-1], the coefficient [Alpha] will serve as the persistence coefficient. An [Alpha] close to one implies high persistence, an [Alpha] close to zero implies very low persistence.

2. Technological shocks are shocks to the production function. An adverse technological shock would shift down the production function causing a reduction in the marginal productivity of labor (MPL). A basic criticism to RBC models asks how such productivity shocks might arise in real life. (Technological "declines" are empirically unimportant.) Oil shocks are an obvious example, but probably not enough to explain business cycles. The consensus among RBC theoreticians is that small changes in the price of raw materials could generate productivity shocks consistent with RBC assumptions. Changes in the price of raw materials may induce firms to retire capital earlier with the subsequent reduction in MPL.

3. See for example Long and Plosser (1983) and Long and Plosser (1987).

4. See for example Rowthorn and Wells (1987) p. 15.

5. These are standard assumptions; see for example Shapiro and Watson (1988) and Blanchard and Quah (1989).

6. This follows the paper by Shapiro and Watson (1988).

7. In this paper it will be assumed that the lag polynomial has roots outside the unit circle.

8. Time subscript will be eliminated whenever possible.

9. See for example Evans (1989).

10. Tables 1-3 report the result of equation (13) using: (1) p = 2 and (2) p = 1. These equations were estimated with and without a trend; however, only the results without a trend are reported because the trend coefficient was insignificantly small.

11. See for example Fuller (1976) and Dickey and Fuller (1979).

12. It can be argued that the VAR estimate is not efficient because of possible correlation between the shocks. I estimated the system using Seemingly Unrelated Regression, but the results were not different.

13. See Blanchard and Summer (1987).

14. Manufacturing will include durable and non durable goods. The construction employment is added to manufacturing. Only the mining sector is left out but the level of employment in that sector is very small.

15. The services sector will include transportation, wholesale and retail trade, finance insurance and Real estate, and other services as defined by the U.S. Department of Labor.

16. The sources for data for this paper are: Employment, Hours and Earnings (Bureau of Labor Statistics), for employment in different sectors and Labor Force Statistics Derived from the Current Population Survey 1948-87, for unemployment rate.

17. MANUF1 is the first difference of employment in manufacturing, SERV1 is the first difference of employment in services and UNEMPLSA is the seasonally adjusted unemployment rate.

18. The shock to the unemployment rate equation.

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