Jobless Recovery: Is it Really Happening - October 1995

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B. Econometric Estimations and Dynamic Simulations

a) An Employment Equation

In this section, we attempt to quantify the impact of industrial restructuring, the increase in real wages and the decrease in the real cost of capital on the evolution of employment during the 1991-93 recovery. To that end, we propose to estimate an employment equation where the level of employment depends on lagged employment, real GDP, real wages, restructuring and the real cost of capital over the period 1970:1-1989:2. We then conduct an out-of-sample dynamic simulation across the recession and subsequent recovery (i.e. 1990:1-1995:2) to determine the extent to which our equation can account for the weak recovery in employment. The employment equation is as follows:

where E and y are level of employment and real GDP respectively, w is the hourly rate of compensation in constant dollars and r_k is the real cost of capital in machinery and equipment. Finally, the restructuring variable is an index of the sectoral dispersion of employment.

The variable used for real wages (w) is an hourly rate which reflects the total cost of labour ⁷ including salaries, wages and supplementary labour income ⁸. The real-cost-of-capital variable is based on estimates by the Department of Finance. It is expected a priori that, for a given level of output, a decrease in the real cost of capital will result in a decrease in labour demand and consequently a positive estimated coefficient. Finally, an index of the dispersion in sectoral employment demand is used to simulate the effect of economic restructuring in response to sectoral shifts in demand. According to Samson (1985), this index is calculated by taking a weighted sum of the difference between the rate of growth of sectoral employment and the rate of growth of aggregate employment:

where e_it=employment in industry i; Et=aggregate employment; and n=number of sectors. ⁹ The higher this index, the more sectoral restructuring of the economy there is and consequently the greater the negative impact on employment is expected to be. ¹⁰

Stationarity tests were performed on each series. ¹¹ In every case, the augmented Dickey-Fuller statistics indicate that the series are non-stationary. We then performed cointegration tests to determine whether there was a long-term relationship among these variables which would be stationary. The results of the Johansen cointegration tests indicate that there could be up to 3 cointegrating relationships. However, our ability to identify restrictions to impose on the parameters of the cointegration vector is severely limited by the fact that there is no theoretical framework to explain what long-term relationship among these variables should exist a priori. In addition, the reliability of the cointegration tests is weakened by the limited number of observations. We therefore estimate the equation in quarterly rates of growth so that all the series are stationary. ¹²

b) Results of Estimations of the Employment Equation

The results of the estimation of the final version of the employment equation over the 1970-1989 period are presented below. The additional lagged variables in the original equation (equation [3]) were omitted because the coefficients are generally not significantly different from zero. The t-statistics are in parentheses.

The estimation employment equation yields fairly robust results. This equation accounts for approximately 65 per cent of the variation in employment growth between 1970 and 1989, as measured by the adjusted R² statistic, which is respectable since the relationship is expressed in terms of quarterly rates of growth.According to the Durbin-H statistic, there is no problem of first-order autocorrelation in the equation. As well, all the estimated coefficients of the regression have the expected sign except the real cost of capital. Of the three explanatory variables we are studying (excluding lagged employment and GDP), only the coefficient of the real wages variable is statistically significantly different from zero at the usual 5 per cent confidence level.

According to this estimation, it appears that sectoral variations in employment did not have a significant effect on the evolution of aggregate employment during the estimation period. It is possible that our measure did not adequately capture these effects. Finally, our results indicate that the evolution of the real cost of capital did not have a significant negative impact on employment growth during the estimation period.

We therefore re-estimated the equation without including the restructuring and real-cost-of-capital variables. The results of this estimation over the period 1966:1-1989:4 are as follows:

This equation accounts for approximately 64 per cent of the variation in employment between 1966 and 1989. All the estimated coefficients have the expected sign and are significantly different from zero at the 5 per cent confidence level. ¹³ The diagnostic tests of this regression are shown below:

Table 1: Diagnostic tests of the regression
[confidence levels (p values) in parentheses]

LM (1 to 4)	0.05 (0.69)	0.19 (0.49)	0.89 (0.28)	1.64 (0.47)
ARCH (1 to 4)	0.15 (0.18)	0.13 (0.23)	0.06 (0.39)	0.01 (0.91)
White	13.05 (0.37)
Jarque-Bera	1.21 (0.55)
skewness	-0.07
kurtosis	2.46

The LM statistics test for the presence of autocorrelation of order 1 to 4. These statistics indicate that autocorrelation is not a problem in our equation. In addition, based on the Jarque-Bera test, we can reject the hypothesis of nonnormality of errors. The ARCH statistics are used to detect effects of autoregressive conditional heteroskedasticity of the errors of order 1 to 4. According to this test, ARCH effects could be present. In addition, based on the White test, we cannot not reject the hypothesis of homoskedasticity of errors at a very high confidence level. The t-statistics shown above were therefore corrected to account for heteroskedasticity, which enabled us to obtain consistent standard deviations. ¹⁴

It is important to note that including wages as an explanatory variable could introduce a simultaneity bias into the estimation as it is probable that real wages are not determined completely exogenously. However, it is not clear how this problem can be easily avoided. This could be the subject of future research. As well, the results could be sensitive to the formulation of the equation because Cozier and Mang (1994) obtain slightly different results with another equation.

c) Dynamic Simulation of the Employment Equation

To determine the extent to which our equation can account for weak employment growth, we conducted a out-of-sample dynamic simulation of the employment equation over the period 1990:I-1995:II without including the effect of restructuring and the real cost of capital (we omitted the restructuring variable and the real-cost-of-capital variable because their estimated coefficients are not significantly different from zero). This simulation is presented in Chart 4.

Chart 4 : Actual and Projected Employment Based on GDP and Real Wages

Although the equation underestimates the employment level between 1992:3 and 1993:3 and overestimates the employment level after the third quarter of 1994, in general it accurately predicts the evolution of employment during the recovery. It accurately predicts the trough in employment in the second quarter of 1992, and the employment level predicted for the fourth quarter of 1993 is very close to the actual level. It therefore appears that the evolution of GDP and real costs of labour can account for the evolution of employment during the recent recession and the subsequent recovery.

We want to assess the relative impact of the evolution of real wages and GDP on the evolution of employment. We therefore estimated the relationship between employment and GDP, without including real wages, over the period 1966:1-1989:4 and then conducted a dynamic simulation of the regression across the recession and subsequent recovery. ¹⁵ The results of this simulation are shown in Chart 5.

Chart 5 : Actual and Projected Employment Based on GDP

Although the equation is not able to predict the trough in employment in the second quarter of 1992, it is a fairly good predictor of the evolution of employment after 1994. In particular, the equation accurately predicts the stagnation of employment since the beginning of 1995.

A comparison of the two dynamic simulations shown above suggests that the historical relationship between GDP and employment did not appear to change in the recent recession. ¹⁶ It seems that the evolution of GDP can alone account for nearly all the evolution of employment. In fact, according to forecasting performance tests, the equation based solely on GDP is, on average, a better predictor of the evolution of employment over the period 1990:1-1995:2. ¹⁷

It appears that the real costs of labour can account for only minor shifts in the level of employment, such as the decline in employment between 1991:3 and 1992:3. The growth in real wages was strongest during this period. As well, the fact that real wages began to decline in 1994 could also explain why the original equation overestimates the employment level after 1994 (Chart 4 above). This suggests that the decrease in real wages could have a favourable impact on employment in the future, but for some reason this effect has not yet materialized.

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⁷ The hourly rate is calculated using the following formula: w = W/H * 1/P, where W is total quarterly compensation per employee, H is total paid hours per employee, and P is the GDP deflator at factor cost.

⁸ This includes employer contributions to unemployment insurance, the Canada and Quebec Pension Plans and private pension plans, workers' compensation and health insurance plans.

⁹ To calculate this variable, we used the rate of growth of employment in 9 sectors of the economy: agriculture; other primary industries; manufacturing; construction; transportation, communication and utilities; retail and wholesale trade; finance, insurance and real estate; commercial, community, business and personal services; and public administration.

¹⁰ It is important to note that this measure has been criticized in the literature because it does not distinguish between sectoral shocks and aggregate demand shocks which have an asymmetric effect across sectors. See Prasad (1993).

¹¹ Stationarity tests were performed over the period 1966:1-1995:2 for the employment, GDP and real-cost-of-labour variables; 1970:1-1995:2 for the index of dispersion of sectoral employment; and 1970:1-1993:4 for the real cost of capital.

¹² We tested the stationarity of the first difference of the natural logarithm of each series. In every case, based on the augmented Dickey-Fuller statistic, we can reject the hypothesis that the first difference of the natural logarithm of the variables is non-stationary at the 1% confidence level.

¹³ The t-statistics shown above were corrected to account for heteroskedasticity. See the discussion on the diagnostic tests of the regression.

¹⁴ We used White's method.

¹⁵ The results of this regression are:

¹⁶ Chow's test was performed to verify the stability of the coefficients over the estimation and simulation period. On the basis of this test, we cannot reject the hypothesis that the coefficients are the same over the estimation and simulation period.

¹⁷ Three performance indicators were evaluated: the root mean square error, the mean absolute error and the Thiel inequality coefficient. In all cases, these indicators indicate that the equation which includes real wages (equation [5]) has less predictive capability than the equation which does not include real wages (equation [6]).

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