4  A forecasting model of New Zealand employment growth

To evaluate the forecast ability of the composite index of leading indicators we included the index in a forecasting model of quarterly employment growth. Following (Auerbach 1982), the model includes lags of the composite index and past changes of employment only. We did not attempt to identify other series not included in the index that might help in forecasting New Zealand employment growth.

The model is estimated using ordinary least squares (OLS) over the period 1987Q2 to 2001Q4. Statistical significance, residual based tests and forecasting performance led to the selection of the following specification

(10)

where is the first difference operator, employment at time , denotes the composite index of leading indicators at time for , is a white noise error, denotes a constant and are coefficients, for . The results of the estimation are reported in Table 2.

Lagged changes in the composite index of leading indicators are statistically significant determinants of employment growth and have the expected positive sign. The composite index lagged one quarter has the largest coefficient. This is not surprising given that at one lag, job ads, the component series with the largest weight, is strongly correlated with employment. Lags five and seven of the composite index are also statistically significant and reflect the often long delay with which employment adjusts to changes in economic conditions. An F-test rejected the null hypothesis that lags two, three, four and six are jointly significant.[9]

Table 2 – Estimation results

Variable	Coefficient	Standard error	T-statistic	P-value
	-1.080	1.074	-1.005	0.319
	0.145	0.103	1.407	0.165
	5.528	0.894	6.183	0.000
	2.448	0.811	3.017	0.004
	2.054	0.821	2.504	0.015

Lagged employment changes are not significant, but were included to correct for first-order serial correlation. The (Durbin and Watson 1951) statistic, which tests for first-order serial correlation in the residuals, indicated that the equation with lagged changes of the composite index only was mis-specified as it rejected the null hypothesis of no positive autocorrelation. Including past employment growth, the Durbin-Watson test can no longer reject the null hypothesis of no autocorrelation (positive or negative).

The R-squared statistic indicates the proportion of variability in employment growth explained by past changes in the composite index and past employment growth. According to this statistic, the model explains about 67 percent of the variation in employment. An F-test confirms that past changes in the composite index and employment are jointly significant determinants of employment growth.

Fitted, or in-sample predictions, of the indicator model and actual employment growth are plotted in Figure 3. Actual and predicted employment changes tend to move closely together, which suggests that the composite index is a good indicator of employment growth. The model identifies most turning points and produces white noise errors. The (Jarque and Bera 1987) test could not reject the hypothesis of normally distributed residuals. Recursive stability tests revealed stable coefficients over the estimation period – the CUSUM test and CUSUM of squares test (Brown, Durbin and Evans 1975) did not reject the null hypothesis of parameter constancy at conventional levels of significance.

Figure 3 - Actual and fitted employment growth

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