is significantly lower (0.885 compared to 0.911). The estimated residuals from this equation are presented in Table 3.8. We do not see any exceptionally large residue (except perhaps for observation 5, which is 1941), nor the long runs of positive and negative iesidu;ds as in Table 3.7.

Example 2

As a second example, consider the data presented in Table 3.9. They give teenage unemployment rates and unemployment benefits in Australia for the period 1962-1980. We will estimate some simple regressions of unemployment rates on unemployment benefits (in constant dollars) and present an analysis of the residuals.*

Defining

y, = unemployment rate for male teenagers 2 = unemployment rate for female teenagers : = unemployment benefit (constant dollars)

There is an increase in r as well but the two rs are not comparable. To compare the two we have to calculate the r between and from the first equation for just the 44 observations (excluding the war years). Then this recomputed H will be comparable to the r reported here. "These are not the equations estimated by Gregory and Duncan. We are just estimating some simple regressions which may not be very meaningful.

3.8 Estimated Residuals for the Consumption Function Omitting the War

Years(1942-1945)

Teenage Unemployment Benefit

Unemployment for 16- and

Rate(%) 17-Year-Olds

Constant Nominal Dollars

Source: R. G. Gregory and R. C. Duncan. "High Teenage Unemployment: The Role of Atypical Labor Supply Behavior," Economic Record, Vol. 56, December 1980, pp. 316-330.

we get the following regressions:

Si = 2.478 + 0.212 : = 0.690

0.234) (0.035)

2 = 3.310 + 0.226JC = 0.660

(1.410) (0.039)

The equation suggests that an increase in unemployment benefit leads to an increase in the unemployment rate. However, the residuals from the two equations presented in Table 3.10 show very large absolute residuals for 1973, 1974, and 1977-1980.

Suppose that as in Example 2, we delete these observations and reestimate the equations. The estimates are

Table 3.9 Teenage Unemployment Rates and Unemployment Benefits

fi = 2.156 + 0.203JC = 0.876

(0.610) (0.023)

= 2.799 + 0.225x = 0.955

(0.394) (0015)

The estimates of the coefficients of jt did not change much. The r values are higher but again to the values we have to compute the implied from the first equation using just these 13 observations. (The we compute is for and S.)

However, is the deletion of the six observations with high residuals the correct procedure in this case? The answer is "no." In Example 2 the deletion of the war years was justified because the behavior of consumers was affected by wartime controls. In this example there are no such controls. However, the large residuals are due to lags in behavior. First, with an increase in unemployment benefit rate, there will be an increase in the labor force participation. There will be time lags involved in this. Next there are the time lags involved in qualifying for benefits, filing of claims, receipt of benefits, and so on. Thus there are substantial time lags between x and y„ and jc and . The large negative residuals in 1973 and 1974 and the positive residuals in 1977-1980 are a consequence of this. Further, one can see a trend in these residuals from 1973-

Table 3.1© Residuals from the Regressions of Unemployment Rates on Unemployment Benefits