## Info

Notes: RES 1 = residuals from regression (12.5.1).

SRES 1 = standardized residuals = RES1 /2.6755. RES(-1) = residuals lagged one period.

464 PART TWO: RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL

Alternatively, we can plot the standardized residuals against time, which are also shown in Figure 12.8 and Table 12.5. The standardized residuals are simply the residuals (ut) divided by the standard error of the regression (VO2), that is, they are (ut¡a). Notice that ut and a are measured in the units in which the regressand Y is measured. The values of the standardized residuals will therefore be pure numbers (devoid of units of measurement) and can be compared with the standardized residuals of other regressions. Moreover, the standardized residuals, like ut, have zero mean (why?) and approximately unit variance.19 In large samples (ut¡a) is approximately normally distributed with zero mean and unit variance. For our example, a = 2.6755.

Examining the time sequence plot given in Figure 12.8, we observe that both ut and the standardized ut exhibit a pattern observed in Figure 12.1d, suggesting that perhaps ut are not random.

To see this differently, we can plot ut against ut—1, that is, plot the residuals at time t against their value at time (t — 1), a kind of empirical test of the AR(1) scheme. If the residuals are nonrandom, we should obtain pictures similar to those shown in Figure 12.3. This plot for our wages-productivity regression is as shown in Figure 12.9; the underlying data are given in 