Durbin h statistic. In autoregressive models like Eq. (10.7):
Yt = B1 + B2Xt + B3Yt-1 + vt
the usual d statistic is not applicable to detect autocorrelation. For such models, Durbin has suggested replacing the d statistic by the h statistic defined as

where
n = the sample size
= the estimator of the autocorrelation coefficient ρ
var (b3) = the variance of the estimator of B3, the coefficient of lagged Y variable
Durbin has shown that for large samples, and given the null hypothesis that true ρ = 0, the h statistic is distributed as
h ~ N (0, 1)
It follows the standard normal distribution, that is, normal distribution with zero mean and unit variance. Therefore, we would reject the null hypothesis that ρ = 0 if the computed h statistic exceeds the critical h value. If, e.g., the level of significance is 5%, the critical // value is -1.96 or 1.96. Therefore, if a computed h exceeds |l.96|, we can reject the null hypothesis; if it does not ex-ceed this critical value, we do not reject the null hypothesis of no (first-order) autocorrelation. Incidentally, p entering the h formula can be obtained from any one of the methods discussed in the text.
Now consider the following demand for money function for India for the periods 1948 to 1949 and 1964 to 1965:
lnMt = 1.6027 - 0.1024 In Rt + 0.6869 In Yt + 0.5284 In Mt-1
se = (1.2404) (0.3678) (0.3427) (0.2007) R2 = 0.9227
d = 1.8624
where M = real cash balances
R = the long-term interest rate
Y = the aggregate real national income
a. For this regression, find the h statistic and test the hypothesis that the preceding regression does not suffer from first-order autocorrelation.
b. As the regression results show, the Durbin-Watson d statistic is 1.8624. Tell why in this case it is inappropriate to use the d statistic. But note that you can use this d value to estimate ρ(‰ˆ 1 - d / 2).

Transcribed Image Text:

1- n• var(b3)