## Consequences Of Using Ols In The Presence Of Autocorrelation

As in the case of heteroscedasticity, in the presence of autocorrelation the OLS estimators are still linear unbiased as well as consistent and asymptotically normally distributed, but they are no longer efficient (i.e., minimum variance). What then happens to our usual hypothesis testing procedures if we continue to use the OLS estimators? Again, as in the case of het-eroscedasticity, we distinguish two cases. For pedagogical purposes we still continue to work with the two-variable model, although the following discussion can be extended to multiple regressions without much trouble.13

### OLS Estimation Allowing for Autocorrelation

As noted, /32 is not BLUE, and even if we use var(02)AR1, the confidence intervals derived from there are likely to be wider than those based on the GLS procedure. As Kmenta shows, this result is likely to be the case even if the sample size increases indefinitely.14 That is, /32 is not asymptotically efficient. The implication of this finding for hypothesis testing is clear: We are likely to declare a coefficient statistically insignificant (i.e., not different from zero) even though in fact (i.e., based on the correct GLS procedure) it may be. This difference can be seen clearly from Figure 12.4. In this figure we show the 95% OLS [AR(1)] and GLS confidence intervals assuming that true p2 = 0. Consider a particular estimate of 02, say, b2. Since b2 lies in the

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