INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 103 far, so it might look almost irrelevant. In particular, the proofs of the unbiasedness of the OLS regression coefficients did not use this condition. There are however two explanations for the presence of heteroscedasticity. The first explanation has to do with making the variances of the regression coefficients as small as possible, so that in a probabilistic sense, maximum precision is achieved. If there is no heteroscedasticity and if the other Gauss–Markov conditions are satisfied, the OLS regression coefficients have the lowest variances of all the unbiased estimators that are linear functions of the observations of Y. If heteroscedasticity is present, the OLS estimators are inefficient because there are still other estimators that have smaller variances and are still unbiased. The other reason is that the estimators of the standard errors of the regression coefficients will be wrong. This is because their computation is based on the assumption that the distribution of the disturbance term is homoscedastic. Otherwise, they are biased. As a consequence, the ttests and also the usual Ftests will be invalid. It is therefore quite likely that the standard errors will be underestimated, so the tstatistics will be overestimated which will have a misleading impression of the precision of the regression coefficients. The coefficient may appear significantly different from 0, at a given significance level, when in fact, it is not. The inefficiency property can be explained quite easily assuming that heteroscedasticity of the type displayed in Figures 1.2 and 1.3 is present. Which is an observation where the potential distribution of the disturbance term has a small standard deviation, similar to that of Figure 1.1.
