## Variance as an Exponential Function of Regressors

As we mentioned before, the linear specification, however simple, is more general than it appears. However, a researcher may explicitly specify the variance to be a certain nonlinear function of the regressors. The most natural choice is an exponential function because, unlike a linear specification, it has the attractive feature of ensuring positive variances. Harvey (1976), who assumed yt — exp (z’,a), proposed estimating a by LS applied to the

regression of log fi? on z, and showed that the estimator is consistent if 1.2704 is subtracted from the estimate of the constant term. Furthermore, the estimator has an asymptotic covariance matrix equal to 4.9348(Z’Z)-‘, more than double the asymptotic covariance matrix of MLE, which is 2(Z’Z)~I.

Error component...

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