A COMPANION TO Theoretical Econometrics

Computational matters

With the continuing increase in computer power it may appear strange to be concerned with computational matters. However, the need to use computationally intensive methods, such as the bootstrap, in conjunction with regular estimation procedures, provides an incentive to look for computational efficiencies of the type discussed by Hirschberg (1992) and Kontoghiorghes and Clarke (1995). Hirschberg (1992) provides a simplified solution to the Liapunov matrix equa­tion proposed by Byron (1982) to estimate a class of SUR models that are often encountered in demand modeling. Kontoghiorghes and Clarke (1995) propose an alternative numerical procedure for generating SUR estimators that avoids directly computing the inverse of X.

When some structure is assumed for the disturbance covariance matrix, or when there are particular patterns in the regressors, general results may be sim­plified to yield computational gains. For example, Kontoghiorghes and Clarke

(1995) develop their approach for the case where the regressors in each equation contain the regressors from the previous equations as a proper subset. Also Seaks (1990) reminds practitioners of the computational simplifications available when cross-equation restrictions need to be tested in SUR models which contain the same set of regressors in each equation.