A computationally efficient method for bootstrapping systems of demand equations: A comparison to traditional techniques

Abstract

The solution to a Liapunov matrix equation (LME) has been proposed to estimate the parameters of the demand equations derived from the Translog, the Almost Ideal Demand System and the Rotterdam demand models. When compared to traditional seemingly unrelated regression (SUR) methods the LME approach saves both computer time and space, and it provides parameter estimates that are less likely to suffer from round-off error. However, the LME method is difficult to implement without the use of specially written computer programs and, unlike traditional SUR methods, it does not automatically provide an estimate of the covariance of the parameters. This paper solves these two problems, the first by providing a simplified solution to the Liapunov matrix equation which can be written in a few lines of code in computer languages such as SAS PROC MATRIX/IML TM or GAUSSTM; the second, by bootstrapping the parameter covariance matrix.

Alternative Forms for Restricted Regressions

“…3 In the case of the symmetry restrictions alone Byron (1982) and Hirschberg (1992) demonstrate that the number of computations may even fall to a far smaller proportion if the estimated covariance structure is not required. Obviously the parameters in (12) and (13) are not the same ones although it is common practice to refer to them by the same names.…”