Additional approximations to the distribution of a structural coefficient estimator for the case of two included endogenous variables

Abstract

Four new approximations t o the exact distribution of the two-stage l e a s t squares estimator of astructuralcoefficient for

the case of two included endogeneous variables are introduced and compared with the others in the literatur e . Two of the new approximations are based on the Pearson distribution and are found to be adequate throughout the parameter space. A normal approximation using exact moments and an approximation based on the saddlepoint method (Holly and Phillips,1979) are found to be

poor for a wide range of parameter values.

Keywords:

• twostage least squares
• small sample distribution
• approximation
• econometrics