Econometrica: Nov, 1979, Volume 47, Issue 6

A Saddlepoint Approximation to the Distribution of the k-Class Estimator of a Coefficient in a Simultaneous System

https://doi.org/0012-9682(197911)47:6<1527:ASATTD>2.0.CO;2-J
p. 1527-1548

A. Holly, P. C. B. Phillips

A new approximation based on the saddlepoint method of approximating integrals is derived for the probability density of the k-class estimator in the case of the equation with two endogenous variables. The two tails of the density are approximated by different functions, each of which bears a close relationship with the exact density in the same region of the distribution. Corresponding approximations are also derived for the distribution function and the method of derivation should be useful in other applications. Some brief numerical results are reported which illustrate the performance of the new approximation.