Semiparametric Estimation of the Box-Cox Model Preliminary and Incomplete

This paper investigates the finite sample performance of three semiparametric estimators of the Box-Cox model. Two of the semiparametric estimators are the nonlinear two-stage least squares (NL2SLS) estimator proposed by Amemiya and Powell (1981) and a rescaled version (RNL2SLS) proposed by Powell (1996) to eliminate an inconsistent minimizer of the NL2SLS objective function. These estimators are special cases of the general-method-of-moments (GMM) estimator. The third estimator is one recently proposed by Foster, Tian and Wei (FTW) (2000), which is based on the empirical distribution function of the dependent variable. The Monte Carlo results show that there is no best estimator across the experimental designs considered. The NL2SLS and RN2SLS estimators tend to suffer from near nonidentification due to a flat objective function, and, although the FTW estimator is better than NL2SLS and RNL2SLS for many designs, it can perform badly for certain designs. The results also show that first-order asymptotic theory may provide a poor approximation to the finite sample distributions of the estimators.