Finite-sample refinement of GMM approach to nonlinear models under heteroskedasticity of unknown form

It is quite common to observe heteroskedasticity in real data, in particular, cross-sectional or micro data. Previous studies concentrate on improving the finite-sample properties of tests under heteroskedasticity of unknown forms in linear models. The advantage of a heteroskedasticity consistent covariance matrix estimator (HCCME)-type small-sample improvement for linear models does not carry over to the nonlinear model specifications since there is no obvious counterpart for the diagonal element of the projection matrix in linear models, which is crucial for implementing the finite-sample refinement. Within the framework of nonlinear models, we develop a straightforward approach by extending the applicability of HCCME-type corrections to the two-step GMM method. The Monte Carlo experiments show that the proposed method not only refines the testing procedure in terms of the error of rejection probability, but also improves the coefficient estimation based on the mean squared error (MSE) and the mean absolute error (MAE). The estimation of a constant elasticity of substitution (CES)-type production function is also provided to illustrate how to implement the proposed method empirically.