Robust Inference for Nonlinear Moment Condition Models with Possible Weak Identification

The award funds work that will develop new methods for analyzing economic data. Researchers working with economic data often rely on asymptotic approximations in making statistical inferences. However, we know that standard asymptotic theory fails when identification is weak. Therefore these approximations are not very accurate in a number of cases. The PI proposes a possible solution. The new methods could potentially be used in a variety of applications. The project advances science by developing new methods for conducting formal statistical tests of certain kinds of economic theory.

The PI plans to develop testing procedures in nonlinear Generalized Method of Moments (GMM) models that have correct asymptotic size for a virtually unrestricted parameter space, except for uniform moment bounds on the moment function and its derivative. The proposed test is a generalized form of the Conditional Likelihood Ratio (CLR) test. He then wants to show that this tests have (near) optimality properties in terms of power for certain models and classes of tests.