Appendix A: Asymptotic Properties of the GMM Esti- mators and Diagnostic Tests
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چکیده
The additional regularity conditions required for consistency are stated in Hansens Theorem 2.1. It follows from assumption 3 that a T a:s: ! a 0 = D0 0W 0 . De ne h 0(b ) = a 0[E(R) D0b ]. Given that D0 has full column rank and W 0 is positive de nite, the function h 0(b ) has a unique zero, b z = (D 0 0W 0D0) D0 0W 0E(R ). Since the model is true E(R) = D0b 0. Substituting this into the expression for b z we have b z = b 0. From Hansens (1982) Theorem 2.1, b̂ a:s: ! b 0. Similarly, it follows from assumption 3 that a T a:s: ! a 0 with
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