Tham khảo tài liệu 'handbook of empirical economics and finance _3', tài chính - ngân hàng, tài chính doanh nghiệp phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Efficient Inference with Poor Instruments A General Framework 43 Second the interpretation of the matrix AT in terms of reparametrization is underpinned by the proof of Theorem which shows that Yr . . . . . . A X1TR . X T R . . X tR RAt with R R . R . . R 1. J LI I X I I X XI . i V 2 I X X 2 . . V IT X X I I I X X X lyvXLXlXX I X X I . X X 2 . . -L- X I I . R is a nonsingular matrix of size p with each submatrix Ri of size p si AT is a diagonal matrix with L diagonal blocks equal to iTIdSi. It is worth reinterpreting Theorem in terms of the asymptotic distribution of the estimator of a new parameter vector4 h R-16 hi h2 hL . Theorem states that R-10 t is a consistent asymptotically normal estimator of the true unknown value q0 R-100 while each subvector qj of size si is attached to a specific slower rate of convergence VT iT. It is clear in the appendix that this reparametrization is performed according to the directions which span the range of the Jacobian matrix of the rescaled efficient moment conditions d 0 that is according to the columns of the matrix R. Even though the knowledge of the matrix R and corresponding rates iT is immaterial for the practical implementation of inference procedures on structural parameters as shown in Section it may matter for a fair assessment of the accuracy of this inference. As an illustration Subsection studies the power of score-type tests against sequences of local alternatives in different directions. In the context of the consumption-based capital asset pricing model CCAPM discussed in Stock and Wright 2000 and Antoine and Renault 2009 there are two structural parameters 01 the subjective discount factor and 02 the coefficient of relative risk aversion of a representative investor. Antoine and Renault 2009 provide compelling evidence that a first parameter qu estimated at fast rate Vt is very close to 01 the estimation results show that q1 - while any other direction in the parameter
