tailieunhanh - Bài giảng Chapter 5: Inference & prediction

Bài giảng Chapter 5: Inference & prediction tập trung trình bày các vấn đề cơ bản về waldtests; least souares discrepancy; the restricted least souares estimator;. Hy vọng tài liệu là nguồn thông tin hữu ích cho quá trình học tập và nghiên cứu của các bạn. | Advanced Econometrics Chapter 5 Inference Prediction Chapter 5 INFERENCE PREDICTION I. WALD TESTS Nested models If we can obtain one model from another by imposing restrictions on the parameters we say that the Z models are nested. Non-nested model If neither model is obtained as a restriction on the parameters of the other model. There two models are non-nested. Example A Wald test is for choosing between nested models. fa 01 02 X 2 03 X 3 8 1 Y 0. 02 X 2 S1 A Wald test is for choosing between non-nested models. fa 01 02 X 1 Y a a H fat px 02 X 03 Z 8 1 Y ị a a2 H a3M ị 8 We ll be concerned with several possible restrictions on p in the usual model. 8 N 0 ơ21 X non-stochastic ran X k. The general form of r restrictions R p q rxkk X1 rX1 R p q rxkk x1 rX1 R q re known non-random assume rank R r k . 1 0 0 0 1 0 0 1 1 0 1 1 01 02 03 04 0 1 0 Nam T. Hoang University of New England - Australia 1 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 5 Inference Prediction 00 02 0 04 1 0 0. r number of restrictions. II. LEAST SQUARES DISCREPANCY Suppose just estimate the model by OLS obtain 1___ 0u X X X Y u unrestriction . Let m R0u - q Let s consider the sampling distribution of m m R 3u - q a linear function of 3U rx1 E m E RPU - q RE Pu - q R0 - q E m 0 if R0 q VarCov m EarCov R 3u - q VarCovRpu RVpuR Rơ2 X X -1R ơ2R X X -1R So m N 0 ơ22 R X X -1 R if R0 q From the theorem for construction of Hausman s test we have m N 0 S m VarCov m - x r So W RPu - q R X X -1 R R 3 -q X Under H0 R0 q if ơ22 is known. Usually we don t know ơ22 we can replace ơ22 by any consistent estimator of ơ22 say ơ22 with plimcr ơ2e then will get the same asymptotic test distribution 2r Reject H0 if W critical value this test is asymptotic test . Nam T. Hoang University of New England - Australia 2 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 5 Inference Prediction F-statistics We can modify the Wald test statistics slightly and get the exact test not .