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Bài giảng Chapter 4: Estimation by instrumental variables

Mời các bạn cùng tìm hiểu endogeneity; estimation by intrumental variables; two-stage least soures estimation;. được trình bày cụ thể trong "Bài giảng Chapter 4: Estimation by instrumental variables". Hy vọng tài liệu là nguồn thông tin hữu ích cho quá trình học tập và nghiên cứu của các bạn. | Advanced Econometrics Chapter 4 Estimation By Instrumental Variables Chapter 4 ESTIMATION BY INSTRUMENTAL VARIABLES Instrumental Variable Estimators I. ENDOGENEITY Now suppose s Xare not independently generated Cov s X 0 and E s X 0. There are 4 sources of this problem 1. Errors in measurement of independent variables Suppose that the true regression equation is given by yi fa0 faxi Si where E s E sixi 0 Note Cov si xi E si xi - x E si xi - E si x E si xi s--V-- 0 So if Cov si Xị 0 E si Xị 0 Suppose x xi ei Assume E e E eixi 0 estimate yi fa fax ui where ui Si - p1ei correlated with x xi ei through terms ei Cov ui x 0 Nam T. Hoang University of New England - Australia 1 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 4 Estimation By Instrumental Variables 2. Variables on both sides o f regression equation are jointly determined endogenous - RHS variables are endogenous. ht 30 31et ui e a0 a1hi Sị a0 a 30 a e O -iro 1 1 -a131 1 -a131 ui 1 ------- et 1 -a131 Cov ui ei 0 3. Omitted variables w 33 3s 32 a Si Estimate wi 30 3s u Where ui 32a Sị if ai and si are correlated Cov ui si 0 4. Lagged dependent variables Yt-1 as a regressor and auto correlated errors. Yt a 3Xt ẢYt-1 St St PSt-1 ut Cov st Yt-1 0 because Yt-1 and St both contain st-1. Model 1 Y X 3 S n k 2 X and S are not generated independently 3 E sX t 0 4 E SS X Ji 5 X consists of stationary random variables with E Xi Xi plim 1 XX s XX n Nam T. Hoang University of New England - Australia 2 University of Economics - HCMC - Vietnam Advanced Econometrics Chapter 4 Estimation By Instrumental Variables Now p lim X s Y 0 and n p lim p p - p lim - X s p Tp Y p XX Xx n _____VV _ 0 p is an inconsistent estimator. A 1 1 1 1 p is also no longer unbiased E p X p XX -1X E s X p --V--J 0 II. ESTIMATION BY INSTRUMENTAL VARIABLES Suppose we can find a set of kvariables W that have two properties n7.k 1. Exogeneity validity They are uncorrelated with the disturbance s. 2. Relevance They are correlated .