Two Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments
نویسنده
چکیده
This paper considers the IV estimation of spatial autoregressive models with endogenous regressors in the presence of many instruments. To improve asymptotic e¢ ciency, it may be desirable to use many valid instruments. However, nite sample properties of IV estimators can be sensitive to the number of instruments. For a spatial model with endogenous regressors, this paper derives the asymptotic distribution of the 2SLS estimator when the number of instruments grows with the sample size, and suggests a bias-correction procedure based on the leading-order many-instrument bias. The paper also gives the Nagar-type approximate MSEs of the 2SLS estimator and the bias-corrected 2SLS estimator, which can be minimized to choose instruments as in Donald and Newey (2001). A limited Monte Carlo experiment is carried out to study the nite sample performance of the instrument selection procedure. JEL classi cation: C13, C21
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Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments
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Lemma A.3 Under Assumption 4 (iii), we have (i) P i P 2 ii = o(K), P i 6=j PiiPjj = K 2 + o(K), P i 6=j PijPij = P i 6=j PijPji = K + o(K); (ii) P iMiiPii = o(K), P i 6=jMiiPjj = Ktr(M) + o(K) = O(K), P i 6=jMijPij = P i 6=jMijPji = tr(M) + o(K) = O(K); (iii) P iM 2 ii = O(K), P i 6=jMiiMjj = tr (M) P iM 2 ii = O(K ), P i 6=jMijMij = tr(MM 0) P iM 2 ii = O(K), P i 6=jMijMji = tr(M) P iM 2 ii = ...
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