Appendices to Two Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments
نویسندگان
چکیده
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 = O(K); and (iv) if Assumption 5 (ii) also holds, P iM 2 ii = o(K).
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