1. Why is the TS2SLS estimator preferable in small samples?
Because using too many moment conditions often results in poor finite-sample performance of the GMM estimator (e.g., Tauchen, 1986, and Andersen and Sorensen, 1996), the TS2SLS estimator may be preferable in small samples.
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2. What is the value of the TSIV estimator?
0. (28)Proposition 3. Under Assumption 2, θ̃TS2SLS and θ̃RTSIV are consistent and asymptotically normally distributed with asymptotic covariance matrices ΣTS2SLS and ΣRTSIV , respectively, whereΣTS2SLS = (σ11 + κβ ′Σ22β)[E(s1iwiz ′ i)E(s1iziz ′ i) −1E(s1iziw ′ i)] −1 (29)and ΣRTSIV is the upper-left k × k submatrix of (G′RTSIV V −1RTSIV GRTSIV )−1,GRTSIV = − [ E(s1iziw ′ i) E(s2izix ′ i)β0 E(s2ivech(ziz ′ i))] ,VRTSIV = [ (σ11 + κβ′Σ22β)E(s1iziz′i) + E[(s1i + κ 2s2i)ziz′iΠ ′ββ′Πziz′i] E[(s1i + κ 2s2i)ziz′iΠ ′βvech(ziz′i) ′]
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3. What is the difference between the two TSIV estimators?
Under the conditions in which both estimators are consistent, the authors have shown that the commonly used TS2SLS approach is more asymptotically efficient because it implicitly corrects for differences in the empirical distributions of the instrumental variables between the two samples.
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