Baltagi and Li (1992) showed that for estimating a single equation in a simultaneous panel data model, EC2SLS has more instruments than G2SLS. Although these extra instruments are redundant in White (1986) terminology, they may yield different estimates and standard errors in empirical studies with finite N and T. We illustrate this using the crime data of Cornwell and Trumbull (1994). We show that the standard errors of EC2SLS are smaller than those of G2SLS for this example. In general, we prove that the asymptotic variance of G2SLS differs from that of EC2SLS by a positive semi-definite matrix. Although this difference tends to zero as the sample size tends to infinity, in small samples, this difference may be different from zero and can lead to gains in small sample efficiency. This proof is extended to the system equations 3SLS counterparts.
Baltagi, Badi and Liu, Long, "A Note on the Application of EC2SLS and EC3SLS Estimators in Panel Data Models" (2009). Economics - Faculty Scholarship. 89.
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