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Statistica Sinica 20 (2010), 1725-1747



Zhiguo Xiao$^1$, Jun Shao$^2$ and Mari Palta$^2$

$^1$Fudan University and $^2$University of Wisconsin, Madison

Abstract: Panel data allow correction for measurement error without assuming a known measurement error covariance matrix or using additional validation/replication data to estimate the measurement error covariance matrix. Griliches and Hausman (1986) proposed using the generalized method of moments (GMM) or optimal weighting to efficiently combine instrumental variable (IV) estimators. Wansbeek (2001) applied GMM based on moment conditions expressed in the form of the Kronecker product. This paper studies some issues crucial to applications of these two approaches, including the estimability of the regression parameter under Griliches and Hausman's or Wansbeek's approach, how to choose instruments, what is the optimally weighted IV estimator, how to explicitly construct GMM estimators, how to remove the redundancy of the moment conditions constructed by Wansbeek (2001), and the existence of optimal GMM estimators. We unify Griliches and Hausman's and Wansbeek's approaches by establishing their equivalence. We also consider models with exogenous regressors and models with nonclassical assumptions. We apply the methods in this paper to revisit an investment controversy, viz., whether financially constrained firms respond to internal funds such as cash flow more sensitively than financially unconstrained firms.

Key words and phrases: Equivalence, GMM, instrumental variable, measurement error, panel data, Tobin's q.

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