Econometrics & Applied Economics Seminar - Seojeong Lee (University of New South Wales)

Room 605, Level 6, FBE Building, 111 Barry Street, Carlton

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Title: Complete Subset Averaging with Many Instruments

Abstract: We propose a two-stage least squares (2SLS) estimator whose first stage is the equal-weight average over a complete subset with k instruments among K available, which we call the complete subset averaging (CSA) 2SLS. The approximate mean squared error (MSE) is derived as a function of the subset size k by the Nagar (1959) expansion. The CSA-2SLS estimator is obtained by choosing k minimizing the sample counterpart of the approximate MSE. We show that this method achieves asymptotic optimality among the class of estimators with di fferent subset sizes. A feature of equal-weight averaging is that all the instruments are used. To deal with averaging over irrelevant instruments, we generalize the approximate MSE under the presence of a possibly growing set of irrelevant instruments, which suggests choosing a smaller k than otherwise. An extensive simulation experiment shows potentially huge improvements in the bias and the MSE by using the CSA-2SLS when instruments are correlated with each other and there exists large endogeneity. As an empirical illustration, we estimate the logistic demand function in Berry, Levinsohn, and Pakes (1995) and find the estimated coffecient value is better
supported by economic theory than other IV estimators.