In this paper we propose a two-stage least squares (2SLS) estimator whose first stage is based on the equal-weight average over a complete subset . We derive the approximate mean squared error (MSE) that depends on the size of the complete subset and characterize the proposed estimator based on the approximate MSE. The size of the complete subset is chosen by minimizing the sample counterpart of the approximate MSE. We show that this method achieves the asymptotic optimality . To deal with weak or irrelevant instruments, we generalize the approximate MSE under the presence of a possibly growing set of irrelevant instruments, which provides useful guidance under weak IV environments. The Monte Carlo simulation results show that the proposed estimator outperforms alternative methods when instruments are correlated with each other and there exists high endogeneity. As an empirical illustration, we estimate the logistic demand function in Berry, Levinsohn, and Pakes (1995)  .
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 thecomplete 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 different 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 to choose a smaller k than otherwise. An extensive simulation experiment shows potentially huge improvement 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 coefficient value is better supported by economic theory than other IV estimators .
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complete subset averaging (CSA) 2SLS
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that depends on the size of the complete subset and characterize the proposed estimator based on the approximate MSE. The size of the complete subset is chosen by
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asymptotic optimality among the class of estimators with different subset sizes. A feature of equal-weight averaging is that all the instruments are used.
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provides useful guidance under weak IV environments. The Monte Carlo simulation results show that the proposed estimator outperforms alternative methods
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and find the estimated coefficient value is better supported by economic theory than other IV estimators