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 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 .
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 subset size is chosen by minimizing the sample counterpart of the approximate MSE. We show that this method achieves the asymptotic optimality among the class of estimators with different subset sizes. To deal with averaging over a growing set of irrelevant instruments, we generalize the approximate MSE to find that the optimal k is larger than otherwise. An extensive simulation experiment shows that the CSA-2SLS estimator outperforms the alternative estimators when instruments are correlated with each other . As an empirical illustration, we estimate the logistic demand function in Berry, Levinsohn, and Pakes (1995) and find the CSA-2SLS estimate is better supported by economic theory than the alternative estimates .
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complete subset averaging (CSA) 2SLS
complete subset averaging (CSA) 2SLS
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CSA-2SLS estimator is obtained by choosing k
subset size is chosen by
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the
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A feature of equal-weight averaging is that all the instruments are used.
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a growing set of
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under the presence of a possibly growing set of irrelevant instruments, which suggests to choose a smaller k
to find that the optimal k is larger
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potentially huge improvement in the bias and the MSE by using the
that the
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estimator outperforms the alternative estimators
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and there exists large endogeneity
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estimated coefficient value
CSA-2SLS estimate
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other IV estimators
the alternative estimates