Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Sep, 2001, Volume 69, Issue 5

Choosing the Number of Instruments
p. 1161-1191

Stephen G. Donald, Whitney K. Newey

Properties of instrumental variable estimators are sensitive to the choice of valid instruments, even in large cross‐section applications. In this paper we address this problem by deriving simple mean‐square error criteria that can be minimized to choose the instrument set. We develop these criteria for two‐stage least squares (2SLS), limited information maximum likelihood (LIML), and a bias adjusted version of 2SLS (B2SLS). We give a theoretical derivation of the mean‐square error and show optimality. In Monte Carlo experiments we find that the instrument choice generally yields an improvement in performance. Also, in the Angrist and Krueger (1991) returns to education application, when the instrument set is chosen in the way we consider, it turns out that both 2SLS and LIML give similar (large) returns to education.

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