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Choosing the Number of Instruments

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  • Donald, Stephen G.
  • Whitney Newey

Abstract

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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Suggested Citation

  • Donald, Stephen G. & Whitney Newey, 1999. "Choosing the Number of Instruments," Working papers 99-05, Massachusetts Institute of Technology (MIT), Department of Economics.
  • Handle: RePEc:mit:worpap:99-05
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    1. Richard Blundell & Alan Duncan & Costas Meghir, 1998. "Estimating Labor Supply Responses Using Tax Reforms," Econometrica, Econometric Society, vol. 66(4), pages 827-862, July.
    2. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-1476, November.
    3. Aronsson, Thomas & Palme, Marten, 1998. "A Decade of Tax and Benefit Reforms in Sweden: Effects on Labour Supply, Welfare and Inequality," Economica, London School of Economics and Political Science, vol. 65(257), pages 39-67, February.
    4. Blomquist, S.N., 1991. "Flexible Functional Forms and Coherency for Labor Supply Models," Papers 1991j, Uppsala - Working Paper Series.
    5. Andrews, Donald W. K., 1991. "Asymptotic optimality of generalized CL, cross-validation, and generalized cross-validation in regression with heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 47(2-3), pages 359-377, February.
    6. Blomquist, N. Soren, 1983. "The effect of income taxation on the labor supply of married men in Sweden," Journal of Public Economics, Elsevier, vol. 22(2), pages 169-197, November.
    7. N. S. Blomquist & U. Hansson-Brusewitz, 1990. "The Effect of Taxes on Male and Female Labor Supply in Sweden," Journal of Human Resources, University of Wisconsin Press, vol. 25(3), pages 317-357.
    8. Agell, S.A. & Meghir, C., 1995. "Male Labour Supply in Sweden : Are Incentives Important?," Papers 12, Uppsala - Working Paper Series.
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