Abstracts
Abstract
This paper proposes and discusses an instrumental variable estimator that can be of particular relevance when many instruments are available and/or the number of instruments is large relative to the total number of observations. Intuition and recent work (see, e.g., Hahn, 2002) suggest that parsimonious devices used in the construction of the final instruments may provide effective estimation strategies. Shrinkage is a well known approach that promotes parsimony. We consider a new shrinkage 2SLS estimator. We derive a consistency result for this estimator under general conditions, and via Monte Carlo simulation show that this estimator has good potential for inference in small samples.
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Appendices
Acknowledgements
We would like to thank an anonymous referee for helpful comments on a previous draft.
Bibliography
- Angrist, J., and A. Krueger (1991). “Bootstrap and Randomization Tests of Some Nonparametric Hypotheses.’’ Quarterly Journal of Economics, 106: 979-1014.
- Bai, J., and S. Ng (2010). “Instrumental Variable Estimation in a Data Rich Environment.’’ Econometric Theory, 26: 1577-1606.
- Bai, Z., and G. H. Golub (1997). “Bounds for the Trace of the Inverse and the Determinant of Symmetric Positive Definite Matrices.’’ Annals of Numerical Mathematics, 4: 29-38.
- Bekker, P. A. (1994). “Alternative Approximations to the Distributions of Instrumental Variable Estimators.’’ Econometrica, 62: 657- 681.
- Chao, J. C., and N. R. Swanson (2004). “Asymptotic Normality of Single-Equation Estimators for the Case with a Large Number of Weak Instruments.’’ in Corbae, D., S. Durlauf and B. Hansen (Eds), Frontiers of Analysis and Applied Research: Essays in Honor of Peter C. B. Phillips, Cambridge, U.K.: Cambridge University Press.
- Chao, J. C., and N. R. Swanson (2005), “Consistent Estimation with a Large Number of Weak Instruments.’’ Econometrica, 73: 1673-1692.
- Donald, S. G., and W. K. Newey (2001), “Choosing the Number of Instruments.’’ Econometrica, 69: 1161-1191.
- Hahn, J. (2002), “Optimal Inference with Many Instruments.’’ Econometric Theory, 18: 140-168.
- Hahn, J., J. Hausman, and G. Kuersteiner (2001). “Accuracy of Higher Order Bias and MSE Approximations.’’ Econometrics Journal, 7: 272-306.
- Hansen, C., J. Hausman, and W. K. Newey (2006). “Many Instruments, Weak Instruments and Microeconometric Practice.’’ Working Paper, MIT.
- Kapetanios, G., and M. Marcellino (2007). “Cross-sectional Averaging and Instrumental Variable Estimation with Many Weak Instruments.’’ Economics Letters, 108: 36-39.
- Kapetanios, G., and M. Marcellino (2010). “Factor-GMM Estimation with Large Sets of PossiblyWeak Instruments.’’ Computational Statistics and Data Analysis, 54: 2655-2675.
- Morimune, K. (1983). “Approximate Distributions of k-class Estimators when the Degree of Overidentification is Large Compared with the Sample Size.’’ Econometrica, 51: 821-842.
- Newey, W. K. (2004). “Many Weak Moment Asymptotics for the Continuously Updated GMM Estimator.’’ Working Paper, MIT.
- Phillips, P. C. B. (1983). “Exact Small Sample Theory in the Simultaneous Equations Model.’’ in Z. Griliches and M. D. Intriligator (Eds), Handbook of Econometrics, Vol. I, Amsterdam: North-Holland, pp. 449-516.
- Rothenberg, T. (1984). “Approximating the Distributions of Econometric Estimators and Test Statistics.’’ in Z. Griliches and M. D. Intriligator (Eds), Handbook of Econometrics, Vol. I, Amsterdam: North-Holland, pp. 881.935.
- Staiger, D., and J. H. Stock (1997). “Instrumental Variables Regression with Weak Instruments.’’ Econometrica, 65: 557-586.
- Stock, J. H., and M. Yogo (2003a). “Asymptotic Distributions of Instrumental Variables Statistics with Many Weak Instruments’.’’ in Andrews, D. W. K. and J. H. Stock (Eds), Identification and Inference for Econometric Models: Essays in Honor of Thomas J. Rothenberg, Cambridge, U.K.: Cambridge University Press.
- Stock, J. H., and M. Yogo (2003b). “Testing for Weak Instruments in Linear IV Regression.’’ in Andrews, D. W. K. and J. H. Stock (Eds), Identification and Inference for Econometric Models: Essays in Honor of Thomas J. Rothenberg, Cambridge, U.K.: Cambridge University Press.