ror.org/026zzn846
Résumés
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.
Parties annexes
Bibliography
- Angrist, J., and A. Krueger (1991). “Bootstrap and Randomization Tests of Some Nonparametric Hypotheses.’’ Quarterly Journal of Economics, 106: 979-1014.10.2307/2937954 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Bai, J., and S. Ng (2010). “Instrumental Variable Estimation in a Data Rich Environment.’’ Econometric Theory, 26: 1577-1606.10.1017/S0266466609990727 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- 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: 29-38.10.2307/2951662 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Bekker, P. A. (1994). “Alternative Approximations to the Distributions of Instrumental Variable Estimators.’’ Econometrica, 62: 657- 681.10.2307/2951662 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- 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.10.1111/1468-0262.00238 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Chao, J. C., and N. R. Swanson (2005), “Consistent Estimation with a Large Number of Weak Instruments.’’ Econometrica, 73: 1673-1692.10.1111/j.1468-0262.2005.00632.x Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Donald, S. G., and W. K. Newey (2001), “Choosing the Number of Instruments.’’ Econometrica, 69: 1161-1191.10.1111/1468-0262.00238 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Hahn, J. (2002), “Optimal Inference with Many Instruments.’’ Econometric Theory, 18: 140-168.10.1017/S0266466602181084 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Hahn, J., J. Hausman, and G. Kuersteiner (2001). “Accuracy of Higher Order Bias and MSE Approximations.’’ Econometrics Journal, 7: 272-306.10.1111/j.1368-423X.2004.00131.x Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Hansen, C., J. Hausman, and W. K. Newey (2006). “Many Instruments, Weak Instruments and Microeconometric Practice.’’ Working Paper, MIT.10.2307/1912160 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Kapetanios, G., and M. Marcellino (2007). “Cross-sectional Averaging and Instrumental Variable Estimation with Many Weak Instruments.’’ Economics Letters, 108: 36-39.10.1016/j.econlet.2010.03.013 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Kapetanios, G., and M. Marcellino (2010). “Factor-GMM Estimation with Large Sets of PossiblyWeak Instruments.’’ Computational Statistics and Data Analysis, 54: 2655-2675.10.1016/j.csda.2010.04.008 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Morimune, K. (1983). “Approximate Distributions of k-class Estimators when the Degree of Overidentification is Large Compared with the Sample Size.’’ Econometrica, 51: 821-842.10.2307/1912160 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Newey, W. K. (2004). “Many Weak Moment Asymptotics for the Continuously Updated GMM Estimator.’’ Working Paper, MIT.Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- 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. 449-516.10.1016/S1573-4412(83)01012-0 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- 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.Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- Staiger, D., and J. H. Stock (1997). “Instrumental Variables Regression with Weak Instruments.’’ Econometrica, 65: 557-586.10.2307/2171753 Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- 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.Google Scholar Rechercher cette référence bibliographique sur Google Scholar
- 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.Google Scholar Rechercher cette référence bibliographique sur Google Scholar