A Pretest to Differentiate Between Weak and Nearly-Weak Instrument Asymptotics

Abstract

We propose a pretest, bootstrap Kolmogorov-Smirnov test, to differentiate between weak and nearly-weak asymptotics. This is based on bootstrapping Wald Continuous Updating Estimator (CUE) based test. Since Wald CUE test has different limits under weak and nearly-weak cases this can be used in a pretest. We also conduct some simulations and show that some of the asset pricing models conform to nearly-weak asymptotics.

Keywords

• Bootstrap, Kolmogorov-Smirnov Test

References

1. Anderson, T.W. and H. Rubin (1949). Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations. Annals of Mathematical Statistics, 20, 46-63.
2. Andrews, D.W.K. (1994). Empirical Process Methods in Econometrics. Handbook of Econometrics, 4, 2247-2294.
3. Antoine, B. and E. Renault (2007). Efficient GMM with nearly-weak identification. Working paper. Department of Economics, University of North Carolina-Chapel Hill.
4. Caner, M. (2010). Testing, Estimation in GMM and CUE with Nearly-Weak IdentiŞcation. Econometric Reviews, 29, 330-363.
5. Hahn, J. and G. Kuersteiner (2002). Discontinuities of Weak Instrument Limiting Distributions. Economics Letters, 75, 325-331.
6. Hall, P. and J.L. Horowitz (1996). Bootstrap critical values for tests based on generalized method of moments estimators. Econometrica, 64, 891-916.
7. Hansen, L.P., J. Heaton and A. Yaron (1996). Finite Sample Properties of Some Alternative GMM Estimators. Journal of Business and Economic Statistics, 14, 262-280.
8. Kleibergen, F. (2005). Testing Parameters in GMM Without Assuming That They Are IdentiŞed. Econometrica, 73, 1103-1124.

9. Mood, A.M., F.A. Graybill and D.C. Boes (1974). Introduction to the Theory of Statistics. New-York: Mc-Graw Hill.
10. Phillips, P.C.B. and J.Y. Park (1988). On the Formulation of Wald Tests of Nonlinear Restrictions. Econometrica, 56, 1065-1083.
11. Stock, J.H. and J.H. Wright (2000). GMM with Weak Identification. Econometrica, 68, 1055- 1096.