On the Validity of Durbin-Wu-Hausman Tests for Assessing Partial Exogeneity Hypotheses with Possibly Weak Instruments

Doko Tchatoka, Firmin (2012): On the Validity of Durbin-Wu-Hausman Tests for Assessing Partial Exogeneity Hypotheses with Possibly Weak Instruments.

Abstract

We investigate the validity of the standard specification tests for assessing the exogeneity of subvectors in the linear IV regression. Our results show that ignoring the endogeneity of the regressors whose exogeneity is not being tested leads to invalid tests (level is not controlled). When the fitted values from the first stage regression of these regressors are used as instruments under the partial null hypothesis of interest, as suggested Hausman and Taylor (1980, 1981), some versions of these tests are invalid when identification is weak and the number of instruments is moderate. However, all tests are overly conservative and have no power when the number of instruments increases, even for moderate identification strength.

• Item Type: MPRA Paper
• Language: English
• Keywords: Partial exogeneity; sized distortions; weak identification
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C30 - General; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Andrews, D. W. K. , Stock , 2006. Inference with weak instruments. In: R. Blundell, W. Newey , T. Pearson, eds, Advances in Economics and Econometrics, Theory and Applications, 9th Congress of the Econometric Society Vol. 3 . Cambridge University Press, Cambridge, U.K. , chapter 6.

Baun, C. F., Schaffer, M. E. , Stillman, S. , 2003. Instrumental variable and GMM: Estimation and testing. Technical report, Department of Economics, Boston College, USA Boston, USA.

Chaudhuri, S. , Rose, E. , 2009. Estimating the veteran effect with endogenous schooling when instruments are potentially weak. Technical report, IZA Discussion Papers No.4203.

Doko Tchatoka, F., Dufour, J.-M., 2011a. Exogeneity tests and estimation in IV regressions. Technical report, Department of Economics, McGill University, Canada Montreal, Canada.

Doko Tchatoka, F. , Dufour, J.-M. , 2011b. On the finite-sample theory of exogeneity tests with possibly non-gaussian errors and weak identification. Technical report, Department of Economics, McGill University, Canada Montreal, Canada.

Dufour, J.-M., 2003. Identification, weak instruments and statistical inference in econometrics. Canadian Journal of Economics 36(4), 767–808.

Durbin, J., 1954. Errors in variables. Review of the International Statistical Institute 22, 23–32.

Guggenberger, P. , 2010. The impact of a Hausman pretest on the size of the hypothesis tests. Econometric Theory 156, 337–343.

Hahn, J., Ham, J. , Moon, H. R. , 2010. The Hausman test and weak instruments. Journal of Econometrics 160, 289–299.

Hansen, C., Hausman, J. , Newey, W. , 2008. Estimation with many instrumental variables. Journal of Business and Economic Statistics 26(4), 398–422.

Hausman, J. , 1978. Specification tests in econometrics. Econometrica 46, 1251–1272.

Hausman, J., Taylor, W., 1981. Panel data and unobservable individual effects. Econometrica 49(6), 1377–1398.

Hausman, J., Taylor, W. E., 1980. Comparing specification tests and clissical tests. Technical report, Department of Economics, MIT Boston, MA.

Staiger, D. , Stock, J. H. , 1997. Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586.

Wu, D.-M. , 1973. Alternative tests of independence between stochastic regressors and disturbances. Econometrica 41, 733–750.