Doko Tchatoka, Firmin Sabro (2012): Specification Tests with Weak and Invalid Instruments.

PDF
MPRA_paper_40185.pdf Download (217Kb)  Preview 
Abstract
We investigate the size of the DurbinWuHausman tests for exogeneity when instrumental variables violate the strict exogeneity assumption. We show that these tests are severely size distorted even for a small correlation between the structural error and instruments. We then propose a bootstrap procedure for correcting their size. The proposed bootstrap procedure does not require identification assumptions and is also valid even for moderate correlations between the structural error and instruments, so it can be described as robust to both weak and invalid instruments.
Item Type:  MPRA Paper 

Original Title:  Specification Tests with Weak and Invalid Instruments 
Language:  English 
Keywords:  Exogeneity tests; weak instruments; instrument endogeneity; bootstrap technique 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C30  General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General 
Item ID:  40185 
Depositing User:  Firmin Doko Tchatoka 
Date Deposited:  20. Jul 2012 10:58 
Last Modified:  16. Feb 2013 03:32 
References:  Anderson, T. W., Rubin, H., 1949. Estimation of the parameters of a single equation in a complete system of stochastic equations. Annals of Mathematical Statistics 20, 46–63. Ashley, R. , 2009. Assessing the credibilility of instrumental variables inference with imperfect instruments via sensitivity analysis. Journal of Applied Econometrics 24(2), 325–337. Berkowitz, D., Caner, M. , Fang, Y. , 2008. Are nearly exogenous instruments reliable?. Economics Letters 101, 20–23. Bound, J., Jaeger, D. A. , Baker, R. M. , 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association 90, 443–450. Chaudhuri, S. , Rose, E. , 2009. Estimating the veteran effect with endogenous schooling when instruments are potentially weak. Technical report, IZA Discussion Papers No. 4203. Choi, I., Phillips, P. C. B., 1992. Asymptotic and finite sample distribution theory for IV estimators and tests in partially identified structural equations. Journal of Econometrics 51, 113–150. Davidson, R. , Mackinnon, J. G. , 2007. Testing for consistency using artificial regressions. Computational Statistics and Data Analysis 50, 3259–3281. Doko Tchatoka, F. , 2011. Subset hypotheses testing and instrument exclusion in the linear IV regression. Technical report, School of Economics and Finance, University of Tasmania Hobart, Australia. Doko Tchatoka, F. , Dufour, J.M. , 2008. Instrument endogeneity and identificationrobust tests: some analytical results. Journal of Statistical Planning and Inference 138(9), 2649–2661. 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 finitesample theory of exogeneity tests with possibly nongaussian errors and weak identification. Technical report, Department of Economics, McGill University, Canada Montreal, Canada. Dufour, J.M. , Taamouti, M. , 2007. Further results on projectionbased inference in IV regressions with weak, collinear or missing instruments. Journal of Econometrics 139(1), 133–153. Durbin, J. , 1954. Errors in variables. Review of the International Statistical Institute 22, 23–32. Frankel, J. A., Romer, D., 1999. Does trade cause growth?. American Economic Review 89(3), 379–399. Guggenberger, P. , 2010. The impact of a Hausman pretest on the size of the hypothesis tests. Econometric Theory 156, 337–343. Guggenberger, P. , 2011. On the asymptotic size distortion of tests when instruments locally violate the exogeneity assumption. Econometric Theory forthcoming. Hall, A. R., Rudebusch, G. D. , Wilcox, D. W. , 1996. Judging instrument relevance in instrumental variables estimation. International Economic Review 37, 283–298. Hansen, C., Hausman, J. , Newey, W. , 2008. Estimation with many instrumental variables. Journal of Business and Economic Statistics 26(4), 398–422. Harrison, A., 1996. Oponness and growth: a timeseries, crosscountry analysis for developing countries. Journal of Development Economics 48, 419–447. Hausman, J. , 1978. Specification tests in econometrics. Econometrica 46, 1251–1272. Hausman, J. , Hahn, J. , 2005. Estimation with valid and invalid instruments. Annales d’´Economie et de Statistique 79–80, 25–57. Imbens, G. W. , 2003. Sensitivity to exogeneity assumptions in program evaluation. American Economic Review 93(2), 126–132. Imbens, G.W., Koles´ar, M., Chetty, R., Friedman, J., Glaeser, E., 20011. Inference and identification with many invalid instruments. Technical report, Department of Economics, Havard University Boston, MA. Kiviet, J. F. , Niemczyk, J. , 2006. On the limiting and empirical distribution of IV estimators when some of the instruments are invalid. Technical report, Department of Quantitative Economics, University of Amsterdam Amsterdam, The Netherlands. Kleibergen, F., 2005. Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1124. Mankiw, N. G., Romer, D. , Weil, D. N. , 1992. A contribution to the empirics of economic growth. The Quarterly Journal of Economics 107(2), 407–437. Moreira, M. J. , 2003. A conditional likelihood ratio test for structural models. Econometrica 71(4), 1027–1048. Murray, P. M. , 2006. Avoiding invalid instruments and coping with weak instruments. The Journal of Economic Perspectives 20(4), 111–132. Samuel, B. , Michael, A. C. , 2009. Blunt instruments: A cautionary note on establishing the causes of economic growth. Technical report, Center for Global Development N0. 171. Sargan, J., 1958. The estimation of economic relationships using instrumental variables. Econometrica 26(3), 393–415. Shea, J., 1997. Instrument relevance in multilinear models: A simple measure. Review of Economics and Statistics 79, 348–352. Staiger, D., Stock, J. H., 1997. Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586. Stock, J. H. , Yogo, M. , 2005. Testing for weak instruments in linear IV regression. In: D. W. Andrews , J. H. Stock, eds, Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg . Cambridge University Press, Cambridge, U.K. , chapter 6 , pp. 80–108. Wu, D.M., 1973. Alternative tests of independence between stochastic regressors and disturbances. Econometrica 41, 733–750. Wu, D.M., 1974. Alternative tests of independence between stochastic regressors and disturbances: Finite sample results. Econometrica 42, 529–546. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/40185 