Doko Tchatoka, Firmin Sabro and Dufour, Jean-Marie (2008): Instrument endogeneity and identification-robust tests: some analytical results. Published in: Journal of Statistical Planning and Inference , Vol. 138, (12. March 2008): pp. 2649-2661.
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When some explanatory variables in a regression are correlated with the disturbance term, instrumental variable methods are typically employed to make reliable inferences. Furthermore, to avoid difficulties associated with weak instruments, identification robust methods are often proposed. However, it is hard to assess whether an instrumental variable is valid in practice because instrument validity is based on the questionable assumption that some of them are exogenous. In this paper, we focus on structural models and analyze the effects of instrument endogeneity on two identification-robust procedures, the Anderson-Rubin (1949, AR) and the Kleibergen (2002, K) tests, with or without weak instruments. Two main setups are considered: (1) the level of “instrument” endogeneity is fixed (does not depend on the sample size), and (2) the instruments are locally exogenous, i.e. the parameter which controls instrument endogeneity approaches zero as the sample size increases. In the first setup, we show that both test procedures are in general consistent against the presence of invalid instruments (hence asymptotically invalid for the hypothesis of interest), whether the instruments are “strong” or “weak”. We also describe cases where test consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. These include, in particular, cases where the 2SLS estimator remains consistent, but the AR and K tests are asymptotically invalid. In the second setup, we find (non-degenerate) asymptotic non-central chi-square distributions in all cases, and describe cases where the non-centrality parameter is zero and the asymptotic distribution remains the same as in the case of valid instruments (despite the presence of invalid instruments). Overall, our results underscore the importance of checking for the presence of possibly invalid instruments when applying “identification-robust” tests.
|Item Type:||MPRA Paper|
|Original Title:||Instrument endogeneity and identification-robust tests: some analytical results|
|Keywords:||simultaneous equations; instrumental variables; locally weak instruments; invalid instruments; locally exogenous instruments.|
|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
|Depositing User:||Firmin Doko Tchatoka|
|Date Deposited:||19. Mar 2011 21:28|
|Last Modified:||12. Feb 2013 11:52|
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(1), 46–63. Ashley, R. , 2006. Assessing the credibilility of instrumental variables inference with imperfect instruments via sensitivity analysis. Technical report, Economics Department, Virginia Polytechnic Institute Blacksburg, Virginia. Bekker, P., 1994. Alternative approximations to the distributions of instrumental variable estimators. Econometrica 62, 657–681. Donald, S. G., Newey, W. K., 2001. Choosing the number of instruments. Econometrica 69, 1161– 1191. Dufour, J.-M., 1997. Some impossibility theorems in econometrics, with applications to structural and dynamic models. Econometrica 65, 1365–1389. Dufour, J.-M. , 2003. Identification, weak instruments and statistical inference in econometrics. Canadian Journal of Economics 36(4), 767–808. Dufour, J.-M. , Hsiao, C. , 2008. Identification. In: L. E. Blume , S. N. Durlauf, eds, The New Palgrave Dictionary of Economics 2nd edn. Palgrave Macmillan, Basingstoke, Hampshire, England. forthcoming. Dufour, J.-M., Jasiak, J., 2001. Finite sample limited information inference methods for structural equations and models with generated regressors. International Economic Review 42, 815–843. Dufour, J.-M. , Taamouti, M. , 2003. Point-optimal instruments and generalized Anderson-Rubin procedures for nonlinear models. Technical report, C.R.D.E., Université de Montréal. Dufour, J.-M., Taamouti, M., 2005. Projection-based statistical inference in linear structural models with possibly weak instruments. Econometrica 73(4), 1351–1365. Dufour, J.-M., Taamouti, M., 2007. Further results on projection-based inference in IV regressions with weak, collinear or missing instruments. Journal of Econometrics 139(1), 133–153. Hahn, J., Hausman, J. A., 2003. IV estimation with valid and invalid instruments. Technical report, Department of Economics, Masschusetts Institute of Technology Cambridge. Massachusetts. Hall, A. R., Peixe, F. P. M., 2003. A consistent method for the selection of relevant instruments. Econometric Reviews 2(3), 269–287. Hall, A. R., Rudebusch, G. D., Wilcox, D. W., 1996. Judging instrument relevance in instrumental variables estimation. International Economic Review 37, 283–298. Kadane, J. B., Anderson, T.W., 1977. A comment on the test of overidentifying restrictions. Econometrica 45(4), 1027–1031.
Kivet, 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. , 2002. Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70(5), 1781–1803. Moreira, M. J. , 2003. A conditional likelihood ratio test for structural models. Econometrica 71(4), 1027–1048. Phillips, P. C. B., 1989. Partially identified econometric models. Econometric Theory 5, 181–240. Sargan, J. D., 1958. The estimation of economic relationships using instrumental variables. Econometrica 26(3), 393–415. Small, D. S., 2007. Sensitivity analysis for instrumental variables regression with overidentifying restrictions. Journal of the American Statistical Association 102(479), 1049–1058. Staiger, D., Stock, J. H., 1997. Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586. Stock, J. H.,Wright, J. H., Yogo, M., 2002. A survey of weak instruments and weak identification in generalized method of moments. Journal of Business and Economic Statistics 20(4), 518–529. Swanson, N. R., Chao, J. C., 2005. Notes and comments: Consistent estimation with a large number of weak instruments. Econometrica 73, 1673–1692. Wang, J., Zivot, E., 1998. Inference on structural parameters in instrumental variables regression with weak instruments. Econometrica 66(6), 1389–1404.