Doko Tchatoka, Firmin and Dufour, JeanMarie (2012): Identificationrobust inference for endogeneity parameters in linear structural models.

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Abstract
We provide a generalization of the AndersonRubin (AR) procedure for inference on parameters which represent the dependence between possibly endogenous explanatory variables and disturbances in a linear structural equation (endogeneity parameters). We focus on secondorder dependence and stress the distinction between regression and covariance endogeneity parameters. Such parameters have intrinsic interest (because they measure the effect of "common factors" which induce simultaneity) and play a central role in selecting an estimation method (because they determine "simultaneity biases" associated with leastsquares methods). We observe that endogeneity parameters may not be identifiable and we give the relevant identification conditions. We develop identificationrobust finitesample tests for joint hypotheses involving structural and regression endogeneity parameters, as well as marginal hypotheses on regression endogeneity parameters. For Gaussian errors, we provide tests and confidence sets based on standardtype Fisher critical values. For a wide class of parametric nonGaussian errors (possibly heavytailed), we also show that exact Monte Carlo procedures can be applied using the statistics considered. As a special case, this result also holds for usual ARtype tests on structural coefficients. For covariance endogeneity parameters, we supply an asymptotic (identificationrobust) distributional theory. Tests for partial exogeneity hypotheses (for individual potentially endogenous explanatory variables) are covered as instances of the class of proposed procedures. The proposed procedures are applied to two empirical examples: the relation between trade and economic growth, and the widely studied problem of returns to education.
Item Type:  MPRA Paper 

Original Title:  Identificationrobust inference for endogeneity parameters in linear structural models 
Language:  English 
Keywords:  Identificationrobust confidence sets; endogeneity; ARtype statistic; projectionbased techniques; partial exogeneity test 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C52  Model Evaluation, Validation, and Selection 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 
Item ID:  40695 
Depositing User:  Firmin Doko Tchatoka 
Date Deposited:  16 Aug 2012 12:28 
Last Modified:  03 Feb 2016 08:33 
References:  Abdelkhalek, T. , Dufour, J.M. , 1998. Statistical inference for computable general equilibrium models with applications to a model of the moroccan economy. Review of Economics and Statistics, pp. 520–534. 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. Angrist, J. D. , Krueger, A. B. , 1991. Does compulsory school attendance affect schooling and earning?. Quarterly Journal of Economics CVI, 979–1014. Angrist, J. D., Krueger, A. B., 1995. Splitsample instrumental variables estimates of the return to schooling. Journal of Business and Economic Statistics 13, 225–235. Barro, R., 1977. Unanticipated money growth and unemployment in united states. American Economic Review 67, 101–115. 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. Doko Tchatoka, F. , Dufour, J.M. , 2009. Exogeneity tests, nonGaussian distributions and weak identification : Finitesample and asymptotic distributional theory. Technical report, C.R.D.E., Université de Montréal. Doko Tchatoka, F., Dufour, J.M., 2010. On the finitesample theory of exogeneity tests with possibly nonGaussian errors and weak identification. Technical report, Department of Economics, McGill University, Canada Montréal, Canada. Doko Tchatoka, F., Dufour, J.M., 2011. Exogeneity tests and estimation in IV regressions. Technical report, Department of Economics, McGill University, Canada Montréal, Canada. Dufour, J.M., 1979. Methods for Specification Errors Analysis with Macroeconomic Applications PhD thesis University of Chicago. 257 + XIV pages. Thesis committee: Arnold Zellner (Chairman), Robert E. Lucas and Nicholas Kiefer. Dufour, J.M., 1987. Linear Wald methods for inference on covariances and weak exogeneity tests in structural equations. In: I. B. MacNeill , G. J. Umphrey, eds, Advances in the Statistical Sciences: Festschrift in Honour of Professor V.M. Joshi’s 70th Birthday. Volume III, Time Series and Econometric Modelling. D. Reidel, Dordrecht, The Netherlands, pp. 317–338. Dufour, J.M., 1990. Exact tests and confidence sets in linear regressions with autocorrelated errors. Econometrica 58, 475–494. 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. , 2006. Monte carlo tests with nuisance parameters: A general approach to finitesample inference and nonstandard asymptotics in econometrics. Journal of Econometrics 138, 2649–2661. 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., 2005. Projectionbased statistical inference in linear structural models with possibly weak instruments. Econometrica 73(4), 1351–1365. 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. Engle, R. F., 1982. A general approach to Lagrange multiplier diagnostics. Journal of Econometrics 20, 83–104. Farebrother, R. W., 1976. A remark on the Wu test. Econometrica 44, 475–477. Frankel, J. A., Romer, D., 1999. Does trade cause growth?. American Economic Review 89(3), 379–399. 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., Taylor, W. E., 1981. A generalized specification test. Economics Letters 8, 239–245. Holly, A., 1982. A remark on Hausman’s test. Econometrica 50, 749–759. Hwang, H.S. , 1980. Test of independence between a subset of stochastic regressors and disturbances. International Economic Review 21, 749–760. Irwin, A.D., Tervio, M., 2002. Does trade raise income? evidence from twentieth century. Journal of International Economics 58, 1–18. Kariya, T., Hodoshima, H., 1980. Finitesample properties of the tests for independence in structural systems and LRT. The Quarterly Journal of Economics 31, 45–56. Kiviet, J. F., Niemczyk, J., 2007. The asymptotic and finitesample distributions of OLS and simple IV in simultaneous equations. Computational Statistics and Data Analysis 51, 3296–3318. Kleibergen, F. , 2002. Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70(5), 1781–1803. 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. Nakamura, A., Nakamura, M., 1981. On the relationships among several specification error tests presented by Durbin, Wu and Hausman. Econometrica 49, 1583–1588. Revankar, N. S., 1978. Asymptotic relative efficiency analysis of certain tests in structural sysytems. International Economic Review 19, 165–179. Revankar, N. S., Hartley, M. J., 1973. An independence test and conditional unbiased predictions in the context of simultaneous equation systems. International Economic Review 14, 625–631. Reynolds, R. A., 1982. Posterior odds for the hypothesis of independence between stochastic regressors and disturbances. International Economic Review 23(2), 479–490. Smith, R. J., 1984. A note on likelihood ratio tests for the independence between a subset of stochastic regressors and disturbances. International Economic Review 25, 263–269. Spencer, D. E., Berk, K. N., 1981. A limitedinformation specification test. Econometrica 49, 1079–1085. 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. 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. Wu, D.M., 1983a. A remark on a generalized specification test. Economics Letters 11, 365–370. Wu, D.M., 1983b. Tests of causality, predeterminedness and exogeneity. International Economic Review 24(3), 547–558. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/40695 