Doko Tchatoka, Firmin (2010): Subset hypotheses testing and instrument exclusion in the linear IV regression.

PDF
MPRA_paper_29611.pdf Download (299kB)  Preview 
Abstract
This paper explores the sensitivity of plugin based subset tests to instrument exclusion in linear IV regression. Recently, identificationrobust statistics based on plugin principle have been developed for testing hypotheses specified on subsets of the structural parameters. However, their robustness to instrument exclusion has not been investigated. Instrument exclusion is an important problem in econometrics and there are at least two reasons to be concerned. Firstly, it is difficult in practice to assess whether an instrument has been omitted. Secondly, in many instrumental variable (IV) applications, an infinite number of instruments are available for use in large sample estimation. This is particularly the case with most time series models. If a given variable, say X(t), is a legitimate instrument, so too are its lags X(t1), X(t2), ... Hence, instrument exclusion seems highly likely in most practical situations. In this paper, we stress that the usual high level assumption of the identification may be misleading when potential relevant instruments are omitted. We propose an analysis of the asymptotic distributions of the LIML estimator and the plugin based statistics when potential instrument are omitted. Our results provides several new insights and extensions of earlier studies. We show that even when partial identification holds, the asymptotic distribution of the LIML estimator of the identified linear combination is no longer a Gaussian mixture, even though it is still consistent. This contrasts with the usual IV estimator of the identified linear combination, which is still asymptotically a Gaussian mixture despite the exclusion of relevant instruments. As a result, the asymptotic distributions of the plugin based subset statistics that exploit the LIML estimator are modified in a way that could lead to size distortions. We provide an empirical illustration using a widely considered returns to education example, which clearly shows that the confidence sets of the returns to education resulting from the plugin principle are highly sensitive to instrument exclusion.
Item Type:  MPRA Paper 

Original Title:  Subset hypotheses testing and instrument exclusion in the linear IV regression 
Language:  English 
Keywords:  Instrument exclusion, robust subset tests, LIML estimator, consistency, size distortions 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C13  Estimation: General 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 C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C30  General 
Item ID:  29611 
Depositing User:  Firmin Doko Tchatoka 
Date Deposited:  16. Aug 2012 12:27 
Last Modified:  19. Mar 2015 10:28 
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. Andrews, D.W. K., Stock, 2006. Inferencewith 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. Bean, C. R., 1994. European unemployment: A survey. The Journal of Economic Literature 32(2), 573–619. Breusch, T., Qian, H., Schmidt, P. , Wyhowski, D. , 1999. Redundancy of moment conditions. Journal of Econometrics 91, 89–111. Card, D., 1995. Using geographic variation in college proximity to estimate the return to schooling.. University of Toronto Press: in L. N. Christo. des, E. K. Grant, and R. Swidinsky (Eds.), Aspects of Labour Market Behaviour: Essays in Honour of John Vanderkamp. Chaudhuri, S., Zivot, E., 2010. A new method of projection based inference in GMM with weakly identified nuisance parameters. Technical report, Department of Economics, New York University N.Y. 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. Corbae, D., Durlauf, S. N., Hansen, B. E., eds, 2006. Econometric Theory and Practice: Frontiers of Analysis and Applied Research. Cambridge University Press, Cambridge, U.K. 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. 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 EconometricModelling. 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., 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., Khalaf, L., Kichian, M., 2006. Inflation dynamics and the new Keynesian Phillips curve: an identification robust econometric analysis. Journal of Economic Dynamics and Control 30(9), 1707–1727. 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 regressionswith weak, collinear or missing instruments. Journal of Econometrics 139(1), 133–153. Guggenberger, P., 2011. On the asymptotic size distortion of tests when instruments locally violate the exogeneity assumption. Econometric Theory forthcoming. Habib, A. M., Ljungqvist, A. P., 2001. Interpricing and entrepreneurial wealth losses in IPOs: Theory and evidence. Review of Financial Studies 14(2), 433–458. Hall, A. R., Inoue, A., Jana, K., Shin, C., 2007. Information in generalized method of moments estimation and entropybased moment selection. Journal of Econometrics 138, 488–512. Hansen, C., Hausman, J., Newey,W., 2008. Estimation with many instrumental variables. Journal of Business and Economic Statistics 26(4), 398–422. Hansen, L. P., Heaton, J., Yaron, A., 1996. Finite sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics 14, 262–280. Kleibergen, F., 2002. Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70(5), 1781–1803. Kleibergen, F., 2004. Testing subsets of structural coefficients in the IV regression model. Review of Economics and Statistics 86, 418–423. Kleibergen, F., 2005. Testing parameters in GMM without assuming that they are identified. Econometrica 73, 1103–1124. Kleibergen, F. , 2008. Subset statistics in the linear IV regression model. Technical report, Department of Economics, Brown University, Providence, Rhode Island Providence, Rhode Island. Kleibergen, F., 2009. Tests of risk premia in linear factor models. Journal of Econometrics forthcoming. Kleibergen, F., Mavroeidis, S., 2008. Weak instrument robust tests in GMM and the new keynesian phillips curve. Technical report, Department of Economics, Brown University, Providence, Rhode Island. Kleibergen, F., Mavroeidis, S., 2009. Inference on subsets of parameters in GMM without assuming identification. Technical report, Department of Economics, Brown University, Providence, Rhode Island. Kocherlakota, N. , 1990. On tests of representative consumer asset pricing models. Journal of Monetary Economics 26, 285–304. Loughran, T., Ritter, J., 2004.Why has IPO underpricing changed over time?. Financial Management 33(3). Malcomson, J.,Mavroeidis, S., 2006.Matching frictions, efficiency wages, and unemployment in the usa and the uk. Technical report, Department of Economics, Brown University, Providence, Rhode Island. Mavroeidis, S., 2004.Weak identification of forwardlookingmodels inmonetary economics.OxfordBulletin of Economics and Statistics 66, 609–635. Mavroeidis, S., 2005. Identification issues in forwardlooking models estimated by gmm with an application to the phillips curve. Journal of Money, Credit and Banking 66(3), 421–449. 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. Poskitt, D. , Skeels, C. , 2009. Assessing the magnitude of the concentration parameter in a simultaneous equations model. The Econometrics Journal 12, 26–44. Staiger, D. , Stock, J. H. , 1997. Instrumental variables regression with weak instruments. Econometrica 65(3), 557–586. Startz, R., Nelson, C. R. N., Zivot, E., 2006. Improved inference in weakly identified instrumental variables regression. in (Corbae, Durlauf and Hansen 2006), chapter 5. Stock, J. H., Wright, J. H., 2000. GMM with weak identification. Econometrica 68, 1055–1096. 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. 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. Zivot, E., Startz, R., Nelson, C. R., 2006. Inference in partially identified instrumental variables regression with weak instruments. in (Corbae et al. 2006), chapter 5, pp. 125–163. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/29611 