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INSTRUMENTAL VARIABLE ESTIMATION IN A DATARICH ENVIRONMENT

Published online by Cambridge University Press:  17 March 2010

Jushan Bai  and
Serena Ng
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Abstract

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We consider estimation of parameters in a regressionmodel with endogenous regressors. The endogenousregressors along with a large number of otherendogenous variables are driven by a small number ofunobservable exogenous common factors. We show thatthe estimated common factors can be used asinstrumental variables and they are more efficientthan the observed variables in our framework.Whereas standard optimal generalized method ofmoments estimator using a large number ofinstruments is biased and can be inconsistent, thefactor instrumental variable estimator (FIV) isshown to be consistent and asymptotically normal,even if the number of instruments exceeds the samplesize. Furthermore, FIV remains consistent even ifthe observed variables are invalid instruments aslong as the unobserved common components are validinstruments. We also consider estimating panel datamodels in which all regressors are endogenous butshare exogenous common factors. We show that validinstruments can be constructed from the endogenousregressors. Although single equation FIV requires nobias correction, the faster convergence rate of thepanel estimator is such that a bias correction isnecessary to obtain a zero-centered normaldistribution.

Information

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 6 , December 2010 , pp. 1577 - 1606
Copyright
Copyright © Cambridge University Press 2010

Footnotes

This paper was presented at Columbia, Duke,Harvard/MIT, Michigan, Queen’s, Yale, UCSD, UCR,UPenn, Wisconsin, Institute of Statistics atUniversite Catholique de Louvain, and SETA in HongKong. We thank seminar participants, GuidoKuersteiner (the co-editor), and two anonymousreferees for many helpful comments andsuggestions. We also acknowledge financial supportfrom the NSF (grants SES-0551275 andSES-0549978).

References

REFERENCES

Amemiya, T. (1966) On the use of principal components of independent variables in two-stage least squares estimation. International Economic Review 7, 283–303.10.2307/2525526CrossRefGoogle Scholar
Amemiya, T. (1985) Advanced Econometrics. Harvard University Press.Google Scholar
Andrews, D., Moreira, M., & Stock, J. (2006) Optimal two-sided invariant similar tests for instrumental variables regression. Econometrica 74, 715–754.CrossRefGoogle Scholar
Arellano, M. & Bond, S. (1991) Some specification tests for panel data models: Monte Carlo evidence and an application to employment equations. Review of Economic Studies 58, 277–298.CrossRefGoogle Scholar
Bai, J. (2003) Inferential theory for factor models of large dimensions. Econometrica 71, 135–172.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2002) Determining the number of factors in approximate factor models. Econometrica 70, 191–221.CrossRefGoogle Scholar
Bai, J. & Ng, S. (2009) Selecting instrumental variables in a data rich environment. Journal of Time Series Econometrics 1(1), article 4 (online).Google Scholar
Bekker, P.A. (1994) Alternative approximations to the distributions of instrumental variables estimators. Econometrica 63, 657–681.CrossRefGoogle Scholar
Bernanke, B. & Boivin, J. (2003) Monetary policy in a data rich environment. Journal of Monetary Economics 50, 525–546.CrossRefGoogle Scholar
Carrasco, M. (2006) A Regularization Approach to the Many Instruments Problem. Manuscript, Université de Montreal.Google Scholar
Chamberlain, G. & Rothschild, M. (1983) Arbitrage, factor structure and mean-variance analysis in large asset markets. Econometrica 51, 1281–2304.CrossRefGoogle Scholar
Chao, J. & Swanson, N. (2005) Consistent estimation with a large number of instruments. Econometrica 73, 1673–1692.10.1111/j.1468-0262.2005.00632.xCrossRefGoogle Scholar
Donald, S. & Newey, W. (2001) Choosing the number of instruments. Econometrica 69, 1161–1192.10.1111/1468-0262.00238CrossRefGoogle Scholar
Favero, C. & Marcellino, M. (2001) Large Datasets, Small Models, and Monetary Europe. IGIER, Working paper 208.Google Scholar
Forni, M., Hallin, M., Lippi, M., & Reichlin, L. (2005) The generalized dynamic factor model, one sided estimation and forecasting. Journal of the American Statistical Association 100, 830–840.CrossRefGoogle Scholar
Hahn, J. & Kuersteiner, G. (2002) Discontinuities of weak instrument limiting distributions. Economics Letters 75, 325–331.CrossRefGoogle Scholar
Hallin, M. & Liska, R. (2007) Determining the number of factors in the general dynamic factor model. Journal of the American Statistical Association 102, 603–617.CrossRefGoogle Scholar
Hansen, L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.CrossRefGoogle Scholar
Hausman, J. (1978) Specification tests in econometrics. Econometrica 46, 1251–1272.10.2307/1913827CrossRefGoogle Scholar
Hausman, J., Newey, W., & Woutersen, T. (2006) IV Estimation with Heteroskedasticity and Many Instruments. Manuscript, MIT.CrossRefGoogle Scholar
Hayashi, F. (2000) Econometrics. Princeton University Press.Google Scholar
Kapetanios, G. & Marcellino, M. (2006) Factor-GMM Estimation with Large Sets of Possibly Weak Instruments. Manuscript, Queen Mary University.Google Scholar
Kloek, T. & Mennes, L. (1960) Simultaneous equations estimation based on principal components of predetermined variables. Econometrica 28, 46–61.10.2307/1905293Google Scholar
Kuersteiner, G. & Okui, R. (2007) Estimator Averaging for Two stage Least Squares. Manuscript, University of California, Davis.Google Scholar
Leeb, H. & Potscher, B. (2008) Can one estimate the unconditional distribution of post-model-selection estimators? Econometric Theory 24, 338–376.CrossRefGoogle Scholar
Meng, G., Hu, G., & Bai, J. (2007) A Simple method for Estimating Betas when Factors are Measured with Error. Mimeo, Boston College.Google Scholar
Moreira, M. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048.CrossRefGoogle Scholar
Onatski, A. (2006) Asymptotic Distribution of the Principal Components Estimator of Large Factor Models when Factors Are Relatively Weak. Mimeo, Columbia University.Google Scholar
Stock, J.H. & Watson, M.W. (2002) Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association 97, 1167–1179.Google Scholar
Wooldridge, J. (2005) Instumental variables estimation with panel data. Econometric Theory 21, 865–869.CrossRefGoogle Scholar