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A JACKKNIFE LAGRANGE MULTIPLIER TEST WITH MANY WEAK INSTRUMENTS

Published online by Cambridge University Press:  11 November 2022

Yukitoshi Matsushita
Affiliation:
Hitotsubashi University
Taisuke Otsu*
Affiliation:
London School of Economics
*
Address correspondence to Taisuke Otsu, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK; e-mail: [email protected].
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Abstract

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This paper proposes a jackknife Lagrange multiplier (JLM) test for instrumental variable regression models, which is robust to (i) many instruments, where the number of instruments may increase proportionally with the sample size, (ii) arbitrarily weak instruments, and (iii) heteroskedastic errors. In contrast to Crudu, Mellace, and Sándor (2021, Econometric Theory 37, 281–310) and Mikusheva and Sun (2021, Review of Economic Studies 89, 2663–2686), who proposed jackknife Anderson–Rubin tests that are also robust to (i)–(iii), we modify a score statistic by jackknifing and construct its heteroskedasticity robust variance estimator. Compared to the Lagrange multiplier tests by Kleibergen (2002, Econometrica 70, 1781–1803) and Moreira (2001, Tests with Correct Size when Instruments Can Be Arbitrarily Weak, Working paper) and their modification for many instruments by Hansen, Hausman, and Newey (2008, Journal of Business & Economic Statistics 26, 398–422), our JLM test is robust to heteroskedastic errors and may circumvent a possible decrease in the power function. Simulation results illustrate the desirable size and power properties of the proposed method.

Type
MISCELLANEA
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

We are grateful to Naoto Kunitomo for helpful comments. Matsushita acknowledges financial support from the JSPS KAKENHI (18K01541).

References

REFERENCES

Ackerberg, D.A. & Devereux, P.J. (2009) Improved JIVE estimators for overidentified linear models with and without heteroskedasticity. Review of Economics and Statistics 91, 351362.CrossRefGoogle Scholar
Andrews, D.W.K., Cheng, X., & Guggenberger, P. (2020) Generic results for establishing the asymptotic size of confidence sets and tests. Journal of Econometrics 218, 496531.CrossRefGoogle Scholar
Andrews, D.W.K., Moreira, M.J., & Stock, J.H. (2006) Optimal two-sided invariant similar tests for instrumental variables regression with weak instruments. Econometrica 74, 715752.CrossRefGoogle Scholar
Andrews, D.W.K. & Stock, J.H. (2007a) Inference with weak instruments. In Blundell, R., Newey, W., and Persson, T. (eds.), Advances in Economics and Econometrics, Theory and Applications: Ninth World Congress , vol. 3, pp. 122173. Cambridge University Press.Google Scholar
Andrews, D.W.K. & Stock, J.H. (2007b) Testing with many weak instruments. Journal of Econometrics 138, 2446.CrossRefGoogle Scholar
Angrist, J.D., Imbens, G.W., & Krueger, A.B. (1999) Jackknife instrumental variables estimation. Journal of Applied Econometrics 14, 5767.3.0.CO;2-G>CrossRefGoogle Scholar
Angrist, J.D. & Krueger, A.B. (1991) Does compulsory school attendance affect schooling and earnings? The Quarterly Journal of Economics 106, 9791014.CrossRefGoogle Scholar
Bekker, P.A. (1994) Alternative approximation to the distribution of instrumental variable estimators. Econometrica 62, 657681.CrossRefGoogle Scholar
Billingsley, P. (1986) Probability and Measure . Wiley.Google Scholar
Blomquist, S. & Dahlberg, M. (1999) Small sample properties of LIML and jackknife IV estimators: Experiments with weak instruments. Journal of Applied Econometrics 14, 6988.3.0.CO;2-7>CrossRefGoogle Scholar
Chao, J., Hausman, J.A., Newey, W.K., Swanson, N.R., & Woutersen, T. (2014) Testing overidentifying restrictions with many instruments and heteroskedasticity. Journal of Econometrics 178, 1521.CrossRefGoogle Scholar
Chao, J. & Swanson, N.R. (2005) Consistent estimation with a large number of weak instruments. Econometrica 73, 16731692.CrossRefGoogle Scholar
Chao, J., Swanson, N.R., Hausman, J.A., Newey, W.K., & Woutersen, T. (2012) Asymptotic distribution of JIVE in a heteroskedastic IV regression with many instruments. Econometric Theory 28, 4286.CrossRefGoogle Scholar
Crudu, F., Mellace, G., & Sándor, Z. (2021) Inference in instrumental variable models with heteroskedasticity and many instruments. Econometric Theory 37, 281310.CrossRefGoogle Scholar
Davidson, R. & MacKinnon, J.G. (2006) The case against JIVE. Journal of Applied Econometrics 21, 827833.CrossRefGoogle Scholar
Dufour, J.-M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 13651387.CrossRefGoogle Scholar
Fuller, W.A. (1977) Some properties of a modification of the limited information estimator. Econometrica 45, 939954.CrossRefGoogle Scholar
Hahn, J., Hausman, J., & Kuersteiner, G. (2004) Estimation with weak instruments: Accuracy of higher-order bias and MSE approximations. The Econometrics Journal 7, 272306.CrossRefGoogle Scholar
Han, C. & Phillips, P.C.B. (2006) GMM with many moment conditions. Econometrica 74, 147192.CrossRefGoogle Scholar
Hansen, C., Hausman, J., & Newey, W.K. (2008) Estimation with many instrumental variables. Journal of Business & Economic Statistics 26, 398422.CrossRefGoogle Scholar
Hansen, C. & Kozbur, D. (2014) Instrumental variables estimation with many weak instruments using regularized JIVE. Journal of Econometrics 182, 290308.CrossRefGoogle Scholar
Hausman, J.A., Newey, W.K., Woutersen, T., Chao, J., & Swanson, N.R. (2012) Instrumental variable estimation with heteroskedasticity and many instruments. Quantitative Economics 3, 211255.CrossRefGoogle Scholar
Kleibergen, F. (2002) Pivotal statistics for testing structural parameters in instrumental variables regression. Econometrica 70, 17811803.CrossRefGoogle Scholar
Kleibergen, F. (2005) Testing parameters in GMM without assuming that they are identified. Econometrica 73, 11031124.CrossRefGoogle Scholar
Kline, P., Saggio, R., & Sølvsten, M. (2020) Leave-out estimation of variance components. Econometrica 88, 18591898.CrossRefGoogle Scholar
Kunitomo, N. (1980) Asymptotic expansions of distributions of estimators in a linear functional relationship and simultaneous equations. Journal of the American Statistical Association 75, 693700.CrossRefGoogle Scholar
Mikusheva, A. & Sun, L. (2021) Inference with many weak instruments. Review of Economic Studies 89, 26632686.CrossRefGoogle Scholar
Moreira, H. & Moreira, M.J. (2019) Optimal two-sided tests for instrumental variables regression with heteroskedastic and autocorrelated errors. Journal of Econometrics 213, 398433.CrossRefGoogle Scholar
Moreira, M. J. (2001) Tests with Correct Size when Instruments Can Be Arbitrarily Weak. University of California, Berkeley. Working paper.Google Scholar
Moreira, M.J. (2003) A conditional likelihood ratio test for structural models. Econometrica 71, 10271048.CrossRefGoogle Scholar
Morimune, K. (1983) Approximate distributions of k-class estimators when the degree of overidentification is large compared with sample size. Econometrica 51, 821841.CrossRefGoogle Scholar
Newey, W. & Windmeijer, F. (2009) GMM with many weak moment conditions. Econometrica 77, 687719.Google Scholar
Phillips, G.D.A. & Hale, C. (1977) The bias of instrumental variable estimators of simultaneous equation systems. International Economic Review 18, 219228.CrossRefGoogle Scholar
Wang, J. & Zivot, E. (1998) Inference on structural parameters in instrumental variables regression with weak instruments. Econometrica 66, 13891404.CrossRefGoogle Scholar