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A test for Kronecker Product Structure covariance matrix

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  • Guggenberger, Patrik
  • Kleibergen, Frank
  • Mavroeidis, Sophocles

Abstract

We propose a test for a covariance matrix to have Kronecker Product Structure (KPS). KPS implies a reduced rank restriction on a certain transformation of the covariance matrix and the new procedure is an adaptation of the Kleibergen and Paap (2006) reduced rank test. To derive the limiting distribution of the Wald type test statistic proves challenging partly because of the singularity of the covariance matrix estimator that appears in the weighting matrix. We show that the test statistic has a χ2 limiting null distribution with degrees of freedom equal to the number of restrictions tested. Local asymptotic power results are derived. Monte Carlo simulations reveal good size and power properties of the test. Re-examining fifteen highly cited papers conducting instrumental variable regressions, we find that KPS is not rejected in 56 out of 118 specifications at the 5% nominal size.

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  • Guggenberger, Patrik & Kleibergen, Frank & Mavroeidis, Sophocles, 2023. "A test for Kronecker Product Structure covariance matrix," Journal of Econometrics, Elsevier, vol. 233(1), pages 88-112.
    • Handle: RePEc:eee:econom:v:233:y:2023:i:1:p:88-112
    DOI: 10.1016/j.jeconom.2022.01.005
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    1. Nathan Nunn, 2008. "The Long-term Effects of Africa's Slave Trades," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 139-176.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Gordon B. Dahl & Lance Lochner, 2012. "The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit," American Economic Review, American Economic Association, vol. 102(5), pages 1927-1956, August.
    4. Motohiro Yogo, 2004. "Estimating the Elasticity of Intertemporal Substitution When Instruments Are Weak," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 797-810, August.
    5. Jean-Marie Dufour & Mohamed Taamouti, 2005. "Projection-Based Statistical Inference in Linear Structural Models with Possibly Weak Instruments," Econometrica, Econometric Society, vol. 73(4), pages 1351-1365, July.
    6. Nicholas S. Souleles & Jonathan A. Parker & David S. Johnson, 2006. "Household Expenditure and the Income Tax Rebates of 2001," American Economic Review, American Economic Association, vol. 96(5), pages 1589-1610, December.
    7. Daron Acemoglu & Davide Cantoni & Simon Johnson & James A. Robinson, 2011. "The Consequences of Radical Reform: The French Revolution," American Economic Review, American Economic Association, vol. 101(7), pages 3286-3307, December.
    8. Kleibergen, Frank & Paap, Richard, 2006. "Generalized reduced rank tests using the singular value decomposition," Journal of Econometrics, Elsevier, vol. 133(1), pages 97-126, July.
    9. David H. Autor & David Dorn & Gordon H. Hanson, 2013. "The China Syndrome: Local Labor Market Effects of Import Competition in the United States," American Economic Review, American Economic Association, vol. 103(6), pages 2121-2168, October.
    10. Raymond Kan & Chu Zhang, 1999. "Two‐Pass Tests of Asset Pricing Models with Useless Factors," Journal of Finance, American Finance Association, vol. 54(1), pages 203-235, February.
    11. David H. Autor & David Dorn, 2013. "The Growth of Low-Skill Service Jobs and the Polarization of the US Labor Market," American Economic Review, American Economic Association, vol. 103(5), pages 1553-1597, August.
    12. Kleibergen, Frank, 2021. "Efficient size correct subset inference in homoskedastic linear instrumental variables regression," Journal of Econometrics, Elsevier, vol. 221(1), pages 78-96.
    13. Alberto Alesina & Paola Giuliano & Nathan Nunn, 2013. "On the Origins of Gender Roles: Women and the Plough," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 469-530.
    14. Daron Acemoglu & Simon Johnson & James A. Robinson & Pierre Yared, 2008. "Income and Democracy," American Economic Review, American Economic Association, vol. 98(3), pages 808-842, June.
    15. Ledoit, Olivier & Wolf, Michael, 2015. "Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 360-384.
    16. Gilles Duranton & Matthew A. Turner, 2011. "The Fundamental Law of Road Congestion: Evidence from US Cities," American Economic Review, American Economic Association, vol. 101(6), pages 2616-2652, October.
    17. Mitchell, Matthew W. & Genton, Marc G. & Gumpertz, Marcia L., 2006. "A likelihood ratio test for separability of covariances," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1025-1043, May.
    18. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    19. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis, 2021. "A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity," Papers 2103.11371, arXiv.org, revised Oct 2022.
    20. Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2007. "On Rank Estimation In Symmetric Matrices: The Case Of Indefinite Matrix Estimators," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1217-1232, December.
    21. Jonathan A. Parker & Nicholas S. Souleles & David S. Johnson & Robert McClelland, 2013. "Consumer Spending and the Economic Stimulus Payments of 2008," American Economic Review, American Economic Association, vol. 103(6), pages 2530-2553, October.
    22. Tomomi Tanaka & Colin F. Camerer & Quang Nguyen, 2010. "Risk and Time Preferences: Linking Experimental and Household Survey Data from Vietnam," American Economic Review, American Economic Association, vol. 100(1), pages 557-571, March.
    23. Daron Acemoglu & Simon Johnson, 2005. "Unbundling Institutions," Journal of Political Economy, University of Chicago Press, vol. 113(5), pages 949-995, October.
    24. Kleibergen, Frank, 2009. "Tests of risk premia in linear factor models," Journal of Econometrics, Elsevier, vol. 149(2), pages 149-173, April.
    25. Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    26. Quang Nguyen & Colin Camerer & Tomomi Tanaka, 2010. "Risk and Time Preferences Linking Experimental and Household Data from Vietnam," Post-Print halshs-00547090, HAL.
    27. Qihui Chen & Zheng Fang, 2019. "Improved inference on the rank of a matrix," Quantitative Economics, Econometric Society, vol. 10(4), pages 1787-1824, November.
    28. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    29. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    30. Patrik Guggenberger & Frank Kleibergen & Sophocles Mavroeidis, 2019. "A more powerful subvector Anderson Rubin test in linear instrumental variables regression," Quantitative Economics, Econometric Society, vol. 10(2), pages 487-526, May.
    31. Lu, Nelson & Zimmerman, Dale L., 2005. "The likelihood ratio test for a separable covariance matrix," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 449-457, July.
    32. Hansen, Lars Peter & Heaton, John & Yaron, Amir, 1996. "Finite-Sample Properties of Some Alternative GMM Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 262-280, July.
    33. Maarten J. Voors & Eleonora E. M. Nillesen & Philip Verwimp & Erwin H. Bulte & Robert Lensink & Daan P. Van Soest, 2012. "Violent Conflict and Behavior: A Field Experiment in Burundi," American Economic Review, American Economic Association, vol. 102(2), pages 941-964, April.
    34. Frank Kleibergen, 2005. "Testing Parameters in GMM Without Assuming that They Are Identified," Econometrica, Econometric Society, vol. 73(4), pages 1103-1123, July.
    35. Frank Kleibergen & Zhaoguo Zhan, 2020. "Robust Inference for Consumption‐Based Asset Pricing," Journal of Finance, American Finance Association, vol. 75(1), pages 507-550, February.
    36. Donald W.K. Andrews, 2017. "Identification-Robust Subvector Inference," Cowles Foundation Discussion Papers 2105, Cowles Foundation for Research in Economics, Yale University, revised Sep 2017.
    37. Edward Miguel & Shanker Satyanath & Ernest Sergenti, 2004. "Economic Shocks and Civil Conflict: An Instrumental Variables Approach," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 725-753, August.
    38. Hansford, Thomas G. & Gomez, Brad T., 2010. "Estimating the Electoral Effects of Voter Turnout," American Political Science Review, Cambridge University Press, vol. 104(2), pages 268-288, May.
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    Cited by:

    1. Patrik Guggenberge & Frank Kleibergen & Sophocles Mavroeidis, 2021. "A Powerful Subvector Anderson Rubin Test in Linear Instrumental Variables Regression with Conditional Heteroskedasticity," Economics Series Working Papers 960, University of Oxford, Department of Economics.
    2. He, Yong & Kong, Xinbing & Trapani, Lorenzo & Yu, Long, 2023. "One-way or two-way factor model for matrix sequences?," Journal of Econometrics, Elsevier, vol. 235(2), pages 1981-2004.

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    More about this item

    Keywords

    Covariance matrix; Heteroskedasticity; Invariance; Kronecker product structure; Linear instrumental variables regression model; Reduced rank; Weak identification;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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