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Testing many restrictions under heteroskedasticity

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  • Anatolyev, Stanislav
  • Sølvsten, Mikkel

Abstract

We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.

Suggested Citation

  • Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    • Handle: RePEc:eee:econom:v:236:y:2023:i:1:s0304407623001677
    DOI: 10.1016/j.jeconom.2023.03.011
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    1. David Card & Ana Rute Cardoso & Joerg Heining & Patrick Kline, 2018. "Firms and Labor Market Inequality: Evidence and Some Theory," Journal of Labor Economics, University of Chicago Press, vol. 36(S1), pages 13-70.
    2. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility II: County-Level Estimates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1163-1228.
    3. Crudu, Federico & Mellace, Giovanni & Sándor, Zsolt, 2021. "Inference In Instrumental Variable Models With Heteroskedasticity And Many Instruments," Econometric Theory, Cambridge University Press, vol. 37(2), pages 281-310, April.
    4. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.
    5. Anna Mikusheva & Liyang Sun, 2022. "Inference with Many Weak Instruments [Specification Testing in Models with Many Instruments]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(5), pages 2663-2686.
    6. Akritas M.G. & Papadatos N., 2004. "Heteroscedastic One-Way ANOVA and Lack-of-Fit Tests," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 368-382, January.
    7. Cattaneo, Matias D. & Jansson, Michael & Newey, Whitney K., 2018. "Alternative Asymptotics And The Partially Linear Model With Many Regressors," Econometric Theory, Cambridge University Press, vol. 34(2), pages 277-301, April.
    8. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    9. Lachowska, Marta & Mas, Alexandre & Saggio, Raffaele & Woodbury, Stephen A., 2023. "Do firm effects drift? Evidence from Washington administrative data," Journal of Econometrics, Elsevier, vol. 233(2), pages 375-395.
    10. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility I: Childhood Exposure Effects," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1107-1162.
    11. Anatolyev, Stanislav & Mikusheva, Anna, 2021. "Limit Theorems For Factor Models," Econometric Theory, Cambridge University Press, vol. 37(5), pages 1034-1074, October.
    12. Anatolyev, Stanislav & Gospodinov, Nikolay, 2011. "Specification Testing In Models With Many Instruments," Econometric Theory, Cambridge University Press, vol. 27(2), pages 427-441, April.
    13. Ted Juhl & Oleksandr Lugovskyy, 2014. "A Test for Slope Heterogeneity in Fixed Effects Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(8), pages 906-935, November.
    14. Berndt, Ernst R & Savin, N Eugene, 1977. "Conflict among Criteria for Testing Hypotheses in the Multivariate Linear Regression Model," Econometrica, Econometric Society, vol. 45(5), pages 1263-1277, July.
    15. John M. Abowd & Francis Kramarz & David N. Margolis, 1999. "High Wage Workers and High Wage Firms," Econometrica, Econometric Society, vol. 67(2), pages 251-334, March.
    16. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    17. Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.
    18. Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2020. "Leave‐Out Estimation of Variance Components," Econometrica, Econometric Society, vol. 88(5), pages 1859-1898, September.
    19. Calhoun, Gray, 2011. "Hypothesis testing in linear regression when k/n is large," Journal of Econometrics, Elsevier, vol. 165(2), pages 163-174.
    20. David Card & Ana Rute Cardoso & Patrick Kline, 2016. "Bargaining, Sorting, and the Gender Wage Gap: Quantifying the Impact of Firms on the Relative Pay of Women," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(2), pages 633-686.
    21. Amy Finkelstein & Matthew Gentzkow & Heidi Williams, 2016. "Sources of Geographic Variation in Health Care: Evidence From PatientMigration," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1681-1726.
    22. Valentin Verdier, 2020. "Estimation and Inference for Linear Models with Two-Way Fixed Effects and Sparsely Matched Data," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 1-16, March.
    23. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    24. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    25. Stanislav Anatolyev, 2019. "Many Instruments And/Or Regressors: A Friendly Guide," Journal of Economic Surveys, Wiley Blackwell, vol. 33(2), pages 689-726, April.
    26. Chao, John C. & Swanson, Norman R. & Hausman, Jerry A. & Newey, Whitney K. & Woutersen, Tiemen, 2012. "Asymptotic Distribution Of Jive In A Heteroskedastic Iv Regression With Many Instruments," Econometric Theory, Cambridge University Press, vol. 28(1), pages 42-86, February.
    27. Chao, John C. & Hausman, Jerry A. & Newey, Whitney K. & Swanson, Norman R. & Woutersen, Tiemen, 2014. "Testing overidentifying restrictions with many instruments and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 15-21.
    28. Stanislav Anatolyev, 2013. "Instrumental variables estimation and inference in the presence of many exogenous regressors," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 27-72, February.
    29. Jochmans, K., 2019. "Heteroskedasticity-Robust Inference in Linear Regression Models," Cambridge Working Papers in Economics 1957, Faculty of Economics, University of Cambridge.
    30. Anatolyev, Stanislav, 2018. "Almost unbiased variance estimation in linear regressions with many covariates," Economics Letters, Elsevier, vol. 169(C), pages 20-23.
    31. Bruce Sacerdote, 2001. "Peer Effects with Random Assignment: Results for Dartmouth Roommates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(2), pages 681-704.
    32. Patrick Kline & Evan K Rose & Christopher R Walters, 2022. "Systemic Discrimination Among Large U.S. Employers [“Teachers and Student Achievement in the Chicago Public High Schools,”]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(4), pages 1963-2036.
    33. Phillips, Garry D A & Hale, C, 1977. "The Bias of Instrumental Variable Estimators of Simultaneous Equation Systems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(1), pages 219-228, February.
    34. Koen Jochmans, 2022. "Heteroscedasticity-Robust Inference in Linear Regression Models With Many Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(538), pages 887-896, April.
    35. Jörg Breitung & Christoph Roling & Nazarii Salish, 2016. "Lagrange multiplier type tests for slope homogeneity in panel data models," Econometrics Journal, Royal Economic Society, vol. 19(2), pages 166-202, June.
    36. Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.
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    3. Anna Mikusheva & Liyang Sun, 2023. "Weak Identification with Many Instruments," Papers 2308.09535, arXiv.org, revised Jan 2024.
    4. Michal Koles'ar & Ulrich K. Muller & Sebastian T. Roelsgaard, 2023. "The Fragility of Sparsity," Papers 2311.02299, arXiv.org, revised Jan 2024.

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    More about this item

    Keywords

    Linear regression; Ordinary least squares; Many regressors; Leave-out estimation; Hypothesis testing; High-dimensional models;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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