Nothing Special   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/26244.html
   My bibliography  Save this paper

Leave-out Estimation of Variance Components

Author

Listed:
  • Patrick Kline
  • Raffaele Saggio
  • Mikkel Sølvsten
Abstract
We propose leave-out estimators of quadratic forms designed for the study of linear models with unrestricted heteroscedasticity. Applications include analysis of variance and tests of linear restrictions in models with many regressors. An approximation algorithm is provided that enables accurate computation of the estimator in very large datasets. We study the large sample properties of our estimator allowing the number of regressors to grow in proportion to the number of observations. Consistency is established in a variety of settings where plug-in methods and estimators predicated on homoscedasticity exhibit first-order biases. For quadratic forms of increasing rank, the limiting distribution can be represented by a linear combination of normal and non-central χ² random variables, with normality ensuing under strong identification. Standard error estimators are proposed that enable tests of linear restrictions and the construction of uniformly valid confidence intervals for quadratic forms of interest. We find in Italian social security records that leave-out estimates of a variance decomposition in a two-way fixed effects model of wage determination yield substantially different conclusions regarding the relative contribution of workers, firms, and worker-firm sorting to wage inequality than conventional methods. Monte Carlo exercises corroborate the accuracy of our asymptotic approximations, with clear evidence of non-normality emerging when worker mobility between blocks of firms is limited.

Suggested Citation

  • Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2019. "Leave-out Estimation of Variance Components," NBER Working Papers 26244, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:26244
    Note: EH LS PE TWP
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w26244.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. David Card & Jörg Heining & Patrick Kline, 2013. "Workplace Heterogeneity and the Rise of West German Wage Inequality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(3), pages 967-1015.
    2. 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.
    3. Raj Chetty & John N. Friedman & Nathaniel Hilger & Emmanuel Saez & Diane Whitmore Schanzenbach & Danny Yagan, 2011. "How Does Your Kindergarten Classroom Affect Your Earnings? Evidence from Project Star," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(4), pages 1593-1660.
    4. David Card & Francesco Devicienti & Agata Maida, 2014. "Rent-sharing, Holdup, and Wages: Evidence from Matched Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(1), pages 84-111.
    5. 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.
    6. Jacob A. Mincer, 1974. "Introduction to "Schooling, Experience, and Earnings"," NBER Chapters, in: Schooling, Experience, and Earnings, pages 1-4, National Bureau of Economic Research, Inc.
    7. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 991-1030.
    8. Dufour, Jean-Marie & Jasiak, Joann, 2001. "Finite Sample Limited Information Inference Methods for Structural Equations and Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(3), pages 815-843, August.
    9. 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.
    10. Anatolyev, Stanislav, 2012. "Inference in regression models with many regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 368-382.
    11. Thibaut Lamadon & Elena Manresa & Stephane Bonhomme, 2016. "Discretizing Unobserved Heterogeneity," 2016 Meeting Papers 1536, Society for Economic Dynamics.
    12. 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.
    13. Peter Arcidiacono & Gigi Foster & Natalie Goodpaster & Josh Kinsler, 2012. "Estimating spillovers using panel data, with an application to the classroom," Quantitative Economics, Econometric Society, vol. 3(3), pages 421-470, November.
    14. Cristian Bartolucci & Francesco Devicienti & Ignacio Monzón, 2018. "Identifying Sorting in Practice," American Economic Journal: Applied Economics, American Economic Association, vol. 10(4), pages 408-438, October.
    15. Koen Jochmans & Martin Weidner, 2019. "Fixed‐Effect Regressions on Network Data," Econometrica, Econometric Society, vol. 87(5), pages 1543-1560, September.
    16. 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.
    17. 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.
    18. Jacob A. Mincer, 1974. "Schooling, Experience, and Earnings," NBER Books, National Bureau of Economic Research, Inc, number minc74-1.
    19. 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.
    20. Robert Gibbons & Lawrence Katz, 1992. "Does Unmeasured Ability Explain Inter-Industry Wage Differentials?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 515-535.
    21. Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2020. "Leave‐Out Estimation of Variance Components," Econometrica, Econometric Society, vol. 88(5), pages 1859-1898, September.
    22. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    23. Bryan S. Graham & James L. Powell, 2012. "Identification and Estimation of Average Partial Effects in “Irregular” Correlated Random Coefficient Panel Data Models," Econometrica, Econometric Society, vol. 80(5), pages 2105-2152, September.
    24. Isaac Sorkin, 2018. "Ranking Firms Using Revealed Preference," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1331-1393.
    25. Katarína Borovičková & Robert Shimer, 2017. "High Wage Workers Work for High Wage Firms," NBER Working Papers 24074, National Bureau of Economic Research, Inc.
    26. Donald W. K. Andrews & Xu Cheng, 2012. "Estimation and Inference With Weak, Semi‐Strong, and Strong Identification," Econometrica, Econometric Society, vol. 80(5), pages 2153-2211, September.
    27. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    28. Stéphane Bonhomme & Thibaut Lamadon & Elena Manresa, 2019. "A Distributional Framework for Matched Employer Employee Data," Econometrica, Econometric Society, vol. 87(3), pages 699-739, May.
    29. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    30. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    31. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    32. Robert Gibbons & Lawrence F. Katz & Thomas Lemieux & Daniel Parent, 2005. "Comparative Advantage, Learning, and Sectoral Wage Determination," Journal of Labor Economics, University of Chicago Press, vol. 23(4), pages 681-724, October.
    33. 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.
    34. Jesper Bagger & Francois Fontaine & Fabien Postel-Vinay & Jean-Marc Robin, 2014. "Tenure, Experience, Human Capital, and Wages," SciencePo Working papers Main hal-01301431, HAL.
    35. M. J. Andrews & L. Gill & T. Schank & R. Upward, 2008. "High wage workers and low wage firms: negative assortative matching or limited mobility bias?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(3), pages 673-697, June.
    36. Angrist, J D & Imbens, G W & Krueger, A B, 1999. "Jackknife Instrumental Variables Estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 57-67, Jan.-Feb..
    37. Francesco Devicienti & Bernardo Fanfani & Agata Maida, 2019. "Collective Bargaining and the Evolution of Wage Inequality in Italy," British Journal of Industrial Relations, London School of Economics, vol. 57(2), pages 377-407, June.
    38. Michel Serafinelli, 2015. "'Good' Firms, Worker Flows and Local Productivity," Working Paper series 15-29, Rimini Centre for Economic Analysis.
    39. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    40. Bryan S. Graham, 2008. "Identifying Social Interactions Through Conditional Variance Restrictions," Econometrica, Econometric Society, vol. 76(3), pages 643-660, May.
    41. 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.
    42. Jesper Bagger & Fran?ois Fontaine & Fabien Postel-Vinay & Jean-Marc Robin, 2014. "Tenure, Experience, Human Capital, and Wages: A Tractable Equilibrium Search Model of Wage Dynamics," American Economic Review, American Economic Association, vol. 104(6), pages 1551-1596, June.
    43. 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.
    44. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, vol. 38(2), pages 311-323, March.
    45. Thomas Lemieux, 2006. "Increasing Residual Wage Inequality: Composition Effects, Noisy Data, or Rising Demand for Skill?," American Economic Review, American Economic Association, vol. 96(3), pages 461-498, June.
    46. Isaiah Andrews & Anna Mikusheva, 2016. "A Geometric Approach to Nonlinear Econometric Models," Econometrica, Econometric Society, vol. 84, pages 1249-1264, May.
    47. 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.
    48. Moulton, Brent R., 1986. "Random group effects and the precision of regression estimates," Journal of Econometrics, Elsevier, vol. 32(3), pages 385-397, August.
    49. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    50. Burdett, Kenneth & Mortensen, Dale T, 1998. "Wage Differentials, Employer Size, and Unemployment," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(2), pages 257-273, May.
    51. Angrist, Joshua D., 2014. "The perils of peer effects," Labour Economics, Elsevier, vol. 30(C), pages 98-108.
    52. John M. Abowd & Robert H. Creecy & Francis Kramarz, 2002. "Computing Person and Firm Effects Using Linked Longitudinal Employer-Employee Data," Longitudinal Employer-Household Dynamics Technical Papers 2002-06, Center for Economic Studies, U.S. Census Bureau.
    53. 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.
    54. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    55. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    56. 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.
    57. repec:hal:spmain:info:hdl:2441/7rep5mp5ij95l94ec64n5tdclp is not listed on IDEAS
    58. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    2. Arellano-Bover, Jaime & Saltiel, Fernando, 2021. "Differences in On-the-Job Learning across Firms," IZA Discussion Papers 14473, Institute of Labor Economics (IZA).
    3. 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.
    4. Di Addario, Sabrina & Kline, Patrick & Saggio, Raffaele & Sølvsten, Mikkel, 2023. "It ain’t where you’re from, it’s where you’re at: Hiring origins, firm heterogeneity, and wages," Journal of Econometrics, Elsevier, vol. 233(2), pages 340-374.
    5. David Card & Jesse Rothstein & Moises Yi, 2024. "Industry Wage Differentials: A Firm-Based Approach," Journal of Labor Economics, University of Chicago Press, vol. 42(S1), pages 11-59.
    6. Morchio, Iacopo & Moser, Christian, 2018. "The Gender Pay Gap: Micro Sources and Macro Consequences," MPRA Paper 99276, University Library of Munich, Germany, revised 24 Mar 2020.
    7. Stéphane Bonhomme & Kerstin Holzheu & Thibaut Lamadon & Elena Manresa & Magne Mogstad & Bradley Setzler, 2023. "How Much Should We Trust Estimates of Firm Effects and Worker Sorting?," Journal of Labor Economics, University of Chicago Press, vol. 41(2), pages 291-322.
    8. Benjamin Lochner & Bastian Schulz, 2024. "Firm Productivity, Wages, and Sorting," Journal of Labor Economics, University of Chicago Press, vol. 42(1), pages 85-119.
    9. Sabrina Di Addario & Patrick Kline & Raffaele Saggio & Mikkel Soelvsten, 2022. "It ain't where you're from it's where you're at: firm effects, state dependence, and the gender wage gap," Temi di discussione (Economic working papers) 1374, Bank of Italy, Economic Research and International Relations Area.
    10. Engbom, Niklas & Moser, Christian & Sauermann, Jan, 2023. "Firm pay dynamics," Journal of Econometrics, Elsevier, vol. 233(2), pages 396-423.
    11. 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.
    12. Jorge Alvarez & Felipe Benguria & Niklas Engbom & Christian Moser, 2018. "Firms and the Decline in Earnings Inequality in Brazil," American Economic Journal: Macroeconomics, American Economic Association, vol. 10(1), pages 149-189, January.
    13. Niklas Engbom & Christian Moser, 2022. "Earnings Inequality and the Minimum Wage: Evidence from Brazil," American Economic Review, American Economic Association, vol. 112(12), pages 3803-3847, December.
    14. Ata Can Bertay & Jose Gabo Carreno & Harry Huizinga & Burak Uras & Nathanael Vellekoop, 2022. "Technological Change and the Finance Wage Premium," Working Papers tecipa-738, University of Toronto, Department of Economics.
    15. 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.
    16. Thibaut Lamadon & Magne Mogstad & Bradley Setzler, 2022. "Imperfect Competition, Compensating Differentials, and Rent Sharing in the US Labor Market," American Economic Review, American Economic Association, vol. 112(1), pages 169-212, January.
    17. Peter Hull & Michal Kolesár & Christopher Walters, 2022. "Labor by design: contributions of David Card, Joshua Angrist, and Guido Imbens," Scandinavian Journal of Economics, Wiley Blackwell, vol. 124(3), pages 603-645, July.
    18. Katarína Borovičková & Robert Shimer, 2017. "High Wage Workers Work for High Wage Firms," NBER Working Papers 24074, National Bureau of Economic Research, Inc.
    19. Fanfani, Bernardo, 2022. "Tastes for discrimination in monopsonistic labour markets," Labour Economics, Elsevier, vol. 75(C).
    20. Babina, Tania & Ma, Wenting & Moser, Christian & Ouimet, Paige & Zarutskie, Rebecca, 2019. "Pay, Employment, and Dynamics of Young Firms," MPRA Paper 95382, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:26244. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.