Leave‐Out Estimation of Variance Components.
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 com...
| Published in: | Econometrica Vol. 88; no. 5; pp. 1859 - 1899 |
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| Main Authors: | , , |
| Format: | Article |
| Published: |
Wiley-Blackwell
Sep2020
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| Subjects: | |
| Online Access: | View this record in EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=146079672&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 146079672 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00129682 ECN jtl: Econometrica issn: 00129682 maglogo: Y pubinfo: dt: Sep2020 vid: 88 iid: 5 pid: 480 pub: Wiley-Blackwell artinfo: ui: 146079672 10.3982/ECTA16410 ppf: 1859 ppct: 40 formats: tig: atl: Leave‐Out Estimation of Variance Components. aug: au: Kline, Patrick Saggio, Raffaele Sølvsten, Mikkel affil: Department of Economics, UC Berkeley NBER Department of Economics, University of British Columbia Department of Economics, University of Wisconsin‐Madison su: Analysis of variance Monte Carlo method Quadratic forms Variances Random variables Big data sug: subj: Analysis of variance Monte Carlo method Quadratic forms Variances Random variables Big data keyword: fixed effects heteroscedasticity leave‐out estimation many regressors random projection Variance components weak identification fixed effects heteroscedasticity leave‐out estimation many regressors random projection Variance components weak identification ab: 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 data sets. 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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