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...

Full description

Bibliographic Details
Published in:Econometrica Vol. 88; no. 5; pp. 1859 - 1899
Main Authors: Kline, Patrick, Saggio, Raffaele, Sølvsten, Mikkel
Format: Article
Published: Wiley-Blackwell Sep2020
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