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Improved Errors-in-Variables Estimators for Grouped Data

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  • Devereux, Paul J.
Abstract
In many economic applications, observations are naturally categorized into mutually exclusive and exhaustive groups. For example, individuals can be classified into cohorts and workers are employees of a particular firm. Grouping models are widely used in economics -- for example, cohort models have been used to study labour supply, wage inequality, consumption, and intergenerational transfer of human capital. The simplest grouping estimator involves taking the means of all variables for each group and then carrying out a group-level regression by OLS or weighted least squares. This estimator is biased in finite samples. I show that the standard errors in variables estimator (EVE) designed to correct for small sample bias is exactly equivalent to the Jack-knife Instrumental Variables Estimator (JIVE). Also EVE is closely related to the k-class of instrumental variables estimators. I then use results from the instrumental variables literature to develop an estimator (UEVE) with better finite-sample properties than existing errors in variables estimators. The theoretical results are demonstrated using Monte Carlo experiments. Finally, I use the estimators to implement a model of inter-temporal male labour supply using micro data from the United States Census. There are sizeable differences in the wage elasticity across estimators, showing the practical importance of the theoretical issues discussed in this paper even in circumstances where the sample size is quite large.

Suggested Citation

  • Devereux, Paul J., 2007. "Improved Errors-in-Variables Estimators for Grouped Data," CEPR Discussion Papers 6167, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:6167
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    Cited by:

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    2. Dwayne Benjamin & Loren Brandt & John Giles, 2011. "Did Higher Inequality Impede Growth in Rural China?," Economic Journal, Royal Economic Society, vol. 121(557), pages 1281-1309, December.
    3. Rumman Khan, 2021. "Assessing Sampling Error in Pseudo‐Panel Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(3), pages 742-769, June.
    4. Robert E.B. Lucas & Lyn Squire & T. N. Srinivasan (ed.), 2010. "Global Exchange and Poverty," Books, Edward Elgar Publishing, number 13102.
    5. Kasey S. Buckles & Daniel M. Hungerman, 2013. "Season of Birth and Later Outcomes: Old Questions, New Answers," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 711-724, July.
    6. Vitaliy Oryshchenko, 2010. "Does Foreign Ownership Matter for Enterprise Training? Empirical Evidence from Transition Countries," Chapters, in: Robert E.B. Lucas & Lyn Squire & T. N. Srinivasan (ed.), Global Exchange and Poverty, chapter 10, Edward Elgar Publishing.
    7. Benoit Dostie, 2012. "Labour Supply and Taxes: New Estimates of the Responses of Wives to Husbands’ Wages," Cahiers de recherche 12-02, HEC Montréal, Institut d'économie appliquée.
    8. Klára Kalíšková, 2020. "Tax and transfer policies and the female labor supply in the EU," Empirical Economics, Springer, vol. 58(2), pages 749-775, February.
    9. Paul J. Devereux, 2007. "Small-sample bias in synthetic cohort models of labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 839-848.
    10. Abe, Yukiko & Tamada, Keiko, 2010. "Regional patterns of employment changes of less-educated men in Japan: 1990-2007," Japan and the World Economy, Elsevier, vol. 22(2), pages 69-79, March.
    11. Allan Seuri, 2019. "Estimating tax income elasticities using a group-averaged synthetic tax instrument," Economics Bulletin, AccessEcon, vol. 39(3), pages 2137-2141.
    12. Francisca Antman & David J. McKenzie, 2007. "Earnings Mobility and Measurement Error: A Pseudo-Panel Approach," Economic Development and Cultural Change, University of Chicago Press, vol. 56(1), pages 125-161, October.
    13. Hou, Feng & Lu, Yuqian & Morissette, René, 2009. "Marriage, Cohabitation and Women’s Response to Changes in the Male Wage Structure," CLSSRN working papers clsrn_admin-2009-45, Vancouver School of Economics, revised 30 Aug 2009.
    14. Daniel A. Ackerberg & Paul J. Devereux, 2009. "Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 91(2), pages 351-362, May.
    15. René Morissette & Feng Hou, 2008. "Does the labour supply of wives respond to husbands' wages? Canadian evidence from micro data and grouped data," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 41(4), pages 1185-1210, November.

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    More about this item

    Keywords

    Errors-in-variables; Grouped data;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply

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