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Using the Helmert-transformation to reduce dimensionality in a mixed model: An application to a wage equation with worker and firm heterogeneity

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Abstract

A model for matched data with two types of unobserved heterogeneity is considered - one related to the observation unit, the other to units to which the observation units are matched. One or both of the unobserved components are assumed to be random. Applying the Helmert transformation to reduce dimensionality simplifies the computational problem substantially. The framework has many potential applications; we apply it to wage modeling. Traditionally, unobserved individual and firm heterogeneity in wage equations have been represented by fixed effects. However, because of the presence of time-invariant covariates, we argue that specifications with random effects also deserve some attention. Our mixed model allows identification of the effects of time invariant variables on wages, such as for instance education. Using Norwegian manufacturing data it turns out that the assumption with respect to firm-specific unobserved heterogeneity affects the estimate of the return to education considerably.

Suggested Citation

  • Øivind A. Nilsen & Arvid Raknerud & Terje Skjerpen, 2011. "Using the Helmert-transformation to reduce dimensionality in a mixed model: An application to a wage equation with worker and firm heterogeneity," Discussion Papers 667, Statistics Norway, Research Department.
  • Handle: RePEc:ssb:dispap:667
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    File URL: http://www.ssb.no/a/publikasjoner/pdf/DP/dp667.pdf
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    1. Gruetter, Max & Lalive, Rafael, 2009. "The importance of firms in wage determination," Labour Economics, Elsevier, vol. 16(2), pages 149-160, April.
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    4. Thierry Lallemand & Robert Plasman & François Rycx, 2005. "Why do large firms pay higher wages? evidence from matched worker-firm data," ULB Institutional Repository 2013/8743, ULB -- Universite Libre de Bruxelles.
    5. Paulo Guimarães & Pedro Portugal, 2010. "A simple feasible procedure to fit models with high-dimensional fixed effects," Stata Journal, StataCorp LP, vol. 10(4), pages 628-649, December.
    6. Jan Eeckhout & Philipp Kircher, 2011. "Identifying Sorting--In Theory," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 872-906.
    7. Robert Plasman & François Rycx & Ilan Tojerow, 2007. "Wage differentials in Belgium: the role of worker and employer characteristics," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 50(1), pages 11-40.
    8. Vasso Ioannidou & Steven Ongena, 2010. ""Time for a Change": Loan Conditions and Bank Behavior when Firms Switch Banks," Journal of Finance, American Finance Association, vol. 65(5), pages 1847-1877, October.
    9. 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.
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    More about this item

    Keywords

    High-dimensional two-way unobserved components; Matched employer-employee data; ECM-algorithm;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials

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