Using the Helmert-Transformation to Reduce Dimensionality in a Mixed Model: Application to a Wage Equation with Worker and Firm Heterogeneity

29 Pages Posted: 24 Jul 2011 Last revised: 16 Apr 2023

See all articles by Øivind Anti Nilsen

Øivind Anti Nilsen

Norwegian School of Economics (NHH) - Department of Economics; IZA Institute of Labor Economics; CESifo (Center for Economic Studies and Ifo Institute) - Ifo Institute

Arvid Raknerud

Statistics Norway - Research Department

Terje Skjerpen

Statistics Norway

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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. This mixed model allows identification of the effect of time-invariant variables on the observation units. Applying the Helmert transformation to reduce dimensionality simplifies the computational problem substantially. The framework has many potential applications; we apply it to wage modeling. Using Norwegian manufacturing data shows that the assumption with respect to the two types of heterogeneity affects the estimate of the return to education considerably.

Keywords: matched employer-employee data, ECM-algorithm, high-dimensional two-way unobserved components

JEL Classification: C23, C81, J31

Suggested Citation

Nilsen, Oivind Anti and Raknerud, Arvid and Skjerpen, Terje, Using the Helmert-Transformation to Reduce Dimensionality in a Mixed Model: Application to a Wage Equation with Worker and Firm Heterogeneity. IZA Discussion Paper No. 5847, Available at SSRN: https://ssrn.com/abstract=1893927 or http://dx.doi.org/10.2139/ssrn.1893927

Oivind Anti Nilsen (Contact Author)

Norwegian School of Economics (NHH) - Department of Economics ( email )

Helleveien 30
N-5045 Bergen
Norway

IZA Institute of Labor Economics

P.O. Box 7240
Bonn, D-53072
Germany

CESifo (Center for Economic Studies and Ifo Institute) - Ifo Institute ( email )

Poschinger Str. 5
Munich, 01069
Germany

Arvid Raknerud

Statistics Norway - Research Department ( email )

P.O. Box 8131 Dep, N-0033
N-0033 Oslo
Norway

Terje Skjerpen

Statistics Norway ( email )

N-0033 Oslo
Norway

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