Scandinavian Working Papers in Economics

Discussion Paper Series in Economics,
Norwegian School of Economics, Department of Economics

No 11/2011: Using the Helmert-transformation to reduce dimensionality in a mixed model: Application to a wage equation with worker and firm heterogeneity.

Øivind Anti Nilsen (), Arvid Raknerud and Terje Skjerpen
Additional contact information
Øivind Anti Nilsen: Dept. of Economics, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Economics, Helleveien 30, N-5045 Bergen, Norway
Arvid Raknerud: Statistics Norway, Postal: P.O. 8131 Dep, N-0033 Oslo, Norway
Terje Skjerpen: Statistics Norway, Postal: P.O. 8131 Dep, N-0033 Oslo, Norway

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 identi…cation of the e¤ect of time-invariant variables on the observation units. Applying the Helmert transformation to reduce dimensionality simpli…es 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 a¤ects the estimate of the return to education considerably.

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

JEL-codes: C23; C81; J31

27 pages, First version: July 5, 2011. Revised: October 4, 2011.

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