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