July 2011

IZA DP No. 5847: Using the Helmert-Transformation to Reduce Dimensionality in a Mixed Model: Application to a Wage Equation with Worker and Firm Heterogeneity

revised version published as 'Estimation of a model for matched panel data with high-dimensional two-way unobserved heterogeneity' in: Empirical Economics 53, 2017, pp. 1657–1680

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.