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

Comments and suggestions made during the presentations at the 6th Nordic Econometric in Sønderborg, the 17th International Panel Data Conference in Montreal and the 65th European Meeting of the Econometric Society in Oslo in 2011 are highly appreciated, and so are comments on a previous version of this paper at ESEM 2009 in Barcelona.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. _____________ Keywords: High-dimensional two-way unobserved components, Matched employer-employee data, ECM-algorithm