Using the Helmert-Transformation toReduce Dimensionality in a Mixed Model:Application to a Wage Equation withWorker and Firm Heterogeneity

A model for matched data with two types of unobserved heterogeneity is considered – onerelated 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 modelallows identification of the effect of time-invariant variables on the observation units. Applyingthe Helmert transformation to reduce dimensionality simplifies the computational problemsubstantially. The framework has many potential applications; we apply it to wage modeling.Using Norwegian manufacturing data shows that the assumption with respect to the twotypes of heterogeneity affects the estimate of the return to education considerably....