Estimation of a partially linear seemingly unrelated regressions model: application to a translog cost system

This article studies a partially linear seemingly unrelated regressions (SUR) model to estimate a translog cost system that consists of a partially linear translog cost function and input share equations. The parametric component is estimated via a simple two-step feasible SUR estimation procedure. We show that the resulting estimator achieves root-n convergence and is asymptotically normal. The nonparametric component is estimated with a nonparametric SUR estimator based on the Cholesky decomposition. We show that this estimator is consistent, asymptotically normal, and more efficient relative to the ones that ignore cross-equation correlation. We emphasize the importance and implication of the choice of square root of the covariance matrix by comparing the Cholesky and Spectral decompositions. A model specification test for parametric functional form is proposed. An Italian banking data set is used to estimate the translog cost system. Results show that marginal effects of risks on cost of production are heterogeneous but increase with risk levels.