A Note on Estimation of Empirical Models for Margins of Exports with Unknown Non-linear Functional Forms: A Kernel-Regularized Least Squares (KRLS) Approach

Empirical models for intensive or extensive margins of trade that relate measures of exports to firm characteristics are usually estimated by variants of (generalized) linear models. Usually, the firm characteristics that explain these export margins enter the empirical model in linear form, sometimes augmented by quadratic terms or higher order polynomials, or interaction terms, to take care or test for non-linear relationships. If these non-linear relationships do matter and if they are ignored in the specification of the empirical model this leads to biased results. Researchers, however, can never be sure that all possible non-linear relationships are taken care of in their chosen specifications. This note uses for the first time the kernel-regularized least squares (KRLS) estimator to deal with this issue in empirical models for margins of exports. KRLS is a machine learning method that learns the functional form from the data. Empirical examples show that it is easy to apply and works well. Therefore, it should be considered as a useful addition to the box of tools of empirical trade economists.