Cross-validation selection of regularisation parameter(s) for semiparametric transformation models

We propose cross-validation criteria for the selection of regularization parameter(s) in the semiparametric instrumental variable transformation model proposed in Florens and Sokullu (2016). In the presence of an endogenous regressor, this model is characterized by the need to choose two regularization parameters, one for the structural function and one for the transformation of the outcome. We consider two-step and simultaneous criteria, and analyze the finite-sample performance of the estimator using the corresponding regularization parameters by means of several Monte-Carlo simulations. Our numerical experiments show that simultaneous selection of regularization parameters provides significant improvements in the performance of the estimator. We also apply our methods to the choice of regularization parameters in the estimation of two-sided network effects in the German magazine industry.