*This paper investigates the impact of the universal basic income on the intensive margin of labour. The models developed in the literature mainly focus on the relevance of UBI for unemployment, then we propose to add the issue of working time. We extend the model developed by Hungerbühler, Lehmann, Parmentier and Van der Linden (2006) to compare UBI with unemployment benefit. We use an optimal taxation framework with heterogeneous agents in skills who choose both their extensive and intensive margins. Search-matching frictions cause unemployment. Labor demand from firms is endogenous. The hourly wage is negotiated between workers and firms.

**We propose a new methodology for automatic model selection using a non-parametric approach. Automatic model selection is twofold: from a candidate set, variables have to be selected as well as the structure of their link function. First we will give a brief review of existing methods in variable selection and provide insights of the forthcoming work. Then we present a new method for identification of the structure of the relationship in order to improve both understandability of the results and efficiency of the estimation.  We benefits from non-linear dimensionality reduction tools to achieve this goal. Our estimator has the property to be robust to collinearity and its generalization to the non-linear case, it also provides an interesting framework for outliers detection. A major difference from the literature is that our methodology is applied in an unsupervised manner, with no assumptions on causality. We claim that since causality is a model in itself it should not be part of the automatic procedure and be left as a choice to the econometrician.