Modelling Unobserved Heterogeneity in Discrete Choice Models of Labour Supply

The aim of this paper is to analyse the role of unobserved heterogeneity in structural discrete choice models of labour supply for the evaluation of tax-reforms. Within this framework, unobserved heterogeneity has been estimated either parametrically or nonparametrically through random co- efficient models. Nevertheless, the estimation of such models by means of standard, gradient-based methods is often difficult, in particular if the number of random parameters is high. Given the relative big set of pa- rameters that enter in labour supply models, many researchers have to reduce the role of unobserved heterogeneity by specifying only a small set of random coefficients. However, this simplification affects the estimated labour supply elasticities, which then might hardly change when unob- served heterogeneity is considered in the model. In this paper, we present a new estimation method based on an EM algorithm that allows us to fully consider the effect of unobserved heterogeneity nonparametrically. Results show that labour supply elasticities do change significantly when the full set of coefficients is assumed to be random. Moreover, we analyse the behavioural effects of the introduction of a working-tax credit scheme in the Italian tax-benefit system and show that the magnitude of labour supply reactions and post-reform income distribution do change signifi- cantly when unobserved heterogeneity is fully considered.