Bimic+: microsimulation with labor supply

This paper introduces BIMic+, the labor supply extension of the tax and benefit microsimulation model of the Bank of Italy, BIMic (Curci, Savegnago and Cioffi, 2017). The model follows the Random Utility approach (McFadden, 1974; Aaberge, Dagsvik, and StrØm,1995; Van Soest, 1995). The model focuses on the labor supply behavior of wage earners and imputes wages for workers who are not employed through a two-step Heckman estimation procedure. The utility function departs from the quadratic functional form, which is common in this literature, to avoid decreasing utility in disposable income, a violation of a critical assumption in consumer theory and that underlies all redistributive analyses and is crucial for computing equivalent variations. The main arguments of the utility function are hours and disposable income. The latter is calculated through the static module, BIMic, for each counterfactual hours option. With respect to the literature, we innovate by: (i) matching the observed distribution of hours as a constraint into the optimization problem to avoid overfitting issues (as opposed to the usual approach of drawing taste shocks until the estimated hours match the observed ones). We do so in a way that also matches the distribution of labor income from aggregated tax returns. (ii) organizing the output of the model according to a strand of the public finance literature theoretically connected to optimal taxation. For each policy, we want to characterize the willingness to pay of beneficiaries and the net government cost, taking into account behavioral responses to the policy. We also propose to use these quantities to compute the marginal value of spending public funds in such a policy (Hendren and Sprung-Keyser, 2020; Bourguignon and Landais, 2022). In the last section of our paper, we simulate the labor supply effects of a policy reform as an illustration of how to use our model and its output; specifically, we focus on a cut in social security contribution for mothers with at least two children introduced in Italy in 2024.