Sergio Firpo | Searcharxiv

arXiv2023

Loss aversion and the welfare ranking of policy interventions

This paper develops theoretical criteria and econometric methods to rank policy interventions in terms of welfare when individuals are loss-averse. Our new criterion for "loss aversion-sensitive dominance" defines a weak partial ordering of the distributions of policy-induced gains and losses. It applies to the class of welfare functions which model individual preferences with non-decreasing and loss-averse attitudes towards changes in outcomes. We also develop new statistical methods to test loss aversion-sensitive dominance in practice, using nonparametric plug-in estimates; these allow inference to be conducted through a special resampling procedure. Since point-identification of the distribution of policy-induced gains and losses may require strong assumptions, we extend our comparison criteria, test statistics, and resampling procedures to the partially-identified case. We illustrate our methods with a simple empirical application to the welfare comparison of alternative income support programs in the US.

econ.EM↗

arXiv2022

Uniform inference for value functions

We propose a method to conduct uniform inference for the (optimal) value function, that is, the function that results from optimizing an objective function marginally over one of its arguments. Marginal optimization is not Hadamard differentiable (that is, compactly differentiable) as a map between the spaces of objective and value functions, which is problematic because standard inference methods for nonlinear maps usually rely on Hadamard differentiability. However, we show that the map from objective function to an $L_p$ functional of a value function, for $1 \leq p \leq \infty$, are Hadamard directionally differentiable. As a result, we establish consistency and weak convergence of nonparametric plug-in estimates of Cramér-von Mises and Kolmogorov-Smirnov test statistics applied to value functions. For practical inference, we develop detailed resampling techniques that combine a bootstrap procedure with estimates of the directional derivatives. In addition, we establish local size control of tests which use the resampling procedure. Monte Carlo simulations assess the finite-sample properties of the proposed methods and show accurate empirical size and nontrivial power of the procedures. Finally, we apply our methods to the evaluation of a job training program using bounds for the distribution function of treatment effects.

econ.EM↗