Gelbach in logit

: a covariate decomposition for the logit model applied to the minimum wage’s heterogeneous impact

Abstract

Sequentially adding control variables to a regression to investigate their effect on a structural parameter is econometrically meaningless when controls are intercorrelated, as the order in which control variables are added will influence how the structural parameters change. As a solution, I develop a novel order-invariant conditional decomposition for the logit model. Furthermore, this logit decomposition can explain which variables are responsible for the heterogeneous treatment effect on the treated. I illustrate the utility of the decomposition with an application. Using a natural experiment to estimate the displacement effects of the minimum wage in Portugal, I find its effects to be heterogeneous. Moreover, by using the decomposition, I find that the heterogeneous impacts are 65% explained by firms, 28% by the worker, and 7% by tenure; implying that the primary determinant of the minimum wage effect on workers’ displacement is the firm they work for.

Date of Award	25 Jan 2023
Original language	English
Awarding Institution	Universidade Católica Portuguesa
Supervisor	Pedro Raposo (Supervisor)