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

  • Miguel Salema de Araújo Coutinho Caldeira (Student)

Student thesis: Master's Thesis


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 Award25 Jan 2023
Original languageEnglish
Awarding Institution
  • Universidade Católica Portuguesa
SupervisorPedro Raposo (Supervisor)


  • Gelbach decomposition
  • Logit covariate decomposition
  • Logit two-way fixed effects
  • Minimum wage
  • AKM model
  • Separations
  • Triple difference estimator
  • Natural experiment


  • Mestrado em Economia

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