Modelling with Sensitive Variables

The paper deals with models in which the dependent variable, some explanatory variables, or both represent sensitive data. We introduce a novel discretization method that preserves data privacy when working with such variables. A multiple discretization method is proposed that utilizes information from the different discretization schemes. We show convergence in distribution for the unobserved variable and derive the asymptotic properties of the OLS estimator for linear models. Monte Carlo simulation experiments presented support our theoretical findings. Finally, we contrast our method with a differential privacy method to estimate the Australian gender wage gap.