Modeling with Sensitive Variables

The paper deals with models in which the dependent variable, some explanatory variables, or both represent unobserved sensitive data. We introduce a novel discretization method that reveals sufficient information from the sensitive variable to approximate the parameter(s) of interest. Multiple discretization schemes are employed, and we show convergence in distribution for the unobserved variable. The asymptotic properties of the OLS estimator for linear models are derived and discussed. Monte Carlo simulations support our theoretical findings and demonstrate finite-sample properties. Finally, we contrast our method with other alternative methods for estimating the Australian gender wage gap.