  This paper deals with econometric models in which the dependent variable,
some explanatory variables, or both are observed as censored interval data.
This discretization often happens due to confidentiality of sensitive variables
like income. Models using these variables cannot point identify regression
parameters as the conditional moments are unknown, which led the literature to
use interval estimates. Here, we propose a discretization method through which
the regression parameters can be point identified while preserving data
confidentiality. We demonstrate the asymptotic properties of the OLS estimator
for the parameters in multivariate linear regressions for cross-sectional data.
The theoretical findings are supported by Monte Carlo experiments and
illustrated with an application to the Australian gender wage gap.
