Statistical disclosure limitation is widely used by data collecting institutions to provide safe individual data. However, the choice of the disclosure limitation method severely affects the quality of the data and limit their use for empirical research. In particular, estimators for nonlinear models based on data which are masked by standard disclosure limitation techniques such as blanking or noise addition lead to inconsistent parameter estimates. This paper investigates to what extent appropriate econometric techniques can obtain parameter estimates of the true data generating process, if the data are masked by noise addition or blanking. Comparing three different estimators - calibration method, the SIMEX method and a semiparametric sample selectivity estimator - we produce Monte-Carlo evidence on how the reduction of data quality can be minimized by masking.