Disclosure risk from interactions and saturated models in remote access

Empirical research using micro data via remote access has been advocated in recent time by statistical offices since confidentiality is easier warranted for this approach. However, disclosure of single values and units cannot be completely avoided. Binary regressors (dummy variables) bear a high risk of disclosure, especially if their interactions are considered as it is done by definition in saturated models. However, contrary to views expressed in earlier publications the risk is only existing if besides parameter estimates also predicted values are reported to the researcher. The paper considers saturated specifications of the most popular linear and nonlinear microeconometric models and shows that in all cases the disclosure risk is high if some design points are represented by a (very) small number of observations. For two of the models not belonging to the exponential family (probit model and negative binomial regression model) we show that the same estimates of the conditional expectations arise here although the parameter estimates are defined by a modified equation. In the last section we draw attention to the fact that interaction of binary regressors can be used to construct strategic dummy variableswhich lead to hight disclosure risk as shown, for example, in Bleninger et al. (2010) for the linear model. In this paper we extend the analysis to the set of established nonlinear models, in particular logit, probit and count data models.