Consistent Estimation of a Simple Linear Model Under Microaggregation

A problem statistical offices are increasingly faced with is guaranteeing confidentiality when releasing microdata sets. One method to provide safe microdata to is to reduce the information content of a data set by means of masking procedures. A widely discussed masking procedure is microaggregation, a technique where observations are grouped and replaced with their corresponding group means. However, while reducing the disclosure risk of a data file, microaggregation also affects the results of statistical analyses. The paper deals with the impact of microaggregation on a simple linear model. We show that parameter estimates are biased if the dependent variable is used to group the data. It turns out that the bias of the slope parameter estimate is a non-monotonic function of this parameter. By means of this non-monotonic relationship we develop a method for consistently estimating the model parameters.