Estimation of a linear regression under microaggregation with the response variable as a sorting variable

Microaggregation is one of the most frequently applied statistical disclosure control techniques for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. However, while reducing the disclosure risk of data files, the technique also affects the results of statistical analyses. The paper deals with the impact of microaggregation on a linear model in continuous variables. We show that parameter estimates are biased if the dependent variable is used to form the groups. Using this result, we develop a consistent estimator that removes the aggregation bias. Moreover, we derive the asymptotic covariance matrix of the corrected least squares estimator.