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.