Reconciling household surveys and national accounts data using a cross entropy estimation method

This paper presents an approach to reconciling household surveys and national accounts data that starts from the assumption that the macro data represent control totals to which the household data must be reconciled, but the macro aggregates may be measured with error. The economic data gathered in the household survey are assumed to be accurate, or have been adjusted to be accurate. Given these assumptions, the problem is how to use the additional information provided by the national accounts data to re-estimate the household weights used in the survey so that the survey results are consistent with the aggregate data, while simultaneously estimating the errors in the aggregates. The estimation approach represents an efficient “information processing rule” using an estimation criterion based on an entropy measure of information. The survey household weights are treated as a prior. New weights are estimated that are close to the prior using a cross-entropy metric and that are also consistent with the additional information. This approach is implemented to reconcile household survey data and macro data for Madagascar. The results indicate that the approach is powerful and flexible, supporting the efficient use of information from a variety of sources to reconcile data at different levels of aggregation in a consistent framework.