On the estimation of distributional household wealth: Addressing under-reporting via optimization problems with invariant Gini coefficient

The Household Finance and Consumption Survey (HFCS) provides valuable information for the monetary policy and financial stability purposes. The dataset shows, however, inconsistencies with National Account (NtlA) statistics, as the aggregated HFCS micro data do usually not match the corresponding NtlA macro data. Therefore, we suggest a solution to close the gap via an optimization problem that aims at preserving for each wealth instrument the level of inequality measured by the Gini coefficient. In addition, a lower and an upper bound of inequality are derived, that can be reached by extreme allocations of the wealth discrepancies across the households. Finally, based on the German HFCS, we compare the findings with another approach suggested in the literature that uses a "multivariate calibration". The comparison indicates that the multivariate calibration may reallocate households' wealth beyond the observed discrepancies, thereby leading to Gini coefficients that exceed the analytically derived upper bound of inequality.