A Mixed Approach for Data Fusion of HBS and SILC

This paper presents an effective procedure for matching data from the Italian Household Budget Survey (HBS) and the Survey on Income and Living Conditions (SILC), carried out by the Italian National Statistical Institute. In recent years, there is an emerging consensus on the need for distributional measures of well-being as a joint function of income and consumption, that should be jointly explored for explaining the households’ economic conditions. However, the Italian National Statistical Institute does not maintain a unified database on income and expenditures for consumption. One of the most widespread approaches for fusing data is to use statistical matching techniques, which are based on the Conditional Independence Assumption. This assumption implies that the variables of interest are independent, given a set of common auxiliary variables with strong explicative power on income and consumption. Between the auxiliary variables, we also exploit suitable variables which are proxy of income, thus permitting to impute income on HBS, and proxy of consumption, thus permitting to impute consumption on SILC. The joint distribution of the proxies can be considered as a proxy of the joint distribution between income and consumption. Moreover, through the use of two synthetic measures, we reduce the dimensionality of the set of auxiliary variables, simultaneously preserving as much as possible of the available common information and the correlation structure between the auxiliaries and income, as observed in SILC, and between the auxiliaries and consumption, as observed in HBS. The contribution to the existing literature is various. In particular, we obtain a pooled sample with income and consumption, while previous attempts aimed at imputing only one of the two variables of interest in one survey. Second, the uncertainty deriving from the lack of information on the joint distribution of income and consumption is reduced with respect to previous works. Finally, the use of proxies, the high quality of the other auxiliary variables, as well as the particular mixed-mode matching procedure, permit to take advantage of all the available information reducing it to only two dimensions, so that the Conditional Independence can be considered a mild assumption. Keeping in mind that an effective matching for also imputing wealth, that is the third pillar of the households’ economic wellbeing, is yet to come, the joined dataset could permit several types of analyses on economic inequalities and fiscal policies.