Imputation of income data with generalized calibration procedure and GB2 law: illustration with SILC data

In sample surveys of households and persons, questions about income are often sensitive and thus subject to a higher non-response rate. Nevertheless, the household or personal incomes are among the important variables in surveys of this type. The distribution of such collected incomes is not normal, neither log-normal. Hypotheses of classical regression models to explain the income (or their log) are not fulfilled. Imputations using such models modify the original and true distribution of the data. This is not suitable and may conduct the user to wrong interpretations of results computed from data imputed in this way. The generalized beta distribution of the second kind (GB2) is a four parameters distribution. Empirical studies have shown that it adapts very well to income data. The advantage of a parametric income distribution is that there exist explicit formulae for the inequality measures like the Laeken indicators as functions of the parameters. We present a parametric method of imputation, based on the fit of a GB2 law on the income distribution by the use of suitably adjusted weights obtained by generalized calibration. These weights can compensate for non ignorable non-response that affects the variable of interest. We validate our imputation system on data from the Swiss Survey on Income and Living Conditions (SILC).

, The 59th ISI World Statistics Congress, Hong Kong