Imputation of Income Data with Generalized Calibration Procedure and GB2 distribution: Illustration with SILC data

In sample surveys of households and persons, questions about income are important variables and often sensitive and thus subject to a higher nonresponse rate. The distribution of such collected incomes is neither normal, nor log-normal. Hypotheses of classical regression models to explain the income (or their log) are not satisfied. Imputations using such models modify the original and true distribution of the data which is not. Empirical studies have shown that the generalized beta distribution of the second kind (GB2) it fits income data very well. We present a parametric method of imputation relying on weights obtained by generalized calibration. A GB2 distribution is fitted on the income distribution in order to assess that these weights can compensate for nonignorable nonresponse that affects the variable of interest. The success of the operation greatly depends on the choice of auxiliary and instrumental variables used for calibration, which we discuss. We validate our imputation system on data from the Swiss Survey on Income and Living Conditions (SILC) and compare it to imputations performed through the use of IVEware software running on SAS. We have made great efforts to estimate variances through linearization, taking all the steps of our procedure into account.

Submitted article