We propose to develop a method of imputation for income variables allowing direct analysis of the distribution of such data, particularly the estimation of complex statistics such as indicators for poverty and social exclusion as well as the estimation of their precision.

 

In sample surveys of households and persons, questions about income are often sensitive and thus subject to a higher nonresponse rate. Nevertheless, the household or personal incomes are among the important variables in surveys of this type. Empirical studies have shown that the generalized beta distribution of the second kind (GB2) fits income data very well. We present a parametric method of imputation relying on weights stemming from generalized calibration. A GB2 distribution is fitted on the income distribution in order to determine whether these weights can compensate even 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 the Swiss Survey on Income and Living Conditions (SILC) data and compare it to imputations performed through the use of IVEware software. We have used the generalized linearization technique based on the concept of influence function to estimate the variance of complex statistics such as Laeken indicators. Through simulations, we show that the use of Gaussian kernel estimation to estimate an income density function results in a strongly biased variance estimate. We propose two other density estimation methods that significantly reduce the observed bias.