Estimation of Fuzziness for Respondents' Quantitative Data on Income

The problem of impreciseness of data from different sources is in the focus of the research. While values of income based on diary notes may be considered as relatively exact measuring results, the values of income in other surveys founded on memory of respondents are rather ambiguous. The ambiguity reveals itself first of all in the tendency of rounding numbers. The usage of rounded values for identification of statistical and econometric models can make the estimates of the parameters biased. To prevent this effect, we propose using survey data in fuzzy format and show the way to estimate the measure of fuzziness. The main idea behind this estimation is in finding such measure of ambiguity (fuzziness) that provides the closest distribution of fuzzy data to the distribution of corresponding exact (crisp) data. As a source of crisp data, we use the household budget survey provided by the Federal State Statistics Service, and the Russian Longitudinal Monitoring Survey RLMS HSE supplies us with fuzzy data for corresponding period of time. It is shown that the algorithm presented in the paper allows us to improve data to a good level of conformity.