The measurement of income inequality under inflation. Correction formulae for three inequality measures

Inflation which occurs during the period of time in which a survey is taken will affect measures of inequality of the distribution of incomes or expenditures recorded in such a survey. This paper examines the effect of inflation on three commonly used measures of income inequality: the variance of the logarithm of incomes and Theil's two entropy measures. It is shown that inflation always exaggerates the actual degree of inequality if the sample is drawn from the entire population at each point in time. When the sample is drawn from different regions of a country at different times, underestimation of inequality is possible. Correction formulae are derived for all three inequality measures and for the entire class of generalized entropy measures which include the two Theil measures.