Incomes in South Africa since the fall of Apartheid

ing from the Selection Problem We begin by describing the approach of DiNardo, Fortin, and Lemieux (1996). Note that the density functions for income in periods t and t′ may be written as f(y|T = t) = ∫ g(y|x, T = t)h(x|T = t)dx (20) and f(y|T = t′) = ∫ g(y|x, T = t′)h(x|T = t′)dx (21) respectively, where g(y|x, ·) is the density of income given the observable attributes of the individual and the survey year, h(x|·) is the density of attributes given the survey year, and T is a random variable describing the year in which a given individual in the pooled dataset of observations from both survey years was surveyed. First, suppose that we are interested in how the distribution of income in period t would differ, were the observables as they were in period t′. (Note that this change in endowments is the “residual 11 Throughout this section, we utilize the notations Yi, Y , and y in place of lnWi, lnW , and lnw. This is purely to keep the notation uncluttered.