Approximating income distribution dynamics using aggregate data

This paper proposes a methodology to approximate individual income distribution dynamics using only time series data on aggregate moments of the income distribution. Under the assumption that individual incomes follow a lognormal autoregressive process, this paper shows that the evolution over time of the mean and standard deviation of log income across individuals provides sufficient information to place upper and lower bounds on the degree of mobility in the income distribution. The paper demonstrates that these bounds are reasonably informative, using the U.S. Panel Study of Income Dynamics where the panel structure of the data allows us to compare measures of mobility directly estimated from the micro data with approximations based only on aggregate data. Bounds on mobility are estimated for a large cross-section of countries, using data on aggregate moments of the income distribution available in the World Wealth and Income Database and the World Bank's PovcalNet database. The estimated bounds on mobility imply that conventional anonymous growth rates of the bottom 40 percent (top 10 percent) that do not account for mobility substantially understate (overstate) the expected growth performance of those initially in the bottom 40 percent (top 10 percent).