The first moment of income density functions and estimation of single-parametric Lorenz curves

This paper discusses the first moment, i.e., the mean income point, of income density functions and the estimation of single-parametric Lorenz curves. The mean income point is implied by an income density function and associated with a single-parametric Lorenz function. The boundary of the mean income point can show the flexibility of a parametric Lorenz function. I minimize the sum of squared errors in fitting both grouped income data and the mean income point and identify the best parametric Lorenz function using a large panel dataset. I find that each parametric Lorenz function may do a better job than others in fitting particular grouped data; however, a zero- and unit-modal single-parametric Lorenz function is identified to be the best of eight typical optional functions in fitting most (666 out of 969) observations of a large panel dataset. I perform a Monte Carlo simulation as a robustness check of the empirical estimation.