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.

Robust determinants of income distribution across and within countries.

Multicollinearity widely exists in empirical studies, which leads to imprecise estimation and even endogeneity when omitted variables are correlated with any regressors. We apply an innovative strategy, different from the usual tools (instrumental variable, ridge regression, and least absolute shrinkage and selection operator), to estimate the robust determinants of income distribution. We transform panel data into (quasi-) cross-sectional data by removing country and time effects from the data so that all variables become zero mean and orthogonal to the country dummies and time variable, and multicollinearity becomes very low or even disappears with the quasi-cross sectional data in any specifications regardless of country dummies and time variable being included or not. Our contribution is threefold. First, we build a general method to address the multicollinearity issue in panel data, which is to isolate the common contents of correlated variables and ensures robust estimates in different specifications (dynamic or static specifications) and estimators (within- or between-effects estimators). Second, we find no evidence for the Kuznets hypothesis within and across countries; investment is economically and statistically the most robust determinant of income inequality; meanwhile, labor income share shows robustly and consistently positive effects on income inequality, which challenges the related literature. Last, simulations with our estimates show that the total marginal effects of development (regarding GDP, capital stock and investment) on income inequality are very likely to be positive within and between countries except that the impacts on middle-60% and top-quintile income shares are not so likely to increase income inequality across countries.

Rising mean incomes for whom?

Not everybody is benefiting equally from rising mean incomes. We discuss the mean-income population share (MPS), the population percentage of earners below mean income, whose evolution can capture how representative rising mean values are for middle income households. Tracking MPS and its associated income share MIS over time indicates to what extent economic growth is inclusive of both the middle and the bottom of the income distribution. We characterize MPS and MIS analytically under different growth scenarios and compare their parametric estimation using micro-level and grouped income data. Our empirical application with panel data of 16 high- and middle-income countries shows that in the last decades rising mean incomes have mostly not favored middle income households in relative perspective, while the overall welfare effects of the changes in MPS and the correlation structure with the Gini coefficient are mixed.