Estimation of the income distribution and detection of subpopulations: An explanatory model

Empirical evidence, obtained from non-parametric estimation of the income distribution, exhibits strong heterogeneity in most populations of interest. It is common, therefore, to suspect that the population is composed of several homogeneous subpopulations. Such an assumption leads us to consider mixed income distributions whose components feature the distributions of the incomes of a particular homogeneous subpopulation. A model with mixing probabilities that are allowed to vary with exogenous individual variables that characterize each subpopulation is developed. This model simultaneously provides a flexible estimation of the income distribution, a breakdown into several subpopulations and an explanation of income heterogeneity.

[1]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[2]  J. Aitchison,et al.  The Lognormal Distribution. , 1958 .

[3]  William H. Press,et al.  Numerical recipes , 1990 .

[4]  Ganapati P. Patil,et al.  Statistical Distributions in Scientific Work , 1981 .

[5]  J. Hills.  New inequalities : the changing distribution of income and wealth in the United Kingdom , 1996 .

[6]  F. Bourguignon.  On the Measurement of Inequality , 2003 .

[7]  Empirical Analyses of Inequality and Welfare , 2022 .

[8]  Mark Trede,et al.  Tails of Lorenz curves , 2002 .

[9]  R. Davidson,et al.  Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality , 1998 .

[10]  Mark Trede,et al.  Evaluating Parametric Income Distribution Models , 1996 .

[11]  Stephen P. Jenkins,et al.  Did the middle class shrink during the 1980s? UK evidence from kernel density estimates , 1995 .

[12]  R. Murnane,et al.  U.S. Earnings Levels and Earnings Inequality: A Review of Recent Trends and Proposed Explanations , 1992 .

[13]  S. Jenkins,et al.  The changing shape of the UK income distribution: kernel density estimates , 1996 .

[14]  A. V. D. Vaart,et al.  Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities , 2001 .

[15]  B. Lindsay.  Mixture models : theory, geometry, and applications , 1995 .

[16]  S. Pudney.  Income and wealth inequality and the life cycle. A non-parametric analysis for China , 1993 .

[17]  Russell Davidson,et al.  Distribution-Free Statistical Inference with Lorenz Curves and Income Shares , 1983 .

[18]  R. Davidson,et al.  Statistical Inference for the Measurement of the Incidence of Taxes and Transfers , 1997 .

[19]  R. Hathaway.  A Constrained Formulation of Maximum-Likelihood Estimation for Normal Mixture Distributions , 1985 .

[20]  日野 寛三,et al.  対数正規分布(Lognormal Distribution)のあてはめについて , 1994 .

[21]  S. Jenkins.  Trends in the UK Income Distribution , 2000 .

[22]  A. Shorrocks,et al.  The Class of Additively Decomposable Inequality Measures , 1980 .

[23]  Debraj Ray,et al.  On the Measurement of Polarization , 1994 .

[24]  George E. Policello.  Conditional Maximum Likelihood Estimation in Gaussian Mixtures , 1981 .

[25]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[26]  J. Marron,et al.  Simultaneous Density Estimation of Several Income Distributions , 1992, Econometric Theory.

[27]  A. L. Harris.  Pure Capitalism and the Disappearance of the Middle Class , 1939, Journal of Political Economy.

[28]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[29]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[30]  R. Davidson,et al.  Asymptotic and Bootstrap Inference for Inequality and Poverty Measures , 2007 .

[31]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[32]  S. Jenkins,et al.  How much inequality can we explain? A methodology and an application to the USA , 1994 .

[33]  S. Jenkins.  Recent trends in the UK income distribution: what happened and why? , 1996 .

[34]  Stephen P. Jenkins,et al.  How Much Inequality Can We Explain? A Methodology and an Application to the United States , 1995 .

[35]  James B. McDonald,et al.  Some Generalized Functions for the Size Distribution of Income , 1984 .

[36]  J. Oga,et al.  Recent Trends in the , 1993 .

[37]  Frank A. Cowell,et al.  Thinking about Inequality , 1999 .

[38]  R. Redner,et al.  Mixture densities, maximum likelihood, and the EM algorithm , 1984 .

[39]  W. Li,et al.  On a mixture autoregressive model , 2000 .

[40]  B. Lindsay,et al.  Measuring the relative effectiveness of moment estimators as starting values in maximizing likelihoods , 1994 .

[41]  N. Mendell,et al.  Probabilistic Measures of Adequacy of a Numerical Search for a Global Maximum , 1989 .

[42]  Y. Weiss.  The Risk Element in Occupational and Educational Choices , 1972, Journal of Political Economy.

[43]  H. Alker,et al.  On measuring inequality. , 1964, Behavioral science.