We develop Bayesian inference for an unconditional quantile regression model. Our approach provides better estimates in the upper tail of the wage distribution as well as valid confidence intervals for the Oaxaca-Blinder decomposition. We analyse the recent changes in the U.S. wage structure using data from the CPS Outgoing Rotation Group from 1992 to 2009. We find that the largest part of the recent changes is explained mainly by differences in returns to education while the decline in the unionisation rate has a small impact, and that earnings inequality is rising more at the top end of the wage distribution.Keywords: Bayesian inference, unconditional quantile regression, influence function, OaxacaBlinder decomposition.JEL classification: C1, C11, C13, C14, C21.Acknowledgments: We are grateful to Stephen Bazen for pointing out several references and providing stimulating comments. We would like also to thank Tony Atkinson and Karim Abadir for their helpful suggestions. Of course, the usual disclaimers apply.
We provide a Bayesian inference for a mixture of two Pareto distributions which is then used to approximate the upper tail of a wage distribution. The model is applied to the data from the CPS Outgoing Rotation Group to analyze the recent structure of top wages in the United States from 1992 through 2009. We find an enormous earnings inequality between the very highest wage earners (the "superstars"), and the other high wage earners. These findings are largely in accordance with the alternative explanations combining the model of superstars and the model of tournaments in hierarchical organization structure. The approach can be used to analyze the recent pay gaps among top executives in large firms so as to exhibit the "superstar" effect.
Abstract:In this study, we provide a Bayesian estimation method for the unconditional quantile regression model based on the Re-centered Influence Function (RIF). The method makes use of the dichotomous structure of the RIF and estimates a non-linear probability model by a logistic regression using a Gibbs within a Metropolis-Hastings sampler. This approach performs better in the presence of heavy-tailed distributions. Applied to a nationally-representative household survey, the Senegal Poverty Monitoring Report (2005), the results show that the change in the rate of returns to education across quantiles is substantially lower at the primary level.
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