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# Lubrano

## Publications

We show that least squares cross-validation methods share a common structure which has an explicit asymptotic solution, when the chosen kernel is asymptotically separable in bandwidth and data. For density estimation with a multivariate Student t(ν) kernel, the cross-validation criterion becomes asymptotically equivalent to a polynomial of only three terms. Our bandwidth formulae are simple and noniterative thus leading to very fast computations, their integrated squared-error dominates traditional cross-validation implementations, they alleviate the notorious sample variability of cross-validation, and overcome its breakdown in the case of repeated observations. We illustrate our method with univariate and bivariate applications, of density estimation and nonparametric regressions, to a large dataset of Michigan State University academic wages and experience.

What is the role of income polarization for explaining differentials in public funding of education? To answer this question, we provide a new theoretical modelling for the income distribution that can directly monitor income polarization. It leads to a new income polarization index where the middle class is represented by an interval. We implement this distribution in a political economy model with endogenous fertility and public/private educational choices. We show that when households vote on public schooling expenditures, polarization matters for explaining disparities in public education funding across communities. Using micro-data covering two groups of school districts, we find that both income polarization and income inequality affect public school funding with opposite signs whether there exist a Tax Limitation Expenditure (TLE) or not.

The paper examines the question of non-anonymous Growth Incidence Curves (na-GIC) from a Bayesian inferential point of view. Building on the notion of conditional quantiles of Barnett (1976. “The Ordering of Multivariate Data.” Journal of the Royal Statistical Society: Series A 139: 318–55), we show that removing the anonymity axiom leads to a complex and shaky curve that has to be smoothed, using a non-parametric approach. We opted for a Bayesian approach using Bernstein polynomials which provides confidence intervals, tests and a simple way to compare two na-GICs. The methodology is applied to examine wage dynamics in a US university with a particular attention devoted to unbundling and anti-discrimination policies. Our findings are the detection of wage scale compression for higher quantiles for all academics and an apparent pro-female wage increase compared to males. But this pro-female policy works only for academics and not for the para-academics categories created by the unbundling policy.

This chapter reviews the recent Bayesian literature on poverty measurement together with some new results. Using Bayesian model criticism, we revise the international poverty line. Using mixtures of lognormals to model income, we derive the posterior distribution for the FGT, Watts and Sen poverty indices, for TIP curves (with an illustration on child poverty in Germany) and for Growth Incidence Curves. The relation of restricted stochastic dominance with TIP and GIC dominance is detailed with an example based on UK data. Using panel data, we decompose poverty into total, chronic and transient poverty, comparing child and adult poverty in East Germany when redistribution is introduced. When panel data are not available, a Gibbs sampler can be used to build a pseudo panel. We illustrate poverty dynamics by examining the consequences of the Wall on poverty entry and poverty persistence in occupied West Bank.

Two main nonpharmaceutical policy strategies have been used in Europe in response to the COVID-19 epidemic: one aimed at natural herd immunity and the other at avoiding saturation of hospital capacity by crushing the curve. The two strategies lead to different results in terms of the number of lives saved on the one hand and production loss on the other hand. Using a susceptible–infected–recovered–dead model, we investigate and compare these two strategies. As the results are sensitive to the initial reproduction number, we estimate the latter for 10 European countries for each wave from January 2020 till March 2021 using a double sigmoid statistical model and the Oxford COVID-19 Government Response Tracker data set. Our results show that Denmark, which opted for crushing the curve, managed to minimize both economic and human losses. Natural herd immunity, sought by Sweden and the Netherlands does not appear to have been a particularly effective strategy, especially for Sweden, both in economic terms and in terms of lives saved. The results are more mixed for other countries, but with no evident trade-off between deaths and production losses.

The growth incidence curve of Ravallion and Chen (2003) is based on the quantile function. Its distribution-free estimator behaves erratically with usual sample sizes leading to problems in the tails. The authors propose a series of parametric models in a Bayesian framework. A first solution consists in modeling the underlying income distribution using simple densities for which the quantile function has a closed analytical form. This solution is extended by considering a mixture model for the underlying income distribution. However, in this case, the quantile function is semi-explicit and has to be evaluated numerically. The last solution consists in adjusting directly a functional form for the Lorenz curve and deriving its first-order derivative to find the corresponding quantile function. The authors compare these models by Monte Carlo simulations and using UK data from the Family Expenditure Survey. The authors devote a particular attention to the analysis of subgroups.

OECD countries have experienced a large increase in top wage inequality. Atkinson (2008) attributes this phenomena to the superstar theory leading to a Pareto tail in the wage distribution with a low Pareto coefficient. Do we observe a similar phenomena for academic wages? We examine wage formation in a public US university using for each academic rank a hybrid mixture formed by a lognormal distribution for regular wages and a Pareto distribution for top wages, using a Bayesian approach. The presence of superstars wages would imply a higher dispersion in the Pareto tail than in the lognormal body. We concluded that academic wages are formed in a different way than other top wages. There is an effort to propose competitive wages to some young Assistant Professors. But when climbing up the wage ladder, we found a phenomenon of wage compression which is just the contrary of a superstar phenomenon.

This study investigates the differences between zombie firms and non-zombie firms in corporate social responsibility activities such as reporting, disclosure and fulfillment. Using Chinese listing company data collected from 2009 to 2016, we apply a three stage model with a double Heckman correction to deal with potential self-selection/endogeneity bias and to measure the differences consistently. We found that zombie firms are less willing to release standalone corporate social responsibility reports than non-zombie firms. Among companies that release standalone corporate social responsibility reports, the corporate social responsibility disclosure of zombie firms is at least not worse than non-zombie firms, but the corporate social responsibility fulfillment is significantly lower. We conclude from this gap between disclosure and fulfillment to the hypocritical behavior of zombie firms, due to the absence of control in corporate social responsibility. We suggest that government should enhance supervision over zombie firms’ corporate social responsibility activities and subsidies towards them in order to lower their economic damage. Supplementary analyses provide some clues concerning the heterogeneity of inconsistence in term of external support characteristics, ownership and censorship which require further studies.

TIP curves are cumulative poverty gap curves used for representing the three different aspects of poverty: incidence, intensity and inequality. The paper provides Bayesian inference for TIP curves, linking their expression to a parametric representation of the income distribution using a mixture of log-normal densities. We treat specifically the question of zero-inflated income data and survey weights, which are two important issues in survey analysis. The advantage of the Bayesian approach is that it takes into account all the information contained in the sample and that it provides small sample credible intervals and tests for TIP dominance. We apply our methodology to evaluate the evolution of child poverty in Germany after 2002, providing thus an update the portrait of child poverty in Germany given in Corak et al. (Rev. Income Wealth 54(4), 547–571, 2008).

The paper examines the question of non-anonymous Growth Incidence Curves (na-GIC) from a Bayesian inferential point of view. Building on the notion of conditional quantiles of Barnett (1976. “The Ordering of Multivariate Data.” Journal of the Royal Statistical Society: Series A 139: 318–55), we show that removing the anonymity axiom leads to a complex and shaky curve that has to be smoothed, using a non-parametric approach. We opted for a Bayesian approach using Bernstein polynomials which provides confidence intervals, tests and a simple way to compare two na-GICs. The methodology is applied to examine wage dynamics in a US university with a particular attention devoted to unbundling and anti-discrimination policies. Our findings are the detection of wage scale compression for higher quantiles for all academics and an apparent pro-female wage increase compared to males. But this pro-female policy works only for academics and not for the para-academics categories created by the unbundling policy.