## thesis in Marseille

Today, I went to Marseille for a PhD thesis defence: I biked to the RER train station (yay!) and the early (7am) flight was smooth, with clear views of nuclear plants along the way… I had previously and critically refereed the thesis, called “Essays on on the econometrics of inequality and poverty measurements” ; despite its strongly applied economics title it indeed was primarily an econometric work about mixtures and quantile regression. The thesis author and PhD incumbent Abdoul Aziz Ndoye being from Senegal, he had prepared a buffet after the defence with Senegalese (yummy) delicacies that I definitely enjoyed after such an early (Oat Squares, thanks to A&C.!) breakfast. (Actually, Aziz had presented a poster in Kyoto so some of you may have met him already!) The afternoon train ride to Montpelier was smooth as well, with nice views of Provençal villages along the way. (Too bad the train line does not stick more to the coastline, though.)

While the part on mixtures was rather traditional (still using Chib’s approach to evaluate marginal likelihoods and decide about the number of components in the mixture, while “resolving” the label switching problem by using assymmetric priors based on the sample quantiles [ok, “priors”!]), I got more interested in the quantile regression part. Maybe because quantile regression is mostly new to me, I have some difficulties in getting the motivation for (regular) quantile regression: I would see an estimation of the whole conditional cdf as linear in the regressor as a more natural goal than picking one or several probability levels to estimate the corresponding quantile. Also, the thesis follows an alternative approach called RIF where the density of the observables y is first estimated by a mixture of (log-)normals and then a quantile regression is operated on

$q_\tau+\mathbb{I}_{y>q_\tau}/f_Y(q_\tau),$

reintroducing the explanatory variables after estimating a joint density on the y’s, which puzzles me as well. (Note that this part of the thesis, written jointly with Michel Lubrano, got a Best Presentation Prize at the Scottish Economics meeting in 2012 and got published in the associated journal.) Overall, this is an innovative and interesting piece of work, even though it cannot be completely envisionned as a Bayesian resolution.

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