Unconditional Quantile Regressions

Abstract

We propose a new regression method for modelling unconditional quantiles of an outcome variable as a function of explanatory variables. The method consists of running a regression of the (recentered) influence function of the unconditional quantile of the dependent variable on the explanatory variables. The influence function is a widely used tool in robust estimation that can easily be computed for each quantile of interest. The estimated regression model can be used to infer the impact of various explanatory variable on a given unconditional quantile, just like the regression coefficients are used in the case of the mean. Our approach can thus be used, for example, to decompose quantiles as a function of the different explanatory variables (as in a standard Oaxaca-Blinder mean decomposition), or to predict the effect of changes in policy or other variables on quantiles.

The Gender Gap in Agricultural Productivity: The Role of Market Imperfections

“…A method that is similar in spirit to the mean decomposition uses the recentred influence function (RIF) regressions proposed by Firpo, Fortin, and Lemieux (2009) and provides a straightforward framework within which across-group differences in any distributional statistic could be decomposed. We rely on the RIF decomposition to provide estimates of the decomposition of the gender gap at different deciles of the agricultural productivity distribution.…”

Explaining personality pay gaps in the UK

“…Nevertheless, this decomposition approach has three main disadvantages: first, it is not directly applicable to decompose differences in any statistics other than the mean; second, it imposes a linearity assumption between outcomes and explanatory variables; and third, when the range of possible values assumed by X differs for the comparison and reference groups, it considers out of the sample predictions. A solution to the first disadvantage has been recently provided by Firpo et al (2007), who showed how to extend the Blinder-Oaxaca mean decomposition to other statistics using the re-centred influence function (RIF) approach (see Firpo et al, 2009). We use this new method to decompose differences in quantiles of the pay.…”

Distribuição de salários de professores e outras ocupações: uma análise para graduados em carreiras tipicamente ligadas à docência

“…Para o caso dos quantis, Firpo et al (2009) mostra que a melhor forma para fazer as estimações é primeiramente calcular os quantis amostrais e em seguida estimar a densidade do ponto através dos métodos de kernel. A estimativa da RIF de cada observação é obtida associando as estimativas de Q τ com F (Q τ ), ou seja, os elementos detalhados dos efeitos composição e estrutura são computados da mesma forma que a média.…”

“…Desse modo, embora não seja nosso objetivo identificar uma relação causal entre salários e escolha ocupacional, ao restringir a análise a essa faixa etária, haveria menor interferência de fatores como experiência prévia no mercado de trabalho nos diferenciais salariais. Por fim, realizamos a decomposição do diferencial salarial entre docentes e não docentes de acordo o método proposto por Firpo, Fortin & Lemieux (2009) que possibilita analisar diferentes quantis da distribuição salarial.…”