Économie et Statistique n° 471 Professional mobility of apprentices - Low-cost housing: monetary advantage and impact on housing conditions - The impact of participation in competitiveness clusters on SMEs and intermediate enterprises - Quantile regression in practice
Quantile regression in practice
The use of quantile regression has become increasingly widespread over the last decade. It is based on a similar approach to that used in classical linear regression. In the same way that classical linear regression uses a linear modelling of the conditional expectation of the variable of interest as a function of its determinants, quantile regressions consist in assuming that the conditional quantiles of this variable of interest are linear. However, they supply a richer description than linear regressions, since it is possible to study the whole of the conditional distribution of the variable of interest instead of only its mean. This form of analysis is particularly interesting in evaluation measures of government policies: a programme may have a limited mean effect but increase the lowest levels of the variable of interest sufficiently to ensure that its implementation is desirable. Quantile regressions also serve to describe the determinants of variations in income inequalities. Additionally, they are sometimes better suited to certain types of data (censored and truncated variables, presence of outliers, nonlinear models, etc.). Quantile regressions can now be performed easily with numerous statistics software programmes. This article outlines the statistical principles underlying this modelling as well as the extensions that have been developed to respond to the classical econometric problem of the endogeneity of certain explanatory variables (panel data, instrumental variables, etc.). It also provides a guide to interpreting the results of a quantile regression, the analysis of which may be less intuitive than that of a linear regression. For a better understanding of the possible uses of quantile regression, two concrete applications are presented as an illustration.