## Project CEMAPRE internal

Title | Tail index regression model and Quantile Order Regression |

Participants | João Nicolau (Principal Investigator) |

Summary | (1) In extreme value statistics, the tail index is an important measure to gauge the heavy-tailed behavior of a distribution. Our goal is to link the tail index to the linear predictor induced by covariates, which constitutes the tail index regression model. This model may have interesting applications in finance and wages, income, etc. In particular, we want to use it in connection to Current Population Survey (CPS). The CPS is, however, subject to an important limitation: the data are right censored ('topcoded'). Topcoded data cause problems for inequality analysis because they censor the range of incomes that are observed. Inequality is underestimated because very high incomes appear as less high incomes. Also, due to the complex sampling design for the CPS, we need to account for the "weights" to produce representative statistics. (2) We also want to focus on a new models that we call Quantile Order Regression (QOR). Standard linear regression models allows us to estimate the impact of an explanatory variable on the dependent variables. In contrast, the QOR approach allows us to estimate the variation in the order of the quantile of the dependent variable. The QOR model is therefore suitable for applications to income, health and other types of inequalities, and more generally, the factors that explain the relative position of individuals, households, firms, cities, states, countries, etc., with respect to the dependent variable. |