The Burr XII quantile regression for salary-performance models with applications in the sports economy

The present paper proposes a quantile regression model based on a new parameterization of the Burr XII distribution. We establish a systematic structure on the quantiles of the response variable as a function of explanatory variables, making the model suitable for the modeling of asymmetric data with heavy tails. The estimation of the model parameters is conducted through the maximum-likelihood method, and their performance in finite sample sizes is evaluated through a Monte Carlo simulation study. We also present some diagnostic tools and selection criteria for the new regression model. To illustrate the usefulness of the model, we present and discuss an empirical application to the salaries of players in the Western division of the American League of the Major League Baseball in the 2019 season. We observe a relationship between the teams, and other indicators of performance, and their players' salaries. Salary-performance models have been extensively explored in the sports economy, thus being a potential area for new applications of the proposed regression model in the microeconomic context. Furthermore, the proposal can also be used in macroeconomics, finance, and business management.

Automated summary

This paper proposes a quantile regression model based on a new parameterization of the Burr XII distribution, suitable for modeling asymmetric data with heavy tails. The model parameters are estimated using the maximum-likelihood method and their performance is evaluated through a Monte Carlo simulation study. Diagnostic tools and selection criteria for the new regression model are also presented. An empirical application to the salaries of players in the Western division of the American League of the Major League Baseball is discussed to illustrate the usefulness of the model.