Identification of the reliability test (𝑅²) in case of an unknown common cause.

Details

Supervisors

Van Bellegem, Sébastien ; San Martin Gutiérrez, Ernesto

Faculty

Faculté des sciences économiques, sociales, politiques et de communication

Degree label

Master [120] en sciences économiques, orientation économétrie, à finalité approfondie

Abstract

This work aims to investigate the identification of the reliability test in situations where there is a non-measured common cause. A common cause is one or more variables, say 𝜃, that is responsible for the correlation of other variables, say 𝑋, 𝑌 and 𝑍. In this work, we shall consider an univariate common cause, that fully explains the correlation between 𝑋, 𝑌 and 𝑍, in other words, whose partial correlation is equal to zero, once the influence of 𝜃 is removed. The study considers three different scenarios, each resting on the base assumption that the variables have finite second moments: the first one assumes a linear model for the conditional expectations, the second one assumes a normal distribution of the random variables, and the third one demonstrates that the partial correlation formula can not work on non linear cases and leaves a trail to a new coefficient. The Projection Theorem in a Hilbert space (Rudin [1987]) and Spearman’s partial correlation coefficient from his work "General Intelligence" (Spearman [1904]) are utilized as primary tools.