Identification of a Common Cause under the Weak Axiom of Local Independence

Details

Supervisors

Van Bellegem, Sébastien

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 focuses on identifying an unobserved variable, which we represent as a hidden variable theta (also called the "common cause" or "global factor"), where we only observe a signal without assuming its complete distribution. The manuscript is divided into two main sections, the first one aims to reconstructing the vector theta under an univariate linear model. The second one aims at reconstructing the common cause under a multivariate linear model for which we observe other common causes. The first chapter delves into the identification of the common cause within a linear model framework and establishes a method for identifying the full vector theta, allowing for the explicit inclusion of this hidden variable in the model. We outline conditions under which the parameter beta for each observed variable can be identified. The second chapter moves into identifying the common cause within a multivariate linear model and establishes a method to enhance the number of observations of the vector theta, while taking into account other observed common causes. We also discuss the implications of this methodology for the construction of indexes, and improving the reliability of the production functions and financial models through various applications.