When Functions Become the Unit of Analysis

Specialeforsvar: Jonas Gyde Hermansen

Titel:  When Functions Become the Unit of Analysis: A functional regression perspective on the causal effect of democracy on economic growth

Abstract:  The field of functional data analysis (FDA), dealing with data in form of functions defined on a continuum, is today one of the most active fields of statistical research, offering new methods of data analysis based on the mathematics of functional analysis in Hilbert spaces. The purpose of this thesis is to present and prove mathematical results of FDA, and functional regression in particular, so as to perform a functional regression analysis addressing one of the oldest empirical questions of social science: Does there exist a causal effect of democracy on economic growth? We do so in order to asses, by example, whether FDA as a statistical theory has reached a point, where it can inform empirical questions normally addressed by methods of classical multivariate statistics. We find that FDA rests on a solid mathematical foundation that, however, relies on stronger and untestable assumptions about smoothness in order to make parameters of interest well-defined and identifiable. In particular, we show that the problem of estimation in the simple functional linear regression model is inherently ill-posed, requiring methods of regularization to obtain numerical results. In the end we put the mathematics into practice and show that a functional regression analysis investigating the effect of democracy on economic growth nuances the empirical findings from classical panel data methods. Discussing the results we do not find the functional approach of today to be an improvement upon classical approaches since the resulting claims of association and causality seem less credible. However, we believe that the contours of potential from a functional perspective are promising, especially if functional methods of statistical and causal inference get properly develop.

Vejleder: Helle Sørensen
Censor:   Anders Rønn-Nielsen, CBS