The Application and Analysis of Mathematical Statistics Methods in Contemporary Economics

Abstract

: This paper considers three fundamental statistical methodologies, namely causal machine learning, high-dimensional regularized regression and network analysis which have been developed in the statistical sciences and deployed to the empirical problems in economics. The paper will first describe modern difference-in-differences frameworks that can be used to deal with bias in staggered adoption environments using design-based inference and doubly robust estimation. It discusses next double/debiased machine learning, a process of learning the low-dimensional parameters when the high-dimensional nuisance functions are involved where flexible learners and cross-fitting are applied. The LASSO and its biased versions are brought out as a solution to variable selection and post-selection inference in high-dimensional models. Network analysis is considered as a graph-theoretic approach to measure systemic interdependence, and has been applied to financial connectedness. The topic of hypothesis testing is re-explored as a developing inferential instrument, which focuses on multiple testing corrections. In all these methods, the paper provides the conceptual framework, workflow, advantages, and limitations of each method. It then addresses policy assessment, financial stability and nowcasting of the macroeconomy. Lastly, it discusses such issues as interpretability and privacy of data, and clarifies the future trends such as AI-integration or real-time economic sensors. The current review emphasizes how modern statistics has been transformative in changing the face of economics to become a more empirical and data-centered science.