Statistical Modeling of Financial Data with Skew-Symmetric Error Distributions

Abstract

Based on corporate financial data for almost all companies listed on the Prime Market of the Tokyo Stock Exchange in fiscal year 2021, we gradually refine a model to explain firms’ sales by the number of employees and total assets. Starting from a Cobb–Douglas-type functional form linearized by a log transformation, the assumption of a skew-symmetric distribution in the error structure and the introduction of industry dummies are shown to be useful not only in searching for a good-fitting model, but also in ensuring the accuracy of important parameters such as the labor share. The introduction of industry dummies helps to improve the accuracy of the model as well as to allow for interpretation as sector-wise total factor productivity.

Keywords

• corporate financial data
• log-log model
• skew-symmetric distributions
• industry dummies
• total factor productivity