How log-normal is your country? An analysis of the statistical distribution of the exported volumes of products

TL;DR

This study analyzes the statistical distributions of exported product volumes across 148 countries, revealing that distribution shapes vary with economic development and confirming log-normality primarily in intermediate economies.

Contribution

It classifies countries into three distribution types based on development level and links these shapes to macroeconomic indicators, providing new insights into export volume distributions.

Findings

Less developed countries show incomplete log-normal distributions.

Intermediate economies exhibit full log-normal distributions.

High development countries have asymmetric export volume distributions.

Abstract

We have considered the statistical distributions of the volumes of the different products exported by 148 countries. We have found that the form of these distributions is not unique but heavily depends on the level of development of the nation, as expressed by macroeconomic indicators like GDP, GDP per capita, total export and a recently introduced measure for countries' economic complexity called fitness. We have identified three major classes: a) an incomplete log-normal shape, truncated on the left side, for the less developed countries, b) a complete log-normal, with a wider range of volumes, for nations characterized by intermediate economy, and c) a strongly asymmetric shape for countries with a high degree of development. The ranking curves of the exported volumes from each country seldom cross each other, showing a clear hierarchy of export volumes. Finally, the log-normality hypothesis has been checked for the distributions of all the 148 countries through different tests, Kolmogorov-Smirnov and Cramer-Von Mises, confirming that it cannot be rejected only for the countries of intermediate economy.