Microscopic models for the study of taxpayer audit effects

TL;DR

This paper develops a microscopic dynamic model to analyze how different tax enforcement strategies affect income distribution, tax evasion, and societal inequality over time using a complex systems approach.

Contribution

It introduces a novel kinetic model incorporating heterogeneity in income and evasion behavior to study enforcement effects on tax compliance.

Findings

Higher audit fractions reduce tax evasion.

Stricter penalties decrease evasion and alter income distribution.

Enforcement regimes significantly impact societal income inequality.

Abstract

A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus is on effects of enforcement regimes, characterized by different choices of the audited taxpayer fraction and of the penalties imposed to noncompliant individuals. A complex systems perspective is adopted: society is considered as a system composed by a large number of heterogeneous individuals. These are divided into income classes and may as well have different tax evasion behaviors. The variation in time of the number of individuals in each class is described by a system of nonlinear differential equations of the kinetic discretized Boltzmann type involving transition probabilities.