Wealth Taxation as a Drift Modification: A Fokker-Planck Approach to Tax Neutrality

Paper: arXiv 2603.05283

Authors: Anders G Frøseth

Abstract

We reformulate the neutral wealth tax framework of Froeseth (2026; arXiv:2603.05264) in the language of stochastic dynamics and statistical physics. Individual wealth under geometric Brownian motion satisfies a Langevin equation with multiplicative noise; the probability density of wealth across a population then evolves according to a Fokker-Planck equation. A proportional wealth tax at market value enters as a uniform reduction of the drift coefficient, preserving the diffusion structure and all relative probability currents. This drift-shift symmetry is the physical content of tax neutrality. Each channel through which neutrality breaks down in practice - book-value assessment, liquidity frictions, forced dividend extraction, migration, and market impact - corresponds to a specific violation of this symmetry: a state-dependent, asset-dependent, or flow-dependent modification of the Fokker-Planck equation. The framework clarifies when wealth taxation is a benign rescaling of the dynamics and when it introduces genuinely new physics.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides an elegant conceptual synthesis bridging financial asset pricing (SDF framework) and econophysics (Fokker-Planck dynamics). However, it is entirely theoretical with zero empirical data, backtesting, or statistical validation, placing it firmly in the ‘Lab Rats’ quadrant.

Research Flowchart

  flowchart TD
    A[Research Goal: Reformulate Neutral Wealth Tax Framework via Stochastic Dynamics & Statistical Physics] --> B[Inputs: Individual Wealth under Geometric Brownian Motion & Proportional Wealth Tax]
    B --> C[Methodology: Model Wealth via Langevin Equation with Multiplicative Noise]
    C --> D[Compute Population Wealth Density Evolution via Fokker-Planck Equation]
    D --> E[Mathematical Finding: Wealth Tax Acts as a Uniform Drift-Shift, Preserving Diffusion & Relative Currents]
    E --> F[Application: Map Practical Tax Neutrality Breakdown to Specific Symmetry Violations in the Fokker-Planck Equation]
    F --> G[Outcomes: Establish Physical Content of Tax Neutrality & Differentiate Benign Rescaling from New Physics]