Paper: arXiv 2603.16006

Authors: Anders G Frøseth

Abstract

We extend the Fokker-Planck framework of Froseth (2026, arXiv:2603.05283) to populations of investors with heterogeneous, persistent return-generating ability. When the drift coefficient in the Langevin equation for log-wealth varies across investors, the proportional wealth tax remains a uniform drift shift but ceases to be neutral in the economic sense: its real incidence differs across ability types, and the stationary wealth distribution changes shape. We derive the extended Fokker-Planck equation on the joint space of log-wealth and ability, characterise the conditions under which the drift-shift symmetry breaks, and identify the consequences for asset prices and portfolio allocations. The analysis connects the neutrality results of Froseth (2026, arXiv:2603.05264) and the Fokker-Planck dynamics of Froseth (2026, arXiv:2603.05283) to the heterogeneous-returns literature, notably the “use-it-or-lose-it” mechanism of Guvenen, Kambourov, Kuruscu, Ocampo-Diaz and Chen (2023).

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using Langevin equations and Fokker-Planck PDEs on joint state spaces to model wealth dynamics and tax policy. However, it is purely theoretical with no empirical backtesting or real-world data validation provided in the summary.

Research Flowchart

  flowchart TD
    A[Research Goal: Assess Wealth Tax Neutrality with Heterogeneous Investor Returns] --> B[Inputs: Langevin Dynamics & Heterogeneous Ability Types]
    B --> C[Derive Extended Fokker-Planck Equation on Joint Space]
    C --> D[Analyze Drift-Shift Symmetry & Capital Allocation]
    D --> E[Outcome: Neutrality Breaks via Use-It-or-Lose-It Mechanism]
    D --> F[Outcome: Real Incidence Differs & Wealth Distribution Reshapes]