Paper: arXiv 2603.15974

Authors: Anders G Frøseth

Abstract

A proportional wealth tax - a levy on the stock of wealth - preserves portfolio neutrality by acting as a uniform drift shift in the Fokker-Planck equation for wealth dynamics. We extend this result to the full system of ownership taxes (eierkostnader) that a shareholder faces: a corporate tax on gross profits, a capital income tax on the risk-free return, a dividend and capital gains tax on the excess return, and a wealth tax on net assets. Each tax modifies the drift of the wealth process in a distinct way - multiplicative rescaling, constant shift, or regime-dependent compression - while leaving the diffusion coefficient unchanged. We show that the combined system preserves portfolio neutrality under three conditions: (i) the capital income tax rate equals the corporate tax rate, (ii) the shielding rate equals the risk-free rate, and (iii) the wealth tax assessment is uniform across assets. When these conditions hold, the after-tax excess return is a uniform rescaling of the pre-tax excess return by the factor $(1-τ_c)(1-τ_d)$, and the drift-shift symmetry of the wealth-tax-only case generalises to a drift-shift-and-rescale symmetry. We classify the distortions that arise when each condition fails and show that flow-tax distortions and stock-tax distortions are additively separable: they do not interact. The shielding deduction - a feature of several real-world tax systems, including the Norwegian aksjonaermodellen - emerges as the mechanism that restores the symmetry between equity and debt taxation within this framework. Calibrated to the Norwegian dual income tax, conditions (i) and (ii) hold by institutional design; the only binding distortion is non-uniform wealth tax assessment, which generates portfolio tilts roughly 300 times larger than any residual flow-tax channel.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework modeling wealth dynamics and taxation via the Fokker-Planck equation, demonstrating strong theoretical novelty and clarity. However, it relies primarily on calibration to institutional parameters rather than extensive empirical backtesting or data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate portfolio neutrality across full system of flow and stock taxes] --> B[Model Framework: Fokker-Planck wealth dynamics & continuous-time portfolio choice]
    B --> C[Inputs: Corporate tax τc, Capital income tax τi, Dividend/Gains tax τd, Wealth tax τw, Shielding rate rS]
    C --> D[Analytical Derivation: Decompose drift & diffusion shifts; test neutrality conditions]
    D --> E[Calibration: Empirical testing on Norwegian Dual Income Tax system]
    E --> F[Findings: Neutrality holds under 3 conditions; Flow & Stock distortions additively separable]
    E --> G[Empirical Outcome: Non-uniform wealth tax is sole binding distortion, driving ~300x larger tilts than flow taxes]