AI 中文总结
该论文在对数财富的Fokker-Planck框架下，对比信息论（JKO自由能间隙）与输运几何（平方2-Wasserstein距离）两种准则，刻画了比例税类下的最小扭曲财富税最优解，发现二者最优工具选择存在差异，且校准结果受投资组合波动率影响。
AI 中文摘要
我们在对数财富的Fokker-Planck框架下，基于两种不同的规范准则刻画了最小扭曲财富税：一是与Mirrleesian决策扭曲传统一致的信息论度量——JKO自由能间隙；二是与Saez-Zucman分布压缩传统一致的、距T时刻无税分布的平方2- Wasserstein距离（$W_2$）。限定于姊妹论文（Froseth 2026）中保持中性的(C1)-(C3)税则类，两种最优解在由企业股息留存率$k=(1-\tau_c)(1-\tau_d)$和比例财富税率$\tau_w$参数化的二维设计平面上均有闭式解。JKO最优解将制度轴按无量纲比率$\rho=\Sigma_0 m_0/\sigma^2$划分为三个阶段，其中$m_0=\mu-\sigma^2/2$为几何平均对数收益率：低$\rho$时为纯财富税阶段，中$\rho$时为混合工具阶段，高$\rho$时为纯流量税阶段。相比之下，该校准下的$W_2$最优解是退化的：在整个制度轴上均指向纯流量税端点。通过钝度指数$B(m_0)=b/(a m_0)$可对准则差异给出经济上有意义的解读，该指数衡量财富税渠道相对于流量税渠道的每单位收入平均位移超调量；JKO对$B$线性加权，$W_2$对其二次加权，两种规范传统对应于这种加权方式的差异。具有挪威特征的校准在股票占比高的投资组合波动率下处于JKO混合工具阶段，但在典型房地产占比高的家庭的实际有效波动率下会进入纯流量税阶段。
英文摘要
We characterise minimum-distortion wealth taxation under two contrasting normative criteria within a Fokker-Planck framework on log-wealth: the JKO free-energy gap, an information-theoretic measure aligned with the Mirrleesian decision-distortion tradition, and the squared 2-Wasserstein distance from the no-tax distribution at horizon $T$, a transport-geometric measure aligned with the Saez-Zucman distributional-compression tradition. Restricting to the neutrality-preserving (C1)-(C3) schedule class of a companion paper (Froseth 2026), both optima admit closed forms in the two-dimensional design plane parametrised by the corporate-dividend retention $k = (1-τ_c)(1-τ_d)$ and the proportional wealth-tax rate $τ_w$. The JKO optimum partitions the regime axis into three phases as a function of the dimensionless ratio $ρ= Σ_0 m_0/σ^2$, with $m_0 = μ- σ^2/2$ the geometric mean log-return: a pure wealth-tax phase at low $ρ$, a mixed-instrument phase at intermediate $ρ$, and a pure flow-tax phase at high $ρ$. The $W_2$ optimum, by contrast, is degenerate in this calibration: it pins to the pure flow-tax corner across the whole regime axis. The criterion contrast admits an economically meaningful reading via a bluntness index $B(m_0) = b/(a m_0)$ that measures the wealth-tax channel's mean-displacement-per-revenue overshoot relative to the flow-tax channel; JKO weights $B$ linearly, $W_2$ weights it quadratically, and the two normative traditions correspond to this difference in weighting. Norwegian-flavoured calibrations sit inside the JKO mixed-instrument phase under stock-heavy portfolio volatility but move into the pure flow-tax phase under the realised effective volatility of typical real-estate-heavy households.
Comments41 pages, 3 figures, 2 tables. Companion paper to arXiv:2603.05264, arXiv:2603.05277, arXiv:2603.05283, and arXiv:2607.06153
