Extensions to the Wealth Tax Neutrality Framework

Abstract

Froeseth (2026) shows that a proportional wealth tax on market values is neutral with respect to portfolio choice, Sharpe ratios, and equilibrium prices under CRRA preferences and geometric Brownian motion. This paper investigates the robustness of that result along two dimensions. First, we extend the neutrality frontier: portfolio neutrality, including all intertemporal hedging demands, is preserved under stochastic volatility (Heston and general Markov diffusions) and Epstein-Zin recursive utility, but breaks under non-homothetic preferences such as HARA. Second, we identify four channels through which implemented wealth taxes depart from neutrality even under CRRA: non-uniform assessment across asset classes, general equilibrium price effects in inelastic markets, progressive threshold structures, and endogenous labour supply. Each channel is formalised and, where possible, calibrated to the Norwegian wealth tax system. The progressive threshold introduces a tax shield that increases risk-taking near the exemption boundary, an effect opposite in sign to the HARA distortion, and, at the extreme, generates a participation margin at which investors exit the tax jurisdiction entirely. We formalise this tax-induced migration as the extreme response at the progressive threshold and examine the Norwegian post-2022 experience as a case study. The full framework is applied to evaluate the Saez-Zucman proposal for a global minimum wealth tax on billionaires and the related French proposal for a national minimum tax above EUR 100 million.

Figures (6)

• Figure 1: Portfolio distortion under HARA preferences. The dashed line shows the CRRA benchmark (constant across wealth). Solid curves show the optimal risky share under HARA utility for three wealth tax rates. The shaded region between the $\tau_w = 0$ and $\tau_w = 1\%$ curves is the tax-induced distortion $\Delta w^*$. Each curve begins at the floor wealth $H(\tau_w) = \zeta / (r_f - \tau_w)$; higher taxes raise $H$ and shrink the feasible domain. Calibration: $\mu - r_f = 5\%$, $\sigma = 20\%$, $\gamma = 3$, $\zeta = 100{,}000$ NOK, $r_f = 3\%$.
• Figure 2: Portfolio tilt $\Delta w^*$ toward each asset class relative to bank deposits, under the Norwegian assessment system. The tilt is computed from \ref{['eq:delta_w_nonuniform']} with $\tau_w = 1.0\%$, $\gamma = 4$, and asset-class volatilities $\sigma = 0.20$ (listed shares), $\sigma = 0.15$ (commercial property), $\sigma = 0.10$ (housing classes). Assessment fractions $\alpha_i$ are shown below each bar. The two-order-of-magnitude spread illustrates the strong incentive to hold primary housing over financial assets.
• Figure 3: Decomposition of the price impact of a wealth-tax-induced demand shift. Supply is fixed at $\bar{Q}$. The wealth tax shifts demand left by $\Delta F = \tau_w \phi P_0$. The total price decline from $P_0$ to $P_1^I$ decomposes into two components: (i) the fundamental effect (light red), equal to $\Delta P^E = \tau_w \phi$, which is the decline that would occur under perfectly elastic demand; and (ii) the amplification wedge (light blue), equal to $(M{-}1)\,\Delta P^E$, which is the excess decline due to market inelasticity. The total impact is $M$ times the fundamental effect, where $M \approx 5$ is the Gabaix--Koijen multiplier. The diagram shows the full tax liability as the demand shift; actual equity outflows are smaller once dividend and liquid-income channels are accounted for (see \ref{['sec:imh_calibration']}).
• Figure 4: Opposing portfolio distortions under progressive taxation with HARA preferences. The dashed line is the CRRA benchmark. The blue curve shows the progressive-only effect (CRRA investor with threshold): the tax shield $H_\tau$ increases risk-taking. The red curve shows the HARA-only effect (proportional tax): subsistence floor $H$ reduces risk-taking. The purple curve combines both: $w^* = w^*_{\mathrm{neutral}} \cdot (W - H + H_\tau)/W$. The shaded region shows the magnitude of the progressive offset. Norwegian bracket 1 calibration: $H = 5$M NOK, $H_\tau = 950{,}000$ NOK, same parameters as Figure \ref{['fig:hara_distortion']}.
• Figure 5: Migration decision in $(W, c_i)$ space. Each line shows the indifference locus $c_i = \mathrm{PV}_{\tau}(W)$: investors below the line migrate; those above stay. A tax increase from 0.85% to 1.0% rotates the line upward, expanding the "migrate" region (shaded wedge). The 2% Zucman rate further expands it. All lines emanate from the exemption threshold $\bar{W}_1 = 1.9$M NOK. Under citizenship-based taxation (US), the effective cost shifts upward by $\mathrm{PV}_{\text{exit}}$, compressing the "migrate" region. Calibration: $r_f = 3\%$, $g = 2\%$.

Theorems & Definitions (25)

• Remark : Heston returns and the location-scale family
• Proposition 1: Portfolio neutrality under stochastic volatility
• proof
• Remark : Interpretation
• Proposition 2: Portfolio neutrality under general Markov diffusions
• proof
• Proposition 3: Portfolio distortion under HARA preferences
• proof
• Remark : Effective risk aversion
• Remark : Dollar amount vs. portfolio share