Use It or Lose It
The objection
The most common argument against a wealth tax goes something like this: a wealth tax punishes smart investors for taking the risky bets that build successful companies. Tax the stock of wealth, and you penalise precisely those who have demonstrated the ability to deploy capital well. Capital migrates away from the skilled, toward the government. Everyone loses.
It is an intuitive argument, and it deserves a careful answer.
Two equations
The distinction between a capital income tax and a wealth tax can be stated in two lines. Let \(a_i\) denote the wealth of investor \(i\), \(r_i\) the rate of return, and \(\tau_k\), \(\tau_a\) the tax rates on capital income and wealth respectively. Under a capital income tax, after-tax wealth is
\[ a_i^{\text{after-tax}} = a_i + (1 - \tau_k) \cdot r_i \, a_i \]
Under a wealth tax, assessed on the end-of-period market value, it is
\[ a_i^{\text{after-tax}} = (1 - \tau_a) \cdot (a_i + r_i \, a_i) \]
The income tax scales only the return \(r_i a_i\) — the tax base is the flow. The wealth tax scales the entire end-of-period position \((1 + r_i) a_i\) — the tax base is the stock.
When every investor earns the same return — \(r_i = r\) for all \(i\) — the two systems are equivalent up to a rate adjustment. But when returns vary across investors, they diverge. The income tax burden is proportional to the individual return: a high-return investor pays more; a zero-return investor pays nothing. The wealth tax falls on the entire position: even a zero-return investor pays \(\tau_a \, a_i\).
Two kinds of silent partner
This algebraic distinction maps onto two different economic mechanisms, both of which can be described as the government acting as a “silent partner” — but the partnership works through different channels.
Domar and Musgrave showed in 1944 that an income tax with full loss offset acts as a silent partner on the return margin: the government shares proportionally in both gains and losses on the risky part of your portfolio. The rational response is not to take less risk, but more — you scale up your risky position until your after-tax risk exposure matches what you had before. The government absorbs part of the variance; you restore the original bet. The Sharpe ratio is unchanged.
Stiglitz extended this in 1969, drawing out the contrast with a wealth tax. The wealth tax creates a different kind of partnership — one on the position margin. The government holds a proportional claim on your assets, scaling down your entire portfolio by the same factor \((1 - \tau_a)\). The return per unit of remaining wealth is unaffected. The portfolio neutrality result from the earlier papers in this series makes this precise: a uniform proportional wealth tax preserves the Sharpe ratio, the tangency portfolio, and the optimal asset allocation.
The two partnerships have opposite behavioural signatures. Under the income tax, investors respond by taking larger risky positions — leveraging up to restore their pre-tax risk exposure (the Domar–Musgrave effect). Under the wealth tax, the risk composition is unchanged — you hold the same portfolio, just less of it (neutrality).
Where high returns come from
So far, so clean. But these results assume investors are identical — or at least that they differ only in scale. The interesting question is what happens when investors earn different returns, and here the story gets more complicated.
Guvenen, Kambourov, Kuruscu, Ocampo, and Chen (2023, Quarterly Journal of Economics) built a model where entrepreneurs differ in productive ability. A high-ability entrepreneur extracts more output from a unit of capital than a low-ability one. In their model, the wealth tax has a powerful efficiency property they call “use it or lose it”: because the tax falls on the stock rather than the return, high-ability entrepreneurs face a lower effective tax rate relative to what they earn. Wealth — and with it the ability to deploy capital — migrates toward the more productive. The numbers are striking: an optimal wealth tax delivers a welfare gain of 9.61% in consumption-equivalent terms, compared with 6.28% under optimal capital income taxation. And when they eliminate return heterogeneity entirely in a robustness check, the welfare advantage drops to 0.005%. The entire case rests on the heterogeneous-returns channel.
This is a strong result, and the mechanism is real. But it rests on a specific interpretation of why investors earn different returns. In the Guvenen et al. model, all return heterogeneity is productive ability — a parameter \(z\) that enters the production function directly. An entrepreneur with high \(z\) is simply better at turning capital into output.
The empirical world is messier. When we observe that some investors persistently earn higher returns than others, at least three things could be going on:
Genuine skill. Some investors really are better at identifying opportunities, managing operations, or allocating capital. A venture capitalist who consistently picks winners, a restaurateur who outperforms the local competition through superior execution — these are the \(z\) that Guvenen et al. have in mind.
Structural advantage. Some returns persist not because of individual ability but because of market position. A two-competitor market in a small town, a regulatory licence that limits entry, relationship capital built over decades — these generate persistent excess returns that have little to do with the skill of the current owner. Replace the owner with someone of average ability, and the returns might barely change.
Winner-take-all dynamics. In digital markets especially, small early advantages compound into dominant positions through network effects, data accumulation, and switching costs. Two founders of identical ability launching identical products months apart can earn vastly different returns — the first mover captures the market; the second gets nothing. The return to the dominant firm reflects structural lock-in, not ongoing skill.
The question that matters
Return to the objection we started with: a wealth tax punishes smart investors. The Guvenen et al. result says the opposite. When returns reflect genuine productive ability, the wealth tax rewards skill — it reallocates capital toward high-ability entrepreneurs, not away from them. The “use it or lose it” mechanism is precisely a mechanism for directing capital toward those who use it best. If the objection were right, the model would show welfare losses. It shows welfare gains of nearly 10%.
So the first reversal is straightforward: an optimally constructed wealth tax does not punish skill. It amplifies it.
But there is a second, harder question. The mechanism reallocates capital toward whoever earns high returns — and it does not ask why they earn them. If high returns reflect genuine skill, the reallocation is efficient and everyone benefits. If they reflect structural advantage — a local monopoly, a regulatory barrier, a platform locked in by network effects — then the same mechanism channels capital toward the parts of the economy where competition is weakest. It allocates not toward talent, but toward where capitalism is not working well.
This is the question we are working on in an upcoming paper. The Fokker–Planck framework developed in the earlier papers of this series provides the analytical structure to condition on the source of return heterogeneity. The answer will not be a single number — it will vary by sector, by market structure, and by institutional context. But it determines what the “use it or lose it” mechanism is actually doing: rewarding productive ability, or entrenching incumbency.