How should we regulate inequality?

Your answer, whether it comes from intuition or models, is probably based on a set of economic building blocks. Perhaps the most famous building block of all is the equity-efficiency trade-off. Our models value equality, which comes at the cost of efficiency. Because we build complex castles around this basic stone, essentially all the models we teach and publish assume that economic inequality has no meaningful effects on society – that inequality does not affect the quality of democratic systems, the amount of social unrest, the trust between people, and so on.

This is not a well-understood fact, even at the top of the field. So let me take a few steps back. Why do our models work this way? The core reason is that inequality itself usually has no value for individuals. The standard equity concern is about maximising individual incomes – especially at the bottom – not minimising inequality. As we will see, this is a meaningful difference.

But first I will introduce a building block that changes this idea and explain why economic inequality is an externality. I will discuss income inequality here, but the thought process for wealth inequality is similar. First, we all affect income inequality through our market actions (by our choice of profession, say). Second, income inequality probably affects at least one thing that we all care about. Suppose, for example, that inequality increases the amount of crime. After a period of high inequality, you wake up one morning to find that your bike has been stolen. Inequality has affected you. Not because you are altruistic, jealous, or ethical – you simply liked your bike. Inequality was already, indirectly, in your utility function.

The same idea holds true for any other consequence of inequality. Inequality has value not necessarily because we care about inequality itself – although we may do that as well, of course – but because we prefer to live in societies that function better. In other words, even narrowly self-interested individuals can be affected by inequality. And since we all affect economic inequality, economic inequality is an externality.

These effects can be large. In 360 BCE, Plato warned that “a state which is desirous of being saved from the greatest of all plagues” should avoid “extreme poverty [and] excess of wealth, for both are productive of both these evils”. More recently, Alan Greenspan noted that “you can see the deteriorating impact of [inequality] on our current political system”, and Pope Francis stated that “inequality is the root of social evil”. In a recent working paper, Max Lobeck and I found that most US citizens – Democrats and Republicans both – strongly believe that inequality has harmful consequences on crime, growth, democratic institutions, and much more.

The beauty of thinking about inequality as an externality is that it allows us to connect such thoughts on inequality to established economic theory. Why should we tax the rich? In standard theory, the only reason is to gather revenue to redistribute to the poor. If you cannot gather revenue, you should never tax. This leads to extreme inequality in many ‘optimal’ steady-state solutions – an example of why maximising bottom incomes is not the same as minimising inequality.
Based on such logic, state-of-the-art models have recently implied that we shouldn’t tax capital (Barro and Chari 2024) or that we shouldn’t increase tax progressivity when inequality rises (Heathcote et al. 2022). The inequality externality angle is not considered in these models. And, as we know, externalities simply make model implications differ – in these cases meaningfully.

With this perspective, we can re-visit some of our most famous economic theorems. The First Welfare Theorem, the Atkinson and Stiglitz (1976) theorem, and the models in Chamley (1986) and Judd (1985) all assume no externalities and thus (implicitly) that economic inequality affects nothing in society. These theorems speak directly to distributional issues, but inequality itself is not worth anything in the underlying frameworks. It is a strange state of affairs. The First Welfare Theorem is particularly noteworthy, as the core justification for the efficiency of markets also assumes that inequality has no inefficiencies.

Inequality’s externality properties are also missing in the modern literature. In the otherwise excellent Guvenen et al. (2023) article on the “efficiency and redistributional effects of wealth taxation”, inequality’s societal consequences are not mentioned. The same is true in practically every other model maximising social welfare, which means much of public finance and macroeconomics (including Saez 2001, Preston and Blundell 2019, Jacquet and Lehmann 2021, Saez et al. 2021). Optimal taxation and cost-benefit analyses are particularly salient examples. The classes we teach rarely, if ever, mention this caveat.

What are the policy implications if inequality is an externality? Frank Cowell and I unpack this question in our recent paper (Støstad and Cowell 2024). We introduce various-sized inequality externalities into the optimal income taxation model and explore the consequences. Our main takeaway is simple: top income tax rates are particularly affected.

Why? Think about a small tax increase at the top, which has two main effects. First, revenue is mechanically gathered. This, unsurprisingly, reduces inequality. But then there is the second main effect, which is agents’ behavioural responses. People stop working when they’re taxed. This reduces revenue, leading to the classic equity-efficiency trade-off. At the top, though, behavioural responses also reduce inequality. When top-earners stop working, inequality decreases. From the externality angle, this is welfare-positive, even though the revenue loss is of course still problematic. In other words, both the mechanical and behavioural effects at the top reduce inequality. This means that we can change inequality easily. It also means that optimal top tax rates are very sensitive to the size of the inequality externality.

To repeat, reducing inequality is trivial. We could simply set a 100% tax rate on the top and inequality would tumble. That’s not optimal, though – we also care about revenue. So, what is the trade-off? We use three imperfect methods to find orders of magnitude for the inequality externality. Our median estimate implies that the average American would pay 13% of their income for inequality to change to Denmark’s level.

How does this change optimal tax rates? The optimal top marginal income tax rate is an already high 63% in the no-externality case (the revenue-maximising Laffer rate). Using the median inequality externality estimate, the top optimal marginal tax rate rises to the much higher 81%. If inequality’s negative consequences are more severe, optimal top rates can go higher – easily above 90%. If inequality is good, on the other hand – say it increases innovation or growth, for example – the optimal top rate can fall to below 0%.

This means that the optimal top tax rate strongly depends on inequality’s externality effects. The range of values we find is much larger than one can find by changing standard empirical parameters. It turns out that the magnitude of the inequality externality is crucial. Which makes sense – after all, a major goal of the tax system is to regulate inequality. So while elasticities and Pareto parameters are significant, we may have been so focused on these empirically estimable values that we missed the forest for the trees. It is possible that the most crucial tax design question is whether equality is more efficient than inequality.

Most important for myself, though, is the simple idea that inequality is an externality. I have found that thinking in these terms simplifies many complex situations. It is a building block. And even if we disagree on effects and magnitudes, it is useful to formalise such disagreements. Policy advice is only as good as the materials we build with, and it is not possible to build a square castle with round stones.

What, then, is the power of treating inequality as an externality? It allows us to summarise the many complex societal consequences of inequality into one simple idea. That idea is practically useful and can easily be added into standard economic thought. The results are often surprising, upending long-held economic wisdom. Most of all, it is simply the power of having a square stone.

## References

Atkinson, A B and J E Stiglitz (1976), “The design of tax structure: direct versus indirect taxation”, *Journal of Public Economics* 6(1–2): 55–75.

Barro, R J and V V Chari (2024), “Taxation of Capital: Capital Levies and Commitment”, NBER Working Paper No. 32306.

Chamley, C (1986), “Optimal taxation of capital income in general equilibrium with infinite lives”, *Econometrica: Journal of the Econometric Society* 54(3): 607–22.

Guvenen, F et al. (2023), “Use it or lose it: Efficiency and redistributional effects of wealth taxation”, *The Quarterly Journal of Economics *138(2): 835–94.

Heathcote, J, K Storesletten and G L Violante (2020), “Presidential address 2019: How should tax progressivity respond to rising income inequality?”, *Journal of the European Economic Association* 18(6): 2715–54.

Jacquet, L and E Lehmann (2021), “Optimal income taxation with composition effects”,* Journal of the European Economic Association* 19(2): 1299–341.

Judd, K L (1985), “Redistributive taxation in a simple perfect foresight model”, *Journal of Public Economics* 28(1): 59–83.

Mirrlees, J A (1971), “An exploration in the theory of optimum income taxation”, *Review of Economic Studies *38(2): 175–208.

Preston, I and R Blundell (2019), “Principles of tax design, public policy and beyond: The ideas of James Mirrlees, 1936–2018”, VoxEU.org, 25 January.

Saez, E, S Stantcheva and T Piketty (2011), “Taxing the 1%: Why the top tax rate could be over 80%”, VoxEU.org, 8 December.

Saez, E (2001), “Using elasticities to derive optimal income tax rates”, *Review of Economic Studies* 68(1): 205–29.

Støstad, M N and F Cowell (2024), “Inequality as an externality: Consequences for tax design”, *Journal of Public Economics*, forthcoming.