<p>The literature on optimal income taxation kicked off with <a href="https://www.jstor.org/stable/pdf/1910538.pdf" rel="nofollow noreferrer">Diamond, Mirrlees (1971)</a>. In their model, people differ only by ability, i.e. the highest earning person is the most productive one. As a consequence, any marginal tax rate on this person will be detrimental to production and hence to social welfare (in this model). Therefore, the optimal top marginal tax rate is zero! </p>

<p>The main innovation was initiated by Emmanuel Saez (<a href="http://www.nber.org/papers/w7628.pdf" rel="nofollow noreferrer">Saez (2001)</a> and <a href="http://www.nber.org/papers/w18521.pdf" rel="nofollow noreferrer">Piketty, Saez (2012)</a>). The basic idea is that the social planner maximizes a social welfare function (SWF) that captures the fact that individuals are to some degree inequality averse. Plus, they allow the introduction of welfare weights, i.e. a normative decision on whose well-being matters for the society as a whole. The innovation of this literature is the formulation, that allows to calculate an optimal tax rate based on observable (or, rather, estimatable) figures. This is referred to as the <em>sufficient statistic</em> approach. See e.g. Eq.7 in Piketty, Saez (2012) for the optimal top tax rate <span class="math-container">$\tau$</span>:</p>

<p><span class="math-container">$$\tau = \frac{1-g}{1-g+a *e} $$</span> </p>

<p>This depends only on three parameters: <span class="math-container">$e$</span> is the extent to which top income earners are able to dodge the tax. In the basic model, this is only labor supply, but later contributions (incuding the one you cite, but also <a href="https://www.jstor.org/stable/pdf/23269968.pdf" rel="nofollow noreferrer">Saez et al. (2012)</a>, [yes, Saez again]) acknowledge that there are many other avoidance strategies. <span class="math-container">$g$</span> is the social welfare weight of the top-income earners and <span class="math-container">$a$</span> is an indicator of the income distribution.</p>

<p>The optimal top marginal tax rates above 70% stems basically from the assumption that <span class="math-container">$g$</span> is zero, i.e. society as a whole does not really care about the richest. Another key factor is the magnitude of <span class="math-container">$e$</span>. If I argue that with a sufficiently high top tax rate, all millionaires will leave the country, I assume a high <span class="math-container">$e$</span>, which drives down <span class="math-container">$\tau$</span>. There are also researchers that came up with different values for <span class="math-container">$a$</span>. One quite well-known criticism is from <a href="https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.23.4.147" rel="nofollow noreferrer">Mankiw et al. (2009)</a>. They back up their arguments however, e.g. on less reliable data, which is why I don't find it very substantiated at least on the top tax rate issue.</p>

<p>For a general discussion on optimal taxation beyond the top tax rate, see also <a href="https://www.aeaweb.org/articles/pdf/doi/10.1257/jep.25.4.165" rel="nofollow noreferrer">Diamond and Saez (2011)</a>.</p>

<p>Summing up, the Saez literature is a great tool to link data and economic theory and has been heavily used. Empirically, estimating the various margins of <span class="math-container">$e$</span> is very difficult and has been tried numerous times. The top tax rate of 70% or higher is debatable as it has some normative settings. But overall, this literature has made compelling arguments in favor of progressive taxation and higher taxation of inheritances. It might be my personal bias, but I'm not aware of any fundamental, substantiated criticism to the Saez approach.</p>

CC BY-SA 4.0
2019-01-17T11:44:41.233Z
How this literature makes case for high capital taxes? If I remember my public economics right then due to Chamley-Judd result which implies all capital taxes are born by labor and hence optimal capital taxes are zero. Also if I remember correctly Saez literature usually works in partial equilibrium and general equilibrium analysis usually works against taxes, I think I recall even Saez admitted that his estimates should be think of as upper bounds
1muflon1
CC BY-SA 4.0
2019-01-17T12:19:24.210Z
Do you have a reference for an general equilibrium study on that issue? Which equilibrium effects work towards lower optimal tax rates? Maybe I was a little too strong on capital income taxation, Saez and co. mainly talk about inheritance and bequest taxation (which might be seen as a special case of capital income). I edited my answer accordingly.
E. Sommer
CC BY-SA 4.0
2019-01-17T14:09:20.770Z
part1 or capital tax generally the literature shows that rates should be low. You can check the Chamley-Judd paper and some subsequent reviews. Indeed the Saez paper is about inheritance. You should edit that. For the general equilibrium theory of taxation I don’t know any paper that focuses on income tax, I think if you would make one it would earn you Nobel prize because even partial equilibrium analysis is already complex and takes lifetime to learn. However, for the tax areas where this is more feasible usually dynamic general equilibrium models show lower tax rates
1muflon1
CC BY-SA 4.0
2019-01-17T14:44:52.477Z
Part2 actually good sources and papers you can already find in the Picketty and Saez 2012 paper. They themselves state on page 28 that they abstract from dynamic, GE and few other considerations if you look at the papers cited on these topics in that paper they generally point that optimum taxes should be lower. This being said it’s hard to say how much lower. Probably they would still be be quite large hence I would take the Saez estimations as the upper bound.
1muflon1
CC BY-SA 4.0
2019-01-17T14:48:22.577Z
Thanks. I think the key innovation of Saez is to allow for more heterogeneity, i.e. wealth does not have to be the consequence of individual effort. Once you allow for that, the optimal solution looks different.
E. Sommer
CC BY-SA 4.0
2019-01-17T14:57:20.107Z
Sure. As long as there are some economic rents you can tax them 100% without any loss of efficiency. Also definitely Saez research points to higher top marginal rates than people used to believe. My point is just that his results should be interpreted with little bit of caution.
1muflon1
CC BY-SA 4.0
2019-01-18T17:30:25.037Z
Fair enough, feel free to edit my post.
E. Sommer
CC BY-SA 4.0
2019-01-16T12:33:37.047Z
2019-01-17T12:19:49.303Z
2019-01-17T12:19:49.303Z
E. Sommer
<p>Some of you might know of US politician Alexandria Ocasio-Cortez, a member of the Democratic Party as well as the Democratic Socialists of America. In a recent interview she had on 60 Minutes, she suggested the idea of raising the top marginal tax to 70% for income above 10 million dollars. The recent conversation surrounding this proposal is unsurprisingly heated (though mostly unproductive, as people struggle to understand what a marginal tax rate entails).</p>

<blockquote>
  <p><em>My question is what recent literature is there for determining the optimal top marginal tax rate of a country?</em> </p>
</blockquote>

<p>For example, in <strong><a href="https://www.nber.org/papers/w17616" rel="nofollow noreferrer">Piketty, Saez, and Stantcheva (2011)</a></strong>, the optimal marginal tax rate they estimate is 83% (on a cursory search through the paper, I cannot find for what level of income though) looking at labor supply and tax avoidance elasticities, but also at a "compensating bargaining" elasticity that tends to make the optimal rate higher than other models they cite.</p>

<p>A good answer will briefly explain what the literature you cite argues for, with some criticisms and/or defenses of the literature and its possible shortcomings. Recent literature of course is preferred, but if an older model is needed to explain newer ones, it is fine to cite those too.</p>

<reference-request><optimal-taxation>
Optimal Top Marginal Tax Rates
Kitsune Cavalry
# Optimal Top Marginal Tax Rates

(Asked by: username_0 on 2019-01-15)

Some of you might know of US politician Alexandria Ocasio-Cortez, a member of the Democratic Party as well as the Democratic Socialists of America. In a recent interview she had on 60 Minutes, she suggested the idea of raising the top marginal tax to 70% for income above 10 million dollars. The recent conversation surrounding this proposal is unsurprisingly heated (though mostly unproductive, as people struggle to understand what a marginal tax rate entails).

> *My question is what recent literature is there for determining the optimal top marginal tax rate of a country?*

For example, in **[Piketty, Saez, and Stantcheva (2011)](https://www.nber.org/papers/w17616)**, the optimal marginal tax rate they estimate is 83% (on a cursory search through the paper, I cannot find for what level of income though) looking at labor supply and tax avoidance elasticities, but also at a "compensating bargaining" elasticity that tends to make the optimal rate higher than other models they cite.

A good answer will briefly explain what the literature you cite argues for, with some criticisms and/or defenses of the literature and its possible shortcomings. Recent literature of course is preferred, but if an older model is needed to explain newer ones, it is fine to cite those too.

**Tags:** reference-request, optimal-taxation

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## 1 answers

### Answer by username_1 on 2019-01-16. Score: 2 | Accepted answer

The literature on optimal income taxation kicked off with [Diamond, Mirrlees (1971)](https://www.jstor.org/stable/pdf/1910538.pdf). In their model, people differ only by ability, i.e. the highest earning person is the most productive one. As a consequence, any marginal tax rate on this person will be detrimental to production and hence to social welfare (in this model). Therefore, the optimal top marginal tax rate is zero!

The main innovation was initiated by Emmanuel Saez ([Saez (2001)](http://www.nber.org/papers/w7628.pdf) and [Piketty, Saez (2012)](http://www.nber.org/papers/w18521.pdf)). The basic idea is that the social planner maximizes a social welfare function (SWF) that captures the fact that individuals are to some degree inequality averse. Plus, they allow the introduction of welfare weights, i.e. a normative decision on whose well-being matters for the society as a whole. The innovation of this literature is the formulation, that allows to calculate an optimal tax rate based on observable (or, rather, estimatable) figures. This is referred to as the *sufficient statistic* approach. See e.g. Eq.7 in Piketty, Saez (2012) for the optimal top tax rate $\tau$:

$$\tau = \frac{1-g}{1-g+a \*e} $$

This depends only on three parameters: $e$ is the extent to which top income earners are able to dodge the tax. In the basic model, this is only labor supply, but later contributions (incuding the one you cite, but also [Saez et al. (2012)](https://www.jstor.org/stable/pdf/23269968.pdf), [yes, Saez again]) acknowledge that there are many other avoidance strategies. $g$ is the social welfare weight of the top-income earners and $a$ is an indicator of the income distribution.

The optimal top marginal tax rates above 70% stems basically from the assumption that $g$ is zero, i.e. society as a whole does not really care about the richest. Another key factor is the magnitude of $e$. If I argue that with a sufficiently high top tax rate, all millionaires will leave the country, I assume a high $e$, which drives down $\tau$. There are also researchers that came up with different values for $a$. One quite well-known criticism is from [Mankiw et al. (2009)](https://pubs.aeaweb.org/doi/pdfplus/10.1257/jep.23.4.147). They back up their arguments however, e.g. on less reliable data, which is why I don't find it very substantiated at least on the top tax rate issue.

For a general discussion on optimal taxation beyond the top tax rate, see also [Diamond and Saez (2011)](https://www.aeaweb.org/articles/pdf/doi/10.1257/jep.25.4.165).

Summing up, the Saez literature is a great tool to link data and economic theory and has been heavily used. Empirically, estimating the various margins of $e$ is very difficult and has been tried numerous times. The top tax rate of 70% or higher is debatable as it has some normative settings. But overall, this literature has made compelling arguments in favor of progressive taxation and higher taxation of inheritances. It might be my personal bias, but I'm not aware of any fundamental, substantiated criticism to the Saez approach.

> **Comments:**
> **username_2**: How this literature makes case for high capital taxes? If I remember my public economics right then due to Chamley-Judd result which implies all capital taxes are born by labor and hence optimal capital taxes are zero. Also if I remember correctly Saez literature usually works in partial equilibrium and general equilibrium analysis usually works against taxes, I think I recall even Saez admitted that his estimates should be think of as upper bounds  
> **username_1**: Do you have a reference for an general equilibrium study on that issue? Which equilibrium effects work towards lower optimal tax rates? Maybe I was a little too strong on capital income taxation, Saez and co. mainly talk about inheritance and bequest taxation (which might be seen as a special case of capital income). I edited my answer accordingly.  
> **username_2**: part1 or capital tax generally the literature shows that rates should be low. You can check the Chamley-Judd paper and some subsequent reviews. Indeed the Saez paper is about inheritance. You should edit that. For the general equilibrium theory of taxation I don’t know any paper that focuses on income tax, I think if you would make one it would earn you Nobel prize because even partial equilibrium analysis is already complex and takes lifetime to learn. However, for the tax areas where this is more feasible usually dynamic general equilibrium models show lower tax rates  
> **username_2**: Part2 actually good sources and papers you can already find in the Picketty and Saez 2012 paper. They themselves state on page 28 that they abstract from dynamic, GE and few other considerations if you look at the papers cited on these topics in that paper they generally point that optimum taxes should be lower. This being said it’s hard to say how much lower. Probably they would still be be quite large hence I would take the Saez estimations as the upper bound.  
> **username_1**: Thanks. I think the key innovation of Saez is to allow for more heterogeneity, i.e. wealth does not have to be the consequence of individual effort. Once you allow for that, the optimal solution looks different.  
> **username_2**: Sure. As long as there are some economic rents you can tax them 100% without any loss of efficiency. Also definitely Saez research points to higher top marginal rates than people used to believe. My point is just that his results should be interpreted with little bit of caution.  
> **username_1**: Fair enough, feel free to edit my post.  

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