Optimal capital tax

Personal literature review.

Literature on optimal capital taxation

Optimal taxation would involve individualized lump-sum taxes based on individuals’ earning ability (Kaplow 2006).  However, differences in earning ability are unobservable, so income is used as a signal of underlying ability – the problem is that taxing income will change people’s choices and so is distortionary.

Optimal labour income taxes were discussed by (Mirrlees, 1971) – with a surprising amount of foresight regarding the types of extensions that have come out of the literature over the last 50 years.  The rejection of distortions to productive efficiency, and thereby not taxing intermediate goods, was then argued in Diamond-Mirrlees ( (Diamond & Mirrlees, 1971)a and (Diamond & Mirrlees, 1971)b).

Justification for a tax rate of zero on capital income comes from linking the two in (Atkinson & Stiglitz, 1976) *.  Given this is a comparative-static GE result, a seemingly separate dynamic result from Chamley-Judd ( (Chamley, 1986) * and (Judd, 1985) *) also reinforced the conclusion.  The two broad arguments for a zero rate of tax on capital income are:

  1. Atkinson-Stiglitz:  Any type of tax on capital income is a differential tax on commodities (through time) which leads to a misallocation not just due to this acting as a tax on labour, but also an intertemporal misallocation – so assuming that labour and consumption are separable in utility (such that consumption doesn’t tell us anything about an individuals ability) it is most efficient to simply tax labour to raise revenue.
  • Chamley-Judd results:  This result has been discussed in two ways – however only the first way is consistent (Jacobs & Rusu, 2018). 
  • A tax on capital is an increasing tax on consumption through time (Judd, 1999) * – making this consistent with the (Atkinson & Stiglitz, 1976) result.  This is also stated in terms of the taxation of capital (including human capital) as being taxation of an intermediate good – however (Diamond & Saez, 2011) * disagree with this interpretation.
  • The supply of capital becomes infinitely elastic in the long run, so the entire burden of a tax on capital income is borne on labour.  However, this is generally not accepted – the issue here is that the result still holds for a small open economy where the gross interest rate does not change (Jacobs & Rusu, 2018).

Put this way both view boil down to the same key distortion associated with capital income taxation, which we wish to avoid, is that it involves taxing consumption at different periods of time differently.

So to justify a tax on capital income we need to justify why we would want to tax consumption at different periods of time differently – is there a second best argument, a distinction between consumption at points in time, another intertemporal allocation issue, or a corresponding market failure?

This logic suggests a number of channels that could justify why the optimal tax rate on capital income may be different from zero (note that this is probably not exhaustive, and there may be repetition in cases where I accidentally interpreted the same argument in different terms eg some of the following examples are just cases of “non-separable utility”.).

Although all these issues are mentioned by a number of papers, the key assumptions used to practically estimate higher capital taxes are highlighted in red.


  • Non-separable utility: If labour/leisure and consumption are not separable in utility then it provides information about ability which allows for a tax/subsidy.
  • Capital income as varyingly complementary to leisure over time: (Kaplow, 2008) * points out that, with the taxation of labour income causing one distortion it is optimal (in a second best sense) to tax complements to leisure.  (Jacobs & Rusu, 2018) points out that the Chamley-Judd result can be recovered as long as preferences are separable between consumption and leisure through time.  If these preferences differ over time (eg where you would have a form of age-based taxation that is higher when capital income tends to be higher in a lifecycle) you can justify a positive capital tax in the absence of other information (eg using an age based tax).
  • Heterogenous saving/consumption tastes by ability:  (Saez, 2002)a * argues a similar point to the one above but instead focused on subgroups – focusing on the idea that those with high ability have a higher taste for savings (eg if high income people were forced to work less to have the same income as lower income individuals, their savings rates would still be higher).  This is further explained in (Golosov, Troshkin, Tsyvinski, & Weinzierl, 2011) *.
    • Sidenote 2: It is key to remember that heterogenous preference for leisure complicates a number of results – although this is more about the structure of tax schedules.  However, I raise it as once we start allowing for heterogeneity to drive “unequal treatment” in taxation we have to be consistent! http://qed.econ.queensu.ca/pub/faculty/boadway/Difpref190700.pdf



  • Complementarity between capital income and work incentives:  If having capital decreases the cost of work, this would lower the optimal capital tax rate (Saez & Stantcheva, 2018) *
  • Heterogeneous tastes, or a pecuniary taste, for different assets:  If individuals have pecuniary reasons for holding a given asset, then there is a motivation for taxing that asset.  If there are pecuniary reasons for holding assets/wealth in general that can motivate a capital tax.
  • Myopia and short-planning horizons
  • Self-insurance (precautionary motive) and bequest motives for capital accumulation: Other motives for saving or investing (eg precautionary motives given expectations of a borrowing constraint, a preference to build up a bequest).

Abilities and endowments

  • Different endowments: Inheritance of human and financial capital (related to bequest motives) and differences in initial wealth give a role for redistribution (Saez, 2002)b *
  • Differing abilities to obtain returns out of financial assets:  If heterogenous returns on investment income is a signal of underlying skill level, the return to capital should be taxed. (Kristjansson, 2016) *
  • Unanticipated change in individuals skills over time (New Dynamic Public Finance):  Justifies a regressive (in income) wealth tax to increase work effort (Kocherlakota, 2005) * (Golosov, Kocherlakota, & Tsyvinski, 2003) *.

Imperfect markets/income identification

  • Undiversifiable risk in capital incomes: Capital income tax can work as a form of insurance – implying that the optimal capital tax rises with income risk (Krueger & Ludwig, 2018) *
  • Borrowing constraints: With borrowing constraints there are individuals who want to borrow but can’t.  Taxing labour instead of capital worsens this constraint, with a corresponding efficiency cost.  (Hubbard, Judd, & Hall, 1986) *.
  • Uninsurable risk in labour income: Uninsurable shocks to labour productivity with borrowing constraints offer a justification for capital taxation (Conesa, Kitao, & Krueger, 2009) *
  • Tax avoidance/income shifting/distinguishing entrepreneurial compensation vs the return to capital: (https://ideas.repec.org/a/cup/macdyn/v15y2011i03p326-335_00.html) – can’t find a pdf version.

Other model based complications

  • Dynamic inefficiency in OLG models without age dependent taxes: The economy doesn’t reach its full productive capacity as current generations do not take into account the effect of their savings on future generations. (Atkinson & Sandmo, 1980) * (Garriga, 2017) * 
  • The response of wage distributions to the capital stock – and thereby distribution of pre-tax income Stiglitz 1985 mentioned in (Piketty & Saez, 2012).
  • Capital-skill complementarityhttp://home.cerge-ei.cz/slavik/paper/slidesKSY.pdf – if capital and skills/ability are complementary then this justifies a larger tax on capital.
  • According to (Straub & Werning, 2014) * the Chamley-Judd result is also dependent on the elasticity of intertemporal substitution (1/sigma).  Here this elasticity needs to be greater than 1, such that consumption falls as the future real interest rate rises.  Without this then there is a justification for a positive capital tax.  The strength of this critique is questioned in (Chari, Nicolini, & Teles, 2016) *.
  • Substitutability of research spending and new capital constructionhttps://ideas.repec.org/a/red/issued/05-30.html
  • Taxation of “excess return”:  The argument here appears to be that, by taxing excess return, you do not distort behaviour while raising revenue (Bastani & Waldenstrom, 2018).
  • Optimal human capital accumulation:  With labour taxes reducing human capital accumulation, a tax on capital to reduce this intertemporal wedge can be efficient (Jacobs & Bovenberg, 2009) *.

Additional normative dimensions

  • Taxing wealth or the RFRR in order to incentivise efficient use of assets (Guvenen, Kambourov, Kuruscu, Ocampo-Diaz, & Chen, 2018) *.
  • Social welfare weights may be explicitly correlated with capital, where only consumption taxes only act as a levy on wealth rather than reducing wealth inequality (Saez & Stantcheva, 2018) *.

What should the top capital rate be?

Most literature suggests that capital income should be taxed – but that it should generally be at a lower rate than labour. (Banks & Diamond, 2008) * describes it well.

The conclusion that capital income should be taxed does not however lead to the conclusion that the tax base should simply be total income, i.e. the sum of labour income and capital income.  This chapter leans towards relating marginal tax rates on capital and labour incomes to each other in some way (as in the US), as opposed to the Nordic dual tax where there is a universal flat rate of tax on capital income.

However both (Saez & Stantcheva, 2018) * (including (Piketty & Saez, 2012) *) and (Conesa, Kitao, & Krueger, 2009) * suggest that it may be optimal to tax capital more highly than labour – both focused on redistributive grounds.  As a result, it is important to understand where their results come from.  Below we will focus on optimal linear capital taxes, rather than the non-linear results, for practical purposes.

(Piketty & Saez, 2012) * aims to tie together a lot of these threads in order to provide a general model of the optimal capital tax rate.  This should be seen alongside the top marginal labour tax rate paper (Piketty, Saez, & Stantcheva, 2013) * and the (Saez & Stantcheva, 2018) * paper that attempted more tractable optimal capital tax model.

The paper works through two directions.

Firstly, with perfect capital markets they give a case for inheritance tax (of 50-60%) in the following way:

The key feature of our model is that inequality permanently arises from two dimensions: differences in labor income due to differences in ability, and differences in inheritances due to differences in parental tastes for bequests and parental resources. Importantly, top labor earners and top successors are never exactly the same people, implying a non-degenerate trade-off between the taxation of labor income and the taxation of capitalized inheritance. In that context, in contrast to the famous Atkinson-Stiglitz result, the tax system that maximizes social welfare includes positive taxes on bequests even with optimal labor taxation because, with inheritances, labor income is no longer the unique determinant of life-time resources.

Secondly, with capital market and uninsurable shocks they look at the optimal mix between a one-off inheritance tax and lifetime capital taxation (this is section 5).  However, they don’t really seem to go into detail here – just pointing out that a “fuzzy boundary” for labour and capital income, and uninsurable risks, are reasons why we might tax capital income instead of just bequests.

As a result, it is the initial bequest result that drives their recommendation of relatively high rates of capital taxation.  This involves assumptions of differential tastes for wealth and bequests (page 11) and stochastic shocks in earnings ability across generations defined with a real rate of return higher than economic growth (making bequests accumulate across generations).  This framework will tend to push for the taxation of capital.

(Saez & Stantcheva, 2018) * aims to provide a clearer model that highlights the efficiency-equity trade-off that cuts to the core assumptions that give taxation of capital income.

They then point out that two different assumptions could lead to the result of zero capital taxation – no value placed in the welfare function on the distribution of capital income, and infinite (long run) elasticity of capital.

In order to prevent this infinite elasticity wealth needs to be in the utility function (Note: uncertainty about future earnings achieves the same thing).  To get a distribution of wealth outcomes, heterogenous wealth preferences are required.  These two assumptions are key to the idea of an optimal capital tax.  For the level of the tax they state:

Because capital income is much more concentrated than labor income, we find that, if the supply elasticities of labor and capital with respect to tax rates were the same, the top tax rate on capital income would be higher than the top tax rate on labor income

As a result, a higher LR supply elasticity for capital gives a lower optimal rate.  The importance of the bequest motive is then key for determining the optimal capital tax rate.

There is no “benchmark” for comparison.  So although the tax rate gives maximum welfare the aggregate trade-offs involved are unclear.  Pg 136 offers a table that summarises the assumptions changing the optimal capital tax rate.

The (Conesa, Kitao, & Krueger, 2009) * result does not rely on wealth in utility or bequest motives.  Instead they rely on a lifecycle model with borrowing constraints for households, ex-ante heterogeneity in labour productivity (across cohorts), endogenous labour supply, and idiosyncratic income risk through shocks to labour productivity.  As long as these factors all hold, and age-based taxation is not available, capital taxation can fill a similar redistributive role.

The high capital income tax result of this paper is generated by the fact that it is an indirect age-based tax, that helps to redistribute for realised productivity outcomes that were not expected ex-ante – use of a progressive labour tax would reduce labour supply in this case, which is a distortion that can be reduced with the capital tax.

Simulations in this paper show that this is a welfare maximising choice – but it does come with lower GDP, labour supply, capital, and consumption than the benchmark.  This implies to me that the benchmark comparison (which isn’t clearly outlined in the paper, other than a suggestion that it matched stylized facts about the US) must involve significantly less redistribution.

As a result, if current taxation is the result of lower preferences for redistribution than that implied by this model, the level of capital taxation (which is based on such redistribution) would be significantly lower.

Tax equality

The one thing the literature seems to agree on is that the tax rate on labour and capital should not be the same.  However, as has been emailed the “fuzzy boundary” between labour and capital income is being stated as a reason why they should be the same.

This was a good article with respect to Phil’s point that lower taxation of capital income encourages identifying labour income as capital income – and that this is a big part tax avoidance towards the top of the income distribution in the US.


The income data they are talking about for this is here:


One point that is missing from the article is that, if lower taxation of capital income is justified on the basis of capital being more response to taxation then we if this “labour income” is also more responsive than other types of labour income the same argument would hold.  Given that a lot of it involves returns to innovation this could potentially dovetail into the literature on top tax rates and innovation (https://www.nber.org/reporter/2018number3/stantcheva.html) – which in turn could justify this unequal treatment in a way the article doesn’t note as a possibility.  


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