NBER WORKING PAPER SERIES A SIMPLER THEORY OF OPTIMAL CAPITAL TAXATION Emmanuel Saez Stefanie Stantcheva Working Paper 22664 http://www.org/papers/w22664 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 September 2016, Revised October 2017 We thank Alan Auerbach, Stephen Coate, Emmanuel Farhi, Mike Golosov, Henrik Kleven, Thomas Piketty, Joel Slemrod, Matthew Weinzierl, Nicolas Werquin, Daniel Waldenström, and numerous seminar and conference participants for useful discussions and comments. We acknowledge financial support from the MacArthur Foundation, and the Center for Equitable Growth at UC Berkeley. We thank Nina Roussille for excellent research assistance. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2016 by Emmanuel Saez and Stefanie Stantcheva. All rights reserved.
Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. A Simpler Theory of Optimal Capital Taxation Emmanuel Saez and Stefanie Stantcheva NBER Working Paper No. 22664 September 2016, Revised October 2017 JEL No. H20,H21 ABSTRACT This paper develops a theory of optimal capital taxation that expresses optimal tax formulas in sufficient statistics.
We first consider a simple model with utility functions linear in consumption and featuring heterogeneous utility for wealth. In this case, there are no transitional dynamics, the steady-state is reached immediately and has finite elasticities of capital with respect to the net-of- tax rate. This allows for a tractable optimal tax analysis with formulas expressed in terms of empirical elasticities and social preferences that can address many important policy questions. These formulas can easily be taken to the data to simulate optimal taxes, which we do using U.
tax return data on labor and capital incomes. Second, we show how these results can be extended to the case with concave utility for consumption. The same types of formulas carry over by appropriately defining elasticities. We show that one can recover all the results from the simpler model using a new and non standard steady state approach that respects individual preferences even with a fully general utility function.
Emmanuel Saez Department of Economics University of California, Berkeley 530 Evans Hall #3880 Berkeley, CA 94720 and NBER saez@econ.edu Stefanie Stantcheva Department of Economics Littauer Center 232 Harvard University Cambridge, MA 02138 and NBER sstantcheva@fas.edu 1 Introduction The public debate has long featured an important controversy about the proper design of capital taxation. Arguments typically center around an equity-efficiency trade-off: who owns the capital and how strongly would capital react to higher taxes? The economics literature has developed dynamic, complex models, which have emphasized different results depending on the structure of individual preferences and shocks, the government’s objective, and the policy tools available. Many of the highly salient questions in the policy debate on capital taxation have been very difficult to address in these complex models. A few examples are how to take into account income shifting between the capital and labor income bases, different types of capital assets, heterogeneity in individuals’ preferences or returns to capital, nonlinear taxation, and broader social fairness and equity considerations.
Bridging the gap between economic theory and the policy debate seems especially important in the current context with growing income and wealth inequality, and where a large fraction of top incomes comes from capital income (Saez and Zucman, 2016; Piketty et al. The goal of this paper is to connect the theory of optimal capital taxation to the public debate by providing a framework in which many policy questions related to capital taxation can be addressed. This framework permits the derivation of robust optimal capital tax formulas expressed in terms of elasticities of capital supply with respect to the net-of-tax rate of return that can be estimated in the data, and distributional considerations which society may have. The aim is to build a model which generates an empirically realistic response of capital to taxes,1 is sufficiently tractable to yield results for a variety of policy topics related to capital taxation, but general enough for these results to be robust to a broader set of models.
We start in Section 2 with a simple model in continuous time with the following two in- gredients. First, individuals derive utility from wealth. We provide several microfoundations for this wealth in the utility specification: bequest motives, entrepreneurship, or services from wealth. It implies that the steady-state features finite supply elasticities of capital with respect to tax rates.2 It also implies that there is bi-dimensional heterogeneity in capital and labor 1 Our model generates finite elasticities of capital responses to capital taxes.
In contrast, the famous result of Chamley (1986) and Judd (1985) that in the long-run the optimal capital tax should be zero–arises because the elasticity to a long-run tax increase is infinite due to anticipation effects (see Piketty and Saez (2013b)). 2 The magnitude of capital income elasticities is an empirical question. Our model nests the case of infinite steady state elasticities from the standard Chamley-Judd model as a special case. Other possible modeling devices to obtain finite elasticities would be introducing uncertainty as in the Aiyagari (1995) model as shown 1 incomes across individuals.
As a result, the famous zero capital tax result of Atkinson and Stiglitz (1976) does not apply. Second, utility of consumption is linear so that there are no consumption smoothing issues and individual responses to tax changes are immediate.3 While necessary to analyze insurance issues as in the New Dynamic Public Finance literature,4 con- sumption smoothing due to concave utility seems, at a first pass, less important for thinking about taxation of top incomes, where most of the capital is ultimately concentrated, and long- run taxation.5 While we generalize this model later on to allow for concave utilities (and the anticipatory and sluggish responses of capital to taxation they generate), the simpler version with linear consumption is extremely tractable and amenable to studying a wide range of issues about optimal capital taxation, such as nonlinear capital taxation, income shifting, cross-elasticities between capital and labor income, consumption taxation and others in Section 3. It highlights the main forces shaping capital taxation which are obscured in more complex models. Another key (and perhaps the main) advantage is that it resolves the highly thorny issue of how to tax the existing capital stock and does not require making a judgment about what type of reform to consider (e.: anticipated, unanticipated, steady state focused).
Confronting these dilemmas in earlier papers required making normative judgments on the social welfare objective, none of which are entirely satisfactory (see Section 5). We can describe four sets of findings that we obtain by putting this newly gained simplicity to use. First, we derive formulas for optimal linear and nonlinear capital income taxation that can be expressed in terms of the elasticity of the supply of capital income with respect to the by Piketty and Saez (2013b) or discount rates that depend on consumption (as in Judd (1985)). We argue that utility of wealth is much simpler and fits the data better in Section 2.3, but do relate our results to these alternative models in Section 5.
3 Anticipated tax reforms do not create any effect until they actually take place, which greatly simplifies the analysis by eliminating the need to model anticipation effects and expectations about policy. This is unlike in the Chamley (1986) and Judd (1985) theory where unanticipated capital taxes are desirable while anticipated long-distance capital taxes are not. 4 Golosov et al. (2003) founded this literature.
Golosov et al. (2006) provide a comprehensive overview. 5 To draw the analogy to the labor income tax literature, responses of labor to taxes are also part of a dynamic decision process if we acknowledge longer-term and slowly adjusting margins such as occupational choice and human capital acquisition. Two strands of the literature have thought of labor taxation in a dynamic way: the heterogeneous agents macro literature as in Jones et al.
(1993) and the modern New Dynamic Public Finance literature. While providing useful insights, this literature has not been central in the public policy debate on taxation. The missing piece in optimal capital tax theory that we propose here is an approach that can yield a static-equivalent model, which abstracts from transitional dynamics, and as was adopted for labor income following the seminal contribution of Mirrlees (1971). 2 net-of-tax rate of return, the shape of the capital income distribution, and the social welfare weights at each capital income level.
We also derive formulas which take into account policy issues that have traditionally been hard to deal with in dynamic optimal capital tax models. These include, among others, income shifting between capital and labor, economic growth, heterogeneous returns to capital across individuals, and different types of capital assets and heterogeneous tastes for each of them. Second, we derive a formula for the optimal tax on comprehensive income (labor plus capital income) that takes exactly the same form as the traditional optimal labor income formula. This formally justifies the use of the optimal labor income formulas to discuss optimal income taxation as has been done without rigorous justification in a number of studies (e., Diamond and Saez (2011)).
The comprehensive income tax is the fully optimal tax if there is perfectly elastic income shifting between the labor and capital income bases when labor and capital are taxed differentially. Third, we can analyze consumption taxation in this model as well by making the assumption that real wealth (i., the purchasing power of wealth) enters individual utilities. In this case, a consumption tax makes people accumulate more nominal wealth so that their steady-state real wealth is unchanged. Hence, consumption taxation ends up being equivalent to labor taxation plus an initial wealth levy.6 It is thus not a sufficient tool to address capital inequality when capital inequality re-emerges even after an initial wealth equalization as in our model and as seems to be the case from empirical experiences (e., Eastern Europe’s transition to a market economy and in particular Russia as recently analyzed in Novokmet et al.
Fourth, our approach is very amenable to considering a broader range of justice and fairness principles related to capital taxation, through the use of generalized social welfare weights as in Saez and Stantcheva (2016). Given the prevalence of discussions about fairness and equity with regard to capital taxation, having a tractable way to incorporate broader and more diverse equity considerations is key.7 We consider several salient ethical standpoints from the policy debate. To give just one example, if wealth inequality is considered fully fair (i., the generalized social welfare weights are uncorrelated with capital and capital income is not a tag) the optimal 6 The same equivalence holds in standard OLG models traditionally used to discuss transitions from income to consumption taxation (Auerbach and Kotlikoff, 1987). 7 Put simply, to obtain the optimal tax for different justice and fairness principles, the reader can use all the formulas derived and “plug in” the corresponding generalized social welfare weights.
3 capital tax is zero. In Section 4, we put our formula in sufficient statistics to use by calibrating optimal taxes based on U. tax data on labor and capital income. 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.
The model highlights which elasticities should fruitfully be estimated in the data, including the cross-elasticities between capital and labor (Section 3.2) and the elasticities and cross-elasticities for different types of capital assets (Section 3.
