by Fabian Kinderman and Dick Krueger
Appeared originally at Voxeu.org.
Optimal tax rates for the rich are a perennial source of controversy. This column argues that high marginal tax rates on the top 1% of earners can make society as a whole better off. Not knowing whether they would ever make it into the top 1%, but understanding it is very unlikely, households especially at younger ages would happily accept a life that is somewhat better most of the time and significantly worse in the rare event they rise to the top 1%.
Recently, public and scientific attention has been drawn to the increasing share of labour earnings, income, and wealth accruing to the so-called ‘top 1%’. Robert B. Reich in his 2009 book Aftershock opines that: “Concentration of income and wealth at the top continues to be the crux of America’s economic predicament”. The book Capital in the Twenty-First Century by Thomas Piketty (2014) has renewed the scientific debate about the sources and consequences of the high and increasing concentration of wealth in the US and around the world.
But what is a proper public policy reaction to such a situation? Should the government address this inequality with its policy instruments at all, and if so, what are the consequences for the macroeconomy? The formidable literature on optimal taxation has provided important answers to the first question.1 Based on a static optimal tax analysis of labour income, Peter Diamond and Emmanuel Saez (2011) argue in favour of high marginal tax rates on the top 1% earners, aimed at maximising tax revenue from this group. Piketty (2014) advocates a wealth tax to reduce economy-wide wealth inequality.
Motivated by their analyses and recommendations, in our own research on optimal taxation at the top of the earnings distribution (Kindermann and Krueger 2014) we address the following substantial questions:
- What are the consequences of high marginal tax rates on the top 1% for macroeconomic performance?
- Is squeezing the maximum tax revenue out of the top 1% earners actually beneficial for society as a whole and if so, how large would the welfare gains be?
- Would a higher marginal tax rate on top earners only reduce earnings inequality, or would it also have a significant impact on the distribution of wealth, rendering a wealth tax obsolete or at least less pressing?
Modelling high labour earnings: A combination of luck and effort
Any analysis that wants to use models to reliably quantify the consequences of changing income taxes at the top 1%, and tax progressivity more generally, requires a quantitative theory that leads to earnings and wealth concentration in the economy consistent with the data. In our work we borrow the modelling strategy from Castaneda et al. (2003), who attribute large earnings realisations to a combination of luck and effort. Luck refers to an innate talent, a brilliant idea, amazing sports or entertainment skills or the like that carries the potential to generate a high income (economists call this ‘individual labour productivity’).2 Labour effort is needed since one still has to work hard in order for this potential income to materialise.
Attributing differences in labour earnings to differences in individual productivity is by no means novel to the work of Castaneda et al. (2003). What does make their work rather unique and very useful for our purposes is the way the structure of individual productivity over the life cycle is parameterised. This structure can be roughly summarised by two key elements:
- When starting working life at young ages, each individual rationally expects it to be possible, but not very likely, that she would end up as a top earner with very high individual productivity sometime during her working life.
- Having high individual productivity is a persistent but not a permanent state. While one might generate very high earnings for several years, there is a substantial risk of reverting to lower ‘normal’ individual productivity. Fully aware of this risk, individuals with high productivity understand that now is their time to generate most of their lifetime income, and choose their labour supply and savings accordingly.
We incorporate this structure of individual labour productivity into a life cycle model and compute the welfare-maximising marginal tax rate on the top 1% earners. We find that it is very high – on the order of 90%. We now explain why this is so, in two steps. We first argue that these high marginal rates are useful for generating substantial tax revenue. We then discuss why the welfare-maximising rate is lower, but not all that much lower.
High marginal tax rates can boost tax revenues from top earners
When we search for the marginal tax rate on the top 1% earners that maximises tax revenue from this group, we find it to be very substantial.3 In fact, tax rates between 80% and 95% will do the job. The main reason for this is that earners in the top 1% income bracket react with only moderate changes in effort to changes in marginal tax rates. When one thinks about the structure of individual productivity over the life cycle outlined above, it is clear why this is the case. Even with high marginal tax rates, individuals at the very top of the labour productivity distribution can still generate a substantial amount of after-tax income, and they will do so to save and thereby insure against their uncertain and, in expectation, much lower future labour income.
Very high marginal tax rates don’t necessarily mean very high average tax rates
But what do high marginal tax rates on top earners mean from a practical perspective? Let’s take the example of a tax reform with a new marginal rate of 90% on the top earners. This certainly does not imply that a person earning $500,000 has to pay $450,000 in taxes. The highest marginal tax rates only apply to income above a certain threshold, in our 90% example (and in the context of our model) to any dollar earned above $300,000. For any income below this threshold, lower marginal tax rates apply.
In addition, increasing marginal tax rates for top earners boosts tax revenue from labour income quite substantially. This additional revenue can then be used to reduce marginal tax rates at the lower range of the income distribution. Consequently, in the tax system with high marginal tax rates on the top 1% earners, everyone whose income is below $200,000 a year would actually pay lower taxes than in the status quo tax system. And someone who makes half a million would still carry home more than $220,000, although admittedly her take-home pay is significantly less than under the status quo.
Consequences of the tax reform for the macroeconomy
Raising taxes on top income earners not only hurts the income of these people, but the macroeconomy as well. Reducing the incentives for the most productive people in society to put effort into generating income leads to a reduction in labour hours provided by the top 1% earners on the order of about 30%. This causes aggregate labour input and total wealth to contract by 4% and 14%, respectively, over the next three decades. The consequences for aggregate resources available for consumption are equally dire, and decline by 7%.
A proper criterion of optimality
Does this contraction of aggregate activity mean that increasing marginal tax rates at the top is a bad thing? Like most economists, we would argue that basing such a judgment on the macroeconomic consequences of the tax reform alone is misguided.4 In fact, just like reducing inequality or maximising tax revenue, boosting macroeconomic performance should not be considered a goal in and of itself. Consider a very simple example: The government could certainly reduce inequality in the economy to zero by confiscating all income and wealth and redistributing it equally among all households. In such a situation, people would likely stop working and saving as there are no individual incentives for doing so. The outcome would be a disastrous collapse of consumption for everyone. Few people would argue that such a situation is socially desirable, despite perfect equality.
In economics, life satisfaction is commonly measured as the flow of happiness generated by one’s own consumption and own leisure, often also termed ‘individual welfare’. This is fairly uncontroversial, at least among economists. What is controversial are the weights the government should give to the welfare of different individuals when it decides on optimal policy. There are young and old people, people alive in the future, poor people, and rich people. All these groups are differentially affected by a change in policy. But how should the differential effects on all these individuals be summarised in one measure of aggregate or social welfare? Our choice is to consider a government that compensates all people for a change in tax policy by giving them additional wealth (or confiscating wealth) to make each household as well off under the new tax system with high top marginal tax rates as they were in the status quo US tax system. After carrying out all these wealth compensations, would the government still have a surplus left over? And if so, how large is it? To maximise this surplus is the ultimate goal our benevolent government pursues.5
The value of social insurance
When applying the above notion of social welfare we find, not surprisingly, that the welfare-optimal top marginal tax rate is lower than the revenue-maximising (from the top 1%) tax rate. Interestingly, it is not that much lower.
Why is it lower? Because the top 1% count in the social welfare function, and households currently not in the top 1% might actually get there in the future. Plus, future generations have a chance of getting there, too, and factor this in when calculating individual welfare.
Why is it not that much lower? Because the bottom 99% of the population gain along two dimensions:
- On average, due to the tax reform they face lower average tax rates and their consumption increases over their entire life cycle.
- Consumption inequality (measured as the variance of individual consumption across households) substantially declines as well, at least eventually.
Figure 1 displays average consumption and the variance of consumption for the bottom 99% of the population over their life cycle, in deviations from their initial status quo values. It shows the benefits for this group from increasing marginal tax rates on the top 1%. While average consumption increases unanimously over the life cycle, inequality increases initially but then rapidly declines at older ages. Not knowing whether one would ever make it into the top 1% (not impossible, but very unlikely), households especially at younger ages would be eager to accept a life that is somewhat better most of the time and significantly worse in the rare case they climb to the top 1%. This type of social insurance via the tax system drives our optimality result.
Figure 1. Changes in average consumption and consumption inequality of the bottom 99% of the population from status quo US tax system to a system with high marginal tax rates on top 1% earners
Killing two birds with one stone
We have seen that high marginal tax rates on top earners can increase both average consumption as well as reduce inequality for a large part of the population (the bottom 99%) despite the fact that it might lead to a macroeconomic downturn. But what will happen to the wealth distribution after such a tax reform? Will it still be so unequal that we might want to implement an additional wealth tax, as for example advocated by Piketty (2014)? Our results reveal that this is not the case. By taxing the source of high wealth concentration, namely extraordinarily high incomes, at a high rate, wealth inequality will significantly decline over time. Three decades after the reform has been implemented, the share of wealth accruing to the fifth quintile of the population (i.e. the wealthiest 20%) will have shrunken from currently about 84% to 67%. The Gini index (measuring overall inequality in wealth holdings) declines by a remarkable 15 points. Consequently, an additional wealth tax that aims at reducing additional wealth inequality might seem superfluous.6 Furthermore, relative to a wealth tax, a high marginal tax rate on top labour earnings has the advantage that labour (even at the top of the income distribution) tends to be much less internationally mobile than is wealth, thus leading to a lower extent of tax avoidance.
Conclusions and limitations
Overall we find that increasing tax rates at the very top of the income distribution and thereby reducing tax burdens for the rest of the population is a suitable measure to increase social welfare. As a side effect, it reduces both income and wealth inequality within the US population.
Admittedly, our results apply with certain qualifications. First, taxing the top 1% more heavily will most certainly not work if these people can engage in heavy tax avoidance, make use of extensive tax loopholes, or just leave the country in response to a tax increase at the top. Second, and probably as importantly, our results rely on a certain notion of how the top 1% became such high earners. In our model, earnings ‘superstars’ are made from luck coupled with labour effort. However, if high income tax rates at the top would lead individuals not to pursue high-earning careers at all, then our results might change.7 Last but not least, our analysis focuses solely on the taxation of large labour earnings rather than capital income at the top 1%.
Despite these limitations, which might affect the exact number for the optimal marginal tax rate on the top 1%, many sensitivity analyses in our research suggest one very robust result – current top marginal tax rates in the US are lower than would be optimal, and pursuing a policy aimed at increasing them is likely to be beneficial for society as a whole.
Badel, A and M Huggett (2014), “Taxing Top Earners: A Human Capital Perspective”, Federal Reserve Bank of St Louis Working Paper 2014-017A.
Castaneda, A, J Diaz-Gimenez, and J-V Rios-Rull (2003), “Accounting for the U.S. Earnings and Wealth Inequality”, Journal of Political Economy 111(4): 818–857.
Diamond, P (1998), “Optimal Income Taxation: An Example with a U-Shaped Pattern of Optimal Marginal Tax Rates”, American Economic Review 88(1): 83–95.
Diamond, P and E Saez (2011), “The Case for a Progressive Tax: From Basic Research to Policy Recommendations”, Journal of Economic Perspectives 25(4): 165–190.
Fehr, H and F Kindermann (2014), “Taxing capital along the transition – Not a bad idea after all?”, Journal of Economic Dynamics and Control, forthcoming.
Kindermann, F and D Krueger (2014), “High Marginal Tax Rates on the Top 1%? Lessons from a Life Cycle Model with Idiosyncratic Income Risk”, NBER Working Paper 20601.
Mirrlees, J (1971), “An Exploration in the Theory of Optimal Taxation”, Review of Economic Studies 38(2): 175–208.
Piketty, T (2014), Capital in the Twenty-First Century, Cambridge, MA: Harvard University Press.
Piketty, T, E Saez, and S Stantcheva (2014), “Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities”, American Economic Journal: Economic Policy 6(1): 230–271.
Reich, R B (2011), Aftershock, New York: Random House.
Saez, E (2001), “Using Elasticities to Derive Optimal Income Tax Rates”, Review of Economic Studies 68(1): 205–229.
- Mirrlees (1971), Diamond (1998), and Saez (2001) are fundamental contributions to this literature.
- The words income and earnings are used synonymously here and both refer to income generated from labour (including bonuses, stock options, etc.).
- This is in line with related research on this topic (see e.g. Diamond and Saez 2011 or Piketty et al. 2014).
- In models without household heterogeneity and thus representative agents populating the economy, the connection between aggregate consumption and social welfare is of course much tighter than in models with substantial household heterogeneity like the one we employ.
- This measure of social welfare turns out to be equivalent to maximising a weighted sum of individual lifetime welfares. Fehr and Kindermann (2014) show how different wealth transfer schemes translate into different weights in the aggregate social welfare function.
- Admittedly wealth inequality is still substantial after the proposed reform.
- Badel and Huggett (2014) offer some insight into how revenue-maximising top tax rates change when high productivity is mainly attained by human capital investment.
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