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American Economic Review: Papers & Proceedings 2015, 105(5): 43–47 http://dx.doi.org/10.1257/aer.p20151059

Yes, r . So What?† > By . Gregory Mankiw*

Thomas Piketty’ book Capital in the the great achievements of human history and Twenty-First Century captured the public’s the best way to organize a society, as I do, these attention in a way that few books by econo- conclusions present a significant challenge. mists have. Though its best-seller status was a The first thing to say about Piketty’s logic surprise, probably even to its author, it has the is that it will seem strange to any economist ingredients that foster wide appeal. The book trained in the neoclassical theory of economic addresses a pressing issue of the day in a man- growth. The condition r g should be familiar. ner that is learned, literary, speculative, provoc- In the textbook Solow growth> model, it arrives ative, and fascinating from beginning to end. naturally as a steady-state condition as long While largely a work of economic history, it as the economy does not save so much as to does not stop there. Piketty ultimately leads the push the capital stock beyond the Golden Rule reader to a vision of what the future may hold level Phelps 1961 In this model, r g is not and advice about what policymakers should do a problem,( but r ). g could be. If the> rate of about it. That vision is a dystopia of continu- return is less than Pareto improvements links in Piketty’s chain of argument are espe- unexploited. cially fragile. Other aspects of Piketty’s book There is, moreover, good reason to doubt that may well pass the test of time, but the bottom r g leads to the “endless inegalitarian spiral” line—his vision of the future and the consequent that> Piketty describes. Imagine a wealthy person policy advice—most likely will not. living in an r g economy who wants to ensure The book documents that the rate of return on that he has an> endless stream of wealthy descen- private capital r exceeds the economy’s growth dants. He can pass his wealth on to his chil- rate g, and it argues that this will likely con- dren, but to ensure that his descendants remain tinue to be the case, perhaps by a larger amount wealthy, he faces three obstacles. in the future. Piketty 2014, p. 571 boldly First, his heirs will consume some of the calls this fact “the central( contradiction) of cap- wealth they inherit. For this purpose, the rele- italism.” He reasons that if r g, the wealth vant measure of consumption includes not only of the capitalist class will grow> faster than the food, shelter, and riotous living but also political incomes of workers, leading to an “endless and philanthropic contributions, which can be inegalitarian spiral” p. 572 To someone who sizable for wealthy families. A plausible esti- views relatively unfettered( capitalism). as one of mate of the marginal propensity to consume out of wealth, based on both theory and empirical * Department of Economics, Harvard University, evidence, is about 3 percent. Thus, if wealth Cambridge, MA 02138 -mail: [email protected] . I earns a rate of return of r, wealth accumulates at am grateful to Laurence (Ball, Ben Friedman, David Laibson,) a rate of about r 3. Lisa Mogilanski, Lawrence Summers, Gabriel Unger, and Second, as wealth− is passed down from gen- Matthew Weinzierl for comments. † Go to http://dx.doi.org/10.1257/aer.p20151059 to visit eration to generation, it is divided among a growing number of descendants. This would the article page for additional materials and author disclo- ( sure statement. not be a problem for the wealthy patron if his 43 44 AEA PAPERS AND PROCEEDINGS MAY 2015 heirs’ mating­ were perfectly assortative—that horizons, it seems unlikely that, looking for- is, if they all married someone of equal wealth. ward, r will start exceeding g by more than 7 But matters of the heart are rarely so neat. To percentage points. If the real return remains sta- get a rough calibration of this effect, suppose) ble at 5 percentage points, the economy’s growth everyone has a typical family of two children, rate would need to become a negative 2 percent. so the number of descendants doubles every Secular stagnation would not be enough; we generation. Because generations are about 35 would need secular decline. Alternatively, if years apart, the number of descendants grows future growth is 2 percent per year, the real rate at a rate of 2 percent per year. Thus, if family of return to capital would need to rise from its wealth accumulates at a rate of r 3, wealth per historical 5 percent to more than 9 percent. That descendant grows at a rate of r − 5. figure is nowhere near the return that pension Third, many governments impose− taxes on and endowment managers are now projecting both bequests and capital income. In the United from a balanced portfolio of stocks and bonds. States today, the estate tax rate is 40 percent Hence, the forces of consumption, procre- above a threshold . In Massachusetts, where I ation, and taxation are, and will probably con- live,( the state imposes) an additional estate tax tinue to be, sufficient to dilute family wealth with a top rate of 16 percent. As a result, at the over time. As a result, I don’ see it as likely that margin, about half of a family’s wealth is taxed the future will be dominated by a few families away by the government once every generation. with large quantities of dynastic wealth, passed If we again assume a generation is 35 years, from generation to generation, forever enjoying then estate taxation reduces the accumulation the life of the rentier. of dynastic wealth by about 2 percent per year. But suppose I am wrong. Suppose the dynas- In addition, capital income taxation during a tic accumulation of capital describes the future, person’s life reduces capital accumulation even as Piketty suggests. I would nonetheless remain further. This effect is roughly an additional 1 skeptical of Piketty’s proposal to place an addi- percent per year, making the total drag of taxes tional tax on wealth. A simple, standard neoclas- about 3 percent per year. Let’s assume, however, sical growth model illustrates the problem with that our dynasty has especially good tax plan- this policy. ning and put the total tax effect at only 2 percent. Consider an economy composed of two kinds Thus, taking taxation into account, wealth per of people—workers and capitalists. Many work- descendant grows at a rate of about r 7. ers supply labor inelastically and immediately We can now recalibrate Piketty’s logic− taking consume their earnings. A few capitalists own these three effects into account. Piketty reasons the capital stock and, because they represent an that resources of the wealthy would grow rela- infinitely-living dynasty, set their consumption tive to the labor income if r g. We can now according to the standard model of an optimiz- see, however, that this condition> is not sufficient ing infinitely-lived consumer as in the Ramsey once consumption, procreation, and taxation are model . Workers and capitalists( come together accounted for. Instead, to obtain the worrisome to produce) output, using a production function “endless inegalitarian spiral,” we would need that experiences labor-augmenting technolog- the return on capital r to exceed the economy’s ical progress, and they earn the value of their growth g by at least 7 percentage points per year. marginal product. In addition, following the This scenario is far from what we have expe- advice of Piketty, the government imposes a rienced. Piketty estimates the real rate of return tax on capital equal to per period, the revenue to be about 4 or 5 percent, which seems plausi- from which is transferredτ to workers. ble for a typical balanced portfolio. Meanwhile, To oversimplify a bit, let’s just focus on this the average growth rate of the US economy has economy’s steady state. Using mostly conven- been about 3 percent. So Piketty is right that r tional notation, it is described by the following has exceeded g, but it has done so by only about equations: 2 percentage points, not the more than 7 percent- age points necessary for the creation of Piketty’s 1 ​cw​ ​ imagined dystopia. ( ) = + τ Moreover, while economists are notoriously 2 ​​​ r g nk bad at predicting the future, especially over long ( ) k = ( − τ − ) VOL. 105 NO. 5 YES, r g. SO WHAT? 45 > 3 r k 0. This result of zero capital taxation­ is ( ) = ′( ) familiarτ = from the optimal tax literature Chamley 4 w f k rk 1986; Judd 1985; and Atkeson, Chari,( and ( ) = ( ) − Kehoe 1999, recently reconsidered by Straub 5 g r , and Werning 2014 In this economy, because ( ) = σ( − τ − ρ) capital taxation reduces). capital accumulation, where ​cw​ ​ is consumption of each worker, ​c​k ​ labor productivity, and wages, it is not desirable is the consumption of each capitalist, w is the even from the standpoint of workers who hold wage, r is the before-tax rate of return on cap- no capital and who get the subsidies that capital ital, k is the capital( stock) per worker, n is the taxation would finance. number of workers per capitalist so nk is the By contrast, suppose the government in this capital stock per capitalist , f k is( the produc- economy were a plutocracy, concerned only tion function for output )net (of) depreciation , about the welfare of the capitalists. In this case, ( ) g is the rate of labor-augmenting technological it would choose to maximize ​ck​ ​subject to the change and thus the steady-state growth rate, above five equationsτ as constraints. The best plu- is the capitalists’ intertemporal elasticity of tocratic policy is a capital subsidy financed by substitution,σ and is the capitalists’ rate of taxes on workers. That is, plutocrats would make time preference. Equationρ 1 says that workers as negative as it can be. If there is some mini- consume their wages plus( what) is transferred mumτ subsistence level for workers, the labor tax by the government. Equation 2 says that cap- and capital subsidy would be driven so high as to italists consume the return on (their) capital after push workers’ consumption down to subsistence. paying taxes and saving enough to maintain the Now consider a government concerned about steady-state ratio of capital to effective work- inequality between workers and capitalists. In ers. Equation 3 says that capital earns its mar- particular, suppose that policymakers want to ( ) ginal product. Equation 4 says that workers increase the ratio ​cw​ ​ ck​ ​. In this case, a positive are paid what is left after( )capital is compen- value for the capital /tax​ is optimal. Indeed, if τ sated. Equation 5 is derived from the capital- maximizing ​cw​ ​ ck​ ​ is the only goal, then the cap- ists’ Euler equation;( ) it relates the growth rate of ital tax should /be​ as large as it can be. Taxing capitalist’s consumption which is g in steady capital and transferring the proceeds to workers state to the after-tax rate (of return. reduces the steady-state consumption of both Because) the steady-state return on capital in workers and capitalists, but it impoverishes the this economy is r g , the condition capitalists at a faster rate. For a standard produc- r g arises naturally.= /σ A + plausibleτ + ρ calibration tion function f 0 and f 0 , a higher capi- > ( ′ > ″ < ) might be g 2, 2, 1, and 1, which tal tax always raises ​c​w​ ck​ ​. leads to r = 5. τIn= this ρeconomy,= σeven= though Thus, in this simple/​ neoclassical growth r g, there= is no “endless inegalitarian spiral.” model, a positive tax on capital has little to Instead,> there is a steady-state level of inequality. recommend it if we care only about levels of Optimizing capitalists consume enough to pre- consumption, but it may look attractive if we vent( their wealth from growing faster than labor are concerned about disparities. To misquote income. If we assume the number of workers Winston Churchill: the inherent vice of the per capitalist) n is large, then capitalists will free-market equilibrium is the unequal sharing enjoy a higher standard of living. In this natural of blessings; the inherent virtue of capital taxa- case, ​cw​ ​ ck​ ​, the ratio of workers’ consumption to tion is the more equal sharing of miseries. capitalists’/​ consumption, can be used as a proxy So far, I have included only one policy instru- for inequality. A more egalitarian outcome is ment—the one recommended by Piketty—but then associated with a higher ratio ​cw​ ​ ck​ ​. we can consider others. A better way to pursue Now consider the policy question: /What​ level equality in this model economy, and I believe of capital taxation should the government set? the real economy as well, is a progressive tax Not surprisingly, τthe answer depends on the on consumption. Such a tax could equalize liv- objective function. ing standards between workers and capitalists If policymakers want to maximize the con- without distorting the intertemporal margin sumption of workers ​cw​ ​subject to equations 1 and thereby discouraging capital accumula- through 5 as constraints, they would choose( ) tion. Under a progressive consumption tax, the ( ) 46 AEA PAPERS AND PROCEEDINGS MAY 2015 capitalists would be just as wealthy as they are am less ­concerned. The wealthy includes sup- ­without it, but they would not fully enjoy the porters of both the right the Koch brothers, fruits of their wealth. Sheldon Adelson and the (left George Soros, With this model as background, let’s move to Tom Steyer , and )despite high levels( of inequal- the big question: Why should we be concerned ity, in 2008) and 2012 the United States man- about inequality in wealth? Why should anyone aged to elect a left-leaning president committed care if some families have accumulated capital to increasing taxes on the rich. The fathers of and enjoy the life of the rentier? Piketty writes American democracy, including George about such inequality as if we all innately Washington, Thomas Jefferson, John Adams, share his personal distaste for it. But before we and James Madison, were very rich men. With embark on policies aimed at reducing wealth estimated net worth in today’s dollars rang- inequality, such as a global tax on capital, it ing from $20 million to( $500 million, they) were would be useful to explore why this inequality likely all in the top 0.1 percent of the wealth matters. distribution, demonstrating that the accumu- One place to look for answers is Occupy Wall lation of capital is perfectly compatible with Street, the protest movement that drew atten- democratic values. Yet, to the extent that wealth tion to growing inequality. This movement was inequality undermines political ideals, reform of motivated, I believe, by the sense that the afflu- the electoral system is a better solution than a ence of the financial sector was a threat to other growth-depressing tax on capital. people’s living standards. In the aftermath of a My own view—and I recognize that this is financial crisis followed by a deep recession, a statement of personal political philosophy this sentiment was understandable. Yet the pro- more than economics—is that wealth inequal- testers seemed not to object to affluence itself. If ity is not a problem in itself. And I do not see they had, Occupy Wall Street would have been anything objectionable if the economically suc- accompanied by Occupy Silicon Valley, Occupy cessful use their good fortune to benefit their Hollywood, and Occupy Major League Baseball. children rather than spending it on themselves. From this perspective, the rentier lifestyle of As a society, we should help those at the bot- capitalists should not be a concern. As we have tom of the economic ladder through such pol- seen, in a standard neoclassical growth model, icies as a ­well-functioning educational system the owners of capital earn the value of their mar- and a robust social safety net funded with a ginal contribution to the production process, and progressive consumption tax . And( we should their accumulation of capital enhances the pro- help people overcome impediments) to saving, ductivity and incomes of workers. thereby allowing more workers to become cap- Another possibility is that we object to wealth italists. But if closing the gap between rich and inequality because it is not fair. Why should poor lowers everyone’s standard of living, as I someone be lucky enough to be born into a fam- believe Piketty’s global tax on capital would do, ily of capitalists whereas someone else is born I see little appeal to the proposal. into a family of workers? The disparity between workers and capitalists is inconsistent with the REFERENCES ideal of equal opportunity. Yet that ideal conflicts with another—the freedom of parents to use their Atkeson, Andrew, . V. Chari, and Patrick . resources to help their children Fishkin 1984 Kehoe. 1999. “Taxing Capital Income: A Bad Moreover, in considering Piketty’s( proposal). Idea.” Federal Reserve Bank of Minneapolis of a global capital tax, we have to ask: Would Quarterly Review 23 3 : 3–17. you rather be born into a world in which we are Chamley, Christophe. 1986.( ) “Optimal Taxation unequal but prosperous or a world in which we of Capital Income in General Equilibrium with are more equal but all less prosperous? Even if Infinite Lives.” Econometrica 54 3 : 607–22. equal opportunity is a goal, one might still pre- Fishkin, James S. 1984. Justice, Equal( ) Opportu- fer unequal opportunities to be rich over equal nity and the Family. New Haven: Yale Univer- opportunities to be poor. sity Press. A final possibility is that wealth inequal- Judd, Kenneth . 1985. “Redistributive Taxation ity is somehow a threat to democracy. Piketty in a Simple Perfect Foresight Model.” Journal alludes to this worry throughout his book. I of Public Economics 28 1 : 59–83. ( ) VOL. 105 NO. 5 YES, r g. SO WHAT? 47 >

Phelps, Edmund S. 1961. “The Golden Rule the Harvard University Press. of Accumulation: A Fable for Growthmen.” Straub, Ludwig, and Iván Werning. 2014. “Posi- American Economic Review 51 4 : 638–43. tive Long Run Capital Taxation: Chamley-Judd Piketty, Thomas. 2014. Capital in the( Twenty-first) Revisited.” Unpublished. Century. Cambridge, MA: Belknap Press of This article has been cited by:

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