N. Gregory Mankiw Tries to Discredit Piketty

In this paper, titled Yes, r > g. So What?. N. Gregory Mankiw tries to show that Thomas Piketty is wrong that if r > g wealth will accumulate in the hands of a tiny number of rich people. It’s short and easy on the math, perhaps because it was part of a symposium rather than a stand-alone paper. For comparison, take a look at this by Piketty and Gabriel Zucman, which requires more than a passing familiarity with math. It seems unlikely that Mankiw had read this paper before he cranked out his, because Piketty addresses the issues Mankiw raises.

Mankiw makes three arguments. First, he says we need to have r > g. Second, he claims that the generational changes and taxation will prevent dynastic wealth. Third, he disagrees with Piketty’s solution which is a wealth tax. Let’s take them in turn.

1. The idea that r, the rate of return to capital, is greater than g, the rate of growth of the economy, is common in mainstream economic theory.

If the rate of return is less than the growth rate, the economy has accumulated an excessive amount of capital. In this dynamically inefficient situation, all generations can be made better off by reducing the economy’s saving rate. From this perspective, we should be reassured that we live in a world in which r > g because it means we have not left any dynamic Pareto improvements unexploited.

Mankiw’s standard is whether the economy can produce Pareto Improvements, meaning an improvement in the wealth of one or more people that doesn’t reduce the wealth anyone else. Mankiw simply ignores the fact that fabulous wealth carries with it the ability to influence the political process to extract more wealth, which is what Piketty says. Surely Mankiw isn’t arguing that won’t happen, because it does. Take, for example, the pharmaceutical industry where the business model is to increase prices with no additional benefit to anyone.

Then look at his cure. How exactly will the bottom 60% benefit by saving less? They won’t, because they are barely saving. They cannot come up with $400 to fix a car. Most of the rest wouldn’t be able to save less; they need to save for retirement, and to pay what their kids can’t make in this rotten economy. What Mankiw means is that the very top, the .1%, would have to spend a lot more, But what are they going to buy? Expensive trips on private jets? Van Gogh paintings? That isn’t going to help the economy or make anyone’s life better. The fact is that this argument points directly to the need to hike taxes on the idle money of the rich.

2. Mankiw’s second argument is an effort to show that taxes and generational changes will decrease dynastic wealth. Mankiw doesn’t confront the detailed argument Piketty makes on those very points. I introduce it here, and link to the detailed argument for those interested. Instead, Mankiw offers a simple model that proves his point, and could be understood by anyone who read his introduction to economics textbook; for typographical reasons, subscripts are not used for cw and ck

To oversimplify a bit, let’s just focus on this economy’s steady state. Using mostly conventional notation, it is described by the following equations.

(1) cw = w + τ k

(2) ck = (r − τ − g)nk

(3) r = f ′(k)

(4) w = f(k) − rk

(5) g = σ(r − τ − ρ),

where cw is consumption of each worker, ck is the consumption of each capitalist, w is the wage, r is the (before-tax) rate of return on capital, k is the capital stock per worker, n is the number of workers per capitalist (so nk is the capital stock per capitalist), f(k) is the production function for output (net of depreciation), g is the rate of labor-augmenting technological change and thus the steady-state growth rate, σ is the capitalists’ intertemporal elasticity of substitution, and ρ is the capitalists’ rate of time preference. Equation (1) says that workers consume their wages plus what is transferred by the government. Equation (2) says that capitalists consume the return on their capital after paying taxes and saving enough to maintain the steady-state ratio of capital to effective workers. Equation (3) says that capital earns its marginal product. Equation (4) says that workers are paid what is left after capital is compensated. Equation (5) is derived from the capitalists’ Euler equation; it relates the growth rate of capitalist’s consumption (which is g in steady state) to the after-tax rate of return.

Note that we didn’t get a definition of the symbol τ, which in conventional notation means taxes. As we learn a couple of paragraphs down, Mankiw means not general taxes, but taxes on returns to capital. As he tells us, all the money from taxes is consumed by the workers (equation (1)), that is, the total amount of taxes on capital is transferred directly, in the form of grants or indirectly in the form of services, to wage-earners and none of it is consumed by the capitalists. in the real world, capitalists consume a great deal of the expenditure on taxes, whether the taxes are on capital or income or otherwise. Obviously we need to put a non-trivial number into equation (2) to show that capitalists consume a portion of the taxes, and make an appropriate modification to equation (1) if we want this model to make minimal contact with the real world.

Mankiw says that in this model, there is no steady increase in inequality.

In this economy, even though r > g, there is no “endless inegalitarian spiral.” Instead, there is a steady-state level of inequality. (Optimizing capitalists consume enough to prevent their wealth from growing faster than labor income.)

This outcome was baked into the model with equation (2). If instead, we assume the same equations, but add a non-trivial number to equation (2), then the capitalist accumulates that non-trivial amount each year, and wealth inequality increases naturally even in his steady-state economy.

Also baked into this model is the remarkable idea that “capital earns its marginal product” and the rest of the money is paid out in wages. That’s just so far from reality that it makes the whole exercise pointless. But it enables Mankiw to justify rejecting Piketty’s recommendation of high wealth taxes. Mankiw explains that if the government wants to protect capital, it pushes the tax on capital into negative numbers, and the capitalists will push wages to subsistence level. But,

Taxing capital and transferring the proceeds to workers reduces the steady-state consumption of both workers and capitalists, but it impoverishes the capitalists at a faster rate.

Taxing returns to capital hurts everyone in this model. Of course, if capitalists are taxed at the rate of their actual consumption of tax receipts, the non-trivial amount that should be added to equation (2), then you would get Mankiw’s desired outcome of a non-increasing inequality. Or you could go a bit higher, and start reducing inequality without resort to his suggestion of a consumption tax.

Mankiw’s sterile model doesn’t explain the facts documented by Piketty and his colleagues, but it does demonstrate nicely the state of mainstream economics. Obviously the American Economic Association wanted a paper from Mankiw challenging Piketty, no matter its quality. Mankiw is an established figure, and thus the beneficiary of the social structure of the field described by Marion Fourcade and her colleagues in the section of this paper headed Inequality Within, p. 96,

Second, we document the pronounced hierarchy that exists within the discipline, especially in comparison with other social sciences. The authority exerted by the field’s most powerful players, which fosters both intellectual cohesiveness and the active management of the discipline’s internal affairs, has few equivalents elsewhere.

Testing The Limits on Wealth Inequality

In this post, I pointed out that we are going to see an empirical test of Piketty’s theory of rising wealth inequality. The theory itself is not well understood, and Piketty has revisited it since the publication of Capital in the Twenty-First Century, and published an economist’s dream of a paper in full mathematical glory here. The American Economics Association devoted space in its journal to arguments about the theory, giving Piketty an opportunity to discuss his theory in what I think is a very readable paper, and one worth the time.

He starts by saying that the relation between r, the rate of return to capital, and g, the rate of growth in the overall economy, are not predictive. They cannot be used to forecast the future, and are not even the most important factor in rising wealth inequality. The crucial factors are institutional changes and political shocks. Neither can the relation tell us anything about the decrease in the labor share of national income. He points to supply and demand for skills and education in this paper, as he does in his book, but this is a at best an incomplete explanation, owing more to the neoliberal view that the problems of workers are their fault than to a clear understanding of social processes in the US. A better explanation lies in tax law changes, changes in labor law and enforcement of labor law, rancid decisions from the Supreme Court, failure to update minimum wage and related laws, and government support for outsourcing and globalization.

What the theory does say is the subject of Part II.

I now clarify the role played by r > g in my analysis of the long-run level of wealth inequality. Specifically, a higher r − g gap will tend to greatly amplify the steady-state inequality of a wealth distribution that arises out of a given mixture of shocks (including labor income shocks).

In other words, as the raw number r – g increases, wealth inequality reaches a limit at a higher level, and income and wealth mobility become lower.

The important point is that in this class of models, relatively small changes in r − g can generate large changes in steady-state wealth inequality. For example, simple simulations of the model with binomial taste shocks show that going from r − g = 2% to r − g = 3% is sufficient to move the inverted Pareto coefficient from b = 2.28 to b = 3.25. Taken literally, this corresponds to a shift from an economy with moderate wealth inequality — say, with a top 1 percent wealth share around 20–30 percent, such as present-day Europe or the United States — to an economy with very high wealth inequality with a top 1 percent wealth share around 50–60 percent, such as pre-World War I Europe.

The inverted Pareto coefficient β is a measure of inequality used by Piketty and his colleagues. Here’s how he explains it in this paper:

That is, if β = 2, the average income of individuals with income above $100,000 is $200,000 and the average income of individuals with income above $1 million is $2 million. Intuitively, a higher β means a fatter upper tail of the distribution. From now on, we refer to β as the inverted Pareto coefficient.

The theoretical basis for this result can be found here, where Piketty and his colleague Gabriel Zucman provide a typical economists mathematical explanation. I’ve read some of this paper, but it is tough going.

The returns to capital, especially business capital, are quite a lot higher than the levels given in Piketty’s example. Here’s the chart:

The returns to all capital after tax are about 7%. Paul Krugman put up a blog post saying that a realistic growth rate is about 2.2% at best for the next few years. This gives a difference r – g = 4.8%. Then using the equations on page 1356, we get an estimate that the inverted Pareto coefficient would be in the range of 11, which is a lot higher than the levels Piketty uses in the quoted material. By way of comparison, with that number, the average wealth of people with more than $10 million net worth would be $110 million. In the example Piketty gives for the top .1% with β =3.25, the figure would be $32.5 million.

Piketty notes that these coefficients are a rapidly rising function of r – g, which is apparently the case. In a recent paper, Emmanuel Saez and Gabriel Zucman estimate that the top .1% has a wealth share of 22% as of 2012, and there is every reason to think that has risen.

With Piketty’s general rule standing alone, there is no obvious limit to the level of wealth inequality, but in practice there are many practical reasons that it will level off. Some people will have more children, so the fortunes are divided into smaller shares. Some are lucky in investments and others aren’t. There are external shocks, wars and depressions. There are divorces, which split fortunes. Some people are able to earn high levels of labor income on top of capital income, increasing their wealth. Some die early, so their offspring are forced to spend more of their capital income to preserve their existing level of consumption. Others have expensive tastes and spend too much. These external forces eventually bring about a more or less static level of wealth inequality. Overall, this static level is higher when the fraction g/r is lower.

The time periods in the theoretical models used by Piketty and his colleagues are generational, they run 30 years. The big changes in wealth inequality began in the 70s, I’d guess, but became prominent enough that they were noticed in the late 80s and early 90s as the Reagan/Bush era tax cuts took hold, and regulatory structures were dismantled. By 2000, the final touches of formal deregulation were complete, and the Bush administration stopped enforcing most remaining laws leaving capital accumulation without restraint from legal pressure. It’s been about 15 years with little change, about half a cycle. The results follow the line Piketty and his colleagues predicted, and every year the new data supports their theories.

From this we can see that the coming empirical test is the maximum level of wealth inequality, or to put it another way, it’s a test of the downward pressures on the limits of wealth accumulation.

As a nation we have only taken the smallest possible steps to stem that tide, such as slow increases in the minimum wage, and tiny increases in taxes on the wealthiest to the extent they choose not to evade taxation in all sorts of allegedly legal ways. Neither of the presumptive candidates has any intention of making the kinds of changes necessary to change the outcome.

That brings us to the second empirical test: the level of wealth inequality that a civilized nation will accept before demanding change.

Or maybe the test is whether we are so cowed we won’t ever make any demands on our new lords and masters.

Empirical Test of Piketty’s r > g Theory Coming

Bernie Sanders forced the issue of wealth inequality into the presidential campaign, which presented a real problem for neoliberals of the Democratic persuasion. They want us to believe that the market rewards people in accordance with their merit and hard work. It doesn’t. They want us to believe everyone can get ahead if they get a good education and work hard. Not so. So the neoliberal dems fall back on their version of trickle-down: economic growth is the cure. So what is the future of economic growth?

Earlier this year Gerald Friedman did a study of the potential impact of Bernie Sanders’ economic ideas, saying they would create enormous economic growth. That drew fire from many liberal economists, including Paul Krugman who wrote several blog posts saying Friedman’s numbers were ridiculous, and using that as a opportunity to bash Sanders supporters for naiveté and for encouraging impossible expectation. On February 23, he put up a post with his own predictions of growth: a fraction over 2%. And that, he says, is good enough.

And let me say that the great thing about a progressive agenda is that it doesn’t require big growth promises to make it work, because the elements of that agenda are good things in their own right. Conservatives need to promise miracles to justify policies whose direct effect is to comfort the comfortable (cutting taxes on the rich) and afflict the afflicted (slashing social insurance); progressives only need to defend themselves against the charge that doing good will somehow kill economic growth. It won’t, and that should be enough.

But what about inequality in this scenario? Thanks to Thomas Piketty and his book Capital in The Twenty-First Century, we can say with some certainty that it isn’t going to get better with this kind of thinking. Remember Piketty’s basic finding: if r > g, wealth inequality will increase to a very high level. In this formulation, r is the rate of return to capital, and g is the growth rate of the economy. Here’s a chart from the St. Louis Fed showing the rate of return to capital in the US:

With the exception of the immediate post-Great Crash years, the All capital after tax line doesn’t sink below 5%, and the most recent figures show it near 7%. Here’s the definition, found in Note 5:

“Business” capital includes nonresidential fixed capital (structures, equipment, and intellectual property) and inventories. “All” capital includes business capital and residential capital.”

Piketty’s definition of capital is broader than this definition of “all”, but there isn’t any reason to think that will have a material effect on the overall number. In other words, r is about 5% higher than g, so we can expect a steady increase in wealth inequality.

The Republicans couldn’t care less: they nominated a billionaire. What’s on offer from the Democratic Party? Here’s Hillary Clinton’s webpage on economic issues. It’s mostly neoliberal ideas, from cutting taxes to deregulation to trade (see the part on small businesses), and some liberal ideas: investment in infrastructure and research, equal pay, paid leave and affordable child care. Her new idea? Let’s give tax breaks to companies that share profits with workers. Also, raise the minimum wage to $12 some day, and some tiny steps to increasing taxes on the rich by closing loopholes and making sure rich people pay more taxes than Warren Buffett’s secretary.

We are going to get an empirical test of Piketty’s idea, but we already know how it will turn out. The rich have nothing to fear.