# Why I Care about Inequality

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

“Inequality” is a term that has been tossed about quite a bit. The Occupy movement, to Piketty’s book, to debates over the minimum wage, to Greg Mankiw‘s defense of the 1%. Just today Mark Thoma published an op-ed on inequality. A few days ago John Cochrane had a post about why we care about inequality.

One of Cochrane’s main points is that the term “inequality” has been used in so many contexts, and to refer to so many different things, that it is ceasing to lose meaning. I’ll agree with him on this completely. If you want to talk about “inequality”, you have to be very clear about what precisely you mean.

There are three things that people generally mean by “inequality”:

1. The 1% versus the 99%. That is, the difference in average annual income of the top 1% of all households versus the average annual income of the bottom 99%.
2. The stagnation of median real wages and those below the median.
3. The college premium, or the gap in earnings between those who finished college and those who did not (or did not attend).

When I say I care about inequality, I mean mainly the second – the stagnation of median wages – but this is going to take me into territory covered by the first – the growth in top 1% income. There are things to say about the college premium, but I’m not going to say them here.

Why do I care about the stagnation of median wages?

• Because I’m going to be better off if everyone shares in prosperity. I want services like education, health care, and home repairs to be readily available and cheap. The way to achieve that is to invest in developing a large pool of skilled workers – teachers, nurses, electricians, carpenters. Those at the bottom of the distribution don’t have sufficient income to make those investments privately, so that requires public provision of those investments (i.e. schools) or transfers to support private investments. You want to have an argument about whether public provision or transfers are more efficient? Okay. But the fact that there is an argument on implementation doesn’t change the fact that stagnant wages are a barrier to these investments right now.
• Because people at the bottom of the income distribution aren’t going to disappear. We can invest in these people, or we can blow our money trying to shield ourselves from them with prisons, police officers, and just enough income support to keep them from literally starving. I vote for investment.

One response to this is that I don’t care about inequality per se, I care about certain structural issues in labor markets, education, and law enforcement. So why don’t we address those fundamental structural issues, rather than waving our hands around about inequality, which is meaningless? Because these strutural issues are a problem of under-investment. The current allocation of income/wealth across the population is not organically producing enough of this investment, so that allocation is a problem. In short, if you care about these structural issues, you cannot escape talking about the distribution of income/wealth. In particular, you have to talk about another kind of inequality, the 1%/99% kind.

Let me be very clear about this too, because I don’t want anyone to think I’m trying to be clever and hide something. I would take some of the income and/or wealth from people with lots of it, and then (a) give some of that to currently poor people so they can afford to make private investments and (b) use the rest to invest in public good provision like education, infrastructure, and health care.

Would I use a pitchfork and torches to do this? No. Would I institute “confiscatory taxation” on rich people? No, that’s a meaningless term that Cochrane and others use to suggest that somehow rich people are going to be persecuted for being rich. I am talking about raising marginal income tax rates and estate tax rates back to the archaic levels seen in the 1990s.

• Because rich people spend their money on useless stuff. Not far from where I live, there is a new house going up. It will be over 10,000 square feet when it is complete. 2,500 of those square feet will be a closet that has two separate floors, one for regular clothes and one for formal wear. If that is what you are spending your money on, then yes, I believe raising your taxes to fund education, infrastructure, and health spending is a net gain for society.

Don’t poor people spend money on stupid stuff? Of course they do. Isn’t the government an inefficient provider of some of these goods, like education? Maybe. But even if both those things are true, public investment and/or transfers to poor people will result in some net investment that I’m not currently getting from the mega-closet family. I’m happy to talk about alternative institutional settings that would ensure a greater proportion of the funds get spent on actual investments.

• Because I’m not afraid that some embattled, industrious core of “makers” will decide to “go Galt” and drop out of society, leaving the rest of us poor schleps to fend for ourselves. Oh, however will we figure out how to feed ourselves without hedge fund managers around to guide us?

This is actually a potential feature of higher marginal tax rates, by the way, not a bug. You’re telling me that a top tax rate at 45% will convince a number of wealthy self-righteous blowhards (*cough* Tom Perkins *cough*) to flee the country? Great. Tell me where they live, I’ll help them pack. And even if these self-proclaimed “makers” do stop working, the economy is going to be just fine. How do I know? Imagine that the entire top 1% of the earnings distribution left the country, took all of their money with them, and isolated themselves on some Pacific island. Who’s going to starve first, them or the remaining 300-odd million of us left here? The income and wealth of the top 1% have value only because there is an economy of another 300-odd million people out there willing to provide services and make goods in exchange for some of that income and wealth.

So, yes, I care about 1%/99% inequality itself, because I cannot count on the 1% to privately make good investment decisions regarding the human capital of the bottom 99%. And the lack of investment in the human capital of the bottom part of the income distribution is a colossal waste of resources.

# Wealth and Capital are Different Things

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

Piketty’s book is like a giant attention-sucking vortex. I can’t seem to escape it. This time I’m thinking about the criticism of Piketty’s analysis that has to do with rates of return on capital. Piketty says that if ${r > g}$, where ${r}$ is the return to capital, and ${g}$ is the growth rate of aggregate GDP, then wealth will become more and more concentrated.

Critiques of Piketty have questioned the assumptions underlying this conclusion. The most recent one I’ve seen is in Larry Summers’ review piece. Let’s let him sum up the issues:

This rather fatalistic and certainly dismal view of capitalism can be challenged on two levels. It presumes, first, that the return to capital diminishes slowly, if at all, as wealth is accumulated and, second, that the returns to wealth are all reinvested. Whatever may have been the case historically, neither of these premises is likely correct as a guide to thinking about the American economy today.

With respect to the first assumption regarding the rate of return, here is what Summers says:

Economists universally believe in the law of diminishing returns. As capital accumulates, the incremental return on an additional unit of capital declines.

But Summers has fallen into what I think is a really common trap for economists. He presumes that his second statement (“As capital accumulates, the incremental return on an additional unit of capital declines”) contradicts Piketty’s assumption (“that the return to capital diminishes slowly, if at all, as wealth is accumulated”). These two statements are not mutually exlusive.

The issue is that Summers is confounding wealth and capital. This is not helped by Piketty, who uses “capital” in his title and in the book the way that normal people use it, as a synonym for “wealth”. But from the perspective of an economist, these two concepts are not the same thing. The capital that Summers refers to in his critique (often denoted ${K}$) is a subset of the measure of national wealth (${W}$, as I’ll call it) that Piketty documents.

Without going too deep into this, Piketty’s measure of wealth consists of three parts: real estate, corporate capital, and financial assets. Only real estate and corporate capital are what economist have in mind when they say capital (${K}$). Wealth, however, consists of all three parts, so that Piketty’s wealth is ${W = K + F}$, where ${F}$ is the value of financial assets. Asserting that the return to capital falls as the capital stock increases – as Summers does – does not imply that the return to wealth falls as the stock of wealth increases. Even if we assume that financial markets work so efficiently that the return to capital and the return to financial assets are identical, this does not mean that the return to wealth necessarily falls as wealth accumulates.

To see this, consider a really slimmed down version of the “bubble asset” model from Blanchard and Fischer (1989, p. 228). We have that the return on capital is ${r = f'(K)}$, where ${f'(K)}$ is the marginal product of capital. The ${f'(K)}$ is the derivative of the production function, and represents the marginal increase in output we’d get from adding one more unit of capital. Under our typical assumptions about diminishing returns, as ${K}$ goes up ${r}$ goes down. This is what Summers is using as his critique.

An efficient financial market would ensure that financial assets (F) would also have a return of ${r}$. If they did not, then people would buy/sell financial assets until the return was equal. (Yes, I’m ignoring risk entirely, but that doesn’t change the main point here). So the return on all wealth is equal to ${r}$, and note that this is pinned down by the value of ${K}$ alone.

Now, we have assumed that ${r}$ falls as ${K}$ increases. Does this imply that ${r}$ falls as wealth (${W}$) increases? No. The relationship between ${r}$ and ${W}$ depends entirely on the composition of the change in ${W}$. If ${W}$ rises because ${K}$ rises (say ${F}$ stays constant), then the rate of return on wealth falls because the marginal product of capital has declined. This is what Summers and others have in mind.

However, it’s perfectly plausible that ${W}$ rises even though ${K}$ falls, because the value of financial assets (${F}$) are increasing even more quickly. In this case, the marginal product of capital has increased, and the rate of return on wealth has increased. In this case, the rate of return rises with wealth.

Is it reasonable for an economy to experience falling capital but a rising value of financial assets? Sure. The point of Blanchard and Fisher’s model of bubbles is that even though all individuals are acting rationally at all times, the economy can take off onto a weird path where the stock of capital (${K}$) gets run down while the value of financial assets (${F}$) rises. Eventually this is unsustainable, as we’d run out of capital, but there is no reason that a situation like this cannot persist for a while.

Will the return to wealth necessarily rise as wealth accumulates? No. There are other equally reasonable paths that the economy could take where wealth accumulation is driven mainly by capital accumulation and the rate of return falls as wealth accumulates, consistent with the Summers critique. The point I want to make is that there is no particular reason to believe in a fixed relationship between wealth and the return on capital. They can move completely independently of each other.

So Piketty can easily be right that we are currently in a world where both the wealth/income ratio is increasing and the rate of return on wealth is rising (or remaining roughly constant), and that this could persist for some indefinite period. On the other hand, it was not inevitable that this was going to happen, and it could just as easily end tomorrow as in 100 years.

I think the story that is milling around beneath the surface of Piketty’s book is that recent wealth accumulation has been primarily of financial assets, not capital. Hence the return has stayed high and the concentration of wealth has continued. If the returns on that wealth are continually reinvested in financial assets as opposed to capital, then Piketty’s death spiral of wealth concentration would likely be the outcome. To avoid that death spiral, you’d want to get the returns on wealth reinvested into real capital so that the return on capital (and hence wealth) gets pushed down.

# Piketty and Income Shares

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

Doug Gollin, Oxford University econ. professor, my coauthor, and an amateur ninja (I may have made up that last one), left a great reply to my post on Piketty and Growth Economics.

But for the record, it is not at all straightforward to read these income shares from national accounts data. The “true” labor and capital shares cannot be easily inferred from macro data – and they are also difficult to pin down in firm-level micro data.

Before we get going, let’s be clear that this is not a criticism about transcription errors or cherry-picking of results, as in Chris Giles‘ recent FT report. For more than you probably care to digest on that subject, see this link which has a nice roundup of the hubbub.

Specifically, Doug has the following concern:

The national income and product accounts for most countries report something called employee compensation. This sounds like labor income, but it leaves out some important forms of labor income, such as the labor income of the self-employed.

This is something that Doug has looked closely at before (see here), and that prior research is pretty clear that there are big adjustments to be made regarding the earnings of the self-employed. Simply put, earnings for the self-employed (which Piketty calls “mixed” income) are reported as capital income in national accounts, but contain both labor income (the implicit wage I pay myself while running my own firm) and capital income (the implicit return I get for having emptied my savings account to start a company). So the national accounts data do not accurately reflect the distribution of income between labor and capital.

Further, the amount of self-employed income as a share of national income tends to shrink as countries develop (think of people moving from farms to factories, and going from self-employed to wage-workers). Over the time frame that Piketty is looking at, there would have been distinct changes (declines, almost certainly) in the share of self-employed income within all of the countries he examines.

Piketty’s strategy with the “mixed” income of self-employed is to split it up into labor and capital income using the same ratio he observes in the reported labor and capital income. So if employee compensation is 2/3 of reported labor and capital income in the national accounts, then as I understand it Piketty assumes that self-employed income is also 2/3 labor income and 1/3 capital income.

Is this a problem? Here’s how it might be. If self-employment income is really fundamentally different (perhaps it is 90% labor and only 10% capital) then the shift over time away from self-employment would have necessarily changed the distribution of income between capital and labor. That is, Piketty could be overstating capital’s share in 1890 because he assumes that 1/3 of self-employment income is capital income, while really only 10% of self-employment income is capital income. Some of the deep declines in the capital share he documents around WWI and WWII may simply reflect the shift of workers out of self-employment (with it’s incorrectly small labor share) and into wage work (which is accurately measured as labor income). That period is one of rapid industrialization, so presumably the shift from self-employment to wage work would have been quite large.

So one point is that Piketty has possibly overstated capital’s share in the early period (roughly 1870-1910). Whether this is enough to materially change his overall story is unclear to me. You’d need data on self-employment shares and take some stand on how self-employment income is split between labor and capital. A second point is that Doug may have provided part of the explanation for the big drop in capital income around WWI and WWII. It may reflect a structural shift away from self-employment and towards wage work.

Doug also notes a concern over going from the functional distribution of income (labor vs. capital shares) to the size distribution of income (incomes of top 1% of individuals). As Doug notes: “Not all capital income accrues to rich people, and not all labor income goes to the poor or the working classes.”. And he is absolutely correct about that, but I don’t think that Piketty necessarily falls into that trap. The first section of the Piketty book is really about the functional distribution of income: capital’s share of national income. He establishes (perhaps shakily) some stylized facts on this share based on national accounts.

The second section of the Piketty book is about the size distribution of income, where he looks at variation in the earnings of the top 5% (or 1% or 10%) using individual tax records and surveys from various countries. Piketty is not confounding the capital share with the share going to the top 5%. He has separate sources for those two series. He then further digs into the tax records to establish where those top 5% are getting their income. Long story short, the top 5% are getting an increasing share of their income from wages (or what is reported as wages, at least, to tax authorities) over time. But it is also true that the top 5% earn almost 100% of the total reported capital earnings in the tax data (or what is reported as capital earnings to tax authorities). This is where Piketty then draws a link between capital’s share of national income and the income share of the top 5% – given that he observes that historically nearly all of capital income is earned by the top 5% or so, then an increase in capital’s share of income will lead to a larger share of income for that 5%.

# Piketty and Growth Economics

NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site.

Reviews of Thomas Piketty’s “Capital in the 21st Century” are second only to cat videos on the internet, it seems. Not having any cats, I am unable to make a video, so you’re stuck with a review of Piketty’s book.

I was particulary struck by the implications of this work for economic growth theory. The first section of the book studies capital/output ratios, one of the core elements of any model of growth that includes capital. Piketty provides a long time series of this ratio, showing that in Europe it tended to hover around 7 during the 1800’s and early 1900’s, then dropped dramatically following World War I, stayed at around 3 until the 1970’s, and now is rising towards 6. In the U.S., it has been less variable, going from around 4.5 in the 1800’s to about 3 in the 1960’s, and now is back up to about 4.5.

The projection that Piketty makes is that the capital/output ratio will tend to be about 6-7 across the world as we go into the future. The main reason is that he expects population growth to decline, and the capital/output ratio is inversely related to population growth. In a standard Solow model with a fixed savings rate ${s}$, the capital/output ratio is ${K/Y = s/(n+\delta+g)}$, where ${n}$ is population growth, ${\delta}$ is depreciation, and ${g}$ is the growth of output per worker. You can see that as ${n}$ goes down, the ${K/Y}$ ratio rises.

By itself, this doesn’t imply much for growth theory, in that the expected ${K/Y}$ ratio in the future is entirely consistent with Piketty’s claim regarding population growth. He might be wrong about population growth, but if ${n}$ does in fact fall, then any growth model would have predicted ${K/Y}$ will rise.

The interesting implication of Piketty’s work is on the returns to capital. In particular, the share of national income that goes to capital. His figures 6.1-6.3 document that this share has changed over time. From a share of about 35% in the 1800’s in both Britain and France, the share dropped to about 20-25% in both countries by the mid-20th century. Most recently, the capital share is starting to rise across many countries, going up about 10 percentage points between 1970 and 2010.

One of the bedrock assumptions made in most growth models is a Cobb-Douglas production function, which implies (under conditions of perfect competition) that capital’s share in output is fixed by a technological parameter, typically called ${\alpha}$ and typically assumed to be ${\alpha = 0.3}$. Over time, the share of output going to capital is constant at this value of ${\alpha}$. Growth economists lean on this assumption because of work done by Nicholas Kaldor, who established as a “stylized fact” that capital’s share in output is constant at about 0.3–0.35. As Piketty points out, though, Kaldor established this fact using a very small time series of data from a particularly unusual time period (roughly the mid-20th century).

The fact that capital’s share of output has changed distinctly over long time frames means that this baseline assumption is called into question. What does it mean? I have two immediate thoughts.

• Perfect competition is not a good assumption. This is probably trivially true; there is no such thing as a perfectly competitive economy. But what Piketty’s data would then indicate is that the degree of imperfection has possibly changed over time, with economic profits (not accounting ones) rising in the late 20th century. We have lots of models of economic growth that allow for imperfect competition (basically, any model that involves deliberate research and development), but we do not talk much about changes in the degree of that competition over time.
• The production function is not Cobb-Douglas. Piketty talks about this in his book. The implication of rising capital shares that coincide with rising capital/output ratios is that the elasticity of substitution between capital and labor is greater than one. For Piketty, this contributes to increasing inequality because capital tends to be owned by only a small fraction of people. For growth economists, this raises interesting possibilities for what drives growth. With a sufficiently large elasticity of substitution between capital and labor, then growth can be driven by capital accumulation alone. To see this, imagine perfect substitutability between capital and labor in production, or ${Y = K + AL}$, where ${A}$ is labor-specific productivity. Output per worker is ${y = K/L + A}$. As the capital/labor ratio rises, so does output per worker. This continues without end, because there are no longer decreasing returns to capital per worker. Even if technology is stagnant (${A}$ does not change), then output per worker can go up. We tend to dismiss the role of capital per worker in driving growth, but perhaps that is because we are wedded to the Cobb-Douglas production function.

The remainder of Piketty’s book is very interesting, and his own views on the implications of rising inequality have been subject to an intense debate. But from the perspective of growth economics, it is the initial section of the book that carries some really interesting implications.