# Should Developing Countries Try to Create a Business Elite?

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

La Porta and Shleifer released a working paper recently on the informal economy (which I believe is a draft for a future issue of the Journal of Economic Perspectives, but I could be wrong). They give an overview of what we currently know about the size and characteristics of informal firms.

The thing that stuck out most after reading this was the strong evidence that big, formal firms do not grow out of small, informal ones. In other words, small informal firms tend to stay small and informal. Big formal firms are created as formal firms, and while they may start relatively small, they generally start out bigger than most informal firms will ever be. While institutions/regulations may make incent some people to run informal firms, these regulations are not preventing informal firms from becoming formal. There is essentially no transition in any country of informal firms into formal ones.

This is important because big formal firms are much, much more productive (per worker, or in terms of total factor productivity) than small informal ones. So big formal firms are the source of nearly all the significant gains in aggregate productivity within countries. You don’t see any highly developed nations dominated by small, informal firms. And fostering the growth of big formal firms is different (according the La Porta and Shleifer) from fostering the growth of small informal ones.

A similar sentiment can be found in a recent column by Daniel Altman, titled “Please Don’t Teach this Woman to Fish“. As the tag line to the article says: poor countries have too many entrepreneurs and too few factory workers. Promoting small (almost universally informal) firms can improve living standards slightly, but does not lead to the massive productivity gains that generate big gains in GDP per capita.

So what does it take to promote big formal firm growth? La Porta and Shleifer suggest that a big constraint is highly trained managers and/or entrepreneurs that can handle running a large firm. Improving the average level of education is less important, in this case, than extending the tail of the education distribution. Nearly all big formal firms are run by college-educated managers, so developing countries need to generate more of those kind of people. Getting everyone to go from 6 to 7 years of education won’t do it – it would be better to leave nearly everyone at 6 years, but add a few extra people with 16 years or 18 years of education.

Yes, you also need an institutional/regulatory structure that makes it low-cost for those college-educated managers to open and operate firms, obviously. But apparently having a good regulatory structure won’t buy you anything without the stable of potential managers.

So here’s a question(s) related to education policy in developing countries. Would they be better off spending their budget providing scholarships for students to got to college (perhaps abroad) and/or paying for high-achieving students to intern or work abroad at large firms for a while. If you could get GE to hire 100 students into their managerial program, would that ultimately be better for development than achieving universal secondary schooling? Is it worth it to the whole country to create an elite cadre of managers who own/run large formal firms?

# Some Self-Promotion

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

The CSAE blog has put up a research summary about my paper with Markus Eberhardt, on agricultural technology and agricultural productivity (which are different things).

# Does Culture Matter for Economic Growth? Part Deux.

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

I ended up getting a lot of feedback (pushback?) on my post regarding culture and economic growth. The TL;DR version is this: if culture influences utility functions, then comparing economic development levels between cultures not very interesting because it doesn’t ultimately inform us about welfare.

Several people got back to me about ways that culture could matter for economic development without necessarily implying differences in utility functions. While not doing full justice to each comment, I think the common thread was this: coordination failures.

Perhaps you have some cultural norm that says to distrust strangers. In some kind of repeated dynamic game, your first choice is to deviate/defect/cheat, and this leads to a bad equilibrium where everyone continues to deviate/defect/cheat. This means you do not take advantage of mutually beneficial transactions. In contrast, a culture that says to trust strangers will choose to cooperate as a first choice, and this leads to a good dynamic equilibrium where everyone continues to cooperate (lend to each other, transact with each other, make long-term contracts with each other) and allows for greater economic specialization.

Now, if the cultural norm of distrusting strangers is there to minimize the utility loss (shame?) from being cheated, then its still just a utility function difference, and we can’t really say that people are worse off from distrusting strangers. They are, after all, avoiding something that hurts them very badly. But if the cultural norm of distrusting strangers is just some odd historical outcome, then I could see how this cultural norm is really affecting not just economic development, but also welfare. People would like to coordinate on “cooperate” and achieve the good long-run equilibrium, but no one has any incentive to act alone.

That said, cultural norms of distrusting strangers (or trusting them) aren’t random. They must have some basis in past cultural experience, and so I’d be worried that it directly influences utility in some manner. But as a general proposition, the idea that culture has an influence on economic development and welfare because of coordination failures seems like a good avenue to pursue.

The idea that culture is tied up with solving coordination problems runs through a lot of the work of Avner Greif. His 1994 paper on cultural beliefs and economic outcomes compares an individualist culture (Genoese traders) with a collectivist one (Maghribi traders) in how they dealt with severe principal-agent issues. Summarizing, the Genoese developed a vertical structure that relied on formal institutions to mediate disputes, while the Maghribi developed a horizontal structure that relied on intra-group cooperation to mediate distputes (i.e. punish cheaters).

Greif does not explain why the Genoese or Maghribi adopted these different attitudes, he just documents that the choice of vertical versus horizontal structure makes sense given their cultural attitudes. He’s also clear about ranking these systems:

Hence although in the long run the Italians drove the Muslim traders out of the Mediterranean, the historical records do not enable any explicit test of the relative efficiency of the two systems (p.942-43)

So it’s not immediately obvious whether the collectivst culture was worse for economic outcomes (perhaps the Genoese had other advantages we don’t know about). But to my prior point, even if the collectivist culture was demonstrably worse for the economic outcomes, we don’t know anything about how individualism and collectivism entered the utility functions of these groups. Hence we don’t know whether the Genoese or the Maghribi were better off with their system.

The one way I see that you could definitively argue that the collectivist culture was “worse” was if the Genoese and Maghribi shared a common utility function, and the move to collectivism by the Maghribi was the result of a random historical event unassociated with that utility function. By random I mean, if we re-ran world history 1000 times, then in about half of them we should see the Genose ending up with collectivist institutions and the Maghribi with individualistic ones.

That seems like a tall order. I’d be shocked if the Maghribi’s collectivist culture, and hence adoption of a horizonatal structure that (might have) had a detrimental effect on their economy, was just random noise.

Obviously world history didn’t start with the Genoese and Maghribi, and their predisposition for collectivism and individualism was the result of historical events leading to that specific time and location. So perhaps there were a series of random occurrences over history that snowballed into the collectivist culture of the Maghribi and the individualist of the Genoese.

Which is a long way of saying that countries could share a common utility function (making GDP or income comparisons meaningful), have different cultures due to a series of historical contingencies, and that those cultural traits could have meaningful economic effects because of how they influence coordination problems. In that case, then it would be meaningful to talk about culture’s effect on GDP, because culture is essentially capturing some kind of historical path dependence.

# Measuring Real GDP

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

This morning Angus Deaton and Bettina Aten released an NBER working paper (gated, sorry) about understanding changes to international measures of real GDP and poverty that occurred following the release of a new round of price indices from the International Comparison Project (ICP).

Price indices? Methodological nuance? I know, ideal subject matter to drive my web traffic to zero.

For those of you still here (thanks mom!), the paper by Deaton and Aten is a great chance to understand where comparisons of real GDP across countries come from, and to highlight that these comparisons are inherently imprecise and should be used with that in mind.

The basic idea of the Penn World Tables, or any other attempt to measure real GDP across countries, is to compute the following

$\displaystyle RGDP_i = \frac{NGDP_i}{PPP_i} \ \ \ \ \ (1)$

where ${RGDP_i}$ is the real GDP number we want, ${NGDP_i}$ is the nominal GDP reported by a country, and ${PPP_i}$ is the “purchasing-power-parity” price index for that country. While there can be severe issues with the reporting of nominal GDP, particularly from poor countries with a bare-bones (or no) national statistics office, the primary concern in these calculations is with the ${PPP_i}$.

Think of ${PPP_i}$ as the cost of one “bundle of goods” in country ${i}$. So dividing nominal GDP by ${PPP_i}$ gives us the number of real bundles that a country produced. If we do that for every country, we can compare the number of real bundles produced across countries, and that crudely captures real GDP.

The ICP produces these measures of ${PPP_i}$ for each country. I’m going to avoid the worst sausage-making aspect of this, because it involves lots of details about surveys to find prices for specific goods, how to get the right “average” price for each good, and then how to roll those back up to ${PPP_i}$ for each country. The important thing about the methodology for computing ${PPP_i}$ is that there is no right way to do it. There are methods that might be less sensible (i.e. let ${PPP_i}$ be the price of a can of Diet Coke in a country) than what the ICP does, but that doesn’t imply that the ICP is correct in some absolute sense.

It also means that the ICP can, and does, change methodology over time. The paper by Deaton and Aten works through the changes in methodology from 1993/5 to 2005 to 2011 and how we measure real GDP. The tentative conclusion is that the 2005 iteration of the ICP probably was over-stating the ${PPP_i}$ levels for many developing African and Asian countries. From the equation above, you can see that over-stating the ${PPP_i}$ means under-stating real GDP. So in 2005, we were likely too pessimistic about the economic conditions in a lot of these developing countries. Chandy and Kharas found that using the 2005 values of ${PPP_i}$ implied that 1.215 billion people in 2010 lived below the World Bank’s $1.25 per day poverty line. Using the 2011 values of ${PPP_i}$ instead, there are only 571 million people living below$1.25 per day. That’s a reclassification of some 700 million people. Their domestic income stayed the same, but the 2011 ICP suggests that they were paying lower prices for their “bundle of goods” than we assumed in 2005, and hence their real income went above $1.25. But as I said before, these are tentative conclusions because there is no way of knowing this for sure. Deaton and Aten’s conclusion is that the 1993/5 and 2011 rounds of the ICP seem more consistent with each other, and 2005 looks like an outlier. So just to keep things comparable over time, we should probably avoid the 2005 numbers. But again, who knows. It’s quite possible that mankind’s true welfare is measured in the number of cans of Diet Coke that we can produce. Measuring real GDP or global poverty levels is – to put it kindly – a fuzzy process. There is not the right method for this. As you can see, the measurements can be pushed around a lot by differences in methodology that are inherently trying to make apples-to-oranges comparison (I mean that literally – how do you value apples compared to oranges in national output? What’s the right price? It’s different in Washington, Florida, and Wisconsin. So how do you compare the total “real” value of fruit consumption in different states or countries?). The implication is that we shouldn’t be asking real GDP measures or poverty line measures to do too much. For really crude comparisons, real GDP from the Penn World Tables is fine. The U.S. has higher real GDP per capita than Kenya, and the Penn World Tables pick that up. Is it a 40/1 ratio? A 35/1 ratio? A 20/1 ratio? Not entirely clear. Different methodologies for computing ${PPP_i}$ in the US and Kenya will yield different results. But is it really important if it is 40/1 versus 20/1? In either case, it is clear that Kenya is poorer. We can go forth and try to explain why, or make some policy advice to Kenya to help close the gap, or go to Kenya to work on interventions to alleviate poverty there. Where these real GDP comparisons, or poverty line counts, should not be used is in finer-grain comparisons. Is Kenya’s real GDP per capita lower or higher than Lesotho’s? According to the Penn World Tables, in 2011 Kenya’s was lower. But should we do any kind of serious analysis based on this? No. The difference is as likely to be from discrepancies in how we measure ${PPP_i}$ for those countries as from real economic differences in capital stocks, human capital, technology, or institutions. Real GDP comparisons are best thought of as similar to baseball stats. The top career OPS (on-base plus slugging percent) players are Babe Ruth, Ted Williams, Lou Gehrig, Barry Bonds, and other names you might recognize. Players like Albert Pujols and Miguel Cabrera are in the top 20, giving you a good idea that these guys are playing at a level similar to the greats of all time. You can’t use this career OPS to tell me that Pujols is definitively better than Stan Musial or definitively worse than Rogers Hornsby. But career OPS does make it clear that Pujols and Cabrera are definitely better than guys like Davey Lopes, Edgar Renteria, and Devon White (and distinguishing between Lopes, Renteria, and White is hopeless using OPS). The fact that ICP revises the ${PPP_i}$ values over time doesn’t make them useless, just as OPS isn’t useless even though it ignores defense and steals. But you cannot ask too much of the real GDP measures that are derived using them. They are useful for big, crude comparisons, not fine-grained analysis. # Does Culture Matter for Economic Growth? NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site. There’s been an increasing number of papers concerned with culture and its relationship to economic growth. I happened to just see this working paper by Di Tella and MacCulloch (2014), but the idea of culture being an important determinant of economic development levels has been hanging out there in the literature for a long time. Weber’s theory of the Protestant work ethic is probably the starting point for any discussion of this topic. More recent work tends to try and be more empirical than Weber, often using World Values Surveys as a means of measuring cultural elements. This is what Di Tella and MacCulloch do in their working paper. [If you’d like a good introduction to the culture literature, check out James Fenske’s course materials, in particular his “Foundations of Development” course]. I think this is pretty interesting reading, but I’m starting to get a little antsy about the use of the cross-country empirical work. Not in a standard “Identification!!” way, although that’s an issue, but in a slightly deeper way. In particular, why bother regressing GDP per capita (or growth, or any measure of economic activity) on cultural variables at all? Culture affects economic activity through the choices that people make about how to allocate scarce resources. In other terms, while culture may be a fundamental determinant of economic activity, it acts through proximate factors like (but not exclusive to) the accumulation of capital, the adoption of technology, or labor market participation decisions. So if we are going to describe how culture influences economic activity, we need to describe how culture influences those proximate factors. The decisions regarding saving, technology adoption, and labor market participation are similar in that they involve some sort of constrained optimization problem. That is, there is some budget constraint and some utility function, and people do the best they can to maximize utility while keeping within that budget. I have some income, for example, and I need to decide how much of it to consume and how much to save. I have some profits as a firm, and I need to decide whether to invest in a new technology, or distribute the profits to my stockholders. I have a finite amount of time, and I need to decide whether to stay home and raise my kids or put them in day care and go back to work. All constrained optimization problems. So if culture is going to influence economic activity, it has to influence those constrained optimization problems. And there are really only two options then. Either culture influences budget constraints, or it influences utility functions. I haven’t seen any argument that culture actually changes the budget constraints of people, firms, or governments. Finite resources are finite no matter what you believe. So culture probably acts through utility functions, changing people’s preferences towards the future, or towards education, or towards material success, or towards the environment, or whatever. Maximizing utility does not mean that people are individualistic money-grubbers. You can write down a utility function where someone cares about other people’s welfare, or a function where someone really enjoys free time with their kids, or highly values the environment, or values the success of their group. Culture, if it has economic effects, would presumably act by changing exactly what is valued in the utility functions of people or households. Take as an example the common cultural distinction that Americans are more individualistic than Europeans. This would manifest itself in a utility function in the U.S. that is heavily weighted towards individual income, say, versus any measure of community income. In Europe, the opposite would apparently hold. Then, given the same budget, Americans would make choices aimed towards better personal outcomes (e.g. low tax rates and social safety nets) while Europeans wouuld makes choices aimed towards better group outcomes (e.g. high tax rates and social safety nets). So here’s the issue that I mentioned at the top. If culture leads to different utility functions, which in turn lead to different measurable economic outcomes, then why should we bother with measuring economic outcomes? Let me take this from the opposite angle. If everyone has identical utility functions, then measurable economic outcomes (GDP, average wages) have some information about relative welfare across countries. But if everyone has a different utility function, then measurable economic outcomes don’t necessarily provide any information about relative welfare. If one culture derives utility from having massive families with lots of kids, and doesn’t really care about consumption goods, then what does their low GDP per capita tell me? Nothing. It doesn’t tell me they have lower welfare than a high GDP per capita culture. If you tell me that culture is important for economic outcomes, then you’re telling me that utility functions vary across cultures. But if utility functions vary across cultures, then cross-culture comparisons of economic outcomes don’t imply anything about welfare. So aren’t the regressions with culture as an explanatory variable self-defeating, even if they are econometrically sound? I could well be over-thinking this, and I’d be happy to hear a good argument for what the culture/growth or culture/income regressions are supposed to be telling me. # Potential “Potential Output” Levels NOTE: The Growth Economics Blog has moved sites. Click here to find this post at the new site. John Fernald has a new working paper out at the San Fran Fed on “Productivity and Potential Output Before, During, and After the Great Recession”. The main take-away from the paper is that productivity growth started to slow down even before 2008, particularly in industries that produce IT products or are significant users of IT products. Because of this, even in the absence of the Great Recession, we would have seen slower trend growth in GDP. What Fernald’s results imply is that the economy is not as far from its potential GDP as we might think. And the idea that we’re way below potential GDP is something lingering underneath a lot of the discussion about economic policy (tapering, stimulus, etc…). Matt Yglesias just had a post noting that while the U.S. is well below it’s pre-2007 trend for GDP, Europe is even farther below it’s trend. Regardless of the conclusion you want to draw from that regarding policy, the assumption is that the pre-2007 trend is where GDP “should” be. Back to Fernald’s paper. He finds that productivity growth was already declining prior to 2007, and therefore where GDP “should” be is a lot lower than the naive pre-2007 trend line would indicate. This is easier to see in a picture. The purple dashed line is from the CBO’s 2007 projection, and that is essentially just an extrapolation of the trend in GDP from about 1990-2007. Compared to that measure of potential GDP, we are doing very poorly, with actual GDP (the black line) falling nearly$2 trillion short of potential.

Fernald’s alternative calculations that take into account the slowdown in productivity growth that started in the mid-2000’s suggest a much lower estimate of potential GDP. His estimate (the red line) is a prediction of what GDP would have been without the financial crisis, essentially. It falls well below the CBO 2007 estimate. It suggests that the economy today is only perhaps $400 billion short of potential GDP. His numbers make a big difference in how you think about policy, if only at the quantitative level. If you’re for some kind of further monetary expansion or a new fiscal stimulus, then the size of that boost should be calibrated to a$400 billion shortfall, not a \$2 trillion one.

Why does Fernald come up with lower numbers for potential output than the naive forecast in 2007? Without going into the nitty-gritty, he looks at productivity growth (think output per hour) and finds that around 2003Q4, it stops growing as quickly as it did from 1995-2003. What Fernald chalks this up to is the exhaustion of the IT productivity boost. At the time, people thought that the IT revolution might have permanently raised labor productivity growth rates It appears to rather have had a “level effect” – we had a boost in the level of labor productivity, but now it will continue to grow at the normal rate. Again, this is easier to see in pictures, courtesy of Fernald’s paper.

You can see that the 1995-2003 period is exceptional in having high labor productivity growth, and that since 2003 we’ve had growth in labor productivity at about the same rate as 1973-95. Anyone who uses the 1995-2003 period to extrapolate labor productivity growth (like the CBO was implicitly doing in 2007) would overestimate potential output.

This isn’t to say that the CBO or anyone else was being lazy or duplicitous. In 2007, if you looked at the data on labor productivity, there would not be enough evidence to suggest that growth in labor productivity had fallen. The data from 1995-2007 would not be enough to tell you if we had experienced a “level effect” from IT that led to a temporary boost to growth rates, or a “growth effect” from IT that had permanently raised growth rates. You can only tell the difference now because we see the slowdown in productivity growth, so in retrospect it must have been a “level effect”.

Regardless, Fernald’s paper suggests that the scope of the Great Recession is less “Great” than previous estimates would lead you to believe. And given that the trend growth rate in labor productivity is driven primarily by technological innovation, then boosting that growth rate means hoping that someone will invent a new technology that has a transformative power similar to IT.

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

This group of papers is one of the first that I cover in class, because it’s useful to frame much of the growth/development research. The concept is that real GDP per capita is produced using a function something like ${y = A F(k,h)}$. Real GDP thus depends on total factor productivity (${A}$), capital (${k}$), and human capital/labor (${h}$). So variation in real GDP per capita depends on variation in ${A}$, ${k}$, and ${h}$ across countries. All your favorite theories about institutions, geography, culture, innovation, etc.. must operate through one of these three proximate factors. To focus ourselves on what is important, we’d like to know which of the three proximate factors are actually responsible for the variation in real GDP per capita we see.

One way to do this is to first assume a Cobb-Douglas production function for ${F()}$ and take logs

$\displaystyle \ln{y}_i = \ln A_i + \alpha \ln{k}_i + \beta \ln{h}_i. \ \ \ \ \ (1)$

Conceptually, one could then run a regression of ${y_i}$ (the ${i}$ index specifies the country) on ${k_i}$ and ${h_i}$. We don’t have information on ${A_i}$ directly, so we could treat that as the error term. We could get even fancier and replace ${k_i}$ and ${h_i}$ with some terms based on savings rates or human capital accumulation rates, consistent with theory. Regardless, we’d then look at the R-squared or partial R-squared’s to tell us how important each factor was. This is, in a nutshell, what Mankiw, Romer, and Weil (1992) are up to.

One problem with this is that TFP (${A}$) is not uncorrelated with ${k}$ and ${h}$, so the regression estimates of ${\alpha}$ and ${\beta}$ are going to be biased, and hence so are our R-squares. I wrote a whole post about this here.

So rather than run the regression, we could pull values for ${\alpha}$ and ${\beta}$ from some other source and just calculate the R-squares without actually running the regression. This is essentially what the development accounting literature is doing, with Hall and Jones (1999) and Klenow and Rodriguez-Clare (1997) being the classic examples. The upshot of these papers is that variation in ${A}$ accounts for at least 50% of the differences in ${y}$ across countries, and maybe more. ${k}$ accounts for maybe 30-40%, and ${h}$ only 10-20%. So TFP is the most important proximate factor.

The other papers are then riffs on this basic idea. Gollin (2002) is about whether ${\alpha}$ or ${\beta}$ themselves vary across countries (they do) and whether they are correlated with real GDP per capita (they are not). Caselli (2005) shows that differences in how exactly you account for ${k}$ and ${h}$ are not necessarily important for overall result that TFP matters most. You can also do this kind of accounting for a single country over time, to see the sources of growth. The Young (1995) and Hsieh (2002) papers are a back and forth over how to do this for several East Asian countries, differing in technique and data sources. Hsieh and Klenow (2007) is included in this section of the class because it helps establish that domestic savings rates do not vary much across countries, and so we cannot expect capital variation to matter a lot either.

The reading list here is light on human capital. I talk about Hendricks (2002) work on trying to measure ${h}$ more accurately using immigrant data from the U.S., and Weil’s (2007) paper on including health as part of human capital. The reason for the light coverage is that German Cubas, one of our junior faculty, is going to be teaching a graduate course this year that focuses a lot of human capital. So I only touch on it in my course.

As usual, PDF and Bibtex files with the reading lists are on the “Papers” page.

# 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.