# Why Don’t Growth Economists Study Growth Anymore?

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John Seater (NC State) left a really interesting comment on one of my recaps of the NBER Growth session papers.

It appears from the summaries in this blog that none of the other five papers was a growth paper. Now, literally anything in economics can have an effect on growth, so one could say that all five papers had implications for growth. However, it sounds as if none of the five papers summarized here addressed those implications. I am curious about why static analysis dominated a meeting ostensibly dedicated to studying economic growth. My impression from the programs for the Growth meeting in recent years is that most of the papers presented there are not about growth. What is going on? Has the Growth meeting ceased to be a growth meeting?

The short answer, John, is yes. The NBER Growth meeting really has ceased to be about growth, per se. I guess the broader question lurking around is whether this is a good or a bad thing. Let me see if I can take a shot at answering it from both directions.

The positive (or neutral) response is that growth papers aren’t about dynamics any more because the dynamics are determined by changes in steady states. People study the comparative statics of steady states in their models. Transition between those steady states – the dynamics – then just depend on the rate of accumulation of capital stocks (human and physical). Those rates don’t seem to be very different, so the transition rate isn’t the interesting aspect to study. The static difference in steady states is what determines the growth rates.

In terms of trend growth rates (how fast the economy grows in steady state), people probably implicitly have in their heads that those trend rates are similar across countries. Why? Because you look at the long-run paths of output per worker in most countries and they seem parallel, growing at the same rate in steady state. So that seems relatively less important in explaining cross-country differences.

The negative (or skeptical) response is that we’re missing something crucial by ignoring variation in growth rates. We’re assuming that the transitional growth rate is the same no matter what causes the static shift in steady states. Maybe that isn’t right. More importantly, maybe the trend growth rate isn’t identical across countries. While a lot of relatively well-off countries grow at very similar rates in steady state, poor countries don’t. Several of them grow very slowly, so slowly that they are falling behind rich countries.

Differential growth rates mean that we cannot just look at static differences across countries. Those differences are growing over time, so our static stories cannot be enough to explain them. We need explicit theories of why poor countries grow slowly, not just why the are poor to begin with.

Furthermore, even if countries do grow at the same rate in steady state, we’re still really interested in what that rate is. Growth at 2% per year doubles income every 35 years. Growth at 1% doubles it every 70. That’s a big difference in living standards over time. So studying growth rates is important in and of itself, outside of the question of cross-country comparisons.

I’ll freely admit that as a field, growth generally has strayed away from studying “growth”, in the traditional sense. But I don’t have a huge problem with where we are on this – I find the “what makes rich countries rich” question to be somewhat more compelling than the “is growth 1 or 2 percent per year” question. But it’s worth remembering that the latter question on growth rates has huge ramifications for absolute living standards over long periods of time – never underestimate compound growth.

# Hsieh and Moretti on Allocations across Cities

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Last post on the NBER growth session. Chang-Tai Hsieh (Chicago) and Enrico Moretti (Berkeley) presented a paper on wage dispersion across cities in the U.S. Wage dispersion (New Yorkers earn more than people in Cleveland) either represents compensation for living costs (housing in New York is more expensive than in Cleveland), a real difference in productivity (New Yorkers are more productive than Clevelanders), or some combination of the two.

What Chang and Enrico find is that the increase in wage dispersion across cities in the U.S. over the last thirty-ish years is due almost entirely to rising house prices in six cities: NY, DC, Boston, San Fran, San Jose, and Seattle. Wages have gone up rapidly in those cities, but that is basically just compensating their citizens for the higher costs of living.

Now, given the costs of living, the allocation of population across cities in the U.S. is efficient. That is, there is no reason for someone from Cleveland to move to New York on the margin. Their increased wage in New York only compenstates them for the higher housing cost, and so there is no change in their real wage.

However, if we do not take the costs of living as given, then the allocation of population is not efficient – there is a (surprise again!) misallocation. If there were not housing restrictions in NY and San Fran, and housing prices were not so ridiculously high, lots of people would move there because these are high-productivity cities. So one can back out the implied cost of housing restrictions across the whole U.S., and Chang and Enrico find that aggregate output is lower by about 10-14% because of them. That is, by preventing new housing in San Fran, restrictions drive up housing prices, which keep Clevelanders from moving, when in fact Clevelanders would be more productivite in San Fran.

The best part of the paper is the implied change in city sizes if you did remove restrictions. Chang and Enrico calculate that New York’s population would rise by 890%(!!) without restrictions on housing.

As an aside, Ed Glaeser (Harvard) gave the discussion of this paper. It was my first exposure to Ed, and all I have to say is that he should do the last discussion of the day at every conference, everywhere. Just when you are checking your phone for messages and thinking about beer, he steps in and gives a great energetic talk that keeps your attention. And the bow tie. The man can actually pull off a bow tie.

# Herrendorf and Schoellman on Labor Allocations

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The next post on the NBER growth session. Berthold Herrendorf (ASU) and Todd Schoellman (ASU) looked at the (surprise!) misallocation of labor between agriculture and non-agriculture. They look at the wage gap between ag and non-ag in a panel of 39 countries. The question is how much of the gap is due to human capital differences between ag and non-ag workers.

Across their sample, the average wage premium for non-ag is 1.79. That is, non-ag workers earn about 79% more than ag workers per hour. If you control for human capital using a standard Mincerian return to years of schooling of 10%, then this average premium falls to 1.36. The wage \textit{per unit of human capital} in non-ag is 36% higher than in agriculture. The raw wage premium is 1.79 because non-ag workers have higher average education levels.

What Todd and Berthold do to advance on this is to consider the possibility that the returns to education are different between sectors. They provide evidence that this is in fact the case. For each year of schooling, agricultural workers get a smaller bump in wage than do non-ag workers. Thus non-ag workers have even higher implied human capital than ag workers. They have more years of schooling, and those years of schooling provide them with more human capital. If you make this adjustment, then the average wage premium for non is 0.92, or non-ag workers earn about 8% \textit{less} per unit of human capital than in ag. Essentially, Todd and Berthold can account for the entire observed wage gap.

This is intriguing because it suggests that the labor markets in these countries are getting things roughly right. This doesn’t mean ag workers earn the same as non-ag workers, they don’t. But this is because ag workers provide less human capital to the market than non-ag workers, not because ag workers are underpaid for their human capital. I’ll do some self-promotion in that their work complements my own finding that wage gaps between sectors in developing countries are not a big source of aggregate productivity losses.

One conclusion from their work is that movements of workers between sectors are not by themselves a source of growth. With the marginal return to HC being the same across sectors, there is no boost to productivity coming just from moving workers around. If we do observe shifts of labor from ag. to non-ag then that represents shifts due to differential productivity growth in the sectors or to non-homothetic preferences.

# Restuccia and Santaeulalia-Llopis on Land Misallocation

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Next entry in the NBER growth session recap. Diego Restuccia (Toronto) and Raul Santaeulalia-Llopis (Wash. U.) presented their paper on land misallocation and productivity. Essentially, what Diego and Raul are trying to do is apply the firm-level study of Hsieh and Klenow (2009) methodology to farms (you might be starting to sense a theme to the day by now). Specifically, they have detailed data on farm plots from Malawi, and use this to see how much the marginal product of land varies across farming households.

They then ask the counter-factual question of: how much would agricultural output rise if we re-allocated land across farmers to equalize the marginal product of land? Essentially, if I could make sure that high-productivity farmers were able to receive more land, and low-productivity farmers less, how much could we raise aggregate output? Their finding is that output would go up by a factor of 3! This is way off the charts compared to anything that people have done with firms (where output might rise by a factor 1.5).

Big numbers like that lead to questions. The obvious concern is that they are incorrectly measuring the marginal product of land. Working in their favor is that they have clear measures of actual real output (bushels of maize). This means they do not have to make any assumptions about prices to try and deflate revenues, as we often need to do with firms.

You might also be worried that they are attributing land-quality differnces to households. That is, household A looks really productivity in the data because they have good land, not because they are really good at farming. Diego and Raul have really fine-grained measures of land characteristics. Conceptually they can control for land quality. But how do you construct a single-valued index of land quality from 11 different characteristics (slope, elevation, acidity, etc…). There is conceivably some kind of “true” agronomic function that transforms these into a single measure of quality, but it is almost certainly highly non-linear and involves all sorts of weird covariances between the measures. So if you want to be skeptical about their results, I think this is the primary worry.

Let’s take their results as true for the moment, though. One explanation for the vast degree of misallocation goes back to subsistence constraints, as I discussed in a different context before. If I need to ensure that all farming households can achieve a minimum output (and markets are not developed enough for people to borrow/lend over time if they can’t), then you’re bound to have big misallocations. You’d in fact have to give bad farmers even more land than good farmers. A very low absolute level of productivity is thus a determinant of misallocation.

On the other hand, if all the land is really highly productive, then small plots are sufficient to ensure subsistence. This means that we can give all the bad farmers small plots, and let the good farmers operate the surplus land. So a high level of absolute productivity will ensure a better allocation. Inherent land productivity thus has two separate influences on outcomes: a direct one through increasing output, and an indirect one in ensuring better allocations of land.

# David, Hopenhayn, and Venkateswaran on Misallocation

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Next installment of the NBER growth session recap. The second paper was by Joel David (USC), Hugo Hopenhayn (USC), and Venky Venkateswaran (NYU Stern). Their jumping off point is the apparent mis-allocation of factors of production across firms. The standard of comparison here is Hsieh and Klenow (2009), who find that mis-allocation of factors is lowering output by something like 50% in China and India.

So why are factors mis-allocated? David, Hopenhayn, and Venkateswaran propose that this is partly due to informational issues. That is, firms themselves do not know ex-ante (when they are deciding on how much capital or labor to hire) exactly what their productivity will be ex-post. Hence they make mistakes, and part of what we observe in the ex-post data are these mistakes. So rather than explicit taxes, subsidies, or other frictions, poor information about future productivity drives mis-allocation.

To get some quantitative feel for how important this is, they focus on listed companies. These have the advantage of an extra source of information on future prospects, the stock price. There is a neat little information extraction problem they show solves nicely that allows them to use the observed productivity of firms and the stock prices to back out the degree of uncertainty firms have ex-ante. With this, they suggest that in the U.S. roughly 40% of variation in productivity firms is a surprise to firms. In India, about 80% of variation in productivity is a surprise. Because of the poorer information, Indian firms make bigger mistakes on average, and so there is more ex-post mis-allocation.

It’s a clever explanation for mis-allocation, and is one of those stories that in some sense has to be true to some extent. There is no way firms have perfect information on future productivity (or demand, which is essentially the same thing in these models). The question is how big of an effect it is, and they suggest it’s pretty sizable.

One question that came up in my head afterwards was whether the degree of uncertainty is related to the level of returns. That is, Indian firms have a lot of uncertainty (risk) in their productivity draws, apparently. Is that high risk associated with higher rewards? If it is, then we can’t really say that this is mis-allocation, per se. Firms are making optimal decisions ex-ante, and there happens to be a willingness to tolerate risk in the economy. If, on the other hand, high risk is associated with low rewards, then there really is a mis-allocation in the sense that they are making uninformed decisions.

# Oberfield and Raval on Capital/Labor Elasticity of Substitution

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I was in Boston for the NBER summer institute on Friday, sitting in on what it typically called either “Growth day” or “Jones/Klenow” after the organizers. Regardless, here’s the program. It’s a chance to see what is some of the cutting/bleeding edge research in economic growth.

The first paper I saw was by Ezra Oberfield of Princeton and Devesh Raval of the Federal Trade Commission (I missed the Grossman/Helpman paper because I like to sleep, and didn’t get to Boston until 10:15am – sue me). They were doing two things. (1) providing an estimate of the aggregate elasticity of substitution (EOS) between capital and labor and (2) using that to try and account for the decline in labor’s share of income over the last 30-40 years.

On (1), they made the point that the aggregate EOS is not a technological constant, but rather is an artifact of the micro-level EOS. Specifically,

$\displaystyle \sigma^{agg} = (1-X)\sigma^{micro} + X \epsilon \ \ \ \ \ (1)$

where ${\sigma^{micro}}$ is the EOS at the plant level. The weighting term ${X}$ reflects the variation in capital shares across firms. ${\epsilon}$ is the elasticity of demand for plant output. The demand elasticity is in to account for the fact that some of the response to a change in factor prices is to move demand away from the plants that tend to use the more expensive factor.

Regardless, Ezra and Devesh provide evidence that ${X}$ is really close to zero, so essentially this demand adjustment is negligible, and the aggregate EOS is roughly equivalent to the micro EOS. They estimate this from plant-level data, and find something like 0.52, meaning that capital and labor are not easily substituted for each other. Over time, the aggregate EOS is roughly stable at around 0.70, based on their values for ${X}$ and ${\epsilon}$.

On (2), given their aggregate EOS, the implication is that the decline of labor’s factor share is biased technical change. Increased automation, IT investment, and offshoring, among other things, have driven down labor’s share of output down over time.

Changes in factor prices alone (wages and rental rates) would have raised labor’s share of output over this period, they find. The force of biased technical change was so strong it overcame that tendency.

It’s worth noting how important finding the EOS1, then firms can switch easily from labor to capital. Relatively cheap capital is substituted for labor, and labor’s share drops. If EOS>1, then the decline in labor share is driven in part by more expensive labor, and hence the implied degree of biased technical change is smaller.