“Railroads of the Raj: Estimating the Impact of Transportation Infrastructure,” D. Donaldson (2013)

Somehow I’ve never written about Dave Donaldson’s incredible Indian railroad paper before; as it has a fair claim on being the best job market paper in the past few years, it’s time to rectify that. I believe Donaldson spent eight years as LSE working on his PhD, largely made up of this paper. And that time led to a well-received result: in addition to conferences, a note on the title page mentions that the paper has been presented at Berkeley, BU, Brown, Chicago, Harvard, the IMF, LSE, MIT, the Minneapolis Fed, Northwestern, Nottingham, NYU, Oxford, Penn, Penn State, the Philly Fed, Princeton, Stanford, Toronto, Toulouse, UCL, UCLA, Warwick, the World Bank and Yale! So we can safely say, this is careful and well-vetted work.

Donaldson’s study considers the importance of infrastructure to development; it is, in many ways, the opposite of the “small changes”, RCT-based development literature that was particularly en vogue in the 2000s. Intuitively, we all think infrastructure is important, both for improving total factor productivity and for improving market access. The World Bank, for instance, spends 20 percent of its funds on infrastructure, more than “education, health, and social services combined.” But how important is infrastructure spending anyway? That’s a pretty hard question to define, let alone answer.

So let’s go back to one of the great infrastructure projects in human history: the Indian railroad during the British Raj. The British built over 67,000 km of rail in a country with few navigable rivers. They also, luckily for the economist, were typically British in the enormous number of price, weather, and rail shipment statistics they collected. Problematically for the economist, these statistics tended to be hand-written in weathered documents hidden away in the back rooms of India’s bureaucratic state. Donaldson nonetheless collected almost 1.5 million individual pieces of data from these weathered tomes. Now, you might think, let’s just regress new rail access on average incomes, use some IV to make sure that rail lines weren’t endogenous, and be done with it. Not so fast! First, there’s no district-level income per capita data for India in the 1800s! And second, we can use some theory to really tease out why infrastructure matters.

Let’s use four steps. First, try to estimate how much rail access lowered trade costs per kilometer; if a good is made in only one region, then theory suggests that the trade cost between regions is just the price difference of that commodity across regions. Even if we had shipping receipts, this wouldn’t be sufficient; bandits, and spoilage, and all the rest of Samuelson’s famous “iceberg” raise trade costs as well. Second, check whether lowered trade costs actually increased trade volume, and at what elasticity, using rainfall as a proxy for local productivity shocks. Third, note that even though we don’t have income, theory tells us that for agricultural workers, percentage changes in total production per unit of land deflated by a local price index is equivalent to percentage changes in real income per unit of land. Therefore, we can check in a reduced form way whether new rail access increases real incomes, though we can’t say why. Fourth, in Donaldson’s theoretical model (an extension, more or less, of Eaton and Kortum’s Ricardian model), trade costs and differences in region sizes and productivity shocks in all regions all interact to affect local incomes, but they all act through a sufficient statistic: the share of consumption that consists of local products. That is, if we do our regression testing for the impact of rail access on real income changes, but control for changes in the share of consumption from within the district, we should see no effect from rail access.

Now, these stages are tough. Donaldson constructs a network of rail, road and river routes using 19th century sources linked on GIS, and traces out the least-cost paths from any one district to another. He then non-linearly estimates the relative cost per kilometer of rail, sea, river and road transport using the prices of eight types of salt, each of which were sold across British India but only produced in a single location. He then finds that lowered trade costs do appear to raise trade volumes with quite high elasticity. The reduced form regression suggests that access to the Indian railway increased local incomes by an average of 16 percent (Indian real incomes per capita increased only 22 percent during the entire period 1870 to 1930, so 16 percent locally is substantial). Using the “trade share” sufficient statistic described above, Donaldson shows that almost all of that increase was due to lowered trade costs rather than internal migration or other effects. Wonderful.

This paper is a great exercise in the value of theory for empiricists. Theory is meant to be used, not tested. Here, fairly high-level trade theory – literally the cutting edge – was deployed to coax an answer to a super important question even though atheoretical data could have provided us nothing (remember, there isn’t even any data on income per capita to use!). The same theory also allowed to explain the effect, rather than just state it, a feat far more interesting to those who care about external validity. Two more exercises would be nice, though; first, and Donaldson notes this in the conclusion, trade can also improve welfare by lowering volatility of income, particularly in agricultural areas. Is this so in the Indian data? Second, rail, like lots of infrastructure, is a network – what did the time trend in income effects look like?

September 2012 Working Paper (IDEAS version). No surprise, Donaldson’s website mentions this is forthcoming in the AER. (There is a bit of a mystery – Donaldson was on the market with this paper over four years ago. If we need four years to get even a paper of this quality through the review process, something has surely gone wrong with the review process in our field.)

“What Determines Productivity,” C. Syverson (2011)

Chad Syverson, along with Nick Bloom, John van Reenen, Pete Klenow and many others, has been at the forefront of a really interesting new strand of the economics literature: persistent differences in productivity. Syverson looked at productivity differences within 4-digit SIC industries in the US (quite narrow industries like “Greeting Cards” or “Industrial Sealants”) a number of years back, and found that in the average industry, the 90-10 ratio of total factor productivity plants was almost 2. That is, the top decile plant in the average industry produced twice as much output as the bottom decline plant, using exactly the same inputs! Hsieh and Klenow did a similar exercise in China and India and found even starker productivity differences, largely due a big left-tail of very low productivity firms. This basic result is robust to different measures of productivity, and to different techniques for identifying differences; you can make assumptions which let you recover a Solow residual directly, or run a regression (adjusting for differences in labor and capital quality, or not), or look at deviations like firms having higher marginal productivity of labor than the wage rate, etc. In the paper discussed in the post, Syverson summarizes the theoretical and empirical literature on persistent productivity differences.

Why aren’t low productivity firms swept from the market? We know from theory that if entry is allowed, potentially infinite and instantaneous, then no firm can remain which is less productive than the entrants. This suggests that persistence of inefficient firms must result from either limits on entry, limits on expansion by efficient firms, or non-immediate efficiency because of learning-by-doing or similar (a famous study by Benkard of a Lockwood airplane showed that a plant could produce a plane with half the labor hours after producing 30, and half again after producing 100). Why don’t inefficient firms already in the market adopt best practices? This is related to the long literature on diffusion, which Syverson doesn’t cover in much detail, but essentially it is not obvious to a firm whether a “good” management practice at another firm is actually good or not. Everett Rogers, in his famous “Diffusion of Innovations” book, refers to a great example of this from Peru in the 1950s. A public health consultant was sent for two years to a small village, and tried to convince the locals to boil their water before drinking it. The water was terribly polluted and the health consequences of not boiling were incredible. After two years, only five percent of the town adopted the “innovation” of boiling. Some didn’t adopt because it was too hard, many didn’t adopt because of a local belief system that suggested only the already-sick ought drink boiled water, some didn’t adopt because they didn’t trust the experience of the advisor, et cetera. Diffusion is difficult.

Ok, so given that we have inefficient firms, what is the source of the inefficiency? It is difficult to decompose all of the effects. Learning-by-doing is absolutely relevant in many industries – we have plenty of evidence on this count. Nick Bloom and coauthors seem to suggest that management practices play a huge role. They have shown clear correlation between “best practice” management and high TFP across firms, and a recent randomized field experiment in India (discussed before on this site) showed massive impacts on productivity from management improvements. Regulation and labor/capital distortions also appear to play quite a big role. On this topic, James Schmitz wrote a very interesting paper, published in 2005 in the JPE, on iron ore producers. TFP in Great Lakes ore had been more or less constant for many decades, with very little entry or foreign competition until the 1980s. Once Brazil began exporting ore to the US, labor productivity doubled within a handful of years, and capital and total factor productivity also soared. A main driver of the change was more flexible workplace rules.

Final version in 2011 JEP (IDEAS version). Syverson was at Kellogg recently presenting a new paper of his, with an all-star cast of coauthors, on the medical market. It’s well worth reading. Medical productivity is similarly heterogeneous, and since the medical sector is coming up on 20% of GDP, the sources of inefficiency in medicine are particularly important!

“Chinese Economic Performance in the Long Run,” A. Maddison (2007)

Many economists know the rough contours of Western economic history well. Real income of unskilled laborer and farmer households was at no time and in no place more than, at best, three times subsistence income (see Scheidel for a nice summary of this evidence). Peaks in per capita GDP were reached in the heyday of ancient Rome and the early Arab caliphate. Regional regression was nothing strange – Europe in 1000 was using less advanced technology in many cases than the Romans had, credit markets were essentially nonexistent, long-distance or even regional trade had dried up, and no city in Europe existed with a population of even 10,000 people at the turn of the millennium. Living standards begin to rise slowly after the Black Death, first in Renaissance Italy, and then in the Netherlands and England. The Industrial Revolution finally severs the Malthusian noose by the mid-1800s, when living standards for most members of society begin to rise from their historical norm.

But what of China? Before he died, one of Angus Maddison’s final projects was compiling data on historic China. In Chinese culture, the classic periods in history are the Tang and Song dynasties, roughly from the 7th to the 12th centuries, with brief interludes, and perhaps the late Yuan and early Ming, from the late 13 to the late 1400s. Did China escape the Malthusian curse? They also did not. It seems likely that incomes were roughly at subsistence until the Tang dynasty in the 9th century, when income per capita rose perhaps 30 percent. That peak would not be seen again until around 1970!

Now, in a Malthusian world, you can still grow, or be more advanced economically, but that growth is eaten up by population growth. The main pattern in China seems to be a massive shift in population density in the south, meaning south of the Yangtse, after the beginning of the Song dynasty. Woodblock printing, allowing for the dissemination of guides to more productive agriculture, appeared in this era. Chinese agriculture appears to have been much more advanced that that of Europe or India; indeed, more of China’s farmland was irrigated in 1400 than America’s today, and not until the 20th century did Europe reach grain yields seen in China in 1400. If you know your Joseph Needham, you know much of this is driven by Chinese agricultural inventions like the curved mouldboard and the use of crop rotation (not seen in Europe until the eighteenth century!). Population rose ten-fold from 1400 to 1950 despite little change in per capita income. A nontrivial increase in caloric yield per acre of farmland came from the introduction of new world crops like maize and the sweet potato, which appear in China during the Ming dynasty. Nonagricultural rural work also appears to have been much more developed than in medieval Europe, with William Skinner’s “hexagonal trade” existent during nearly all of the post-Tang dynasties. Such trade allowed cities to develop – around 1000, China had almost 100 cities with population above 10,000, as compared to none in Europe!

More recently, industrialization gets a late start. The 1800s are a giant disaster for China, with wars against Europeans, Russians and Japanese (China lost essentially all of these), the Taiping rebellion that kills tens of millions in the nation’s heartland, Muslim rebellions in the Northwest, and a near complete lack of institutional modernization of the type seen in Japan. By 1890, only 10 miles of rail are found in the whole country, and modern industry makes up only one-half percent of the economy. Despite some fits and starts during the Republican era (especially in Shanghai and Japanese-controlled Manchuria), by the end of World War 2 and the Chinese Civil War, per capita income is no higher than it was during the Tang dynasty. Perhaps the non-vilification of Mao in today’s China has to do with the fact that, even with near-complete autarky, the Great Leap Forward and the Cultural Revolution, per capita income still nearly doubled during the Maoist era, and the industrial share of GDP rose up to match the agricultural share. That is, despite all of the human rights disasters, the Maoist economic performance was simply unheard of in Chinese history. Nearly all of this growth came from capital deepening and (especially) increases in labor supply and the human capital embodied in that labor supply; literacy rose from 20 percent to about 80 percent. And, of course, the economic history since 1976 is well-known – in only three years of the past 37 has GDP per capita grown slower than six percent, an unprecedented streak in the history of the globe.

http://browse.oecdbookshop.org/oecd/pdfs/product/4107091e.pdf (Full PDF version of the published book – big thumbs up to the OECD for making these public. If you are a Chinese speaker, prepare to be annoyed by Maddison’s habit of using Wade-Giles transliteration, i.e., Cheng Ho instead of Zheng He, Yung-lo Emperor instead of the Yangle Emperor, Kwangtung for Guangdong, Tseng Kuo-fan for Zeng Guofan. Speaking of Maddison, his historic income tables (.XLS) are a great way to while away a rainy afternoon. Who knew Australia was once the world’s richest place, or that Sri Lanka was historically a particularly wealthy part of Asia, or that Venezuela was wealthier per capita than all of Western Europe in the middle of the 20th century?)

“The Human Capital Stock: A Generalized Approach,” B. Jones (2012)

(A quick note: the great qualitative economist Albert O. Hirschman died earlier today. “Exit, Voice and Loyalty” is, of course, his most famous work, and probably deserves more consideration in the modern IO literature. If a product changes or deteriorates, our usual models have consumers “exiting”, or refusing to buy the product anymore. However, in some kinds of long-term relationships, I can instead voice my displeasure at bad outcomes. For instance, if the house has a bad night at a restaurant I’ve never been to, I simply never return. If the house has a bad night at one of my regular spots, I chalk it up to bad luck, tell the waiter the food was subpar, and return to give them another shot. Hirschman is known more for his influence on sociology and political science than on core economics, but if you are like me, the ideas in EVL look suspiciously game theoretic: I can imperfectly monitor a firm (since I only buy one of the millions of their products), they can make costly investments in loyalty (responding to a bad set of products by, say, refunding all customers), etc. That’s all perfectly standard work for a theorist. So, clever readers, has anyone seen a modern theoretic take on EVL? Let me know in the comments.)

Back to the main article in today’s post, Ben Jones’ Human Capital Stock paper. Measuring human capital is difficult. We think of human capital as an input in a production function. A general production function is Y=f(K,H,A) where A is a technology scalar, K is a physical capital aggregator, and H (a function of H(1),H(2), etc., marking different types of human capital) is a human capital aggregator. Every factor is paid its marginal product if firms are cost minimizers. Let H(i)=h(i)L(i) be the quantity of some class of labor (like college educated workers) weighted by the flow of services h(i) provided by that class. We can measure L, but not h. The marginal product of L(i), the wage received by laborers of type i, is df/dH*dH/dH(i)*h(i). That is, wage depends both on the amount of human capital in workers of type i, as well as contribution of H(i) to the human capital aggregator.

Consider the ratio of wages w(i)/w(j)=[dH/dH(i)*h(i)]/[dH/dH(j)*h(j)]. Again, we need to the know how each type of human capital affects the aggregator to be able to go from wage differences to human capital differences. If the production function is constant returns to scale, then the human capital aggregator can be rewritten as h(1)*H(L(1),[w(2)*dH/dH(1)]/[w(1)*dH/dH(2)]…). If wages w and labor allocations L were observed, we could infer the amount of human capital if we knew h(1) and we knew the ratios of marginal contributions of each type of human capital to the aggregator. Traditional human capital accounting assumes that h(1), the human capital of unskilled workers, is identical across countries, and that the aggregator equals the sum of h(i)L(i). Implicitly, this says each skill-adjusted unit of labor is perfectly substitutable in the production function: a worker with wage twice the unskilled wage, by the above assumptions, has twice the human capital of the unskilled worker. If you replaced her with two unskilled workers, the total productive capacity of the economy would be unchanged.

You may not like those assumptions. Jones notes that, since rich countries have many fewer unskilled workers, and since marginal product is a partial equilibrium concept, the marginal productivity of unskilled workers is likely higher in rich countries than in poor ones. Also, unskilled worker productivity has complementarities with the amount of skilled labor; a janitor keeping a high-tech hospital clean has higher marginal product than an unskilled laborer in the third world (if you know Kremer’s O-Ring paper, this will be no surprise). These two effects mean that traditional assumptions in human capital accounting will bias downward the relative amount of human capital in the wealthy world. It turns out that, under a quite general function form for the production function, we only need to add the elasticity of unskilled-skilled labor substitution to our existing wage and labor allocation data to estimate the amount of human capital with the generalized human capital function; critically, we don’t need to know anything about how different types of skilled labor combine.

How does this matter empirically? There seems to be a puzzle in growth accounting. Highly educated countries almost always correlate with high incomes. Yet traditional growth accounting finds only 30% or so of across-country income difference can be explained by differences in human capital. However, empirical estimates of the elasticity of substitution of unskilled and skilled labor are generally something like 1.4 – there are complementarities. Jones calculates for a number of country pairs what elasticity would be necessary to explain 100% of the difference in incomes with human capital alone. The difference between Israel (the 85th percentile of the income distribution) and Kenya (the 15th percentile) is totally explained if the elasticity of substitution between skilled and unskilled labor is 1.54. Similar numbers prevail for other countries.

So if human capital is in fact quite important, why explains the differences in labor allocation? Why are there so many more skilled workers in the US than in Congo? Two things are important to note. First, in general equilibrium, workers choose how much education to receive. That is, if anyone in the US is not going to college, the difference in wages between skilled and unskilled labor cannot be too large. For the differences in wages to not grow too large, there must be a supply response: the amount of unskilled laborers shrinks, causing each unskilled worker’s marginal product to rise. Israel has a ratio of skilled to unskilled labor 2300% higher than Kenya, but the skilled worker wage premium is only 20% higher in Israel than in Kenya. If the elasticity of substitution is 1.6, service flows from skilled workers in Israel are almost 100 times higher than in Kenya, despite an almost identical skilled-unskilled wage premium. That is, we will see high societal returns to human capital in the share of skilled workers rather than in the wage premium.

Second, why don’t poor countries have such high share of human capital? Adam Smith long ago wrote that the division of labor is limited by the size of the market. At high levels of human capital, specialization has huge returns. Jones gives the example of a thoracic surgeon: willingness to pay for such a surgeon to perform heart surgery is far higher than willingness to pay a dermatologist or an economics professor, despite similar levels of education. Specialization, therefore, increases the societal return to human capital, and such specialization may be limited by small markets, coordination costs, low levels of existing advanced knowledge, or limited local access to such knowledge. A back of the envelope calculation suggests that a 4.3-fold difference in the amount of specialization can explain the differences in labor allocation between Israel and Kenya, and that this difference is even lower if rich countries have better ability to transmit education than poor countries.

This is all to say that, in some ways, the focus on TFP growth may be misleading. Growth in technology, for developing countries, is very similar to growth in human capital, at least intuitively. If the Solow residual is, in fact, relatively unimportant once human capital is measured correctly, then the problem of growth in poor countries is much simpler: do we deepen our physical capital, or improve our human capital? This paper suggests that human capital improvements are most important, and that useful improvements in human capital may be partially driven by coordinating increased specialization of workers. Interesting.

2011 working paper, which appears to be the newest version; IDEAS page.

“Why was it Europeans Who Conquered the World?,” P. Hoffman (2012)

Talk about an ambitious title! Take it as given that, by the eighteenth century, Europeans had a huge advantage in gunpowder-based technology and tactics, and that this was the primary reason they were able to colonize large swaths of the globe. Why was it that Europeans had such an advantage? The substance gunpowder did not originate in Europe, as is well-known. But Europeans did not even originate certain important tactics, like volley fire with layers of infantry. Nonetheless, from 1600-1800, weapons manufacturing productivity, firing rate, and naval firepower had all increased at an annual rate in Europe which far exceeded the rate of total economic growth or total productivity growth anywhere in the world up to that point. Why?

A common story is that competition in Europe was important. There were many small states who fought often, and hence better and better technology was selected. And Europeans were belligerent indeed! From 1500-1800, the Austrians were at war with a power 24% of the time, the English 53 percent, and the Spanish 81 percent of the time. The problem with the competition thesis, Hoffman points out, is that we have other similar entities: the Chinese were constantly fighting nomads in the north and west, the Japanese were in frequent warfare until the Tokagawa in 1600, and the small states of India were no peaceful assembly before the conquests of the British East India Company. So why, then, Europe?

Hoffman’s explanation is the following. Technology improves from learning by doing. It improves faster the more and the longer you practice, and disseminates easier when costs of dissemination are low. In war, then, gunpowder improves rapidly when countries fight, and when their fighting involves heavy expenditure. Countries go to war when the expected gain from fighting exceeds the expected cost (and they fight rather than settling immediately based on their expectations of the outcome because arbitrary transfers are not easy when the “prize” for winning is something like glory). Countries differ in their variable costs of war because of, for instance, differential abilities to extract tax revenue, and they differ in their benefits from winning war; Indian states may have, for example, had lower benefits from winning war because interdynastic conflict was frequent compared to Europe, and hence the winner of a war may have been sacked by his brother before even having a chance to bask in the glory of victory. Note that “death and destruction” was not a cost of war for most states in this period; indeed, from 1500-1790, not a single European monarch was deposed due to loss in battle in anything but a civil war! Shall we call this the original agency problem?

This model looks a lot like a micro theory tournament plus diffusion of inventions gained from learning by doing. Solve for the equilibrium, as Hoffman does, and you will see that rapid progress in arms technology requires that there is a lot of war using a lot of resources among combatants geographically close enough for technology to transfer easily, and conditions for that to happen are that countries for which gunpowder is effective in war are evenly matched in their ability to raise an army, and that the prize for winning (measured in glory or whatever) is high compared to the costs of battle (measured in the cost of raising revenue for an army, etc.). The Ottomans in this period had too little ability to raise revenue for war. The Chinese were unified internally and fought externally mostly with cavalry, since guns were not terribly effective against steppe nomads. Japan was unified by 1600, hence had no incentive to fight internally and improve their weapons technology, and the fixed cost of invading China or Korea was seen to be too high after some late 16th century adventures. In India, interdynastic battles were so frequent that the benefit of total warfare, as opposed to light skirmishes, was too limited, and hence even though war was frequent, it was at such a low level that there was limited learning-by-doing.

An interesting hypothesis. As invention is my own field of research, I am a bit skeptical of the learning-by-doing mechanism, however. Despite what schoolkids are taught, necessity is absolutely not the mother of invention. We need many things, but we only invent very few of them. Rather, technological feasibility tends to be the important constraint on technological improvement. My hunch is that a detailed investigation of specific microinventions in European military technology would show that they rely heavily on complementary developments in private industry, in scientific research, or in “common” engineering. Indeed, I would suspect that many of the important inventions come from places not known for their belligerence; Hoffman even mentions an important Swiss cannon foundry whose technology was critical to French artillery in the 1700s. Such importation from non-military external sources is not uncommon: later on, we have the American engineer Hiram Maxim inventing an early machine gun, and the Dutchman Fokker playing the most important role in airplane technology in World War I. The ability of the UK and Germany to procure these inventions has less to do with the frequency of war in those countries, but instead simply results from the fact that Western Europe and America had, by this time, developed large amounts of non-military engineering talent.

March 2012 working paper (no IDEAS version). This paper was published in the September 2012 issue of the Journal of Economic History. If you find it interesting, Hoffman recently published a book Why the West Rules – For Now which has come highly recommended to me by a well-known historian of this era. [CORRECTION: As noted by Mark Schaffer below, Why the West Rules is by Ian Morris, not Philip Hoffman. Nonetheless, it is still a great book!]

“Directed Technical Change,” D. Acemoglu (2002)

If I increase the supply of something, its price should go down. And if I decrease the supply, its price should rise. Some markets do not seem to follow this pattern, however, with skilled labor in the US since 1970 being a famous example. As the percentage of college-educated workers has risen the U.S., the premium paid to the college educated has also risen. How can this be? One hypothesis is skill-biased technical change: the innovation that has occurred over the past few decades, computers included, has been complementary with the skills of educated workers. When might we expect innovation to complement certain factors?

An old and incorrect answer, previously discussed on this site, is that innovation will replace “expensive” factors of production. If labor is dear, for instance, firms will try to invent machines to replace labor. This intuition is wrong: in competitive markets, all factors are paid their marginal products, so saying labor is “dear” is just like saying labor is productive. And you might imagine we’d want to develop innovations that are complementary to our most productive factors!

Daron Acemoglu has a nice paper from a few years back – already very highly cited – dealing with these issues. Take a good produced using two factors with a CES production function; that is, the way in which factors are substituted for one another does not depend on how much of each factor we are already using. Let each factor have its marginal productivity improve by technology multipliers A1 and A2, and let innovations (which increase A1 or A2) be developed in any structure where the amount of new innovation responds in the natural way to the social value created by improving the technology multiplier. Acemoglu uses a monopoly innovator, but broader assumptions here about how social value is captured will not change the basic point.

The social value of innovations in each factor are increasing in the price paid to the factor and the total quantity of that factor used. If one factor is, say, skilled labor, then my incentive to create innovations improving the productivity of skilled labor depends both on how much skilled labor will be used, and on how productive the marginal skilled labor already is (since my invention is a multiplier on the existing marginal product). Imagine now that I increase the relative supply of skilled labor, exogenously. Will I see more or less skilled labor-augmenting invention? On the one hand, there is more skilled labor, so I can sell my innovation to a bigger market, but on the other hand this extra labor has a lower marginal product, so there is less productivity to enhance. Which effect dominates? With CES production, there is a simple rule. If the two factors are gross substitutes, an increase in the relative supply of a factor will increase the incentive to develop innovations augmenting that factor, and vice versa for gross complements. That is, with gross substitutes, an increase in the supply of one factor will not affect the relative factor prices (read: relative marginal products) very much, so the effect of an increased amount of that factor which I can augment dominates the effect of lower marginal product on that factor.

In the short run, before innovations can be created, the now more abundant factor sees its rent (wage) decline. This is the usual substitution effect. But what about in the long run, after technology is created? Here we need to model explicitly the monopolists who create inventions. It turns out that if the elasticity of substitution between factors is sufficiently high, an exogenous increase in the relative supply of one factor will increase the rent received by that factor. That is, the long run factor demand curves will slope up! This is because when the factors are gross substitutes (the elasticity of substitution is at least 1), innovation will be directed toward the now more abundant factor. The higher the elasticity, the more innovation. At some point, there is so much productivity-enhancing innovation directed toward the more abundant factor that even though the marginal units of this factor were relatively unproductive without the innovation, and hence received a lower wage, the response by innovators will be high enough that the now-more-abundant factor is paid even more than it was before the exogenous supply increase. A quick aside: theoretically, the increased elasticity (though not the sign change) of long-run response vis-a-vis short-run response is well known. It is called the Le Chatelier Principle and comes to economics via Paul Samuelson. Milgrom and Roberts have a lovely paper on why Le Chatelier works. The three theorems in this paper are proof positive of the usefulness of monotone comparative statics. Topkis is used to prove a result in two lines that must have taken pages to prove, and in less generality, with earlier techniques.

Consider again the concrete example of skilled labor since 1970. Goods are produced with skilled and unskilled labor. The supply of skilled labor increases, due to the GI Bill and other exogenous factors. This causes the skill premium to fall initially. If the elasticity of substitution is above 2, the long run wage premium to skilled labor will increased due to the effect of incentives to develop technologies augmenting the now larger base of skilled labor. This is one explanation for why you may have seen skill-biased technological change after the 1960s, and why there may have been enough of it to raise the skill premium. (Note that the elasticity of substitution itself is fixed in this model, but you might imagine that certain types of innovations may affect this factor.)

Those interested in Acemoglu’s work may enjoy an empirical paper by a PhD student on the job market this year, Walker Hanlon, applying Acemoglu’s result to the context of the Cotton Crisis, the shift in Britain from using US to using Indian cotton during the US Civil War. He has some nice data showing that even though Indian cotton became relatively abundant, there was a great amount of invention dealing with gins and other techniques for handling idiosyncratic issues in the Indian supply, and that the elasticity of substitution between US and Indian cotton was high enough that, indeed, the relative price of Indian cotton to US cotton rose by the end of the Civil War despite the relative abundance of the Indian cotton.

Final REStud version, Oct 2002 (IDEAS)

“The Three Horsemen of Riches: Plague, War and Urbanization in Early Modern Europe,” N. Voigtlander & H.-J. Voth (2012)

Malthus was, broadly, right in his description of the world before 1800. Almost all income was agricultural income, and agricultural income was dependent largely on a fixed factor of production, land. As production technology became better (which happened at a very slow rate), wages increased, lowering death rates and increasing birth rates, which led to growing population. As population increased, less fertile land was brought into production, lowering per capita income. Per capita income fell until the birth-death ratio was again in steady state, with society at a higher level of population than before the new technology, but no richer overall.

This story is only broadly true, however. We do see regions diverge slightly: Europe becomes twice as rich as China by the 1700s, for instance. In a Malthusian world, how is this possible? Voigtlander and Voth propose an interesting new mechanism – their model is much more complicated than what I present here, but the spirit is the same.

Take as given that increased wages led to greater urbanization (people above subsistence have a taste for goods that can only be produced in cities), and that the Malthusian mechanism above holds, returning us to the subsistence steady state after shocks. Europe is rather unique in the following way: higher levels of urbanization there were quite deadly by world standards. Voigtlander and Voth mention three particular reasons why. First, European cities tended to both be filthy and high density. Human waste was often just tossed onto the street in Europe, whereas in China it was much more common to carry the waste to the countryside for use as fertilizer; partly for this reason, China had relatively high rural mortality, and Europe relatively high urban mortality. Second, geography and political circumstances in the early modern era meant that warfare was much more common in Europe than in other parts of the world. Wars of this era generally just meant increased death by disease rather than mass destruction of capital. Third, urban centers traded more, and common disease resistance across regions in Europe was not as prevalent as in China.

Think of this on a standard Malthusian graph. Putting quantity on the vertical axis and income on the horizontal axis, in the steady state equilibrium, the wage is determined by the intersection of a downward sloping death schedule (higher wages=less mortality) and an upward sloping birth schedule (higher wages=more births). A population shock hits: in this case, the Black Death kills an enormous percentage of Europe’s population beginning in the 1300s. Lower population means a temporarily higher wage in the Malthusian mechanism. The higher wage leads to greater urbanization. In Europe, but not in other regions experiencing negative population shocks, the greater urbanization leads to a higher death rate. That is, the death schedule shifts up and to the right. The new steady state intersection of the birth and death schedules that we return to is at a higher income than before the shock. So long-run incomes have increased following a temporary shock, even in the Malthusian world. A nice trick! Note also the counterintuitive nature of the result: Europe prospers in the centuries after the first plague precisely because of its violent, disease-ridden nature. That means you should be careful to interpret the results as explaining why incomes rose, not as arguing for any increase in welfare.

The authors also attempt to show, via a calibration exercise, how relatively important urbanization, disease spread from trade and disease/killing from war are in allowing Europe to grow. These type of exercises are not really for me, but check it out if you are interested – they assign most of the income gains in Europe to the effects of more frequent warfare made possible by taxing urban workers.

Dec. 2011 Working Paper (IDEAS)

“Patent Laws, Product Lifecycle Lengths, and the Global Sourcing Decisions of U.S. Multinationals,” L. K. Bilir (2011)

It’s something of a mystery in the IP literature why small, developing countries would ever enforce intellectual property rules. The standard tradeoff is higher prices in exchange for more innovation. But the innovation is useful no matter where it comes from. So unless you are a relatively large, prosperous country, it’s unlikely to be worthwhile trading off higher prices within your country due to the limited monopoly of IP for a tiny increase in inventive activity. Indeed, the US did not enforce foreign copyrights, for example, until the 20th century, much to the consternation of Charles Dickens. Of course, in practice many nations strengthen IP laws because they are coerced into doing so in exchange for other beneficial trade liberalization – see the TRIPS agreement. But outside of trades of this type, might there be another reason for strengthening IP in the developing world?

L. Kamran Bilir argues that there might be in a new working paper which she presented here earlier this week. Multinationals make up the bulk of international trade (and international technology transfer) and have many options of where to place their new plants. But they are worried that if they locate in a region with weak IP, there is a strong incentive for some local company in that region to rip off their product. Assume that such imitation can only happen if a plant or affiliate plant of the MNC is located in the foreign country. Assume also that figuring out how to imitate involves some stochastic investment by a would-be imitator. A simple model gives the following predictions. First, products whose commercial usefulness is very short don’t worry about imitators: by the time the iPhone is knocked off, Apple has a new model ready to go. These industries will always produce overseas in order to access cheap labor, regardless of formal IP laws. Second, products whose commercial usefulness is of moderate length might be coerced to locate overseas earlier in the product lifecycle if, at the margin, IP laws strengthen. The idea is that, with relatively stronger IP, the incentive to imitate will be weaker because stronger IP lessens the expected profits the imitator can expect to make; you might imagine “stronger IP” as “higher probability that the government will shut you down for selling products that violate a foreign patent.” Third, products with long commercial lifecycles spend less of the product lifecycle producing overseas after an IP strengthening than the marginal intermediate-length products. The response of MNC offshoring to IP changes, then, is nonmonotonic in the product lifecycle length.

Bilir then uses data, in a number of different specifications, from dozens of countries and over 30 years. She finds precisely this nonmonotonic effect. The measure of “average product lifecycle” (or, in another specification, 90th percentile product lifecycle) is constructed from forward citations in the US patent database by industry, and of course you might question this portion of the methodology, but it’s not ridiculous on face; you might also not like the measure of IP strength used, though it is pretty standard in this literature for better or worse. The nonmonotonic effect of stronger third world patents is seen not just in affiliate sales, but also in affiliate size and in the number of affiliates employed. A sensible interpretation is that third world countries can use stronger IP protection to attract MNC investment, but that policies will be unsuccessful for firms like software with short lifecycles and will be relatively unsuccessful with products like machine tools that have long lifecycles. What’s nice here is that the impact of IP on MNC location is identified in and of itself: IP changes often happen concurrently with other liberalizations in a nation’s economy. The identifying power here is that year and country fixed effects will pick up those other liberalizations while the differential impact of the IP strengthening across sectors with different product lifecycles (presumably affected in similar ways by non-IP reforms) let us isolate IP.

Two more things I would like to see. First, the formal tradeoff between reliance on secrecy and reliance on patents seems important here. This is related both to the ease of knocking off a product (drugs, for example, are easy to reverse engineer) and the importance of local legal systems in maintaining non-patent contracts like “do not disclose” policies. Perhaps this should enter the model? Second, I have an idiosyncratic preference for welfare estimates in policy-related papers, even if such estimates are only back-of-the-envelope. In this case, assuming standard learning-by-doing and technology transfer to affiliates, is it worth it for, say, China or Nigeria to increase their enforcement of IP (raising domestic prices) in exchange for some new jobs and tech transfer for the new MNC affiliates? A rigorous discussion here would lengthen the paper too much – it is already quite a monster – but a two page rough-and-dirty estimate would be useful indeed.

http://www.stanford.edu/~kbilir/Bilir_IP_and_MNCs.pdf (July 2011 Working Paper)

“The Burden of Knowledge and the ‘Death of the Renaissance Man’: Is Innovation Getting Harder?,” Benjamin Jones (2009)

I do love a good piece of applied theory. I think of applied theory as the following. Gather some set of stylized facts about the world. Make zero attempt whatsoever to identify causal arguments from the data itself; no IV estimation, no discontinuity design, no random assignment, no natural experiments, etc. Rather, write a model of economic behavior which can simultaneously generate all of the above facts. To the extent that the model also implies some other facts about the world, don’t worry about it; the model is a metaphor, as I’ve discussed on this site in the past. I don’t mean to imply that a model is good iff it can explain some limited sphere we care about, as Friedman argued. I mean a model is good if it can provide a plausible guide to our thinking about an inherently messy social science problem: that is what is meant by “metaphor.”

I can’t help but see the following problem in other empirical literature (whether pure reduced form, or filled with fancy econometrics), particular that in the non-econ social sciences, since applied theory of the type described above is very uncommon outside our field: without a model, I don’t know how to evaluate counterfactuals. I don’t know how to give advice to future policymakers when some fact changes vis-a-vis the period examined in the paper. I have to worry too much about data quality, and social science data is uniformly terrible. Most importantly, I am often limited to examining questions of a very specific type, a problem particularly common in the natural experiment crowd. This is because the amount of economic theory that I can include in an exclusion restriction, for example, is much less than I could include in a full model. This isn’t to say that papers can’t do nice modeling *and* nice theory: the best do both! Ben Handel’s health insurance paper, or Todd and Wolpin’s PROGRESA paper, certainly do both. I am also aware that the vast majority of empirical economists do not agree with all (or even any!) of the above: I’m going to post Imbens’ counterargument to the benefits of applied theory here soon.

In any case, in The Burden of Knowledge, Ben Jones uses Hall’s patent database to establish the following stylized facts. Teamwork increases over time and is higher in fields requiring more base knowledge. Specialization, measured in the (inverse of the) probability of an inventor switching fields from one patent to the next, is increasing over time and is lower in fields requiring more base knowledge. Age of inventors when they get their first patent is increasing over time, but does not appear to vary based on the base level of knowledge in the inventor’s field. Base knowledge is measured in an interesting way. A field requires more base knowledge if patents in the “tree” of patents cited by a patent. That is, my patent cites 6 other patents, which each cite 6 more, which each cite 6 more, and all of the rest are patents from before 1975 (and thus not in the data), then my patent’s tree has 216 cites. A quick glance at summary statistics suggests that this measure is correlated with what intuitively seem like “more advanced” fields.

At this point, no attempt whatsoever is made to establish a causal relationship using the data. Instead, Jones writes down a macroecon-style general equilibrium model. Every individual chooses to invent in a given field, or else to be a production worker. Inventors are paid rents equal their marginal productivity, and workers are paid via a no-profit function on firms. Each field is represented as a cylinder, with the height representing the difficulty of reaching the frontier in that field, and the outside of the circle representing various specializations within the field. An inventor “buys” a field, and a breadth within that field represented as an arc on the base of the cylinder, paying an amount that is a function of the area of that slice of the cylinder.

Over time, ideas arrive at each inventor at a rate which varies across fields. Buying more breadth gives you a higher arrival rate for ideas. Having more inventors near you lowers the arrival rate (you duplicate inventions, basically). A higher level of societal productivity can either increase the arrival rate, as in Romer, or decrease it, as in the “easy inventions are being fished-out” hypothesis. In order to implement an invention, the “circle must be covered”: the inventor must pay other inventors in his field such that their combined breadth covers the circle.

Now just solve the model in equilibrium, along a balanced growth path, meaning societal productivity growth is constant (letting population grow at some exogenous rate). The model gives that, at any time, spending on education is proportional to lifetime income for the inventor. This proportionality holds regardless of the difficulty of the field. Since education is just a portion of a cylinder, this immediately gives that breadth is higher in fields where the state-of-the-art difficulty is lower. Since inventions are implemented only when the circle is covered, teamwork must increase in more difficult, more specialized fields. I find the cylinder model of innovation quite elegant. On the other hand, I don’t know why 20 pages of algebra and explanation should be required to explain the last two paragraphs of results: would that economics journal editors edited more strictly for length!

The interesting empirical extension, I think, is this: some inventions are “stepping stones”, in that in order to discover C, I must first learn A and B, and even after C is discovered, I can only know C if I know A and B. For instance, let A be arithmetic, B be algebra and C be calculus. Other inventions are all-encompassing: once I know C, I know everything relevant to the world in A and B and no longer really need them. Once you know modern control and dynamic programming, you can solve any problem you would have solved with calculus of variations, plus more: for applied work, CoV doesn’t need to be learned at all anymore. Inventions of the second type are much more socially beneficial than the first type. Which type is becoming more common over time, though?

http://www.kellogg.northwestern.edu/faculty/jones-ben/htm/burdenofknowledge.pdf (Final WP – final version in ReStud 2009)

“Culture and Institutions: Economic Development in the Regions of Europe,” G. Tabellini (2010)

The subtitle of this paper should be “Historical institutions do not explain why Southern Italy fares so poorly.” Particularly since the work early last decade by Acemoglu and his coauthors, there has been a lot of research into how historical institutions affect modern economic outcomes; for instance, colonies that made for good plantations 300 years ago tend to see lower incomes today, presumably because the optimal institution in the plantation era has to some level persisted, and such institutions are not conducive to growth. But this argument is not wholly convincing: revolutions, such as those in the post-colonial era, have effected enormous changes in institutions without overthrowing the historical legacy. What might explain this? Tabellini looks to Italy for answers. Historical institutions also affect culture, culture persists, and culture helps determine economic outcomes (e.g., trustworthy societies see higher growth). The author uses regional output data from eight European countries, where modern institutions are roughly identical within each region, to assess whether differences in historical institutions (say, high illiteracy) might have persisted (say, through less trust of others) to differences in modern outcomes.

Credit to the author for honesty – the instrumental variables he uses do not appear, in the sense of statistical tests, to be particularly valid. Nonetheless, the result that historic institutions can have effects through routes other than modern formal institutions is robust to sensitivity analysis. My bigger worry is whether anything whatsoever about historic institutions is captured through this paper. In particular, might it just be that culture itself was different in Northern and Southern Italy in 1850, and that the culture has persisted, with no reference to prior institutions? I think the same critique is valid for much of the work in this strain of literature. Nonetheless, measuring historic culture as distinct from governments and economies is a difficult thing indeed – even Max Weber was not wholly successful.

http://www.mitpressjournals.org/doi/pdf/10.1162/jeea_a_00001 (Final JEEA version, available free without registration as of the date of this post)