Monday, July 15, 2013

What models predict the hockey stick? Only one that I am aware of (although I am new to the field - so please suggest others)

David Friedman puts his finger on something that has always bothered me about the "bourgeoisie virtues" argument of Deirdre McCloskey. It's a popular one and for good reason - what self-respecting economist is going to respond by minimizing the importance of attaching dignity to bourgeois values? In full disclosure I haven't read the books - this is something that's bothered me from talks she's given about it as well as discussions of it on the blogosphere.

The point is that economic growth is a hockey stick and that bourgeois values explain the rapid growth of that hockey stick. But Friedman points out that if we want to explain the hockey stick we really ought to have some sense of the equilibrium process that produces the thousands of years of (more or less) stagnant human existence that form the horizontal part of the hockey stick.

He reaches out for Malthus - an excellent choice - but then puzzles over what went wrong with Malthus. Like McCloskey he only really explains half the hockey stick.

The only growth model that I know of that explains the whole hockey stick, and the demographic transition to boot is the Galor-Weil model with endogenous fertility and a trade-off between quality and quantity of children that eventually results in a demographic transition. I'm not sure if Friedman is familiar with it, but it contains some of the features that he discusses (most notably a relationship between population density and productivity growth). It also adds human capital, which you need more of as productivity growth gets higher. This is the mechanism that causes the demographic transition to set in.

"Unified growth theory", as it's called, is one of the most exciting things I've ever studied in economics. Unfortunately I'm not sure I'm smart enough to push the frontiers of this cutting edge work, but hopefully I'll get opportunities to play around with it. And it's nice precisely because it takes insights like this from classical economics seriously. I am not sure McCloskey has the answer on growth theory - I prefer to take her thesis as an extension of her rhetoric in economics research agenda, and an important contribution to the way discourse shapes the evolution of market economies. I am not sure it's the key to understanding growth.


  1. I find Deirdre's model quite compelling as a partial explanation. There is an anthropological theory that cave art was a way to demonstrate to our mates that we were able to provide basic resources with more leftover. That is more about sexual selection, but it has the same premise of the benefits to accumulating more than simple sustenance.

    David's 2% growth perspective pastes over the punctuated way that progress typically occurs. Deirdre seems to make a case for the empowerment of the entrepreneur. The light vs candle example David brings up is also used in George Gilder's new book, Knowledge and Power. He sets up a model of technological progress analogous to Information theory. Innovation is by nature unexpected. So you might picture many individual hokey sticks. His primary example is Qualcomm's impact on cellular signaling. He has a chapter on Romer and suggests that copying of institutions provided a low entropy background, making high entropy innovation possible.

    I think the flat part is best explained by the suppression of the entrepreneur.

    1. "Innovation is by nature unexpected."

      NOOOO! Some innovations are a surprise but not all. Thomas Edison's greatest success was the establishment of an industrial research lab which sought out innovation in a systematic way. Long after Edison was gone that lab gave us, for example, information theory and the transistor. In the time of Lavoisier people knew there were discoveries to be made in chemistry and sought them out.

    2. If it is something "new" then it has to be a surprise. If we knew it before, it would not be an innovation. Gilder compares innovation to information in information theory. Only surprise qualifies as information. People may know discoveries are to be made, but they don't know what those discoveries are or what impact they will have. We don't even know if they will be adopted despite how beneficial they could potentially be.

      I see it as analagous to genetic mutations. Suppose we knew the rate of mutation of DNA in an organism and managed to correctly predict what parts of what proteins would be mutated, quantitative predictions of the utility of those mutations and the probability that the new gene gets fixed in the population, would be very problematic in any model.

    3. Though that tends to be true of the large leaps that are sometimes made it isn't generally true.

      We normally define innovation as the application of invention to practical tasks in the commercial world. I work on silicon chips, so I'll use that as an example. The circuits on these chips are composed from many "blocks" that provide particular functions, often these are made from even small sub-blocks. A great deal of optimization goes into each of these. This is done by simulation or by building and testing. This refinement is so steady that it's very hard to define it as a "surprise". The combined result of this is that each type of block is constantly being improved. So, if you make a chip of type X using the library blocks that a particular company owns in, say 2010, then you do the same thing in 2013 the result in 2013 is likely to be better. Of course there are "surprises", I spend a lot of time dealing with those myself. Quantitative estimates of how change will occur are very difficult, but things aren't entirely surprising.

  2. There are loads of possible explanations for the long period of stagnation before 1770, and loads of explanations for the long period of growth that followed it. Finding which is right is an incredibly complex task. It will take many decades to get close, it already has taken centuries since people have been debating this since it happened.

    1. On the "loads of explanations" point, this is an important thing to keep in mind. Obviously you don't need a single theory to explain all parts of the hockey stick either, but it's understandably dissatisfying to just attribute the arrangement of all those explanations to luck. I'm not one that needs to endogenize everything, but I prefer to leave parameters non-endogenized if I have a choice - not whole processes - which is part of the appeal of Galor-Weil.

  3. Some people are sceptical that there was a growth "Hockey Stick", I'm not sure myself. Some economists at the time didn't believe it for example, this is Nassau Senior from 1850:-

    "The comforts and conveniences which we now expect in an ordinary lodging, are more than were enjoyed by people of opulence a century ago: and even a century ago a respectable tradesman would have been dissatisfied if his bed-room had been no better furnished than that of Henry VIII., which contained, we are told, only a bed, a cupboard of plate, a joint-stool, a pair of andirons, and a small mirror. And yet Henry was among the richest and the most magnificent sovereigns of his times. Our great grand-children perhaps will despise the accommodations of the present Age, and their poverty may, in turn, be pitied by their successors."

    1. If you doubt that there was a growth "Hockey Stick", check out Oded Galor's presentation "From Stagnation to Growth: Uni…fied Growth Theory". The presentation (ungated) is available on the Internet. He provides more than sufficient evidence to prove that one occurred. Why is a different matter.

  4. I think its safe to say that Ben Franklin and Thomas Edison made major contributions to economic growth. Thomas was one of 7 children and Benjamin was one of 17. I think the Malthusian explanation is exaggerated.

    The one-offs are critical contributors and difficult to account for. Look at Elon Musk. His open source release of his hyperloop plan could revolutionize travel. It might be possible to account for such advancements in a model, but from what little Ive read, I think Unified growth theory has a long way to go to do that.

    1. I'm not sure what you mean by "the Malthusian explanation is exaggerated". Do you mean the quantity/quality tradeoff I mentioned? That's not really Malthusian - that's just a budget constraint point. As far as Franklin and Edison go, I don't think the presence of notable distributional tails changes any of this. Put it this way - I can't think of how distributional tails changes the story, but maybe you could explain.

    2. Actually, I have too many thoughts on the population aspect. I'm not convinced that population growth is a cause of wealth stagnation. To me that seems to similar to people with a scarcity mindset who say immigration will reduce jobs. I realize that resources are finite, but innovation is not. I would think that resources per capita is only a limiting factor if the the output/resource ratio is static or growing very slowly.

      I brought up the family size due to some side thoughts. The main point I intended to make was that BF, TE and other individuals contributed greatly our prosperity and technological advancement. Some version of their contributions would have come about anyway, and I may put too much emphasis on entrepreneurs, but I have to question whether hurdles to individuals like them were unsurmountable in the past.

    3. Ken P.,

      Galor and others shows a strong inverse relationship between population and prosperity before the industrial revolution. It's not a controversial result. After the IR takes off, both population and per-capita income rise rapidly.

  5. The Enlightenment values of individual freedom and rational inquiry played a big role in the technological take off. If you want to really understand you probably need to look at technological and scientific progress from 1750 to 1900. The advances in chemistry and physics between 1750 and 1900 had no precedent since the harnessing of fire and the first use of stone tools a million years earlier. The fact that there were enormous scientific advances waiting to be made is what made the hockey stick possible.

    1. This is an important point. One way to put this is that entrepreneurial discovery of new ways to produce technological growth came online.

      Although I didn't talk about it here there's one thing that's always bothered me about unified growth theory too - and that's that the mechanism for technological growth is for the most part population density (a Smithian mechanism, in other words). That's fine but it seems to me there are other important determinants.

      Given that shock to technology, you have an explanation for the take-off and then the demographic transition, which I still like.

      So next we need an explanation for the emergence of the scientific method...

    2. "So next we need an explanation for the emergence of the scientific method..."

      At the risk of offending lots of people - I suggest that the modern roots of the Enlightenment and the scientific method both lie in the Reformation.

    3. All,

      There is a good book on this subject. See "Energy and the English Industrial Revolution". The summary follows.

      "The industrial revolution transformed the productive power of societies. It did so by vastly increasing the individual productivity, thus delivering whole populations from poverty. In this new account by one of the world's acknowledged authorities the central issue is not simply how the revolution began but still more why it did not quickly end. The answer lay in the use of a new source of energy. Pre-industrial societies had access only to very limited energy supplies. As long as mechanical energy came principally from human or animal muscle and heat energy from wood, the maximum attainable level of productivity was bound to be low. Exploitation of a new source of energy in the form of coal provided an escape route from the constraints of an organic economy but also brought novel dangers. Since this happened first in England, its experience has a special fascination, though other countries rapidly followed suit."

      The bottom line is that once mankind adopted the steam engine (and its progeny, the internal combustion engine, the steam turbine, the gas turbine, etc.), the conventional Malthusian constraints no longer applied.

      To put this in perspective, Americans consume around 80 times as much industrial energy as chemical energy from food.

      Why the industrial revolution came first to the UK? Why it happened when it did? Why it didn't happen earlier or elsewhere? These are all valuable questions.

      However, that doesn't change the bottom line. The hockey stick is a coal and steam engines story. Anything else simply misses the facts.

  6. Any model that predicts a hockey stick (hyperbolic change) in unexceptional circumstances is surely wrong. Any model that does not predict geometric change (a straight line on log paper) in normal times is questionable. (Although we may get asymptotic change as limits are approached.)

    There are S-curves (ogives) that look like a hockey stick at first, but then level off in the limit.

    1. Yes - this is what's so nice about the Unified Growth Model! It explains the demographic transition which is the very beginning of the leveling off.

      Granted, I'd be more willing to accept genuine hockey sticks in the case of technological growth (or at least a much, much longer delay until leveling off)

    2. That is, for an explanation of the sweeping changes of the 18th century I would look to historians instead of modelers. :)

    3. A leveling off could occur because of resource limits. It could also occur for social reasons, such as a return to a caste society. Most of human history has been one of low growth. In fact, in ecology a dominant species is one that is in balance with its environment. High growth alleviates the problem of inequality, as it allows those on the bottom to better their living conditions. What kind of society do we want for a low growth future?

  7. Timur Kuran has some interesting papers on 'Collective Conservatism,' which certainly apply to this case.

    But more than that, there were some historical episodes where there was the glimmer of "Bourgeois Dignity." Novgorod in Russia, some of the Italian states, Ming China. These examples just didn't persist, for one reason or another (usually because if they started getting rich, someone would come take them over).

    One factor is army vs navy as the primary military force. Armies produce human capital specific to mobile land hierarchy that can extract value by inhibiting trade; navies benefit from (and develop) human capital that encourages trade (hence the Navigation Acts), usually. So, in France it was the case that "engineer" meant "engineer for the army" while in Britain, engineers had a multitude of purposes. "Bourgeois Dignity" is difficult to maintain when the army is a central feature. It's no surprise, I think, that 1) Britain did not develop until the island was no longer fighting and 2) Britain and Japan were the first in their respective regions to develop, for this reason. Britain really didn't have that much of a leg up on Prussia and France, except that their conflicts decreased the centrality of their aristocracy and the continent's conflicts increased the importance of the aristocracy. (I think this story is fairly consistent, too, with AJR's 2005 "The Rise of Europe."

    1. The simple fact that the sea provides a natural defence has always been useful to Britain. The relationship between Britain and mainland Europe has generally been asymmetric. European powers had no friendly port to dispatch troops to on the British Isles. But because there are many nations in Europe, Britain always had a friendly port to land an army in on the European mainland if they wanted to.

      This advantage was something understood at the time, for example here is the speech given by John of Gaunt in Shakespeare's Richard II:

      "This fortress built by Nature for herself
      Against infection and the hand of war,
      This happy breed of men, this little world,
      This precious stone set in the silver sea,
      Which serves it in the office of a wall"
      Or as a moat defensive to a house,
      Against the envy of less happy lands"

      I think this is one of the main reasons why Britain was the first European country to have an industrial revolution. It doesn't explain why Europe as a whole reached conditions that were ripe for that revolution in the 18th century.

  8. "There are loads of possible explanations for the long period of stagnation before 1770,"

    There might be loads out there but only one that works. Malthus. Precisely because this period was so long you need and explanation that can apply across centuries, even milennia. And across widely varied societies, from hunter-gatherers, to feudal serfdom, to quasi-market oriented economies. Institutions rise and fall. Technology accelerates and decelerates. Revolutions and wars and scientific achievements. Yet, income stagnates for 100,000+ years pretty much everywhere. There really is no other explanation other than demographic forces.

    This doesn't mean of course that everything before the Industrial Revolution boiled down to demographic factors. The speed of the demographic dynamics matters too. If someone invented a better windmill the increase in standard of living from such an innovation could still persist for a century or two - although it was slowly ground away by the expanding population. If you want to know what caused the price revolution of the 16th century in Europe, it's best to forget about demographic forces (though some historians have tried, incorrectly, making that Maltusian too) and look a the M and V. That doesn't change the fact that as a broad framework for understanding long swatches of history Malthus is pretty much the only game in town.

    "and loads of explanations for the long period of growth that followed it."

    And this is true as well, but here you're on firmer ground. The Industrial Revolution happened only once. Barring collapse of our civilization, a Neolithic restart and then another Industrial Revolution at some point in the future... well, it's possible to fit an infinite number of regression lines through a single data point. So yes it's entirely possible that more than one theory or cause is consistent with the data we have for The Singularity. And it's entirely possible, likely even, that given we only really have one observation, we won't ever really understand what happened.

    It's not all bad. Those lines still have to pass through that single point. Whatever theory one wants to fit to the data, it still has to fit the data. Maybe the best we can do is to limit it to a SET of plausible explanations, eliminating hokey or not-quite-there stories. And as far as that goes Galor & Weil is very much in that set. McCloskey... I'm not so sure about.

    Also, it looks to me that if you just modify the word "labor" in Friedman's post to "human capital" then that sounds a lot like Galor & Weil, just without the formal modelling.

    1. "Yet, income stagnates for 100,000+ years pretty much everywhere."

      You mean before 10,000 years ago. Right?

    2. We know that ordinary people in that past were poor, but apart from that we don't know very much. It's not at all clear if ordinary people in, say, 18th century England were richer or poorer than those in 14th century England. The statistics aren't there, certainly things can be imputed without the need for statistics and that's an ongoing task, but it hasn't produced a clear consensus.

      You accept that there were variations in technology and these produced variations in wealth. But, you only accept one force acting in the other direction: the size of the population. But there are many other candidates, for example, disease and war. There need not be one sole explanation and there may be a single explanation that isn't population. Take war for example. Suppose, like Shakespeare's John of Gaunt, that whenever the wealth of a country increases due to productivity that wealth is taken by neighbouring countries in wars. Similarly, if the wealth of an area of a country increases it's taken by the elite of that country for it's purposes. That would explain just as well why income always stagnated in the long-run before 1770.

    3. " It's not at all clear if ordinary people in, say, 18th century England were richer or poorer than those in 14th century England"

      Actually for England for these time periods we do have a pretty good idea. Not perfect, but pretty good. Because English history was so damn boring, in relative terms, by the standards of an average country in the world, lots of data was collected and kept and it wasn't destroyed in wars, civil wars, invasions or upheavals.

      Late 14th century Englishmen had a standard of living roughly comparable to that of mid 18th century Englishmen. Early 15th century Englishmen were most likely richer than their 200 years later counter parts.

  9. Agriculture was independently developed in four or five places over a relatively narrow time frame. Maybe give a thought to the "economic" forces that could have driven that sort of "simultaneous" independent development.

  10. Absalon, yes, in a way that's a potentially more productive research agenda. There's more observations that any theory has to fit so we can possibly get a more precise answer.

    Here are two interesting blog posts on the topic (not mine)

  11. Dears, I am always stunned by the highly endogenous character of blogging. Dan confesses that he hasn't read the book . . . yet elaborates his opinion of it! Dear Dan: Really, now! Oh, well.

    I'm working busily on Vol 3, and as I said to David Friedman on his blog (at least David had started to read the Actual Book!):

    The book makes a pretty extensive, quantitative case that trade, exploitation, coal, markets couldn't explain a one-time hockey stick blade---until the ideological changes of the 17th and especially the 18th century (David expresses it well by noting that inherited wealth was long thought blameless compared with earned wealth, about which suspicion hung). Briefly, if the modern world is unique, as it is, then routine economics (except Austrian discovery) can't explain it, since other and older societies had all the material conditions put forward in the routine: property rights, trade, exploitation, coal, whatever. One has to be comparative and historical to test such a claim. Theory won't do it, which is what is disappointing about "new" growth theory.
    In the next volume, which will be the third and last (I've decided that six volumes would be lunacy), I develop the evidence for the hockey stick, in case you doubt the uniqueness of the modern world. (Put your orders in early to the U of Chicago Press, for a late 2014 pub!). I start of course with a Malthusian explanation for the handle. You can also explain the handle (I note there) with exploitation by elites and with density-causing-disease. But anyway, lacking modern liberty and dignity for ordinary people the frenetic innovation of the past 200 years couldn't get going, and most of our ancestors dragged along at $3 a day. Now worldwide we earn and spend $33 a day, and in the steadily multiplying rich countries over $100 a day: a hockey stick indeed, and uniquely modern.

    Regards, Deirdre

    1. "But anyway, lacking modern liberty and dignity for ordinary people the frenetic innovation of the past 200 years"

      I sure hope you haven't built a career around that proposition. The early impetus for scientific advances seems to have come from elites. Freeish markets helped as did civil rights for the upper middle class but "modern liberty and dignity for ordinary people" is a result of the technical revolution of 1750 to 1880, not the cause.

    2. Hmmm... I was pretty careful to say I was NOT responding to the book BECAUSE I hadn't read it.

      Deirdre I don't think I've mentioned you once on this blog disapprovingly. I'm a big fan. I just think Galor-Weil has a lot to offer and I think David Friedman has really gotten in there and highlighted what it offers.

    3. In other words, please don't confuse an endorsement of Galor-Weil with a criticism of McCloskey. I don't generally think of these discussions as battles.

    4. "But anyway, lacking modern liberty and dignity for ordinary people the frenetic innovation of the past 200 years"

      Until 1832, suffrage in the UK was limited to 1.5% of the adult population. By 1830 iron production had already reached 678,000 tons per year (versus 17,000 tons in 1740). Coal production was rising towards 30 million tons per year. Steam engine capacity totaled 250,000 horsepower (versus 20,000 in 1800).

      This looks a lot more like an exogenous technology shock (energy revolution) than a change in the conditions of society.

  12. Part 1,

    Let me try to make two related points here. First, the rapid rise in population and prosperity in the UK would have been impossible without the energy revolution. Second, the energy revolution represents an exogenous shock that explains the rapid rise in population and prosperity better than UGT. My first point is simply a statement of fact. The growth in output and prosperity of the UK in the 19th century would have been impossible without coal and new energy technology for exploiting coal. Without coal any growth in population and per-capita output would have quickly stopped because of resource constraints. The second point is a conjecture. However, it is (in my opinion) a conjecture that better fits the facts.

    A few statistics should help here. They are from table 5.1 in "Energy Economics: Growth, Resources, and Policies" by Richard John Eden. UK coal consumption rises from 3 MT in 1700, to 11 MT in 1800, to 97 MT in 1869. Per-capita consumption rises from 0.3 tons (per person, per year) in 1700, to 0.7 tons in 1800, to 3.1 tons in 1869. As a percentage of total energy consumed, coal goes from 80% in 1700, to 80% in 1800, to 99% in 1869. Note that the industrial use of coal grew even faster than these numbers indicate. According to the same source, even as late as 1800, 50-67% of all coal was still being used for domestic heating.

    The growth in industrial energy production was dramatic. In 1800, the total capacity of UK steam engines might have been 20,000 HP (12,500 from Watt's engines). By 1850, capacity had reached 300,000 HP in industry alone (excluding transportation, pumping water, etc.).

    A critical part of the energy revolution was in the production of iron and (later) steel. Early on, the UK faced wood shortages. Wood shortages drove the early adoption of coal as domestic fuel. The consumption of wood for pig iron production apparently contributed to wood shortages. There are many references to UK wood shortages in the Stuart period (1603 - 1714). The use of coke from coal as a substitute for charcoal from wood made possible explosive growth in iron output. Once again, statistics should help. UK pig iron production rose from 28,000 metric tons in 1750, to 80,000 metric tons in 1790, to 171,000 metric tons in 1800, to 1.4 million metric metric tons in 1840, to 6.059 million metric tons in 1870. Production increases of the magnitude would have been impossible without the replacement of charcoal from wood with coke from coal

    All of these numbers show that the inclined part of the hockey stick is physically impossible with the energy revolution. That's the easy part. The harder point (to demonstrate) is that the right hand section of the hockey stick is a consequence of an exogenous technology shock rather than some endogenous process. Several points tend to support the latter explanation rather than the former.

    The Watt engine was invented in 1769 and put into production (with Boulton) after 1775. It immediately reduced coal consumption by 75% and later by well more than 90% (estimates vary). The Newcomen engine was only 0.5% efficient so there was much scope for improvement. However, the significance of the Watt engine is not just lower coal consumption. The Watt engine could (and was) built on a much small scale (Newcomen engines were the size of a building) and was much less capital intensive. Newcomen engines, by their nature, could only be built in certain special locales and used (almost exclusively) to pump water from mines. Watt engines, being smaller, lighter, cheaper, and coal efficient, could be deployed anywhere (including ships and trains) as the prime movers of industrial civilization.

  13. Part 2,

    Essentially, industrial civilization took off as soon as Watt (and his immediate successors) started building engines. That might be a coincedence. However, given the deep and immediate impact of these engines, it does not appear to be. The knee of the hockey stick matches the introduction of the modern steam engine. Nothing else really does. It's worth noting that hockey sticks appear in other countries, as soon as they adopt the coal/steam nexus as an economic driver. It's also worth noting the knee of the global CO2 hockey stick is around 1800, just as the modern steam engine is taking off.

    Why did it happen first in the UK? A number of factors made the UK the optimial locale for the first energy shock. The UK had large, easily worked (close to the surface), and well distributed coal resources. Coal mining (for domestic heat) had been underway on a moderately large scale for a long time. Coal was already sold more or less throughout the UK for warmth (and limited other purposes). Primitive steam engines (Newcomen) were already in use on a large enough scale (several hundred) that improving on them seemed to be a reasonable idea. In the late 18th century, the UK was the only place in the world with the preconditions for energy shock to occur.

    The Roman Empire provides an important contrast. Rome faced energy shortages (wood) as early as zero AD. Energy intensive industries moved into Northern Europe to exploit the large remaining forests of the region. Logically, Rome should have shifted to coal for domestic heat and eventually metallurgy and industry. Of course, that never happened. Italy has essentially no coal resources and the parts of the Roman Empire that did have coal, were the periphery, not the economic core.

    In a sense, the Guttenberg printing press provides an analogy. Guttenberg's press was introduced around 1450. In that year, there might have been a total of only 30,000 books (actual books, not separate titles) in all of Europe. By 1500, as many as 20 million books had been printed. Of course, explosive growth continued after 1500. That's a classic technology shock. A new idea appears, is quickly adopted, and changes 'everything'. The Guttenberg press radically raised productivity in printing. It didn't transform entire economies. Printing was too small a fraction of output (before and after) for that to happen. By contrast, the steam engine was systematically transformative and still is.

    To close let me offer a few quotes

    "The wonderful progress of the present century is, in a very great degree, due to the invention and improvement of the steam engine, and to the ingenious application of its power to kinds of work that formerly taxed the physical energies of the human race."~Robert H. Thurston

    "By 1850, one-half of the world's iron and a full two-thirds of its coal production would come from British mines"

    "I sell here, Sir, what all the world desires to have—POWER" - Matthew Boulton


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