Saturday, October 17, 2015

Can we extrapolate growth into the distant past?

Paul Romer on economic growth [1]:
My conviction that the rate of growth in GDP per capita at the technological frontier had to be increasing over time sprang from a simple calculation. Suppose the modern rate of growth of real GDP per capita (that is the growth rate after taking out the effects of inflation) is equal to 2% per year and that income per capita in year 2000 is €40,000. If this rate had prevailed for the last 1000 years, then in the year 1000, income per capita measured in the purchasing power of dollars today would have been €0.0001, or 0.01 cents. This is way too small to sustain life. If the growth rate had been falling over time instead of remaining constant, then the implied measure of GDP per capita in the year 1000 would have been even lower.
Emphasis mine. That is one possible conclusion. The other is that an RGDP per capita of €0.0001 (let's call this the Romer point) implies that there wasn't a functioning monetary economy in the year 1000. This second view can be described in the information transfer framework where it also makes sense of the price revolution of the 1500s (or so). Here is the picture I have in mind:

I use the price level P instead of RGDP per capita [2] not only because it is more relevant in the information equilibrium picture, but also better illustrates what is going on in my view. It's not that real output was zero, but rather the price of everything was effectively zero: there wasn't a functioning monetary economy. The market (information equilibrium relationship) P : N ⇄ M hadn't been established, I(N) > I(M) so that P k Mᵏ⁻¹. Real output R = N/P would be undefined. The gray line indicates ideal information equilibrium while the blue line is the realized economy (non-ideal at first, ideal later). There was a transition to a monetary economy in Europe, historically identified by the price revolution [3], followed by economic growth.

This picture is similar to what happens in the p-V diagram in the liquid-gas transition (discussed before here). But that brings up what I'll admit is an unfair characterization of Romer's argument, but it is not incorrect.

Romer's argument that proceeding back in time assuming a growth rate of 2% per year implies income too small to sustain life in the year 1000 is analogous to saying:
Looking at the p-V diagram for an isothermal process, it appears you can eventually compress an ideal gas into a volume smaller than an atom therefore the number of degrees of freedom in p = (2/f) U/V must be shrinking as a function of volume.
That is a plausible guess, but what really happens is that the gas condenses into a liquid and you go from ideal information equilibrium to non-ideal information transfer between the process variables U and V. Inter-molecular forces begin to matter. You undergo a phase transition. The correct conclusion to draw from the argument is that the gas should behave differently, but the argument is not evidence that you know in what way it behaves differently.

Romer should have drawn the conclusion that the economy in the year 1000 must have been different from a modern economy, not that the rate of growth must be increasing over time.

In terms of the price level picture (note: Romer is arguing about RGDP growth) the solution he proposes to the Romer point (real output isn't worth anything in the year 1000) above looks like this:

That is to say, we increase the estimated value of real output in the year 1000 by changing how we calculate it -- using an accelerating growth model instead of constant growth. But maybe real output wasn't worth anything in terms of money in the year 1000 [4].

As the title asks: can we extrapolate growth into the distant past? The real question is: can we extrapolate a monetary economy into the distant past?

Update 10/18/2015

John Handley points out (correctly) that Romer is talking about real growth. I noted that above, but here's a less hand-waving version of the idea that real output measures output in terms of money, but not necessarily physical widgets:



[1] I changed the dollar signs to € to prevent problems with my mathjax script, but even there we see why this might be a bit strange. Why would you measure income in dollars in the year 1000? Who would take fiat currency in the year 1000 except possibly in China?

[2] As I mention here, the real rate of growth may not be a well-founded concept.

[3] I think this price revolution might refer to the gold standard and there might be a different one associated with fiat currency.

[4] I was under the impression that I said something on the blog along the lines of if we measured output in terms of widgets we probably wouldn't have the decelerating growth of secular stagnation ... but I can't find it. The thing is that the information transfer model is a model of stuff measured in terms of money. The aggregate output of bread in terms of money has a different history than the aggregate output of bread in terms of loaves.


  1. I doubt if we can talk about a non-monetary economy in Europe before the modern or late medieval period, even during the Dark Ages. Perhaps there was persistent non-ideal information transfer because of difficulties and restrictions on trade. The medieval idea of a just price, if applied, would hinder price from transmitting information, for instance.

    1. There was also a simple lack of money. It was a big deal when silver was found in the (modern) Czech Republic:

      Most people lived on subsistence farming; there was no excess output to sell, therefore no need for money!

    2. My comment just got eaten, so here is a short version.

      Agreed that medieval Europe did not have enough money. Neither did the British American colonies before they started to print it. Britain was stingy with its money, which is why we adopted the Spanish dollar. The colonies were largely agricultural economies, but printing their own money spurred economic growth.

    3. Additional comment:

      Neither the European Feudal lords, nor the British landlords, nor the slaveholders of the American South, who had enough money for their own ends, were interested in providing money for the rest of the economy. We can see the same dynamic today.

    4. Yes -- understanding of monetary economics was a bit constrained by the zero-sum theory that you needed to accumulate gold in your national treasury in order to fund the military (and not import things because that meant you lost gold). There were laws against exporting gold and silver based on that theory. ... Mercantilism.

    5. Also -- I have no idea what happened to your comment. I checked the spam folder, but it wasn't there.

    6. Thanks for checking for my note. I have had problems using OpenID on a few blogs. It happens. ;)

  2. Jason,

    The key part of Romer's reasoning is the word "real". If real GDP per capita were equal to what could be bought with 0.01 cents in 2000, then life would be impossible. This is what Romer meant. So, for a more in depth example, say 0.01 2000 cents could buy you 1/10th of a slice of bread. No one can live on that for an entire year, so growth must have been accelerating.

    1. I don't think that anybody disagrees about the acceleration of growth. But the question is one of continuity (in the practical, not mathematical sense). If there was a discontinuity, then one would expect a large acceleration at the discontinuity. The question then becomes, Has growth been accelerating since the discontinuity. Romer's conclusion that growth has been accelerating over time assumes no discontinuity with its local acceleration. Jason's example of a physical phase transition is a good example of a discontinuity. I think that he labels the two economic phases wrong, but I also suspect that the largest acceleration of economic growth in European countries occurred by the 19th century. Growth may have been rapid since then, but that does not mean that it has been accelerating.

    2. Hi John,

      I did understand he was talking about real output; I was trying to address the extrapolation at the same time as showing a different version. Maybe that was unsuccessful.

      However, the physical analogy about extrapolating compressing an ideal gas is applicable -- it doesn't depend on the details.

      Maybe an easier way to see it:

      Imagine if instead of the year 1000, the relevant year was 1,000,000 BCE. Humans would not have existed and measuring the economy of Australopithecus in terms of "real dollars" would be reductio ad absurdam... But not in the intended way.

      My key point is extrapolating a monetary economy into the distant past is problematic.

  3. It'd be fun to compare notes with an economic historian. I don't know any of those, however if I had a question about 10th century use of coins or other money in some region of Earth, I'd run it past J.P. Koning: he seems to be pretty good on that kind of thing.

    Then there's that guy who wrote "Debt: the first 5000 years" (David Graeber). He's an anthropologist I think. The book had some interesting parts, but I found myself skipping about trying to find them (it had some very dull sections too in my view). He had mixed reviews amongst the econ bloggers (e.g. David Andolfatto).

    He did try to document, in broad strokes, the use of money and debt in China, Europe, India and the Middle East over the past 3 millennium or so. Whether he got it right or not is another issue.

    I had the impression that coins were invented in the Hellenistic world about 600 BC or so, and their usefulness was tied to paying an army. There was a similar timeline in India. They system derailed (to some extent) for a period of time when the age of coin driven empires crashed in both places.

    He talked about Europe post-fall of Rome, and how the Roman units of money lived on even though nobody was minting coins for some time. And systems of law were eventually established with payments in those units, though the coins themselves may never have actually circulated (but debts were recorded in those values?).

    It's pretty fuzzy now... I probably got some of that wrong. And maybe David's write up was suspect in parts anyway.

    1. Hi Tom,

      There is a difference between using money and a monetary exchange market ... at least in the information equilibrium picture.

      Most histories of money in the West trace back to Lydia around 500 bce. I am unsure if there was enough of it around to function as an ideal information transfer process, however.

      I read Graeber's book which was interesting, but I am not convinced it is right because of the weird errors and Graeber's weird defensiveness about them. I am (still) reading this one:

      Of course, there are my posts on the subject as well:

      However, my main point was that it's hard to translate "real output" into physical widgets ... which I make explicit here:


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