Sunday, August 16, 2009

Crucial Assumptions

"All theory depends on assumptions which are not quite true. That is what makes it theory. The art of successful theorizing is to make the inevitable simplifying assumptions in such a way that the final results are not very sensitive. A "crucial" assumption is one on which the conclusions do depend sensitively, and it is important that crucial assumptions be reasonably realistic. When the results of a theory seem to flow specifically from a special crucial assumption, then if the assumption is dubious, the results are suspect."

(Robert M. Solow, "A contribution to the theory of economic growth", Quarterly Journal of Economics 70(1): 65-94, p65)

This is the opening paragraph of Solow's Nobel-Prize winning paper on economic growth. His innovation was to replace Harrod and Domar's assumption that the aggregate production function was a Leontief function with the neoclassical assumption that labor and capital are substitutes. He then explored the implications of the model with a Cobb Douglas function and a CES function with elasticity of substitution greater than unity.

I've been working on the theory of growth both for my Environmental Economics Research Hub project and a longer term project on the role of energy in economic growth (that was one of the themes of my PhD dissertation after all :)) and thinking about assumptions. I've been reading Galor and Weil's unified growth theory. It is an elegant model where before the industrial revolution there is only one stable growth equilibrium with low rates of technological change and education and after it only a high technological change and education equilibrium. In the intervening period of the industrial revolution two equilibria are active. The crucial assumption that leads to this result is that the rate of technological change is a rising function of the size of the population. This isn't an unreasonable assumption but strangely it is the one thing that isn't clearly "micro-founded" in the model. The model also doesn't explain why the industrial revolution started in England. If population size is critical, why not China? Or even Italy?

The world's first iron bridge (1779) at Ironbridge. I visited there when I was 17 or 18.


  1. I think that part of the key to the industrial revolution is in the fact that Abraham Darby and co. were Quakers. The Protestant movement in Europe and especially the Puritan roots of the US can be shown to be crucial in the development of the West. Free thought, the ability to envision change and the dialectics of redemption could never have happened in Catholic Italy. These are Jewish concepts that were reinvented by the Protestants when they started reading printed Bibles.

  2. That's a classic theory about the industrial revolution but not one that economists like nowadays. They might ask: "So why was Protestantism not popular in Italy?" or "Why was it popular in England?" And as Tony Wrigley showed (Continuity and Chance, 1988), the industrial revolution didn't start in the Protestant Netherlands. As you might guess I think it's got something to do with that iron bridge and the coke that the original Darby used to smelt iron :) I've just finished the first draft of a paper on this, but I'm not putting it up until I've double checked all the math and maybe use some real data in my simulation model.

  3. I do not deny that the industrial revolution could not have occurred without coke. However the fact that the breakthrough was made by a bunch of Quakers was also not incidental. Look at what the Puritans did in N America compared with what the Catholics did Central and S America or even the South of what became the USA.

    Why did Protestantism not take off in Southern Europe? That's a similar question to why Judaism was invented by ancient Hebrews, why Islam developed in Arabia and why the Far East went in a completely different theological direction. Peoples have different cultures and national character and create or adopt different cultural and philosophical edifices.

    If what you are hinting is that national culture is affected by natural resources, then that's also an interesting idea. Certainly ancient middle eastern theology was influenced by natural resources (mainly availability of water), so I suppose the existence of coke could also affect theology.

  4. Yes institutions are important and they were supportive in the Protestant countries and not in many others. As you say the Spanish Empire was very different to the British Empire. The industrial revolution could have happened earlier in China but the government apparently reversed direction and stopped it in its tracks. At least that is what Prescott and Parente argue (Barriers to Riches, 2000). In my research I'm taking the institutions for granted though. I'm explaining how you can't get an industrial revolution without an increased energy supply or innovations that increase the effective supply of energy. That might be obvious but it isn't explicitly in existing mainstream models of the industrial revolution. The data for Sweden at least strongly support my model.