Monday, November 30, 2009

Romer's Growth Theory


It is generally presumed that Paul Romer will win a Nobel prize for his 'endogenous growth theory', so I was intrigued when Kling and Schultz interviewed him in their new book From Poverty to Prosperity. As mentioned yesterday, the book hits on a lot of issues I find interesting, not so much as providing a novel big idea, but noting a lot of outstanding puzzles and how the non-Left Establishment thinks about them.

Growth Theory is about long term economic growth, abstracting from business cycles. Given the power of compounding, and the ephemeral and intractible nature of business cycles, it is rather a shame for most economists to focus on recessions because over they don't matter too much over time. Sure, the East Germany had fewer recessions than West Germany, but over a couple generations, West Germany had 3 times the living standard. Wisdom is primarily prioritizing tasks according to importance and solubility.

Robert Solow started growith theory in the 1950s, and it basically broke the macroeconomy into three drivers: capital, labor, and productivity. It did not explain productivity, but did highlight that this factor seemed to be what really mattered, so no longer could one say, Tanzania needed more 'capital', because after you apply the model econometrically the problem is not capital or labor, but their productivity. Solow's growth model does not tell us how things work, but it did dismiss a popular incorrect idea, no small feat.

Romer highlights the fact that great economists, according to economists, are those that create great models. These models usually merely formalize existing intuition, as the Welfare Theorems of Arrow and Debreu really just proved the 'Invisible Hand' using set theory (ie, that a competitive equilibrium is Pareto Optimal, and that a Pareto Optimal Equilibrium is a competitive equilibrium). Or consider the Lucas Islands model, which modelled economic fluctuations as the result of unpredictable monetary growth an inflation. In the 1970's, this was a leading explanation of business cycles, but no longer. Nonetheless, the model remains in the canon because it is self-contained, has a lot of intuition, and inspires economists as to what they are trying to create. The hope is that one creates a mathematical model, like the Black-Scholes equation, that sheds light on new truths. Good models fit to existing phenomena should generalize in unexpected ways. Alas, this is rarely the case in economics, as the model usually remain parochial explanations of the economic fact that inspired it(eg, the Phillips Curve).

Romer's model is instigated by the fact that while there is convergence within various economies, such as Developed economies, there is not convergence among all of the economies. So, Japan, France, and the US all vary around a single value, but Africa remains mired in poverty, seemingly unaffected by worldwide economic growth. The existing Solow Growth Model could not explain this, except to trivially note the African economies had lower productivity, a parameter in the Solow Growth Model. The Romer model has the form

Y=F(x(i),k(i),K)

and x(i) is the labor of an individual, k(i) a firm's capital (assume people are also firms). K=sum(k(i)), reflecting the idea that bigger economies have more knowledge, and thus, greater productivity. F is increasing in all its arguments. The key technical point he makes is to assume Y is a concave function of k(i) and x(i), which is necessary for an equilibrium to exist, yet because F is increasing in K, you have increasing returns to scale in aggregate. Thus, a competitive equilibrium exists even with increasing returns to scale, because their individual effect on total output K is insignificant (otherwise, with increasing returns to scale, everyone soon chooses infinity to maximize their production/utility).

Most interestingly you get multiple equilibria, in that if you can coordinate everyone to invest a lot, growth is higher than otherwise. This highlights the potential for good institutions to incent greater growth, say by offering more secure property rights, or intellectual property laws. Prosperity becomes a coordination problem, seemingly soluble by abstruse mathematics.

This is the cause of great joy among economists because it allows for lots of modelling: you can prove an equilibrium exists in the infinite horizon case using Hamiltonians, which have proved very useful in physics (the gold standard for science). The end result of this is Bob Lucas's Recursive Methods in Economic Dynamics, a book with a lot of math but not much insight (ever since John Nash successfully used a fixed point theorem to prove his eponymous equilibrium, economists have been eager to apply fixed point theorems to other problems, without much success).

The new growth theory tries to explain productivity 'endogenously', as opposed to Solow's exogenous treatment. Yet what is Romer's take away, when translated into words? First, he repeats again and again that higher productivity leads to higher productivity. But that can't be right, in the sense that growth rates of developed countries are not increasing over the past 100 years. I think what he means is that developed countries keep growing, while undeveloped ones don't, do to their 'bad equilibrium'. So we are back to, why does the US have the good one and not Haiti?

Then Romer seems really happy about noticing that productivity is not merely more stuff, but stuff differently arranged. He notes there's a machine that using carbon, oxygen, hydrogen and a few other atoms that is smaller than a car, renews itself, fixes itself, and creates valuable output. What is it? A cow! See, all we have to do is arrange atoms into cow-like things, and the future of robot maids, jetpacks, and holodecks will finally arrive. I don't see this kind of insight rising above the fantasies of your average comic book reader.

In Romer's Fora.tv talk, he talks about theses issues, and highlights that a growing economy has 4 major pieces:

1) competition
2) entry
3) emulation
4) exit (loser firms are reallocated to winner firms)

He gets excited by the idea that many countries could be like Hong Kong in the pre-Chinese era, taking Britain's superior laws, customs, and technology. Yet, even in the US, things like competition, entry, and exit are heavily legislated against by entrenched interests. Sure, Haiti or Paraguay could allow in foreigners to set up franchises, but they don't, because that seems to many as exploitation, and has the stench of racism. So we are back to the old ideas about international trade, the distribution of wealth, and especially the distribution of wealth among various ethnicities. A ruling clique would keep their people poor rather than turn over, say, Petrobras to Exxon.

Japan in 1854 seems the best model for an economy that emulated existing technology, where the Japanese noted their technical deficiency after being defeated by the US Navy and then adopted Western technology without having the Westerners actually own anything. So the question is why did Japan do this, but not the hundred or so other undeveloped countries? Romer's big idea seems best addressed by much less mathematical analysis; his model is sterile when applied to the real world.

Romer's asking the right questions, but as Michele Boldrin noted in Against Intellectual Monopoly, the question about the value of various forms of patents is an empirical one, not deducible from theory. Clearly Romer's work motivated Kling and Schultz's chapter 2, which highlights the nature of our industrial revolution, which is truly remarkable. But to think that Romer's 'economic growth theory' has anything really to add, I haven't seen it.

2 comments:

Jim Glass said...

the Japanese noted their technical deficiency after being defeated by the US Navy and then adopted Western technology without having the Westerners actually own anything. So the question is why did Japan do this, but not the hundred or so other undeveloped countries?

Romer's ... model is sterile when applied to the real world.


Maybe move on from there to Public Choice?

Robert Johnson said...

Eric,

I really appreciate your practical approach to economics, generally.

"The hope is that one creates a mathematical model, like the Black-Scholes equation, that sheds light on new truths. Good models fit to existing phenomena should generalize in unexpected ways. Alas, this is rarely the case in economics, as the model usually remain parochial explanations of the economic fact that inspired it."

Yours is a scientific approach, expecting models to yield useful predictions about phenomena as yet unobserved (or unnoticed).