This one is for the Three-Toed Sloth, who kindly linked to some of my past entries.
So I was paging through Dani Rodrik's recent anthology on conundrums of economic growth, In Search of Prosperity, when I got to the chapter on the Philippines. The Philippines is the sort of place that makes growth economists' heads hurt. It's a nation of eighty million avid consumers steeped in American institutions for fifty years, and American popular culture for fifty more. English is the lingua franca to such an extent that

*Scrabble*is incredibly popular there, that and basketball. I mean, they show the high school games on the sports channel. And the general level of education is very high; the Philippines may export housemaids to the Persian Gulf, but it exports computer technicians and medical personnel to the United States, where they're the highest-earning immigrant group here. You can't throw a stone in Manila without hitting a diploma mill. But it's been economically stagnant for decades. In Rodrik's anthology, Lant Pritchett has a paper which compares the Philippines versus Vietnam, or in his words, "a Socialist Star and a Democratic Dud", the Philippines being the Democratic Dud. Elsewhere in his paper, it's "Tarzan of the Jungle" versus "George of the Jungle" growth. There is something about the Philippines that brings out bad pop culture wordplay in people, including Filipinos themselves. Come take comparative advantage of us. Pritchett's conjecture is simple:[A]lthough in some ways 'institutions' may have improved under democracy, 'institutional uncertainty' has increased. This increase in institutional uncertainty -- the reliability with which economic actors can anticipate the rules of the game (no matter how good or bad those rules might be) -- may account for a stagnation in the level of supportable output that accounts for the Philippines' growth dynamics.But that's not the interesting part of the paper.

Pritchett does something very unusual in his paper. He analyzes economic transitions -- say, from low growth to high growth -- in the same way a spectroscopist analyzes atomic transitions. The analogy is a little complicated, so bear with me.
In emission spectroscopy, light is given off when an electron in an excited atom moves from a higher energy state to a lower energy state. The frequency of the light is proportional to the energy difference, so if you measure one, you can determine the other. In days of old, this was done by measuring a fine ruler against the light's projected spectrum; hence the name, spectroscopy.
While there are an infinite number of energy states in an atom, they're like rungs on a compressed ladder, with the uppermost levels kind of smearing into each other, but the lower ones remaining discrete. This means that not all frequencies of light are going to be emitted when an atom is excited, say in a vacuum tube, which is why neon lights are red, and not white, which would be a mix of many different frequencies.
From this thumbnail description, you might think an electron could hop from any rung to any other. But it turns out even in the simplest atom, some hops -- some transitions -- are very very unlikely, or 'forbidden', for reasons based on the rules of quantum mechanics. These can be seen (or not seen, as the case may be) via spectroscopy.
Upshot: by analyzing an atomic spectrum, one can determine an atom's internal quantum structure.
So far so good. Pritchett is attempting to come up with a generalized model of growth, the world economy's equivalent of its quantum structure, by analyzing the pattern of its economic transitions. Yearbooks are his spectroscope.
He comes up with six "growth states", analogous to energy levels in an atom: technological leadership with steady growth; subsistence economies with zero growth, or the poverty trap; nonconvergent moderate growth; rapid growth; growth implosion; and non-poverty zero growth, or stagnation.
From these, he constructs a six-by-six grid, or in the jargon, a transition matrix. One side of the grid is the before axis, the other is the after axis. It's like a logic puzzle, or a dice chart.
After analyzing the historical data on the grid, it turns out that some economic transitions just plain don't happen. In the jargon, they're forbidden. Growing technological leaders don't implode, moderate growth doesn't ever turn into technological leadership. Also, the grid is not symmetrical. Some transitions don't occur in reverse.
Pritchett assigns numbers to this grid to come up with a five-by-five probability matrix -- or actually, a four-by-four one, and an assumption that once you are a growing technological leader, you will remain so. The four remaining categories are stagnation, implosion, plateau, and boom (he merges the stagnant and the subsistence poverty trap categories together). After a lot of implied tweaking, he came up with a set of results that fit the world situation from 1870 to 1995. I'd be amiss if I didn't provide them to you.
In Pritchett's model, if you start off as a country in economic stagnation, you have an 88.5% chance of remaining stagnant the next year, a 10% chance to implode even further, a 1.05% chance to hit a plateau of moderate growth, and a 0.45% chance to boom.
If you are a country that is imploding, there is a 40% chance that you will recover to stagnation, and a 60% chance that you will implode even further.
If you are a country experiencing a moderate plateau of growth, you have but a 10% chance of stagnating in the next year, an 80% chance of maintaining your plateau, and a 10% chance of an economic boom.
And finally, if you are a country in a boom, you have a 10% chance of dropping down to a moderate plateau, and a 90% chance of keeping that boom going another year.
I leave the long-term behavior of this probability matrix as an exercise for the reader.
What does this say about the underlying factors of growth? Well, Pritchett isn't sure:

After this low growth persists for an extended period, then it is not clear how one escapes this "non-poverty trap, low or zero growth" state into a rapid (or at least moderate) growth. If the problem is systemic uncertainty -- that is, uncertainty about economic prospects and performance under the system of institutions as operating -- it is not clear that individual, piecemeal economic reforms, even cumulated, can shift the growth state. [...] I have attempted to make some progress, not in producing such a model, a task for another day, but in producing what such a model will produce.But it sounds like an interesting start.

Let me see if I've got the transition matrix right:

a=Stagnation

b=Implosion

c=Plateau

d=Boom

e=Technological Leadership

a b c d e

a 0.8850 0.1000 0.0105 0.0045 0.0000

b 0.4000 0.6000 0.0000 0.0000 0.0000

c 0.1000 0.0000 0.8000 0.1000 0.0000

d 0.0000 0.0000 0.1000 0.9000 0.0000

e 0.0000 0.0000 0.0000 0.0000 1.0000

I'll run some Markov Chain stuff and see what there is to see.

Any chance you can modify to fill in the transition probabilities to absorbing state 'e', which were dropped off of the simplified version?

Bernard

Posted by: Bernard Guerrero | October 01, 2004 at 02:17 PM

"In Pritchett's model, if you start off as a country in economic stagnation, you have an 88.5% chance of remaining stagnant the next year, a 10% chance to implode even further, a 1.05% chance to hit a plateau of moderate growth, and a 0.45% chance to boom."

Perhaps it's just the sleep deprivation talking, but I immediately thought of the board game version of this. "Tiger: The Exciting Game of Macroeconomic Development". The dice would be odd.

Posted by: Gareth Wilson | October 01, 2004 at 03:30 PM

Bernard, that's right. You might find this utility useful.

The problem is, in Pritchett's model, that a boom to a leadership transition depends on cumulative factors, which violate Markov assumptions. So there's no good way to model it in a small matrix, though there is a crude way to do it in a large sparse one. Pritchett explicitly calls this his "toy collection" model, so it's probably not best to let it bear too much load.

Here's a theoretical question to chew on: why is the matrix so strongly asymmetric, especially in the bad states?

Gareth, you might use four dice, one for each state. Three regular, one weighted. Or a modified Snakes and Ladders; I believe William Easterly has made that analogy.

C.

Posted by: Carlos | October 01, 2004 at 04:43 PM

While there are few things I like better than a nice phenomenological Markov model, I hve my doubts about this one. It sounds like Pritchett is treating each country's history as an independently generated sample-path, with a common generating process. Even at this level of coarse-graining, though, it seems to me that this isn't a good approximation, since growth states are spatially correlated. A better approach would be a Markov random field, done on a graph (nodes = countries, edges = trading links, perhaps) and not a simple lattice. This only brings us closer to the board game, of course. If someone wants to make it, I can guarantee you at least one sale; it'd be the perfect gift for my father.

Posted by: Cosma | October 01, 2004 at 05:56 PM

Bummer, looks like it stabilizes at approximately 63%-16%-9%-12% for states 'a' through 'd' respectively. I worked up a little MATLAB script to produce a track of transitions and plotted 'em. If anybody wants to see the .xls or .m, please let me know.

Posted by: Bernard Guerrero | October 01, 2004 at 07:14 PM

"This only brings us closer to the board game, of course. If someone wants to make it, I can guarantee you at least one sale; it'd be the perfect gift for my father."

Hmmnnn. Gotta think about how to make it gamier. Or, er, something like that...

Posted by: Bernard Guerrero | October 01, 2004 at 07:46 PM

With any finite Markov chain, with probability 1 the trajectory enters a strongly connected component of the chain and then stays there forever. Within each component, there's a stable long-run distribution over states, so every finite chain eventually settles down to one such distribution; the only question is which component it gets trapped in. Here there's only one component, so that doesn't arise. If you find the eigenvectors of the transition matrix, you'll see that the distribution Bernard got is the eigenvector for the largest eigenvalue, which is 1.

Posted by: Cosma | October 01, 2004 at 11:28 PM

Bernard, you wussed out. I did it like General Anna in The Pushcart War, by hand. Hey, it's only 4 by 4: (1 + .25 + .15 + .195)x = 1 .

Cosma, good to hear from you! Yeah, growth in the real world is spatially correlated, but less strongly than it appears at first glance, and especially in the post-WWII era, when transport and other costs have dropped so much.

The classic example is Botswana, which fifty years ago was a landlocked, artificial region on the map, filled with Iron Age cattle herders, and neighbor to the most predatory state on the continent; and today is as rich as 1975 Wyoming, while most of the region is still stagnant, or worse.

William Easterly brought up a similar point a few years back: if a model of random growth gives the same overall distribution of fast growing and stagnant countries as the real world without introducing geographical factors, should we then include them?

It's odd, because we know -- or at least we think we know -- that they are there.

So I am not sure that the lack of geography is that big of a damper on the model. I think a larger distortion comes from the mix of "grain" sizes of the real world data set. Are Mauritius and the People's Republic of China really the same sort of economic entity?

In the board game, I'd use a map, and overlay circles of colored transparent plastic to denote areal effects.

C.

Posted by: Carlos | October 02, 2004 at 12:21 AM

"Bernard, you wussed out. I did it like General Anna in The Pushcart War, by hand. Hey, it's only 4 by 4: (1 + .25 + .15 + .195)x = 1 ."

Ah, well, you know the old saying. When you've got an automated matrix algebra hammer lying around, everything starts to look like a nail. Besides, I got to see the time-path, such as it was.

Posted by: Bernard Guerrero | October 02, 2004 at 02:09 PM