Computable General Equilibrium Models and Economic History

Kevin O'Rourke

Department of Economics
University College, Dublin

© Kevin O'Rourke, 1995

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I didn't want to give this paper. I am a methodological catholic: McCloskey (1985) convinces me; and anyway, I am too young to be telling other people what to do with their lives. Besides, it's been thirty years since Chambers and Gordon (1966) published their wonderful prairie boom paper, and Temin (1966) and Fogel (1967) wrangled over labor scarcity. CGE modeling: a new direction in economic history? Hardly.

But Robert Whaples is a persuasive fellow, and as you can see, not even prior commitments were considered an acceptable excuse. Here then are some thoughts on historical CGE modeling. In the time available to me, I cannot provide a survey of the literature to date; rather, I will re-state the rationale for these models, indicate what progress has been made since the last surveys on this topic, and deal with some common objections to CGE modeling.

Before I begin, let me give you my bottom line: CGE models are useful in their place, but the range of questions which they can satisfactorily answer is rather narrow. The best definition of a CGE model is: 'theory with numbers'. The theory used is typically static, neoclassical theory, but this is by no means necessary. If you want, you can build unemployment, increasing returns, endogenous growth, or whatever else takes your fancy into a CGE model. (Although you may then run into multiple equilibria, or unstable equilibria, or no equilibria.) If you can model it theoretically, you can calibrate it, and policy analysts have indeed calibrated new trade theory models, new growth models, new economic geography models, and so on. If historians believe that non-convexities matter, CGE analysis offers one (albeit limited) way of testing this intuition.

My own view, for what it is worth, is that traditional neo-classical theory is pretty good at answering static, resource allocation questions. I trust a standard trade model to give me a reasonable handle on the income distribution effects of a tariff. But could I trust any single growth model, no matter how impeccably non-convex, to provide a satisfactory description of long run growth? Give me _The Lever of Riches_ any day. So, I'm very happy to use CGE models when thinking about, say, the impact of terms of trade shocks on late 19th century Irish agricultural employment. I'm reasonably happy to use them when analysing the impact of emigration on Irish wages; although even here I would want to qualify my results, pointing out that a standard trade model may leave out many potentially important effects. To answer a really interesting question, like why Danish co-operatives did so much better than their Irish counterparts in the late 19th century, I obviously need something completely different. Supply and demand remain pretty useful tools for thinking about the long run evolution of market forces. How various societies respond to these market forces is an altogether more challenging question.

Having said all that, here are some frequently asked questions about CGE models, and my stock replies.

Question 1. Why general equilibrium?

We all know that in principle, general equilibrium is preferable to partial equilibrium. Unfortunately, that is all most undergraduate micro courses have to say on the subject. Get to graduate school, and things become even more dismal. Complicated proofs: existence; uniqueness; stability. General equilibrium with uncertainty; with incomplete markets; and so on. Conspicuously lacking from all of this are interesting comparative statics exercises; the result is that most students will wonder what the point is. The only courses in which you actually get to use GE models tend to be international trade and public finance. Therefore these should be core subjects; whereas in fact, a lot of American economists don't take trade theory at all. I suspect that this lacuna explains in part the resistance to CGE modeling among US cliometricians; but it has far more serious consequences than that.

Take the effects of trade on income distribution: a general equilibrium problem if ever there was one. Some US labor economists have examined the issue by relating import penetration to employment and/or wages across industries: a meaningless exercise if labor is mobile between sectors. If labor is mobile, then trade will have the same impact on unskilled labor whether it is employed in textiles, or Intel, or hamburger-flipping. Add further features of the real world -- intersectoral capital mobility, or intermediate inputs -- to the picture, and the need for a GE treatment of the issue becomes crystal clear. Similarly, economic historians cannot understand the impact of US tariffs, or the Corn Laws, on income distribution, without thinking in GE terms. And in fact they have always done so, even if the theorizing was traditionally implicit rather than explicit.

Question 2. Why _computable_ general equilibrium?

There are two obvious reasons why _calibrating_ GE models makes sense. First, while qualitative results are nice, we typically want to know whether a particular exogenous shock mattered a lot or a little. Second, you only get unambiguous qualitative results out of highly simplified models. Use such models, and you are always open to the Fogel (1967) critique, which was that the structure of a particular model may unreasonably limit the range of results obtainable from that model. Go back to the labor scarcity debate, and think about the impact of an increase in land supplies on wages and profits. In a world where food is produced with land and labor, and manufactures are produced with capital and labor, the result is clear: an increase in land supplies leads to wages rising, and profits declining. But what if land, or food, is an input into manufacturing, or capital into agriculture? Now qualitative results will be hard to come by. The results of the simpler model may carry over, or they may not: it is a strictly empirical issue, depending on the parameters of the particular historical economy in question. CGE modeling offers the perfect way to sort out potentially off-setting forces in such a situation.

One important lesson for CGE modellers suggests itself: try to ensure that the theoretical structure of your model is general enough that the Fogel critique does not apply. For example, make sure that factor prices do not depend uniquely on traded product prices.

Question 3. What does CGE modeling involve? Isn't it difficult?

A lot of people seem to think that CGE modeling is difficult: nonsense. Take a very simple partial equilibrium question: how will consumption change when prices rise? To answer this question, we need four things. First, some theory, such as a demand curve. Second, calibration: the original point on this demand curve. Third, an estimate of the size of the shock. And fourth, the elasticity of demand. Many economic historians have cut their teeth on precisely this sort of partial equilibrium, back-of-the-envelope exercise; we all accept it for what it is; and CGE modeling is nothing different.

These same four elements (theory, calibration, shocks, and elasticities) are all you need to perform a CGE exercise. As I have said, the theory can be whatever you want; but Walrasian theory can be easily summarised. (For every sector, price equals cost; for every commodity, demand equals supply; for every household, income equals expenditure.) Calibration involves putting a number on every input, output, consumer demand, trade flow, and factor endowment in your model. Moreover, all these flows have to be compatible with each other. This can take some work, as can the third task, measuring the exogenous shocks. The fourth task, picking elasticities of substitution in the production and utility functions, is as easy or as difficult as it is for the back-of-the-envelope partial equilibrium modeller (although you do also have to pick functional forms).

Question 4. Tell me more about those data requirements?

John James (1984) correctly pointed out that the data requirements for CGE modeling in history are enormous. True, but think of the alternatives. If you are prepared to calibrate a model, rather than estimate it econometrically, then all you need is lots of data for one bench-mark period: a census year, for example. Calibrating theoretical equations to data for one year can be a lot easier than gathering lots of time series data, and estimating structural or reduced form equations. For example, you avoid the econometric problems associated with time series data; not to mention changes in the way statistics were collected over time. It's no coincidence that CGE models have also been widely used in development economics, another data-scarce field.

Calibration is time-consuming though, and the numbers you use have a huge influence on the results. It's telling that in all the seminars I've given, only Bob Fogel has ever given me a really hard time on calibration (he had some questions about model specification too!); yet calibration is at the heart of any CGE project.

Question 5. How do you solve one of these models?

A CGE model is just a system of simultaneous equations. Specifying those equations is pretty straightforward, at least if you stick to Walrasian (or almost Walrasian) models. Now you have to solve them; and this is where the most progress has been made in recent years.(1) In the beginning there was Chambers and Gordon, who solved their model analytically, and therefore needed a model so tractable that it was immediately open to the Fogel critique. Next came matrix inversion programs, and Jeff Williamson, who laboriously took the basic equations of his models, and linearised them through differentiation. This 'Ron Jones' (1965, 1971) technique was open to the criticism that it only gave approximate answers when the shocks imposed were large; but it was the best that could be done in the '70s and early '80s. Now we have simultaneous non-linear equation solvers like GAMS and GAUSS, that can handle shocks as big as you like. Moreover, they come with handy little modules attached, like MPSGE, specifically designed to make life simpler for CGE modellers. Give these programs factor endowments, and production and utility functions, and they will calculate cost functions, factor demand and consumer demand functions, and solve a standard Walrasian model. By adding appropriate side constraints, you can get away from the strict Walrasian framework, if that is what you want. To solve a model, you just need to specify it, and come up with the numbers. Even differentiation is no longer required: the computer does all that for you. This leaves the modeller free to focus on data issues, and economic intuition.

Question 6. Aren't these models just black boxes?

Not if they're constructed and presented properly. I confess to being a little irritated with this criticism. To me, ARCH and GARCH models are black boxes, but I blame myself for this, and not my econometric colleagues. OLS isn't a black box for most of us, because:
a: we have taken econometrics courses
b: we own econometrics software
c: the data used are publicly available and the results can in theory be replicated.

A small (3 or 4-sector) static CGE model will make perfect sense to someone who has taken an upper-level undergraduate trade course. The things you need to understand are: the 2 by 2 ('Heckscher-Ohlin') model; the 3 by 2 specific factors model; the importance of 'bigness' in world markets; the impact of international factor flows; the impact of trade policy; and how the relative numbers of traded goods and factors matters. (Hint: write down some price equals cost equations.) This should give you all the intuition you need. As for the software, it is now easily available. And as for the data: ask the modeller for the working paper, if it isn't in the published version. On replication, finally, you should know that Tom Rutherford in Colorado has been able to replicate lots of CGE results obtained by other researchers. And having replicated the model, you can then do all the sensitivity analysis you like.

Question 7. OK, what about model validation?

In the past I have tried to make my models track reality. Now, I realise that until we can model technical change properly, it isn't worth the effort. The alternative is sensitivity analysis: changing the model's parameters, or specification, and seeing if it matters. We have a relevant folk theorem: changing elasticities doesn't matter a lot, but changing a model's specification does matter. And experience has taught me a few lessons, which may or may not carry over to other applications, such as: your results on income distribution will typically be a lot more robust than your results on outputs or trade flows. Clearly finding better and more systematic ways of subjecting our results to sensitivity analysis is a major challenge for CGE modellers. Equally important is finding a way to present the results of such analyses concisely. Elasticities can be varied continuously, making graphical presentations possible; but how do you document the impact of changing functional forms without swamping the reader in a morass of tables?

There is a deeper point here, however. Some results are extremely robust; but others do depend crucially on key assumptions. One important contribution of CGE modeling can be to bring out clearly the contingent nature of a lot of our knowledge. Solidly grounded uncertainty can be preferable to ignorant certainty.

Question 8. Could you give me that bottom line, again?

CGE models are theory with numbers. Given the present state of theory, CGE models can't unlock the secrets of economic growth. They _can_ tackle more static issues, such as the impact of trade, or trade policy, or fiscal policy, or international factor flows, on the distribution of income between regions, or factors, or households; or on sectoral outputs; or on the distribution of employment between sectors. They can also be used to measure aggregate welfare effects, although I am inclined to doubt the merit of such exercises. Static welfare effects are always small; dynamic effects may be large, but we don't have the theory to understand them.

How much can such static models explain? For 19th century Ireland, and the questions that interest me, the answer seems to be: about 50 percent. CGE models can't provide all or even most of the answers; they do provide a good start.


Paper to be presented at the "New Directions in Economic History Roundtable", 20th Annual Meeting, Social Science History Association, November 16-19, 1995, Chicago, Illinois. I thank Kevin Denny, Morgan Kelly, Peter Neary, Cormac O Grada and Jeff Williamson for their comments; and Alan Taylor for agreeing to deliver the paper in my absence. (1) Even a recent survey like Thomas (1987) seems out-dated today in this respect.


E. J. Chambers and D. F. Gordon (1966), "Primary products and economic growth: an empirical measurement", Journal of Political Economy 74, 315-332.

R. W. Fogel (1967), "The specification problem in economic history", Journal of Economic History 27, 283-308.

J. A. James (1984), "The use of general equilibrium analysis in economic history", Explorations in Economic History 21, 231-253.

R. W. Jones (1965), "The structure of simple general equilibrium models", Journal of Political Economy 73, 557-572.

R. W. Jones (1971), "A three-factor model in theory, trade, and history", in J. N. Bhagwati, R. W. Jones, R. A. Mundell and J. Vanek (eds.), Trade, Balance of Payments and Growth: Papers in International Economics in Honor of Charles P. Kindleberger (Amsterdam: North- Holland).

D. N. McCloskey (1985), The Rhetoric of Economics (Madison: University of Wisconsin Press).

P. Temin (1966), "Labor scarcity and the problem of American industrial efficiency in the 1850's", Journal of Economic History 26, 277-298.

M. Thomas (1987), "General equilibrium models and research in economic history", in A. Field (ed.), The Future of Economic History (Boston: Kluwer-Nijhoff).