Computable General Equilibrium Models and Economic History
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
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
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
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
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
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
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,
M. Thomas (1987), "General equilibrium models and research in
economic history", in A. Field (ed.), The Future of Economic History