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Ricardo’s Theory of Comparative Advantage:
Old Idea, New Evidence
By ARNAUD COSTINOT AND DAVE DONALDSON
The anecdote is famous. A mathematician, be produced in the importing country.” A simi-
Stan Ulam, once challenged Paul Samuelson to lar identification problem arises in the labor lit-
nameoneproposition in the social sciences that erature in which the self-selection of individu-
is both true and non-trivial. His reply was: ‘Ri- als based on comparative advantage is often re-
cardo’s theory of comparative advantage’; see ferred to as the Roy model. As James Heck-
Paul Samuelson (1995, p. 22). Truth, how- manandBoHonore(1990)haveshown,ifgen-
ever, in Samuelson’s reply refers to the fact that eral distributions of worker skills are allowed,
Ricardo’s theory of comparative advantage is the Roy model—and hence Ricardo’s theory of
mathematically correct, not that it is empirically comparative advantage—has no empirical con-
valid. The goal of this paper is to assess the em- tent. Econometrically speaking, the Ricardian
pirical performance of Ricardo’s ideas. model is not nonparametrically identified.
Tobring Ricardo’s ideas to the data, one must How can one solve this identification prob-
overcome a key empirical challenge. Suppose, lem? One possibility consists in making
as Ricardo’s theory of comparative advantage untestable functional form assumptions about
predicts, that different factors of production spe- the distribution of productivity across different
cialize in different economic activities based on factors of productions and economic activities.
their relative productivity differences. Then, These assumptions can then be used to relate
following Ricardo’s famous example, if Eng- productivity levels that are observable to those
lish workers are relatively better at producing that are not. In a labor context, a common strat-
cloth than wine compared to Portuguese work- egy is to assume that workers’ skills are log-
ers, England will produce cloth, Portugal will normallydistributed. Inatradecontext, building
produce wine, and at least one of these two ontheworkofJonathanEatonandSamuelKor-
countries will be completely specialized in one tum (2002), Arnaud Costinot, Dave Donaldson,
of these two sectors. Accordingly, the key ex- and Ivana Komunjer (2011) have shown how
planatory variable in Ricardo’s theory, relative the predictions of the Ricardian model can be
productivity, cannot be directly observed. tested by assuming that productivity levels are
This identification problem is emphasized by independently drawn from Fréchet distributions
Alan Deardorff (1984) in his review of empir- across countries and industries.
ical work on the Ricardian model of trade (p. This paper proposes an alternative empirical
476): “Problems arise, however, most having strategy that does not rely on identification by
to do with the observability of [productivity by functional form. Our basic idea, as in Arnaud
industry and country]. The...problem is im- Costinot and Dave Donaldson (2011), is to fo-
plicit in the Ricardian model itself...[because] cus on agriculture, a sector of the economy in
the model implies complete specialization in which scientific knowledge of how essential in-
equilibrium... This in turn means that the dif- puts such as water, soil and climatic conditions
ferences in labor requirements cannot be ob- map into outputs is uniquely well understood.
served, since imported goods will almost never As a consequence of this knowledge, agrono-
mists are able to predict how productive a given
Costinot: MIT and NBER, Department of Eco- parcel of land, which will we refer to as a ‘field’,
nomics, MIT, 50 Memorial Drive, Cambridge, MA (e-mail: would be were it to be used to grow any one
costinot@mit.edu). Donaldson: MIT and NBER, Department of of a set of crops. In this particular context, the
Economics, MIT, 50 Memorial Drive, Cambridge, MA (e-mail: econometrician therefore knows the productiv-
ddonald@mit.edu). We thank Pol Antràs, Chang-Tai Hsieh, and ity of a field in all economic activities, not just
Esteban Rossi-Hansberg for comments and Meredith McPhail those in which it is currently employed.
and Cory Smith for excellent research assistance.
1
2 PAPERSANDPROCEEDINGS MAY2012
Our strategy can be described as follows. We factor f in country c. Factors of production are
first establish how, according to Ricardo’s the- perfect substitutes within each country and sec-
ory of comparative advantage, total output of tor, but vary in their productivity Ag 0. Total
cf
various crops should vary across countries as output of good g in country c is given by
a function of: .i/ the vector of productivity of g P g g
the fields that countries are endowed with and Qc D F A L ,
.ii/ the producer prices that determine the al- f D1 cf cf
1 g
location of fields across crops. We then com- where Lcf is the quantity of factor f allocated
bine these theoretical predictions with produc- to good g in country c. The variation in Ag is
tivity and price data from the Food and Agri- cf
culture Organization’s (FAO). Our dataset con- the source of Ricardian comparative advantage.
If two factors f1 and f2 located in country c are
g g g g
sists of 17 major agricultural crops and 55 major such that A 2 =A 1 > A 2 =A 1 for two goods
agricultural countries. Using this information, cf2 cf2 cf1 cf1
g and g , then field f has a comparative ad-
we can compute predicted output levels for all 1 2 2 2
vantage in good g .
crops and countries in our sample and ask: How 2
do predicted output levels compare with those Throughout this paper, we focus on the
supply-side of this economy by taking producer
that are observed in the data? prices pg 0 as given. We assume that the al-
Ourempiricalresultsshowthattheoutputlev- c
els predicted by Ricardo’s theory of compara- location of factors of production to each sector
tive advantage agree reasonably well with actual in each country is efficient and solves
data on worldwide agricultural production. De- nP P P o
max C G pgQg G Lg L .
spite all of the real-world considerations from Lg cD1 gD1 c c gD1 cf cf
which Ricardo’s theory abstracts, a regression cf
of log output on log predicted output has a (pre- Since there are constant returns to scale, a com-
cisely estimated) slope of 0.21. This result is ro- petitive equilibrium with a large number of
bust to a series of alternative samples and speci- profit-maximizing firms would lead to an effi-
fications. cient allocation. Because of the linearity of ag-
The rest of the paper is organized as follows. gregate output, the solution of the previous max-
Section I derives predicted output levels in an imization problem is easy to characterize. As
economy where factor allocation is determined in a simple Ricardian model of trade with two
by Ricardian comparative advantage. Section II goods and two countries, each factor should be
describes the data that we use to construct mea- employed in the sector that maximizes Ag pg,
sures of both predicted and actual output. Sec- cf c
tion III compares predicted and observed output independently of where other factors are being
levels and Section IV offers some concluding re- employed.
marks. Assuming that the efficient allocation is
unique,3 we can express total output of good g
I. Ricardian Predictions 2
The present model, like the Roy model in the labor liter-
The basic environment is the same as in ature, features multiple factors of production. In international
Costinot (2009). We consider a world economy trade textbooks, by contrast, Ricardo’s theory of comparative ad-
comprising c D 1;:::;C countries, g D 1;:::;G vantage is associated with models that feature only one factor of
production, labor. In our view, this particular formalization of
goods, and f D 1;:::; F factors of production. Ricardo’s ideas is too narrow for empirical purposes. The core
In our empirical analysis, a good will be a crop messageofRicardo’stheoryofcomparativeadvantageisnotthat
and a factor of production will be a parcel of labor is the only factor of production in the world, but rather that
land or ‘field’. Factors of production are immo- relative productivity differences, and not absolute productivity
differences, are the key determinant of factor allocation. As ar-
bile across countries and perfectly mobile across gued below, the present model captures exactly that idea.
sectors. L 0denotestheinelastic supply of 3In our empirical analysis, 2 out of the 101,757 grid cells in
cf Brazil—the empirical counterparts of factors f in the model—
are such that the value of their marginal products Ag pg is max-
1 cf c
In line with Ricardo’s theory of comparative advantage, the imized in more than one crop. Thus the efficient allocation is
focus of our paper is on the supply-side of the economy, not only unique up to the allocation of these two Brazilian grid cells.
the demand-side considerations that would ultimately pin down Dropping these two grid cells has no effect on the coefficient
prices around the world. estimates presented in Table 1.
VOL.102 NO.2 OLDIDEA,NEWEVIDENCE 3
in country c at the efficient allocation as output data is missing we assume that there is
g P g no production of that crop in that country. Sim-
(1) Qc D f 2Fg Acf Lcf , ilarly, whenever price data is unreported for a
c given observation, both quantity produced and
where Fg is the set of factors allocated to good area harvested are also reported as zero in the
c
g in country c: FAO data. In these instances, we therefore re-
(2) 8 9 place the missing price entry with a zero.5
< Ag g0 = Our data on productivity (Ag ) come from
Fg D f D 1;:::Fj cf > pc if g’ 6D g . cf
c : g0 pg ; version3.0oftheGlobalAgro-EcologicalZones
Acf c (GAEZ) project run by IIASA and the FAO
Equations.1/and 2 captureRicardo’sideathat (IIASA/FAO,2012).Wedescribethisdatainde-
. / tail in Costinot and Donaldson (2011) but pro-
relative rather than absolute productivity differ- vide a brief description here; see also Nathan
ences determines factor allocation, and in turn, Nunn and Nancy Qian (2009). The GAEZ
the pattern of international specialization. project aims to make agronomic predictions
II. Data about the yield that would obtain for a given
crop at a given location for all of the world’s
To assess the empirical performance of Ri- major crops and all locations on Earth. Data on
cardo’s ideas we need data on actual output lev- natural inputs (such as soil characteristics, water
g availability, topography andclimate)foreachlo-
e
els, which we denote by Qc, as well as data to cation are fed into an agronomic model of crop
compute predicted output levels, which we de- production with distinct parameters for each va-
note by Qg in line with Section I. According to
c g riety of each crop. These models condition
equations .1/ and .2/, Qc can be computed us- on a level of variable inputs and GAEZ makes
ing data on productivity, Ag , for all factors of
cf available the output from various scenarios in
production f; endowments of different factors, which different levels of variable inputs are ap-
Lcf; and producer prices, pg. We describe our
c plied. We use the scenario that corresponds to a
construction of such measures here. Since the ‘mixed’ level of inputs, where the farmer is as-
predictions of Ricardo’s theory of comparative sumed to be able to apply inputs differentially
advantage are fundamentally cross-sectional in across sub-plots within his or her location, and
nature, we work with the data from 1989 only; in which irrigation is available. It is important to
this is the year in which the greatest overlap in stress that the thousands of parameters that enter
the required measures is available. g the GAEZ model are estimated from countless
e
Weusedata on both agricultural output (Qc) fieldandlabexperiments,notfromstatisticalre-
and producer prices (pg) by country and crop
c lationships between observed country-level out-
fromFAOSTAT.Outputisequaltoquantityhar- put data (such as that from FAOSTAT which we
vested and is reported in tonnes. Producer prices g
e
are equal to prices received by farmers net of use here to construct Qc) and natural inputs.
taxes and subsidies and are reported in local cur- The spatial resolution of the GAEZ data is
rency units per tonne. Imperfect data reporting governed by the resolution of the natural in-
to the FAO means that some output and price put whose resolution is most coarse, the climate
observations are missing. We first work with a data. As a result the GAEZ productivity pre-
sample of 17 crops and 55 countries that is de- dictions are available for each 5 arc-minute grid
signed to minimize the number of missing ob- cell on Earth. The land area of such a cell varies
servations.4 In the remaining sample, whenever
Suriname, Sweden, Togo, Trinidad and Tobago, Tunisia, Turkey,
USSR, United States, Venezuela, Yugoslavia and Zimbabwe.
4The countries are: Argentina, Australia, Austria, The crops are: barley, cabbages, carrots and turnips, cassava,
Bangladesh, Bolivia, Brazil, Bulgaria, Burkina Faso, Cam- coconuts, seed cotton, groundnuts (with shell), maize, onions
bodia, Canada, China, Colombia, Democratic Republic of the (dry), rice (paddy), sorghum, soybeans, sugar cane, sweet
Congo, Denmark, Dominican Republic, Ecuador, Egypt, El potatoes, tomoatoes, wheat, potatoes (white).
Salvador, Finland, France, Ghana, Honduras, Hungary, Iceland, 5We have also experimented with replacing missing prices
Indonesia, Iran, Ireland, Israel, Jamaica, Kenya, Laos, Lebanon, by their world averages across producing countries adjusted for
Malawi, Mozambique, Namibia, Netherlands, Nicaragua, currency differences. The empirical results in Table 1 are insen-
Norway, Paraguay, Peru, Poland, Romania, South Africa, Spain, sitive to this alternative.
4 PAPERSANDPROCEEDINGS MAY2012
Figure 1: An Example of Relative Productivity Differences. Notes: Ratio of productivity in
wheat (in tonnes/ha) relative to productivity in sugarcane (in tonnes/ha). Areas shaded white
have either zero productivity in wheat, or zero productivity in both wheat and sugarcane. Areas
shaded dark, with the highest value (“>12,033”), have zero productivity in sugarcane and strictly
positive productivity in wheat. Source: GAEZ project.
by latitude but is 9.2 by 8.5 km at the Trop- III. Empirical Results
ics. The median country in our dataset contains
4,817 grid cells but a large country such as the Weare now ready to bring Ricardo’s ideas to
U.S.comprises157,797cells.Sincethegridcell the data. To overcome the identification prob-
is the finest unit of spatial heterogeneity in our lem highlighted by Deardorff (1984) and Heck-
dataset we take each grid cell to be a distinct man and Honore (1990), we take advantage of
factor of production f and the land area of each the GAEZ data, together with the other data de-
grid cell to be the associated endowment, Lcf. scribed in Section II, to predict the amount of
Hence our measure of the productivity of fac- output (Qg) that country c should produce in
tor f if it were to produce crop g in country c
g crop g according to Ricardo’s theory of compar-
c, A , corresponds to the GAEZ project’s pre- ative advantage, i.e. according to equations 1
cf . /
dicted ‘total production capacity (tones/ha)’. We and 2 . We then compare these predicted out-
. /
match countries (at their 1989 borders) to grid put levels to those that are observed in the data
g
cells using GIS files on country borders from the e
(Qc).
Global Administrative Areas database. In the spirit of the ‘slope tests’ in the
Heckscher-Ohlin-Vanek literature, see Donald
Davis and David Weinstein (2001), we im-
plement this comparison by simply regressing,
A sample of the GAEZ predictions can be across countries and crops, data on actual out-
seen in Figure 1. Here we plot, for each grid cell put on measures of predicted output. Like Davis
on Earth, the predicted relative productivity in and Weinstein (2001), we will assess the empir-
wheat compared to sugarcane (the two most im- ical performance of Ricardo’s ideas by study-
portant crops by weight in our sample). As can ing whether .i/ the slope coefficient in this re-
be seen, there exists a great deal of heterogene- gression is close to unity and .ii/ the coeffi-
ity in relative productivity throughout the world, cient is precisely estimated. Compared to these
even among just two of our 17 crops. In the authors, however, we have little confidence in
next section we explore the implications of this our model’s ability to predict absolute levels of
heterogeneity—heterogeneity that is at the core output. The reason is simple: the model pre-
of Ricardo’s theory of comparative advantage— sented in Section II assumes that the only goods
for determining the pattern of international spe- produced (using land) in each country are the
cialization across crops. 17 crops for which GAEZ productivity data are
available. In reality there are many other uses
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