Question
Asked 10 September 2015

Why did Eaton and Kortum model perform so badly?

I am planning to write an open review on Eaton and Kortum's two papers cited below. The first is a well-known paper but the result is highly unrealistic. For example, the authors estimated the cost of moving autarky as 0.2 % for Japan (mobile labor case). Can anybody believe that the loss is so small when energy inputs are banned from importing? Japanese economy would surely go back at best to the level of the late Meiji period Japan (around 1900).
Is there any arguments, discussion or analysis why Eaton and Kortum model performed so badly? Eaton and Kortum (2012) did not mention this point. I.m.h.o, this must be a result of their model building. How do you think?
Eaton, Jonathan, and Samuel Kortum (2002) Technology, Geography, and Trade, Econometrica 70(5): 1741-1779.
Eaton, Jonathan, and Samuel Kortum (2012) Putting Ricardo to Work, Journal of Economic Perspectives 26(2): 65-90.

Most recent answer

Hubert Escaith
World Trade Organization
Good evening.
I would like to add something to my previous post, an issue I should have raised before as it is pretty obvious.
Eaton-Kourtum relies, like most economists’ approaches using micro-data, on a Constant Elasticity of Substitution. A sophisticated synonym is homothetic demand functions. Plus iceberg trade costs: prices are not affected by trade costs, only volumes. In real life, forget it! Demand functions are not homothetic, markets for complex industrial goods (those analysed by Eaton and Kortum) are monopolistic (at least locally, due to the premium attached to branding and reputation) and lead-firms price to market: the market price (and the mark-up margin) varies according to the particular situation of each market (average income, strength of competition, mature or emerging market, etc.).
This said, the alternative to homothetic demand functions and iceberg cost is devilish: you cannot make the hypothesis of a single world price. So, if any individual case is special, it becomes an empirical issue, rather than a theoretical one...
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Popular answers (1)

Yoshinori Shiozawa
Osaka City University
The topic International Trade counts (as of September 14, 2015) 97 questions and 6,003 followers. My question attracted only 25 views. This state may indicate the general atmosphere of researchers who work on international trade. They are not very interested in the theory.
This indifference in theory problems must be a real problem in international trade theory. 
4 Recommendations

All Answers (18)

Jacky Mallett
Reykjavík University
I think you're quite right, this seems to be an example of building a model that fits pre-assumed expectations, rather than the real world. The lack of energy inputs, or indeed any form of raw material input is a major error - especially for countries like Japan - I presume Eaton and Kortum are both American so they probably don't think about that case.
The other major issue is the absence of financial intermediation - the determinants of price are not as simple as they assume, and in particular there doesn't seem to be any recognition of the issues that would be created by long term unidirectional financial flows in their set of assumptions. 
I would have thought the Edo period would be the best example of what happens to Japan under complete autarky, wouldn't it?
2 Recommendations
Yoshinori Shiozawa
Osaka City University
The Eaton and Kortum model is Ricardian one which includes intermediate goods explicitly. This is a great advancement because Ricardian models (or other trade models including Heckscher-Ohlin  model) assume trade of finished goods. As far as Eaton and Kortum include inputs trade in their model, their model considers importation of energies and raw materials. We have to think that there is some grave defects in their treatment of imported inputs.
Japan was in almost complete autarky in Edo period (1603-1867) except for small trades with China, Korea and Nederland. (N.B. Sakoku period is around 1639-1854. There was a gradual change of policies and we cannot determine it exactly). In Meiji period, Japan produced coal and the percentage of energy materials importation was not great. Now, all those resources have been exhausted. It may be right to say that Japan will go back to Edo period level economy when it closes its country. In this sense, Jacky is right.
However, my intention is not to discuss the real effects of going to autarky. It is evident that such a measure is disastrous. I want to pinpoint the reason why Eaton and Kortum model did not worked as it intended.
As for financial intermediation, I agree that it is important. However, it is not the problem of  Eaton and Kortum model. They do not mention on this point explicitly but I suppose they are assuming that financial factors are already reflected in the real volumes of trade.   
2 Recommendations
Yoshinori Shiozawa
Osaka City University
The topic International Trade counts (as of September 14, 2015) 97 questions and 6,003 followers. My question attracted only 25 views. This state may indicate the general atmosphere of researchers who work on international trade. They are not very interested in the theory.
This indifference in theory problems must be a real problem in international trade theory. 
4 Recommendations
Yoshinori Shiozawa
Osaka City University
It may be good to post a new question, because in this question page, a very few researchers are attracted. 
In the mind of international trade economists, theory problem has been in principle settled and no problems are left. Such a sentiment was expressed by Wilfred Ethier with regards to Ricardo theory, although it is a grave error in my opinion. The same observation can be made for trade theory in general.
  • In Comparative Advantage and the Theory of Tariffs: A Multi-Country, Multi-Commodity Model (1961b), Jones stated the many-commodity, many-country version of the Ricardian comparative-cost expression and proved that it picks out the efficient patterns of the specialization. The two-good, constant-cost model of Ricardo has been a staple of the pure theory of international trade for years, and remains the most common textbook vehicle for illustrating the principle of comparative advantage. Extension of the model to many goods and countries (but, of course, just one internationally immobile factor of production) became a hot topic among international trade theorists in the 1940s and 50s after stimulating works by Frank Graham (1948) and the development of liner programming and activity analysis. Jones supplied the crowning achievement of this area of trade theory, answering a question that has bee outstanding since the time of Ricardo. The contribution was so definitive that the Ricardian model has since been used almost entirely as a tool for other purposes and not as a subject of research in its own right. The main exception is the extension, by Samuelson (1964) and by Dorbusch, fisher, an Samuelson (1977), of the model to a continuum of commodities. (p.764)
This is an excerpt from  
Ethier, Wilfred J., 1999 Jones and Trade Theory, Review of International Economics 7(4): 764-768.
As this is written as a Profile of of Ronald W. Jones,  this must contain some compliments but Ethier must have written what he thought it to be true. According to Ethier, there were no theoretical developments except for only two: (1) by Samuelson on what is now called Balassa-Samuelson effect and (2) extension to the model of continuum of commodities.
Ethier is wrong in saying that "The contribution was so definitive that the Ricardian model has since been used almost entirely as a tool for other purposes and not as a subject of research in its own right." He ignored an extremely important  point.
McKenzie and Jones knew that it was necessary to incorporate intermediate goods (or input goods) in the model. McKenzie emphasized the importance of input trade by the following expression (p.179).
  • A moment's consideration will convince one that Lancaster would not be unlikely to produce cotton cloth if the cotton had to be grown in England. On the other hand, the production of raw materials, especially the mining of metallic ores, might not be profitable in backward area without machinery supplied by the industrial countries. The patterns of interdependence are already very complex, but with free trade they would undoubtedly be far more complex than they are now. The low cost of ocean transport would reduce the advantage of internally supply in continental countries.        Lionel W. McKenzie 1954 Specialization and Efficiency in world Production. Review of Economic Studies 21(3) 165-180.
Jones in his 1961 paper could not solve the problem of input trade, although Jones gave an impression that he did. What he could treat was the case where all material input coefficients are the same for all countries. Ethier did not mention this important point.
A clear difficult task lied ahead but Jones and his followers retreated from the difficulty and thought the all is done. This is  really an enigma in the history of economic theories in foreign trade.
Ethier's article is written a bit earlier than Eaton and Kortum. The latter claimed to have succeeded in incorporating intermediate goods. If they were successful or not, this was a big news. If they have failed in giving a good fitness, we must examine where the problem lies. This is the reason why I have posed the question.        
3 Recommendations
Derek Anderson
Virginia Retirement System
As I remember it, the later Bernard Jensen Eaton and Kortum paper added monopolistic competition to Eaton and Kortum's original trade framework, which adds a degree of flexibility to the model, but is still highly abstracted from theory versus actual trade data. I found the strong dependence on the Frechet distribution for determining levels of productivity more a matter of convenience than a matter of creating a model that describes the data well.
1 Recommendation
Yoshinori Shiozawa
Osaka City University
 Derek Anderson is right when he points 
  • I found the strong dependence on the Frechet distribution for determining levels of productivity more a matter of convenience than a matter of creating a model that describes the data well.
 This kind of matter of convenience can be found in other assumptions.
(1) The concept of the efficiency zi(j) (p.1745)
Eaton and Kortum assume that countries have differential access to technology. This is the essential difference between Ricardo theory and Heckscher-Ohlin model. Eaton and Kortum have not deviated from this fundamental. However, when they assume that they can use a concept "efficiency" harmlessly, they are wrong. 
Efficiency they assume is the one in producing a good j in country i. In an abstract level, we may talk of this kind of concepts, but is it right to assume that the cost of production a unit of good i in country j is expressed as ci / zi(j)? Here ci is the input cost in country j
The problem can be break down in two points.
(A) What is ci and how is it measured?
(B) How is the efficiency zi(j) determined?
  the following, (2) discusses the problem A and (3) the problem B.
 (2) What is the input cost ci in a country?
If we suppose Ricardo's original assumption that all necessary things in a production is a certain amount of labor, the input cost is simply the wage rate of a country. How about when other resources, say parts and materials, were inputted? The wage rate does not determine the input cost. If there were several inputs, we should know two kinds of scalars for each item, i.e. the price of the item and the amount of input quantity to produce a unit of a good. 
It is only in later section 4.1 Production (p.1756) that Eaton and Kortum explain how the cost in labor and the cost in material inputs are divided. They assume that production combines labor and intermediates inputs, with labor having a constant share β. 
How is this assumption justified? They say nothing on it. Do they assume a Cobb-Douglas production function? Then, it is easily shown that the input shares remain constant even if wage price ratio changes. However, this is a serious assumption for a Ricardian model. We may say this assumption makes the model in a kind of variants of neoclassical trade theory (HOS model for example). 
First of all, Cobb-Douglas production function is an illusion interpreting accounting identity as an objective expression of production relations. See Hebert A. Simon (1979) Parsimonious Explanations on Production Relations. Scandinavia Journal of Economics 81(4): 459-474. 
Secondly, all Solow-Swan type production functions (which include Cobb-Douglas p.f. as a special case) assumes that prices of all inputs are determines. If not it is impossible to measure aggregate of goods. Remind what was disputed in the capital controversy between Cambridge, England and Cambridge, Massachusetts. 
Thirdly, if this assumption is admitted, this is similar to Marx's assumption that all industries have the same organic composition. Some people think that Ricardo assumed similar assumptions when he wanted to include material costs as a part of the total cost. However, this assumption is too restricted and represents only special cases. See Morishima's Marx's Economics (1973).
Fourth, as a trade theory, to assume that labor has a constant share of total cost is to assume that the cost is proportional to the wage rate. Indeed, if
     wi a0(i,j) = β ci,
whereb a0(i,j) is the labor input coefficient for the production of good j in country i, then
     ci = (1/β) wi a0(i,j).
This reduces the economy into a pure labor input Ricardo model. Eaton and Kortum pretend that their model "can recognize, in a simple way, the preponderance of trade in intermediate products." However, once it decoration is wiped off, their model is identical to Ricardo model except for single factor β. As their essential structure is the same, it is impossible that Eaton and Kortum's model can have a different pattern of specialization than the labor input Ricardo model with input coefficients (1/β) a0(i,j).
(3) Efficiency zi(j)
Eaton and Kortum assume that
  • that country i's efficiency in producing good j is the realization of a random variable Zi (drawn independently for each j) from its country-specific probability distribution Fi(z) = Pr[Zi < z].
The authors think that in this way they have differentiated goods, but goods are all treated symmetrically, although their efficiency may change by chance. This is a kind of card drawing. In a second reshuffling, the good i has completely different efficiency but they are only a realization of the same probability distribution. Prices may change at each reshuffling but consumers are supposed to maximize Dixit-Stiglitz utility function (its continuum version) they do not cause no essential difference.
Eaton and Kortum claim that they have introduced different technology by assuming different distribution function Fi(z). This is a false contention, because there are no proper differences in production technology. Different goods have different efficiency but only by chance. Ricardo assumed that England has comparative advantage in cloth production with respect to Portugal. Is this a result of a chance sorting? Is comparative advantage of a country only determined by lot drawing? Absolutely no. Input coefficient vector of the production of good j in country j is a result of tremendous efforts in the production of good j industry in country i. It may sometime be conditioned by climate and underground resources. Eaton and Kortum pretend to assume different production technique for each good and in reality they treat all goods exchangeable by chance. This is not Ricardo at all. He knew that different commodity requires different set of input goods in different proportions.
2 Recommendations
Yoshinori Shiozawa
Osaka City University
I found by chance that Eaton and Kortum (2002) played an important role in the rise of gravity model.  
In fact, K. Head and Th. Mayer (2013) Gravity Equations: Workhorse,Toolkit, and Cookbook.CEPR Discussion Paper No. 9322, p.6 writes
  • With the publication of Eaton and Kortum (2002) and Anderson and van Wincoop (2003), the conventional wisdom that gravity equations lacked micro-foundations was finally dismissed.
If this is true, why don't people who work with gravity model counter-argue to my question and defend Eaton and Kortum (2002)? One of their theoretical basis is undermined by my argument.
1 Recommendation
Yoshinori Shiozawa
Osaka City University
I have posed a new question below. Please visit it as well.
It ask a comparison between Eaton and Kortum model and another Ricardian trade theory named New Theory of International Values. A comprehensive expalnation is given by my paper (still in a draft stage) below:
1 Recommendation
Yoshinori Shiozawa
Osaka City University
I have been missing one more grave assumption in Eaton and Kortum (2002) which may influenced the bad performance of their model.
In Subsection 4.1, they "assume that production combines labor and intermediate inputs, with labor having a constant share β" (Eaton and Kortum 2002 p.1755). Thus their production function takes the form  
(14)   cj = wiβpj1-β.
This may be an assumption that Ricardo assumed when he wanted to reason in a shorthand way.  However, as a paper of Samuelson (2001, See the reference below) shows it beautifully,  the asymmetry of production function (or input coefficient vectors) is one of the major reasons of great gains from trade of input trade. Samuelson coined a name of this type of gains from trade Sraffa bonus. As his numerical illustration hints, we can consider that Sraffa bonus is much greater than the gains from trade of finished goods. The assumption (14) should not be seen as innocuous when one wants to construct a Ricardian model that comprises input trade.
Reference:
Samuelson, Paul 2001 A Ricardo-Sraffa Paradigm Comparing Gains
from Trade in Inputs and Finished goods, Journal of Economic Literature,
39(4):1204-1214.
2 Recommendations
Yoshinori Shiozawa
Osaka City University
Thank you for the information. I have given a rapid look on four papers you have hinted. They all explain Eaton-Kortum model, but give no reflections on why Eaton-Kourtum model behaves so badly. The authors are all satisfied that they are tractable. None of them are answering my question.
1 Recommendation
Yoshinori Shiozawa
Osaka City University
Although this question page receives no many new answers, it seems there are steadily new readers. The READ count arrive to surpass 450. I hope it will soon arrive at 500.
1 Recommendation
Yi-Fan Chen
National University of Kaohsiung
Could it because we don't really model firm level innovation efforts explicitly? The productivity distribution shifts as firms innovate more, which makes big firms even bigger and exporting more. If the productivity distribution exhibits power law then we should be able to find higher welfare gains.
Although I work with Melitz model, but my recent working paper generates power laws to both productivity and firm size distributions (Pareto distribution is a special case in my framework). It argues that opening up to trade (like signing FTAs) fattens the right tail of both distributions. I also calibrate a symmetric country version of my model, and it suggests that the welfare gains is 40% higher than that implied by a Melitz model with a Pareto distribution.
Also you may want to refer to the work by Kei-Mu Yi (2003, JPE), who argues that including vertical specialization magnifies the trade flow. Potentially this is a channel for welfare gains because it further accounts for the effect of cheaper foreign inputs on the prices and varieties of domestically produced goods.
Xiaojie Liu
Northwestern University
I think the main problem is not about the Frechet distribution or which distribution we like to specify, for example Pareto. But the firm draws the productivity independently from the distribution. In the traditional Ricardian framework, i.e. comparative advantage, we know the productivity in different sectors or across different firms are correlated. But here it is more like absolute advantage from the perspective of the firm. So you will find it hard to reconcile some important fact in the empirics. But this assumption makes the model tractable and provides a benchmark of estimation.
Hubert Escaith
World Trade Organization
Thanks to Yoshinori Shiozawa for indicating me this very interesting discussion. I understand that this approach has strong limitations, due to the search for a theoretically tractable model. It implies some simplification, often under the form of a pre-established mathematical specification of a probability distribution or of supply and demand functions.
Usually, these simplifications are removed by subsequent researchers who drop some of them to have more general results. It is the incremental way neo-classic research program works, anyway. Other schools of economic thinking try to be holistic from the first step.
Some of the assumptions are due to the Ricardian approach itslef, at the difference of the H-O model: technology is a public good and only labour is a pre-determined country-specific parameter.
Other assumptions can be removed while keeping the Ricardian flavour. For example, to answer Xiaojie Liu remark, in their "Trade with Correlation" paper of Oct. 2018 (available on the net), N. Lind and N. Ramondo drop independence, while still assuming Fréchet distribution for productivity. In general, gains from trade are higher once correlations are taken into account. But Japan's ones remain relatively small (this observation started the whole discussion, if I remember well).
Introducing productivity and innovation, as Yi-Fan Chen suggests would make the model a dynamic one, "à la Krugman", with economies of scale (agglomeration, ...). This implies dropping the constant return to scale assumption. Perhaps there is no need of dropping it, if we consider that a same product made using two different technologies are two different varieties, and that countries specialise on varieties according to their labour cost. In this case, productivity will raise due to the demographics of firms: the non-performing ones at world prices (plus trade costs) will exit, increasing the average sectoral productivity even if productivity for any given variety of sectoral product remains the same. My two cents...
2 Recommendations
Jung Hur
Sogang University
The welfare gains of trade has been discussed in the following 2 papers. It is worth reviewing these two papers. For your question, I recommend the second paper.
Arkolakis, Costinot and Rodriguez-Clare, "New Trade Models, Sam Old Gains?", AER 2012, 102(1)
Arkolakis, Costinot, Donaldson, Rodriguez-Clare, "The Elusive Pro-Competitive Effects of Trade", REStudies 2019, 86.
Yoshinori Shiozawa
Osaka City University
Thank you, Jung Hur , for your information. Hubert Escaith advised me to read a paper by the same author:
Arnaud Costinot, Dave Donaldson, and Ivana Komunjer (2012) What Goods Do Countries Trade? Review of Economic Studies 79: 581–608.
I will read those papers, but give me sometime. For these weeks, I am occupied by other duties to do.
2 Recommendations
Hubert Escaith
World Trade Organization
Good evening.
I would like to add something to my previous post, an issue I should have raised before as it is pretty obvious.
Eaton-Kourtum relies, like most economists’ approaches using micro-data, on a Constant Elasticity of Substitution. A sophisticated synonym is homothetic demand functions. Plus iceberg trade costs: prices are not affected by trade costs, only volumes. In real life, forget it! Demand functions are not homothetic, markets for complex industrial goods (those analysed by Eaton and Kortum) are monopolistic (at least locally, due to the premium attached to branding and reputation) and lead-firms price to market: the market price (and the mark-up margin) varies according to the particular situation of each market (average income, strength of competition, mature or emerging market, etc.).
This said, the alternative to homothetic demand functions and iceberg cost is devilish: you cannot make the hypothesis of a single world price. So, if any individual case is special, it becomes an empirical issue, rather than a theoretical one...
1 Recommendation

Similar questions and discussions

What drives the growth of Global Value Chains? Is there no comprehensive framework encompassing the specificities of GVCs?
Question
47 answers
  • Yoshinori ShiozawaYoshinori Shiozawa
"The rise of Global Value Chains (GVCs) has dramatically changed the organization of world production of goods and services in recent decades." Sónia Cabral (2016) thus remarks and continues that "GVCs cannot be perfectly understood with the traditional concepts of comparative advantage applied to countries and broad sectors." She then put it: "In theoretical terms, a comprehensive framework encompassing the specificities is still lacking." (Cabral 2016 p.279)
Satoshi Inomata (2017) implicitly reconfirms Cabral's proposition in his introductory chapter of the new biennial report (WTO et al., 2017) by putting line heading "The global value chain paradigm: New-New-New Trade Theory?".
Is Cabral and Inomata's observation true? My humble but bold contention is different. The new theory of international values presents such a theory that explains what drives the rise of GVCs and how such a process goes on (See Shiozawa 2017) at least from 2017. How do you think of this point?
References
Cabral, Sónia (2016) Global Value Chains: A Survey of Drivers and Measures. Journal of Economic Surveys 30(2): 278-301.
Inomata, Satoshi (2017) Analytical Frameworks for Global Value Chains: An Overview. Chapter 1, pp.15-35. In WTO et al., Global Value Chain Development Report 2017 (Measuring and Analyzing the Impact of GVCs on Economic Development).
Shiozawa, Y. (2017) The New Theory of International Values: An Overview. Chapter 1, pp.3-73. In Shiozawa et. al., A New Construction of Ricardian Theory of International Values, 2017, Spinger, Songapore.

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