Archive for the ‘Theory’ Category

Co-authoring is not about comparative advantage

16 October 2017

Comparative advantage is one of our field’s defining insights and “an essential part of every economist’s intellectual toolkit“. The principle is both true and non-obvious, so understanding it separates those who have taken an economics class from those who have not. While economists are rightfully proud of comparative advantage, there is at least one circumstance in which I think economists overuse it.

If you chat with economists about their co-authored research, you’ll often hear them casually attribute the division of labor within their research team to comparative advantage. I’m sure I’ve said this a number of times myself. But co-authoring is not about comparative advantage.

Suppose producing a paper involves two tasks: solving a model and estimating it. If you are better at both tasks than your co-author, then you ought to do both yourself and break up with your co-author. My advice seems contrary to David Ricardo’s famous insight that there are still gains from specialization and trade when one party has absolute advantage in both tasks. But the optimal assignment of tasks does not always depend on comparative advantage.

The Ricardian production function

The principle of comparative advantage is tied to a particular production function. In the Ricardian model, production functions are linear. Thus, individuals’ marginal products are constant. This fact allows us to describe individuals’ choices in terms of relative productivities and relative prices.

In a Ricardian world, the ordering of task assignments depends only on relative productivities: at any relative price, an individual has comparative advantage in the task in which her relative productivity is higher. Absolute productivities show up in a market-clearing condition that determines the relative prices necessary for supply of each task to equal its demand.

Does this sound like co-authorship? Some of the institutional details are wrong. Co-authors don’t usually pay each other for their output. Adding more people may pay off because each of n co-authors can receive more than 1/n credit. But beyond the unusual features of “selling” your output to academia, the Ricardian model’s description of the production process as a research team just doesn’t fit.

Producing research as a team

As Michael Sattinger (1993) explains, not all assignment models are models of comparative advantage:

Some economists may believe that comparative advantage is the only production principle underlying the assignment of workers to jobs, but this is incorrect. As a counterexample, consider an economy in which a job is associated with the use of a particular machine that can be used by only one person at a time…
The reason comparative advantage does not indicate the optimal assignment in this case is that earnings from a job are no longer proportional to physical output at the job. With cooperating factors of production (either explicit in the form of a machine or implicit via a scarcity in the jobs available), an opportunity cost for the cooperating factor must be subtracted from the value of output to yield the earnings.

In the Ricardian model, absolute disadvantage is not a problem, because quantity can make up for quality. If the laborers assigned to a task have low productivity, more labor can be employed in that task to produce more output. But in many situations, quantity cannot substitute for quality. This is most obvious in sports, where rules constrain team size: a hockey team can only have one goaltender. When jobs are scarce, comparative advantage does not determine the optimal assignment.

In a famous applied theory paper, Michael Kremer explored the consequences of producing in a team in which the number of tasks is fixed, each task may be performed by only one person, and a mistake in any one task diminishes the entire project’s value. The latter feature makes this the “O-Ring Theory of Development”, as the space shuttle Challenger blew up due to the failure of only one of its thousands of components.

This production function sounds more like the economics research process. A paper is a discrete unit of output, and it is likely only as persuasive as its weakest link. Poor writing can totally obfuscate good theory. Rarely can a beautiful theory salvage garbage empirics. And it is hard to believe that input quantity can substitute for input quality: “this paper was written by mediocre theorists, but there were so many of them working on it!”

In Kremer’s O-Ring model, the efficient assignment is that workers of similar skill work together in teams. A great theorist pairs with a great empiricist. As a first pass, this seems a reasonable description of the co-authorships we actually observe.

Co-authoring is not about comparative advantage

Of course, production is more complicated than that. How do we explain the valuable contributions of research assistants to projects when their supervisors (would like to claim that they) have absolute advantage across all tasks? One needs a model of hierarchical or sequential production in which research assistants handle easier problems and then pass on unsolved problems to their supervisors. Luis Garicano, Esteban Rossi-Hansberg, and co-authors have studied these knowledge-based hieararchies in environments ranging from law firms to exporters.

In short, the optimal assignment depends on the nature of the production function. Despite economists’ frequent invocation of our beloved insight, co-authoring is not about comparative advantage.

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Linkages between international trade and urban economics

17 September 2017

Keith Head, Thierry Mayer, and Gianmarco Ottaviano have written a review of the latest Handbook of Regional and Urban Economics, published in 2015. The prior edition was published back in 2004. Part of their review looks at the interplay between international and urban economics:

The fourth volume of this series was published at the high point for the strand of research known as the New Economic Geography (NEG). It was a period when, united by interest in research by Paul Krugman, trade economists and spatial economists associated closely with each other. We attended the same conferences and worked on similar topics. We debated what was new and what was valuable about the NEG — and whether the two sets overlapped. The Nobel Prize received by Krugman in 2008 validated this line of research but also coincided with the time when it faded significantly from the priorities of urban economists.
Since then, with some prominent exceptions, trade and spatial economists have gone their separate ways.

This passage surprised me, since I see substantial overlap and collaboration between spatial and trade economists at the moment. Since I am a relatively young economist, I did not witness the previous peak or subsequent decline in collaboration.

Head, Mayer, and Ottaviano provide an explanation for the separation:

Spatial economists appear to us to have moved more in the direction of labor, both in terms of using similar worker-level data sets and in terms of greater focus on identification of treatment effects. Trade economists, on the other hand, have in some respects followed industrial organization, in terms of using firm- level data and in terms of tying in closely to theoretical models. Perhaps increased availability of micro data is a unified explanation for divergence as trade economists embraced firm-level customs data sets at the same time as urban economists embraced labor (and housing) data sets.
Though there are still some points of contact, the fifth volume of the handbook largely testifies this divergence since 2004. We would argue, however, that the stage is now set for renewed collaboration. Trade economists are increasingly using data on individual workers and urban economists have embraced structural models. Thus, the current separation between trade and spatial economics is probably mainly attributable to focus on different questions.

Another way to think about the linkages would be to look at co-authorships. For example, consider the Handbook chapter just mentioned: Matt Turner is an urban economist who teaches one of the few PhD courses in urban economics, and Steve Redding is the NBER International Trade and Investment program director.

You can also find individuals who span the spatial-trade divide. The Clark Medal committee describes Dave Donaldson as “an empirical trade economist”. The first two papers they mention are about the effects railroads in India and the United States on intranational trade.

Head, Mayer, and Ottaviano describe the separation in terms of research topics as opposed to toolkits:

Spatial economics has become… essentially intranational with virtually no international trade dimension… the model by Redding and Turner shares many properties with perfectly competitive stochastic trade models of “discrete choice” a la Eaton and Kortum (2002), which are the pillars of the recent wave of new quantitative models that are changing the way trade economists look ex ante at the possible implications of alternative policy scenarios. This shows once more that, whereas the questions of interest may have largely diverged between trade and spatial economics, methods have not.

Head, Mayer, and Ottaviano “are eager to see renewed linkages between international trade and urban economics” and somewhat optimistic about future research at this intersection. I am even more optimistic, since I already see many of the same people at both international economics and urban economics conferences.

Along those lines, Steve Redding and Esteban Rossi-Hansberg have written a survey of “Quantitative Spatial Economics,” which amounts to a new generation of work in spatial economics importing the tools developed in quantitative models of international trade. They’ve also issued a call for papers in Trade and Geography:

The endogenous location of economic agents relative to one another in space influences their consumption, production and investment decisions. It affects their pattern and volume of trade, the markets that they participate in, and the way they organize production processes across locations. As such, geography shapes the impact of local, regional, industry, and aggregate shocks, and the effects of national and local policies.

This Spring 2018 meeting of the NBER International Trade and Investment Program will focus on this set of issues. The meeting will welcome researchers interested in these topics from a variety of perspectives, including, but not limited to, international trade, regional and urban economics, labor, development, and macroeconomics. Both empirical and theoretical papers are welcome.

As someone who works at the intersection of international and urban economics, I may be prone to emphasizing the common features of these fields and the connections between them. But if we’re at the point where trade and urban have suffered a separation, I think the linkages are already renewing. I cannot wait to realize the fruits of greater collaboration.

Well, that took a while…

14 August 2013

In August 1935, Gottfrieb Haberler wrote (Theory of International Trade, Preface to the English Edition):

[I]t seems to me that the theory of international trade, as outlined in the following pages, requires further development, in two main directions. The theory of imperfect competition and the theory of short-run oscillation (business cycle theory) must be applied to the problems of international trade. It will soon be possible to do this in a systematic way, since much progress has been made in both fields in recent years.

With regard to the first of these questions, there is the literature which centres around the two outstanding books, Monopolistic Competition by Professor E. Chamberlin and Imperfect Competition by Mrs. Joan Robinson. In the second field where further development is required, it is not so easy to refer to a body of accepted theory.

 Of course, the monopolistic competition revolution did not reach international trade until the late 1970s.

Melitz and Redding on heterogeneous firms and gains from trade

6 June 2013

In a recent VoxEU column, Marc Melitz and Stephen Redding describe the logic of Melitz (Ecma, 2003) and Arkolakis, Costinot, and Rodriguez-Clare (AER, 2012). Those should be familiar to Trade Diversion readers (e.g. ACR 2010 wp, Ossa 2012 wp). They then explain their new paper:

In Melitz and Redding (2013b), we show that firm-level responses to trade that generate higher productivity do in fact represent a new source of gains from trade.

  • We start with a model with heterogeneous firms, then compare it to a variant where we eliminate firm differences in productivity while keeping overall industry productivity constant.

We also keep all other model parameters (such as those governing trade costs and demand conditions) constant.

  • This ‘straw man’ model has no reallocations across firms as a result of trade and hence features no productivity response to trade.

Yet it is constructed so as to deliver the same welfare prior to trade liberalisation. We then show that, for any given reduction in trade costs, the model with firm heterogeneity generates higher aggregate welfare gains from trade because it features an additional adjustment margin (the productivity response to trade via reallocations). We also show that these differences are quantitatively substantial, representing up to a few percentage points of GDP. We thus conclude that firm-level responses to trade and the associated productivity changes have important consequences for the aggregate welfare gains from trade.

How can these findings be reconciled with the results obtained by Arkolakis, Costinot, and Rodriguez-Clare (2012)? Their approach compares models that are calibrated to deliver the same domestic trade share and trade elasticity (the sensitivity of aggregate trade to changes in trade costs). In so doing, this approach implicitly makes different assumptions about demand and trade costs conditions across the models that are under comparison (Simonovska and Waugh 2012). By assuming different levels of product differentiation across the models, and assuming different levels of trade costs, it is possible to have the different models predict the same gains from trade – even though they feature different firm-level responses. In contrast, our approach keeps all these ‘structural’ demand and cost conditions constant, and changes only the degree of firm heterogeneity (Melitz and Redding 2013b). This leads to different predictions for the welfare gains from trade.

One potential criticism of our approach is that one can estimate the trade elasticity (the sensitivity of aggregate trade to changes in trade costs) using aggregate trade data only – without requiring any specific assumptions about the firm-level responses to trade. Whatever assumptions are made about those firm-level responses (and the demand and trade-cost conditions), they should then be constructed so as to match that estimated aggregate elasticity. However, recent empirical work has shown that those underlying assumptions radically affect the measurement of the aggregate trade elasticity, and that this trade elasticity varies widely across sectors, countries, and the nature of the change in trade costs (see for example Helpman et al. 2008, Ossa 2012, and Simonovska and Waugh 2012). There is thus no single empirical trade-elasticity parameter that can be held constant across those different models.

Given the lack of a touchstone set of elasticities, we favour our approach to measuring the gains from trade arising from different models; one that maintains the same assumptions about demand and trade costs conditions across those models.

Harry Johnson on Staffan Linder

29 April 2013

I haven’t seen a book review like this in some time. Harry Johnson didn’t hold back while expressing his opinion of Linder (1961). This is the closing paragraph of his rather blunt five-page review:

In summary, this is at once an ambitious, provocative, and provoking book-ambitious in the breadth and depth of the problems in trade theory it propounds and seeks to solve, provocative in the hypotheses it propounds, and provoking on account both of the perverse misinterpretations of existing theory that the author produces to support his claims to novelty and of the careless botch he makes of the exposition of his own alternative theories. The result is a volume that ought to be read by specialists looking for seminal ideas and interesting research problems,but that cannot be recommended for use by students insufficiently trained to be alert to the substitution of emotive debating points for reasoned argument and of irrelevance for logical analysis. [Economica, 1964]

How big are the gains from trade?

28 May 2012

One of the most-mentioned trade papers of the last couple years is “New Trade Models, Same Old Gains?” by Arkolakis, Costinot & Rodriguez-Clare, now published in the AER. Their theoretical work shows that, for a broad class of theoretical models that includes the Armington, Eaton and Kortum (2002), and Melitz-Chaney approaches, the gains from trade are characterized by a formula involving only two numbers – the domestic expenditure share and the trade elasticity. The former can be straightforwardly obtained from the data. The latter needs to be estimated, which is more involved but feasible. ACR shows that their formula says that US welfare is about 1% higher than it would be under autarky.

In the words of Ralph Ossa, “either the gains from trade are small for most countries or the workhorse models of trade fail to adequately capture those gains.” Different people come down on different sides of that choice. Ed Prescott, for example, is clearly in the latter camp.

Ossa has a new paper, “Why Trade Matters After All“, aimed at reconciling this divide:

I show that accounting for cross-industry variation in trade elasticities greatly magnifies the estimated gains from trade. The main idea is as simple as it is general: While imports in the average industry do not matter too much, imports in some industries are critical to the functioning of the economy, so that a complete shutdown of international trade is very costly overall…

I develop a multi-industry Armington (1969) model of international trade featuring nontraded goods and intermediate goods and show what it implies for the measurement of the gains from trade…

Loosely speaking, the exponent of the aggregate formula is therefore the inverse of the average of the trade elasticities whereas the exponent of the industry-level formula is the average of the inverse of the trade elasticities which is different as long as the elasticities vary across industries.

allowing for cross-industry heterogeneity in the trade elasticities substantially increases the estimated gains from trade for all countries in the sample. For example, the estimated gains from trade of the US increase from 6.4 percent to 42.0 percent if I do not adjust for nontraded goods and intermediate goods and from 3.8 percent to 23.5 percent if I do…

the 10 percent most important industries account for more than 80 percent of the log gains from trade on average.

Eaton & Kortum – “Putting Ricardo to Work”

9 March 2012

This forthcoming Journal of Economic Perspectives article by Jonathan Eaton and Sam Kortum on the Ricardian model of trade is fantastic. It walks the reader from Ricardo (1818) to Mill (1844) to Dornbusch, Fischer, and Samuelson (1977) to Eaton and Kortum (2002) to the modern frontier. Put it on your syllabi.

When trade raises welfare and lowers measured GDP

19 November 2011

This nifty note by Bajona, Gibson, Kehoe, and Ruhl points out that there may be little connection between real GDP and welfare; in fact, welfare-improving trade liberalization may lower measured real GDP. Here’s a simple example in the Heckscher-Ohlin setting:

The intuition behind the decrease in measured real GDP for the autarky to free trade scenario is simple: given factor endowments, the base-year production pattern in country i is the optimal production pattern for country i at the base year prices among all feasible production plans… Any deviation from that production pattern will lower the value of production at those prices.

Freely traded outside goods have non-trivial consequences

10 October 2011

Recall that assuming a freely traded, CRS-produced outside good when writing a trade model is non-trivial [Davis (AER, 1998)]:

In the present paper, I show that what previously was regarded as an assumption of convenience – transport costs only for the differentiated goods – matters a great deal. In a focal case in which differentiated and homogeneous goods have identical transport costs, the home-market effect disappears.

In a recently posted paper (pdf), Svetlana Demidova and Andrés Rodriguez-Clare remind us that a curious result lurking in the heterogeneous firms literature – that unilateral trade liberalization decreases a country’s welfare – hinges on exactly that assumption.

It is interesting to compare this result to that in Demidova (2008) for the setting with CES preferences and Melitz and Ottaviano (2008) for the setting with linear demand, where lowering trade barriers for foreign firms reduces welfare at Home. The reason for this result is that such liberalization in country 1 makes country 2 a better export base, which results in the additional entry of firms there. This entry intensifies competition, which results in less entry and lower welfare in country 1. Our model shows that this result no longer holds when there is no outside good pinning down the wage in both countries.

Chaney (AER, 2008) also assumes a freely traded homogeneous good, so I presume that the same conclusion applies in his environment.

The Demidova & Rodriguez-Clare paper introduces a small open economy version of Melitz (2003), which lets them analyze asymmetric trade policies with endogenous wages very nicely in a (relatively) simple setting. Check it out.

“Ricardo revisited”: Back to 2004

29 March 2011

In a piece titled “Ricardo Revisited: Sino-American Trade and Economic Conflict,” Ralph E. Gomory and William J. Baumol write:

In this note we look carefully at the impact on a developed nation of the economic development of its trading partner; a trading partner that is developing from a rather undeveloped state. If you want to keep the China-U.S. relationship and the impact on the United States of China’s development in mind as a possible example, you will not go far wrong.

We will discuss what a very standard model, the Ricardo model, shows about this situation. We will see that this very familiar model, properly analyzed, has a number of very unfamiliar consequences. Notably:

  1. The economic development of your trading partner can be harmful to you, the home country.  Although the effect of that development starts out good, it ends badly.
  2. That there is a dominant and dominated relation possible between the two countries that is good for the dominant one and bad for the dominated one.
  3. A country can attain a dominant position only by having an undeveloped trading partner. This can occur naturally if the trading partner is simply there in an underdeveloped state, or the underdevelopment can be brought about by mercantilist actions that destroy that partner’s industries.
  4. There is inherent conflict not only between a nation in a dominant position and its trading partner, but also between that dominant nation and what may loosely be called the interests of the world. In a two-country model of the sort we discuss here this simply is measured as the sum of the benefits obtained by the two countries’ economies.  We assert that from a world point of view, having either nation dominant is bad.
  5. While a country cannot gain a dominant position solely by building up its industries, it can avoid a dominated position by developing its own industries and not allowing them to be destroyed.

We will explain more clearly what we mean by these assertions as we go along… We will also explain enough about the Ricardo model to make that intelligible to those not already familiar with it.

A quick skim of their Appendix A shows that this is literally the standard Ricardian model. They’re just going to discuss comparative statics — what happens to the equilibrium outcome when countries’ productivities change? Unfortunately, a lot seems to obscured by their choice of words.

In the model, countries are symmetric in size and the representative consumers have identical Cobb-Douglas preferences. The “dominant” country is the economy with a larger share of world income — this means that it is more productive and/or makes the good with the larger expenditure share. The words “mercantilist” and “destroy” only appear in the introduction and conclusion, so I can’t say how they’re related to the analysis. Productivity is exogenous in the model and there are no policy instruments, so I don’t see how one avoids destroying industries or can actively frustrate the other economy’s productivity growth.

The word choice is frustrating, because some commentators have interpreted this as an attack on mainstream international economics: “Ralph Gomory and William Baumol, who have posited a much more widely applicable, if equally mathematically watertight, challenge to conventional trade theory.”

Nonsense. This is conventional trade theory. Whip out your copy of Dornbusch, Fischer, and Samuelson (AER, 1977) and turn to page 827:

An alternative form of technical progress that can be studied is the international transfer of the least cost technology. Such transfers reduce the discrepancies in relative unit labor requirements — by lowering them for each z in the relatively less efficient country — and therefore flatten the A(z) schedule in Figure 1. It can be shown that such harmonization of technology must benefit the low-wage country, and that it may reduce real income in the high-wage country whose technology comes to be adopted. In fact, the high-wage country must lose if harmonization is complete so that relative unit labor requirements now become identical across countries and all our consumer’s surplus from international trade vanishes.

According to Arvind Panagariya, this result was first shown by Harry Johnson in the 1950s. It had another widespread discussion in 2004 when Paul Samuelson revived it with a JEP article. (I remember blogging that seven years ago!) I see no challenge to orthodoxy here.

The standard Ricardian model doesn’t have intertemporal dynamics, so Gomory and Baumol aren’t in a great position to do welfare analysis, but let’s discuss it nonetheless. Note that free trade is preferable to autarky in every period. So cutting ourselves off from trade with China isn’t the answer. The options are either to (1) improve US productivity or (2) retard Chinese technical progress. I’m not aware of any free trader opposing the former, and the policy instruments available for the latter are, in the words of Avinash Dixit and Gene Grossman, “to ‘bomb China back into the stone age’ of their older lower productivity.”