INTRODUCTION
Calls are often made on humanitarian grounds for developed countries to become actively involved in solving economic problems particular to developing countries, such as funding research on malarial drugs and AIDS vaccines for the poor countries.1
For instance, Jeffrey Sachs (1999) makes the plea, “To the extent that the poor face distinctive challenges, science and technology must be directed purposefully towards them,” and again notes, “It is very rare, alas, that technologies are developed by the private sector to meet specific challenges in the poor countries (for example, for tropical foods or diseases)” (Sachs 2005, p. 282).
We develop a nonaltruistic dynamic trade model of the world with two regions. Preferences are identical, and defined over an inferior (“agricultural”), labor-intensive good and a luxury (“nonagricultural” or “manufacturing”), capital-intensive good. The developing region produces only the inferior good using labor as the sole input, and the developed region produces this, as well as a luxury good that requires both capital and labor. We assume that technology is specific to a region and that the developing countries are unable to commit to future payments in return for technological assistance; consequently, technology transfers must take the form of donations.2
Although this assumption can be justified on the basis of empirical relevance, it is also a conservative one. If rich countries have an incentive to provide technologies specific to poor countries for free, they will be even more likely to do so when they are paid for these technologies.
We initially abstract from the costs of technology improvements and focus on welfare analysis to highlight the basic forces at work; the cost of starting from an abundant technology base and modifying it for use in poor countries is likely to be small for the rich.3
The cost outlays for the Green Revolution, an episode we use to illustrate our framework, were quite low, making this an empirically relevant exercise.
We then study costly technological improvements. Although these costs might not be quantitatively important, explicitly modeling them allows us to analyze the technological investment choices individual regions face, and compare them with each other. With specialization, the rich country would invest more in the poor country's technology than the poor would do on its own. The ensuing terms-of-trade increase would benefit the rich. Without specialization, under reasonable conditions, it is the poor that would invest more than the rich. The rich region experiences no improvement in its terms-of-trade here. The rich country's preference for inappropriate development is shown to be robust to the inclusion of costs.
The above-mentioned dichotomy between improved terms-of-trade and increased production becomes less stark when we analyze the transition from a low level of technology in the poor region to a higher one. For instance, when the rich region is not specialized, there is a terms-of-trade improvement during the transition even though there is none in the steady state. Modeling the dynamics allows us to gain this and other insights. It shows how capital accumulation amplifies the factor allocation effect when there is no specialization. And, as will be seen in Section 2.3, dynamic considerations make the possibility of the rich region improving an inappropriate technology more likely. Characterizing the dynamics also sets the stage for welfare analysis that includes transitions.
Though the model allows us to address issues of broader interest, the Green Revolution appears to be a natural application for it. The establishment of the Consultative Group on International Agricultural Research (CGIAR) in 1971 solidified international efforts in this regard that had begun as early as the 1940s. The cost of such research, although not insignificant, was not particularly high. Evenson and Gollin (2001) report that the funding for the CGIAR has been about 5 billion U.S. dollars since 1971, and its budget for 1998 was $340 million. The achievements of this revolution have been staggering.4
The real price of food in international markets is less than half its level of 50 years ago. The FAO's index of food production per capita for developing countries increased tremendously, as shown in Table 1. See Evenson and Gollin (2001) for a comprehensive summary.
It is well understood that a technology improvement in the poor region's export sector benefits the rich region, and that the terms-of-trade and the minimum consumption requirement are important for the welfare calculations for developing countries. However, our paper adds several novel dimensions to these results. We apply these themes to the issue of technology transfer instead of donation of goods, shifting attention from more conventional foreign aid to donation of technologies.5
The following quotation from the Economist, dated February 22, 2001, is relevant in this regard: “The case for much more generous provision of life-saving drugs to the developing countries is irresistible both morally and as a matter of economics. But it is naive, wrong and in the long run counter-productive, to expect the cost of this aid to be met out of drug-company profits. Instead, rich-world taxpayers should pay. It would be much better to spend aid money on drugs for developing countries than it is to waste it in the usual ways.”
We realize that patent enforcement does have a positive effect on R&D. Our point here is to show that there are also beneficial effects associated with technological imitation, especially across developed-developing country boundaries. This is related to, but different from, the case against intellectual monopoly made by Boldrin and Levine (2002). Also see Sachs et al. (2001) in this regard.
There is an extensive literature on how a country can balance the consumer distortion arising from a tariff with increases in producer surplus and revenues and arrive at an optimal tariff. However, unlike technology improvements, optimal tariffs will hurt the poor region. Optimal tariffs are difficult to implement in practice, given the possibility of retaliation and the inefficiencies in disbursing the collected tariffs. We analyze the case without trade distortions and only briefly consider tariffs in Section 5.
Rivera-Batiz and Romer (1991) are also interested in the effects of economic integration and technological progress. However, they focus on the pure scale effects of integration and “do not consider the general case of trade between countries with different endowments and technologies,” as we do. In Matsuyama (2000), “North,” which specializes in higher income elasticity goods, cannot lose from an improvement its own productivity, whereas “South,” which specializes in lower elasticity goods, may lose from an improvement in its productivity. The possibility of such immiserizing growth can be traced back to Bhagwati (1958). Our model has a simpler goods structure than Matsuyama's. Moreover, the difference in income elasticities is not necessary for our results, merely amplifying the incentives of the rich region. The nonspecialized and specialized regimes we study provide a useful dichotomy in understanding the roles of increased production and improved terms-of-trade in the expansion in value of the rich region's overseas markets. Immiserizing growth will not take place in our framework, provided the negative terms-of-trade effect experienced by the poor is dominated by the higher income generated by the improved technology.
Basu and Weil (1998) model technology improvements as being specific to a given capital-labor ratio in order to explain their slow diffusion across countries. Acemoglu and Zilibotti (2001) quantify the international differences in productivity and output arising from a mismatch between rich-country technologies and poor-country skills. In these papers, the frame of reference for inappropriateness is the poor country; in ours it is the rich country. The mismatch they document further justifies the need for technology development directed toward poor countries. Desmet (2002) notes that transferring a new technology to a poor region that does not have the complementary old technology does not spur development. We consider the case of the rich region transferring technology appropriate to the poor region but inappropriate to itself. Baxter (1992) constructs a model in which reproducible capital, constant-returns-to-scale production, and optimizing agents can turn a standard Hecksher-Olin model into essentially a Ricardian model with specialization in the long run. We have both Ricardian and Hecksher-Olin features in our framework, and high enough agricultural productivity in the poor region can result in long-run specialization by the rich.
Given the likelihood of Pareto improvement, why are such international “interventions” rare? We have considered regions and ignored the individual countries that form a region. The free-riding problems inherent in technology improvement are likely to be a major disincentive for a given rich country to improve a poor region's technology on its own: countries that do not share the cost of research will also benefit. The issues of how sovereign entities form consortia to ensure the provision of this “public” technology, and why certain provisions such as improved crop seeds met with better success than the currently debated provision of life-saving drugs, are interesting in their own right and are the subject of ongoing research. However, in this paper we abstract from such considerations and assume that rich countries effectively coordinate their actions and can be treated as a region. We focus instead on the first step of analytically and quantitatively assessing the benefits, if any, of such a provision, and on the mechanics of trade and the transition that ensues.
The rest of the paper is structured as follows. In Section 2, we present the model and characterize steady state outcomes when the developed region produces both goods as well as when it specializes in the luxury good, when the cost of improvement is assumed away. In Section 3, we conduct the steady state welfare analysis when technology improvement is costly. We characterize the transitional dynamics that follow technology improvements in Section 4. In Section 5, we present a quantitative assessment of the welfare effects by viewing the Green Revolution through the lens of our model. Section 6 concludes.
THE MODEL
We consider a world with two regions—developing, or poor, subscripted by P, and developed, or rich, subscripted by R—whose citizens value consumption of two goods, denoted by superscripts 1 and 2. The instantaneous utility is given by
for region i = P, R. The constant mi>0 is the minimum amount of good 1 that must be consumed by region i. This good can be thought of as a necessity; it is straightforward to show that the income elasticity of demand is smaller than one for good 1, and greater than one for good 2.7
The indexation of m by i allows for the possibility that the norms for a minimum can change with the level of development. Inferiority of food is an empirical reality we cannot ignore. The 2000 World Development Indicators reports that only 13% of consumption expenditures in the United States in 1998 and 14% in the United Kingdom were for food. This figure is much higher for developing countries—49% in Bangladesh, 47% in Indonesia, and 45% in Pakistan. See Chatterjee and Ravikumar (1999) for an exposition on minimum consumption in a macroeconomic context.
Throughout the paper, we interpret the minimum consumption requirements mi as aggregate requirements proportional to population size. Given this, we use the aggregate agent's utility for analysis instead of multiplying individual utility by the number of agents. This is done for ease of exposition and nothing crucial, including the scale effect highlighted below, depends on this. As will be seen from (25), it is the ratio of labor forces between the two regions that matters for the scale effect.
We are interested in specifying a production structure that is tractable for dynamic analysis, while capturing the key incentives the rich region has for improving the poor region's technology. Our investigation of a simple static framework, where the inferior good is labor-intensive and the luxury good is capital-intensive, yields the following results:9
Details of this analysis are available from the authors upon request.
If the rich country has a comparative advantage in the production of good 2 (given endowments and technologies), it would prefer an improvement in the poor country's technology for good 1 rather than good 2. The rich country benefits from an improvement in its terms-of-trade when good 1 is improved.
If the rich country's own technology for good 1 improves, it directly benefits from an increase in its output as well as from an improvement in its terms-of-trade. However, if the poor country is a large enough producer of good 1, and the rich of good 2, the terms-of-trade effect is stronger if the poor country's technology improves. This would give the rich region an incentive to improve an inappropriate technology rather than its own.
The rich region prefers an improvement in the poor country's technology for good 1, say through improved crop seeds, to an improvement in its labor supply, say through drugs that treat tropical diseases. The poor region would allocate some of the increase in labor to producing good 2 and compete with the rich country, numbing the impact on the terms-of-trade. The rich region therefore prefers improvements in directed technologies rather than “general purpose” technologies.
If the rich country's production advantage in good 2 is strong enough, its welfare gain from improving the poor country's technology for good 1 is increasing in the degree of inferiority of that good.
In summary, the rich country benefits most from an improvement in the poor country's technology for the good in which it does not have a comparative advantage, which is produced in large quantities in the poor country, whose technological development cannot spill over to other goods (is directed), and which is inferior. Given these incentives the rich region has for improving the poor region's technology, we focus on a production structure in which the poor country produces only the inferior good. The rich country can produce this good as well as a luxury good. We study the effects of an improvement in the poor country's technology.
The poor region's total production of good 1, YP, is given by
where LP is the total labor force of this country and AP is a productivity measure.10
We have assumed that all poor countries can be lumped into a region and the same technology is appropriate for all. Given that a vast majority of the developing countries are in the arid or semiarid tropics, agricultural and health concerns are likely to be very similar for them.
The rich country produces both goods. Its production of good 1 is given by
where
, and with
denoting the amount of labor used in the production of good 1.11
Note that the rich country has an absolute advantage in the production of food. Given the possibility of technology transfer in this sector, absolute advantage matters (whereas in classic trade models comparative advantage alone matters).
where
is the efficiency parameter for sector 2, LR the total labor force, and KR the stock of physical capital of the rich country.12
Our main results should go through when capital is used in both sectors, provided that the technology for good 1 is less capital-intensive than the technology for good 2.
. Sector 1 can be thought of as representing agriculture, and sector 2, manufacturing (“nonagricultural” in general). Capital evolves according to
where iR denotes gross investment by the rich country. The developed region decides how to allocate its labor between the two sectors and how much to invest in physical capital. We make the realistic assumption that the manufacturing good alone is used for accumulating capital.
The poor country's efficiency parameter, AP, is of fundamental importance for our analysis. We also wish to compare the benefits from increasing AP to those associated with increasing
. Therefore, we will solve for and highlight the dependence of the main variables (prices, quantities, welfare) on AP and
as we proceed.13
We assume that the parameters of the model satisfy the following inequality: APLP>mP+[1/(1−2θ)]mR. This assumption guarantees that, if good 1 is only produced by the poor country, the output will be enough to satisfy both countries' aggregate minimal consumption requirements. It also ensures the empirically plausible outcome of the rich country consuming more of good 2 than the poor country.
To improve the technology from AP to
a country has to expend resources. We assume that this cost, incurred in terms of good 2, is given by the following convex specification:
In this section, the analysis is confined to steady-state comparisons; transitions are analyzed in Section 4. Steady-state expressions for income and factor allocations are used to evaluate benefits from improvements. To make the cost compatible with this interpretation, we assume that the investment cost is borne in the steady state in the form of a perpetual payment,
, where r is the interest rate.14
It can be shown that even if the interest rate is driven endogenously by the developed world, an empirically plausible supposition, the results are qualitatively similar.
If p denotes the relative price of good 2 in units of good 1, the problem of the poor country is
subject to the constraint
The problem of the rich country is
subject to the constraints
There are four crucial ingredients in our analysis: the terms-of-trade effect, the relative sizes of the labor forces (which give rise to a scale effect), the minimum consumption requirement, and costs of technology improvement. We start by ignoring these costs; that is, we ignore the rc term and the choice of
. The main points of the paper can be made within this simpler structure. Costs are explicitly considered in Section 3. Although we retain the minimum consumption requirements in the following expressions, it is easy to abstract from their effect by setting the mis to zero.
Because the poor country has no dynamic choices to make, the solution to its optimization problem is trivially given by:
For the rich country, we form the current value Hamiltonian of the problem,
, and write the first-order conditions as
as well as the budget constraint and the law of motion for capital. Here λ1 and λ are the multipliers on the budget constraint and the law of motion, respectively.
Using (6) and (7) in the budget constraint, we get
If condition (9) holds with equality, both goods are produced by the rich country. This equality implies a sectoral capital-to-labor ratio of
However, if (9) is a strict inequality even when
, the rich country specializes in good 2, and good 1 is produced only by the poor country.
Equilibrium
An equilibrium is simply defined as both regions optimizing according to the problems given above, and the following market clearing condition being satisfied:
Using the first-order conditions for consumption in the two regions in the above equilibrium condition, we can get the following alternate equilibrium condition, which we find more useful:15
By using the rich region's budget constraint with the market clearing condition for good 1, one can obtain the usual balance of trade condition:
The value of the world consumption of good 2 is equated to the value of total consumption of good 1 in excess of the minimum requirements, up to a factor of the utility weights.
As we show below, the rich country will find itself in one of two steady state regimes: specialized in the production of good 2 or producing both goods. It is straightforward to show that the condition for the nonspecialized steady state to obtain is
This assumption is more likely to be satisfied when the rich country is capable of producing larger quantities of good 1 than the poor country; in particular, when
is large enough relative to AP, LR is not too small relative to LP, the ms are sufficiently large, θ is large enough to make the world consumption needs of good 1 large, and β is high enough to make capital, rather than labor, more important for the production of good 2. The presence of the ms makes it more likely for the condition to be satisfied.
We find the dichotomy of steady states useful in illustrating the effects of an increase in the poor country's technology on the rich country's GNP. In the specialization regime, the rich country benefits in the steady state only by an improvement in the terms-of-trade; there is no factor reallocation effect. In the nonspecialization regime, the rich country benefits only by reallocating labor toward the good in which it has a comparative advantage, the luxury good; there is no improvement in its terms-of-trade. The real world would correspond to a convex combination of the two scenarios in our model; as we will see, this is especially true when the transition is considered.
Steady State: Specialization
The case of specialization allows us to highlight the terms-of-trade effect. The following claim anchors the analysis in this case. For notational simplicity, we omit the asterisk notation commonly used for steady state quantities; however, it is to be understood that all quantities are evaluated at the steady state.
Claim 1. When (15) fails to hold, the rich country specializes in good 2. An increase in the technology of the poor country, AP,
- Leaves the rich country's steady state capital stock and its production of good 2 unchanged. However, its steady state terms-of-trade improve and increase its income. The improvement in the terms-of-trade is magnified by the inferiority of good 1.
- Increases the output and the welfare of the poor country if its output is large relative to the minimum consumption levels.
- Increases the steady state welfare of the rich country because the terms-of-trade move in its favor; this welfare effect is magnified by the degree of inferiority of good 1.
(1) Imposing the steady-state conditions
, rearranging (10), and setting
, we get
The steady state capital stock does not depend on AP. If the rich region is specialized for a given AP, we can see from (15) that it will continue to be specialized for higher APs; therefore, increases in AP do not affect output in the rich region. Total steady state output of good 2 net of depreciation,
, is also independent of the poor country's technology.
The trade-balance condition simplifies to
With (5) and (11), this implies that
The steady state price increases with AP, because the world output of good 1 increases, with no increase in good 2. The rich country's income,
, also increases.
The elasticity of the rich country's terms-of-trade with respect to AP is
This elasticity equals one when the minimum consumption levels are zero and increases when they increase. The inferiority of good 1 thus provides an amplification of the terms-of-trade effect and the incentive the rich region has to improve AP.
(2) From (4) we can see that the poor country's consumption of good 1 depends positively on AP. Using the expression for the price, (17), in (5) we get the consumption for the second good as
Therefore,
is a decreasing function of AP for nonzero minimum consumptions. When the ms are zero,
is independent of AP, and given that
increases with AP, the poor country's welfare increases unambiguously with technology improvements. The only way to evaluate the general case is to derive the indirect utility function, which for country i in the steady state (ignoring constants) is
where the incomes (net of depreciation) are given by
Using the expressions for price and output, this becomes
It can be seen that, if APLP>mP+mR/θ, then ∂VP/∂AP>0; this ensures that the income effect for the poor country due to an increase in AP is stronger than the terms-of-trade effect. If this condition does not hold, a donation of technology can be “immiserizing” for the poor country.16
Also, see Matsuyama (2000) in this regard. How does ∂VP/∂AP depend on the poor country's labor force LP? The higher LP makes the country richer, but also increases the terms-of-trade in favor of the rich. However, it can be shown that θ<1/2 is sufficient to guarantee ∂2VP/∂AP∂LP>0.
(3) For the rich country, because p increases with AP, equations (11) and (12) unambiguously show that both
and
increase with AP. Evaluating (19), we get the rich country's welfare as
For the rich country, it is always the case that ∂VR/∂AP≥0 and the inequality is strict whenever mR>0. The terms-of-trade move in favor of the rich country, and its welfare effect can never be negative.
In (22), IP is the only determinant of VR that changes with AP. Setting mR=mP=m, we can show that ∂2VR/(∂IP∂m)>0; therefore, the welfare effect of an increase in AP is magnified by the inferiority of good 1. This is to be expected, as we saw above that the elasticity of the terms-of-trade with respect to AP increases with m. This elasticity decreases with LP, which points to the disincentive the rich country might have for raising it.17
For a more general CES utility specification, if the elasticity of substitution is greater than one, the terms-of-trade effect, including its magnification by the inferiority for good 1, should be more muted. After a technological donation, the poor country's demand for good 2 would increase by less when the elasticity of substitution was higher.
Even though the consumption of good 2 by the poor country,
, decreases with AP, its value,
, increases; the percentage increase of expenditure on good 2 is higher than on good 1. Therefore, the global market for the good produced by the rich countries increases, in value if not in actual units of goods.
Steady State: Nonspecialization
We state the following claim for the steady state in which the rich region produces both goods.
Claim 2. When (15) holds, the rich country produces both goods. An increase in the technology of the poor country, AP,
- Has no effect on the steady state terms-of-trade.
- Increases the rich country's capital stock, its production of good 2, its income, and its welfare in the steady state. These effects are magnified by the size of the poor country's labor force and, in the case of welfare, by the degree of inferiority of good 1.
- Increases the output and the welfare of the poor country.
- Is preferred by the rich country to an increase in its own technology for the corresponding good if the labor force in the poor country is large enough.
(1) The analogue of (16) in this case is
The capital-to-labor ratio in sector 2 is determined by the developed world's technological and preference parameters alone. At the steady state, iR=δKR, as usual.
Combining (22) with (13), we get18
We also note that the relative price of good 2 is continuous across the specialization and nonspecialization regimes, as are the steady-state utility functions, VP and VR. However, there is a discontinuity in the derivatives of VR and VP with respect to AP at the critical value of AP that triggers specialization.
Given (22) and (13), the long-run terms-of-trade are also determined solely by the parameters of the rich country and unaffected by any change in AP.
(2) Although there is no terms-of-trade effect, there is a factor-reallocation effect. Using (14) and (23), we derive the equilibrium choice of
as
where a and b are positive constants. The rich country's employment in sector 1 depends negatively on the poor country's technology, AP, as well as on its labor force, LP. Calculating
, we can see that the negative impact of AP on the labor force devoted to agriculture in the rich countries is magnified by the size of the poor country's labor force. This is a scale effect of technology; the larger the labor force of the poor region working with the technology, the greater the effect of improving it. From (22), one can see that an increase in the steady state labor also increases the capital stock; an increase in the rich country's production of good 2 results.
Since the relative price p does not change, the impact of AP on consumption and on welfare, as given by (19), is confined to its impact on income, Ij. For the rich country, higher AP decreases output in sector 1 but increases it in sector 2. Some algebra shows that
, where c and e are positive constants. Therefore, AP has a positive effect on the rich country's income net of depreciation. As with
the impact of AP on IR is magnified by the size of the poor country's labor force.
The improved efficiency of the poor country allows it to produce more of good 1. This enables the rich country to redirect its labor to the capital-intensive sector 2, where it has a comparative advantage. This increases the marginal product of capital, and causes a long run increase in the accumulated capital. Output in sector 1 falls, but the increase in output in sector 2 is enough to increase the income and welfare of the rich country.
Setting mR=mP=m, we can show that ∂2VR/(∂AP∂m)>0; the welfare effect for the rich country of an increase in AP is magnified by the inferiority of good 1. The effect on steady state welfare is driven only by the GNP net of the minimum consumption. The higher this minimum, the greater is the percentage effect of labor reallocation toward the rich country's production of the luxury good. The increase in IR outweighs the direct negative effect of m on the rich country's welfare.
(3) The positive relationship between IP and AP implies that the poor country's consumption of both goods will also vary positively with AP. Therefore, both regions unambiguously benefit from a more efficient sector 1 in the developing world.19
Because there is no steady state change in the terms-of-trade, ∂2VP/∂AP∂LP>0 obtains here more readily than in the case of specialization.
Though the steady state consumption of both goods increases for the poor country, it increases by a higher percentage for good 2, given that it is a luxury good. The claim often made in policy discourse that improving the condition of the poor countries can only expand the global market for the goods produced by the rich countries is validated in this case too.
(4) What are the implications of an improvement in the rich country's own efficiency of sector 1 (higher
)? From (24), we see that
depends positively on
. This implies that the rich country's output in sector 1 will increase with
; output in sector 2 decreases, however, both through the reduction in labor and through a lower capital stock (see (22)). There will also be a terms-of-trade effect:
. From the expression given earlier, we can see that the steady state income, IR, will increase.
The increase in IR exerts a positive effect on welfare, while the increase in p exerts a negative one. Unlike an increase in AP, here the rich country shifts resources toward a sector of comparative disadvantage and does not benefit from the increased terms-of-trade. The decreased incentive to accumulate capital and the ensuing decrease in the production of good 2 intensify the negative effect from an increase in p, increasing the likelihood that the rich country would actually prefer an improvement to an inappropriate technology instead of its own. A sufficient condition for this to happen is that
This is another manifestation of the scale effect of technology; the rich country prefers an improvement in the technology exploited by the larger labor force. The welfare of the poor country unambiguously decreases, because the rich country has become more competitive in the poor country's export industry.
COSTLY IMPROVEMENTS
We now incorporate the cost of improving AP. We expect to answer questions of the following nature with this analysis:
- Suppose that an invention (idea) for improving AP arrives exogenously—for example, an academic paper on a high-yield seed variety suitable to the tropics. Given costly adoption, how much is each country willing to invest in the invention to create a usable technology out of it—that is, developing a seed or a malarial drug based on the idea?
- Suppose an idea for improving both AP and arrives exogenously. Given costly adoption, are there any conditions under which the rich country chooses to invest in AP instead of In other words, is the earlier conclusion about the rich country's preference for inappropriate technology robust to the inclusion of costs?
Specialization
In this section, we substantiate the following claim:20
We ignore the implications that the explicit introduction of costly investment has for the equilibrium quantities derived in Sections 2.3 and 2.2. For example, total output of the rich country under nonspecialization, IR(AP), would now depend on its expenditure on technology improvement. Since this does not alter the qualitative results below, and the magnitude of this cost is likely to be very small relative to the size of the rich country's GNP, we choose not to consider it explicitly. We also find it analytically convenient to consider welfare changes when the technological change leaves the regime for the rich country—nonspecialized or specialized—unchanged. We study a switch in regime in the sections on dynamics and numerical simulation.
Claim 3. In the specialized regime:
- Given identical cost functions, the rich country will invest more in improving the poor country's technology than the poor country would do on its own (provided θ is small enough).
We differentiate the expressions for VR(AP) and VP(AP) in order to get the first-order conditions governing the technology investment of the rich and the poor regions. The condition for the rich region is
The net benefit to the rich is the added revenue from exports due to improved terms-of-trade.
Optimal investment for the poor region is given by
The positive impact of increased output net of the added cost of imports is equated to the marginal cost. The inequality θ < 0.5 is sufficient to ensure that the investment by the rich exceeds that by the poor.21
The exact condition is ((1−θ)/θ)((IP−mP)/(IP−mP−mR/θ))>1.
A global planner who maximizes a weighted sum of the welfare of both countries would also invest more than the poor country would. Such a planner is not concerned with redistributive effects of a change in p.
Nonspecialization
We prove the following claim:
Claim 4. In the nonspecialized regime:
- Given identical cost functions, the poor country will invest more in improving its own technology than the rich country.
- If the labor force of the poor country is large enough, the rich country would prefer to improve the poor country's technology (the inappropriate one) rather than its own (the appropriate one).
(1) Recall that an increase in AP has no effect on the terms-of-trade, p, but increases IR nevertheless. Therefore, the optimal investment condition will equate the marginal increment in income to the marginal cost of research:
Because IR is strictly increasing in AP and the marginal cost of zero investment is zero, it follows from the above first-order condition that the rich country will always undertake positive investment in AP.
A similar investment rule emerges for the poor country:
Therefore, if the poor country could afford to pay the research cost
, it would also undertake strictly positive investment in AP.
One can evaluate the marginal benefits in (26) and (27) and show that under the plausible conditions δ>ρ and β<2/3, the poor would invest a greater amount than the rich; the effect on the income of the poor is more direct, through improved technology, whereas the effect on the rich is indirect, through labor reallocation.23
A global planner would perceive the sum of the benefits perceived by the individual countries. Consequently, the efficient investment in technology improvement exceeds the investment undertaken by either country acting on its own. Such investment would result in a decentralized setting if markets existed for the rich country to sell or license technology improvements in AP to the poor; such markets have been assumed away in our setup.
(2) If the rich country could improve its own domestic agricultural sector, say by incurring the same quadratic cost function as above, could it be the case that it would still prefer to improve AP rather than
? In the Appendix (Section A), we show that this is indeed possible if LP is sufficiently large. This shows that our result in Section 2.3 is robust to the inclusion of costs of improvement. The endogenous response of technology improvement to the poor country's labor force (the scale effect) makes it possible that the rich country would choose to improve the poor country's technology rather than its own.
DYNAMICS
The steady state comparison of the two regimes reveals stark contrasts. With specialization, there is only a terms-of-trade effect, and the rich country desires an improvement in AP more. Without specialization, there is only a factor reallocation effect, and it is the poor country that desires its technology improvement more. Is the contrast as stark also during transition? To answer this question, to get an insight into the mechanics of the model, and to set the stage for a more realistic quantitative assessment, we study the transitional dynamics in this section. For simplicity, we revert to the case of negligible innovation cost studied in Section 2.
Specialization
We present the differential equations that characterize the dynamic system in terms of KR and p in Appendix A. When the rich country is specialized initially, any increase in AP will only reinforce specialization [see (15)]. There will be no change in the rich country's steady state capital; the steady state price will increase due to an increase in the production of good 1. The adjustment is instantaneous; therefore, dynamic considerations do not alter the steady state comparisons made earlier.
When the rich country is nonspecialized initially, the dynamics are more interesting. In Appendix A.3, we provide phase diagrams for both these cases, show that the transition paths for the relative price and capital stock when the rich region is initially nonspecialized are as shown in Figure 1, and prove the following claim.
Dynamics with specialization: After an increase in AP; nonspl.→spl.
Claim 5. A sudden increase in AP
- When the rich country is already in a specialized regime causes the price, p, to increase immediately to its new steady state value. There is no change in the steady state stock of capital.
- When the rich country is initially nonspecialized, and the increase causes it to become specialized, causes the stock of capital to increase toward its new steady state value monotonically. The price overshoots its final steady state value at the moment of the increase in AP and decreases to it over time.
An increase in AP causes the output of good 1 to increase relative to that of good 2; given the initially fixed nature of the capital stock, p increases. As the capital stock increases, thereby increasing the output of good 2, this price decreases over time, but to a level higher than the initial price. In summary, even when the transition is included, there is always a terms-of-trade effect in favor of the rich country.
Nonspecialization
We present the dynamic equations in terms of the capital stock KR, a state variable, and
, a jumping variable, in Appendix A.24
This choice of the dynamic system variables happens to be convenient. We, of course, cannot use
as a variable in the specialization case discussed above.
In particular, note that, for a given KR, p increases with
which will happen at the instant AP is increased.
In Appendix A, we use phase diagrams to argue that the transition paths for the labor allocation to good 1, the relative price, and the capital stock are as shown in Figure 2, and prove the following claim.
Dynamics without specialization: Transition paths after an increasein AP.
Claim 6. A sudden increase in AP, which still obeys the nonspecialization condition,
Causes the relative price, p, and the labor devoted by the rich country to good 2,
to jump to higher levels at the moment of the increase in AP.
Over transition, steadily decreases this price to the old steady state value; the labor allocated to good 2 decreases to its new, higher steady state value.
Increases capital monotonically from its old steady state value to its new, higher steady state value.
In the very short run, KR is fixed; any increase in rich-country labor allocated toward good 2 is not enough to counteract the increase in the poor-country supply of good 1 due to the increase in AP. The output of good 1 increases relative to that of good 2, and the relative price, p, jumps.25
The initial jump in
could be high enough to cause the rich region to temporarily specialize in good 2.
As will be seen in Section 5, the effect on the welfare of both countries due to an increase in AP is smaller when transition is considered. The transitional behavior of the terms-of-trade is one reason for this. The increase in terms-of-trade obviously exerts a negative effect on the poor country, which produces only good 1. Although the rich country does produce the good whose price has increased, the above-mentioned inertia in the production of good 2 causes the positive production effect to kick in slowly, whereas the negative price effect is immediate.
THE GREEN REVOLUTION: A QUANTITATIVE ILLUSTRATION
In this section, we examine the historical episode of the Green Revolution (GR) in light of our model. The GR closely resembles the experiments we describe in Section 3: rich countries undertook research to improve agricultural technology specific to poor countries. We view the outcome of this research as a positive change in the technological coefficient, AP, of the developing world. We choose empirically plausible values for the parameters of our model and simulate it numerically. We assess the welfare benefits of GR, including transition, by comparing them with the counterfactual situation of no GR. We begin by ignoring the costs of technology improvements for this exercise, which, as mentioned in the Introduction, are not very high. We consider the inclusion of costs later.
We choose ρ=0.07, δ=0.09, and β=0.35 (capital share in rich countries), values typically used in calibrating dynamic models. We set mP=mR=0.5 and θ=0.1, which jointly yield a minimum consumption value close to 90% of the poor region's consumption of good 1 in the pre-GR period. We later study the dependence of the results on m and θ.26
The model implies that
which connects m=mP and θ, for the assumed value of
Our choice of 90% for this ratio was motivated by the following analysis. Under the interpretation that the minimum consumption requirements are subsistence levels, we first used the $1 a day standard of the 1990 World Development Report of the World Bank (measured in 1985 international PPP prices). This would imply a yearly amount of $365 for subsistence alone, a number which the data suggested was significantly above the annual per capita food consumption of the developing countries. As a consequence, we set the ratio to a high enough value of 90% and study the sensitivity of results to m and θ.
We next turn to calibrating the productivity parameters for the two countries. For the poor country's agricultural productivity, we need values for both the counterfactual productivity that assumes no GR (AP) and the improved one under GR
. For the rich, we need values for productivity parameters in both sectors
and
. The rich country's parameters are calibrated under the assumption of GR, as explained below, and held at those values when the counterfactual experiment with no GR is conducted.
We normalize the counterfactual AP=1. We examine some important historical facts concerning the GR in order to choose the range of values for the food technology index following the Green Revolution. Contrary to common belief, the impact of the GR was felt not just in a small group of countries and only a handful of crops. Evenson and Gollin (2001) extensively examine and document the progress of the GR. Their evidence indicates that many developing countries experienced increased productivity and yields in a variety of food crops. In detailed country studies, they document yield increases not just for crops such as rice and wheat—typically associated with the GR—but also for barley, beans, cassava, groundnuts, lentils, maize, pearl millet, and sorghum. They claim, “Technological advances have occurred in all crops, on all continents, and in all ecological zones, although these advances have been uneven.” In addition to the extensiveness of the GR, they also comment on the long-run, highly successful nature of the revolution: The GR “is better understood as a 40-year history of steady productivity gains than as a one-time event. […] Had international research on crop genetic improvement been halted in (say) 1980, the world would be demonstrably worse off.”
How can we map the progress of the GR to a one-time change in AP? In our simple framework, in addition to technological improvements (better seeds), this parameter captures more intensive use of fertilizer and irrigation—which went hand in hand with the adoption of new seeds—and other unmodeled improvements to total factor productivity. Yield increases between 1961 and 2000 would most closely capture the effect of better seeds and increases in complementary inputs.
The UN's Food and Agricultural Organization (FAO) has data on yield growth rates averaged over developing and developed countries.27
FAOSTAT online data was obtained from http://faostat.fao.org.
This is in line with estimates of the growth rate of land-augmenting technology performed by Abler et al. (1994) for the “North” region of India, for the period 1960–1987. The North is one of the four areas into which they divide the agricultural sector in India, and the most successful in terms of GR outcomes. Extrapolating the average growth rate for the period 1960–1987 over the 40-year span of 1960–2000 gives a growth rate of 248%. See their Table 6.3.
Because we hold the rich country's agricultural productivity factor constant and increase only the poor country's productivity, the figure of interest is the gross growth of the developing countries relative to that of developed countries. That is, given the growth rates of the rich and the poor, γR and γP, we are interested is the gross 40-year growth rate factor (1+γP)/(1+γR). The factors for rice and wheat are presented in Table 1.
Even though the relative gain for developing countries was less noticeable in other crops, rice deserves disproportionate attention given its enormous impact on calorie intake. Evenson and Gollin (2001) note: “In a number of countries of Asia, rice accounts for more than half of all human food energy—and in the poorest countries, such as Bangladesh, Myanmar, Cambodia, Laos, Vietnam, and eastern India, it contributes over two thirds of the human energy intake.” We therefore consider 1.6 as our benchmark estimate of
.29
The relative 40-year gross growth rate factors for other crops are 1.23 for potatoes, 1.11 for sorghum, 1.09 for maize, 1.02 for millet, and 1.12 for all cereals.
The ratio of TFP between the first quartile and the third quartile countries in 1985 in Hall and Jones (1999) is 3. Given
we set the rich country's productivity parameters,
, such that the relative TFP between the rich and poor countries, in 1985, is in the ballpark of this figure. Setting
yields a TFP factor of 3.2 in 1985 in the model outcome.30
The rich-poor TFP ratio is calculated as
. That is, the total value of output of the rich country is presumed to have arisen from the aggregate Cobb–Douglas production function,
. We do not use the fourth quartile of countries in the Hall and Jones (1999) productivity list, which are mainly African countries where the Green Revolution did not take root. Calibrating the rich country's technology parameters to a different TFP factor, say 3.75, which is the TFP ratio of the US to India, a “typical” Green Revolution country, will not qualitatively alter the results.
We additionally use output growth, rather than yield growth, to get a lower bound for the increase in AP. Higher yields should materialize less than one-for-one into food production, as the general equilibrium effect of a lower price would deter farmers from expanding output in the same proportion as productivity improvements. FAO also provide indices for total food production per capita. Whereas the corresponding growth rate is an impressive 62.2% for the developing countries, it is only 23% in the developed world. The relative growth rate factor for food production, calculated analogously to the figures in Table 1, is 1.32. We therefore set 1.3 as our lower bound for
. We leave the rich country's technological parameters the same as those of the benchmark case of
.
For an empirical target, which we do not explicitly calibrate to but can compare the simulation outcome with to get some validity on the parameter choices, we use the terms-of-trade data—a 50% decrease in food prices reported in Evenson and Gollin (2001).
The rich region is not specialized before the transfer of technology to the poor region. In Table 2, we present the post-Green Revolution outcomes for the above-mentioned values of the final productivity index,
.31
The differential equations for the dynamic system were computed using MATLAB's ode23 routine; the program is available from the authors.
In the first (“lower bound”) case of
, the new level of technology in the poor region is not high enough to cause the rich one to specialize. As seen in Section 2, the steady state capital of the rich country, as well the labor it devotes to the production of good 2, increase in response to an increase in AP, both by 10.8%. The steady state price does not change; as mentioned earlier, the long-run capital-labor ratio and thus the price are pinned down completely by the rich country's parameters. However, the transition price is higher than the steady state price, overshooting by about 4% at the time of the transfer. In the benchmark case of
, the increase in AP is high enough to cause the rich country to specialize. The food price declines by 36.5%, which is lower than the 50% drop mentioned above. (The price of food will be the inverse of the price of the manufactured good, p, of the model.) We search for the increase in AP that would nail the food price drop of 50%. This happens for
; the outcomes for this case are presented in the last row of Table 2. The steady state capital stock of the rich and the labor it devotes to manufacturing increase by 13.7% in the last two cases.
The welfare gain is shown as an equivalent variation in baseline income, considering only steady states, as well as including the transition, which is “complete” in the 40-year period considered. As
increases, the welfare gain increases for the rich region and decreases for the poor region, even though the poor gain more in percentage terms than the rich in all three cases. In the first case, the gains of the poor outstrip those of the rich by large margins. Indeed, inclusive of transition, the rich country barely gains anything. In the second (benchmark) case, the gains of the poor, 23.1% across steady states, and 21.4% including transition, exceed those of the rich, 12.1% and 9.9%, by smaller amounts. The gap is further narrowed in the last case. For the poor country, the increase in the price of its import good during transition tempers welfare gains. For the rich country, the initial reduction in consumption from increased investment and the slow increase in the production of good 2 temper welfare gains relative to a jump from the old steady state to the new. These figures are consistent with the earlier theoretical results—the large increases in the rich country's terms-of-trade when it is specialized benefit the rich country. The more important finding is that there are realistic parameter values for which both countries benefit from an increase in AP.
Discussion of Welfare Gains
The welfare gains, for the poor in the first case, and for the rich in the last case, might seem excessive. The following points have to be borne in mind while interpreting these numbers. The equivalent increase is based on lifetime utility increases; on an annualized basis, these gains would be smaller. Likewise, when population growth, especially in the poor region, is accounted for, the per capita increase in welfare will be lower. For the rich, clearly a move to specialization and the ensuing terms-of-trade effects magnify the welfare effects. In the context of a full-fledged product ladder model, improving AP might cause both countries to move to more sophisticated goods up the ladder, leading to a more muted terms-of-trade effect.
Table 2 also seems to indicate that the rich country has an incentive to increase the technology as much as possible. However, notice that the welfare gain of the poor is lower with higher AP. It is not enough that a donation is given; it must also be accepted. The above figures also assume negligible costs, and it would be reasonable to assume that convex improvement costs would mute the welfare effect for the rich. On a different front, there would likely be (unmodeled) political pressure from the labor-intensive sector 1 in the rich country to moving toward specialization in good 2.
Finally, it is natural to ask the following question: If welfare increases via donations are so large for the developed countries, why do we not see many more such donations? Technological transfers seen during the GR are likely unique and hard to replicate. Genetically modified seeds adapted to the climate of one specific region are likely to be of little use in a region with a different climate. This eliminates a number of problems that plague other types of donations. For example, in the case of drugs, one concern drug companies have regarding the donation of low-cost medicine to developing countries is the possibility that corrupt officials might hold on to the drugs and resell them to rich consumers in the developed world. Genetically modified seeds are not prone to such corrupt uses. Therefore, despite the success of the GR, as measured by the welfare numbers in Table 2, similar initiatives on such a scale have rarely been seen.
Sensitivity Analysis
The parameters m and θ are the least tightly calibrated above. We vary these one at a time, holding all other parameters at the benchmark levels to study the effect on the results reported above. The results of this analysis are presented in Table 3; the benchmark results are presented in the first row for convenience.
When the utility weight for food, θ, is increased from 0.1 to 0.125, the welfare gain for the poor country increases—from 21.4%, including transition, when θ=0.1, to 39.5% when θ=0.125—but for the rich country, it drops from 9.9% to 5.5%. It is intuitive that the increase in the utility weight of the good that the poor country produces— food—strengthens its position. The price increase of the manufacturing good (decrease in food price) is muted; see (17). The poor country therefore gains in welfare relative to the rich. If θ increases to the point where (15) fails to hold, say a value such as θ=0.3, there is no change in the steady state terms-of-trade, and the poor country gains even more in welfare terms. When the minimum consumption values are increased from 0.5 to 0.525, there is a similar muting of food price decrease, and the poor country benefits more from the technology improvement.
There is a change of regime from nonspecialization to specialization in the above examples, which makes it harder to illustrate the claims made in Sections 2.2 and 2.3 directly. Purely to shed further light on the workings of the model and illustrate the claim in Section 2.3, we consider a change of m from 0.1 to 0.2, which starts the rich country with specialization and leaves it specialized when
The percentage drop in food price increases as m increases, from 42.9% to 50%; that is, the increase in manufacturing price, p, is higher with increasing inferiority, as claimed. The rich country's welfare gain jumps, from 6.3% to 8.9%, as claimed. To illustrate the claim in Section 2.3, we consider a change of m from 0.65 to 0.85, which starts the rich country with lack of specialization and leaves it nonspecialized when
. Although there is no change in the terms-of-trade, as claimed, there is a slight increase in the welfare gain of the rich, from 3.8% to 3.9%. Finally, to illustrate the model's scale effect in the case of nonspecialization, for the m=0.85 case mentioned above, we decrease LR to 0.15 from its benchmark value of 0.217. As argued in the claim in Section 2.3, an increase in the (relative) labor force of the poor country increases the effect of a technology donation. The resource reallocation effect is stronger for the rich country (manufacturing output increases by 49.2% instead of 28.9%), and its welfare gain is greater (5.7% instead of 3.9%).
Considering Costs
In the quantitative analysis, we have thus far ignored the cost to the rich country of improving the poor country's technology. Is this reasonable? The 1998 budget of the Consultative Group for International Agricultural Research (CGIAR), an institution that consolidated the GR research efforts of the international community, was $340 million. This is a mere 0.00153% of the GDP of the developed world.32
This figure is computed by dividing $340 million by the total 1998 GDP of the high-human-development countries, from the 1998 United Nations Human Development Report.
Another way to put the research costs of the rich in perspective is to use the cost specification (1) of our theoretical analysis, even though this is not a calibrated cost function. The present value of the costs is obtained by multiplying the cost of the manufacturing good, p, by this expression. For the benchmark case of
, this cost amounts to about 2% of the rich country's pre-GR steady state income. The steady state income gain of 12.1%, given in Table 2, is much higher than this cost. Evidently, the gains for the rich net of research costs are still positive.
Tariffs
The harm caused to the developing countries by the agricultural protectionism of the developed countries has received considerable attention in the literature.33
See Morisset (1998) for a recent example and the references therein.
Our argument thus far has been that the rich also benefited from the Green Revolution. Therefore, we need to examine the welfare effects of tariffs on rich countries. If the rich region levies a tariff of rate τ on good 1 (its import good) and
how high should this tariff rate be before its steady state welfare gains realized from an increase in AP are negated? If the government repatriates all revenues in a lump-sum fashion to the consumer, a 16% tariff rate is enough to negate the gains for the rich. When the government uses the revenues to purchase goods for its own consumption, the tariff rate has to be three hundred percent to negate the welfare gains for the rich, a high value even for protectionist regimes. Nevertheless, it is clear that the rich countries would realize greater gains if they did not levy tariffs.
CONCLUSION
In this paper we have demonstrated, under various assumptions, that rich countries have an economic incentive to improve the technology specific to poor countries. Although altruistic and humanitarian considerations have cornered most public attention, we show there are also economic reasons for the rich countries to become involved in solving problems particular to developing countries. The welfare effects of the Green Revolution, a classic case of such an “intervention,” are positive in a model simulated with realistic parameter values. With the various changes both rich and poor countries have undergone in the last 40 years, isolating one episode in a macro context is difficult; we therefore view the positive results as an encouraging sign of the applicability of our model.
As mentioned in the Introduction, we have been silent on the issues of coordination among rich countries that make such a collective endeavor possible in the first place, as well as on the nature of commitment, or lack thereof, by the poor to behave in ways expected by the rich who donate the technology to them. Our representative agent framework also ignores political economy questions. Modeling these features explicitly will allow us to better understand why such collective efforts have not been more widespread and are limited to certain types of technological improvements, most notably agriculture. These are topics of ongoing research.
APPENDIX
INAPPROPRIATE VS APPROPRIATE TECHNOLOGY INVESTMENT
When the rich country can simultaneously increase AP and
, the costs
and
are on the left-hand side of the budget constraint. The first-order condition for the optimal investment in AP is (26). The corresponding condition for investments in
is
with equality if the investment in
is strictly positive.
Given (1), the optimal choice of
is
which depends positively on LP, a manifestation of the scale effect. The rich country prefers not to invest in its own technology only if the left-hand side of (A.1) evaluated at
is negative, because the marginal cost is zero with no improvement. Some tedious algebra shows that the condition for this to happen is
where (YP)′ is the new output of good 1 in the poor country given optimal investment in AP. The [(YP)′−mP] term is multiplied by a negative factor. Using (A.2), we get
Therefore, there exists a large enough LP to make the FOC hold with inequality in a strict sense; this is particularly so because (YP)′ includes a term in the square of LP.
The rich country's incentive to invest in the poor country's technology, AP, is amplified by the size of its labor force, LP. With a quadratic cost specification, the improvement in AP is linear in LP. Given the production technology, YP=APLP, the square term in the size of the labor force manifests in the above expression for the improved output. The endogenous response of technology improvement to LP makes it more likely that the rich country would improve the poor country's technology rather than its own, for large enough LP.
DIFFERENTIAL EQUATIONS FOR SPECIALIZATION
The differential equations are
The steady state quantities are
PROOF OF CLAIM 5
To draw the phase diagram for the system in (A.3) and (A.4), note that the
locus is given by
It is clear that this locus is decreasing in p. The
locus is
which is independent of p.
When AP increases, the
locus shifts rightward, while the
locus is unchanged. For a change in AP that causes eventual specialization by the rich country, there are two cases to consider—the case where the rich country was specialized to begin with and where it was nonspecialized. Figure A.1 shows the effect on the phase diagram due to an increase in AP when the rich country is specialized initially. The dotted lines show the new situation. Any increase in AP will only reinforce specialization; see (15). There is no change in the rich country's steady state capital and the steady state price will increase. The adjustment is instantaneous, along the
locus.
Dynamics with specialization: After AP increase; spl. → spl.
When the rich country is nonspecialized initially, the dynamics are more interesting and the new loci (alone) are shown in Figure A.2.
Dynamics with specialization: After AP increase; nonspl. → spl.
The steady state capital stock for the two regimes is
given that
. From (
), for the rich country to be specialized,
and this implies
Therefore, during transition, the capital stock increases monotonically from (KR)*,NS to (KR)*,S according to (A.3). The price p overshoots and decreases monotonically to its new, higher steady state level according to (A.4).
DIFFERENTIAL EQUATIONS FOR NONSPECIALIZATION
The differential equations that characterize the dynamics of the system are34
Detailed derivations are available from the authors on request.
These equations yield the following expressions for the steady state:
PROOF OF CLAIM 6
To draw the phase diagram for the dynamic system given in (A.5) and (A.6), note that the
locus is
It is increasing in
The
locus is
It is decreasing in
The stable manifold is downward-sloping. The phase diagram before and after AP increases is shown in Figure A.3.
Dynamics without specialization: Phase diagram after AP increase.
When AP increases
increase (both by the same factor, to keep
and thus p unaltered). Both loci shift outward. The dotted lines show the new loci and the stable manifold. KR cannot jump at the time of increase in AP. But
does; in fact it overshoots and decreases along the new manifold to its new steady-state value. KR increases to its new steady state value along the new stable manifold. Equation (28) shows that the price p also jumps.
We are grateful to two anonymous referees for their detailed comments, which have considerably improved the paper. We also benefited from useful discussions and comments from V. V. Chari, Alejandro Cuñat, Doug Gollin, Doug Joines, Larry Kotlikoff, Robert Lucas, John Matsusaka, Victor Rios-Rull, Jim Robinson, Manuel Santos, Martin Schneider, and especially Kei-Mu Yi, and participants at the SED meeting at Stockholm, Sweden, the Minnesota Workshop in Macroeconomic Theory, the Winter meetings of the Econometric Society at Washington, D.C., the Trade, Capital Flows and Aggregate Dynamics Workshop at the Federal Reserve Bank of Cleveland, and workshops at Boston University, the University of Toulouse, and MadMac (Madrid Macroeconomics Seminar).
