Trade, Di usion and the Gains from Openness

Transcription

1 Trade, Di usion and the Gains from Openness Andrés Rodríguez-Care Pennsyvania State University and NBER November, 2007 ( rst version: November 2006) Abstract Buiding on Eaton and Kortum s (2002) mode of Ricardian trade, Avarez and Lucas (2005) cacuate that a sma country representing 1% of the word s GDP experiences a gain of 41% as it goes from autarky to frictioness trade with the rest of the word. But the gains from openness, which incudes not ony trade but a the other ways through which countries interact, are arguaby much higher than the gains from trade. This paper presents and then caibrates a mode where countries interact through trade as we as di usion of ideas, and then quanti es the overa gains from openness and the roe of trade in generating these gains. Having the mode match the trade data (i.e., the gravity equation) and the observed growth rate is critica for this quanti cation to be reasonabe. The main resut of the paper is that, compared to the mode without di usion, the gains from openness are much arger (206% 240%) and the gains from trade are smaer (13% 24%) when di usion is incuded in the mode. This ast resut is a consequence of a nove feature of the mode, namey that trade and di usion behave as substitutes, impying that trade generates smaer gains when di usion is present. E-mai address: andres@psu.edu. I thank Fernando Avarez, Costas Arkoakis, Kerem Cosar, Svetana Demidova, Jonathan Eaton, Josh Ederington, Caudio Gonzáez-Vega, Ehanan Hepman, Pete Kenow, Sam Kortum, Kaa Krishna, Giovanni Maggi, Nataia Ramondo, Migue A. Rodríguez, Robert Staiger, Dan Tre er, Jim Tybout, and Gustavo Ventura, as we as seminar participants at the Pennsyvania State University, the University of Wisconsin at Madison, the Fundação Getuio Vargas, the University of Iinois at Urbana Champaign, Ohio State University, Northwestern University, Boston University, Boston Coege, UCLA, the Winter Meeting of the Internationa Trade and Investment Program of the NBER, the University of Chicago, and the Summer Princeton Trade Conference for hepfu comments. I aso thank Yong Hu, Aexander Tarasov and Danie Xu for exceent research assistance. Support for research within the Center for the Study of Auctions, Procurements, and Competition Poicy at Penn State has been provided by a gift from the Human Capita Foundation ( A remaining errors are my own.

2 1 Introduction How much does a country gain from its reationship with the rest of the word? Consider for exampe the recent work by Avarez and Lucas (2005), who buid on Eaton and Kortum s (2002) mode of Ricardian trade. According to their quantitative mode, a sma country ike Argentina, which represents approximatey 1% of the word s GDP, experiences an income gain of 41% as it goes from autarky to frictioness trade with the rest of the word. But the gains from openness, which incudes not ony trade but a the other ways through which countries interact, are arguaby much higher than the gains from trade. Even if a country were to shut down trade, it coud sti bene t from foreign ideas through foreign direct investment (FDI), migration, books, journas, the Internet, etc. The goa of this paper is to construct and caibrate a mode where countries interact through trade and di usion of ideas, and then to quantify the overa gains from openness and the roe of trade in generating these gains. The main resut is that the gains from trade are smaer than those quanti ed by Avarez and Lucas (between 13% and 24% rather than 41% for a country with 1% of the word s GDP) whereas the gains from openness are reativey arge (between 206% and 240% for a country with 1% of the word s GDP). An impication is that shutting down trade woud generate oses that are quite sma in comparison to the oses that woud arise if the country were to become competey isoated by shutting down both trade and di usion. Cacuating the gains from trade in a mode that aows for trade and di usion represents a signi cant departure from the standard practice in the iterature, which is to consider trade as the ony means through which countries interact. This aternative approach has at east two advantages. First, having both trade and di usion in the mode shows that the gains from trade depend on the way in which trade and di usion interact. In the mode I present here, trade and di usion are both substitutes and compements. They are substitutes in that if a country cannot import a good then it may adopt a foreign technoogy for domestic production, and if a country cannot use a foreign technoogy then it may import the goods produced abroad with that technoogy. 1 They are compements in that stronger di usion of ideas from rich to poor countries increases the share of goods that wi be produced in the ater countries, expanding trade. Indeed, the tremendous expansion of exports from China over recent decades can be seen 1 This resut is simiar to the substitutive property between trade and factor ows (Munde, 1957), or trade and mutinationa production (see Hepman, Meitz and Yeape (2004) and Head and Riess (2004) for recent treatments). 1

3 as the resut of this country bene ting from increased transfers of technoogy from rich countries. In the caibrated mode, and focusing on the impications of trade and di usion for advanced countries, the rst channe (substitution) dominates the second one (compementarity), so trade and di usion behave as substitutes. This impies that shutting down trade in this mode eads to smaer osses than in modes with no di usion such as Eaton and Kortum (2002) and Avarez and Lucas (2005). A second advantage from studying di usion and trade together is that one can compare the gains from trade with the overa gains from openness, and this may provide a way to judge whether the numbers are reasonabe. The usua reaction of economists to the cacuated gains from trade in quantitative modes is that they are "too sma." Apparenty, economists have a prior beief that these gains are much higher, so there has been a search for mechanisms through which trade can have a arger e ect, such as scae e ects, intra-industry reaocations or gains from increased variety. But the resut of this search has generay been disappointing (see Tybout, 2003). This paper suggests that the reason for this may be that the gains from trade are in fact "sma," whie economists priors about arge gains may in fact be about the overa gains from openness. More importanty, this strategy may have reevant impications for research and poicy regarding how countries integrate with the rest of the word. In particuar, the resut of this paper that the gains from trade appear to be quite sma reative to the overa gains from openness suggests that both research and poicy shoud at east partiay redirect their attention from trade to a the other ways through which countries interact. More attention shoud be devoted, for exampe, to understanding the importance of FDI and migration in the internationa exchange of ideas, and to think about poicies that countries can foow to speed up the adoption of foreign technoogies. In Eaton and Kortum s (2002) mode of Ricardian trade with no di usion, countries gain from openness through speciaization according to comparative advantage. In the mode I construct here, countries aso gain from di usion of ideas. Both the gains from trade and the gains from di usion come from the same basic phenomenon, namey the sharing of the best ideas across countries. Consider, for exampe, Japan s superior technoogy for producing automobies. This technoogy can be shared through trade by having Japan export automobies or through di usion by having other countries produce their own automobies using Japan s technoogy. In both cases, thanks to the non-rivary of ideas emphasized by Romer (1990), sharing ideas eads to an increase in wordwide income. 2

4 These gains from sharing ideas are the same ones that give rise to aggregate increasing returns to scae in modes of quasi-endogenous growth such as Jones (1995) and Kortum (1997). Consider Kortum (1997). In the simpest version of this mode, the arriva of new ideas is proportiona to the popuation eve and the quaity of each idea is drawn from an unchanging distribution. The technoogy frontier at a certain point in time is the set of best ideas avaiabe to produce the given set of goods, and the average productivity of the technoogy frontier determines the per-capita income eve. A arger economy has more ideas, more ideas impy that the best avaiabe technoogies are more productive, and this aows the economy to sustain a higher income eve. This entais a scae e ect in eves so that income per capita y is increasing with popuation L, y = L, where and are positive constants. Jared Diamond s main argument in his book Guns, Germs and Stee can be interpreted as saying that this scae e ect from sharing ideas is what aowed arge "Eurasia" to attain a superior eve of productivity (Diamond, 1997). For the present purposes, the reevant impication is that a country can achieve a eve of income that is much ower in isoation than sharing ideas with the rest of the word. A scae e ect of the kind just described is the key eement in quasi-endogenous growth modes, as it impies that the growth rate is proportiona to the growth rate of popuation, g = g L. This impication aows for a simpe caibration, which reveas the magnitude of the gains from openness (in steady state eves). With g = 1:5% and g L = 4:8%, 2 the equation g = g L impies that = 0:31, which in turn impies that a country with 1% of the word s popuation enjoys gains from openness equa to 320% (100 0:31 = 4: 2). To quantify the gains from openness and expore the roe of trade in generating these gains, it is necessary to have a mode that is quantitativey consistent with both the observed growth rate and the observed trade voumes. I buid on Eaton and Kortum s (2001) mode of trade and growth, which can be seen as an extension of Kortum (1997) to incorporate trade. A key parameter in this mode,, determines the variabiity of the distribution of the quaity of ideas. 3 2 The rate of growth of y is the rate of growth of income per worker after subtracting the contribution from increases in average human capita and in the capita-output ratio (see Jones, 2002, and Kenow and Rodríguez- Care, 2005). The vaue for g L comes from the rate of growth of researchers in the G5 countries (West Germany, France, the United Kingdom, the United States, and Japan) from 1950 to 1993, see Jones (2002). Note that this is signi canty higher than the 1:1% rate of growth of popuation observed in the OECD in the ast decades because of an increasing share of the popuation devoted to research. Doing this exercise with a ower g L woud ead to even arger gains from openness. 3 In Eaton and Kortum (2001) the quaity of ideas is distributed Pareto with parameter. Thus, the variance of this distribution increases as fas. I instead foow Avarez and Lucas (2005), who ip this parameter 3

5 If is caibrated to match the gravity equation, as is done in Eaton and Kortum (2002), then a puzze emerges in that the impied growth rate is amost an order of magnitude ower than the one we observe for the OECD countries in the ast decades. Aternativey, if is caibrated to match the observed rate of growth in the OECD, then the mode generates too much trade, since the pattern of comparative advantage is too strong and dominates the estimated trade costs. One way to dea with this puzze is by aowing for di usion of ideas across countries. 4 understand why di usion makes it possibe to match both the gravity equation and the growth rate, note that the excessive voume of trade generated by the high needed to match growth of 1:5% per year is dampened when countries can share ideas through di usion rather than trade. Introducing di usion into the mode eads to a gravity equation with a discontinuous border e ect (i.e., trade fas discontinuousy as trade costs increase from zero) that is not present in Eaton and Kortum (2001, 2002). Estimating from this equation eads to = 0:22 rather than Eaton and Kortum s = 0:12, and this heps to increase the mode s impied growth rate from g = 0:29% to g = 0:53%. But this is sti signi canty beow the observed g = 1:5%. To increase the mode s impied growth rate without a ecting its trade impications, I aow for progress and di usion in ideas that are reevant for non-tradabe goods. I refer to these ideas as "NT ideas" to di erentiate them from the ideas associated with tradabe goods, which I wi ca "T ideas." Anaogousy to the roe payed by for T ideas, a parameter determines the variabiity of the distribution of the quaity of NT ideas. One can then use = 0:22 to match the gravity equation, and = 0:2 so that the mode generates g = 1:5%. 5 To Having this mode that is quantitativey consistent with observed growth and trade voumes, I can then cacuate the gains from openness and the roe of trade in these gains. above: the gains from openness are arge (206% The main resut is as stated 240%), whie the gains from trade are in fact smaer than in the mode without di usion (13% 24% rather than 41%). 6 These resuts are around and have a higher increase the variabiity of the quaity of ideas. 4 An aternative approach is to aow for knowedge spiovers as a way to acceerate the rate of growth of ideas (I thank Sam Kortum for suggesting this possibiity). In a previous version of this paper I expored a mode with such spiovers and cacuated the corresponding gains from openness and the roe of trade. The resuts are very simiar to the ones I present beow. 5 In the caibrated mode the growth rate is g = (=2 + )g L. Thus, = 0:22 and = 0:2 together with g L = 4:8% impy g = 1:5%. 6 These gains from openness di er from the ones cacuated above for the simpe caibration to observed growth (i.e., 320%) because the mode deveoped in the paper and its caibration incorporate frictions in the di usion process that ower the gains from openness. 4

6 derived for the case in which there are no trade costs, so these computed gains are an upper bound of the actua gains. An aternative caibration aows for such costs and computes the gains from openness and trade for a set of 19 OECD countries. The resuts impy that Finand, which accounts for roughy 1% of the word s research in the caibrated mode, has gains from openness of 174% and gains from trade of 9%. The average of the corresponding gains for the 19 countries considered are 143% and 9%. This paper is reated to the iterature on trade and endogenous growth associated with Grossman and Hepman (1991) and Rivera-Batiz and Romer (1991), among others. This group of papers showed that trade or internationa knowedge spiovers coud ead to a higher growth rate thanks to the expoitation of scae economies in R&D at the goba eve. This is essentiay what Jones (1995) caed a "strong scae e ect," whereby arger markets exhibit higher growth rates. Jones empirica anaysis showed that such a strong scae e ect is not consistent with the data, however, so there has been a shift towards quasi-endogenous growth modes, where the growth rate is not a ected by scae variabes. In this paper I focus on this cass of modes and expore the quantitative impications of openness on steady state income eves. Another reated iterature is the one that focuses on internationa technoogy di usion. The cosest paper is by Eaton and Kortum (1999), who deveop and caibrate a mode of technoogy di usion and growth among the ve eading research economies. These authors then perform a counterfactua anaysis to see the impications for the U.S. of detaching itsef from sharing ideas with the rest of the word. Using the quasi-endogenous growth mode due to Jones (1995), Kenow and Rodríguez-Care (2005) performed a simiar exercise and found enormous gains from openness for sma countries. This paper can be seen as an extension of this iterature to incude trade into the mode and thereby quantify the gains from openness arising from both trade and di usion. Finay, Coe and Hepman (1995), Keer (1998) and others reviewed in Keer (2004) study the roe of trade as a vehice for "internationa R&D spiovers." The idea is that by importing intermediate and capita goods, a country bene ts from the R&D done in the exporting countries. This is a key feature of the mode of R&D and trade in Eaton and Kortum (2001) as we as the mode I present in this paper. But here such R&D spiovers are interpreted as gains from trade, whereas technoogy di usion is a term reserved for the more narrow concept of information ows that aow countries to directy use technoogies created esewhere. In other words, the gains from internationa R&D spiovers in Coe and Hepman (1995) are here simpy 5

7 measured as gains from trade. A di erent notion is that trade acceerates the internationa ow of technica know-how (see Grossman and Hepman, p. 165). Severa papers have expored this empiricay with mixed resuts (see Rhee et. a., 1984, Aitken et. a., 1997, and Cerides et. a., 1998, and Bernard and Jensen, 1999). This phenomenon is not captured in the mode presented beow. The rest of the paper is organized as foows. In the next section I ay out the basic mode with T ideas and no di usion to introduce the basic notation and assumptions, and to estabish a benchmark against which to compare the resuts of the fu mode. In this section I aso show that if is caibrated to match trade voumes then the impied growth rate is too ow. In Section 3 I present the fu mode, which buids on the mode of Section 2 by adding both technoogica progress in the production of non-tradabes through the introduction of NT ideas, and di usion for both T ideas and NT ideas. In this section I derive anaytica resuts for the gains from openness and the gains from frictioness trade. I estabish the resut discussed above that trade and di usion are substitutes, and show that this impies that the gains from trade are ower than in a mode with no di usion. In section 4 I caibrate the mode to match trade voumes and the observed growth rate, and in Section 5 I use the caibrated mode to quantify the gains from openness and the roe of trade. Section 6 expores the impact of transportation costs on the gains from trade and openness. The na section o ers concuding comments and topics for future research. 2 Trade and growth without di usion In this section I rst present a mode of trade and growth without di usion based on Eaton and Kortum (2001). I then caibrate an enriched version of the mode to compute the gains from trade and the impied growth rate. 2.1 A mode of trade and growth There is a singe factor of production, abor, I countries indexed by i, and a continuum of tradabe intermediate goods indexed by u 2 [0; 1]. The intermediate goods are used to produce a na consumption good via a CES production function with an easticity of substitution > 0. The productivity with which individua intermediate goods are produced (i.e., output per unit of the abor) varies across intermediate goods u and across countries, and this gives rise to 6

8 trade. Let us focus on a singe country for now so that we can momentariy eave aside the use of country subscripts. It is convenient to work with the inverse of productivity. To do so, et x(u) be a parameter that determines the cost of producing intermediate good u. In particuar, et the cost of producing such a good be given by x(u) w, where w is the wage eve. Note that the parameter, which wi be constant across goods and countries, magni es the variabiity of the cost parameter x on the actua cost structure across goods and countries. This parameter wi be crucia in the anaysis that foows. At any point in time the cost parameters x(u) are the resut of previous research e orts in each country. Foowing Kortum (1997) and Eaton and Kortum (2001), research is modeed as the creation of ideas, athough for simpicity here I assume that this is exogenous. particuar, I assume that there is an instantaneous (and constant) rate of arriva of new ideas per person. In the concuding section I argue that the main resuts of the paper shoud not change signi canty if research e orts were endogenous. Ideas are speci c to goods, and the good to which an idea appies is drawn from a uniform distribution in u 2 [0; 1]. Since this interva has unitary mass, then at time t there is a probabiity R(t) L(t) of drawing an idea for any particuar good, where L(t) is the popuation eve at time t. This impies that the arriva of ideas is a Poisson process with rate function L(t), so the number of ideas that have arrived for a particuar good by time t is distributed Poisson with rate (t) R t R(s)ds. Again, since the set of goods has unitary mass, then (t) 0 aso represents the tota stock of ideas (appying to a goods) at time t. (From here onwards, I wi suppress the time index as ong as it does not cause confusion.) Assuming that L grows at the constant rate g L (assumed to be common across countries) then in steady state we must have = R=g L, so aso grows at rate g L. Ideas for producing a particuar intermediate good di er ony in terms of a "quaity" parameter, and the economy s productivity for intermediate good u is determined by the best idea avaiabe for the production of this good. The quaity of ideas is independenty drawn from a distribution of quaity which is assumed to be Pareto with support in [1; 1] and parameter one. 7;8 Letting x(u) be the inverse of the quaity of the best idea that has arrived up to time t 7 Kortum (1997) shows that the Pareto assumption for the distribution of quaity is necessary for there to be a steady state growth path. 8 Eaton and Kortum (2001) assume that the distribution of quaity is Pareto with parameter, whereas here I assume instead a Pareto distribution with parameter 1, with being a parameter that expands the cost di erences across ideas, as in Avarez and Lucas (2005). The two approaches are equivaent except that the here is the inverse of Eaton and Kortum s. In 7

9 for good u, then it is easy to show that x(u) is distributed exponentiay with parameter. 9 Transportation costs are of the iceberg type, with one unit of a good shipped from country j resuting in k ij 1 units arriving in country i. I assume that k ii = 1, that k ij = k ji, and that the trianguar inequaity hods (i.e., k ij k i k j for a i; j; ) Equiibrium Foowing Avarez and Lucas (2005), I reabe goods by x (x 1 ; x 2 :::x I ) rather than u. The price of good x in country i is p i (x) = min j wj k ij x j Letting s i (x) min j n (w j =k ij ) 1= x j o, then p i (x) = s i (x). From the properties of the exponentia distribution it foows that s i (x) is distributed exponentiay with parameter i, 10 where i X j ij and ij (w j =k ij ) 1= j (1) Letting p mi be the price index of the na good, then p 1 mi = R p i (x) 1 df (x) and assuming 1 + (1 ) > 0; 11 we get p mi = C T i (2) where C T = [1 + (1 )] 1=(1 ), with () being the Gamma function. To determine wages we introduce the trade-baance conditions. As shown by Eaton and Kortum (2002), the average price charged by any country j in any country i is the same, and hence the share of tota income in country i spent on imports from country j, D ij, is equa to the share of goods for which country j is the owest cost suppier in country i. In turn, this share is equa to the probabiity that (w j =k ij )x j = min f(w =k i )x g. From the properties of the 9 Letting q represent the quaity of ideas, then Pr(Q q) = H(q) = 1 1=q. Letting v be the quaity of the best idea that has arrived up to time t, then using e x P 1 k=0 xk =k! we get Pr(V v) = P 1 k=0 e () k =k! H(v) k = e =v, and hence x 1=v exp(). There is a discrepancy in that here v 1 (because q 1) whereas the exponentia distribution has range in [0; 1[. As shown by Kortum (1997), this can be safey ignored because quaity eves beow one become irreevant as gets arge. 10 These properties are: (1) if x exp() and k > 0 then kx exp(=k); and (2) if x and y are independent, x exp() and y exp(), then minfx; yg exp( + ). 11 The assumption that 1 + (1 ) > 0 entais < 1 + 1=. In principe, I coud expore whether this inequaity hods given estimates of and given the vaues of that I wi discuss in the text beow. In practice, however, the empirica vaue of depends on the eve of aggregation that we use for inputs, which in turn shoud be determined by the eve at which technoogies di er in the way speci ed in the mode. Thus, the restriction 1 + (1 ) > 0 must be taken as an assumption for now. 8

10 exponentia distribution, this probabiity is D ij ij = i. Given that tota income in country i is L i w i, then the trade baance conditions are simpy L i w i = X j L jw j D ji (3) The previous conditions determine a competitive equiibrium. In particuar, a competitive equiibrium at any point in time is a coupe of vectors p m = (p m1 ; p m2 ; :::; p mi ) and w = (w 1 ; w 2 ; :::; w I ) such that, together with the vector ( 1 ; 2 ; :::; I ) that satis es equations (1) and (2) and D ij ij = i, the trade baance conditions (3) are satis ed Growth and the gains from trade I now turn to the impications of the mode for growth and the gains from trade. Once we choose a numeraire, wages are constant in steady state since a i are growing at the same rate g L. The growth rate in rea wages is then given by the rate of decine in p mi. But from (2) it is cear that p mi fas at rate g L, so the growth rate of rea wages or consumption is g = g L (4) This is a simpe version of Kortum (1997). Note in particuar that growth of income per capita depends on the growth rate of popuation (the hamark of quasi-endogenous growth modes) and that a higher impies a higher growth rate. The reason for this positive roe of is that a high magni es the bene t of high-quaity ideas and this is the mechanism that fues growth in this mode. The gains from trade are determined by the increase in the rea wage, w i =p mi, as a country goes from autarky to trade. In cacuating these gains here and in the foowing sections I primariy focus on the case of frictioness trade because this aows for simper derivations and because this estabishes an upper bound for the gains from trade. In autarky i = w 1= i i. Pugging into (2) and using i = R i =g L yieds w i =p mi = C 1 T (R i=g L ). Simiary, with frictioness trade we have p m = C T X w 1= j j R j =g L. Assuming i =, it is easy to show that there is factor price equaization (i.e., w i = w j for a i; j), and hence the gains from trade are simpy GT i = P Li Since they generate a smaer share of the word s best ideas, smaer economies have more to gain from integrating with the rest of the word. Moreover, a high eads to higher gains 9 L i

11 from trade. As expained in the Introduction, the reason for this is that a high increases the variabiity of cost di erences across countries and hence eads to a stronger pattern of comparative advantage. 2.2 Towards a quantitative mode I now enrich and caibrate the mode to expore its quantitative impications. Foowing Eaton and Kortum (2002) and Avarez and Lucas (2005), I introduce two modi cations. First, it is assumed that intermediate goods are used in the production of intermediate goods, thus generating a "mutipier" e ect that expands the gains from trade and the growth rate. Second, it is assumed that production of the consumption good uses abor directy and not ony through intermediate goods. This is done to capture the existence of non-tradabes that dampen the gains from trade. In the mode of this section (but not in the one of Section 3) this wi aso reduce the growth rate because technoogica progress is con ned to tradabe intermediates. These two modi cations are iustrated in Figure 1 and captured formay as foows. The intermediate goods are used to produce a "composite intermediate good" with a CES production function with easticity, so that p mi - which above was the price index of the consumption good - is now the price index of this composite good. In turn, the composite good together with abor are used to produce intermediate goods with a Cobb-Dougas production function with abor share. One can think of an "input bunde" produced from abor and the composite intermediate good that is in turn used to produce a the intermediate goods. The cost of the input bunde in country i is then c i Bw i p1 mi where B (1 ) 1, whie the cost of intermediate good u in country i is now x i (u) c i. Finay, the consumption good is produced from the composite intermediate good and abor with a Cobb-Dougas technoogy with abor share. Thus, the price of the consumption good is p i = Awi p 1 mi, where A (1 ) 1. Note that if = 1 and = 0 then we are back to the mode above. The individua intermediate goods are the ony tradeabe goods. These modi cations do not substantiay a ect the quaitative resuts above; the ony difference is that now the wage w i must be substituted by the unit cost of the input bunde, c i, in the de nition of ij in equation (1). 12 But there are important quantitative impications. In 12 As shown by Avarez and Lucas (2005), the trade baance conditions are not a ected by the vaues of or (at east for the case in which there are no tari s, as here). 10

12 Figure 1: The Production Structure Fina Good, Awi p Labor, w i Composite Intermediate Good, p mi H HHj * Input Bunde, c i = Bw i p1 mi - Tradabe Intermediate Goods, x i (u) c i 6 CES; particuar, the growth rate is now 1 g = g L (5) If intermediate goods have a high share in the production of intermediate goods (i.e., high 1 so that there is a arge mutipier 1=, then the growth rate wi be higher. Simiary, the growth rate increases with the share of intermediate goods in the production of the consumption good (i.e., 1 ). The term aso a ects the gains from trade, which in the case of i = considered above are 1 GT i = P Li L i ), (1 )= (6) The key parameters of the mode are,,, and g L. Eaton and Kortum (2002) estimate from the gravity equation generated by the mode together with biatera import and price data for the OECD countries. They focus on the way in which determines the impact of trade costs on trade voumes. To isoate this aspect of the gravity equation, Eaton and Kortum focus on "normaized trade ows." Let the normaized biatera imports of country i from country j be D ij =D jj. If there are no trade costs then D ij =D jj = 1 for a i; j. With trade costs we have D ij =D jj = pmj p mi k ij 1= Taking ogs, and etting m ij n(d ij =D jj ) and ij = n(p mj =p mi k ij ), then m ij = (1=) ij (7) 11

13 Eaton and Kortum (2002) construct m ij from 1990 data on trade and production of manufactures for 19 OECD countries and ij from data on prices from the UN ICP 1990 benchmark study, which gives retai prices for 50 manufactured products in these countries. 13 regression with no intercept yieds = 0: An OLS Avarez and Lucas (2005) caibrate the parameters and to match the fraction of U.S. empoyment in the non-tradabes sector and the share of abor in the tota vaue of tradabes produced, respectivey. They nd = 0:75 and = 0:5. For g L I coud use the growth rate of popuation in the OECD over the ast decades, which is g L = 1:1%. But as Jones (2002) has emphasized, there has been an upward trend in the share of peope devoted to R&D in rich countries over the ast decades. According to Jones, the rate of growth of researchers has been 4:8% over the period in the G-5 countries. 15 Pugging these vaues in equation (5) together with Eaton and Kortum s = 0:12 yieds g = 0:29%, which is signi canty ower than the observed rate of growth of productivity in the OECD countries, which is cose to g = 1:5%. One coud, of course, caibrate to match the observed growth rate, but this woud ead to inconsistent impications for the roe of gravity in trade. In particuar, biatera trade voumes woud decine too sowy as trade costs increase. Turning to the gains from trade, these parameters ( = 0:12, = 0:75, and = 0:5) impy from (6) that the gains from frictioness trade for a country with 1% of the word s tota popuation are 100 0:06 = 1: 3, or 30%. 16 If instead we use the "centra vaue" of in Avarez and Lucas (2005), namey = 0:15, then the gains from trade are 41%, as mentioned in the Introduction. 13 The 19 countries incuded in the sampe are Austraia, Austria, Begium, Canada, Denmark, Finand, France, Germany, Greece, Itay, Japan, Netherands, New Zeaand, Norway, Portuga, Spain, Sweden, the United Kingdom and the United States. 14 The OLS estimation yieds 1= = 8:03 with a standard error of 0:15. The R-squared is 0:06. A simpe method of moments estimation of 1= in (7) yieds basicay the same outcome (see Eaton and Kortum, 2002). 15 The G5 countries are France, West Germany, the United Kingdom, the United States, and Japan. Ceary, an increasing share of peope engaged in research impies that the system is not in steady state, but the system can sti attain a constant growth rate where these formuas are vaid (see Jones, 2002). 16 Note that if i = j for a i; j then with frictioness trade wages are equa across countries, so a country with 1% of the popuation aso has 1% of the word s GDP. For convenience, I used this case to refer to the gains from trade in the Introduction. 12

14 3 Di usion, trade and growth In this section I extend the previous mode to introduce internationa di usion of ideas and make it quantitativey consistent with the observed growth rate and trade voumes. First, I aow for technoogica progress in the production of non-tradabes. In particuar, I assume that just as there are ideas that increase the productivity of tradabe intermediate goods, there are ideas that increase the productivity of non-tradabe consumption goods. I wi refer to the rst type of ideas as "T ideas" and to the second type of ideas as "NT ideas." (I wi suppress the T and NT abes except when necessary to avoid confusion.) Second, I aow for internationa di usion of both types of ideas. The introduction of NT ideas into the mode is necessary to have the mode match the observed growth rate, whereas di usion of both T and NT ideas is a key mechanism for the gains from openness that I want to expore. Moreover, as wi be shown, di usion of T ideas heps to make the mode better match the trade data. To mode the roe of NT ideas, I assume that there is a continuum of non-tradeabe consumption goods indexed by v 2 [0; 1]. These goods enter the representative consumer s instantaneous utiity through CES preferences with easticity of substitution. 17 They are produced from abor and the composite intermediate good with a Cobb-Dougas production function at cost Az(v) w p 1 m, where z(v) is a cost parameter associated with good v. Anaogousy to the way in which T ideas determine the cost parameters x(u) for intermediate goods, z(v) is the inverse of the quaity of the best NT idea that has arrived for good v. Note that the parameter pays the same roe in a ecting the cost of non-tradeabe consumption goods as the parameter pays in a ecting the cost of the tradeabe intermediate goods. The generation and di usion of T and NT ideas is assumed to be identica, so I suppress the T and NT abes for now. I assume that the word is composed of two regions: the North and the South. To simpify, I take the South to be a singe economy, whereas the North contains I countries. I denote the set of north countries by N and simiary use S to denote the (unitary) set of South countries. I use index i for north countries and the indexes j and for a countries (i.e., i 2 N and j; 2 N [ S ). Ony countries in the North generate ideas. Ideas at rst are "nationa" (as in the previous section), but then di use to other north countries, from which they nay di use to the South. Thus, there are I + 2 poos of ideas: one poo for each north country, a poo of ideas that have 17 The assumption that the easticity of substitution is the same here as in the production of the composite good is made to minimize notation and pays absoutey no roe in the resuts. 13

15 di used among the north countries (the "north ideas"), and the poo of ideas that have di used to the South. Ideas in the atter poo are avaiabe in a countries, so I refer to these ideas as "goba ideas." Foowing Krugman (1979) and Eaton and Kortum (2006), I assume that di usion is probabiistic, with each idea having a constant probabiity of di using. Let be the rate of di usion among countries in the North and et 0 be the rate of di usion from the poo of north ideas to the poo of goba ideas. Letting N and G be the stocks of ideas in the north and goba poos, respectivey, then _ i = i L i i, _ N = P i 0 N, _ G = 0 N. In steady state the stock of nationa ideas in north country i is i = ( i =(g L + ))L i (8) whie the stock of north ideas is N = e X i (9) where e =( 0 + g L ). Finay, the stock of goba ideas in steady state is G = 0 N =g L (10) A these stocks of ideas grow at rate g L in steady state. 3.1 Equiibrium Let us rst focus on consumption goods. Since they are non-tradabe then we care ony about the best idea avaiabe in each country, irrespective of whether they are nationa ideas or not. That is, for north country i the cost parameter for a consumption good is associated with the best idea across the poos of nationa ideas in i, north ideas and goba ideas. This impies that the cost parameter in north country i for any consumption good is distributed exponentiay with parameter i + N + G. Simiary, the cost parameter for a consumption good in the South is determined by the best goba idea and is distributed exponentiay with parameter G. In equiibrium, consumption goods are sod at cost, hence the price of consumption good v is Az(v) w p 1 m. The price index for the consumption bunde is then p = Aw p 1 m Z 1 z(v) (1 0 1=(1 ) ) dv 14

16 Since z(v) in north country i is distributed exponentiay with parameter i + N + G, then (assuming that 1 + (1 price index for the consumption bunde in i is ) > 0 so that the integra above is we de ned) we have that the p i = Awi p 1 mi C NT ( i + N + G ) (11) where C NT (1 + (1 )) 1=(1 ). The price index for the South is given by a simiar expression with i + N + G repaced by G. Turning to intermediate goods and trade, note that for each good there are n best nationa ideas (one for each north country), a best north idea, and a best goba idea. Recaing that x i (u) denotes the cost parameter for the best nationa idea in country i for intermediate good u, and using x N (u) and x G (u) to denote the cost parameters associated with the best north and goba ideas for this good, respectivey, then we can now abe intermediate goods by ex = (x 1 ; x 2 ; :::; x I ; x N ; x G ). Consider the di erent ways in which a country coud procure a particuar good ex. Just as in the previous section, country coud buy this good produced with nationa ideas from any of the I north countries at minimum cost min i (ci =k i ) x i (reca that i necessariy beongs to N ). But now it can aso buy goods produced with di used ideas: it can buy goods produced in any of the I north countries with north ideas, and it can buy goods produced in any of these countries pus the South with goba ideas. The cost of buying a good produced in country i with the best north idea is (c i =k i ) x N, so the minimum cost of buying a good produced with a north idea is min i (ci =k i ) x N. Simiary, the minimum cost of buying a good produced with a goba idea is min j (cj =k j ) x G (note that this minimization now incudes the possibiity that the good is produced in the South, j = S). Letting ec min j fc j =k j g and ec N min i fc i =k i g, then the price of good ex in country is now n o p (ex) = min min (ci =k i ) x i ; ec N x i N; ec x G (ex) Given the properties of the exponentia distribution, is distributed exponentiay with parameter ^ X i (c i=k i ) 1= j + ec N 1= N + (ec ) 1= G (12) This parameter determines the price index for intermediate goods in country. In particuar, and anaogous to (2), we now have p m = C T ^ (13) 15

17 Wages are determined by the trade-baance conditions, as in (3), but the trade shares are now di erent. To determine these shares, note that (c i =k i ) 1= i =^ is the share of goods which country can procure most cheapy from i produced with i 0 s best nationa ideas. The fact that may aso buy north and goba goods from i estabishes that D i (c i =k i ) 1= i =^ for i 2 N (14) To proceed, et M N arg min i fc i =k i g denote the set of countries from which country woud buy a goods produced with north ideas (i.e., if country buys a good produced with a north idea, it must be buying this good from i 2 M N ). Obviousy, c i =k i = ec N if i 2 M N. The share of goods that country wi actuay buy from countries i 2 M N produced with north ideas 1= is then given by N =^. The fact that may aso buy goba goods from countries ec N i 2 M N estabishes that X D i ec N 0 1 1= X i + N A (15) i2m N i2m N Finay, et M arg min j fc j =k j g denote the set of countries from which woud buy a goods produced with goba ideas. If the South were the unique member of M then country woud buy a goods produced with goba ideas from the South, and then D S = (c S =k S ) 1= G =^ In this case (15) woud have to be satis ed with equaity. If there are north countries in M, however, then country wi import from these countries goods produced with nationa, north and goba ideas, and hence X j2m D j = (ec ) 1= =^ X i2m \ N i + (M \ N ) N + G where (M \ N ) = 1 if M \ N 6=? and (M \ N ) = 0 otherwise. The competitive equiibrium is determined by the vectors p m = (p m1 ; p m2 ; :::; p mi ; p ms ) and w = (w 1 ; w 2 ; :::; w I ; w S ) such that together with the vector (^1; ^ 2; :::; ^ I; ^ S) that satis es equations (12) and (13) and the matrix fd j ; j; = 1; 2:::; I; Sg that satis es (14) trade-baance conditions (3) are satis ed.! (16) (16), the 16

18 In steady state wages are constant, so the common growth rate is given by g = equations (12) and (13) impy that p m decines at rate g L = (using c = Bw p1 (11) we nd g = 1 The growth rate is composed of two terms: the rst term, ( 1 m _p =p. But ), so from + g L (17) )g L, is associated with technoogica progress in tradeabe (intermediate) goods, whereas the second term, g L, is associated with technoogica progress in non-tradeabe (consumption) goods. It is worth noting that the rst term is exacty the same as in the mode with no di usion of the previous section (see equation (5)). This reveas that di usion has no e ect on steady state growth in this mode; as wi become cear beow, there is ony a eve e ect. 3.2 Gains from trade and di usion I now turn to the derivation of the gains from trade and di usion of both T and NT ideas. As in the previous section, I consider the gains from frictioness trade. To do so, I rst derive the rea wage for the case of no trade (with and without di usion), and then for the case of frictioness trade with di usion. I then compare these wages to estabish the gains from trade and di usion, and discuss severa impications from these resuts No trade When there is no trade, the price index of intermediate goods in country, p m, is given by (13) but with ^ = c 1= where is the stock of ideas in country. For each north country i, this stock is composed of ideas originated in i and foreign ideas that have di used (i.e., foreign ideas that have become north or goba ideas), whie for the South this stock is composed entirey of goba ideas. Thus, 8 (1 + =g L ) if no di usion and 2 N >< 0 if no di usion and 2 = S (18) + N + G if there is di usion and 2 N >: G if there is di usion and 2 S From (13) we get p m =w = (BC T ) 1= =. (Note that if there is no di usion, then this expression is not we de ned for the South since in that case = 0.) From (11) we nay get 17

19 the rea wage for country, namey Frictioness trade w =p = (AC NT ) 1 (BC T ) (1 )= (1 )=+ (19) Turning to the characterization of the equiibrium under frictioness trade, it is convenient to introduce the notions of "nationa i goods," "north goods," and "goba goods" (this is reevant ony for intermediate goods). Nationa i goods are those for which the best idea is a nationa idea in country i (i.e., x i = arg min fxg); north goods are those for which the best idea is a north idea (i.e., x N goba idea (i.e., x G = arg min fxg). = arg min fxg); and goba goods are those for which the best idea is a Thanks to di usion and the fact that trade is frictioness, the equiibrium may entai wage equaization across a countries. In this case a countries produce goba goods and a north countries produce north goods. If di usion is not too strong, then wage di erences arise between North and South, and even among north countries. For exampe, the equiibrium coud exhibit an inferior wage in the South, with wage equaization ony among north countries. In this equiibrium a north countries produce north goods, and ony the South produces goba goods. If North-North di usion is weak reative to di erences in research intensities across the North then wage di erences woud arise among north countries. In this case, there woud be a group of north countries with the highest research intensities speciaizing in the production of their "nationa goods," with wages determined by each country s research intensity (as in Eaton and Kortum, 2002, and Avarez and Lucas, 2005), and then a group of north countries with the owest research intensities sharing a common wage and producing north goods. The wage in the South coud be the same as this "ow north wage" or it coud be ower sti. In the ater case, a goba goods woud be produced in the South. To simpify the exposition, I wi focus on the equiibrium with two wage eves: a ow wage in the South and a common wage for north countries. This equiibrium is possibe even if the research intensity di ers among north countries: thanks to di usion, north countries with ow research intensities can speciaize in north goods and attain trade baance in spite of the fact that their stock of nationa ideas per person is reativey ow. The key for this equiibrium con guration is that a north countries produce north goods. Under frictioness trade, this requires that the unit cost of the input bunde be equa across countries, i.e. c i = Bw i p1 mi for a i 2 N, so that there is indi erence about where to buy north goods. I refer to this 18

20 condition as the ECN condition. Since under frictioness trade we have p m = p m for a, then this condition entais w i = w N for a i. In equiibrium, country i wi at east suppy the whoe word of nationa i goods. Using (8), (9), and (10), and etting R i i L i and R N P i R i, the share of nationa i goods among a goods is i =( X i + N + G ) = R i =R N 1 + e + 0 =g L Given the absence of trade costs and the ECN condition, this is aso the share of each country s tota spending that wi be aocated to buying nationa i goods from country i. Letting N R N =L N (with L N P i L i) be the average research intensity in the North, then a condition necessary for an equiibrium with wage equaization among north countries is i = N 1 + e (20) This inequaity ensures that - given the ECN condition - every north country has some resources eft over for producing north goods. This requires that i = N be not too high, for otherwise there woud be a country that woud have so many nationa goods that it woud not be abe to satisfy the word demand for its nationa goods given the ECN condition, and the equiibrium coud not take the form that I have postuated here. Note that the condition is reaxed as e increases. This is because a higher impies that a ower share of goods are nationa goods. The wage in the South reative to the North can be obtained from the conditions L Sw S D S 1 D S and D S = c 1= S =^ G. This yieds 0 1 w S =w N e 0 L 1 + e N A g L S L 1=(1+=) For the conjectured equiibrium with w S < w N we then need the foowing condition: L N w N = (21) g L L S =L N or > g L L S =L N together with 0 < L S (g L + ) g L L N g L L S (22) The rst inequaity or the second and third inequaities together impy that the stock of goba ideas is too ow, so w S =w N < 1. If conditions (20) and (22) are satis ed, then there is an equiibrium of the form that I have conjectured (i.e., wage equaization in the North and w S < w N ). For future reference, note that as di usion increases then wages in South and North become equaized (i.e. w S = w N ). 19

21 Formay, if > g L L S =L N then there exists a 0 such that wages are equaized if 0 0. Simiary, if 0 > g L L S =L N then there exists a such that wages are equaized if. 18 Simiary, wages become equaized for any non-zero and 0 if South is su cienty sma. Now, from (12) and (13) we get p m = (BC T ) 1= w N X j j + N + (w S =w N ) = G = and from (11) and (23) we get the rea wage in north country i, w N =p i = (AC NT ) 1 (BC T ) (1 )= X The corresponding resut for the South is w S =p S = (AC NT ) 1 (BC T ) (1 j j + N + (w S =w N ) = G (1 )= (w N =w S ) = X Gains from di usion and frictioness trade j j + N (23) )= (i + N + G ) (24) + G (1 )= G (25) The overa gains from openness for north country i can be seen as the increase in the rea wage from the case with no trade and no di usion to the case with di usion under frictioness trade. 19 From (19) with i = (1 + =g L ) i and (24), and using the expressions for i, N and G in equations (8) (10), the gains from openness for north country i are GO i = r (1 i )=! 1 + (w N=w S ) = (1 )= 1 =ri + g L (26) (g L + ) = 0 e + g L where r i R i =R N is the share of wordwide research done by i. The rst term captures the gains associated with North-North trade of intermediate goods and di usion of T ideas; the second term captures the gains from trading with the South; and the na term captures the gains from di usion of NT ideas. Ceary, countries that account for a smaer share of wordwide research have more to gain from openness. Moreover, as ong as 0 is not too ow, then! 1 (1 )= impies that w N = w S and hence GO i! ri. Since (1 )= + = g=g L, this coincides with the simpe ogic pursued in the Introduction to compute the gains from openness 18 These vaues for and 0 are de ned by 21 for w S =w N = It is worth emphasizing that in the mode there are no transition dynamics since both the bene ts from trade and di usion take pace instantaneousy. Thus, the increase in the rea wage from isoation to openness is the appropriate measure of the wefare gains from openness. 20