Trade and Productivity

Transcription

1 Trade and Produtivity by Franiso Alalá Universidad de Muria and Antonio Cione Universitat Pompeu Fabra July 2002 (First Version: May 2001) Abstrat: We estimate the effet of international trade on average labor produtivity at the ountry level. Our empirial approah relies on summary measures of trade that, we argue, are preferable on both theoretial and empirial grounds to the one onventionally used. In ontrast to the marginally signifiant and non-robust effets of trade on produtivity found previously, our estimates are highly signifiant and robust even when we inlude institutional quality and geographi fators in the empirial analysis. We also examine the hannels through whih trade and institutional quality affet average labor produtivity. Our finding is that trade works through labor effiieny, while institutional quality works through physial and human apital aumulation. We onlude with an exploratory analysis of the role of trade poliies for average labor produtivity. (JEL F43, O40) Keywords: Trade, Produtivity, Development, Trade Poliy, Institutions. We thank Tito Cordella, Luis Cubeddu, and Walter Garia-Fontes for invaluable help with the data and Rita Almeida for exellent researh assistane. Many thanks also to Daron Aemoglu, Bettina Aten, Franeso Caselli, Gregory Mankiw, Ivan Pastine and seminar partiipants at Bano de España, Bana d Italia, Universita di Bari, Harvard University, LSE and the 2002 European Summer Symposium in International Maroeonomis for helpful omments, and to Bettina Aten, Franiso Rodriguez, and David Romer for kindly providing the data used in Aten (1997), Rodriguez and Rodrik (1999), and Frankel and Romer (1999) respetively. We also benefited from the omments of three anonymous referees. This paper is part of a researh projet finaned by the European Regional Development Fund and the Fundaión Caixa Galiia. Cione gratefully aknowledges finanial support from the Centre de Reera en Eonomia Internaional (CREI) as well as from the Spanish Ministry of Siene and Tehnology through DGICYT grant PB and the European Commission through RTN grants HPRN-CT and HPRN-CT

2 1 Introdution Theories about international trade inreasing aggregate produtivity at the ountry level are nearly as old as eonomis. But how large is this effet empirially? Answering this question is diffiult beause any partiular summary measure of trade is likely to miss some aspets of how trading ativities affet ountries produtivity. Moreover, while international trade may inrease aggregate produtivity, the reverse also seems likely. Empirial work therefore has to make sure to identify the effet of trade on produtivity instead of the other way round. The summary measure of international trade nearly always used in empirial work is nominal imports plus exports relative to nominal GDP, usually referred to as openness. For reent examples see Coe and Helpman (1995), Ades and Glaeser (1999), Gustavsson, Hansson, and Lundberg (1999), Alesina, Spolaore and Waziarg (2000), Dinopoulos and Thompson (2000), and Miller and Upadhyay (2000). Openness is also the measure of trade used in Frankel and Romer s (1999) innovative work on the ausal effet of trade on average labor produtivity at the ountry level. The idea underlying their empirial approah is that trade is partly determined by (geographi) harateristis of ountries that are unrelated to produtivity. These harateristis should therefore allow for estimation of the ausal effet of trade on produtivity using an instrumental-variables approah. They implement this idea empirially for a large set of ountries in 1985 and find a positive, but rather impreisely estimated, effet of trade on average labor produtivity. Aording to their estimate, the effet of trade on produtivity is just signifiant at the 5-perent level (see also Frankel and Rose (2002)). Further researh using the same approah by Irwin and Tervio (2000) has shown, however, that trade no longer affets average labor produtivity signifiantly one ountries distane to the equator is inluded in the empirial analysis. This result suggests that the positive effet of trade on ountries average labor produtivity found by Frankel and Romer may be driven by spatially orrelated omitted variables. We argue that estimates of international trade s effet on average labor produtivity at the ountry level in the existing literature give a misleading piture of the true produtivity-gains aused by trade beause of the summary measure of trade used in the empirial analysis. Summarizing trade using nominal imports plus exports relative to nominal GDP (openness) has drawbaks for empirial ross-ountry produtivity analysis that are easily explained. Suppose that international trade inreases produtivity but that the implied produtivity-gains are greater in the tradable goods setor (e.g. manufaturing) than in the non-tradable goods setor (e.g. servies). 1

3 Will ountries that are more produtive beause of trade have higher values of openness? Not neessarily, beause the relatively greater produtivity-gains in the tradable goods setor lead to a rise in the relative prie of non-tradable goods, whih may derease openness when the demand for non-tradable goods is inelasti. We show this formally in a model where produtivity-gains from international trade arise due to inreasing returns to speialization (Helpman (1981), Krugman (1981), Ethier (1982)). This problem with the onventionally used summary measure of international trade motivates our two simple alternatives, whih we refer to as real openness and tradable GDP openness respetively. Real openness is defined as imports plus exports in exhange rate US$ relative to GDP in purhasing-power-parity US$ (PPP GDP). Using real openness instead of openness as a summary measure of trade eliminates the distortions due to ross-ountry differenes in the relative prie of non-tradable goods. Tradable GDP openness is defined as nominal imports plus exports divided by the nominal value of prodution in the tradable goods setor. Using tradable GDP openness instead of openness therefore eliminates ross-ountry differenes in the value of non-tradable goods from the summary measure of trade. Ultimately, hoosing the best summary measure of international trade for ross-ountry produtivity analysis is an empirial issue. We show that both real openness and (our proxy of) tradable GDP openness are apable of explaining a greater amount of the variation in rossountry produtivity than openness (with real openness performing somewhat better than tradable GDP openness). This result, ombined with our theoretial work, leads us to stress real openness and (our proxy of) tradable GDP openness in our investigation of international trade s effet on ountries average labor produtivity (PPP GDP per worker). Our empirial analysis takes into aount the key role of institutions for average labor produtivity as well as for inome per apita found by Hall and Jones (1999) and Aemoglu, Johnson, and Robinson (2001) respetively. Aemoglu, Johnson, and Robinson estimate the effet of expropriation risk on inome per apita in former olonies, while Hall and Jones onsider the effet of a more broadly defined index of institutional quality (inluding expropriation risk) on average labor produtivity for a larger set of ountries. Both use an instrumental-variables approah to address measurement error and reverse ausation. We adapt their approah in order to estimate how international trade affets average labor produtivity or inome per apita for a given level of institutional quality or expropriation risk. Our empirial work also inorporates geographi fators that may affet average labor produtivity (distane from the equator inluded in the analysis of Irwin and Tervio (2000) for example). The result of our empirial analysis is that the effet of international trade measured either using real openness or (our proxy of) tradable GDP openness on average labor produtivity and inome per apita at the ountry level is highly signifiant and extremely robust to the inlusion of 2

4 institutional quality, expropriation risk, and geography ontrols. For example, using the largest possible sample of ountries in 1985, we find that the instrumental-variables estimate of the elastiity of average labor produtivity with respet to real openness is 1.44 with a standard error of 0.19 when we do not inlude any ontrols for institutional quality and geography in the empirial analysis. International trade is therefore a statistially signifiant determinant of produtivity at the perent level. The estimate implies that an inrease of real openness taking a ountry from the 30 th perentile to the median value doubles produtivity; an inrease of real openness taking a ountry from the 20 th perentile to the median value almost triples produtivity; and an inrease of real openness taking a ountry from the 10 th to the 90 th perentile inreases average labor produtivity by a fator of ten. 1 When institutional quality and geography ontrols (distane from the equator and ontinent dummies) are inluded in the empirial analysis, we find that a 1-perent inrease in real openness raises average labor produtivity by 1.45 perent with a standard error of Hene, the estimated elastiity of average labor produtivity with respet to real openness hardly hanges with the inlusion of institutional quality and geography ontrols. The standard error inreases however. Still, trade remains a statistially signifiant determinant of produtivity at the 0.02-perent level. Similarly, the instrumental-variables estimate of the elastiity of average labor produtivity with respet to (our proxy of) tradable GDP openness is 1.89 with a standard error of 0.38 when we do not inlude any ontrols for institutional quality and geography in the empirial analysis. International trade is therefore a statistially signifiant determinant of produtivity at the 0.01-perent level. When institutional quality and the statistially signifiant geography ontrols are inluded in the empirial analysis, we find that a 1- perent inrease of (our proxy of) tradable GDP openness raises average labor produtivity by 1.66 perent with a standard error of Hene, the estimated elastiity of average labor produtivity with respet to tradable GDP openness also hanges little and remains highly signifiant when institutional quality and geography ontrols are inluded in the empirial analysis. We also inlude the size of ountries workfore in the empirial analysis to allow for aggregate sale effets onditional on international trade. Our results suggest that aggregate sale effets are eonomially and statistially signifiant. For example, when we use real openness as a measure of international trade, we find an elastiity of ountries average labor produtivity with respet to their workfore of around 0.3 with a standard error of around 0.1. Using (our proxy of) tradable GDP openness as a measure of international trade yields similar estimates for aggregate 1 A more preise version of the first statement for example (given that real openness is endogenous) would be that a hange in exogenous variables taking real openness from the 30 th perentile to the median value doubles produtivity. And even this statement may require further qualifiation beause part of the variability of real openness may be due to measurement error. We will return to this issue below. 3

5 sale effets onditional on international trade. These findings onfirm the aggregate sale effets found in Frankel and Romer (1999) and Frankel and Rose (2002) among others. To determine the hannels through whih international trade and institutional quality affet average labor produtivity at the ountry level, we also estimate the effet of trade and institutional quality on the (physial) apital-output ratio, the average level of human apital, and labor effiieny. Our findings indiate that trade is a signifiant determinant of labor effiieny but not of the apital-output ratio or the average level of human apital. Institutional quality, on the other hand, is a signifiant determinant of the apital-output ratio and the average level of human apital but not of labor effiieny. Our theoretial ritiism of openness as a summary measure of international trade in rossountry produtivity analysis rests on the hypothesis that trade raises the relative prie of nontradable goods at the ountry level. This in turn raises the prie level (ompared to some benhmark ountry). We test for these links by estimating the relationship between ountries international trade and their relative prie of non-tradable goods as well as their prie level. Our empirial findings onfirm that international trade has a positive, statistially signifiant effet on the relative prie of non-tradable goods as well as on the prie level. We onlude our empirial work on the link between international trade and average labor produtivity with an exploratory analysis of the effet of trade poliies on trade and produtivity. The analysis leads us to the tentative onlusion that poliies favorable for trade may be an effetive tool for inreasing produtivity. The remainder of this paper is strutured in the following way. Setion 2 explains the potential theoretial drawbaks of openness as a summary measure of trade in empirial ross-ountry produtivity analysis. Our analysis is based on a simple trade model with tradable and non-tradable goods and inreasing returns due to speialization. Setion 3 ontains the equations to be estimated and details on the instrumental-variables approah. Setion 4 disusses the data and the quality of the instruments. Setion 5 presents the results on the effets of international trade and institutional quality on average labor produtivity in 1985 and 1990 using three broad samples, as well as on inome per apita in 1995 using a sample of former olonies. The setion also ontains our estimates of the impat of international trade on the prie level and the relative prie of nontradable goods at the ountry level, and our results on the effet of international trade and institutional quality on the apital-output ratio, the average level of human apital, and labor effiieny. Setion 6 onludes with our exploratory analysis of the ausal effet of trade poliies on real openness and average labor produtivity at the ountry level. 4

6 2 Inreasing Returns to Speialization, International Trade, and Produtivity The potential drawbaks of the ratio of nominal imports plus exports to nominal GDP as a summary measure of trade in empirial work on ross-ountry produtivity an be illustrated using a simple stati, small open eonomies model with inreasing returns to speialization in the spirit of Helpman (1981), Krugman (1981), and Ethier (1982). The key element of the argument is that international trade ends up affeting total fator produtivity in the tradable goods setor more strongly than in the non-tradable goods setor. Suppose that eah ountry an potentially produe a unit measure of ommodities indexed by i [0,1]. Commodities i [0, t ], 0< t < 1, are tradable goods (e.g. manufaturing goods), while the remaining fration 1 t of ommodities are non-tradable goods (e.g. servies). The measure of tradable goods produed in ountry is denoted by d. As the measure of tradable goods produed domestially dereases, ountries are said to have beome more speialized. Firms in tradable goods setors i [0, t] are assumed to be able to produe output y using labor l aording to the following onstant-returns-to-sale prodution funtion y = Bgd (, l ) l, (1) where B is a produtivity parameter speifi to ountry and l is aggregate employment in ountry. The (ontinuously differentiable) funtion g () allows us to apture inreasing returns due to speialization as well as inreasing returns to the aggregate sale of prodution. Inreasing returns to speialization is defined as marginal labor produtivity in tradable goods prodution inreasing as the range of tradable goods produed domestially dereases, g1 ( d, l ) < 0 (subsripts 1,2 denote partial derivatives with respet to the first and the seond argument respetively). Inreasing returns to the aggregate sale of prodution is defined as marginal labor produtivity in tradable goods prodution inreasing with aggregate employment, g2 ( d, l ) > 0. We assume inreasing returns to speialization and to the aggregate sale of prodution throughout our analysis. 2 Suppose that inreasing returns (aptured by g () ) are limited to tradable goods. Non-tradable goods i (,1] t are produed aording to the onstant-returns-to-sale prodution funtion s = Bl. (2) The assumption that inreasing returns are ompletely absent in the prodution of non-tradable goods is made for simpliity only. Our argument goes through as long as inreasing returns are weaker in the prodution of non-tradable goods than in the prodution of tradable goods. 5

7 Households are assumed to supply an aggregate amount of labor L inelastially. Their preferenes over onsumption goods are given by ε 1 ε 1 1 ε 1 ε 1 ε ( min( : [0, ]) ε ε ) (1 β) ( min( : (,1]) ε i i ) U = β x i t + s i t, (3) where x i denotes onsumption of the different tradable goods and s i onsumption of the different non-tradable goods; ε > 0 aptures the elastiity of substitution between tradable and non-tradable goods and 0< β < 1 is a distribution parameter. We assume perfet omplementarity among tradable goods and among non-tradable goods respetively beause the elastiity of substitution within these groups of ommodities plays no role for our argument. The elastiity of substitution between tradable goods and non-tradable goods is ruial for our analysis however. We assume throughout that ε < 1 and hene that the demand for non-tradable goods is inelasti. Goods and labor markets are assumed to be perfetly ompetitive. The prie of all tradable goods in international markets is taken to be idential and normalized to unity. In equilibrium, the relative prie of different non-tradable goods (relative to tradable goods) produed in the same ountry is idential. Aross ountries, the relative prie of non-tradable goods varies endogenously. The relative prie of non-tradable goods produed in ountry is denoted by ρ. The fat that both different tradable goods and different non-tradable goods enter preferenes in a perfetly omplementary way implies that households in ountry onsume the same amount of eah tradable good and of eah non-tradable good. These quantities are denoted by x and s respetively. Household preferenes also imply that the demand for non-tradable goods in ountry relative to the demand for tradable goods is equal to s x = θt ρ ε 1, (4) t ε 1 ε 1 where θ (1 β) t / β(1 t ). In equilibrium, trade of eah ountry with the rest of the world must be balaned. Hene, the total value of (tradable goods) imports ( t d ) x must be equal to the total value of (tradable goods) exports. For simpliity we onentrate on symmetri equilibria where ountries produe the same quantity y of all tradable goods that they export. Denoting the variety of tradable goods that are exported by e, e d, yields that the total value of (tradable goods) exports an be written as e ( y x ). Balaned trade ( t d ) x = e ( y x ) therefore implies that the value of aggregate 2 Rauh and Weinhold (1999) present evidene on the link between speialization in prodution and produtivity growth for 39 less developed ountries. 6

8 onsumption of tradable goods ey + ( d e) x, tx is equal to the value of aggregate prodution of tradable goods tx = e y + ( d e ) x. (5) Wages in the tradable goods setor and in the non-tradable goods setor are equalized in labor market equilibrium. Combined with the assumption that inreasing returns are limited to the prodution of tradable goods, this yields that the equilibrium relative prie of non-tradable goods ρ reflets the produtivity of labor in the tradable goods setor relative to the non-tradable goods setor, ρ = g( d, L ), (6) where we use that aggregate employment l is equal to aggregate labor supply L in equilibrium. Non-tradable goods are therefore relatively more expensive in ountries where the prodution of tradable goods is relatively more effiient. This yields a link between ountries degree of speialization and their relative prie of non-tradable goods that is key to our ritiism of openness as a summary measure of trade. Wage-equalization, balaned trade, and the relative demand for non-tradable goods ombined with market learing and the prodution funtions for tradable goods and non-tradable goods imply that 1 ε 1 ε T = θ ρ = θ T B gd (, L) l (1 t) s gd (, L) B( L l ), (7) where l and L T l T denote the aggregate amount of labor used in the prodution of tradable goods and non-tradable goods respetively. Simplifying yields the aggregate amount of labor employed in the tradable goods setor as a funtion of aggregate equilibrium employment and the measure of tradable goods produed domestially d, l T L = 1 + θ gd (, L) 1 ε Purhasing power parity (PPP) GDP in the model is defined as. (8) YPPP, e y + ( d e ) x + (1 t)ρs, (9) where ρ is the relative prie of non-tradable goods in the benhmark ountry. This definition ombined with the prodution funtions for tradable goods and non-tradable goods yields that YPPP, = B g( d, L ) lt + ρb ( L l T ). (10) Combining PPP GDP with the alloation of labor aross setors implies that PPP average labor produtivity an be written as a funtion of aggregate employment and the measure of tradable goods produed domestially, 7

9 Y gd (, L) + ρθ gd (, L) PPP, = B L 1 ε 1 + θ gd (, L) 1 ε. (11) Differentiating (11), making use of our maintained hypothesis ε < 1, yields that PPP average labor produtivity inreases with aggregate employment and dereases with the measure of tradable goods produed domestially (inreases with the degree of speialization). 2.1 International Trade and Produtivity The model implies that international trade inreases ountries PPP average labor produtivity by allowing them to onsume all the different types of tradable goods while speializing in the prodution of a subset only. But will this effet of trade on produtivity lead to produtivity being a monotonially inreasing funtion of openness? We show that this is not neessarily the ase beause of the effet of speialization on the relative prie of non-tradable goods. The relationship between real openness and average labor produtivity is, however, stritly inreasing. Moreover, we show that the relationship between imports plus exports relative to domesti tradable goods prodution (tradable GDP openness) and average labor produtivity is also stritly inreasing. Openness GDP is defined as Y e y + ( d e ) x + (1 t)ρ s in our model. Openness therefore orresponds to Open ( t d ) x ( t d ) x 1 d / t 2 = 2 = 2 ey d e x ts tx t s gd L 1 + ( ) + ρ(1 ) + (1 ) ρ 1 + θ (, ) ε (12) where the first equality makes use of (5) and the seond equality makes use of (4) and (6). To see that the model may imply a non-monotoni relationship between openness and PPP average labor produtivity, suppose that speialization eonomies are strong in the sense that gd (, L ) as d 0 for all L > 0 (this assumption is not neessary for the argument but simplifies the exposition). In this ase, Open tends to zero as the eonomy beomes more and more speialized (holding aggregate employment onstant), i.e. as d 0. Clearly, Open is also equal to zero when the eonomy produes all tradable goods domestially and does not speialize at all, d = t. Continuity of Open as a funtion of the degree of speialization therefore implies that all levels of openness between zero and the maximum value orrespond to at least two different degrees of speialization. Countries with different degrees of speialization (and the same level of aggregate employment) may therefore have the same level of Open. This implies that ountries with the same level of exogenous produtivity, aggregate employment, and openness may have different PPP average labor produtivity. The result that Open is equal to zero if the ountry is not speialized at all and if the ountry is extremely speialized also yields that Open must at some point derease as the eonomy beomes more speialized (holding aggregate employment 8

10 onstant). An inrease in openness may therefore be assoiated with a derease in PPP average labor produtivity. 3 It is straightforward to show that if ε < 1 then the relationship between PPP average labor produtivity and openness (given aggregate employment) is non-monotoni for many different speifiations of the inreasing returns funtion g( dl, ) even if produtivity in tradable goods prodution does not tend to infinity as the eonomy beomes more and more speialized. To get a better understanding of this result, it is useful to first establish that the value of imports plus exports relative to the value of tradable goods prodution is always inreasing in the degree of speialization. To see this suppose first that the value of tradable goods prodution inreases by one perent beause of an inrease in exogenous produtivity. This inreases the demand for imports by one perent beause onsumers spread the resulting inrease in inome evenly aross all tradable goods. Hene, the value of imports and exports inreases exatly by one perent (beause of balaned trade) and the value of imports plus exports relative to the value of tradable goods prodution remains unhanged. Now suppose that the value of tradable goods prodution inreases by one perent beause of higher total fator produtivity due to the eonomy having beome more speialized. Clearly, in this ase the demand for imports inreases by more than one perent beause, in addition to onsumers spreading the inrease in inome evenly aross all tradable goods, inreased speialization implies that the ountry starts importing goods that used to be produed domestially. Reall that Open is equal to the value of imports and exports divided by GDP, whih in turn is equal to the value of tradable goods prodution plus the value of nontradable goods prodution. The fat that the value of imports plus exports relative to the value of tradable goods prodution is always inreasing in the degree of speialization therefore implies immediately that Open is always inreasing in the degree of speialization if the value of nontradable goods prodution inreases at a rate smaller or equal than the value of tradable goods prodution. Hene, for Open to fall with the degree of speialization it is neessary for the value of non-tradable goods prodution (1 ts ) ρ to inrease at a faster rate than the value of tradable goods prodution ey + ( d e) x = tx with inreased speialization. Rewriting (4) as 1 ρ θρ ε (1 ts ) = ( tx ), yields that this requires the relative prie of non-tradable goods to inrease and the elastiity of substitution between tradable and non-tradable goods to be stritly smaller than unity. These two onditions are very intuitive of ourse. First, if the relative prie of non-tradable goods does not hange, the total value of non-tradable goods prodution inreases at exatly the same rate as inome beause preferenes are assumed to be homotheti (like in almost all of trade theory). Seond, if the relative prie of non-tradable goods inreases with speialization but the elastiity of substitution between tradable and non-tradable goods is greater or equal than 3 For example, suppose that g( dl, ) = ( Ld / ) γ as well as L = 1, γ = 2, ε = 0.5, and t = 0.5. Then (12) implies that Open is a hump-shaped funtion of d with a maximum value (reahed at d = 0.22 ) equal to

11 unity, the total value of non-tradable goods onsumed inreases at a rate smaller or equal than the value of prodution. (The explanation of why Open tends to zero as the eonomy approahes omplete speialization when gd (, L ) as d 0 is that, in this ase, inelasti demand for non-tradable goods implies that the value of non-tradable goods onsumption relative to the value of tradable goods onsumption tends to infinity as the eonomy approahes omplete speialization, while the value of exports relative to the value of tradable goods prodution tends to unity. Hene, Open, whih an be written as 2 (exports/tradables prodution)/ (1+(non-tradables onsumption/tradables onsumption)) tends to zero as the eonomy approahes omplete speialization.) Real Openness Real openness in our model orresponds to ROpen ( t d) x 1 d / t 2 = 2 ey + ( d e) x + ρ(1 ts ) 1 + θρgd (, L) ε, (13) where ρ is the relative prie of non-tradable goods in the benhmark ountry (first introdued in (10)) and we are making use of (4), (5), and (6). Hene, the degree of speialization is stritly inreasing in real openness (and vie versa). To see that (13) implies that PPP produtivity is inreasing in both real openness and aggregate employment, notie that relative produtivity in the tradable goods setor (relative to the non-tradable goods setor) g an be written as an inreasing funtion of both real openness and aggregate employment 1 2 g = hropen (, L), (14) h () > 0, h () > 0. This an be seen formally by impliitly differentiating (13), making use of g = gd (, L ). Combined with the result in (11) that PPP average labor produtivity is inreasing in the relative produtivity of the tradable goods setor, (14) yields that PPP average labor produtivity an be written as a stritly inreasing funtion of real openness, aggregate employment, and the ountry-speifi produtivity parameter B, f () > 0, f () > Y PPP, L = B f( ROpen, L ), (15) Tradable GDP Openness The third onept of openness onsidered in this paper is tradable GDP openness (TROpen ) defined as the value of imports plus exports relative to domesti tradable goods prodution 10

12 ( t d) x TROpen 2 = 2(1 d / t), (16) ey + ( d e) x where we are making used of (5). It follows from (16) that TROpen, like ROpen, is stritly inreasing in the degree of speialization. Hene, PPP average labor produtivity an be written as a stritly inreasing funtion of tradable GDP openness, aggregate employment, and the ountryspeifi produtivity parameter International Trade and the Pries Our theoretial ritiism of openness as a summary measure of international trade in ross-ountry produtivity analysis rests on the hypothesis that the relative prie of non-tradable goods is inreasing in the degree of speialization and hene in real openness as well as in tradable GDP openness (see (6), (14), and (16)). We now show that this link implies that the prie level of ountries (relative to the benhmark) is inreasing in real openness as well as in tradable GDP openness. The prie level in our model is Y e y + ( d e ) x + (1 t) ρ s 1+ θρ P = = Y e y d e x t s 1 ε ε PPP, + ( ) + (1 ) ρ 1+ θρρ, (17) where the last equality makes use of (4) and (5). Hene, the prie level is inreasing in the relative prie of non-tradable goods. Combined with (6), (14), and (16), this yields that the prie level is an inreasing funtion of real openness or tradable GDP openness and aggregate equilibrium employment, P = k( ITrade, L ), (18) where k1() > 0, k 2() > 0and ITrade = ROpen, TROpen. We test for the link between real openness and (our proxy of) tradable GDP openness on the one hand and the relative prie of non-tradable goods and the prie level on the other hand empirially. It is interesting to note that our theoretial work does not imply that the prie level is inreasing in openness, as the possible non-monotoniity between the degree of speialization and openness stemming from (12) translates into a non-monotoniity between openness and the prie level. 4 We are very grateful to a referee for pointing this out and also for suggesting an empirial proxy for TROpen. 11

13 3 Estimation Our empirial work is based on three main estimating equations. The first equation relates average labor produtivity (and inome per apita) aross ountries to international trade and institutional quality using openness as well as real openness and tradable GDP openness as alternative summary measures of the intensity with whih ountries trade. The seond estimating equation relates openness as well as real openness and tradable GDP openness to the prie level and the relative prie of non-tradable goods aross ountries. The third equation relates international trade and institutional quality to apital-output ratios, average levels of human apital, and levels of labor effiieny in order to determine the hannels through whih trade and institutional quality affet average labor produtivity. 3.1 International Trade and Produtivity The equation that we use to estimate the effet of international trade, the aggregate sale of prodution, and institutional quality on ountries average labor produtivity (PPP GDP per worker) is PPP GDP log Workfore (19) = a + a ITrade + a logworkfore + a log Area + a IQual + a X + u where ITrade stands for measures of the intensity with whih ountry trades with the rest of the world, Workfore denotes the size of the ountry s work fore, Area refers to the land area of the ountry in square kilometers, IQual stands for the quality of the ountry s institutions, and X denotes a set of geographi ontrol variables. The variation in average labor produtivity not aptured by our empirial analysis is summarized by u, and a0,..., a 5 denote the parameters to be estimated. The hoie between different measures of the intensity with whih ountries trade is ultimately an empirial question. Equation (19) is therefore estimated using three different, already mentioned measures for ITrade: 1. Open, defined as nominal imports plus exports divided by nominal GDP. This is the measure used in existing empirial researh. Beause theory is inonlusive on how Open is supposed to enter the estimating equation, we also try logopen. The main differene between the two speifiations is that the speifiation with logopen assumes that a 1-point inrease in Open has larger effets on average labor produtivity in ountries that start from lower levels of openness. 12

14 2. Beause of the theoretial drawbaks of Open disussed in the previous setion, we onsider imports plus exports in exhange rate US$ divided by GDP in PPP US$ (ROpen) and logropen as alternative measures of ITrade. 3. We also use a measure of openness that is meant to approximate what we earlier referred to as tradable GDP openness (TROpen ). The proxy we use is nominal imports plus exports divided by nominal GDP in manufaturing and agriulture or, equivalently, Open divided by the share of GDP produed in manufaturing and agriulture. This proxy is referred to as PTROpen. Although not ideal, PTROpen does eliminate the bulk of non-tradable goods and should therefore be a useful alternative for determining whether the theoretial drawbaks of Open disussed earlier are empirially relevant. We also try logptropen for the same reasons as logopen. Area is inluded in the estimating equation to failitate omparisons with the work of Frankel and Romer (1999). See Frankel and Romer as well as Frankel and Rose (2002) for theories that imply that average labor produtivity depends on the land area of ountries. (Like Frankel and Romer, we usually find that area is a statistially insignifiant determinant of produtivity however.) IQual is measured using indies of bureaurati quality, law and order, and property-rights protetion developed by Politial Risk Servies. These indies have previously been used by Knak and Keefer (1995) and Hall and Jones (1999) in their empirial investigations of the effet of institutional quality on eonomi growth and the level of produtivity at the ountry level. The geography ontrols ( X ) used in the estimating equation are ountries distane from the equator and ontinent dummies. These variables are inluded to aount for spatially orrelated omitted determinants of produtivity. Our empirial analysis of the role of international trade in former olonies follows Aemoglu, Johnson, and Robinson (2001) and estimates (19) with inome per apita (instead of average labor produtivity) on the left-hand side and an indiator of expropriation risk instead of institutional quality on the right-hand side. We refer to (19) without institutional quality and geography ontrols as the baseline trade speifiation. The parameters in (19) annot be estimated onsistently using ordinary least squares beause ountries trade intensity, workfore, and institutional quality are endogenous and measured with error. Our estimation strategy therefore relies on instrumental variables. The instruments are onstruted following Frankel and Romer (1999) as well as Hall and Jones (1999) and Aemoglu, Johnson, and Robinson (2001). To determine the ausal effet of international trade on average labor produtivity aross ountries, Frankel and Romer (1999) use a two-step approah to onstrut an instrument for their measure of trade intensity (openness). The first step onsists of estimating a gravity equation for bilateral trade shares that uses ountries geographi harateristis and population only as 13

15 explanatory variables (i.e. the estimating equation does not inlude measures of produtivity or inome). The seond step of the approah aggregates bilateral trade shares predited by the gravity equation to obtain a predited value for ountries trade intensity. This value is then used as an instrument for openness. We use the same approah to onstrut instruments for our measures of trade intensity. The gravity equation estimated to obtain geography-predited bilateral trade shares is τij log = α0 + α1log Distij + α2log Pop PPP GDPi + α log Area + α log Pop + α log Area 3 i 4 j 5 j + α ( Ldl + Ldl ) + α Cb + α Cb logdist 6 i j 7 ij 8 ij ij + α Cb log Pop + α Cb log Area 9 ij i 10 ij i + α Cb log Pop + α Cb log Area 11 ij j 12 ij i + α Cb ( Ldl + Ldl ) + v 13 ij i j ij i (20) where τ ij denotes exports of ountry i to ountry j plus exports from j to i ; Dist ij is the distane between the two ountries; Popi, Pop j denote the population of the two ountries; Areai, Area j denote the area of the two ountries; Ldli, Ldl j are dummies indiating whether ountries i, j are landloked; Cb ij is a dummy indiating whether or not the two ountries have a ommon border; and v ij summarizes the variation in bilateral trade shares no aptured by our empirial approah. 5 The ommon border dummy is inluded by itself in the regression as well as interated with other explanatory variables to apture trade between neighboring ountries more aurately. The ordinary least-squares estimates of the oeffiients in (20) an be used to determine the predited value of the bilateral trade share for all ountries for whih there is data on the righthand-side variables (even if we do not have any bilateral trade data for those ountries). Predited bilateral trade shares are then aggregated to obtain the predited value of aggregate imports plus exports relative to PPP GDP for eah ountry TFit i τij exp Predited Value of log using (20). (21) j PPP GDPi The sum inludes all ountries for whih data on the right-hand-side variables in (20) are available. We use both the variable TFit (whih we refer to as the fitted trade intensity or geography-predited trade) and the variable logtfit as instruments when estimating (19). We also try fitted trade intensities based on gravity equations without population and area respetively as instruments in our empirial analysis. 14

16 Additional instruments to estimate the effet of trade and institutional quality on average labor produtivity and inome per apita ome from the work of Hall and Jones (1999) and Aemoglu, Johnson, and Robinson (2001). Hall and Jones estimate the effet of soial infrastruture defined as a weighted average of what we all institutional quality and the Sahs-Warner (1995) poliymeasure of openness averaged over a ertain period of time on produtivity aross ountries. They address the reverse ausality problem by using the fration of the population speaking English at birth, the fration of the population speaking one of the five primary European languages (inluding English) at birth, the distane from the equator, and the Frankel-Romer fitted trade intensity as instruments. Hall and Jones argue, based on historial onsiderations, that the first three variables are orrelated with past European influene and therefore with the transmission of the (growth-enhaning) European institutional framework. They hek the validity of distane from the equator as an instrument by testing the hypothesis that distane from the equator does not affet produtivity diretly one soial infrastruture is aounted for and find that this hypothesis annot be rejeted at onventional signifiane levels. We find that distane from the equator does not affet average labor produtivity in a statistially signifiant way one institutional quality and trade are inluded in the empirial analysis. Aemoglu, Johnson, and Robinson (2001) estimate the effet of expropriation risk between 1985 and 1995 on 1995 inome per apita in a sample of former olonies using settler mortality between the 18 th and 19 th entury as an instrument for expropriation risk. 6 They demonstrate that histori settler mortality explains a onsiderable amount of the variation in average expropriation risk aross former olonies and argue that this orrelation arises beause the implementation of European, growth-enhaning institutions was more likely when onditions for long-term European settlements were favorable. Following their argument, we use settler mortality as one of the instruments when estimating the effet of international trade on 1995 inome per apita for a given level of expropriation risk. Other instruments used to estimate (19) are the geography ontrols inluded as right-hand-side variables, land area, and population. 3.2 International Trade and Pries The relationship between the prie level and real openness as well as aggregate employment is estimated using the following equation log P = b + b log ROpen + b logworkfore + b Z + v, (22) Distane is alulated as the great-irle distane between ountries prinipal ities. 6 Interestingly, their empirial analysis validates the use of distane from the equator as an instrument in the work of Hall and Jones (1999). 15

17 where v summarizes the variation in the log prie level not aptured by our empirial analysis, and b0,..., b 3 denote the parameters to be estimated. Z ontains the usual geographi ontrols as well as a variable ( z ) that aptures ross-ountry differenes in log-produtivity not explained by inreasing returns to speialization or aggregate employment: z ˆ log( YPPP, / L ) a1log ROpen aˆ logworkfore, where aˆ 2 1, a ˆ 2 are estimates of the effet of log ROpen and logworkfore on log-produtivity obtained using (19). This variable is onsidered as a ontrol to aount for ross-ountry produtivity-differenes not explained by inreasing returns affeting the prie level through the Balassa-Samuelson effet. 7 Equation (22) is estimated using instrumental variables, with the geography ontrols inluded among the right-hand-side variables, the fitted trade intensities, the Hall-Jones language variables, and population as instruments. We also estimate (22) with (our proxy of) tradable GDP openness instead of real openness sine our theoretial work predits that tradable GDP openness and real openness an be used interhangeably. Moreover, we estimate a version of (22) with openness instead of real openness on the right-hand side. The link between ountries prie level and their real openness or tradable GDP openness, as well as their workfore, that we test for using (22) arises through the relative prie of non-tradable goods. We therefore estimate the effet of either logropen or logptropen, ombined with logworkfore, on the relative prie of non-tradable goods aross ountries. This is done by estimating equation (22) with the log of the relative prie of non-tradable goods aross ountries (instead of the prie level) on the left-hand side. Although this equation is a more diret test of our hypothesis than (22), it has two potential drawbaks. First, the number of ountries with data on the relative prie of non-tradables is limited. Seond, the lassifiation of goods into tradables and nontradables is debatable. 3.3 International Trade, Capital, and Labor Effiieny We are also interested in whether trade affets average labor produtivity mostly through physial apital, human apital, or labor effiieny one institutional quality is taken into aount. This issue is analyzed following the approah of Hall and Jones (1999), who in turn follow David (1977) and Klenow and Rodriguez-Clare (1997). The starting point of the approah is the onstantreturns-to-sale Cobb-Douglas aggregate prodution funtion Y = K ( AhL ), where Y denotes α 1 α aggregate output, K aggregate apital, L aggregate employment, h average human apital, and 7 The Balassa-Samuelson hypothesis states that ross-ountry differenes in produtivity are positively orrelated with ross-ountry differenes in the prie level beause ross-ountry produtivity differenes in the manufaturing setor are greater than in the servies setor (see Heston, Nuxoll, and Summers (1994) and Rogoff (1996) for empirial work on the Balassa- Samuelson effet). 16

18 A labor effiieny. 8 In this formulation, α and 1 α apture only the effets of prodution fators on output that are internalized by firms; external effets of the prodution fators on output are inluded in labor effiieny. This prodution funtion implies that average labor produtivity an be written as the produt of labor effiieny, the (physial) apital-output ratio raised to the power α/(1 α), and the average level of human apital, Y K = A h. (23) L Y We analyze how international trade and institutional quality affet the three omponents of average labor produtivity on the right-hand side of (23). This is done by using the log of eah omponent as the left-hand-side variable in (22) (instead of average labor produtivity). α 1 α 4 Data and Quality of the Instruments The data on PPP GDP per worker, the number of workers, population, openness, and the prie level are from the Penn World Tables, Mark 5.6 (PWT). 9 Real openness is obtained by multiplying the PWT variable Openness, whih is defined as Open in this paper, with the PWT variable Prie Level GDP, whih is defined as P in this paper. The shares of GDP produed in manufaturing and agriulture neessary to obtain our proxy of tradable GDP openness are taken from the World Bank s World Development Indiators (2001). The different measures for openness (Open, ROpen, and PTROpen) are highly orrelated. For example, the simple orrelation oeffiient between Open and ROpen for the largest possible sample in 1985 is 0.86, and the simple orrelation oeffiient between Open and TROpen is The 10 ountries with the highest value of Open are (in this order): Singapore, Luxembourg, Hong Kong, Bahrain, Belize, St. Luia, Malta, Lesotho, St. Vinent and Grenada, and Belgium. The 10 ountries with the highest value of ROpen are (in this order): Singapore, Bahrain, Luxembourg, Hong Kong, Puerto Rio, Belgium, Bahamas, St. Luia, and Kuwait. The 10 ountries with the highest value of TROpen are (in this order): Singapore, Hong Kong, Luxembourg, Seyhelles, St. Luia, Djibouti, Belgium, Barbados, Bahrain, and Belize. Evidently, there is onsiderable overlap. Among the bottom-10 ountries there is a similar amount of overlap. For example, 6 of the bottom-10 Open ountries are also among the bottom-10 ROpen ountries (exatly the same 8 Our terminology does not follow Hall and Jones, who refer to A as produtivity, beause this ould generate onfusion with what we all average labor produtivity. We do not refer to A as labor-augmenting tehnology beause A will also apture institutional quality and inreasing returns to speialization as well as to aggregate employment in our empirial analysis 9 This is a revised version of Summers and Heston (1991). The data are available online at The number of workers is obtained by dividing the PWT variable Real GDP Per Capita by the PWT variable Real GDP Per Worker and multiplying the result by the PWT variable Population. 17

19 number as in the top-10). There are some ountries whose position in the ranking hanges onsiderably however. For example, the US goes from being the 147 th ountry from the top in the Open ranking to the 111 th ountry from the top in the ROpen ranking. Lesotho, on the other hand goes from 9 th plae in the Open ranking to 90 th plae in the ROpen ranking. The simple orrelation oeffiient between Open and ROpen for the largest possible sample in 1990 is 0.56 and hene onsiderably lower than in 1985 and only 4 of the bottom-10 ROpen (top-10 ROpen) ountries are among the bottom-10 Open (top-10 Open) ountries. (It should be noted at the outset that our instrumental-variables strategy implies that the results of estimating (19) with, for example, Open or ROpen as alternative measures of international trade may differ onsiderably even if these two variables are highly orrelated.) The prie indies for non-tradable and tradable goods aross ountries relative to the US are taken from Heston, Summers, Aten and Nuxoll (1995) and Aten (1997). They define the relative prie of non-tradables (NT) and tradables (T) as where P i = k k pkqk p q, i = T, NT (24) USk k p is the prie of good k in ountry and q the quantity onsumed. These indies are k k available for 64 ountries. The data used to alulate these indies refers to 94 tradable and 42 non-tradable items in 1985 and ome from the International Comparison Projet (ICP) benhmark. 10 We employ four different samples in our empirial work. The first two samples inlude all ountries for whih the relevant data are available for 1985 and We fous on 1985 and 1990 beause these are benhmark years of the PWT. The third sample onsists of the ountry sample used by Mankiw, Romer, and Weil (1992) and Frankel and Romer (1999). The fourth sample is the group of former olonies in Aemoglu, Johnson, and Robinson (2001). In this last ase, we use (their data on) PPP inome per apita in 1995 on the left-hand side of the estimating equation in (19). 11 Moreover, we use 1995 population from the World Development Indiators (2001) instead of workfore on the right-hand side of the estimating equation beause the urrently available version of the PWT ontains data only up to Our measure of institutional quality is reated following Hall and Jones (1999). They onstrut a measure of institutional quality using data from the International Country Risk Guide 10 We are very grateful to a referee for direting us to the benhmark data. The data are available online at It important to note that tradable goods in this definition are goods that while in priniple tradable might not atually be traded (beause of tariff or non-tariff barriers for example). 11 The soure of their data is the World Development Indiators. 18