TRADE AND PRODUCTIVITY * FRANCISCO ALCALÁ (UNIVERSIDAD DE MURCIA) AND ANTONIO CICCONE (UNIVERSITAT POMPEU FABRA) November 2003 (forthoming The Quarterly Journal of Eonomis) Abstrat: We find that international trade has an eonomially signifiant and statistially robust positive effet on produtivity. Our trade measure is imports plus exports relative to purhasing power parity GDP (real openness), whih we argue is preferable on theoretial grounds to the nominal measure onventionally used. We also find a signifiantly positive aggregate sale effet. Our estimates ontrol for proxies of institutional quality as well as geography and take into aount the endogeneity of trade and institutional quality. Our analysis of the hannels through whih trade and sale affet produtivity yields that they work through total fator produtivity. * We thank Tito Cordella, Luis Cubeddu, and Walter Garia-Fontes for help with the data, Jose Garia-Montalvo and Marek Jaroinski for their eonometri expertise, Rita Almeida, Pablo Fleiss, and Israel Sanho for exellent researh assistane, and David Romer for kindly providing the data and programs used in Frankel and Romer [1999]. The paper has benefited from the omments of editors, anonymous referees, and other olleagues. We gratefully aknowledge finanial support from the CREI and CREA researh institutes, the European Fund for Regional Development and the Fundaión Caixa Galiia, the Fundaión Sénea (PB/03/FS/02), and the Spanish Ministry of Siene and Tehnology (SEC2001-0792/2002-01601).
I. INTRODUCTION How large is the effet of international trade on aggregate produtivity? Answering this question requires dealing with possible reverse ausation from produtivity to trade. Ades and Glaeser [1999], Frankel and Romer [1999], and Alesina, Spolaore, and Waziarg [2000] address this issue and find a signifiant ausal effet of trade on produtivity. Empirial work has sine turned to examining whether estimates of the produtivity gains due to trade may atually be apturing the role of institutions and geography. For example, Rodrik [2000], Rodriguez and Rodrik [2001], and Irwin and Tervio [2002] argue that trade is not a signifiant determinant of produtivity when geography ontrols and proxies of institutional quality are inluded in the empirial analysis. The measure of international trade used in almost all empirial work on the effet of trade on produtivity is nominal imports plus exports relative to nominal GDP, usually referred to as openness. We argue that there are sound theoretial reasons why this measure may result in a misleading piture of the produtivity gains due to trade. To see why suppose that trade inreases produtivity but that produtivity gains, in aordane with the Balassa-Samuelson hypothesis, are greater in manufaturing than in the non-tradable servies setor. Will ountries that are more produtive due to trade have higher openness? Not neessarily, beause the relatively greater produtivity gains in manufaturing lead to a rise in the relative prie of servies, whih may result in a derease in openness. We show this formally in a trade model with gains from speialization. This theoretial drawbak of the openness trade measure motivates our alternative, whih we refer to as real openness. Real openness is defined as imports plus exports in exhange rate US$ relative to GDP in purhasing power parity US$. Using real openness instead of openness as a measure of trade eliminates distortions due to ross-ountry differenes in the relative prie of non-tradable goods.
When measured using real openness, we find that trade is a signifiant and robust determinant of aggregate produtivity. For example, the elastiity of produtivity with respet to real openness is around 1.2 with a standard error around 0.35 when we ontrol for ountry size, geography, and proxies of institutional quality. This estimate implies that an inrease in real openness taking a ountry from the 30 th perentile to the median value raises produtivity by 80 perent, an inrease from the 20 th perentile to the median value raises produtivity by 160 perent, and an inrease from the 20 th perentile to the 80 th perentile raises produtivity by a fator of six. Moreover, we find signifiantly positive aggregate sale effets, onfirming the results of Frankel and Romer [1999] and Alesina, Spolaore, and Waziarg [2000]. The elastiity of produtivity with respet to population size is around 0.3 with a standard error around 0.1 when real openness, geography, and institutional quality are ontrolled for. We also examine the hannels through whih international trade, sale, and our proxies of institutional quality affet aggregate produtivity. Our findings indiate that trade and population size are signifiant determinants of total fator produtivity 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 total fator produtivity. Our empirial approah aounts for the endogeneity of trade and institutional quality by using instruments. The instrument for trade is onstruted following Frankel and Romer [1999] and relies on trade being partly determined by harateristis of ountries that are unrelated to produtivity. The instruments for institutional quality onsidered ome from Hall and Jones [1999] as well as Aemoglu, Johnson, and Robinson [2001] and are based on the link between historial European influene and the transmission of the European institutional framework. Instrumental-variables estimation of our produtivity equation ombining trade with institutional quality raises subtle issues regarding instrument weakness in models with multiple endogenous explanatory variables [Stok, Wright, and Yogo 2002]. We address these issues by using weakinstrument diagnosti tools, by implementing those instrumental-variables estimators that are 2
most robust to instrument weakness, and by testing hypotheses using approahes that are valid asymptotially regardless of the weakness of instruments. The remainder of this paper is strutured in the following way. Setion II explains the theoretial drawbaks of openness as a measure of trade. Setion III ontains the produtivity equation that we estimate. Setion IV disusses the data. Setion V presents the results on the effet of international trade and sale on aggregate produtivity. It also ontains our findings on the effet of trade, sale, and institutional quality on the apital-output ratio, the average level of human apital, and total fator produtivity. Setion VI onludes. II. SPECIALIZATION, TRADE, AND PRODUCTIVITY The drawbaks of openness as a measure of trade an be illustrated using a small open eonomies model with gains from speialization. The key of our argument is that speialization raises aggregate produtivity but that produtivity gains are greater in the tradable goods setor than the non-tradable goods setor. Speialization therefore results in an inrease in the prie of nontradable relative to tradable goods (the trade-related Balassa-Samuelson effet), whih may result in a derease in openness. Our model assumes that all produtivity gains due to speialization our in the tradable goods setor and that the demand for non-tradable goods is ompletely prie inelasti. We show later that these assumptions an be relaxed without affeting our main argument. Suppose that the set of ommodities eah ountry an produe is given by the unit interval. Commodities indexed between zero and t, t < 1 are tradable goods, while the remaining fration 1 t of ommodities are non-tradable goods. The measure of tradable goods produed in ountry is denoted by d. As the measure of tradable goods produed domestially dereases, the ountry beomes more speialized. Firms in tradable goods setors i t are assumed to produe output y using labor l aording to the onstant-returns-to-sale prodution funtion y = A l, with ountry-speifi fator effiieny A taken as given by firms. We assume that fator effiieny in tradable goods prodution is given by 3
(1) A B g( d, l ), where B is an exogenous parameter, l is aggregate employment, and g () allows us to apture gains from speialization assuming g/ d < 0 and inreasing returns to aggregate employment assuming g/ l > 0. We suppose that gains from speialization are limited to tradable goods and that there are no inreasing returns to aggregate employment in the non-tradable goods setor. Firms in nontradable goods setors are assumed to produe output s aording to the onstant-returns-to-sale prodution funtion s= B l. Goods and labor markets are taken to be perfetly ompetitive. We also suppose that all tradable goods sell at the same prie in international markets and take tradable goods as the numeraire. Symmetry in prodution implies that all non-tradable goods produed in the same ountry sell at the same prie in equilibrium. Non-tradable goods pries vary endogenously aross ountries however. Households supply an aggregate amount of labor L inelastially. We assume that preferenes are suh that households want to onsume the same quantity of eah tradable and non-tradable good irrespetive of the prie of non-tradable goods. Wages in tradable and non-tradable goods setors are equalized in labor market equilibrium. The equilibrium prie of non-tradable goods in ountry, ρ, therefore reflets fator effiieny in tradable goods setors relative to non-tradable goods setors, (2) ρ = gd (, L ), where we use that aggregate employment is equal to aggregate labor supply in equilibrium. Nontradable goods are therefore more expensive in ountries where the prodution of tradable goods is more effiient relative to the prodution of non-tradable goods. This yields a link between the degree of speialization and the prie of non-tradable goods that is key to our argument. Balaned trade implies that imports ( t d) x, where t d is the range of imported tradable goods and x denotes onsumption of eah good, are equal to exports d( y x) denotes prodution of eah tradable good. Hene, GDP is equal to aggregate onsumption, where y 4
(3) GDP= dy + ρ (1 tx ) = tx + ρ (1 tx ). Purhasing power parity (PPP) GDP differs from GDP in that the prodution of eah good is valued using pries in a benhmark ountry. Hene, denoting the prie of non-tradable goods in the benhmark ountry by ρ, PPP GDP = tx + ρ(1 t) x. To see how PPP GDP depends on the degree of speialization, we use that balaned trade and labor market learing imply that the share of labor alloated to non-tradable goods prodution is (1 t) ρ /( t+ (1 t) ρ ). Combined with (2) and the prodution funtions in tradable and non-tradable goods setors, this yields PPP GDP t+ ρ(1 t) (4) = B 1. L gd (, L) t+ (1 t) PPP average labor produtivity is therefore inreasing in the degree of speialization and in aggregate employment. In equilibrium, openness (imports plus exports relative to GDP) is given by (5) Open Imports t d = 2 = 2. GDP t+ (1 t) ρ Hene, an inrease in the degree of speialization affets openness in two opposite ways. Holding the prie of non-tradable goods onstant, a higher degree of speialization raises openness as more speialization neessarily implies a larger volume of imports. But, aording to (2), a higher degree of speialization also raises the prie of non-tradable goods, whih lowers openness. As a result, the relationship between the degree of speialization and openness may be nonmonotoni. 1 The non-monotoniity between the degree of speialization and openness implies that higher openness is not neessarily assoiated with higher PPP average labor produtivity. Real openness differs from openness in that GDP is measured in PPP, (6) ROpen Imports t d = 2 = 2. PPP GDP t+ (1 t) ρ 1. In the Appendix we disuss a model due to Rodrik, Subramanian, and Trebbi [2002] where openness also fails to be inreasing in the fundamental variable driving trade beause of systemati differenes in non-tradable goods pries. 5
As the prie of non-tradable goods used to value prodution is the same aross ountries, real openness is a linear and inreasing funtion of the degree of speialization. As a result, PPP average labor produtivity in (4) an be written as an inreasing funtion of real openness. 2 Our model supposes that all gains from speialization our in the tradable goods setor. This assumption is not neessary for speialization to inrease the prie of non-tradable goods. The prie of non-tradable goods inreases even if speialization in the tradable goods setor also inreases produtivity in the non-tradable goods setor, as long as the effet is greater in the tradable than the non-tradable goods setor. In Alalá and Cione [2001] we disuss the link between (real) openness and aggregate produtivity when onsumers substitute among onsumption goods and show that the relationship between real openness and produtivity is monotonially inreasing whatever the elastiity of substitution among tradable and non-tradable goods. We also show that the nonmonotoni relationship between openness and aggregate produtivity may arise as long as the demand for non-tradable goods is prie inelasti. To understand this ondition intuitively it is useful to write openness in (5) as (7) Open Imports Consumption of Tradables =. 2 Consumption of Tradables GDP An inrease in the degree of speialization implies that the share of imported goods in total tradable goods onsumption inreases. Hene, the first term on the right-hand side of (7) inreases with speialization. Whether the seond term inreases or dereases with speialization depends on the elastiity of substitution between tradable and non-tradable goods. If the demand for non-tradable goods is prie elasti, the inrease in the prie of non-tradable goods aused by higher speialization translates into households spending a smaller share of their inome on nontradable goods and a greater share on tradable goods. As a result, the seond term on the right- 2. The monotoni relationship between speialization and real openness ombined with the effet of speialization on the prie of non-tradable goods in (2) implies that the prie level should be inreasing in real openness (trade-related Balassa-Samuelson effet). We present empirial evidene for this relationship in the Appendix. 6
hand side of (7) inreases with speialization. Thus, speialization unambiguously inreases openness when the demand for non-tradable goods is prie elasti. When non-tradable goods demand is prie inelasti however, the seond term on the right-hand side of (7) dereases with speialization and the effet of speialization on openness is ambiguous. While there is no evidene on the prie-elastiity for non-tradable goods in general, the demand for servies, whih onstitutes the largest part of non-tradable goods demand, has been found to be very prie inelasti (see Falvey and Gemmell [1996] for example). Our analysis of the link between (real) openness and aggregate produtivity has also been simplified by the assumption that the fundamental variable determining trade, the degree of speialization of a ountry, is given. In the Appendix, we extend our theoretial framework by endogenizing speialization and analyzing how the effiient degree of speialization depends on an exogenous variable like transport osts. Our extended theoretial framework yields an inverse relationship between transport osts and speialization. This is intuitive beause the effiient degree of speialization equalizes the marginal benefit of speialization, inreased produtive effiieny, and the marginal ost of speialization, inreased total transport osts, and an exogenous inrease in transport osts results in a higher marginal ost of speialization. III. ESTIMATION The equation we use to estimate the effet of international trade and sale of prodution on average labor produtivity aross ountries is the following straightforward extension of the speifiation in Frankel and Romer [1999]: PPP GDP = + + + + + + (8) log a0 a1itrade a2log DSale a3log Area a4iqual a5x u Workfore where ITrade stands for measures of international trade; DSale aptures the domesti sale of prodution using either workfore or population; Area refers to the land area in square kilometers; IQual is a proxy of institutional quality; and X denotes a set of geographi ontrol variables (FR inlude the first three right-hand-side variables only). The main geography ontrols onsidered are distane from the equator and ontinent dummies (Europe, Afria, Ameria, Asia; the omitted 7
ontinent is aptured by the interept). The variation in produtivity not aptured by our empirial analysis is summarized by u. Our preferred measure of trade is log real openness, with real openness defined as imports plus exports in exhange rate US$ divided by GDP in PPP US$. 3 For omparisons with previous empirial work, we also measure trade using openness, defined as nominal imports plus exports divided by nominal GDP, and log openness. The produtivity equation annot be estimated onsistently using ordinary least squares beause trade and institutional quality are endogenous (other variables in the produtivity equation are assumed to be exogenous). We therefore rely on two-stage least-squares estimation. The instrument for trade is onstruted following Frankel and Romer [1999] and the instruments for institutional quality onsidered are taken from Hall and Jones [1999] as well as Aemoglu, Johnson, and Robinson [2001]. To determine the ausal effet of international trade on produtivity aross ountries, Frankel and Romer [1999] use a two-step approah to onstrut an instrument for their measure of trade. The first step onsists of estimating a gravity equation for bilateral trade shares that uses ountries geographi harateristis and size only as 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 geography-based instrument for trade (the approah is explained in some more detail in the Appendix). We use exatly the same approah, exept that we employ more bilateral trade data than FR. The instruments used by Hall and Jones [1999] to estimate the effet of institutional quality on produtivity are: the population share speaking English sine birth; the population share speaking one of the five primary European languages (inluding English) sine birth; the distane from the equator; and the Frankel and Romer [1999] geography-based trade variable. HJ argue, based on historial onsiderations, that the first three variables are orrelated with past European influene 3. Our hoie of log real openness instead of real openness is motivated by eonometri speifiation tests as our theoretial framework does not determine the funtional form of the relationship between real openness and produtivity. The speifiation tests are doumented in Alalá and Cione [2001]. 8
and therefore with the transmission of the (growth-enhaning) European institutional framework. We use the population share speaking one of the five primary European languages sine birth and distane from the equator as instruments, but drop the fration of the population speaking English sine birth, as it does not help in prediting the endogenous variables in our speifiations. Aemoglu, Johnson, and Robinson [2001] use European settler mortality during the 18 th and 19 th entury as an instrument for institutional quality in a sample of former olonies. They demonstrate that histori settler mortality explains a onsiderable amount of the variation in their proxy of institutional quality and argue that this orrelation arises beause the implementation of European institutions was more likely where onditions for long-term European settlements were more favorable. We are also interested in whether trade affets average labor produtivity mostly through physial apital, human apital, or fator effiieny. Our analysis follows the approah of Hall and Jones [1999] and Klenow and Rodriguez-Clare [1997]. Their starting point is the firm-level onstant-returns prodution funtion α 1 α y = k ( E hl), 0 α 1, where y denotes output, k apital, h average human apital, and l employment. E aptures aggregate fator effiieny, whih the firm takes as given. (Fator effiieny is related to total fator produtivity by TFP 1 E α =.) Aggregate externalities, if any, are aptured by fator effiieny. Combining this prodution funtion with perfetly ompetitive produt and fator markets implies that aggregate average labor produtivity Y / L an be written as the produt of fator effiieny, the aggregate (physial) apital-output ratio K/ Y raised to the power α /(1 α), and the aggregate average level of human apital H, α α (9) / ( / ) 1 Y L = E K Y H. This deomposition applied to our theoretial framework (without physial or human apital) yields that Y/ L= E with fator effiieny given by the right-hand side of (4). Extending our theoretial framework by assuming that physial and human apital enter tradable and nontradable goods prodution in the same way, and maintaining onstant returns to sale at the firm 9
level, would yield that aggregate average labor produtivity ould be deomposed exatly as in (9) with fator effiieny ontinuing to be equal to the right-hand side of (4). To determine the hannels through whih trade, sale, and institutional quality affet aggregate produtivity, we estimate their effet on eah of the three omponents of average labor produtivity on the right-hand side of (9). This is done by using the log of eah omponent as the left-hand-side variable in (8). IV. DATA Our empirial work is based on data for 1985. From the Penn World Tables, Mark 5.6, we obtain data on GDP per worker in PPP US$, GDP per apita in PPP US$, population, openness, and the prie level (GDP in exhange rate US$ relative to GDP in PPP US$). Real openness is obtained by multiplying openness by the prie level. 4 Workfore is obtained by dividing PPP GDP per apita by PPP GDP per worker and multiplying the result by population. Our main proxy of institutional quality is onstruted using indiators from Kaufmann, Kraay, and Zoldo-Lobatón [1999] for the period 1997-1998. KKZ use a large amount of data to develop six different indies: government effetiveness; rule of law; graft; voie and aountability; politial stability and violene; and regulatory burden (see the Appendix for details). The six indiators are measured in units ranging from -2.5 to 2.5, with higher values orresponding to better governane outomes. We average the indiators that are losest to the government anti-diversion poliy (GADP) index used by Hall and Jones [1999] (government effetiveness, rule of law, and graft) to obtain an index that mimis the HJ indiator in breadth. 5 This index is referred to as IQual. We also onsider the HJ GADP index and the KKZ rule of law index as alternative proxies of institutional quality. 4. The fat that real openness an be obtained by multiplying openness and the prie level may give the impression that real openness depends on relative non-tradable goods pries, when this operation atually undoes the dependene of openness on relative non-tradable goods pries. 5. GADP ombines indiators of bureaurati quality, law and order, orruption, risk of expropriation, and likelihood of government repudiation of ontrats. 10
The bilateral trade data to obtain the geography-based trade instrument is taken from the Diretion of Trade Statistis published by the International Monetary Fund. These statistis ontain 9426 non-zero observations on bilateral trade for the ountries used to estimate the produtivity equation, whih is approximately 2.5 times the data used by Frankel and Romer [1999]. As our geography-based trade variable relies on more bilateral trade data than the FR variable, it is more representative of the ountries used to estimate the produtivity equation. Distane from the equator is taken from Hall and Jones [1999] and is measured as the absolute value of the latitude of the enter of ountries most populated region. Table I ontains desriptive statistis and a orrelation matrix for seleted variables, inluding (log) openness, (log) real openness, log average labor produtivity, log population, and IQual. It an be seen that real openness has a lower mean than openness. The lower mean is due to the average prie level in our sample being 0.54. Moreover, the orrelation between openness and real openness is high (0.86). Real openness orrelates better with log average labor produtivity than openness however (a orrelation oeffiient of 0.26 in the ase of openness and 0.47 in the ase of real openness, and differenes are even greater when the two trade measures are in logs). 6 These differenes an be explained by the Balassa-Samuelson effet and are onsistent with our theoretial framework. Table II looks at the produtivity of ountries that move at least 25 plaes up or down when using the real openness ranking instead of the openness ranking. It an be seen that ountries moving up are on average about 100 perent more produtive than the average ountry in the sample, while ountries moving down are about 60 perent less produtive than the average ountry in the sample. This implies that ountries moving up more than 25 plaes are almost five times as produtive as ountries moving down more than 25 plaes. The positive relationship between produtivity and the number of plaes ountries move up when using the real openness ranking instead of the openness ranking (using negative numbers for ountries that move down) is onfirmed by the orrelation oeffiient, whih is 0.55. 6. We list the ten ountries with the highest and lowest (real) openness in the Appendix. 11
The three omponents on the right-hand side of (9) are alulated following Hall and Jones [1999]. Average levels of human apital at the ountry level are alulated by ombining data on average shooling and Minerian estimates of the individual return to shooling. The formula used by HJ to alulate the average human apital in ountry is H = exp( φ( S)), where S is average shooling and φ () is a pieewise linear funtion apturing estimated Minerian returns (φ is defined assuming yearly rates of return of 13.4 perent for the first four years, 10.1 perent for years four through eight, and 6.8 perent for eah additional year). We follow exatly the same approah but employ updated average shooling data [Barro and Lee 2000]. Aggregate apital is obtained by applying the perpetual inventory method used by HJ to investment data in the PWT and the physial apital inome share α is set to 1/3. Aggregate effiieny E is alulated by ombining H and /(1 ) K Y with data on average labor produtivity and (9). ( / ) α α The relevant 1985 data are available for 102 ountries. V. RESULTS A. Instrument Quality Table III ontains first-stage regression results for log real openness (logropen) and for our main proxy of institutional quality (IQual). The two olumns with log real openness as a dependent variable allow us to ompare the performane of our geography-based trade instrument (TFitAC) in prediting real openness to the performane of the original Frankel and Romer [1999] instrument (TFitFR). As mentioned earlier, the two instruments only differ in that ours uses more bilateral trade data. The sample used onsists of the 138 ountries where data for estimating the produtivity equation are available. In olumn (1) we show that our geography-based trade instrument is a highly signifiant determinant of log real openness, even after ontrolling for population, area, ontinent dummies, distane from the equator, and the population share speaking one of the five primary European languages sine birth (EuroLang). In partiular, the F-statisti of the hypothesis that our geography-based trade instrument an be exluded from the regression, i.e. that the oeffiient on it is zero, equals 11.66. Hene, the F-statisti of the exlusion hypothesis exeeds the rule of 12
thumb threshold of ten reommended by Staiger and Stok [1997] to avoid weak instrument onerns. Using workfore instead of population to measure sale yields an exlusion hypothesis F-statisti for our geography-based trade instrument of 9.16. Column (2) ontains the results of estimating the first-stage regression for log real openness using the FR geography-based trade instrument. The speifiation is idential to the one in the previous olumn to failitate omparisons. It an be seen that the FR instrument is signifiant at the 10-perent level, but that the exlusion hypothesis F-statisti (3.06) is onsiderably lower than the one obtained using our instrument (and muh below the Staiger and Stok rule of thumb). The exlusion hypothesis F-statisti for geography-based trade drops further when population is replaed by workfore. Overall, the first-stage regression results for log real openness indiate that using more bilateral trade data than FR to onstrut the geography-based trade variable has produed a onsiderably better instrument. In olumn (3) we present the results of the first-stage regression for our main proxy of institutional quality. It an be seen that both the European languages variable and distane from the equator are highly signifiant, even after ontrolling for population, area, ontinent dummies, and geography-based trade. The F-statisti of the hypothesis that these two variables an be exluded from the first-stage regression is 27.35 (not in the table). The Staiger and Stok rule of thumb has been suggested in the ontext of models with one endogenous variable. In models with two or more endogenous variables, instruments an be weak although they are very signifiant in eah first-stage regression. Intuitively, this is beause endogenous explanatory variables predited by the instruments may be lose to ollinear, whih makes it diffiult to separate the effets of these variables. Stok and Yogo [2003] provide a framework that allows testing the hypothesis of weak instruments in models with more than one endogenous variable. The hypothesis tested is that the quality of the instruments is below one of four levels. 7 For the produtivity equation with all geography ontrols estimated using our trade 7. Stok and Yogo work with two definitions of weak instruments. The one that an be implemented for exatly identified models and for models with one degree of overidentifiation is based on the maximal size of 5-perent Wald tests of all endogenous variables. SY provide 5-perent ritial values to test the hypotheses that the maximal 13
instrument, the SY test rejets the hypothesis that the quality of the instruments is below the highest level at the 5-perent signifiane level. Therefore, weak instruments do not appear to be a onern. When we use the FR trade instrument, however, we annot rejet the hypothesis that the quality of the instruments is below the lowest level at the 5-perent signifiane level. Hene, there is strong evidene for instrument weakness when using the FR geography-based trade instrument. We are also interested in the quality of the instruments when the analysis is restrited to the 80 former olonies in our sample beause this subsample permits using the histori European settler mortality instrument of Aemoglu, Johnson, and Robinson [2001] for institutional quality instead of the Hall and Jones [1999] instruments. The first-stage regression for log real openness now yields that the effet of our log geography-based trade instrument is 0.53 with a standard error of 0.24, ontrolling for log population, log area, ontinent dummies, distane from the equator, and log histori European settler mortality (the orresponding result for the full sample is 0.54 with a standard error of 0.16, see olumn (1) of Table III). This ompares very favorably with the performane of the Frankel and Romer [1999] geography-based trade variable, whih turns out to be highly insignifiant in the same regression (the FR instrument is atually a highly insignifiant determinant of real openness even if we ontrol for population and settler mortality only). 8 Still, the F-statisti of the hypothesis that our geography-based trade variable an be exluded from the first-stage regression is now 5.01 and therefore onsiderably below the Staiger and Stok rule of thumb of ten. Moreover, the Stok and Yogo [2003] test never rejets the hypothesis that the quality of instruments is below the lowest level at the 5-perent signifiane level. Beause of the strong evidene for instrument weakness we onlude that the former size of suh Wald tests exeeds 10 perent (rejetion implies that instrument quality is not below the highest level ), 15 perent (rejetion implies that instrument quality is not below the seond-highest level ), 20 perent, or 25 perent (if this hypothesis annot be rejeted, instruments quality is below the lowest level ). The programs to implement the tests used are available upon request. 8. Regressing log real openness on the log FR geography-based trade instrument, log population, and log histori settler mortality using least squares yields a oeffiient of 0.13 with a standard error of 0.18 on the FR instrument. 14
olonies sample annot be relied upon for joint estimation of the effet of trade, sale, and institutions on produtivity. B. Trade and Produtivity Table IV ompares the effet of trade on produtivity when using the onventional openness trade measure to the effet when using the real openness trade measure. The dependent variable is log GDP per worker in PPP US$. The method of estimation is two-stage least squares (TSLS). In olumn (1) we hek whether openness (Open) is a signifiant determinant of produtivity when institutional quality and geography are taken into aount. This is done by estimating the same speifiation as Frankel and Romer [1999], exept that we add our main proxy of institutional quality and signifiant ontinent dummies as determinants of produtivity (following FR we measure sale using workfore). 9 The instruments used are the FR geography-based trade variable, the population share speaking one of the five primary European languages sine birth, distane from the equator, and the exogenous variables inluded in the produtivity equation. 10 The results indiate that openness and sale are insignifiant determinants of produtivity in this ase, while the proxy of institutional quality is highly signifiant. This mirrors findings in Rodrik [2000], Alalá and Cione [2001], and Rodrik, Subramanian, and Trebbi [2002]. Column (2) explores how results hange when we use our geography-based trade instrument instead of the FR instrument. The speifiation is exatly the same as in the previous olumn in all other respets. It an be seen that our proxy of institutional quality remains highly signifiant 9. The proedure we use to selet the geography ontrols in the produtivity equation is to start out with all geography ontrols and eliminate the most insignifiant ones as regressors as well as instruments sequentially until eah remaining geography ontrol is signifiant at the 10-perent level. The exeption to this rule is distane from the equator, whih is maintained as an instrument even when we eliminate it from the produtivity equation. We then make sure that the speifiation is robust in the sense that the exluded geography ontrols taken one by one are not signifiant at the 10-perent level or more signifiant than the inluded geography ontrols when they are put bak into the produtivity equation. 10. Frankel and Rose [2002] also analyze the effet of openness and institutional quality on produtivity but treat institutional quality as an exogenous variable. 15
and sale ontinues to be highly insignifiant. Openness is signifiant at the 10-perent level but insignifiant at the 5-perent level. The signifiane level of the trade variable falls when we use log openness to measure trade, or GADP or rule of law as alternative proxies of institutional quality [Alalá and Cione 2001]. In olumn (3) we estimate the effet of trade on produtivity using the log real openness (logropen) trade measure. We ontinue to ontrol for log workfore, log area, our main proxy of institutional quality, and signifiant ontinent dummies. The instruments used are the FR geography-based trade variable, the European languages variable, distane from the equator, and the exogenous variables inluded in the produtivity equation. The main news is that the effet of trade is now signifiant at the 5-perent level. In olumn (4) we hek how the results using the real openness trade measure hange when we employ our geography-based trade instrument instead of the FR instrument. The speifiation is the same as in the previous olumn in all other regards. The real openness trade measure is now signifiant at the 1-perent level. This remains true when we proxy institutional quality using GADP or rule of law. Summarizing, trade is a highly signifiant determinant of produtivity when we use the log real openness measure, but insignifiant at the 5-perent level when we use the openness or the log openness measures of trade. 11 Table V analyzes the effet of real openness on average labor produtivity in some more detail. Beause we are onerned about workfore measuring sale with error, we now follow Alesina, Spolaore, and Waziarg [2000] in using population instead. Moreover, in Panel A, we inlude all geography ontrols in the empirial analysis. Panel B only inludes signifiant geography ontrols. The method of estimation ontinues to be TSLS. The instruments used are our log geography-based trade variable, the European languages variable, distane from the equator, and the exogenous variables inluded in the produtivity equation. 11. Dollar and Kraay [2003a] use deadal growth regressions to show that inreases in real openness over time raise aggregate produtivity growth. They also estimate the effet of real openness, sale, and institutional quality on produtivity levels but show that results annot be relied upon beause their instruments are very weak (see Dollar and Kraay [2003b] for a detailed analysis). 16
In olumn (1) it an be seen that trade is a signifiant determinant of produtivity at the 1- perent level even when all geography ontrols are inluded in the regression. The elastiity of produtivity with respet to real openness is 1.23. This implies that an inrease in real openness taking a ountry from the 20 th perentile to the median value raises produtivity by 160 perent and an inrease from the 20 th perentile to the 80 th perentile raises produtivity by a fator of six. The elastiity of produtivity with respet to population is 0.27 and signifiant at the 5- perent level. The effet of trade and sale on produtivity remains basially unhanged when we inlude signifiant geography ontrols only. The main news is that our proxy of institutional quality is signifiant at the 1-perent level. Column (2) eliminates the three ountries with the highest level of real openness (Hong- Kong, Luxembourg, and Singapore) to see whether our findings are robust, following Rodrik [2000]. The effet of trade and sale on produtivity hanges very little ompared to the previous olumn. When we inlude signifiant geography ontrols only, institutional quality beomes signifiant at the 1-perent level. In olumn (3) we follow Mankiw, Romer, and Weil [1992] in eliminating all ountries that are major oil produers (these ountries are listed in the Appendix). Again, results hange little relative to the previous olumn, exept that sale is now signifiant at the 1-perent level when we inlude all geography ontrols. Column (4) adds three geography ontrols (East Asia, Latin Ameria, and Sub-Saharan Afria) to the empirial analysis. The elastiity of produtivity with respet to real openness ontinues to be signifiant at the 1-perent level and is now equal to 1. The elastiity of produtivity with respet to population is 0.24 and signifiant at the 5-perent level. Our proxy of institutional quality ontinues to be highly signifiant when we inlude signifiant geography ontrols only. Figure I heks whether outliers drive the effet of trade on average labor produtivity by plotting real openness predited by the instruments against average labor produtivity not explained by variables other than real openness. It an be seen that there seem to be no obvious outliers. All speifiations in Panel B of Table V maintain distane from the equator as an instrument, following Hall and Jones [1999]. The implied overidentifying restrition annot be rejeted for 17
any of the speifiations (the P-values are given at the bottom of the table). In overidentified models, the limited-information maximum-likelihood (LIML) estimator is preferable to TSLS when instruments are weak [Stok, Wright, and Yogo 2002]. When we implement the LIML estimator, we find almost idential oeffiients and standard errors than using TSLS (not in the table). It is also noteworthy that the Stok and Yogo [2003] weak-instrument test for LIML estimation rejets the hypothesis that the quality of instruments is below the highest level at the 5-perent signifiane level. Hene, there is no evidene that LIML estimates may be distorted beause of weak instruments. The effet of real openness and population on produtivity is robust to using GADP or rule of law as alternative proxies of institutional quality. For example, for the speifiations in Table V with all geography ontrols, we find that the elastiity of produtivity with respet to real openness is always greater than 1.1 and signifiant at the 1-perent level whatever the proxy for institutional quality used. The elastiity with respet to population is always greater than 0.26 and signifiant at the 5-perent level. We also analyze the statistial signifiane of real openness as a determinant of produtivity using the Moreira [2003] test statisti, whih is fully robust to instrument weakness asymptotially. Figure II summarizes our results by plotting the TSLS estimates of the effet of real openness and institutional quality on produtivity and the assoiated 95-perent onfidene ellipsoids (the boundary of the loud of rosses). The ellipsoids ontain all ombinations that are not signifiantly different from the TSLS estimates at the 5-perent level. The three graphs orrespond to the speifiations in Table V with all geography ontrols, with the exeption of the speifiation eliminating Hong-Kong, Luxembourg, and Singapore (whih would be indistinguishable from the benhmark). It an be seen that the 95-perent onfidene ellipsoids only ontain points where the effet of real openness on produtivity is stritly positive. Moreira [2003] and Startz, Nelson, and Zivot [2001] also provide fully robust test statistis for the signifiane of individual endogenous variables. These statistis yield that the hypothesis that trade is not a signifiant determinant of produtivity an be rejeted at the 2-perent level for all speifiations in Table V. 18
Our result of a signifiant and robust effet of real openness on produtivity stands in ontrast with Rodrik, Subramanian, and Trebbi s [2002] finding that institutional quality is signifiant and real openness insignifiant when both are inluded in the produtivity equation. 12 RST s empirial analysis of the effet of real openness and institutional quality on produtivity is subjet to two major limitations when ompared to our approah. First, RST do not ontrol for population or other measures of ountry size (the reasons why ountry size should be ontrolled for when estimating the effet of trade on produtivity are detailed in Frankel and Romer [1999] and Alesina, Spolaore, and Waziarg [2000]). Moreover, RST employ instruments that are very weak in their samples one ountry size is taken into aount. Their speifiation and instruments are therefore not useful for disentangling the effets of trade and institutional quality on produtivity. For example, the preferred speifiation of RST ombines the former olonies sample and the European settler mortality instrument with the FR trade instrument. This is the ombination we have shown earlier to result in the trade instrument not prediting real openness at all. 13 Our finding that population and real openness are signifiant determinants of produtivity even when institutional quality is aounted for relies on instruments that are not weak. C. Trade and Total Fator Produtivity Table VI summarizes our analysis of the hannels through whih trade affets average labor produtivity. Column (1) regresses the log of fator effiieny on log real openness, log population, log area, the IQual proxy of institutional quality, and signifiant geography ontrols for the 102 ountries where data are available. The method of estimation is TSLS and the instruments are our geography-based trade variable, the European languages variable, distane 12. Their empirial work fouses on showing that trade is not a robust determinant of produtivity when measured using openness. But in their robustness heks they also follow Alalá and Cione [2001] and Dollar and Kraay [2003a] in onsidering the real openness trade measure. 13. Rodrik, Subramanian, and Trebbi also estimate the effet of real openness and institutional quality on produtivity by ombining the Dollar and Kraay [2003a] geography-based trade instrument with the European settler mortality instrument or the European language instruments. Dollar and Kraay [2003b] show that both ombinations result in very weak instruments. 19
from the equator, and the exogenous variables inluded in the estimating equation. It an be seen that both real openness and population are signifiant determinants of fator effiieny at the 5- perent level while our proxy of institutional quality is highly insignifiant. (As fator effiieny and total fator produtivity are related by TFP 1 E α =, the marginal effets of trade and sale on log total fator produtivity an be obtained by multiplying the oeffiients in the table by 1 α = 2/3.) Columns (2) and (3) repeat the analysis using the log of the physial apital-output ratio raised to the power 0.5 and the average level of human apital respetively as left-hand-side variables. Now real openness and population are insignifiant and institutional quality is signifiant. Hene, our results suggest that trade and sale raise average labor produtivity through total fator produtivity while institutional quality works through apital aumulation. VI. SUMMARY Our analysis of the effet of international trade on aggregate produtivity aross ountries emphasizes real openness (imports plus exports in exhange rate US$ relative to GDP in purhasing power parity US$) as a measure of trade. We argue that real openness is a better measure of trade than openness beause the openness measure is distorted by ross-ountry differenes in the prie of non-tradable relative to tradable goods. The distortions arise beause openness is dereasing in the relative prie of non-tradable goods, and non-tradable goods are relatively more expensive in ountries where prodution is more effiient (the Balassa-Samuelson effet). Cross-ountry differenes in the relative prie of non-tradable goods do not affet real openness beause the prodution of non-tradable goods in different ountries is valued at the same pries. Using the real openness trade measure, we find that the ausal effet of trade on produtivity aross ountries is statistially and eonomially signifiant as well as robust. We also find that produtivity is affeted in an eonomially and statistially signifiant way by the size of ountries one international trade is taken into aount. Regarding the hannels through whih international trade and sale affet average labor produtivity, our findings indiate that they work through total fator produtivity. 20
One of the important issues that remain to be investigated is to what extent trade poliy is effetive in raising produtivity levels. This requires extending the empirial analysis by allowing trade to be determined by trade poliy as well as geography and finding valid instruments for endogenous trade poliy. 21
APPENDIX 1: DATA Obtaining the geography-based trade instrument The gravity equation estimated to obtain the geography-based bilateral trade share of ountry i with ountry j is τij log = α + α log Dist + α log DSale + α log Area + α log DSale + α log Area PPP GDPi 0 1 ij 2 i 3 i 4 j 5 j + α ( Ldl + Ldl ) + α Cb + α Cb logdist + α Cb logdsale + α Cb logarea 6 i j 7 ij 8 ij ij 9 ij i 10 ij i + α Cb log DSale + α Cb log Area + α Cb ( Ldl + Ldl ) + v 11 ij j 12 ij i 13 ij i j ij 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 (great-irle distane between ountries prinipal ities); Ldl, Ldl are dummies indiating whether ountries i, j are landloked; i j 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 not aptured by our empirial approah. 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 equation is estimated using least squares, employing the Frankel and Romer [1999] data for the right-handside variables and International Monetary Fund Diretion of Trade Statistis bilateral trade data. The ordinary least-squares estimates of the oeffiients in the bilateral-trade equation are used to determine the predited value of the bilateral trade share. Predited bilateral trade shares are then aggregated to obtain the geography-based value of aggregate imports plus exports relative to PPP GDP for eah ountry TFit i τij exp Fitted value of log. j PPP GDP i Comparing the data on openness and real openness The ten ountries with the highest value of Open are (in this order): Singapore (3.18), Luxembourg (2.11), Hong Kong (2.09), Bahrain (1.88), Belize (1.83), St. Luia (1.65), Malta 22
(1.6), Lesotho (1.54), St. Vinent and Grenada (1.52), and Belgium (1.51). The ten ountries with the highest value of ROpen are (in this order): Singapore (2.63), Bahrain (1.72), Luxembourg (1.51), Hong Kong (1.21), Puerto Rio (1.15), Belgium (1.08), Bahamas (1.0), St. Luia (0.94), and Barbados (9.67). Evidently, there is onsiderable overlap. Among the bottom-ten ountries there is a similar amount of overlap. The ten ountries with the lowest value of Open are: Myanmar (0.13), Laos (0.14), India (0.15), Iran (0.15), Argentina (0.17), USA (0.18), USSR (0.18), Mozambique (0.18), Sierra Leone (0.19), and Brazil (0.19). The ten ountries with the lowest value of ROpen are: Bangladesh (0.03) Myanmar (0.04), India (0.04), Nepal (0.05), China (0.05), Mozambique (0.06), Laos (0.07), Sierra Leone (0.08), Brazil (0.08), and Sudan (0.08). There are many 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. Table II lists all ountries moving up or down more than 25 plaes. Institutional quality indies Our IQual institutional quality proxy averages the following three indiators. Government effetiveness, whih proxies mostly bureaurati effiieny (e.g. bureauray/red tape; bureauray as an obstale to business development; strength and expertise of the ivil servie to avoid drasti interruptions in government servies in times of politial instability) but also uses some broader data on the funtioning of government (e.g. effiieny of mail delivery; quality of publi health are; general ondition of roads). Rule of law, whih uses data on different aspets of rime and the workings of the judiiary (e.g. osts of rime; kidnapping of foreigners; independent and impartial ourts) and also issues related to the enforement of ontrats and the protetion of intelletual property rights (e.g. enforeability of private ontrats; enforeability of government ontrats). And graft, whih proxies different aspets related to orruption (e.g. orruption among publi offiials; effetiveness of antiorruption initiatives; mentality regarding 23