NBER WORKING PAPER SERIES ONCE AGAIN, IS OPENNESS GOOD FOR GROWTH? Ha Yan Lee Luca Antonio Ricci Roberto Rigobon

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1 NBER WORKING PAPER SERIES ONCE AGAIN, IS OPENNESS GOOD FOR GROWTH? Ha Yan Lee Luca Anonio Ricci Robero Rigobon Working Paper 0749 hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Massachuses Avenue Cambridge, MA 038 Sepember 004 The auhors are graeful o Ahanasios Vamvakidis for kindly sharing his daase. They also hank Raphael Bergoeing, Sebasian Edwards, Alejandro Mico, Andrea Repeo, and seminar paricipans a IASE in Saniago de Chile, and he World Bank, for very useful discussions and commens. This Working Paper should no be repored as represening he views of he IMF.The views expressed in his Working Paper are hose of he auhor(s) and do no necessarily represen hose of he IMF or IMF policy. Working Papers describe research in progress by he auhor(s) and are published o elici commens and o furher debae. The views expressed herein are hose of he auhor(s) and no necessarily hose of he Naional Bureau of Economic Research. 004 by Ha Yan Lee, Luca Anonio Ricci, and Robero Rigobon. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Once Again, is Openness Good for Growh? Ha Yan Lee, Luca Anonio Ricci, and Robero Rigobon NBER Working Paper No Sepember 004 JEL No. F0, F43, O40, C33 ABSTRACT Rodriguez and Rodrik (000) argue ha he relaion beween openness and growh is sill an open quesion. One of he main problems in he assessmen of he effec is he endogeneiy of he relaion. In order o address his issue, his paper applies he idenificaion hrough heeroskedasiciy mehodology o esimae he effec of openness on growh while properly conrolling for he effec of growh on openness. The resuls sugges ha openness would have a posiive effec on growh, alhough small. This resul sands, despie he equally robus effec from growh o openness. Ha Yan Lee Deparmen of Economics MIT hlee@mi.edu Luca Anonio Ricci Inernaional Moneary Fund lricci@imf.org Robero Rigobon Sloan School of Managemen MIT, Room E Memorial Drive Cambridge, MA and NBER rigobon@mi.edu

3 - - I. INTRODUCTION A fundamenal quesion in developmen and inernaional economics is wheher higher rade openness helps o improve economic growh. Even hough his quesion has received a grea deal of aenion in he lieraure for more han a cenury, we sill do no have, as a profession, a saisfacory answer. In a recen survey, Rodriguez and Rodrik (000) provide a criical analysis of he main conribuions of he pas decade and conclude ha he naure of he relaionship beween rade policy and economic growh remains very much an open quesion (p. 66). However, he auhors inerpre he persisen ineres in his area as reflecing he worry ha he exising approaches haven goen i quie righ (p. 36). The presen paper offers some insighs as o how o exploi differences across counries o address one of he main obsacles o answering he quesion: he problem of simulaneiy, which is pervasive in economeric analysis. Wha mos economiss would consider good measures of he degree of openness of a counry are, unforunaely, closely linked o he level of income. For example, measuring openness as he raio beween he sum of impors plus expors o GDP clearly is a funcion of he growh rae of he economy boh he numeraor and he denominaor are linked o he GDP growh. Wha his implies is ha no even he sign of he bias in he sandard OLS regression can be assessed. Insrumenaion via lags or oher economic indicaors does no offer a valid alernaive if, respecively, openness is serially correlaed or hese oher variables affec growh as much as rade. Dollar and Kraay (003) sugges esimaing he regression in firs differences and insrumening he change in openness via lagged values of openness, which appear uncorrelaed wih oher facors influencing changes in growh. Unforunaely, he simulaneiy bias can exend over ime in he case under consideraion. For insance, if par of he growh rae in he fuure is driven by invesmen oday ha requires impored goods, hen he degree of openness oday depends on fuure growh rae. Hence, using lag values of openness as insrumens does no provide a reliable soluion. Alernaively, oher economic indicaors such as geographic ones have been used as insrumens (see, for example, Frankel and Romer (999)). However, hese insrumens have ofen been criicized as being correlaed wih income as much as wih rade. For example, he graviy lieraure has shown ha geographic variables can be robusly employed o explain rade. A he same ime, hey can also be expeced o affec growh via oher channels, for example, via heir relaion o healh condiions and produciviy, o he qualiy of insiuions, and o he availabiliy of naural resources (see Rodriguez and Rodrik (000) and Baldwin (003)). To he exen he componen of rade ha is insrumened via geography is correlaed wih hese oher facors, he Insrumenal Variables (IV) esimaes are likely o be biased. Dollar and Kraay (003) address he insrumenaion problem by esimaing he growh regressions in firs difference and insrumening he changes in he main explanaory variables (rade and insiuions) via heir lagged levels. Parly due o he differen dynamic naure of he wo variables, he lagged levels of rade predic well changes in rade, bu no changes in insiuions, and vice versa, hus allowing for a beer insrumenaion for rade. In his paper, we ackle he exremely imporan issue of endogeneiy again, bu from a very differen perspecive. Insead of appealing o insrumens ha move he degree of openness bu

4 - 3 - are uncorrelaed wih income growh (which we have already argued ha are difficul o find) we solve he problem of simulaneous equaions by using he relaively new lieraure on idenificaion hrough heeroskedasiciy (IH). In he sandard simulaneous equaions problem he insrumenal variables approach searches for a variable ha shifs he demand (for example) o esimae he supply. In oher words, we need a variable ha moves he mean of he demand curve o esimae he supply. We now know ha his procedure was inroduced in Philip Wrigh s 98 book in Appendix B (see Sock and Trebbi, 003). In he same appendix, Wrigh indicaes ha we could also solve he problem of idenificaion if insead of moving he mean we find a variable ha increases he variance of one of he equaions o infiniy. In oher words, if he volailiy of he innovaions o he demand schedule is infiniely large in comparison o he volailiy of he innovaions of he supply, in he daa we only observe movemens due o innovaions o he demand, and herefore we can esimae he supply schedule direcly. This is known oday as near idenificaion. In 99, Leonief indicaed ha we did no have o move he variance o infiniy, only knowing ha i has changed implies ha he disribuion of he residuals roae along he differen schedules. Rigobon (003a) shows ha his is enough o achieve idenificaion. 3 This approach has been defined in he lieraure as idenificaion hrough heeroskedasiciy (IH from now on) and has been recenly applied o numerous issues plagued by reverse causaliy. 4 Sample heeroskedasiciy, boh across ime and across counries, is very high boh in counry growh raes and in heir degrees of openness. I is herefore possible o use he IH mehod o solve for he problem of endogeneiy, when analyzing our fundamenal quesion of he effec of rade openness on growh. See Fisher (976). 3 Oher heoreical derivaions can be found in Senana (99), Senana and Fiorenini (00). 4 Applicaions where he heeroskedasiciy is modeled as a GARCH process are Caporale, e. al. (00a), Rigobon (00a), Rigobon and Sack (003a). Applicaions where he heeroskedasiciy is described by regimes shifs are Rigobon (00b, 003b), Rigobon and Sack (003b), Caporale e. al. (00b). Applicaions o even sudy esimaion are developed by Rigobon and Sack (004) and Evans and Lyons (003). Finally, several applicaions o panel daa can be found in he lieraure. Hogan and Rigobon (003) apply he mehod o a very large panel daa o esimae he reurns o educaion. Rigobon and Rodrik (004) sudy insead he impac of insiuions on income, and how he differen ypes of insiuions are affeced by income levels and he degree of openness of he counry. Klein and Vella (003) also use heeroskedasiciy o esimae he reurns o educaion. Broda and Weinsein (004) use he inequaliy consrains ogeher wih he heeroskedasiciy o esimae he elasiciies of subsiuion in models of rade o evaluae he gains from variey. Paillo, Poirson, and Ricci (003) use he IH mehod o idenify he impac of exernal deb on growh. Hviding, Nowak, and Ricci (004) invesigae he impac of official reserves on exchange rae volailiy.

5 - 4 - Our resuls sugges ha openness has a small posiive effec on growh, which is no paricularly robus. They also sugges ha mos of he empirical works ha claim o find a srong and robus resul are insead likely o capure eiher he reverse causaliy effec or he effec of oher economic and policy disorions ha are correlaed wih openness (such as he black marke premium, his laer poin being already discussed by Rodriguez and Rodrik, 000). This paper is organized as follows: Secion II, presens he esimaion problem and derives he esimaor used in he paper. In Secion III, we presen our resuls using idenificaion hrough heeroskedasiciy. Finally, Secion IV concludes. II. ENDOGENEITY As was argued, good measures of openness are in general closely relaed o he growh rae. This generaes he sandard endogeneiy problem. To simplify he discussion we absrac from oher conrols and concenrae mainly on he simulaneous equaions problem. Therefore, assume ha openness and growh are described by he following sysem of equaions: y = α o + ε () o = β y + η where y is he growh rae, and o is he degree of openness. We are ineresed in esimaing α, bu as i is well known ha wih sandard economeric mehodologies we canno consisenly esimae α when eiher β is differen from 0 or he variance of η is finie unless openness and growh are coinegraed even if we are willing o make he srong assumpion ha he srucural shocks have finie variance and are uncorrelaed. The resuls discussed below apply for any disribuion. Assume we esimae he firs equaion by OLS no aking ino consideraion he simulaneous equaions problem. The esimaion is biased because he righ hand side variables are correlaed wih he residuals. In paricular, in equaion: y = α o + ν he OLS esimae is given by he general expression: α = = α + β ( o ' o ) o ' y σ ε ( αβ ) σ + β σ This equaion encompasses all cases where he problem of simulaneous equaions disappears: Exclusion resricions: if β = 0, he bias goes o zero which should be obvious given ha β = 0 is assuming he problem away. This is wha ypically is assumed when exclusion resricions are imposed on he sysem of equaions. For example, mos of he macro lieraure using VARs and idenifying he model using he Choleski decomposiions implicily are making his assumpion. η ε

6 - 5 - Near idenificaion: Assume ha he variance, hen i is easy o verify ha if he oher variance is finie hen he bias goes o zero. Near idenificaion is one of he mos used assumpions in even sudy papers. Unforunaely, i is usually assumed implicily, insead of explicily. Coinegraion or infinie variance: if he variables are coinegraed, or similarly if he observable variables (y and o) have infinie variance even hough he residuals have finie variance, hen he expression ( α β ) would be close o zero. In his case, i is eviden ha he bias goes o zero. We know from he coinegraing lieraure ha if he variables are random walks bu have a coinegraing relaionship (which means ha a linear combinaion of hem is saionary), hen he model is super consisen and we can run OLS. In his model, if ( αβ ) = 0 we have a similar resul. Having infinie variance for each of he variables, bu finie variance for he linear combinaion of hem is equivalen o having wo coinegraing relaions: y = α o + ν, and o = β y + π. The problem in pracice is ha we will no know which of he wo we are esimaing, bu here will be no inconsisency in he esimaes. There are oher assumpions ha have been used o achieve idenificaion: long-run resricions usually assume ha he sum of lag coefficiens is zero for some ype of shock. Addiionally, parial idenificaion can be achieved if sign resricions are imposed. We believe ha hese assumpions do no apply o he problem of growh and openness, and herefore, we do no discuss hem. Observe ha we can also have an esimae for he coefficien in he second equaion. The esimae for β is also biased. β = = β + α ( y ' y ) σ η y ' o σ η ( αβ ) α σ + σ In summary, boh esimaes are biased if we canno jusify exclusion resricions, or ha one of he variances is infiniely large, or ha he variables are coinegraed, or ha here are long-run resricions (which is a form of exclusion resricion). We believe ha he problem of simulaneiy beween growh and openness canno be solved by appealing o hese assumpions. Indeed, mos of he lieraure does no appeal o hem because hey are impossible o raionalize in his paricular framework. η ε A. Reversed Regressions: OLS Bounds Before proceeding owards he IH mehodology, i is ineresing o discuss a very old lieraure sudying he bounds of he OLS esimaes in he presence of misspecificaion from he correlaion of he explanaory variables and he residuals (his is a general problem which encompasses oher issue in addiion o simulaneous equaions). The purpose of he bounds is o

7 - 6 - highligh or show he exen of he misspecificaion. The mehod was used by Leonief (99) and i was recovered by Leamer (98) and Edwards (99). Assume we have a general problem of misspecificaion ha can be summarized by he simple relaionship y = a + ν o where he righ hand side variable o is correlaed wih he residual ν. Noice ha his is exacly he firs equaion in our sysem of equaions, bu here we would like o offer he general discussion when his correlaion arises from muliple sources, no jus from reverse causaliy (and hence we use differen erms for parameers and residuals han in equaion ). I is well known ha, in he presence of his misspecificaion, we canno esimae a consisenly. Indeed, here are wo forms of esimaing a. y = a + ν (a) o o = a = b y y + ~ ν + ~ ν (b) I is imporan o indicae ha boh regressions are equally wrong! Leonief sudied his problem and realized ha depending on he sources of he misspecificaion he OLS esimaes in hese wo regressions provide bounds for he rue coefficien. The esimae in equaion (a) provides one bound, and he inverse of he esimae on equaion (b) provides he oher bound. A special case arises when he misspecificaion in he model is due o simulaneous equaions. In paricular, assume oupu and openness are given by our model equaion (). Then he OLS esimae in equaion (a) is (he same as before): σ ε a ˆa = ( o ' o ) o ' y = α + β ( αβ ) σ + β σ while he esimae of /a in equaion (b) is (noe ha he wo expressions are idenical): ˆ σ η bb = ( y ' y ) y ' o = β + α( αβ ) α σ + σ = α α η η ε ( αβ ) η ε ε σ α σ + σ Noe ha if we are ineresed in he esimaion of α, we wan o solve b ˆ b for ε insead of β. α We can in fac use boh esimaes ˆ and ˆ o compue he range where he rue coefficien α a a b b mus lie if he model is correc. To illusrae he range, consider he wo possible cases, where α and β have differen or similar signs.

8 - 7 - If α and β have differen signs, he bias in equaion (a) makes he OLS coefficien smaller (in absolue value) han he rue one. In oher words, aˆ a Similarly, i is also easy o show ha in equaion b he bias is also oward zero. Hence we can wrie b ˆ b < α Therefore, < α aˆ < α <. a bˆ b In oher words, if he wo schedules have differen signs, hen he rue coefficien lies beween hese wo esimaes. The inuiion of his resul is very simple. Firs, i is imporan o realize ha equaion a is he OLS run in one direcion, while equaion b is he OLS regression in he oher direcion. If he schedules have differen signs, simulaneous equaions will bias he OLS coefficiens oward zero, because he OLS coefficien is a linear combinaion of he wo coefficiens one posiive, and he oher negaive. Hence he OLS coefficiens in boh regressions are smaller in absolue erms han he rue ones. However, he coefficien in he firs equaion (a) aemps o esimae α and he coefficien in he second one (b) / α. This is wha deermines he range. When he wo schedules have he same signs he range of coefficiens is differen. In his case, he bias in he OLS in boh equaions (a and b) is away from zero. 5 So, if boh coefficiens are posiive he OLS is larger han he rue one, and if he coefficiens are negaive he OLS ones are smaller han he rue ones. Neverheless, his means ha in absolue erms, α < min ˆ Again, his implies a range of coefficiens ha is admissible. The inuiion in his case, follows he same reasoning as before, where he difference is due o he fac ha in boh equaions he esimaed coefficiens are larger han he OLS ones. a a, bˆ b 5 We absrac here from he case where α*β>, i.e., when boh he observable variables (y and o) as well as he residuals of a) and b) have infinie variance. This case is no very common and migh arise in he presence of misspecificaion due o he omission of variables ha are necessary o achieve coinegraion.

9 - 8 - For our purposes, if one has a prior ha growh and openness posiively affec each oher, he reasoning above would lead o he expecaion ha he rue coefficiens are smaller han he respecive OLS bounds. Noe also, ha each of he OLS esimaes has a confidence inerval. Hence, he exac bounds would need o ake ino accoun such inervals a he desired significance level. B. Idenificaion Through Heeroskedasiciy In his paper we appeal o a differen mehodology: idenificaion hrough heeroskedasiciy. In his secion we derive he basic esimaor closely following Rigobon (003a). Assume we are ineresed in esimaing firs he following simulaneous equaion sysem. y = α o + ε o = β y + η where ε and η are he srucural innovaions. The firs equaion summarizes he growh equaion we are ineresed in esimaing. I measures he effec of openness on growh, and he srucural residual can be inerpreaed as innovaions o growh ha are independen of all conrols and oher shocks. The second equaion is he openness equaion. I describes how growh affecs he degree of openness of he economy. The innovaions o his equaion are inerpreed as hose changes in he degree of openness ha are no explained by he covariaes. Assume ha he innovaions have mean zero, are uncorrelaed, and idenically disribued. Addiionally, assume ha he coefficiens are he same across all realizaions. In his model, he only saisic we can compue from he sample is he covariance marix of he observable variables i.e., we can compue he variance of growh, he variance of he openness, and heir covariance. However, under our assumpions his covariance marix is explained by four unknowns: α, β, and he variances of ε and η. This is he sandard idenificaion problem in simulaneous equaions here are fewer equaions (momens in his case) han he number of unknowns. Algebraically, he covariance marix of he reduced form is σ + + ε β σ η ασ ε βση Ω = ( αβ ) α σ + ε σ η where he lef hand side can be esimaed in he daa and in he righ hand side we have he heoreical momens. Assume ha he daa can be spli in wo ses according o he heeroskedasiciy of he residuals, i.e., ha he residuals in hese wo ses have differen variances. Remember ha in he original

10 - 9 - model we have already imposed ha he coefficiens are he same across all observaions. In hese wo sub-samples we can esimae wo variance covariance marices: Ω Ω = = ( αβ ) σ ε, + β σ η σ ε, + β σ η, ε, σ ε, ε, + βσ η, + σ η, + βσ ( ) αβ α σ ε, + σ η, his implies ha now here are six momens ha can be esimaed in he sample, which are explained by six coefficiens: he wo parameers of ineres and four variances. Noice ha here are as many equaions as unknowns. In he sandard lieraure of sysem of equaions his means ha he sysem saisfies he order condiions. To fully solve he problem, hen, we have o verify ha he six equaions are linearly independen which is known as he rank condiion. As is shown in Rigobon (003a) his requires ha he relaive variances of he residuals shifs across he sub-samples: σ ε, σ ε, σ σ η, The inuiion why shifs in he variances achieve idenificaion is quie simple and is closely relaed o he insrumenal variable inuiion. Consider he sandard demand-supply idenificaion problem. If we are ineresed in esimaing he demand schedule, he IV mehodology ells us ha we need o find some variable or shock ha shifs he supply schedule, so he slope of he demand can be compued. So, he sandard inuiion searches for somehing ha moves he means. In he IH mehodology, we search for somehing (like a regime change) ha shifs he variance insead of he mean. The differen variances in he sample provide enough informaion o idenify he coefficiens in boh equaions (direc effec and reverse causaliy effec). The shif in he variance roaes he ellipse where he residuals are disribued. Tha roaion in he ellipse occurs along he schedules we are ineresed in esimaing. Noe ha he analogy can be brough o he limi in he known case of near-idenificaion. Assume ha he variance of he supply shocks is infiniely large compared o he demand shocks. In his case, he ellipse enlarges along he demand so much ha in he limi i becomes he demand. Therefore, even when we do no know when he supply moves, he likelihood ha i is moving is one, hence all he variaion observed is along he demand equaion. This is known as near-idenificaion, and even hough here is no movemen in he mean, he problem of idenificaion has been solved. As should be eviden from he previous derivaion a crucial assumpion is he sabiliy of he parameers. Even hough his assumpion seems unpalaable in many applicaions, in cross secional panel regressions sandard IV mehods are implicily assuming i already. One, η, ασ α ασ η,

11 - 0 - advanage of he mehod we describe is ha if here are more han wo regimes we can es he overidenifying resricions. The idenificaion assumpion in he IH mehodology is ha he daa is heeroskedasic (which is easily esable) and ha he srucural shocks are uncorrelaed (his is he mainained assumpion). We esimae he model using GMM where he momen condiions are he zero correlaion among he idenified srucural errors. On he oher hand, esimaion using MLE is more difficul given ha i is hard o impose he momen condiion so crucial for idenificaion. C. Adding Conrol Variables I should be obvious ha adding addiional conrols has no impac on he idenificaion problem. Assume ha oupu and openness are described by his sysem of equaions. (3) ( ) ( ) + + Φ = β α η ε φ β α A where o y L X L o y where X are he conrols or exogenous variables. In his model, if he variables are no coinegraed (which imposes some consrains on Φ ) and we canno impose exclusion resricions on he exogenous variables (which imposes consrains on ( ) L ( ) L φ no having a single erm equal o zero), he problem of idenificaion canno be solved wih sandard mehodologies. The reason is ha he reduced form in his model, which is (4) ( ) ( ) = + Φ + = o y o y A where o y L A X L A o y η ε ν ν ν ν φ,,,, canno be idenified from he daa. To illusrae his issue assume ha R is a posiive definie marix ha we use o pre and pos muliply each of he reduced form coefficiens as follows: (5) ( ) ( ) ( ) ( ) ( ) ( ) + Φ + = o y o y L R AR X L R AR o y,, ν ν φ

12 - - The momens from equaion (4) and (5) are idenical and herefore, because here are no consrains on R oher han posiive definie, here exiss a coninuum of soluions for A ha are consisen wih he reduced form momens. Noice ha if we know for example ha one coefficien of φ ( L) is zero for some lag and some exogenous variable x, hen pre-muliplying ( L) φ for an arbirary marix R will violae he resricion. Therefore, if we know ha one variable is no included in one of he equaions, we can idenify he sysem. This is exacly he inuiion of exclusion resricions which in his case will imply ha ha variable can be used as an insrumen. ( ) ( ) One ineresing aspec of he reduced form model is ha A φ L and A Φ L are consisenly esimaed by using OLS. In oher words, if we were o know wha he marix A is, hen recovering all he coefficiens of he srucural model (3) would be rivial. In oher words, he challenging problem is he esimaion of marix A. Noice ha from equaion (4) he reduced form residuals have he exac same properies as he endogenous variables. Hence, he easies procedure is o use a wo sep esimaor: Firs, i is possible o esimae he reduced form model (4) which is similar o esimaing a reduced form VAR and recover heir residuals. Second, hose residuals can be used, hen, o esimae he conemporaneous marix A. III. RESULTS We employ sandard growh regression variables in a panel of 8 periods of 5 years each, spanning from o , and abou 00 counries. The descripion of he variables and he corresponding main saisics are presened in he Appendix. In paricular, in he IH esimaion we use four measure of openness, whose sign is adjused so ha a high value means a more open regime: size of rade (share), a ariff indicaor (arind), impor duies (impdup), and black marke premium (bmp). 6 7 We perform some preliminary regressions of growh on he conrol variables and on openness wih sandard mehodologies, such as fixed effec or difference-gmm, o derive some 6 Vamvakidis (00) included he black marke premium among he conrol variables, raher han as a measure of openness. We regressions we presen do no include black marke premium in he lis of conrol variables, as in several sudies i has been used as a proxy for openness. Inroducing i as a conrol variables in all he regression does no aler he hrus of he resuls. 7 Edwards (99, 998) argues ha he relaion beween openness and growh should be analyzed wih as many measures of openness as possible and he uses nine of hem. However, several such measures are unemployable in our seup as hey are mainly available as a crosssecion.

13 - - benchmark o assess he imporance of properly conrolling for endogeneiy (he resuls are presened in he Appendix). The firs mehod addresses he omied variable bias by adding counry-specific dummies, bu canno conrol for endogeneiy. The second mehodology implicily accouns for fixed effecs by esimaing he model in firs difference, bu also aemps o address he endogeneiy issue by insrumening curren variables wih previous lags (we adoped he opion ha allows for all lags o be used). However, if variables are serially correlaed, which is expeced o be he case for openness and growh, lags are no a very good insrumen. The resuls provide a weak evidence for he effec of openness on growh, as only he black marke premium indicaor is robusly associaed wih growh. We now urn o he derivaion of he OLS bounds discussed above and hen o he implemenaion of he IH esimaion. A. Reversed Regression Before esimaing he IH coefficiens i is insrucive o analyze he bounds of he rue coefficiens following Leonief s reversed regressions. Conrolling for fixed effecs as well as he oher sandard variables, we compued he OLS and reversed OLS regressions for he four measures of openness: Share, Impor Duies, Tariff Index, and Black Marke Premium. 8 Remember from Secion IIA ha hese wo OLS esimaors deermine he bounds where eiher α or β belong. Indeed, his will be used in he second sep o deermine he validiy of he idenificaion. The OLS resuls are shown in Table ; he resuls for α are of course idenical o hose in Table Aa in he Appendix. 9 Table. OLS esimaes wih fixed effecs Measure of Openness OLS eq. a ( a ) ˆa OLS eq b ( bˆ b ) Poin T-sa Poin T-sa aˆ a Bounds for α / bˆ b Share Tariff Index Impor Duy Black Marke Premium The Sachs and Warner measure could no be employed because of he peculiar heeroskedasiciy paern ha i would involve: high difference of variance across groups and minimal difference wihin groups. 9 Given he presence of srong serial correlaion, we run he regression also wih lags (even hough he lieraure on growh has generally no included lags). The hrus of he resuls is unchanged.

14 - 3 - Noice ha he poin esimaes for he effec of openness on growh (α ) are marginally significan on he share variable, highly significan on he black marke premium variable, and no significan for he ohers. Apar for he impor duy measure (which is insignifican), hey are all posiive. The las wo columns of Table show he bounds ha he rue coefficiens have o saisfy. 0 As an example, le s consider he black marke premium measure. The coefficiens α or β have he same sign. Hence, according o Secion IIA, he rue coefficien would need o be smaller han he minimum of he wo bounds, which in his case is 0.6. Hence, if our IH esimaor correcs properly for endogeneiy, i will need o respec such a condiion. The main message of Table is ha he bounds are very large, indicaing ha he endogeneiy bias is poenially very large. B. IH Esimaion: Sandard Seup In his secion we presen he resuls from esimaing he impac of openness on growh using he OLS esimaes and he IH mehodology. The procedure is he following:. We esimae equaion (4) and recover he residuals from he VAR. As was argued before he residuals share he exac same conemporaneous properies as our variables of ineres. Iniially, we will no inroduce lags of growh and openness, o replicae sandard growh specificaions. We will subsequenly add a dynamic srucure o accoun for serial correlaion.. We esimae he uncondiional covariance marix for each counry and spli he daa ino four groups: high-low variance of openness, and high-low variance of growh, where high and low values are defined wih respec o he median. As was argued before we only need wo differen covariance marices o solve he problem of idenificaion. By appealing o four covariance marices we have an overidenified sysem of equaions and we can evaluae he validiy of he model. In he robusness secion we discuss he implicaions of he differen splis. 3. Given he four covariance marices we compue he conemporaneous coefficiens by GMM, where he momen condiions for each regime are: 0 Remember ha each esimae has a confidence inerval, which is no aken ino accoun in he las wo columns of Table 3, bu would need o be aken ino accoun o derive a precise bound. In our paricular case, he esimaes have he same sign. Hence, he precise bound would be higher in absolue erms han wha is repored in he las wo columns of Table 3 by he corresponding confidence inerval a he desired significance level.

15 σ + + ε, i β σ η, i ασ ε, i βσ η, i Ωi = ( ) αβ α σ ε, i + σ η, i 5. To compue he sandard errors we use he opimal weighing marix for he GMM. We use a wo-sep esimaion o compue he opimal weigh. The esimaion is as follows: From he sample we compue he covariance marix from each of he group of counries. This provides momens. These momens have o be explained wih 0 parameers: 8 srucural shock variances, and he wo coefficiens of ineres. GMM reduces he weighed disance beween hese heoreical momens and he sample ones. 6. Alernaively, i is possible o specify he GMM by minimizing he idenificaion assumpion (ha he srucural shocks are uncorrelaed) in he differen regimes. In Table, we presen he esimaes using he IH mehodology. Because he IH mehodology can esimae he impac of openness on growh and he impac of growh on openness we presen boh coefficiens: he impac of openness on growh (α) and he impac of growh on he measuremen of openness (β). Table. IH esimaes wih fixed effecs Measure of Openness α β Poin T-sa Poin T-sa Share Tariff Index Impor Duy Black Marke Le s analyze firs he effec of openness on growh (α), which is he focus of he paper. When comparing he IH resuls (Table ) and OLS ones (Table ), we find ha for he measures ha were significan in Table he eliminaion of he endogeneiy bias moves he poin esimaes in he direcion which we would have expeced. In fac, as discussed in Secion IIA, for he share and black marke premium measures he IH esimaes should be smaller han he OLS esimaes. Indeed, his is he case. The inuiion lies in he fac ha boh variables affec each oher posiively and he OLS esimaes capure a compounding of boh effecs. Regarding he effec of growh on openness (β) for he same wo measures, we find a posiive and highly significan effec. These resuls confirm he prior ha par of he posiive effec of openness on growh found in he lieraure should acually be ascribed o he reverse causaliy i.e., he one ha goes from growh o openness. The nex sep is o sudy how robus hese resuls are o changes in he definiions of he regimes. Here, mosly, we have o esimae he coefficiens using differen splis. Before showing he resuls i is imporan o menion ha, as i is argued in Rigobon (003a), he esimaes should be consisen o changes in he windows defining he splis. The inuiion is he

16 - 5 - following: we have said ha he sysem of equaions is idenified if he rue daa have heeroskedasiciy. In oher words, he heeroskedasiciy provides addiional equaions ha allow us o solve he problem of idenificaion. Now, misspecificaions of he windows (or splis) implies ha he covariance marices esimaed in he daa are linear combinaion of he rue ones. This is he crucial sep ha he mispecified model conforms marices ha are linear combinaion of he rue ones! Hence, if he original sysem of equaions has a soluion, hen he one from he mispecified splis is a linear combinaion of he original one. Therefore, he soluion is he same as he one from he rue sysem of equaions, and here is only a loss in efficiency. The sandard spli used in he ex assumes ha each counry belongs o a paricular group of variance, where high variance is defined as he variance above median. In a second spli, we define high variance as he uncondiional momen above he mean variance (his is a very small change in he definiion of he windows). In a hird spli, we look a he differen periods of 5 years: we compue he cross-secional covariance for each 5-year period year and rea each 5-year window as a separae regime. The las spli is o use 5-year windows again bu now group he window in four disinc groups of high-low variance of each of he wo endogenous variables. The resuls are shown below in Table 3. The firs wo mehods use he differen volailiies across counries o creae he groups, while he second wo mehods use he differen volailiy across ime o spli he daa. Table 3. IH esimaes wih fixed effecs for differen splis 3 4 Share Tariff Index Impor Duy Black Marke sa below coefficiens Table 3 shows he esimaes for he effec of he black marke premium on growh for he four differen splis. As can be seen, he esimaes are generally close even hough he splis involve very differen arrangemens of he daa. Tariff index and impor duy show significan sabiliy of he coefficien across specificaions. This corresponds o he mehodology employed by Paillo, Poirson, and Ricci (003), wih a program kindly provided by Rigobon.

17 - 6 - The change in he spli made he larges impac on he esimaes for he Share variable. For such variable, he firs wo splis produce insignifican coefficiens (alhough hey have opposie signs), while he second wo splis produce significan, posiive, and similar coefficiens. We find ha firs esimae is no saisically differen from he oher hree (even hough some are highly differen from zero). However, i is possible o rejec he hypohesis ha he second coefficien is saisically he same o he hird or fourh (a 5 percen confidence). This suggess a rejecion of he model when he share variable is used in he esimaion. There are several possible reasons for his rejecion when using share, which mainly perain o specificaion issues. Firs, he omission of lags in he endogenous variables (o he exen hese lags belong in he specificaion), which implies ha a common shock is unaccouned for. Second, he relaive imporance of ime-series variaion versus cross-secional variaion, given ha splis and rely mainly on he firs variaion and splis 3 and 4 on he second one. Oher reasons relae o he exisence of non-lineariies, of a common shock, or of oher endogenous variables unaccouned in he specificaion. We did no find rejecions in he oher hree variables which signals o us ha here is somehing peculiar wih he Share measure ha requires furher analysis. The nex wo Secions will furher address his issue. C. IH Esimaion: Accouning for Serial Correlaion As was argued before in he OLS secion, here are imporan serial correlaions unaccouned for in he ypical growh regression. In his secion we evaluae how he esimaes change when we include lags in he specificaion. This is no a sandard growh specificaion bu one ha we were ineresed in exploring o be sure ha he heeroskedasiciy is no he resul of an unmodeled lag srucure. Measure of Openness Table 4a. OLS esimaes wih fixed effecs for he firs spli OLS eq. a ( a ) ˆa OLS eq b ( bˆ b ) Poin T-sa Poin T-sa aˆ a Bounds for α / bˆ b Share Tariff Index Impor Duy Black Marke Premium In Table 4a, we presen he bounds for he case in which we allow fixed effecs and lags. As can be seen, he same resul as before is found. The implied bounds for he rue coefficiens are exremely large. For each of he openness measures i goes from less han 0. o more han.5. This indicaes he severiy of he endogeneiy problem. In Table 4b we presen he resuls comparable o hose in Table wih he spli. The resuls are similar o hose in Table, regarding he share and black marke premium measure. However, he posiive effec of openness as measure by ariff on growh becomes significan

18 - 7 - and he relaion beween impor duy and growh becomes posiive in boh direcions alhough i remains insignifican. Table 4b. IH esimaes wih fixed effecs and lags in firs sep for he firs spli Measure of Openness α β Poin T-sa Poin T-sa Share Tariff Index Impor Duy Black Marke Table 4c repors he resuls comparable o hose in Table 3: he effec of openness on growh, wih he four splis. As before, he resuls are very similar o hose in Table 3 for share (differen coefficiens under he firs wo and he second wo splis) and black marke premium (very significan and posiive). However, he coefficiens of he ariff and impor duy indices are now posiive, much closer o significance, and sable. Table 4c. IH esimaes wih fixed effecs and lags in firs sep for he four splis 3 4 Share Tariff Index Impor Duy Black Marke D. IH Esimaion: Accouning for Serial Correlaion and Cross-Secional Variaion The previous wo subsecions show (Tables 3 and 4c) a puzzling resul, which appears o be a rejecion of he model when using share. The IH coefficiens for he effec of share on openness appear o be differen when using splis and or splis 3 and 4, wheher lags are presen or We esimaed he model also using differen normalizaions and weighing marices for he Generalized Mehod of Momens (GMM). The message from hose specificaions is almos idenical o he one shown here (excep, obviously, for he poin esimaes ha change wih each normalizaion). Those esimaions are no shown in his paper and are available from he auhors upon reques.

19 - 8 - absen in he specificaion. This puzzling resul arises only when using share and no when using any of he oher hree measures of openness. Noice ha splis and spli he daa by counry characerisics i.e., counries wih large variance in one variance go o some groups, and so on. Under crieria hree and four we use ime o spli he daa, eiher because every 5-year period is one group (spli 3), or because 5-year periods wih large variance in one variance go o one group (spli 4), and so on. This means ha in he splis 3 and 4, he IH esimaion will rely mainly on he ime-series heeroskedasiciy o esimae he coefficiens, while splis and will rely relaively more on cross-counry variaion. As he regressions in he previous subsecions were based on fixed effec, he main crosssecional variaion was auomaically eliminaed. This could imply ha splis and wih fixed effecs would no allow he IH esimaor o correc properly for endogeneiy when he main source of variaion is cross-secional. I urns ou ha share, or he firs-sage residuals for share (when no conrolling for fixed effec), have much larger cross-secional variaion han imeseries variaion. This could explain why he problem of differen coefficiens for he splis and versus 3 and 4 was so pronounced wih share. Splis and were unreliable for share as hey could no pick is main source of variaion, and heeroskedasiciy is essenial for he IH correcion of endogeneiy. In order o avoid his problem, in his secion we esimae he model using random effecs. As he previous subsecion has shown he imporance of allowing for lags, we reain hem in he specificaion. In Tables 5a and 5b we reproduce he OLS bounds and poin esimaes for he random effecs case. As can be seen, he bounds coninue o be exremely large. In Table 5c we presen he resuls for all he differen splis. Noice ha, in comparison o he previous cases, now all variables, including share, have very sable coefficiens. Openness as measured by share and black marke premium have a posiive and significan coefficien, even hough he coefficiens are smaller han he OLS esimaes presened in Table 5a. Also observe ha he ariff index and impor duy have posiive coefficiens, alhough no significan and hey are reasonably close o he resuls from Table 4c. Table 5a. OLS esimaes wih lags and random effecs for he firs spli Measure of Openness OLS eq. a ( a ) ˆa OLS eq b ( bˆ b ) Poin T-sa Poin T-sa aˆ a Bounds for α / bˆ b Share Tariff Index Impor Duy Black Marke Premium

20 - 9 - Table 5b. IH esimaes wih lags and random effecs for he firs spli Measure of Openness α β Poin T-sa Poin T-sa Share Tariff Index Impor Duy Black Marke Table 5c. IH esimaes wih lags and random effecs for he four splis 3 4 Share Tariff Index Impor Duy Black Marke In summary, we find ha he cross-secional variaion is crucial in undersanding he effec of share on growh. However, i is imporan o menion ha random effecs allow us o use he cross-secional variaion, bu may carry an omied variable bias, as we are no conrolling for counry-specific effecs. Neverheless, a leas we are sure we know ha we are properly conrolling for endogeneiy and we canno blame reverse causaliy (i.e., he effec of growh on openness) for he posiive and significan resul of share on growh. Hence, Tables 4c and 5c should be joinly considered our preferred specificaions. On he one hand, hey boh conrol for he dynamic srucure. On he oher hand, Table 4c properly conrols for counry-specific effecs, while Table 5c ensures ha he IH esimaion works properly if we allow i o make use of he cross-secional variaion. When reading boh Table 4c and 5c, we find ha openness, as measured by share, black marke premium, and, o a lesser exen, a ariff index, has a posiive and significan effec on growh. Finally, and equally imporan, our esimaes in Tables 4c and 5c are smaller (or no significanly larger) han hose from simple OLS presened in Tables 4a and 5a, respecing he bounds condiions idenified in Secion IIA. This is exacly he direcion we would have expeced if endogeneiy is a problem in he daa. IV. CONCLUSIONS Academics and policymakers have devoed enormous energy o he quesion of wheher openness is good for growh. Mos of he evidence is based eiher on case sudies or on

21 - 0 - regression analysis. We have learned a grea deal in he las decades by sudying boh bu he quesion is sill open. The main inconveniences are ha case sudies are always hard o replicae and are affeced heavily by counry idiosyncrasies, while regression analysis is plagued wih endogeneiy issues. I should be clear, now, ha insrumens o solve he problem of simulaneous equaions have been impossible o find in his case. Mos of he lieraure moved oward proxies of openness such as black marke premium as alernaives, wih he unforunae problem of finding variables ha migh be correlaed wih oher inefficiencies no necessarily relaed o he degree of openness. The problem does no seem o have a soluion wihin he sandard economeric mehodologies. Furhermore, he bes available insrumen, disance, used by Frankel and Romer (999), canno accoun for he ime series variaion of he openness variables and should also ener he growh equaion direcly because i can proxy for qualiy of insiuions, ec. Hence, even he bes insrumen for openness available in he lieraure has several limiaions. In his paper we ackle he same quesion, using similar daa, bu resoring o a differen procedure: idenificaion hrough heeroskedasiciy. This procedure uses insrumenal variables ha move he variances insead of he means. In he daa, i is he case ha he variaion on second momens is richer han he variaion on means, hus providing scope for using heeroskedasiciy o esimae he conemporaneous relaionships. We find ha mos measures of openness would have a posiive effec on growh, even when conrolling for he effec from growh o openness. Furhermore, we also show ha our esimaes are smaller han he OLS esimaes exacly wha we would have expeced if endogeneiy is an issue in he daa. Our resuls are robus o several specificaions when openness is measured by rade over GDP and exremely robus when openness is measured by black marke premium. However, as poined ou already by Rodriguez and Rodrik (000) and Baldwin (003), among ohers, black marke premium is capuring no only openness bu also reflecs many oher economic and policy disorions. Hence, he focus on he rade aspec of openness may be oversaed. In oher words, he exreme robusness of black marke premium may sugges ha i is openness in a broad sense as par of he overall economic, policy, and insiuional environmen ha is conducive o growh. 3 We esimaed a very simple model in which oher variables noably all hose which are ypically available on a cross-secion basis have been excluded. Primarily, we have no 3 Baldwin (003) suggess ha: One can inerpre openness in narrow erms o include only impor and expor axes or subsidies as well as explici nonariff disorions of rade or in varying degrees of broadness o cover such maers as exchange-rae policies, domesic axes and subsidies, compeiion and oher regulaory policies, educaion policies, he naure of he legal sysem, he form of governmen, and he general naure of insiuions and culure.

22 - - included he qualiy of insiuions in he esimaion (Rigobon and Rodrik (004) sudy his broader case) which could sill poenially explain he posiive correlaion beween openness and growh. Furhermore, we have reaed some of he conrol variables as exogenous when some of hem could perhaps be considered endogenous. Fuure research should exend he curren mehodology o include hose aspecs. From he mehodological poin of view, his paper shows, once again, ha he variaion ha exiss in he daa can be used o solve idenificaion issues affeced by endogeneiy. I can herefore be used o invesigae oher unanswered quesions in he growh lieraure, especially hose relaed o he impac of policies, as hese are likely o be dependen on he level of developmen and growh of a counry. These quesions are no only exremely imporan from he heoreical poin of view, bu hey are crucial policy issues ha need our aenion.

23 - - APPENDIX We mainly employ he daase used recenly by Vamvakidis (00) and we complemen i wih wo measures on rade openness from he Economic Freedom Nework. The panel encompasses 8 periods of 5 years each, spanning from o , and abou 00 counries. The main saisics of all variables are presened in Table A. Growh is measured by real GDP growh per capia (ypcg). The se of conrol variables encompasses iniial real GDP per capia (ypc0), he raio of invesmen o GDP (iy), he level of inflaion (infl), he raio of M o GDP (m), he growh rae of populaion (popg), he naural logarihm of he level of educaion (Ledu, noe ha in he Table A he variable is presened in levels) and he age dependency raio, i.e., he raio of dependens o working-age populaion (age). We have five openness measures: he raio of he sum of impors and expors o GDP (share), impor duies as a percenage of impors (impdup), he average years of openness indicaed by he Sachs and Warner index (swyo), he difference beween official exchange rae and black marke rae (bmp) and a ariff indicaor which is he average of revenue from axes on inernaional rade as a percenage of expors plus impors, he mean ariff rae, and he sandard deviaion of he ariff raes (arind). The las wo measures are from he Economic Freedom Nework daase. All openness measures are adjused so ha a high value means a more open regime. The Appendix also repors he resuls ha are obained by regressing growh on he conrol variables and on openness, using sandard mehodologies such as fixed effecs and difference GMM (Tables Aa and Ab). 4 The resuls provide a weak evidence for he effec of openness on growh. Only he black marke premium indicaor is robusly associaed wih growh (a posiive coefficien represen negaive effec of he premium on growh), while he Sachs and Warner indicaor is significan only in he fixed effec esimaion. Noe ha he Sachs and Warner index is highly dominaed by is black marke premium componen, and is herefore likely o capure he same effec. 4 We run he difference-gmm wih he one sep robus esimaor (he one sep is preferred for inference on he coefficiens). The ess rejec he null of no firs order auocorrelaion, bu do no rejec he null of no second order auocorrelaion (in he presence of second order auocorrelaion he esimaes would be biased). The robus opion does no deliver he Sargan es for he overidenifying resricions. When we run he one sep homoskedasic esimaor, he Sargan es ofen rejecs he null hypohesis ha he overidenifying resricions are valid. However, when we run he difference-gmm wih he wo sep esimaor (which would parially accoun for heeroskedasiciy bu is no reliable for inference on coefficiens) or wih lags (which would accoun for serial correlaion bu is no sandard in growh lieraure), he Sargan es acceps he null hypohesis ha he overidenifying resricions are valid. We do no repor such addiional resuls, as heeroskedasiciy and o a smaller exen serial correlaion are discussed carefully in he paper.