Gravity-equations-Workhorse-or-Trojan-horse-in-explaining-trade-and-FDI-patterns-across-time-and-space_2010_International-Business-Review.pdf

gravity equations workhorse or trojan horse in explaining trade and fdi patterns across time and space remco c j zwinkels a sjoerd beugelsdijkb aerasmus school of economics erasmus university the netherlands bfaculty of economics and business administration university of groningen the netherlands 1 introduction a central research question in international business ib is why fi rms operate outside their own country and what determines the size and geographic distribution of these foreign activities to explain these trade and foreign direct investment fdi fl ows ib scholars have used gravity models since its inceptionin 1993 respectively 1970 39 studies on the country level determinants of fdi and exports published in this journal or the journal of international business studies are implicitly or explicitly embedded in a gravity model see appendix a similarly the economic geography literature makes use of gravity equations in order to explain the geographical dissemination of trade and fdi see e g bosker pantulu bergstrand 1985 and have produced some of the clearest empirical results in international economics and business gerachi leamer for an overview see frankel 1997 gravity models postulate that the magnitude of merchandise trade and fdi fl ows between countries is conditional on several characteristics of these countries notably their economic size and level of economic development and on factors stimulating or discouraging the movement of merchandise or investment between countries bergstrand 1985 brainard 1997 these factors include transportation costs typically proxied by the presence or absence of a shared land border by geographic distance and formal trade barriers often proxied by the presence or absence of free trade agreements the increased availability of data on cultural and institutional characteristics of country pairs has triggered further research attempting to explain the size and geographic distribution of both trade and fdi by for example the role of host country international business review 19 2010 102 115 a r t i c l ei n f o article history received 10 september 2008 received in revised form 3 august 2009 accepted 4 september 2009 keywords fdi gravity equation time series trade a b s t r a c t gravity equations are a widely used tool in the international business ib literature to explain country level trade and fdi fl ows against the background of its increased popularity and data availability a range of commonly made econometric mistakes have recently been discussed intheliterature mostlypertainingtothe omitted characteristics ofcountriesorcountrypairsingravitymodels inthispaperwecomplementthisliterature by focusing on the time series aspects of gravity models something that has become crucial with the increased use of panel data specifi cally we concentrate on the possible non stationarity of both the dependent variable trade or fdi fl ows and of one or more of theexplanatoryvariables in this paper we i show that thereis indeed a problem with the non stationarity of variables commonly used in gravity equations ii show that not correcting for this yields overestimated results and iii propose an effective solution 2009 elsevier ltd all rights reserved corresponding author tel 31 104081428 e mail addresses zwinkels ese eur nl remco c j zwinkels s beugelsdijk rug nl sjoerd beugelsdijk contents lists available at sciencedirect international business review journal homepage 0969 5931 see front matter 2009 elsevier ltd all rights reserved doi 10 1016 j ibusrev 2009 09 001 political risk and corruption cuervo cazurra 2008 globerman habib sethi guisinger phelan de groot linders rietveld pajunen 2008 culture and cultural distance dow huang 2007 loree frankel rose 2004 srivastava hayashi 2000 if the distribution of a certain variable is constant over time it is said to be stationary if not it is considered non stationary think in this respect for example of a variable with a clear positive trend because of this trend both the mean and the variance of this variable will increase over time as such its distribution is time varying and the variable therefore non stationary if the variables on both the left and the right hand side of a regression equation have a certain positive trend one will always fi nd a signifi cant statistical relation between the two when applying traditional techniques the source of this statistical relation however might solely be the trend and thus be spurious this not only affects the variables having this trend but may affect the results obtained for the other independent variables as well if on the other hand thevariablesshareacommontrendbecauseofunderlyingcausal economic mechanisms theestimationresultsare correct and the variables are said to be co integrated the estimates for the stationary variables in the model however remain biased this issue of non stationarity and co integrated variables is potentially harmful in the context of gravity equations fidrmuch in press herwartz 2003 because some of the independent variables typically found in gravity models potentially have an upward trend comparable to trade or fdi like for example gdp in this paper we investigate the time series aspects of gravity equations and test whether fdi and trade are co integrated with independent variables typically used in gravity equations by doing so we follow up on baldwin and taglioni 2006 who recently showed that gravity equations are very often mis specifi ed a phenomenon observed by dow and karunaratna as well 2006 587 taking their guidelines into account we complement their analyses and illustrate the importance of taking the time series aspects of gravity models more seriously than has been done so far as such we contribute to the methodical aspects of our empirical understandingofthegeographicdistributionanddeterminantsoftradeandfdi giventheincreaseduseofgravityequations in ib this is of great importance for the set up of our empirical models to properly test our theoretical predictions on this distribution and its determinants and the subsequent policy implications using data on us outward fdi and us exports for 1983 2003 we fi rst estimate a traditional gravity equation we subsequently show that gdp political risk and fdi respectively exports are both non stationary and co integrated correcting for this misspecifi cation we re estimate the gravity equations on exports and fdi we show that correcting for co integration leads to i lower signifi cance levels of many variables between the corrected and uncorrected model and ii lower effect sizes of many of these variables these fi ndings are important because they suggest that not properly controlling for the time series aspects of exports and fdi leads to overestimated coeffi cients and signifi cance levels and hence to a biased picture of the determinants of trade and fdi and their relative importance we conclude that not properly including the time series aspects of panels will turn the workhorse that the gravity model currently is into a trojan horse 2 background the gravity model used to explain trade and fdi patterns was inspired by newton s gravity equation in physics in which the gravitational forces exerted between two bodies depend on their mass and distance linders 2006 the application of this mechanism in the fi eld of international trade and later fdi was pioneered by tinbergen 1962 and linnemann 1966 despite its intuitive attractiveness initial criticism was that its theoretical foundations were weak resulting in attempts to improve its theoretical core anderson 1979 was the fi rst to provide strong theoretical underpinnings of the gravity model followed by bergstrand 1985 helpman and krugman 1985 and deardorff 1998 consequently frankel 1997 claims that the gravity model has gone from an embarrassing poverty of theoretical foundations to an embarrassment of riches frankel 1997 53 thispopularityofthegravitymodelisclearlyrefl ectedintheoverviewprovidedinappendixa itprovidesanoverviewof all articles published in the international business review since 1993 and the journal of international business studies since 1970 that have implicitly or explicitly used the gravity model to test the effect of country level determinants of fdi or exports 1most of the 39 articles concern cross sections but increasingly authors have used panel data of these 39 articles 19 are panels 15 of these 19 panel based studies have been published in the last decade 1 firm level studies are included as so far that they have used country level variables to explain aggregate patterns of fi rm level decisions r c j zwinkels s beugelsdijk international business review 19 2010 102 115103 interestingly we have found three studies in which the non stationarity of variables is explicitly discussed these are coccari 1978 dale and bailey 1982 and globerman and shapiro 1999 whereas the latter is a pure gravity application the fi rst two specifi cally deal with forecasting methods given the explicit focus on time series aspects it is no surprise that these authors have dealt with time series econometrics including non stationarity of the recent panel estimations we found none in which non stationarity was discussed most recent panel based gravity models do include time dummies or split up their sample in sub periods although the inclusion of year dummies is useful baldwin cheng egger kalirajan 1999 baldwin and taglioni 2006 summarize this debate and suggest guidelines to minimize the probability of econometric misspecifi cation ingravitymodels theiranalysisconcernstradefl owsbutcanbeextendedtofdifl owsaswell thecommonmisspecifi cation is threefold according to baldwin and taglioni 2006 and relates to i the averaging and summing of imports and exports total trade and inward and outward fdi ii the defl ation of trade and fdi data using consumer price indices and iii omitted variables resulting from the improper cross sectional setup of the gravity equation despite their suggestions on how to improve the econometric specifi cation of gravity models the time series aspect of gravity models has received much more limited attention one of the larger issues in time series analysis is the non stationarity of variables engle this growth in mean and variance will spill into the residuals since the coeffi cients are obviously constant one key assumption behind ols concerns constant mean and variance of the residuals since the ols technique consists of minimizing the squared residuals more weightwillconsequentlybe attached toperiodsinwhichthe meanand varianceare relativelylarge as aresult laterperiods will be overly infl uential in the estimation procedure in the case of macro economic variables like a country s gdp economic growth causes gdp to be non stationary nelson as gdp is non stationary trade would therefore also be non stationary stationarity of data is crucial because not taking proper account of it does not only yield ineffi cient estimates as is the case with serial correlation or heteroskedasticity but also biased estimates in more practical terms since many studies involving gravity equations attempt to quantify the impact of trade or fdi barriers a biased estimate of the size of a certain relation could lead to stronger weaker or even reversed policy recommendations in a worst case scenario hence when one of the variables in the empirical model is non stationary the assumptions underlying ols will be violated as such adjustments need to be made non stationarity in economic data can be solved by taking fi rst differences of the non stationary data obviously the nature of the research question changes when doing so instead of explaining the relation between the level of an independent variable and the level of the dependent variable the model now tests for the strength and nature of the relation between the growth of the dependent and independent variables 3 also fi rst differencing leads to effi ciency losses since information is discarded when the variables on the left and the right hand side share a common trend i e are co integrated estimation yields super consistent results when this is the case the typical method that is applied is the so called vector error correction model vecm in which both the long run equilibrium relation between variables is estimated as well as the out of equilibrium mean reversion dynamics apart from these potentially non stationary variables gravity equations typically contain more explanatory variables which are likely to be stationary think in this respect of membership dummies of trade groups nafta wto and geographicandculturaldistance manyofthesevariablesdonotvaryovertime andtakingfi rstdifferencescausethistypeof 2 we thank one of the reviewers for pointing this out 3 it may also seem attractive from a technical point of view to take the ratio of exports to gdp or fdi to gdp as dependent variables if they are co integrated however doing so also changes the nature of the research question moreover the question arises what to do when more than one independent variable is non stationary or even co integrated with the original dependent variable r c j zwinkels s beugelsdijk international business review 19 2010 102 115104 variablesto disappearfromthe equation thisis problematic because it isexactly these time invariant variablesthatoften arethevariables ofinterestingravityequations inclusion in thevecminthecaseofco integrated regressorsisalso not an option because of the stationary nature of these variables therefore an alternative empirical approach needs to be applied we discuss this below and show the importance of taking the time series aspects more seriously than has been done so far 3 empirical illustration 3 1 data 3 1 1 exports our fi rst dependent variable is the log of us merchandise exports in millions of constant 2000 us dollars between 1983 and 2003 from the imf s direction of trade statistics in order to deal with baldwin and taglioni s 2006 comment regarding the proper defl ation of trade fl ows we used the export price index from the bureau of labor statistics from the us department of labor to convert export fl ows to 2000 prices 3 1 2 fdi the second dependent variable is the stock of outward us foreign direct investment in constant 2000 us dollars from 1983 to 2003 obtained from the bureau of economic analysis bea fdi data are incorrectly defl ated using the consumer price index this is however controlled by using time dummies in the estimation see baldwin hennart 1991 unfortunately fdi data do not enable us to make this distinction beugelsdijk smeets sethi et al 2003 tadesse the henisz political risk measure is available for the full sample period although these proxies for political stability are only correlated at 0 27 in the full sample we consider them to be substitutes 3 1 6 regional trade agreements we include three dummy variables indicating whether a specifi c host country participates in one of the main economic integration agreements involving the us specifi cally we include a dummy coded 1 if the host country was a member of the wto or its predecessor gatt a dummy coded 1 if it participated in nafta or its predecessor cusfta and a dummy taking the value 1 in case the host country is israel for the usis trade agreement 5 3 1 7 cultural distance followingprevious research we measurethe cultural distancebetweenthe us and host countriesby the kogut and singh 1988 index which is based on the differences in scores on each of hofstede s 1980 dimensions of national culture 4 because we only use the united states as home country instead of the full matrix of bilateral trade and fdi fl ows our dataset is not susceptible to the mistake regarding total versus unidirectional trade and fdi fl ows as discussed in baldwin and taglioni 2006 a second advantage of applying one base countryisthefactthatitmakespairdummiesidenticaltocountrydummies therefore whenincludingcountrydummiesbothissuesarisingfrompairsand countries are taken into account and one of the other mistakes identifi ed by baldwin and taglioni 2006 is resolved 5 note that the nafta variable coded 1 for canada as of 1989 and mexico as of 1994 partly measures the existence of a shared land border with the us another variable commonly included in gravity models mccallum 1995 leamer frankel 1997 r c j zwinkels s beugelsdijk international business review 19 2010 102 115105 although the kogut singh index has been criticized shenkar 2001 we use the ks index to keep our dataset comparable to existing studies 3 1 8 common language parallel to the cultural distance variable we include a dummy taking the value 1 if two countries share a common offi cial language data are taken from cia world fact book as used in rose 2004 the above set of independent variables is included in a gravity equation explaining fdi or exports our full sample contains 21 years and 64 countries but due to missing observations the data set is reduced to 774 when including the henisz measure or 801 when including the icrg measure observations in order to exclude the possibility that our comparisonof thedifferent modelspecifi cationsis drivenby differencesinsample sizewe performallour regressionson the same sample of observations table 1 presents the descriptive statistics and correlations the descriptive statistics in table 1 do not show any particularlynoteworthyresults exceptfortheautocorrelation ac forexports fdi gdpandbothpoliticalriskvariablesthe autocorrelation is signifi cant and close to one this is a fi rst indication that these variables are non stationary the correlation matrix reveals a high correlation between gdp and exports otherwise interesting is the positive but low correlation between exports and distance the correlation between explanatory variables is relatively low such that multi collinearity issues are not relevant in our case 3 2 methodology we proceed in several steps first we estimate a standard gravity subseq