Distance and border effects in international trade: A comparison of estimation methods

Magerman, Glenn; Studnicka, Zuzanna; Van Hove, Jan Working Paper Distance and border effects in international trade: A comparison of estimation methods Economics Discussion Papers, No. 2015-69 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Magerman, Glenn; Studnicka, Zuzanna; Van Hove, Jan (2015) : Distance and border effects in international trade: A comparison of estimation methods, Economics Discussion Papers, No. 2015-69, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/125169 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Licensed under the Creative Commons License - Attribution 3.0 Discussion Paper No. 2015-69 | December 17, 2015 | http://www.economics-ejournal.org/economics/discussionpapers/2015-69 Distance and Border Effects in International Trade: A Comparison of Estimation Methods Glenn Magerman, Zuzanna Studnicka, and Jan Van Hove Abstract This paper compares various estimation techniques used to determine the impact of distance and borders on international trade. The results consistently confirm the significantly negative distance effect, while the border effect, measured by evaluating whether intra-continental trade exceeds inter-continental trade, appears to be ambiguous and dependent on the estimation method. In addition, also the size of both effects varies substantially across estimation methods. Finally, the authors generally find that the estimations are in line with the respective weighting schemes of each estimation method. (Published in Special Issue Distance and Border Effects in Economics) JEL F10 F14 Keywords Distance effect; border effect Authors Glenn Magerman, KU Leuven – Center for Economic Studies (CES) & Leuven Centre for Irish Studies Address: KU Leuven – University of Leuven, Faculty of Business and Economics, Centre for Economic Studies, Naamsestraat 69, 3000 Leuven, Belgium, [email protected] Zuzanna Studnicka, KU Leuven – Center for Economic Studies (CES) & Leuven Centre for Irish Studies, Belgium Jan Van Hove, KU Leuven – Center for Economic Studies (CES) & Leuven Centre for Irish Studies, Belgium, & INFER Glenn Magerman gratefully acknowledges financial support from the USA Fulbright Foundation Belgium-Luxembourg, the Otlet-La Fontaine scholarship granted by Yves Moreau at the Department of Engineering at the University of Leuven, the NBB 2014 Sponsorship program at the National Bank of Belgium and the Junior Mobility grant by the University of Leuven. Zuzanna Studnicka gratefully acknowledges financial support from FWO Flanders (Research Grant G.0365.10N) as well as from the Flemish Government. The authors acknowledge useful feedback on previous versions by Joris Tielens, Janez Kren, Jan-Pieter Laleman, Sophie Soete, Geert Dhaene, Huw Edwards and two anonymous referees. Citation Glenn Magerman, Zuzanna Studnicka, and Jan Van Hove (2015). Distance and Border Effects in International Trade: A Comparison of Estimation Methods. Economics Discussion Papers, No 2015-69, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2015-69 1 Introduction “There is very little that economists fully understand about global trade but there is one thing that we do know – commerce declines dramatically with the distance” (Leamer, 2007).The negative impact of distance on trade is indeed one of the most robust findings in international economics (see e.g., Leamer 1993; Frankel 1997a; Disdier and Head, 2008). Trade is not only reduced by distance, but also by international borders (see e.g., McCallum, 1995; Wei, 1996; Anderson and van Wincoop, 2003; Obstfeld and Rogoff, 2001; Coughlin and Novy, 2012). Adjacent countries trade more than non-adjacent ones (see e.g., Leamer 1993; Helliwell, 1997), leading to the so-called adjacency or contingency effect. Consequently intra-national/continental trade exceeds inter-national/continental trade. These well-established empirical results appear in the estimates of the so-called gravity equation based on various kinds of trade models, either assuming perfect competition (e.g., Anderson, 1979; Deardoff, 1995; Eaton and Kortum, 2002), monopolistic competition (e.g., Bergstrand, 1989, 1990) or a demand system with translog preferences (Novy, 2013). The importance of distance and borders as determinants of trade flows may be explained by the variety of barriers to trade they reflect. Distance and border effects account not only for the geographical barriers between two trading partners, but also for various costs traders may incur when transporting a good to its final consumer (see e.g., Anderson and van Wincoop, 2004, for surveys on the relationship between physical distance and trade costs). Moreover, as argued by Blum and Golfarb (2006), distance may also capture consumers’ tastes, since it reduces trade even in online products where trade costs should be zero. Theoretical work argues that the magnitude of the distance effect should be equal to one. Empirical evidence by and large confirms this theoretical prediction. In general, according to the meta-analysis by Disdier and Head (2008), based on 1,467 estimates from 103 papers, the size of the distance effect is close to 0.9. However, the estimated magnitude of the distance effect varies depending on the countries or periods studied. In addition, because of increasing globalization and advances in transport technology, the world is shrinking. Therefore, one may expect that the distance coefficient decreases over time. Empirical studies measuring the evolution of trade elasticity with respect to distance are, however, not conclusive. Some authors find little change in the trade elasticity to distance (see e.g., Leamer 1993). Also Disdier and Head (2008) argue that the distance effect is rather constant after a rise around mid twentieth century. Frankel (1997a), Soloaga and Winters (2001), Berthelon and Freund (2008), among others, obtain evidence for an increasing 2 distance effect, whereas Boisso and Ferrantino (1993), Eichengreen and Irwin (1998), Brun et al. (2005), Felbermayr and Kohler (2006), Coe et al. (2007), amongst others, observe a negative evolution in the distance effect over time. There are several possible explanations for these contradictory results. For example, Brun et al. (2005) argue that infrastructure is responsible for the decline of the distance effect. According to Felbermayr and Kohler (2006), the non-decreasing distance effect found in previous studies, can be explained by the fact that these studies do not take into account the extensive margin of trade. Finally, Berthelon and Freund (2008) show that the increase of the overall distance coefficient is due to the changes of distance coefficients across industries. They explore two possible reasons for these changes. First, in some industries, goods have become more substituable. Second, trade costs have changed too. The author argues that the first phenomenon is the most important one. The empirical literature on border effects was inspired by the seminal work of McCallum (1995), who shows that Canadian provinces trade up to 22 times more with each other than with US states (the so-called “home bias”). This finding was confirmed, for a longer time period by Helliwell (1996) and Helliwell and McCallum (1995). Similarly, Wei (1996) finds that OECD countries buy about 2.5 times more from themselves than from identical foreign countries1Helliwell (1997) points to an even larger border effect, but it is approximately halved by for countries sharing a common border and common language. Following a similar approach as Wei (1996) and Helliwell (1997), Nitsch (2000) finds that domestic trade within a European Union country is seven to ten times larger than trade with another European Union country.2Finally, note that most of these studies observe a trade increasing effect for adjacent countries. These findings, and in particular the finding by McCallum (1995), were revisited by Anderson and van Wincoop (2003) who show that the spectacularly high border effects come from omitting the multilateral resistance term in McCallum’s specification and from the small size of the Canadian economy. Moreover, although most studies following McCallum (1995) include a multilateral resistance term in the form of a remoteness variable, they still do not account for national border barriers. Thus, Anderson and van Wincoop (2003) show that the inclusion of the multilateral resistance term 1Wei (1996) assumes that a country’s purchases from itself equal the difference between its production and exports. In his analysis, he assumes that the internal distance equals half of the distance from the country’s economic centre to the border of the nearest neighbour. 2Note that Helliwell (1996, 1997), Wei (1996) and Nitsch (2000) employ the method of seemingly unrelated regressions (SUR). 3 considerably reduces McCallum’s ratio of inter-provincial trade to provincestate trade (from 16.4 to 10.7). Moreover, when using US data instead of Canadian data, they find that trade between states exceeds trade between states and provinces only by a factor 15. Finally, they also find that borders reduce trade between the US and Canada by 44 per cent and among other industrialized countries by 29 per cent. Interestingly, as demonstrated by Wolf (2000), the home bias exists not only at the international level, but also at the intranational level. According to this author, trade between US states is about three times lower than trade within states.3Adjacent states trade 2.6 times more with each other. In addition, the distance coefficient is similar to the coefficients found for international trade. Hillberry and Hummels (2003) explain the finding of Wolf (2000) by the importance of wholesale activities for intra-state trade. More recently, Coughlin and Novy (2012) compare international borders with domestic borders. More precisely, they compare trade between and within individual US states with trade between states and foreign countries. They find that a state’s border is a larger trade barrier than an international US border. One of possible explanation is related to Hillberry and Hummels (2008) who find that trade within the US is heavily concentrated at the local level. Trade within a single ZIP code is on average three times higher than trade with partners outside the ZIP code. Hillberry and Hummels (2008) explain their finding by co-location of producers in supply chains to exploit informational spillovers, minimize transportation costs and facilitate just-intime production. According to Coughlin and Novy (2012), producers also concentrate in order to benefit from external economies of scale in the presence of intermediate goods and associated agglomeration effects (see e.g., Rossi-Hansberg, 2005), as well as from the hub-and-spoke distribution systems and wholesale shipments (see, Hillberry and Hummels, 2003). It means that the domestic border effect reflects the local concentration of economic activity rather than trade barriers associated with crossing a state border. From this literature review it appears that the sensitivity of the distance and border effectrs in trade have been tested for various countries, regions and periods. So far, the sensitivity of these effects to the applied estimation methods has not been tested yet in a consistent manner. This paper aims to fill this gap. The remainder of the paper is organized as follows. In the next section we discuss the main econometric approaches mainly or recently followed in the gravity literature. In the third section we present the data and our empiriical approach. Section 4 discusses the results from applying various econometric techniques measuring distance and border effects. Section 5 3Note that he does not take into account the multilateral resistance term. 4 presents some robustness checks. Section 6 concludes. 2 The Econometrics of Gravity While the earliest implementation of the gravity model in international trade was just an intuitive copy of its counterpart in physics, most models of international trade now derive an aggregate bilateral demand system that can be written as a form of the original gravity equation. Following the notation of Head and Mayer (2014), we write the general gravity model as: Xij =GSiMjφij (1) where Xij denotes nominal exports from country ito j,Gis a gravity constant, Siand Mjare the capabilities of exporter and importer respectively, and φij is a function of the impact of trade barriers to bilateral trade flows, with 0 ≤φij ≤1. Using homothetic budget shares and general equilibrium market clearing conditions for the exporter, one can derive a structural basis for eq.1, so that: Xij =Yi Pi Xj Πj φij (2) where Yiis gross output of exporter i,Xjis the total consumption value of goods in j,Piand Πjare multilateral trade resistance terms (MTR).4Subsequently in most empiric applications, Yiand Xjare proxied by exporter’s GDP and importer’s GDP respectively. The bulk of theory in the gravity literature is related to static and crosssectional models. At the same time most empirics are performed in a panel setting, and this for two main reasons: i) there is plenty of panel data available at the country level and even at the sector or product level; and ii) using time-invariant regressors (such as distance and borders) can infer causation of the model with respect to predicted trade flows.5However, even in panel settings almost all the estimated models are still static, not dynamic.6 4In Anderson and van Wincoop (2003), the authors enforce Xi=Yi(balanced trade) and φij =φji (symmetric trade costs), which leads to Pi= Πjas a unique solution to their system of market clearing conditions. 5At the same time, observations of individuals (countries in our case here) are not independent over time. This introduces spurious correlation and generates standard errors that are too small. That’s why (at least with large Nand small T) we should cluster observations at the highest level of aggregation, i.e. the country-pair level since we observe bilateral flows. 6There is some work on dynamic panel models in international trade, for instance Harris 5 2.1 From OLS to NLS... The general functional form of the empirical gravity model is given by Y=exp(Xβ)η(3) where Xis a vector of regressors with elements xij,βis a vector of coefficients to be estimated, and ηis a vector of idiosyncratic error terms with random noise so that E(ηij|X) = 1.7Clearly, eq.3 can accomodate both eq.1 and eq.2. Traditional estimation of the gravity model log-linearizes the model and uses OLS to estimate the parameters of interest, β: y=Xβ+ε(4) where y=ln(Y) and ε=ηexp(Xβ). This linear transformation is often applied in empirical trade research, but it causes three issues. The first two issues are pointed at by Santos Silva and Tenreyro (2006), the third one is new, and constitutes the focus of this paper. i) The validity of the model depends on the orthogonality of ηwith respect to the regressors - which is violated with heteroscedastic errors; ii) the estimation runs on only positive values, as ln(0) is undefined, which leads to the exclusion of zero-trade flows in estimating bilateral trade; iii) the specified loss function that minimizes the objective implies how observations are weighted in estimating the parameters of interest. Let’s elaborate a bit on each of these. 1. Heteroscedasticity One cause of heterogeneity is omitted variable bias. If the model is misspecified due to omitted variables or the exclusion of a (non)-linear combination of regressors which are correlated with the error term, this leads to a non-homogeneous pattern of the residuals of the model (see also robustness tests). When estimating eq.4, one assumes that there is no information in the noise, or equivalently Y|X∼N(·), where N(µ,σ) is the Normal distribution with a given mean µ=Xβand standard deviation σand lnη ∼N(0, σ). However, when the error term is heteroscedastic, the variance of the error term is not constant (σi6=σ, ∀i). Heteroscedasticity does not affect the unbiasedness of the OLS estimator, but it affects the efficiency, since it does not minimize the variance. It also affects the estimated p-values and Matyas (2004), Harris, Kostenko, Matyas and Timol (2009) and Baltagi et al. (2014). 7Here exp(·) is the exponential function, E(·) stands for the expectations operator, and Xis a vector of variables with appropriate length clear from the context. 6 and to a lesser extent confidence intervals and prediction intervals. The estimated standard errors are biased and the bias can go either way. If heteroscedasticity is moderate, we can transform the estimation equation or use robust methods to correct for the standard errors such as White’s (1980) standard errors if we consider the estimation equation correctly specified. Also, Weighted Least Squares can be used to offset the heteroscedasticity problem and produce an efficient estimator. However, deriving the correct weighting matrix through iteration can be a tedious task (see below). 2. Positive values Running the estimation procedure only on positive values can bias the estimated coefficients, as zero trade flows can contain valuable information. Santos Silva and Tenreyro (2006) advocate a Poisson Pseudo Maximum Likelihood (PPML) estimator to deal with both heteroscedasticity and zero-trade flows simultaneously, and we will describe the PPML below. However, PPML does not directly account for structural zeros, as derived from models with fixed costs of exporting (see Melitz, 2003; Helpman et al., 2008) or models of Bertrand competition as in Eaton and Kortum (2002). Some patches have been proposed such as selection models with a 2-stage estimation procedure, where the first stage estimates the amount of zeros in the system, and the second stage subsequently estimates the bilaterel trade values. While Helpman et al. (2008) use a selection model that is derived from theory and accounts for firm heterogeneity, alternatives such as Zero Inflated models deliver biased results as the gravity model does not relate to count models, only the first-order conditions of the PPML coincide with those of the Poisson model.8 3. Loss function The specified loss function of any estimation procedure to be minimized affects how estimates for βare obtained. The loss function used in OLS is the least squared errors function, which puts larger weight on larger observed errors. The objective to minimize is that of the Sum of 8Since the Helpman et al. (2008) procedure can only be performed on a small subset of countries (in order to be computationally able to use fixed effects), we do not present the results of those estimations here. In addition, since the count data alternatives of Negative Binomial and Zero Inflated models are biased, we do not go into further details on their estimation in this paper. 7 Squared Residuals (SSR) ˆ β= arg min β SSR(β) = arg min βX(y−Xβ)2(5) where ˆ βis the estimate of βthat minimizes the objective function. The first-order conditions are ∂SSR(β) ∂β =−2X0y+ 2X0Xβ= 0, or β= (X0X)−1Xy, where X0is the transpose of X.9There is a unique minimum if Xhas full rank. In the linear model and under normality of the error terms, the first-order conditions with respect to βof the objective to be optimized under Least Squares and Maximum Likelihood (ML) coincide. In the linear model with normally distributed errors, the log-likelihood function `(β|X) = −n 2ln(2π)−n 2ln(σ2)−1 2σ2(y− Xβ)0(y−Xβ) is the objective function to be maximized. The firstorder conditions write ∂` ∂β = (X0X)−1Xy =ˆ βOLS. Instead of log-linearizing equation 3, we can estimate the coefficients from the model in the original exponential function. Using non-linear least squares (NLS) and optimizing SSR, the objective to estimate parameters of the model becomes: ˆ β= arg min β SSR(β) = arg min βX[Y−exp(Xβ)]2(6) with a system of first-order conditions: ∂ˆ β ∂β =X[Y−exp(Xβ)]exp(Xβ)X= 0 (7) The first factor (Y−exp(Xβ)) is the model to be estimated, minimizing the errors, and the factor exp(Xβ)Xrepresents weights to each observation in minimizing those errors. Some authors (Frankel and Wei, 1993; Frankel, 1997b; Anderson and van Wincoop, 2003) have proposed using the NLS method in estimating the gravity equation: the function gives more weight to observations where exp(Xβ) is large, so that countries with larger Siand Mjfor instance, get more weight.10 There is economic intuition for this weighting scheme, as countries with higher GDP tend to report more accurately and therefore get more weight in estimating the model. However, Santos Silva and Tenreyro (2006) state that i) this does not address 9From the second-order conditions, this is a minimum: ∂2SSR(β) ∂β2= 2X0X≥0. 10This is not only GDP, but also other variables that might be used in this dimension such as the MTR, and also the distance function. 8 Figure 1: Estimation of the distance coefficient cross methods -1.6 -1.4 -1.2 -1 -.8 -.6 -.4 Coefficient 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Yea r OLS LSDV BB PPML GPML Note: Multiple cross-section estimates across estimation methods. The estimation equation is given by eq.2, controlling for the observable variables in the distance function: ln(GDP) exporter, ln(GDP importer, ln(distance), adjacency, common official language, colonial ties and RTAs. We also control for WTO membership status for the exporter and importer. Exporter and importer fixed effects are used in the LSDV, PPML and GPML models. The coefficients for distance are all significant at the 0,1% level across all years and estimation methods. Standard errors are robust and clustered at the country-pair level. Table 2 shows the estimated parameters for interversus intra-continental trade flows over the pooled period 1998-2011. Note that we observe that the distance coefficient is in line with the cross-sectional estimates as before. Moreover, we see that the adjacency effect is positive, tough insignificant in the BB setting. Furthermore, all the control variables have the expected signs and sizes. We obtain interesting insights into the border effect by continents. We first focus on the LSDV specification. After correcting for multilateral trade resistance, GDP and bilateral observables, we see that some continents trade relatively more globally than intra-continentally. This is the case for Europe and Asia, with Europe being the most open continent. In other words, these continents are globally more connected, a finding we see in reality. Note that this is not at odds with the well-known fact that e.g. intra-European trade exceeds extra-European trade since it is the effect after controlling for the regular gravity explanations. The Pacific is the most “closed” continent, in the sense that it trades relatively more inside the Pacific than across the globe. When we turn to other estimation methods, results change dramatically depending on the procedure used. Hence contrary to our findings for the distance effect, the border effect appears to be much more sensitive to 15 the selected estimation methody. In the biased OLS setting (not correcting for MTR), most results are insignificant, and Asia is trading relatively more inside Asia. Similar to our findings for the distance effect, also now LSDV and BB line up nicely. Based on both methods, the Americas are more open, while Europe is not. For the non-linear methods of PPML and GPML, we find contradictory coefficients for Europe. It is also interesting to note that this continental border effect is in contrast with the regional flows as in Anderson and van Wincoop (2003). In their findings, the border effect is always negative. Apparently things change in the global context. Finally, Figure 2 shows the evolution of the estimated coefficients for the intra-continental predicted trade over the years 1998 to 2011, where we have used the LSDV method as representation. 16 Table 2: Borders by continents (1) (2) (3) (4) (5) OLS LSDV BB PPML GPML lnGDP(exporter) 1.092*** 1.099*** (0.0198) (0.0195) lnGDP(importer) 0.857*** 0.864*** (0.0299) (0.0298) ln(distance) -1.023*** -1.298*** -1.399*** -0.494*** -1.385*** (0.0992) (0.0848) (0.109) (0.0888) (0.0227) Adjacency 0.912** 0.777* 0.508 0.415*** 1.029*** (0.221) (0.293) (0.241) (0.110) (0.0646) Common Language 0.700*** 0.702*** 0.568*** 0.0751 0.654*** (0.0508) (0.0625) (0.0478) (0.0619) (0.0350) Colonial Ties 1.015*** 0.926*** 1.026*** 0.403* 1.408*** (0.128) (0.0573) (0.135) (0.193) (0.0621) RTA 0.851* 0.711* 0.833* 0.477*** 0.486*** (0.243) (0.206) (0.233) (0.0587) (0.0273) WTO exporter 0.561** 0.528*** (0.110) (0.0756) WTO importer 0.289* 0.271** (0.0774) (0.0420) Europe 0.006 -0.506* -0.0539 0.440*** -0.922*** (0.197) (0.130) (0.131) (0.119) (0.0478) Americas 0.343 0.410 -0.494* 0.675*** 0.300*** (0.198) (0.194) (0.174) (0.122) (0.0780) Asia 0.240** -0.350** -0.237* -0.100 -0.121** (0.0498) (0.0629) (0.0904) (0.151) (0.0396) Africa -0.0309 0.295* -0.0793 0.669*** 0.430*** (0.213) (0.0904) (0.147) (0.0545) (0.0569) Pacific 2.495*** 1.333** 0.923* 1.110*** 1.915*** (0.237) (0.202) (0.270) (0.173) (0.191) Constant -31.28*** 5.953** -40.30*** 11.85*** 10.73*** (1.951) (0.894) (1.096) (1.017) (0.332) adj. R20.671 0.735 0.674 Country FE No Yes No Yes Yes BIC 1232841.3 1324651.3 1230787.3 6.40034e+10 8388126.5 N 283586 319276 283586 532029 532029 Notes: Model specifications are (1) OLS, (2) Least Squares Dummy Variable, (3) Baier and Bergstrand (2009) Taylor approximation method, (4) Poisson Pseudo-Maximum Likelihood and (5) Gamma PseudoMaximum Likelihood. In model (3), all the bilateral variables are first-order Taylor approximated. Country FE depict exporter and importer fixed effects. Adjusted R2and/or the Bayesian Information Criterion (BIC) are given where possible. Robust and clustered standard errors are between parenthesis, clustered at the continent level. Significance levels: 5% (*), 1% (**) and 0,1%(***). 17 Figure 2: Evolution of the dummy estimates of continents over time -1 0 1 2 Coefficient 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Year Europe Americas Asia Africa Pacific Note: Multiple cross-section estimates across estimation methods. The estimation equation is given by eq.2, controlling for the observable variables in the distance function: ln(GDP) exporter, ln(GDP importer, ln(distance), adjacency, common official language, colonial ties and RTAs. We also control for WTO membership status for the exporter and importer. Exporter and importer fixed effects are used in the LSDV, PPML and GPML models. The coefficients continents dummies are all significant at the 0,1% level across all years and estimation methods. Standard errors are robust and clustered at the country-pair level. 5 Robustness Checks We check for several potential sources of misspecification. First, following the comments in Head and Mayer (2014), we check convergence of the different estimators under different sample sizes. Since the estimated coefficients based on OLS and GPML are close, while the PPML coefficients are lower, Head and Mayer (2014) ague that this might be due to misspecification of the model if the sample size is big enough. We draw random subsamples from our data, of 75, 50 and 25% respectively. Figure 3 shows the estimated coefficients for distance over time by estimation method. Across all sample sizes, PPML consistently delivers lower estimates for distance, and the ranking of the other estimates remains the same. In this setting, we cannot recreate the convergence of all estimates as proposed by Head and Mayer (2014) in their simulation setting, who state that, if sample size is large enough, and absent of misspecification, the estimates of OLS, PPML and GPML should coincide. Secondly, we draw the residual versus fitted values plot for the LSDV method in Figure 4.21 Since we deal with so many observations, traditional scatter plots are not very efficient. Instead, we propose to use a local polyno21We also run the residual plots for the other estimation methods. Patterns are similar. 18 mial smoother plot to represent the underlying scatters. The local polynomial has two added advantages for residual analysis: i) the polynomial smoother is an indicator for potential non-linearities or other patterns in the residuals, and ii) the 95% confidence intervals of the smoother are a nice way to depict potential heteroscedasticity: if there are irregularities in the width of the confidence intervals, this indicates non-constant variance of the error terms. We rerun the original specification of Section 4.1, but now for the year 2005 only, to evade potential auto-correlation.22 There is i) a clear structure in the residuals that resembles a third-degree polynomial and ii) potential heteroscedasticity could show up in the left tail of the distribution of the fitted values. We are confident that heteroscedasticity is not affecting our results in any major way (we also check the pattern of heteroscedasticity using PPML, giving almost identical results), and focus on the non-linear pattern of the residuals. To see where the structure comes from, we plot the residuals against each regressor. The residual plots of all regressors look fine, except the residual plot against distance uncovers the same structure as the residuals versus fitted plot. We should therefore rerun the model with a polynomial approximation for distance: it might be the case that the linear specification of the distance function is just not correct, and we just assumed it following the bulk of the gravity literature. Also, given our global sample, the effect of distance might not be well approximated by a linear relationship, where this might be more appropriate for local sub samples such as Europe. We rerun the model with a second and third order polynomial for distance, which in effect lowers the pattern in the residual plots, but completely disrupts all of the gravity estimates. We also check if there is a non-linear pattern inside continents, so to see that the non-linearities do not come from the global sample. We see the same residual pattern recurring for each isolated subsample. We therefore prefer to keep with the main stream of the literature and use the log-linear distance function. However, the correct specification of the distance function is an interesting topic in its own. Finally, we check for potential multicollinearity between distance and the border effect, since this might also drive misspecification. We find VIF test results for all variables in the model (excluding the fixed effects) between 1 and 1.5, where VIF values of above 5 or 6 might indicate potential multicollinearity problems. We therefore also reject this potential problem. 22We also ran the model on the pooled version and the panel version, all giving very similar results. 19 Figure 3: Subsample estimates for distance -1.6 -1.4 -1.2 -1 -.8 -.6 -.4 Coefficient 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Yea r OLS LSDV BB PPML GPML (a) Subsample 75% -1.6 -1.4 -1.2 -1 -.8 -.6 -.4 Coefficient 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Yea r OLS LSDV BB PPML GPML (b) Subsample 50% -1.6 -1.4 -1.2 -1 -.8 -.6 -.4 Coefficient 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Yea r OLS LSDV BB PPML GPML (c) Subsample 25% Note: Multiple cross-section estimates across estimation methods. Exporter and importer fixed effects are used in all models except OLS and BB. The coefficients for distance are all significant at the 0,1% level across all years and estimation methods. Standard errors are robust and clustered at the country-pair level. Figure 4: Residual versus fitted plots -5 0 5 10 Residuals -5 0 5 10 15 20 Linear prediction 95% CI Polynomial Smoother kernel = epanechnikov, degree = 0, bandwidth = .26, pwidth = .4 Local polynomial smooth Note:A local polynomial smoother represents the underlying scatter plot. The gray band indicates the 95% confidence interval, the y= 0 line is indicated in red. 6 Conclusion This paper compared the distance and border effects on global bilateral trade flows using various econometric techniques. We clearly confirm the negative distance effect, but its magnitude appears to vary across estimation methods. The distance effect is also constant over time in all methods. The observed variety is in line with the theoretical expectations. Our evidence for the border effect by continents is more ambiguous. Generally speaking, we can confirm that intracontinental trade exceeds intercontinental trade, contolling for various other trade explanations. 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