Do Borders Really Slash Trade? A Meta-Analysis

The finding that international borders significantly reduce trade, first reported by McCallum (1995), has become a stylized fact of international economics. A high ratio of trade within national borders to trade across borders, after controlling for other trade determinants, implies large unobserved border barriers, an implausibly high elasticity of substitution between domestic and foreign goods, or both. Obstfeld and Rogoff (2001) include the border effect among the six major puzzles in international macroeconomics, and dozens of researchers have attempted to shrink McCallum’s original estimates.

Researchers have proposed several methodological solutions to the border puzzle, such as the inclusion of multilateral resistance terms, consistent measurement of within- and between-country distance, and use of disaggregated data. But the border effects reported in the literature are, on average, still close to those estimated by McCallum (1995): regions are likely to trade with foreign regions about fifteen times less than with regions in the same country (as documented in Figure 1). Apparently, individual explanations of the puzzle have been unsuccessful.

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We show that innovations recently introduced to the gravity equation explain away a large portion of the border effect when their impacts are combined. Methodology matters: the use of disaggregated data, consistent measurement of within- and between-country distance, data on actual road or sea distance instead of the great-circle distance, control for multilateral resistance, and the use of the Poisson pseudo-maximum likelihood estimator all bring systematically different estimates of the border effect compared to the standard of the gravity equation prior to the 2000s. Distinguishing between partial and general equilibrium effects of borders is also important. Using previously reported results, we construct a large synthetic study that employs best practice methodology and find that, when properly measured, borders reduce international trade worldwide by only one third compared to a counterfactual world without borders.

The border effects differ significantly across regions—we obtain large estimates for emerging countries, but relatively small estimates for most OECD countries. Our results suggest that border effects tend to be larger for smaller economies, which is in line with Anderson and van Wincoop (2003). Tariff and nontariff barriers to trade for individual countries are also positively correlated with the reported border effects. Moreover, our results are consistent with a significant home bias in preferences contributing to the border puzzle. In contrast, we fail to find a strong link between border effects for individual countries and country-specific variables related to information barriers, insecurity, and contracting costs.

We employ the framework of meta-analysis, the quantitative method of research synthesis (Stanley, 2001). Meta-analysis has been used in economics by, for instance, Card and Krueger (1995) on the employment effects of minimum wage increases, Disdier and Head (2008) on the impact of distance on trade, Havranek and Irsova (2011) on the relation between foreign investment and local firms’ productivity, and by Chetty, Guren, Manoli, and Weber (2011) on the intertemporal elasticity of substitution in labor supply. We collect 32 aspects of studies, such as the characteristics of data, estimation, inclusion of control variables, number of citations, and information on the publication outlet, and also examine 9 country characteristics. To explore how these characteristics affect the estimates of the border effect, we employ Bayesian model averaging (Raftery, Madigan, and Hoeting, 1997). The method addresses the model uncertainty inherent in meta-analysis by estimating regressions comprising the potential subsets of the study aspects and weighting them by statistics related to the goodness of fit.

The only other quantitative survey on this topic is presented by Head and Mayer (2014, pp. 160–165), who compute the mean and median reported estimates of several important coefficients in the gravity equation, including the border effect, but do not explore why the estimates vary. They collect 279 estimates from 21 studies, in contrast to 1,271 estimates from 61 studies included in our meta-analysis. Head and Mayer (2014) also include estimates of intranational home bias (for example, Wolf, 2000), which we prefer to exclude and focus on the effect of international borders. In consequence, only 10 studies overlap in the datasets of the two meta-analyses.

The remainder of the paper is organized as follows. Section 2 describes how we collect data from studies and discusses the basic properties of the dataset. Section 3 tests for publication selection bias in the literature. Section 4 explores method heterogeneity in the estimated border effects and constructs best practice estimates for different regions. Section 5 relates the border coefficients estimated for different regions to country-level characteristics. Section 6 concludes the paper. The online appendix at http://meta-analysis.cz/border provides the data, code, additional statistics, and list of studies included in the meta-analysis.

The authors usually estimate a log-linearized version of (1) with exporter and importer fixed effects to control for multilateral resistance terms. Some authors use nonlinear estimators, and even for the linear estimation there are many method choices the authors must make. We identify 32 aspects of study design that may potentially influence the estimate of the border effect and explain them in detail in Section 4. We collect estimates of home reported in studies, which is the semi-elasticity corresponding to the ratio of within to between-country trade flows; the border effect can be obtained by exponentiating the semi-elasticity. It is convenient to analyze the semi-elasticities because authors provide standard errors for them and the estimates should be approximately normally distributed.

It is important to stress that the estimates of home from (1) do not measure the counterfactual effect of removing borders, but merely a partial equilibrium effect disregarding any changes in multilateral resistance terms and output. Head and Mayer (2014, pp. 165–170) discuss in great detail the differences between partial and general equilibrium effects of various trade costs, and the influential paper by Anderson and van Wincoop (2003) was the first one to focus on this distinction in the context of border effects. The estimated coefficient home ignores any third-country effects, which are, however, likely because any change in trade costs between two countries changes multilateral resistance with respect to other countries. Additionally, changes in trade costs induce changes in wages and output, which also have to be properly accounted for in any counterfactual exercise. We would prefer to collect and analyze estimates of the general equilibrium effects of borders if there were enough of them in the literature. Since only a couple of studies report general equilibrium effects, we collect estimates of home, derive the estimate conditional on best practice methodology, and then in Section 4 use the exact hat algebra by Dekle, Eaton, and Kortum (2007) to approximate the counterfactual experiment of removing borders.

Our data sources are studies that estimate the semi-elasticities; we call them primary studies and search for them using the RePEc database. We use the following search query for titles, keywords, and abstracts of papers listed in the database: (border OR home bias) AND trade AND gravity. The search yields 370 hits since 1995. We read the abstracts of all the studies and download those that show promise of containing empirical estimates of the border effect. (Some of the 370 studies are theoretical in nature, which is apparent from the abstract, and we do not download those.) Additionally, we examine the references of the studies and obtain other papers that might provide empirical estimates. We stop the search on January 1, 2014. The list of all studies examined is available in the online appendix at http://meta-analysis.cz/border.

We apply three inclusion criteria. First, the study must investigate the effect of international borders. That is, we exclude studies estimating intranational border effects (for example, Wolf, 2000). We expect the mechanism driving border effects in intranational trade to be different enough to call for a separate meta-analysis. Second, we exclude papers that include the “same nation” dummy in the gravity equation as a control variable for territories, such as the overseas departments of France (for example, Rose, 2000). The “same nation” dummy has little variation and often captures trade between a large country and its small territories. (We exclude 7 such studies, mostly taken from the list of studies included in the survey by Head and Mayer, 2014). Third, we only include studies that provide standard errors for their estimates—or statistics from which standard errors can be computed. Without estimates of standard errors, we cannot test for publication bias in the literature. While we conduct the search using English keywords, we do not further exclude any studies based on the language of publication: two studies written in Portuguese are included.

The 61 studies that conform to our selection criteria are listed in the online appendix. Of these, 48 are published in refereed journals and 13 are working papers or mimeographs; later in the analysis we control for the publication outlet of the study and other aspects of quality. The median study in our sample was published in 2007, which shows that the literature estimating border effects is alive and well, with more and more studies coming out each year. Together, the studies have received almost 11,000 citations in Google Scholar, or about 800 on average per year, which suggests the importance of border effects for international economics.

We collect all estimates of the semi-elasticity from the primary studies. The approach yields an unbalanced dataset, since some studies report many more estimates than other studies, but has three big advantages. First, it is demanding and sometimes impossible to select the authors’ preferred estimate to represent each study, so by collecting all estimates we avoid the most subjective stage of meta-analysis. Second, throwing away information is inefficient, and many studies report estimates employing alternative methods or datasets, which increases the variation in our dataset. Third, using multiple estimates per study we can employ study-level fixed effects, which removes all characteristics idiosyncratic to individual studies. In total, we gather 1,271 estimates of the semi-elasticity; the median primary study reports 13 estimates.

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Figure 2 shows a box plot of the estimates reported in the primary studies; the heterogeneity both between and within studies is substantial. It is apparent, however, that most studies report at least some estimates close to 3, near the original estimate by McCallum (1995). A large portion of the heterogeneity in the estimates may be due to differences in data, and especially different countries for which the border effect is evaluated. Table 1 shows the mean estimates for the countries and country groups that are examined most commonly in the literature.

We say that an estimate corresponds to the border effect of a particular country if identification of the semi-elasticity comes from trade flows within the country. For example, if data on trade flows between Canadian provinces are used, such as in McCallum (1995), we consider the estimated border effect Canadian, although the estimation also includes data on the US (flows between Canadian provinces and the US states). Some authors used both province-to-province trade flows and state-to-state flows (for example, Anderson and van Wincoop, 2003); the resulting estimates of the border effect correspond to both Canada and the US and are not shown in the table. The estimates for all other countries and groups of countries are nevertheless included in the overall mean reported in the last row of the table. (Relatively common are also estimates that identify the border effect for the entire world or that use internal trade for Japan, Germany, and Spain.)

Table 1 also shows the corresponding confidence intervals constructed using clustered standard errors. Many meta-analyses cluster standard errors at the study level, because estimates reported in the same primary study are likely to be dependent. Nevertheless, we are not aware of any meta-analysis that also tries to take into account the dependence in estimates due to the use of similar datasets. A few studies in our sample use the same dataset, especially the one introduced by Anderson and van Wincoop (2003), but many others simply add a few years to data used elsewhere. So, we consider datasets to be the same or very similar if they provide data on the same region and start in the same year, and additionally cluster standard errors at the level of similar datasets. The implementation of two-level clustering follows the approach of Cameron, Gelbach, and Miller (2011).

The left-hand part of the table shows unweighted estimates; the right-hand part shows estimates weighted by the inverse of the number of observations reported in each study. Using these weights, we assign each study the same importance; otherwise, studies reporting many semi-elasticities drive the results. The mean unweighted estimate of the semi-elasticity equals 3, virtually identical to the original estimate of the parameter by McCallum (1995). This semi-elasticity implies a border effect of \(\exp (3)=20\), which means that an average region in an average country trades twenty times more with regions in the same country than with foreign regions of similar characteristics. The 95 percent confidence interval for the mean estimate of the border effect is (13, 34), which shows substantial uncertainty due to differences in methodology.

In Table 2, we report the mean estimated semi-elasticities for particular subsets of methods and studies. When compared with Table 1, it seems that the effect of methods on results is less pronounced than the effect of the choice of the region for which the border effect is estimated. Some method choices bring systematically different results, but the impacts get muted when we move to the right-hand part of the table where each study is assigned the same weight. Estimates obtained using panel or disaggregated data tend to be somewhat larger, while the use of actual within-country trade flows (as opposed to approximating internal trade using production data) and inclusion of zeros are associated with smaller estimates. Published studies report mean estimates virtually identical to those of unpublished studies, and the average results also do not change much in time. Because authors often change several data and method characteristics simultaneously, and there are many additional aspects of study design that might influence the estimates; in Section 4, we use meta-regression analysis to investigate in detail the marginal effects of data and method choices on the reported border effects.

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Figure 3 shows the histogram of the estimated semi-elasticities. We see that almost all the estimates are positive; in the data we only have 22 negative estimates, 1.7 percent of all the semi-elasticities. The median estimate is very close to the overall mean and equals 2.9. The median estimate of the median semi-elasticities reported in individual studies equals 2.6, which is virtually identical to the mean of the estimates weighted by the inverse of the number of estimates reported per study. The closeness of the mean and median together with the shape of the histogram suggests that there are no serious outliers in our dataset, so we do not exclude any estimates from the meta-analysis.

The journals in which the primary studies are published differ greatly in prestige and rating. On the one hand, some studies are published in top field and general interest journals; on the other hand, many estimates come from studies published in local outlets. To illustrate the potential differences in quality, we distinguish a group of studies published in top field or top or second-tier general interest journals: the American Economic Review, Journal of International Economics, International Economic Review, European Economic Review, and Journal of Applied Econometrics. Eleven studies in our sample are published in these journals and they report a median semi-elasticity of 1.7, implying a border effect of 5.5, less than a third of the overall mean effect. Studies in respected journals seem to report smaller semi-elasticities, but the pattern may be explained by differences in methodology. Another potential reason for such differences is publication selection if good journals put a premium on solving the border puzzle.

Publication selection bias arises when estimates have a different probability of being reported based on their magnitude or statistical significance. Sometimes, it is called the “file drawer problem” (Rosenthal, 1979): researchers may hide in their file drawers estimates that are insignificant or have an unintuitive sign and search for estimates that are easier to publish. Publication bias has been identified in empirical economics by, for example, DeLong and Lang (1992), Card and Krueger (1995), Ashenfelter, Harmon, and Oosterbeek (1999), Havranek and Irsova (2012), and Havranek (2015). In a survey of examinations of publication bias, Doucouliagos and Stanley (2013) find that most fields of empirical economics are seriously affected by the problem. Because the potential presence of publication bias has implications for the weights that should be used in meta-analysis, we test for the bias before we proceed to the analysis of heterogeneity.

If researchers preferentially report estimates that are statistically significant and have the expected sign, the literature as a whole exaggerates the effect in question. For example, Stanley (2005) finds that the mean estimate of the price elasticity of water demand is exaggerated fourfold because of publication bias. The problem is widely recognized in medical science, and the best medical journals now require registration of clinical trials before publication, so that researchers can find the results of all trials, even though some are not submitted for publication. In a similar vein, the American Economic Association has agreed to establish a registry of randomized experiments “to counter publication bias” (Siegfried, 2012, p. 648).

The presence of publication bias can be examined visually using the so-called funnel plot (Egger, Smith, Scheider, and Minder, 1997). It is a scatter plot showing the magnitude of the estimated effects on the horizontal axis and the precision (the inverse of the estimated standard error) on the vertical axis. If the literature is not influenced by publication bias, the most precise estimates of the effect will be close to the mean underlying effect. As the precision decreases, the estimates get more dispersed, forming a symmetrical inverted funnel. In the presence of publication bias, the funnel becomes asymmetrical (if researchers discard estimates of a particular sign or magnitude), or hollow (if researchers discard statistically insignificant estimates), or both.

We report the funnel plot for the border effect literature in Figure 4. Panel (a) shows the funnel for all estimates; panel (b) shows only the median estimates for each study. We make three observations from the funnels. First, both funnels are relatively symmetrical, with the most precise estimates being close to the average reported semi-elasticity. Second, the funnels are not hollow, and even estimates with very little precision (and, thus, small p values) are reported. Third, the funnel in panel (a) has multiple peaks, which suggests heterogeneity in the estimated border effects. Signs of heterogeneity are not surprising given our estimates of cross-country differences in the previous section. We conclude that typical funnel plots reported in economics meta-analyses show much clearer signs of publication bias than what we observe in the literature on border effects (see, for example, Stanley and Doucouliagos, 2010).

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The analysis presented so far has shown that border effects vary across regions and that such country heterogeneity is at least as important as the effects of method choices. A natural extension of the previous section is to try to explain the sources of country heterogeneity by substituting country-level characteristics for regional dummy variables. The meta-analysis framework is well suited for such an exercise because it allows us to examine heterogeneity in the border coefficients reported by many studies for a large number of regions (countries or groups of countries) while controlling for differences in methodology.

Nevertheless, the 61 studies in our sample taken together have examined the border effect for 31 regions, a number which would still not allow for a meaningful regression analysis. To extend the number of unique observations and thus variation for country-level variables, we use the fact that studies estimate the border effect for different time periods. To each estimate of the border effect we assign the value of the country characteristic that is the closest available to the average year of the data period used in the primary study. This approach yields 188 unique observations of country-level characteristics for 1,271 estimates of the border effect, which means that proper clustering is necessary not to inflate the statistical significance of our results. As in other parts of the analysis, we use two-way clustering at the level of studies and datasets.

What factors can explain the estimated border effects? The estimates, of course, only represent a reduced form of measuring the effect of various trade frictions. The extensive survey by Anderson and van Wincoop (2004) mentions the following categories of frictions that might help decompose the border effect: language barriers, currency barriers, information barriers, contracting costs and insecurity, and nontariff policy barriers. While the first two categories are in most cases controlled for by the authors of primary studies themselves, using meta-analysis we can examine the relative importance of the remaining three categories of frictions. For the selection of individual country-level characteristics, we turn to the theoretical models of the border effect. (A detailed description and summary statistics of country-level variables are available in the online appendix.)

The best known model, Anderson and van Wincoop (2003), stresses the role of relative country size (aside from the paper’s focus on theory-consistent methodology): smaller countries are expected to exhibit larger border effects. The intuition is that small countries tend to trade relatively more with the rest of the world compared to large and therefore typically less open economies. A border barrier between a small and a large country thus has a stronger effect on multilateral resistance of the regions in the smaller country, which increases within-country trade to a larger extent for the small country than for the large one. On the other hand, Balistreri and Hillberry (2007) argue that this implication of the model hinges of the assumption of symmetric border costs. To examine the empirical relevance of country size for the border effect, we include the ratio of GDP of the home country (that is, the country for which the border effect is estimated, as defined in Section 2) to the average GDP of foreign countries (the other countries included in the estimation). Many studies examine the border effect using data on interprovincial trade in Canada and province–state trade between Canada and the US; in such studies, Canada is considered the home country and we include the ratio of Canadian GDP to the US GPD for the average year of the data period used for estimation.

Wilson (2015) provides a comprehensive theoretical framework for the examination of the causes of the border effect. He shows that the effect can be explained by three categories of frictions: trade costs, differences in taste, and information barriers; the model stresses the role of information. Trade costs associated with crossing the border, such as tariff and nontariff barriers, can of course explain a sizable part of the border effect, and we include the corresponding country-level controls for these two factors. To capture consumers’ preference for local products, we include two variables. The first one measures the difference in GDP per capita between the home country and foreign countries: we hypothesize that tastes are correlated with the level of development of the country. In other words, consumers in the home country are more likely to prefer domestic goods when the available foreign goods come from a country at a substantially different stage of development. As a second proxy for home bias in preferences, we include national pride measured by the percentage of answers “very proud” to the question: “How proud are you of your country?” in the World Values Survey.

Concerning information barriers, they are mentioned as potential contributing factors to the border effect by both Anderson and van Wincoop (2004) and Wilson (2015). We choose the number of fixed broadband subscriptions per 100 people in the home country as a measure of Internet usage and proxy for information barriers. With the spread of online shopping, consumers have more information on the availability and prices of foreign goods, which is likely to affect border effects. Next, Anderson and van Wincoop (2004) mention contracting costs and insecurity as a potential factor contributing to the border effect. We control for the volatility of the exchange rate in the home country, because excess volatility contributes to insecurity and may hamper foreign trade; moreover, Parsley and Wei (2001) show that exchange rate volatility helps explain the observed cross-border price dispersion. Additionally, we include the financial development of the home country, because with restricted access to credit the opportunities for domestic firms to engage in foreign trade are limited. Finally, we include the World Bank’s measure of rule of law in the home country relative to foreign countries, which is also associated with contracting costs and insecurity. Schwarz (2012) shows that differences in the quality of institutions are responsible for a large part of the observed cross-border price dispersion.

Despite the low power of the exercise, we find that country size is strongly associated with the reported border effect; the corresponding parameter is statistically significant at the 1 percent level in all three specifications. The results suggest that smaller countries exhibit larger border effects, which is consistent with the model presented by Anderson and van Wincoop (2003). As expected, a part of the border effect can be explained by tariffs, since researchers report larger border effects for countries with higher tariffs. The corresponding parameter is statistically significant at the 1 percent level in the first specification and has p values of 0.12 and 0.16 in the remaining specifications. Equally important are nontariff barriers, which also contribute to border effects (the p values for this coefficient estimated in the three models are 0.13, 0.04, and 0.01, respectively).

The control for a country’s financial development is included in two out of three models and is statistically significant at the 5 percent level in one of them. The sign of the coefficient is negative, which corroborates the hypothesis that domestic credit availability is an important determinant of foreign trade and thus the size of the border effect. But the finding is not robust: in the second specification, the coefficient gets nowhere near statistical significance with a p value of 0.42. Exchange rate volatility does not affect the size of the reported border effect significantly. In contrast, the difference in GDP per capita between the home and foreign country is important, which suggests that local tastes might play a role in explaining the border effect. Nevertheless, our second proxy for local tastes, national pride, is insignificant. Similarly insignificant are proxies for information barriers and contracting costs.

In sum, our results are consistent with the model of Anderson and van Wincoop (2003) and stress the role of country size in explaining the differences in reported border coefficients. Trade costs, such as tariff and nontariff barriers, also appear to matter for border effects, although these factors obviously do not explain the US–Canada border effect found to be substantial by many studies. Relatively less important are information barriers and contracting costs, at least for our chosen proxies. It is, however, necessary to note that even when we include method variables we are still unable to explain about 50 percent of the variance in the reported border effects (although such levels of the R-squared are typical in meta-analyses; see Disdier and Head, 2008).

We conduct a meta-analysis of the effect of international borders on trade. Using 1,271 estimates from 61 studies and controlling for differences in study quality, we show that the available empirical evidence suggests a mean reduction of 33 percent in international trade due to borders (and an increase of 277 percent in intranational trade due to borders). Good practice methodology in estimating border effects yields smaller estimates. Our results are close to those of Anderson and van Wincoop (2003), who find that borders reduce trade among industrialized countries by 29 percent. The innovations introduced in the last decade to estimating the gravity equation alleviate the border puzzle worldwide and almost solve it for some OECD countries. Nevertheless, even after controlling for the advances in methodology we obtain large border effects for transition and developing countries.

Our meta-analysis suggests that the country-level differences in border effects can be partially explained by theory-motivated variables. For instance, the model by Anderson and van Wincoop (2003) implies that larger countries should exhibit smaller border effects, and this is precisely what we observe in the empirical literature. Moreover, trade costs are positively associated with border effects, as larger border effects are reported for countries with larger tariff and nontariff barriers to international trade. We also find that pairs of countries with similar levels of GDP per capita tend to share smaller border effects, which might reflect the importance of consumer tastes.