Lothar Krempel and Thomas Plümper

krempel@mpi-fg-koeln.mpg.de
thomas.pluemper@uni-konstanz.de

Exploring the Dynamics of International Trade by Combining the Comparative Advantages of Multivariate Statistics and Network Visualisations

An  online version and the color images are available under:
Version 2.1. 14.07.1998    http://www.mpi-fg-koeln.mpg.de/~lk/netvis/visualtrade
Paper prepared for the Joint Conference of the International Studies Association and the European Council for Political Research, Vienna, 16.-19.09.98. An earlier version was presented at the Sunbelt XVIII and Fifth European International Social Networks Conference, Sitges, Spain, May 1998. We thank Steffen Baumann, ..., and the participants at the various conferences for helpful and encouraging comments.

1 Introduction

There is little doubt that multivariate regression analysis is among the most appropriate tools to test hypotheses if sufficiently reliable data is available. During the last decades statistical analysis has been refined and an ever growing set of statistical tests and sophisticated approaches enable the researcher to cope with all kinds of ambiguities in the analyzed data sets (White 1980; Beck/ Katz 1995; Cramer 1986). Crucial for obtaining valid parameter estimates with regressions is the degree to which the common assumptions of regression analysis are met, especially that of the independence of the error terms and whether these have the same variance. While statistical analysis provides tests to check whether a given model meets these assumption or not, these tests are not very instructive on how to improve a given model in case the assumptions are hurt. To cope with these problems within the research process we suggest to extend the researcher's toolkit by a second technology. Tools for visualizing social structures can improve the specification of a given model if there is structure in the error terms. These visualizations allow not only to monitor the spatial organization of the resulting estimation errors but also guide the researcher how to improve the quality of the parameter estimates.
In this article we will show how the visualization of the overall structure of world trade provides a very useful tool to enhance and analyze gravity models. The problem of international trade analyzed in this paper can be considered as fairly typical for the use of quantitative estimates. Crude estimates for trends in economic processes can be obtained by comparing parameter estimates cross-sectionally and between different points in time. The ratio of corresponding estimates provides an insight into the dynamics of international economic activities. Furthermore, since the internationalization of economic activities can easily be measured y an analysis of the bilateral trade flows between countries, the widely acknowledged standard problem of social research - the small-N problem, does not occur. [1] On the other hand, the large number of observations makes an interpretation of error terms problematic. This is, where network visualization tools can help. The fruitfulness of the interplay of both technologies for that purpose is based on the fact that both extract different kinds of information gravity models are usually based on. While statistical tools treat flows as independent units, visualizations can make use of any relational information that describes the pairs of the observations as they are used for the regression analysis. Visualizations provide the researcher with a view of the overall system.
Our purpose here is twofold. First, we link statistical analyses and visualization techniques and use both tools in parallel for a stepwise improvement of gravity models. And second, we apply the method to the analysis of international economic processes, showing that concepts aimed at the explanation of global economic processes grasp just aspects of global economic processes. We conclude, therefore, that economic integration is best studied by a non-eclectic mixture of seemingly competing theories.

2. Specifying the Model by Stepwise Approximation

In this section we develop a baseline gravity model. The estimates presented in this section are based on bilateral trade between the thirty biggest trading nations in 1994. In the comparative static extension of this model in the section 3 the number of countries is widened to 45 countries. Furthermore, we present some evidence by comparing the estimates for the fifteen years between 1980 and 1994.
A commonly accepted method to inspect the factors influencing trade flows within a set of countries is to perform a regression analysis on the volume of all trade flows occurring between these countries. This implies that the flows between different countries are independent from each other. Even though this assumption is certainly not completely beyond criticism, economists are still willing to accept it. As we have emphasized earlier, a sufficient model in technical terms is not only characterized by the amount of explained variance. Any parameter estimates are only valid in the absence of systematic errors. The tool employed to detect systematic error components is the mapping of the residuals on the overall geographical structure of trade.

2.1. The Technology of NetVis-Visualization

In an earlier paper (Krempel/ Plümper 1997) we have shown that the information contained in the trade data can be used to reconstruct this overall pattern of global trade. The emerging structure is a very useful basis for the evaluation of specific international occurring phenomena. The technique of projecting the residuals on a structure allows to locate a given systematical pattern. Consequently, using such visualizations supplies the researcher with additional information. As opposed to this it is difficult to retrieve this particular supplementary information from the outcomes of statistical procedures by itself. The fallacy of multivariate regression as an analytical tool may very well be that it has basic shortcomings for both, small-n as well as large-n regressions.
For the visualizations in this paper we use a placement of the countries, which tries to preserve the rank order of their geographical distances. A placement reflecting the distances between all countries involves to map the surface of a sphere (the globe) onto a 2 dimensional plane - a task for which geographers usually choose one out of several projections rules. Each of these rules is known to produce systematic distortions of the distances in the resulting images. For our purpose a schematic placement of the countries seems to be most appropriate. The distance structure used for all images in this article has been produced with a spring embedder (Eades 1984, Davidson and Harrel 1996). This is an algorithm that is capable of handling all the distances simultaneously and thereby produces an equilibrium solution for the total structure. Additionally these algorithms can make the resulting image more readable by allowing to impose additional constraints on the solution. Dense centers are spread, while huge distances get shrunk. In addition, all bilateral trade flows are mapped onto this placement. The volume of flows is symbolized by the size of the arrows linking any two nodes in the image.
In order to link the visual approach to the statistical analysis, we use the overall trade structure to inform us about the volume of the flows and colors to inform us about the quality of estimates. By mapping the error terms, we not only evaluate the model's fit but also try to show what is not captured by a given model. The visualization of the errors reveals any systematic organization in the unexplained variance, which is distance or neighborhood related. We have stressed before that any well fitting model implies a random distribution of the error terms. Thus it is of special interest if we find any coherent pattern when mapping the errors of a specific model onto the trade flows' visualizations. Any such pattern identified is thus an indicator of the insufficiency of a model, because the assumption of the randomness of the error terms is clearly violated.
This visual approach has several advantages compared to other ways of evaluating the model's quality. Contrary to classical statistical procedures that try to validate the model assumptions by testing for heteroskedasticity and autocorrelation (Hanushek/ Jackson 1977, Wonnacott/ Wonnacott 1979), the visualizations of the errors do not only give evidence about the insufficiency of a model but also help to locate where and to which degree single countries constitute exceptions that are not captured with a specific model. In other words, this procedure helps us to eliminate the sources of heteroskedasticity and autocorrelation instead of just circumventing its consequences as White-corrected standard errors (White 1980) or similar procedures do.
Whether a given trade flow is misrepresented can be easily inspected visually. If flow estimates of a given dyad are false, the connecting arrows between the couple of nods appear colored. To capture stronger distortions visually, we use different degrees of deviation of the estimated trade value from the observed. The information that we gathered in the arrows is aggregated to country information in the nodes. Nodes symbolize the total of the imports and the exports by the degree to which parts or even all of a country's trade is deviating from the estimates of a given model. The degree, a specific country is consistently over- or underestimated, can easily be read from the countries symbols used in the visualizations.
In the aggregate, systematic estimation errors for even larger regions should appear as similar colored clusters in the visualizations. Areas of large standard errors point to geographic imperfections of a given model. Moreover, functional imperfections of a given model can also be detected if the researcher has good working hypothesis about a possible correlation between two functional variables. We will later show that a loose economic tie between nations belonging to the British Commonwealth of Nations still exists. Trade between two Commonwealth Nations are positively influenced by political, cultural or economic links, or - if one is unwilling to except that cultural factors determine this effect - one may think in terms of an easing of business activity due to a common language.
Supplementing the statistical modeling efforts with the above described visualizations does not only provide useful information about the appropriateness of a model but also makes it easier to think of additional factors. We stepwise include detected variables to enhance the model and its prediction. After a series of such refinements and enhancements we will proceed to the final step of our analysis. We introduce dummy variables for the different regions of world trade and turn to a larger sample of countries to test the robustness of our findings and to analyze the international economic dynamics in comparative statics analysis. The estimates for these regions obtained in the last step can be understood to give a comparative characterization of the preferences for regional trade in absence of distance, size of GNP and maritime transportation, joint borders etc.

2.2 Improving the Gravity Model by `Eye-Bowling'

The basis of our analysis is a selection of the 30 biggest countries as traders in the world trade and their bilateral (asymmetric) trade in 1994. The dependent variable is the log of the values of goods traded from a country i to country j. As open economics differ from closed economics since they can borrow resources from the rest of world or lend them abroad (Obstfeld/ Rogoff 1996: 1), trade flows from i to j are not necessarily identical to the value of the flow from j to i. The most simple model uses the distance between the trading partners as a proxy for transportation costs. While transportation costs is only one component of the overall transaction cost (tariffs and non-tariff barriers to trade, communication costs, market entry costs, information collection costs etc.. ), it is nevertheless the best single indicator available and it should to a certain extent reflect any changes in world trade stemming from an increasing internationalization.
The degree of economic internationalization can best be estimated by starting with a simple model. The first and most simple model tries to explain the trade flows between all countries by their geographical distance. In this first iteration of `stepwise approximation' we use the (log) distance as a single explaining variable for all countries. Geographic distance is a crude but very basic indicator for transportation cost. Hence, we estimate
)
Furthermore, we use the log of distance as a first independent variable. With increasing geographical distance the volume of trade should decrease. The choice of the logarithm of the distances is consistent with the fact that transport is a combination of fixed and variable cost. The loading and unloading of freight is more costly than the actual transport. Choosing the log distance as a proxy for the variable cost reflects the diminishing increase of the variable cost with long distance transport according to the `iceberg model' of economic geography (Krugman 1998).
The distances used for our analysis are based on the location of the capitals of all countries and are computed as the grand circle distances. Even though these distances are a fair indicator for the transportation costs of distant countries, they appear to be not completely without problems. Problematic are dyads consisting of neighboring countries or dyads in which the capital of at least one of the countries is strongly dislocated from the country's geographical center. If both conditions are given, we expect a crucial underestimation of real trade by the model. Consider Hong Kong and China (Beijing) where most of the trade take place between Hong Kong and the southern provinces of China. Residuals Model 1

Using the geographical distance as a single independent variable in our first model, we find an explained variance of 17 percent in 1994. The negative estimate for b = -.8274 indicates that distance and transportation costs still matter in the world trade of 1994. A closer look at the visualization of the errors reveals, that especially the large trade flows are heavily underestimated in this model. For the large traders (symbolized with the size of their spheres, respectively the pies for their total imports (top) and exports (bottom), we find, that almost all of their trade is underestimated: large countries trade more than can be estimated with the knowledge of the distance of their trading partners. The reverse is true for small countries.
Model 2 corrects this wrong specification be introducing country size into the
model. We additionally take the GNP of both trading partners into account.

Such a model usually creates the core of a gravity model: "Flows in human geography are often termed spatial interactions, and a spatial interaction model is an equation that predicts the size and direction of some flow (the dependent variable) using independent variables which measure some structural property of the human landscape." (Thomas/ Huggett 1980).
The basic principle of a gravity model is Newton's law of gravity. They commonly assume that large objects exhibit a greater `pulling power' than small objects and that close objects are far more likely to be attracted by each other. Gravity models are known to produce good fit when estimating the amount of goods traded between countries.[2] They assume that the trade flows rise with the size of the GNP of both countries: while two large neighboring countries are expected to have the largest amount of trade, the volume is expected to decrease with the growing distance by a factor b as estimated in the model.
We have experimented with the size of exporting/importing countries and larger/smaller countries respectively without finding any significant differences. Hence, size differentials and especially the size of the smaller country may be less influential on actual trade flows than economists usually seem to believe. The effects of the GNP are given by the parameters c and d.
Residuals Model 2

Including the GNP of all countries to estimate the trade flows dramatically improves the explained variance to 60 percent for the 1994 model and increases the number of (almost) correctly estimated flows from 238 to 325 (as can be read from the distribution in the upper right). While the quality of estimates has improved for many countries, we find the trade between the US and Japan still to be underestimated with this second model. This is also true for much of the trade in the Asian region and for the trade from Asia to the USA. Therefore, the third model includes a dummy for all bilateral trade occurring between countries located on the same ocean: either the Pacific or the Atlantic. This allows to estimate the beneficial effect of maritime trade routes and their lower transportation cost. For both variables we expect the signs of the coefficients to be positive, indicating higher trade volumes to occur between countries that profit from maritime trade.
The inclusion of maritime trade improved the model further to 62.8 percent of explained variance and improves especially the estimates for flows that were miscalculated in model 2. A separate estimate of the two major oceans displays that the parameter estimate for the trade in the Pacific Rim is higher than the estimate for the Atlantic (0.5072 versus 0.3811). Most of the shipping costs seem to be a result of loading and unloading.
While the estimate for the trade between Japan and the US is now only moderately misrepresented (to low), the trade between Hong Kong and China and somewhat more surprisingly also the trade between Korea, Singapore and Malaysia are consistently estimated too low. We correct further imperfections by including a border dummy for all dyads of countries sharing a common border. The coefficients are expected to be positive. It is more likely that neighboring countries have higher trade volumes. Taking the increased trade volumes between neighboring countries into account, the overall model improves to 64 percent of the explained variance. While the increase in trade for neighboring countries is found to be quite strong, it is, however, much smaller than the estimate for the impact of the overall distance. Looking at the errors after removing the common border effect from the errors, we still find that the trade in Asia is underestimated to a considerable degree, namely between Hong Kong and China but also the trade between and with Malaysia and Singapore.
Our final approximation also includes dummies for different world regions and allows us to access the degree to which regional trade integration exists in different geographical areas, discounting all explanations that we have introduced through the use of the less complex models. The estimates for the different regions provide information about the extent local economic integration leads to more trade in specific world regions than would be expected form the pure knowledge of distance, size of GNP, maritime and common borders alone. Such an estimate of local integration slightly differs from studies that simply relate to the growth of local trade only. The degree of local integration as it is expected for regional economic areas, the EU, the NAFTA, and the Asian members of APEC respectively denoted by FTA-dummies leads us to expect positive parameter estimates.

We find a further improvement of our model. 69 percent of all variance in world trade is now explained and a correct estimates for more than 339 flows is given.

Residuals Model 5
The intraregional trade estimates are strongest for Asia (0.4851), and are not significant for North America (0.2085) and Europe (-0.1706). Evaluating the error terms of this fifth model, in which now all regional effects are discounted, almost all flows are estimated with modest distortions only. Though this is the most improved model advanced in this article, there still exist some systematic errors as the visualization shows.
As the estimate for the trade between Hong Kong and China has improved by treating it as intra-Asian trade, most of the imperfections of the fifth model are still connected to Hong Kong. This effect of Hong Kong's harbor function for mainland China diminished with the Chinese unification. Furthermore, underestimation also occurs for the flows between the countries of the old British Empire, respectively the Commonwealth countries, namely Great Britain, Hong Kong and Australia. This leads us to suspect a language effect of international trade: Trade between countries of a single language trade more, an effect that seems to last even in a `globalized' world economy (language is controlled in Plümper 1998).

3. A Simple Gravity Model and the Dynamics of International Economic Integration

In the remainder of this paper we shortly evaluate the dynamics of international economic integration by and large based on the model specification developed in section 2. We show that the model can contribute to an ongoing debate in International Political Economy. Within this research tradition, the sources of global economic processes are widely discussed. At least three major theories can be distinguished. We refer to these theories as globalization theory, regionalization theory and macroeonomic imbalances theory. Note, however, that globalization and regionalization theory lack a coherent microeconomic foundation.
Globalization scholars basically accept that globalization is a phenomenon that covers all countries and world regions. In their view, the tendency towards a closer integration stems from a relative easing of international economic transactions compared to national business activity (Frieden/ Rogowski 1996). The costs of international economic exchange relative to within-border transactions exogenously decrease as a result of technological change and political liberalization. Thus, the perspective of a globalizing economy implies that borders and geographical distance get less important: more and more goods are expected to be traded over longer distances due to reduced transportation and transaction cost.
The most widely heeded competitor for the globalization line of reasoning is regionalization theory. Proponents of this theory consider regional dynamics instead of global dynamics as the driving force behind economic internationalization. Regional free trade areas such as NAFTA, the European Union and the ASEAN support this view (Coleman/ Underhill 1998). The abolition of tariffs and non-tariff barriers to trade and the establishment of preferential treatments for their member states is aimed to increase the volume of trade within the regions. Authors from globalization and regionalization traditions disagree if the dynamics of international economic processes mainly stem from regional or global forces. While the hypothesis of globalization literature implies a general easing of international economic exchange, scholars analyzing regions usually stress the huge and increasing share of interregional trade. In their view, the `relative easing' of economic transactions not only place within the three dominant world regions, namely in Europe (the EU), North-America (NAFTA) and South-East-Asia (APEC), but also are caused by regional liberalization measures and therefore policy-driven.
A third view, shared by just a small fraction of authors, most notably by Paul Krugman (Krugman 1990; Krugman 1996), understands global economic processes as a consequence of global economic imbalances. The increasing budget deficit of the industrialized states and the growing differences in national saving and investment figures serves as an engine of international capital flows: Due to the accounting identities between capital flows and trade in commodities and services these negative capital flows need to be balanced by international trade. Krugman expects bilateral economic interactions to change most between countries, with large imbalances of national savings and national investment. International economic integration does not play a mayor role in fuelling global economic processes. Countries characterized by a trade deficit are net importers of capital, whereas countries with a savings surplus export capital. The most prominent country with a national saving deficit is the USA, minor capital importers are most of the rapidly developing countries of South East Asia. Japan on the other hand is the main example for a country with a high surplus.
The three theories differ fundamentally in regard to the expected localization of global economic processes. While overall decreasing transportation costs should lead to a diminishing effect of geographical distance in general. Moreover, the theory predicts that the structure of world trade remains fairly stable. On the other hand, a stronger regionalization should increase the estimated parameter of regional dummies due to a relative increase in intra-regional economic transactions and a relative decline in interregional trade. And according to the inequality school we should expect most change to occur within the Pacific area, while the Transatlantic and European economic relations remains stable.
To our knowledge, none has assumed overlapping processes. In what follows, we use an extended version of the model developed in section 2 to separate the three dynamics from each other and to estimate their sole contribution to the current dynamics of the world economy. Gravity models are especially useful for this analyses, because they may separate regional from intra-regional transactions. However, one striking feature of commonly used gravity models is the neglect of dynamic aspects of spatiality. This limits its usefulness for the currently widely debated aspect of international economic integration. Since globalization theories deal with the consequences of economic processes, a dynamic or a comparative static gravity model is a necessary condition for a contribution of spatial models to globalization theory. As yet, economic geography scholars have only modestly engaged in analyzing economic dynamics. To our knowledge, the problem of spatial dynamics has been dealt with in an complex simulation study of Fujita, Krugman and Venables (forthcoming) and just a few spatial models analyze the long run effects of economic differentiation and concentration. Anthony Venables (1995) has assumed that factors of production are less mobile between countries than between different regions of the same country and analyzed the spatial order resulting from this plausible assumption. Krugman and Venables (1995) has used this model to show how gradually declining transportation costs lead to a first spontaneous differentiation into a high-wage core and a low-wage periphery and eventually to a convergence of wages as the periphery industrializes.
We may conclude that in spite of the considerable fruitfulness of gravity models for the analyses of spatial economic processes, the existing studies do not contribute to the ongoing debate on global economic processes as much as seems to be possible. We believe that gravity models can contribute to the globalization debate. Globalization theory is still dominated by armchair reasoning while only a handful of scholars engage in sophisticated empirical studies (see for example Garrett 1995, 1998; Lawrence 1996; Hallerberg/ Basinger 1998) and an theoretical underpinning of empirical results (Krugman 1995). Economic geography offers the promise to combine the globalization theories with a more rigorous theoretical foundation. Differences between the following model and the model developed before are due to the degree of complexity. The model estimated below is much more complex with regard to the differentiation between world regions. Moreover, the parameters of the model are calculated with data based on 1880 dyads of countries. The data includes the 45 most important trading nations. The difference between the 1880 actually included cases and the 1936 possible dyads result from the exclusion of dyads, in which one of the countries does not report or the total amount of trade actually reported does not exceed 10.000$ per year. We may justify this omission, since data becomes fairly imprecise and extremely volatile, if a dyad of countries' trades just small values.


The results calculated from the data is exhaustively discussed in another paper (Plümper 1998). We nevertheless present the estimated coefficients in the following table to show that the model leads to fairly reasonable and interesting results. The reported results are by no means trivial.
 
 
1980 1982 1984 1986 1988 1990 1992 1994
Y-Intercept -13,1164 
(0,5049) 
**** -12,9857 
(0,4930) 
**** -12,9599 
(0,4901) 
**** -12,8653 
(0,4345) 
**** -12,5309 
(0,4041) 
**** -12,5739 
(0,4033) 
**** -12,3768 
(0,3843) 
**** -12,3748 
(0,3701) 
****
LogDIST -0,7268 
(0,0493) 
**** -0,7431 
(0,0482) 
**** -0,7432 
(0,0488) 
**** -0,6350 
(0,0439) 
**** -0,6260 
(0,0410) 
**** -0,6238 
(0,0406) 
**** -0,6385 
(0,0380) 
**** -0,7083 
(0,0371) 
****
LogGDPx 1,0090 
(0,0291) 
**** 1,0173 
(0,0288) 
**** 0,9797 
(0,0286) 
**** 0,9373 
(0,0248) 
**** 0,9291 
(0,0230) 
**** 0,9143 
(0,0228) 
**** 0,9355 
(0,0218) 
**** 0,9402 
(0,0213) 
****
LogGDPm 0,8805 
(0,0290) 
**** 0,8604 
(0,0287) 
**** 0,8984 
(0,0284) 
**** 0,8900 
(0,0247) 
**** 0,8594 
(0,0229) 
**** 0,8715 
(0,0226) 
**** 0,8389 
(0,0216) 
**** 0,8606 
(0,0211) 
****
EAST-EUROPE 0,8718 
(0,2731) 
*** 0,7541 
(0,2666) 
*** 0,7629 
(0,2698) 
*** 0,8715 
(0,2431) 
**** 0,7437 
(0,2270) 
*** 0,6019 
(0,2247) 
*** 0,4908 
(0,2102) 
** 0,2204 
(0,2040) 
WEST-EUROPE 0,1476 
(0,0613) 
** 0,2464 
(0,0596) 
**** 0,2833 
(0,0603) 
**** 0,2993 
(0,0547) 
**** 0,2638 
(0,0514) 
**** 0,2768 
(0,0512) 
**** 0,2015 
(0,0480) 
**** 0,1640 
(0,0463) 
****
ASIA 0,3840 
(0,0586) 
**** 0,4555 
(0,0572) 
**** 0,4131 
(0,0579) 
**** 0,4884 
(0,0521) 
**** 0,5227 
(0,0486) 
**** 0,5787 
(0,0481) 
**** 0,5415 
(0,0451) 
**** 0,4692 
(0,0438) 
****
SOUTHAMERICA 0,3726 
(0,1509) 
** 0,2477 
(0,1474) 
* 0,2836 
(0,1492) 
* 0,2138 
(0,1344) 
0,3502 
(0,1255) 
*** 0,3152 
(0,1242) 
** 0,2816 
(0,1161) 
** 0,2719 
(0,1127) 
**
NORTHAMERICA 0,0234 
(0,2726) 
0,0952 
(0,2665) 
0,0267 
(0,2700 
0,0539 
(0,2458 
0,1334 
(0,2264) 
0,1568 
(0,2241) 
0,2141 
(0,2097) 
0,2664 
(0,2036) 
AFRICA -0,0638 
(0,4589) 
0,2804 
(0,4483) 
0,4404 
(0,4538) 
0,5488 
(0,4086) 
0,7754 
(0,3814) 
** 0,8365 
(0,3772) 
** 0,8593 
(0,3528) 
** 0,5851 
(0,3426) 
*
OCEAN 1,1533 
(0,4573) 
** 1,1580 
(0,4466) 
*** 1,1643 
(0,4521) 
** 1,1827 
(0,4071) 
*** 1,1080 
(0,3800) 
*** 1,2284 
(0,3759) 
*** 1,2689 
(0,3516) 
**** 1,1916 
(0,3414) 
****
BORDER 0,1619 
(0,0889) 
* 0,1663 
(0,0869) 
* 0,1743 
(0,0880) 
** 0,2421 
(0,0792) 
*** 0,2596 
(0,0739) 
**** 0,2763 
(0,0731) 
**** 0,3106 
(0,0684) 
**** 0,2253 
(0,0665) 
****
EU-AS 0,0759 
(0,0372) 
** 0,1189 
(0,0364) 
*** 0,1018 
(0,0369) 
*** 0,1038 
(0,0333) 
*** 0,1198 
(0,0311) 
**** 0,1651 
(0,0309) 
**** 0,1161 
(0,0289) 
**** 0,1111 
(0,0280) 
****
NA-EU -0,2151 
(0,0690) 
*** -0,1524 
(0,0674) 
** -0,2021 
(0,0685) 
*** -0,2313 
(0,0613) 
*** -0,2046 
(0,0572) 
**** -0,2039 
(0,0569) 
**** -0,2529 
(0,0533) 
**** -0,2940 
(0,0514) 
****
AS-NA -0,0092 
(0,0780) 
0,0405 
(0,0765) 
-0,0376 
(0,0780) 
0,0046 
(0,0696) 
0,1307 
(0,0649) 
** 0,1630 
(0,0644) 
** 0,1264 
(0,0604) 
** 0,1235 
(0,0586) 
**

Table 1: The Dynamics of International Trade Source: Thomas Pümper: The Dynamics of International Trade, unpubl. Manuscript, Universität Konstanz, 1998.

Table 1 shows that all three theories of global economic integration discussed in section 2 help to explain some aspects of global economic processes, while others remain unexplained.
Globalization theory nicely explains the decline in the estimated parameter of logDISTij between 1984 and 1992. However, it is unable to explain why the trade limiting effect of sheer distance declines as rapidly as it does and is even less well-equipped to specify why the negative effect of distance increases between 1992 and 1994. Globalization theorists face a crucial challenge in explaining this aspect. If economic processes were truly global in their character and were the effect of an exogeneous easing of international economic transaction, the estimated coefficients of the three dummies for interregional trade, EU-AS, AS-NA, NA-EU, should be increasing, thereby indicating that interregional trade is growing (in relative terms), simply because the negative impact of distance on trade diminishes.
Regionalization theory also explains some aspects and ignores others. The rapid increase in the estimated coefficient for intra-North.American trade, the growing importance of trade between neighboring countries between 1980 and 1992 supports the regionalization hypothesis. However, the results remain puzzling. The degree of Asian integration sharply declines after 1990, western European integration peaks in 1986 and - most puzzling - the estimated coefficient of EUROPE is much smaller than the ASIA coefficient. This seems to indicate that the assumed superiority of European integration is partly misleading, at least if one controls for country size, distance and borders. Only if we add the border effect to the regional integration effect the estimated coefficient reaches the size of the ASIA coefficient.
Economic imbalances theory perfectly predicts the sharp increase in the AS-NA coefficient. Trade between Asian and North-American countries increases as the American twin deficit worsens. Moreover, since European saving figures are below its Asian counterparts, economic imbalances also nicely predicts that a similar increase does not take place between Europe and North-America.
Tu sum up, we gain somewhat mixed results. Each of the three existing theories explains only very small parts of the story of global economic integration. Hence, we should be far from being satisfied with existing reductionistic theories.

4. Conclusion

Multiple Regressions and Network Analysis illustrate that single factor explanations of global economic integration are presumably misleading. On the one hand, we observe that distance still matters. Geography has a huge impact on bilateral trade flows. Even a simple model with three independent variables, namely the gross domestic product of the importer and exporter respectively as well as the distance between both countries, is a fair approximation to and nicely predicts bilateral trade flows. On the other hand, the strong economic integration between South-East-Asia and North America, especially the US, does not entirely follow the pattern of capital exporter/ capital importer as expected by Krugman. In general, however, it seems fair to conclude that the notion of a truly globalized economy is by far less appropriate than the notion of regionalization. The amount of trade flows differs widely according to the continent, the trading partners are located on. Here, the estimated coefficient of the 'Euro-dummy' compared to the coefficients of the North America and Asia-Dummies seems to be most puzzling. Given that European countries are close neighbors and institutional barriers to trade have almost completely been re-moved during the process of European integration, it is hardly trivial, why European countries trade less with each other than a dyad located in any other world region.
However, even though some results are surprising, we do not believe that they are a methodological artifact. Quite the opposite is the case, gravity models are a good starting point for the empirical analysis of international trade. In the medium run, the newly developing branch of economic geography should improve neoclassical approaches to international trade and bring economic modeling and the raw world of observable facts a bit closer together.

References

[1] We implicitly assume that bilateral trade between one dyad does not effect the bilateral between another dyad of countries. But even though this is almost certainly a false assumption, it is less clear that any other simple assumption is more appropriate.
[2] Mainstream economics almost completely ignored spatial issues and therefore also neglected geographic aspects the gravity models are devoted to. Fair to say that work on economic location lied outside the intellectual core of economics. This neglect had a simple reason: Almost all neoclassical authors assume perfect markets. Hence, to say anything useful and interesting about geographic aspects of economic exchange, it is necessary to relax the assumptions of constant-returns and perfect competition that dominates economic textbooks and journals. For decades, economists have been unwilling to do so. This picture has changed dramatically only during the last decade. Gravity models have become fairly popular in economics, mainly because economists have turned their attention to the location of economic activity (Krugman 1998: 161). Paul Krugman (1991; 1992; 1998), Alan Deardorff (1997) and Anthony Venables (1995) among others have begun to integrate economic geography into economics.