Modelling International Trade

odelling International Trade A study of the EU Common arket and Transport Economies ichael Olsson and artin Andersson 2 The School of Technology and Society University of Skövde P.O. Box 48 Skövde, SE-54 28, Sweden e-mail: michael.olsson@his.se 2 Jönköping International Business School Abstract: In this paper, Swedish export is investigated, and data for export value and the number of firms that export is analysed. The main purpose is to compare constrained gravity models to gravity models without constraints. It is shown that constrained gravity models represent the export data in a relatively better way. The EU common market and transport economies are introduced into versions of the constrained gravity model, and the results show that the model fits the data even better. Key words and phrases: Trade, export, gravity model, common market, transport economies. Introduction For a small country like Sweden, international trade is of tremendous importance, since it enables additional use of specialisation and scale economies in production. The size of the Swedish international trade has been increasing over time. One way to illustrate this is to look at the sum of export and import as a share of GDP, which has risen from 42 per cent to 84 per cent between the years 95 and 24 (Hansson, 27). Given the magnitude of these transport flows, it is central to be able to model them as accurate as possible. This is the overall purpose with this proect, and the idea is that with better models, our understanding of international may be deepened. Earlier studies of international trade using the gravity model cover a wide range of topics. Just to mention a few, Feenstra, arkusen and Rose (2) aims to differentiate among alternative trade theories, Redding and Venables (24) analyse international income inequality, De Groot et. al. (24) focus on institutions, Okubo (24) study border effects, Antonucci and anzocchi (26) investigate Turkey s trade relation with the European Union, and Okubo (27) examine trade bloc formation. In all these studies, the gravity model is used at least as a first step, and they all use the gravity model in a straightforward way, without additional constraints. Andersson (27) writes, The doubly constrained

gravity model is not generally discussed in the literature on international trade. In this paper, two main types of gravity models are used: ) without constraints, and 2) with constraints. In the first step, these model types are compared. In this study, the monetary value of trade and the number of firms that trade internationally are analysed, and for both these variables, the basic version of the constrained gravity model fits the data better. A common result in all these models is that the foreign income effect and the distance friction affect the value of export more than the number of export firms. In the next step, the basic version of the constrained gravity model is extended in two distinct ways. First, the model is extended to incorporate the spatial structure of the EU common market, which improves the fit to the data even more. Second, transport economies are introduced into the model, which also improves the fit to the data. The paper is structured as follows. In the next section, the models are presented. The models are evaluated using a goodness-of-fit measure, which is presented in Section 3. An overview of the data is given in Section 4. In Section 5, the results are summarised. The paper ends with a discussion and suggestions for future studies. 2. odels In Section 2., the standard unconstrained gravity model is presented. In Section 2.2, the corresponding version of the constrained gravity model is described. In the following, this is referred to as the basic version of the constrained gravity model. In Sections 2.3 and 2.4, extensions of the basic constrained gravity model are illustrated. 2. The standard unconstrained gravity model In the following, countries are identified by i and, and the actual and estimated monetary value of trade between two countries is labelled i, and i,, respectively. In gravity models of international trade, trade between two countries is related to the economic size of the countries, and the economic activity is measured by the GDP of the exporting country, Y i, and the GDP of the importing country, Y. Higher economic activity is expected to imply more trade, i.e. there is a positive home income effect, α, and foreign income effect, β, respectively. oreover, there is distance friction, φ, so that the distance,, between countries is negatively related to trade. The impact of other variables may be introduced into the model, g (Z). In earlier studies, examples of such variables include information about common language, shared border, GDP per capita, free trade agreement, religion, colonial relation, and factor endowments. The standard unconstrained gravity model is generally stated in (). In the first part of the analysis g (Z) is left out of the analysis. In Section 2.2, the corresponding constrained gravity model is discussed. However, additional variables are incorporated later on (Section 2.3 and Section 2.4). The functional form expressed in (2) is assumed, which in logarithmic form is (3). d i, i, = f ( Yi, Y, d ) + g( Z) + + () ln α β = κy Y exp{ φd } (2) i = κ + α + β φ (3) ln lnyi lny d 2

The total monetary value of export from a specific country is monetary value of import to a particular country is X, i =, the total I, =,, and the total transport distance is D = i d. The corresponding estimated values of the total monetary value of export from a country is X, i =, the total monetary value of import to a country is I, = i, and the total transport distance is D = i d. In some ways, the results from such unconstrained models are not consistent with the data. First, the estimated import to a country most likely is not equal to the actual import, and the estimated export is likely to deviate from actual export. In the OLS procedure it is enforced that, but this does not imply that X, i = X, i and/or I, = I,. = i i Second, the same applies for the total amount of transportation per country. The amount of transportation is not constrained to the actual level in this form of the gravity model, and therefore the most likely outcome is that D D. When export from only one country is investigated, the aggregate export is estimated correct using OLS, but the inconsistency regarding the transport distance remains. In this study, there is ust one origin, i = Sweden, and therefore i is suppressed in the following notation, and the export flows are identified completely by the destination country. There is no home income effect in this model; it is embedded in the constant term. The estimated model is given by (4), which is referred to as odel. Johansson and Nilsson (27) find that vary over time. In the following, is referred to as proximity preference. In addition to the monetary value of export,, the model is used to study the number of export firms, N, (5). ln = + β lny φd, where lnκ + α lnyi ln N = + β lny φd, where lnκ + α lnyi i i = (4) = (5) If one were to investigate the imports to one country one would be able to estimate the home income effect, but then one would not be able to estimate the foreign income effect. In order to be able to estimate both a full trade matrix is needed. 2.2 The basic constrained gravity model The monetary value of trade is used to illustrate the model. The constrained model of international trade is stated in (6). Here i +, ( ln ) is optimised given a number of constraints. This is the important feature of constrained optimisation, and the constraints enforced are: i (i) that the actual export from each country is equal to the estimated export, =, X, i X, i (ii) that the actual import to a country is equal to the estimated import, =, and I, I, 3

(iii) that the actual amount of transportation used (for export) is equal to the estimated amount of transportation, D = D. The solution to (5) is = exp{ + µ φd }. It is possible to enforce a constraint for i transportation used for imports, but not while keeping a constraint for transportation used for export. The reason is that at this aggregate level, these two constraints are effectively the same, and for that reason, one is redundant. Λ = i ( + ln ) + X ) + i (, i + i µ I + ) + (, i + φ D d ) (6) ( i In this study, only the flows originating in Sweden, i = Sweden is studied, and therefore we are left with the model in (7), where i is suppressed. The export flows are identified by the destination country. Here, the constraints enforced are: (i) that the actual export from Sweden is equal to the estimated export, X = X, (ii) that the actual amount of transportation used (for export) is equal to the estimated amount of transportation, D = D. The solution is = exp{ φ d }, where the proximity preference and the distance friction is labelled and φ, respectively. This solution is based solely on trade flows and it is not related to the income levels. We introduce a foreign income effect into the model by enforcing that the solution should have the following structure: β = Y exp{ φd }, where, the foreign income effect is denoted β. In log form, this solution has the same structure as (4). This is referred to as odel 2, and the main difference is that in this model the constraints are strictly enforced. Finding the solution is an iterative procedure, and in each step, the parameter β is estimated by relating + φd + ln to ln Y, using OLS. In addition to the monetary value of trade, odel 2 is also applied to the number of export firms, (8). Then there is a specific foreign income effect, β. Λ = ( + ln ) + ( X + ) + φ ( D d ) (7) Λ = N ( + ln N ) + ( X N + N ) + φ ( DN N d ) (8) 2.3 The common market in the constrained gravity model In this section, a third model is introduced. It is a model of constrained type and it builds on odel 2. Here, two groups of countries are formed: a) the EU countries, and b) the rest of the world. When the spatial configuration of the EU is introduced into the model, the 4

Swedish export can be analysed for these categories, since either the export is destined for a country in the first category, EU, or the second category, ROW. By doing this, a proximity preference and a distance friction for each type of trade can be estimated. An explanation for this formulation is that trade within EU can be classified as free trade, while trade out of EU is relatively less free. Another reason for this is that there may be different transportation patterns for trade, and one example of this would be that within Europe land transportation dominates. This kind of modelling is, in spirit, similar to analysis of commuting using local, regional, and inter-regional commuting (Johansson et al, 23). odel 3 for the monetary value of export is stated in (9). In this version of the model, the constraints enforced are: (i) that the actual export from Sweden to countries located within EU is equal to the EU EU estimated export to the countries, X = X, (ii) that the actual export from Sweden to countries outside of EU is equal to the estimated ROW ROW export to the countries, X = X, (iii) that the actual amount of transportation used (for export) to countries located within EU EU EU is equal to the estimated amount of transportation, D = D, and (iv) that the actual amount of transportation used (for export) to countries located outside of ROW ROW EU is equal to the estimated amount of transportation, D = D. It is assumed that the foreign income effect, β, is the same for all countries. Export to β EU EU countries in EU is estimated at = Y exp{ φ d }, where the distance friction and EU EU the proximity preference is φ and, respectively. Export to countries not in EU is β ROW ROW estimated at = Y exp{ φ d }, where the distance friction and the proximity ROW ROW preference is φ and, respectively. The model is also solved for the number of export firms, and then the formulation estimated is given by (). EU EU ROW ROW Λ = ( + ln ) + ( X + ) + ( X + ) + EU ROW ROW ( D ROW ROW EU EU + φ ( D d ) + φ d ) (9) EU EU EU ROW ROW Λ = N ( + ln N ) + ( X N + N ) + ( X N + N ) + ROW EU EU + φ ( D N d ) + φ N d ) () N EU EU ROW ROW ( DN ROW 2.4 Transport economies in the constrained gravity model In this section, a fourth model is described, and with this model, only the number of firms is modelled (). The second model, given by (7), is extended to capture transport economies, and this is accomplished by adding the two constraints in (8), using the fact that the total 5

monetary value of export is the product of the number of firms trading and the average monetary value of export per firm (to destination ), m. (i) The estimated monetary value of trade is controlled to be equal to the actual monetary value of trade, = m N. X, (ii) The estimated transport distance is forced to be equal to the actual transport distance, D m N d. = In this model, both the distance friction and the proximity preference may vary with the monetary value of trade per firm. Hence, transport economies can be captured with this set up. With this model distance friction is φ + σ m, and the proximity preference is + ρ m. Λ = N ( + ln N ) + ( X N + N ) + φ ( DN N d ) + ( D + ρ ( X + m N, ) + + σ m N d ) () 3. The Chi-square goodness of fit The Chi-square measure of how well the models replicate actual trade is defined in the 2 following way: C = ( T T ) / T, where T is a symbol of the trade measure in question, i.e. either export value or the number of firms. Four different models are estimated and their fit is labelled C, C 2, C 3 and C 4, respectively. Hence, how well odel 2, odel 3 and odel 4 replicates the data in comparison to model is measured by C 2 /C, C /C, and 3 C 4 /C respectively. These quotas are referred to as the relative Chi-square measures. The models are evaluated using C, C 2 /C, C /C, and 3 C 4 /C. Hypotheses: In this paper, three hypotheses are tested, and they are: H: The first hypothesis is that the basic constrained gravity model represent the data relatively better compared to the gravity model without constraints, which is supported if C C. 2 / < H2: The second hypothesis is that the fit to the data is improved by introducing the spatial structure of the European Union into the constrained version of the gravity model. This is supported if C 3 / C2 <, which is equivalent to C 3 / C < C2 / C. H3: The third hypothesis is that the performance of the constrained model is improved by allowing for competition effects. This is supported if C 4 / C2 <, which is equivalent to C / C < C C. 4 2 / 6

4. Data The data is taken from the database kept at the Jönköping International Business School. The firm data originates from Statistics Sweden and in this proect, the total export value and the number of exporting firms are used. Each destination country can be described by a specific economic size and transport distance. The source for data on GDP is the World Development Indicators 25. Knowing the latitude and longitude coordinates of the capitol in each of the countries, the distance is calculated as the minimum distance along the surface of the sphere of the earth. For a deeper description of these data, see Andersson (27). The models discussed in the previous section are all estimated for six years, 998-23. 5. Results In Section 5., the gravity model without additional constraints (odel ) is compared to the basic form of the constrained gravity model (odel 2), and the results identify the main differences between unconstrained and constrained models. In Section 5.2, the results from the model with the EU common market (odel 3) are presented. The results from the model allowing for transport economies (odel 4) are collected in Section 5.3. 5. Unconstrained versus constrained models of trade The results from using the gravity model without additional constraints (odel ) are summarised in Tables and 2. In Table, the results for the number of firms are presented. The number of exporters increase with the importing countries GDP, i.e. there is a positive foreign income effect. The foreign income effect 23 is estimated at.6992. The distance between countries has a negative impact on the number of export firms, and the distance friction 23 is estimated at.28( 4 ). The model seems to fit the data approximately equally well for each year, which is seen by the relatively stable Chi-square measures. Table : Results from odel using number of export firms. The proximity preference, foreign income effect, distance friction, and Chi-square 998-23. Year Proximity Income effect Distance friction Chi-square β φ, E-4 C 998 -.5.683.546 493,64 (.53) (9.33) (4.85) 999 -.5958.734.9488 55,347 (2.23) (2.3) (4.48) 2 -.6399.77.298 466,27 (2.23) (2.9) (4.84) 2 -.5676.744.54 454,744 (2.2) (2.) (4.96) 22 -.7293.727.288 478,759 (.94) (9.65) (5.24) 23 -.456 (.59).6992 (9.25).28 (5.57) 495,45 In Table 2, the results for the monetary value of export are shown. The foreign income effect 23 is estimated at.789. It is observed that the foreign income to a larger degree affects the value of trade than the number of export firms. The distance fiction 23 is estimated at.6883( 4 ). This means that distance has a relatively larger impact on the 7

monetary value of trade than the number of exporters. It is an interesting observation that the impact of foreign income as well as distance is relatively higher regarding value than number of exporters. Table 2: Results from odel using monetary value of trade. The proximity preference, foreign income effect, distance friction and Chi-square 998-23. Year Proximity Income effect Distance friction Chi-square β φ, E-4 C 998-7.28 (5.86) 999-7.7864 (6.32) 2-7.822 (6.84) 2-6.792 (5.67) 22-6.96 (4.77) 23-4.98 (4.6).539 (23.74).86 (23.73).9 (25.77).572 (23.94).27 (2.86).789 (22.66).5996 (5.35).655 (5.36).596 (5.4).832 (6.27).794 (5.85).6883 (5.98),3,94,98,283,264,489,743,22,43,775,83,242,267,989,7,564,38,793,67,24,452,82,65,846 The results from the basic version of the constrained gravity model (odel 2) are summarised in Tables 4 and 5. The results for the number of exporters are found in Table 4. By comparing odel to odel 2, it is seen that the overall pattern is the same, but the estimates from odel 2 of the proximity preference is relatively higher, foreign income effect is relatively lower, and the distance friction is relatively higher. The foreign income effect 23 is estimated at.67, and the distance friction 23 is estimated at 4.8353( ). Table 3: Results from odel 2 using number of firms. The proximity preference, foreign income effect, distance friction, and relative Chi-square 998-23. Year Proximity Income effect Distance friction Chi-square β φ, E-4 C 2 / C 998-8.727.657.8283.64 999-9.959.6653.847.63 2-9.3853.6749.787.69 2-9.2652.679.8263.68 22-9.77.6884.665.68 23-9.25.67.8353.62 The results for the monetary value of trade are seen in Table 5. The foreign income effect 23 is estimated at.55, and the distance friction 23 is estimated at 2.389( 4 ). The results indicate that foreign income as well as distance has a relatively larger impact on the monetary value of trade. The number of exporters are also affected, but not to the same extent. odel 2 fit the data relatively better, which is seen by the lower Chi-square measures. In every case, the relative Chi-square measure is below one, which supports hypothesis H. 8

Table 4: Results from odel 2 using monetary value of trade. The proximity preference, foreign income effect, distance friction, and relative Chi-square 998-23. Year Proximity Income effect Distance friction Chi-square β φ, E-4 C 2 / C 998-4.4489.747 3.4959.73 999-5.2982.59 3.544.79 2-5.529.49 3.29.8 2-5.735.977 3.29.87 22-5.396.4 2.2966.9 23-3.843.55 2.389.79 5.2 Common market The spatial structure of the European common market was built into a constrained gravity model. Therefore, the model results in two measures of proximity preferences and two measures of distance friction. In Table 5, the results for the number of exporters are presented. The EU proximity preference 23 is estimated at -9.698, while the ROW proximity preference is estimated at -9.578. This means that given everything else, more firms export outside of EU. The EU and ROW distance friction 23 is estimated at 4 7.849( ) and 2.886( 4 ), respectively. The impact of distance is much higher inside the EU than outside of EU. The foreign income effect 23 is estimated at.694, which is somewhat higher than the estimates from the earlier models. Table 5: Results from odel 3 using number of firms. The proximity preference, distance friction, income effect, and relative Chi-square 998-23. Year Proximity preference Distance friction Income effect Chi-square EU ROW EU ROW φ, E-4 φ, E-4 β 3 998-9.2633-8.557 6.9989 2.9285.6742.42 999-9.466-8.8636 7.3956 2.895.6865.44 2-9.76-9.53 7.6924 2.825.6959.48 2-9.5836-9.85 7.494 2.8634.698.47 22 -.723-9.5546 7.8729 2.75.746.42 23-9.698-9.578 7.849 2.886.694.39 In Table 6, the results from the analysis of the monetary value of trade are collected. The EU proximity preference 23 is estimated at -3.4442, while the ROW proximity preference is estimated at -3.656. The spatial structure of the EU affects both the number of exporter as well as the value of export, but the impact is not the same. Here, the value of export out of EU is relatively lower than the value out of EU. The EU and ROW distance friction 23 is estimated at 8.7432( 4 ) and 2.867( 4 ), respectively. The impact of distance is clearly higher within the EU. The foreign income effect 23 is estimated at.6, which also is a higher estimate than the earlier models gave. Also with this set up of the model is it the case that both foreign income and distance affects the value of trade more than the number of exporters. 9

Table 6: Results from odel 3 using monetary value of trade. The proximity preference, distance friction, income effect, and relative Chi-square 998-23. Year Proximity preference Distance friction Income effect Chi-square EU ROW EU ROW φ, E-4 φ, E-4 β 3 998-4.46-4.2695 8.388 3.9439.82.68 999-5.37-5.58 7.295 3.9348.93.79 2-5.63-5.284 7.658 3.746.93.78 2-4.6394-4.88 8.6826 3.7553.34.78 22-4.928-4.9732 8.8589 3.336.4.69 23-3.4442-3.656 8.7432 2.867.6.62 The results from odel 3 can be compared to the results from odel 2, and then it is observed that the estimated distance frictions and the foreign income effect are higher using odel 3. The fit to the data is clearly improved, since the relative Chi-square measures are reduced, which is support for hypothesis H2. 5.3 Transport economies We extended the gravity model so that it would be possible to capture transport economies, and the results are summarised in Table 7. The constant part of the proximity preference 23 is estimated at -9.48, and the variable part of the proximity preference is estimated 7 at.54m. This means that relatively many of the exporters are relatively small, and this tendency seems to have become stronger over the years. The constant part of the distance friction 23 is estimated at 3.859( 4 ). The variable part of the distance friction 23 is estimated at.36m. There is friction, but the friction is somewhat reduced for large export values. The constant part has increased during the studied period, while the variable part has been reduced and even turned negative. The foreign income effect 23 is estimated at.733, which is relatively high in comparison to the results produced by the other models. The foreign income effect seems to have been reduced during the studied period. It is clearly verified that the relative Chi-square measures are reduced, which means that hypothesis H3 is verified. Table 7: Results from odel 4 using number of firms. The proximity preference, distance friction, income effect, and relative Chi-square 998-23. Year Proximity preference Distance friction Income effect Chi-square ρ, E-7 φ, E-4 σ, E- β C 4 /C 998-2.29 -.2.976 2.79.8285.35 999-2.66 -.35 2.428 2.29.8453.34 2-3.5425 -.24.7454 2.29.8797.37 2-2.788 -.32.8587.63.8492.36 22-9.963 -.5 2.7768.94.744.4 23-9.48 -.54 3.859 -.36.733.36 6 Concluding remarks and suggestions for future studies In this paper, the export from Sweden was studied. In a study of export, an estimate of the proximity preference, foreign income effect, and the distance friction is produced, but there is no way to estimate the home income effect. It would be interesting to compare these results to the outcome using import flows. In a model of import, an estimate of the home income effect would be part of the result. Another interesting extension to this work is to

solve the models for a full trade matrix, since in a study using a full trade matrix both a home and foreign income effect would be estimated simultaneously. In this work, we used the monetary value of trade, but an alternative measure would be the actual volume of trade (measured in for example tons). It would be interesting to do such a study if ust to compare the outcome. In this study, we used the gravity model in a relatively clean form, and in the future, it is possible to add more variables to the models. One obvious extension to this work is to combine the model that captured the spatial structure of the EU common market to the model that aimed at estimating transport economies. There is a potential to estimate many other versions of the models presented in this paper. For example, in the version in which the spatial structure of EU was incorporated it was assumed that the foreign income effect was the same within and out of EU. The models may be changed to investigate whether that is the case or not. References Andersson, (27) Disentangling Trade Flows: Firms, Geography and Technology, JIBS Dissertation Series 36. Jönköping International Business School, Jönköping. Antonucc D. & anzocch S. (26) Does Turkey have a special trade relation with the EU? A gravity model approach. Economic Systems, V. 3, (2): 57-69. De Groot, H.L.F., Linders, G-J., Rietveld, P. & Subramanian, S. (24) The institutional determinants of bilateral trade patterns. Kyklos, V. 57, (): 3-24. Feenstra, R.C., arkusen, J.A. & Rose, A.K. (2) Using the gravity equation to differentiate among alternative trade theories. Canadian Journal of Economics, V. 34, (2): 43-447. Hansson, H. (27) Svensk handel. SNS Förlag, Stockholm. Johansson, B., Klaesson, J. & Olsson,. (23) Commuters non-linear response to time distances. Journal of Geographical Systems, V. 5, (3): 35-329. Johansson, B. & Nilsson, D. (27) Globalisation and distribution of exports, in Johansson, I. (Ed.) Institutions for knowledge generation and knowledge flows building innovative capabilities for regions, Research report 27:4, Trollhättan, University West, 489-54. Redding, S. & Venables A.J. (24) Economic geography and international inequality. Journal of International Economics, V. 62, (): 53-82. Okubo, T. (24) The border effect in the Japanese market: A gravity model analysis. Journal of the Japanese and International Economies, V.8, (): -. Okubo, T. (27) Trade bloc formation in inter-war Japan. A gravity model analysis. Journal of the Japanese and International Economies, V.2, (2): 24-236.