THE NON-LINEAR SPECIFICATION OF THE GRAVITY MODEL: AN EMPIRICAL APPLICATION ON INTERNATIONAL TRADE

Transcription

1 THE NON-LINEAR SPECIFICATION OF THE GRAVITY MODEL: AN EMPIRICAL APPLICATION ON INTERNATIONAL TRADE CELESTINO SUÁREZ-BURGUET, INMACULADA MARTÍNEZ-ZARZOSO AND LAURA MÁRQUEZ-RAMOS DEPARTAMENTO DE ECONOMÍA UNIVERSIDAD JAUME I, CASTELLÓN (SPAIN) INSTITUTO DE ECONOMÍA INTERNACIONAL Abstract In this paper, we estimate a linear and a non-linear augmented gravity model with a 62- cross-country sample. In order to analyse for the presence of heterogeneity, we also analyse bilateral trade flows for different groups of countries, classified according their level of economic development. Our results show that, in most cases, the linear gravity equation seems to be a better alternative and that there is heterogeneity in the sample. 1. Introduction Several authors focus on the specification of the model and support the view that nonlinear models explain bilateral trade better than log-linear models. For example, Coe et al. (2002) refer to the failure of declining trade costs an important aspect of globalisation to be reflected in the estimates of the standard gravity model of bilateral trade. They estimate the non-linear specification of the gravity equation and find evidence of the declining importance of geography. Moreover, the non-linear specification takes into account zero values for bilateral trade and the level of the estimated distance coefficients is more consistent with the theory. In this line, Croce et al. (2004) estimate a non-linear gravity model and find that distance has become less relevant over time. However, although the estimated coefficients have been falling over time, their values still reveal the importance of geography on trade. 1

2 In this paper we aim to develop a gravity model and compare its linear and non-linear specification in order to understand the role played by cross-country differences in both, relative factor endowments and relative country size when determining the volume of trade. In Section 2 the theoretical framework and the model specification are developed. Section 3 presents the estimated equation and the main results in this paper. In Section 4 we estimate the non-linear specification of the gravity equation. Finally, Section 5 concludes. 2. Theory and model specification In order to understand the role played by cross-country differences in relative factor endowments and relative country size in the determination of the volume of trade, we develop a model based on Helpman and Krugman (1996). Following Deardorff (1995), Bougheas et al. (1999) and Eaton and Kortum (2002), we introduce transport costs by the Samuelson iceberg type (1954), where only a fraction 1 g = of the quantity exported actually reaches the final destination and delivering a τ unit from the home to the foreign country requires production of more than a unit. Transport costs can be determined by geographical factors, since positive geographical barriers means that τ > 1. Additionally, Bougheas et al. (1999) point out that there is a simple way to introduce infrastructure in the above model. If the role of hard infrastructure is to improve transportation conditions we can think of it as a cost-reducing technology. 1 Therefore, we introduce transport infrastructure by reducing transport costs (τ ) and increasing the fraction of the goods shipped that actually reaches the final destination. However, if one 1 Bougheas et al., 1999, page

3 of the countries improves its transport infrastructure and the other does not improve it with the same intensity, g will change at a different rate. We therefore consider τ as a measure of transport costs in the home country and τ * as a measure of transport costs in the foreign one. According to Deardorff (1995), trade can be valued either exclusive of transport costs (f.o.b) or inclusive of transport costs (c.i.f) for export flows. This author claims that trade flows must be reduced by the amount of the transport costs on an f.o.b basis and, hence, we assume that exports are sold at f.o.b prices and the greater part of transport costs are paid by the importer country. We also include the soft infrastructure following Freund and Weinhold (2004). The authors include the effect of the Internet on trade in their model by assuming that the Internet reduces the fixed cost to enter a particular market and, as they point out, the Internet is likely to reduce this type of entry cost since networks can expand and information can be more easily exchanged. 2 Hence, the richer the soft infrastructure is, the lower the fixed entry costs will be, and this effect can be reflected in the final price of goods (price changes from p to p in the home country, being p > p, and price changes from p to p in the foreign country, being p > p ) and the final price of goods changes their final demand and exports. We use β (β*) to represent the increase in trade as a consequence of lower final prices in our model ( β 1 and β* 1). As a further step, we take into account integration agreements across countries. Anderson and van Wincoop (2003) use a variable b ij to reflect the existence of an international border between i and j. When b ij = 1, regions i and j are located in the same country. Otherwise, b ij takes the value one plus the tariff equivalent of the border 2 Freund and Weinhold, 2004, page

4 barrier between the countries in which the regions are located. The authors use this variable to model unobservable trade costs. In our framework, we can consider a variable I=I* that takes a value of one when countries remove their barriers to trade or when they are integrated within the same economic area. When tariffs or non-tariff barriers deter trade because imports are burdened with taxes in the home country, we have I > 1, and when imports are burdened with taxes in the foreign country, we have I*> 1; thus, there are positive entry costs involved in entering foreign countries. On the other hand, Samuelson (1954) states: What does the governmen t do with the tariff receipts? ( ) The government is assumed to distribute the receipts to the (representative) consumer in a lump-sum fashion. 3 In accordance with Eaton and Kortum (2002), the revenue from generating barriers and the increase in intranational trade due to borders can be incorporated in this framework. We assume that the home (foreign) country s imports from the foreign (home) country are subject to an ad valorem tariff t (t*) on all imports, and therefore the result is an increase in income (as measured by GDP) due to tariff revenue. Taking into account transport costs, infrastructure, integration and tariff variables, the specification of the model is: T = sβ ( X1 * + p' X 2*)(1 + t) + s * β *( X1 + p' X 2)(1 + t*) (1) τ I τ * I * where t 0 and t * 0. Equation (1) shows that artificial barriers deter trade when I > ( 1+ t), as a result of the existence of barriers other than an ad valorem tariff in the home country, and when I * > (1 + t*), there are barriers other than an ad valorem tariff in the foreign country. β and β* represent the increase in trade as a consequence of lower final prices for soft 3 Samuelson, 1954, page

5 investments in infrastructure ( β 1 and β* 1). An increase in these parameters will raise trade volumes. Rewriting equation (1), we obtain, T 1 1 = s β GDP * + s * β * GDP (2) τ I τ * I * Geographical factors play an important role in the determination of transport costs. However, transport and entry costs can be modified by the hardware and software infrastructure. The latter depends on the level of innovation and other factors related to technological innovation, and on the advance in ICT in the countries. The outlined model shows that if imports are burdened with taxes, there are positive costs of entering the market and hence international trade flows decrease. On the other hand, incomes increase by ad valorem tariffs and when incomes of our trade partners are higher, the volume of trade increases. Finally, our model is not able to predict whether technology is altering the effect of distance and other geographical barriers on trade, and the impact of other geographical factors and social relations are not reflected either. In what follows we study these factors more deeply from an empirical point of view and from the theoretical model, expressed in log linear form, we will derive the estimated model. 3. Estimated equation and empirical results Table A.1 in appendix A 4 shows a summary of the data used in our analysis. With respect to infrastructure variables, some additional explanations are needed. We have used TAI (UNDP, 2001) and ArCo (Archibugi and Coco, 2002) to measure technological innovation. Transport infrastructure variables are calculated with data on 4 Appendix A. Table A.1. The first column lists the variables used for empirical analysis, the second column outlines a description of the variables, and the third column shows the data sources. 5

6 kilometres of paved roads and kilometres of motorways per square kilometre, taking into account the quality of the roads. We use equation (3) to calculate the index. Infrastructure ((0.75 paved roads( km)) + motorways( km)) v ariable = (3) 2 Land area ( km ) In order to evaluate the empirical effects of technological innovation and geographical factors on international trade, we derive a gravity model (Oguledo and Macphee, 1994; Deardorff, 1995; Anderson and van Wincoop, 2003) augmented with technological variables and a transport infrastructure index from equation (2). Integration dummies are added in order to analyse the impact of trade agreements on international trade. A number of dummies representing geographical and cultural characteristics are also added. The model is expressed in additive form using a logarithmic transformation. The estimated equation is: lnxij= α + α lny + α lny + α lnp + α lnp + α Adj + α Isl + α Land+ + α CACM+ α CARIC+ α 8 + α lndist + α 14 0 ij i 2 Lang + α ij j MERC+ α TAI + α i i j j NAFTA+ α TAI + α i ij CAN+ α Inf + α Inf + u j 7 UE+ ij (4) where ln denotes natural logarithms. The model is estimated with data for 62 countries in 1999 and a total of 3782 (62*61) bilateral trade flows are obtained (Appendix B, Figure 1). The presence of missing/zero values in the bilateral trade flows data reduces the sample to 3126 observations. We perform OLS estimation on the double log specification as given by equation (4). X ij denotes the value of exports from country i to j, Y i and P i are income and population in the exporter s market, Y j and P j are income and population in the destination market, Adj ij is a dummy that takes a value of 1 when countries share the same border and zero otherwise, Isl takes a value of 1 when the exporter or the importer are islands, Land is a dummy for landlocked countries, CACM is a dummy that takes a value of 1 when both countries belong to the Central American Common Market, CARIC is a dummy that 6

7 takes a value of 1 when both countries belong to the Caribbean Community, MERC is a dummy that takes a value of 1 when both countries belong to Mercosur, NAFTA takes a value of 1 when countries are members of the North American Free Trade Area, CAN is a dummy representing Andean Nations Community members and UE takes a value of 1 when countries are members of the European Union. Since suitable direct measures of distance costs are unavailable, geographical distance between countries is often used as a proxy for transport costs in gravity equations, so Dist ij is the geographical great circle distance in kilometres between the capitals of country i and j. Lang ij is a dummy for countries sharing the same language, and TAI i and TAI j are technological variables measuring technological innovation in the exporter and the importer countries. Inf i and Inf j are infrastructure variables measuring the level of transport infrastructures in the exporter and the importer countries. Finally, u ij is independently and identically distributed among countries. In relation to our main results, Model 1, in Table 1, shows estimation results for equation (4). Geographical variables are important determinants of international trade, therefore we have included other variables different to distance in order to analyse its effect on trade flows. The adjacency coefficient is expected to be positive since countries sharing a border trade more, the island coefficient could be positive or negative 5, and the landlocked coefficient is expected to be negative, since countries without direct access to the sea trade less. Moreover, we expect history, culture, language and social relations also to have important effects on trade. Language is 5 There are some authors that find island effects being positive and significant for both, importer and exporter, whereas others find that the signs depend on the direction of trade, being positive when imports are modelled as the independent variable and negative when exports are modelled as the independent variable (see Soloaga and Winters, 2001). 7

8 included as a proxy for this type of relationship between countries. Its coefficient is expected to be positive. Integration dummies are also considered as social variables. Table 1. Determinants of international trade. Augmented gravity model. Variable Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Constant term *** *** *** *** *** *** (-25.71) (-27.04) (-31) (-32.05) (-21.18) (-24.41) Exporter s income 0.02*** 0.02** 0.05*** 0.04*** 0.02** 0.04*** (2.62) (2.53) (6.35) (5.69) (2.34) (5.61) Importer s income 0.04*** 0.04*** 0.06*** 0.05*** 0.04*** 0.05*** (3.72) (3.61) (5.21) (4.64) (3.51) (4.65) Exporter s population 0.89*** 0.89*** 0.97*** 0.98*** 0.89*** 0.98*** (49.34) (51.41) (53.45) (55.1) (49.5) (53.6) Importer s population 0.66*** 0.67*** 0.71*** 0.72*** 0.67*** 0.72*** (34.92) (35.64) (36.5) (37.46) (34.66) (36.43) Adjacency dummy 0.43*** 0.32** 0.38** ** 0.13 (2.89) (2.15) (2.34) (1.52) (2.03) (0.8) Island dummy -0.46*** -0.47*** -0.27*** -0.31*** -0.46*** -0.28*** (-5.64) (-5.77) (-3.17) (-3.72) (-5.58) (-3.26) Landlocked dummy -0.86*** -0.83*** -1.04*** -0.97*** -0.86*** -1.02*** (-11.34) (-10.99) (-13.82) (-12.92) (-11.29) (-13.68) CACM dummy 1.95*** 1.99*** 2.41*** 2.39*** 1.74*** 1.95*** (8.08) (8.56) (9.27) (9.55) (6.96) (7.22) CARICOM dummy 4.29*** 4.17*** 4.07*** 3.91*** 4.24*** 3.99*** (4.49) (4.38) (4.03) (3.89) (4.44) (3.95) MERCOSUR dummy 2.58*** 2.49*** 2.91*** 2.76*** 2.56*** 2.85*** (7.66) (7.73) (8.72) (8.5) (7.18) (7.62) NAFTA dummy * * (1.16) (1.36) (1.65) (1.51) (1.31) (1.85) CAN dummy 1.22*** 1.05** 1.06** 0.89* 1.26*** 1.14** (2.61) (2.24) (2.22) (1.87) (2.69) (2.4) UE dummy -0.24** -0.35*** ** -0.22** (-2.54) (-3.76) (-1.1) (-2.45) (-2.36) (-0.89) Distance -1*** -0.95*** -0.95*** -0.91*** -1.12*** -1.2*** (-26.72) (-25.44) (-24.82) (-24.13) (-20.55) (-21.8) Language dummy 0.92*** 0.87*** 0.91*** 0.83*** 0.93*** 0.93*** (11.00) (10.49) (10.41) (9.81) (11.16) (10.78) Exporter s TAI 9.12*** 9.17*** 9.01*** - - (46.46) (47.61) (42.97) - Importer s TAI 6.39*** 6.35*** 6.2*** - - (30.7) (31.09) (27.19) - Technological distance (TAI) *** (-9.43) Exporter s ArCo *** 8.04*** 7.48*** - (46.75) (48.74) (43.72) Importer s ArCo *** 5.68*** 5.21*** - (30.08) (32.69) (26.8) Technological distance (ArCo) *** (-11.61) - - Exporter s infrastructure 0.68*** 0.68*** 0.91*** 0.88*** 0.67*** 0.88*** (17.65) (18.26) (25.06) (24.89) (17.34) (23.63) Importer s infrastructure 0.57*** 0.57*** 0.74*** 0.71*** 0.56*** 0.71*** (12.57) (12.89) (17.45) (16.94) (12.31) (16.51) LONGDISTi *** (0.99) (2.75) LONGDISTj ** (1.53) (2.52) 8

9 R-squared Adjusted R-squared S.E. of regression Number of observations Akaike Info Criterion Notes: ***, **, * indicate significance at 1%, 5% and 10%, respectively. T-statistics are in brackets. The dependent variable is the natural logarithm of exports in value (current US$). Income, population and distance are also in natural logarithms. The estimation uses White s heteroscedasticity-consistent standard errors. Model 1: Augmented gravity model (technological innovation measured by TAI); Model 2: Augmented gravity model and estimation of the effect of technological distance on trade (technological innovation measured by TAI); Model 3: Augmented gravity model (technological innovation measured by ArCo); Model 4: Augmented gravity model and estimation of the effect of technological distance on trade (technological innovation measured by ArCo); Model 5 and Model 6: Augmented gravity model and estimation of the effect of information technology on geographical distance and therefore, on trade. Our results show that, in Model 1, income, geographical distance, technological innovation, transport infrastructure and all the dummies are significant and show the expected sign, excluding some integration dummies. Population coefficients are positive although, as Filippini and Molini (2003) point out, demographic variables might have different signs and dimensions across developed and developing countries. The European Union dummy has a negative sign. This result has also been found by other authors (e.g. Cyrus, 2002) although we believe that the reason may be the presence of heterogeneity in the sample or the existence of missing values. We find that this model has a high explanatory power given the high value of the R 2 (78.6%). Model 3 shows estimation results for equation (4), but the technological variable included is the ArCo Index. Results are similar to those obtained in Model 1, but the magnitude of the estimated coefficient for TAI is higher than the estimated coefficient for ArCo. Both indicators are highly correlated (96%). 9

10 Models 2 and 4 include a new variable: technological distance between trading partners (Filippini and Molini, 2003). This is defined as the absolute difference between technological indicators in the exporter and the importer countries. This indicator is based on the insight that two countries can be far away from each other not only geographically, but also from a technological perspective. Technological gaps can deter trade since similar countries trade more. Therefore, we expect a negative correlation between this new variable and the export flows. Model 2 includes the technological distance measured by TAI, and Model 4 includes the technological distance measured by ArCo. Technological distance is significant in both models, increasing the explanatory power in the regressions. Our results support the view that countries tend to trade more when they are closer from a technological point of view. The explanatory power is lower for Models 3 and 4 than for Models 1 and 2. The "beta coefficients" are calculated to determine the relative importance of different variables included in the augmented gravity model (see Table A.2, Appendix A). They are used by some researchers to compare the relative strength of the various predictors within the model and since the beta coefficients are all measured in standard deviations, instead of in variable units, they can be compared to one another. The estimates of Model 1 imply that the highest beta coefficients are, in absolute value, for technological variables (0.504 for TAI in the exporter and for TAI in the importer country), although the beta coefficient for population has also a considerable magnitude. On the one hand, this means that a standard deviation increase in the endowment of technological innovation in the exporter country would lead to a standard deviation increase in the logarithm of exports. On the other hand, a standard deviation increase in the endowment of technological innovation in the importer country would explain a standard deviation increase in the logarithm of bilateral exports. 10

11 Clearly, this indicate that technological variables are important determinants on international trade flows. Freund and Weinhold (2004) fail to show evidence of the role played by the Internet in altering the effect of geographical distance in trade patters. They construct a new variable (LONGDIST) which equals one if the distance between trade partners exceeds the average distance between all countries. Then, they interact it with the growth in the number of Internet hosts in each country. In order to compare our results with those obtained by these authors, we use the same methodology to create a similar variable. We interact LONGDIST with Internet hosts in each country. Our results do not show evidence that Internet use is altering the role of distance on trade, supporting the view of Freund and Weinhold (2004). However, it could be that a more general proxy for technological innovation would be better to measure this effect. In Model 5, we analyse whether technology has an effect on geographical distance. We interact TAI and LONGDIST, obtaining LONGDISTi (LONGDIST*TAI i ) and LONGDISTj (LONGDIST*TAI j ). If technology and the advance of information and knowledge have reduced (increased) the impact of distance on trade, then the coefficient on the interaction term should be positive (negative). However, these coefficients are positive but non-significant. Finally, we use ArCo instead of TAI in Model 6 to analyse the effect of the knowledgebased economies on trade since LONGDIST and LONGDIST are interacted with TAI i and TAI j. Contrary to Freund and Weinhold (2004), our results offer evidence showing that technology advances have reduced the effect of distance on trade since the coefficient of LONGDISTi and LONGDISTj are both positive and significant. In order to understand whether there exists a differential behaviour concerning the determinants of trade flows for developed and developing countries, the 62-country 11

12 sample is divided into three groups according to their level of economic development: countries with high GDP per capita, medium GDP per capita, and low GDP per capita. Countries are ordered from higher to lower income levels, and then an upper level of GDP is composed by calculating the average of the first half of the sample, and an inferior level is set by calculating the average of the second half. Figure 2 (Appendix B) shows the evolution of the average income for the three groups of countries in the period Table 2 shows the main results of the augmented gravity model for developed and developing countries in our sample. Only two groups are considered instead of three in order to have a higher contrast between them. Table 2. Determinants of international trade. Estimation results for high and low income countries. Variable Model 7 Model 8 Constant term *** *** (-3.13) (-4.82) Exporter s income 1.25* (1.66) (-0.65) Importer s income 1.51** (2.11) (-0.73) Exporter s population *** (-0.57) (10.91) Importer s population *** (-0.96) (5.84) Adjacency dummy 0.52** 0.15 (2.53) (0.31) Island dummy 0.28** 4.61 (1.98) (1.24) Landlocked dummy -0.35*** -0.92** (-2.62) (-2.09) CACM dummy *** (3.25) NAFTA dummy (-0.41) - UE dummy 0.11 (0.67) - Distance -0.91*** -1.16*** (-9.44) (-5.92) Language dummy *** (-0.49) (2.72) Exporter s TAI 2.86*** 4.28* (2.62) (1.89) Importer s TAI ** (1.41) (2.13) Technological distance (TAI) (-0.75) (-0.49) Exporter s infrastructure 0.21***

13 (2.81) (-0.95) Importer s infrastructure (-0.31) (1.01) R-squared Adjusted R-squared S.E. of regression Number of observations Akaike Info Criterion Notes: ***, **, * indicate significance at 1%, 5% and 10%, respectively. T-statistics are in brackets. The dependent variable is the natural logarithm of exports in value (current US$). Income, population and distance are also in natural logarithms. The estimation uses White s hete roscedasticity-consistent standard errors. Model 7: Determinants of trade in developed countries; Model 8: Determinants of trade in developing countries. Model 7 presents the OLS results for the augmented gravity equation in the richest countries. Results show that importer s and exporter s income, adjacency, island and landlocked dummies, geographical distance, exporter s TAI and exporter s transport infrastructure are significant. These variables have the expected sign. Demographic variables (population of the countries) are non-significant. As Filippini and Molini (2003) explain, 6 in developed countries the demographic transition is over, consequently the trend of population growth is stable and almost close to zero ( ) we expect a non-significant or negative coefficient. Variables in this model explain 87.6% of the variability in exports. In Model 8, the augmented gravity model is estimated for low-income countries. Exporter s and importer s population, being landlocked, the integration dummy, geographical distance, the language dummy, and the exporter s and importer s TAI are significant and they have the expected sign. Demographic variables for exporters and importers have a positive relation with trade, indicating that greater availability of cheap 6 Filippini and Molini, 2003, page

14 labour force for industries in developing countries fosters trade and the existence of economies of scale. This model has a lower explanatory power (67.9%) than the model for the richest economies, which could be due, in part, to the data for developed countries being of higher quality. In Models 7 and 8, we add the same technological differences variable as was included in Model 2. We can observe that when trade is among countries with a similar level of development, technological endowments are more important for trade than the technological gap existing among these countries. In relation to the income coefficients, Garman et al. (1998) analyse economic integration in a number of developing countries and support the notion that the costs and benefits of integration are unevenly distributed among members of an integration agreement in favour of the richest countries. This is because the income coefficients obtained for Latin American countries have a smaller magnitude than those reported in other studies of European trade. However, our results do not show clear evidence that the costs and benefits of integration and globalisation are unevenly distributed among the richest and the poorest countries since income coefficients, although they are very low in magnitude, are not significant for low-income economies. Technological and transport infrastructure variables are expected to have a positive influence on trade. Results show that they are non-significant for importers when trade is among high-income countries, and only technological variables are significant for low-income economies. One explanation could be the non-arrival at a minimum level of transport infrastructure in developing countries. Technological innovation and transport infrastructure can be considered as barriers to trade for those countries with lower endowment levels; thus, investing in these variables could foster international trade and 14

15 increase the participation of developing economies in a more globalised and integrated world. 4. Estimation of a non-linear model Some authors focus on the specification of the gravity model and support the view that non-linear models explain bilateral trade better than log-linear models. For example, Croce et al. (2004) study the performance of four trading blocs (MERCOSUR, NAFTA, CACM and the Andean Community) by applying an extension of Anderson and van Wincoop s (2003) gravity equation. They estimate a non -linear equation and they find that it explains an important part of the determinants of trade flows. The variables population, distance, adjacency, language and integration variables have the expected sign and are significant. Additionally, Coe et al. (2002) refer to the failure to reflect declining trade costs, an important aspect of globalisation, in estimates of the standard gravity model of bilateral trade. They estimate the non-linear specification of the gravity equation and find evidence for the declining importance of geography. They prefer the non-linear specification since it takes into account zero values for bilateral trade and the level of the estimated distance coefficients is more consistent with theory. Croce et al. (2004) also find that distance has become less relevant over time. However, although the estimated coefficients fell over time, their values still reveal the importance of geography on trade. From equation (2) we derive the empirical model to be estimated, which is given by (5): T = ij c(1) c(2) c(3) c(4) c(5) c(6) ( s β ( GDP*) + ( s*) ( β *) GDP ) µ = α CACM + α CARIC + α MERC + α NAFTA+ + α CAN + α UE + α Adj + α Lang + α Land + α Isl ij 8 3 ij 9 4 τ 10 c(7) e ( Inf ) µ ij c(8) ( Inf *) c(9) + ε ij (5) 15

16 We measure the volume of trade with the logarithm of bilateral export flows between countries in our sample, s (s*) is measured by population in both countries, and β (β*) is proxied by ArCo i and ArCo j (Archibugi and Coco, 2002); their coefficients are expected to be positive since higher technological innovation fosters lower prices and more trade. GDP (GDP*) is the gross domestic product (PPP, current international $) and τ is proxied by the geographical great circle distance between the exporter and importer countries. The geographical distance coefficient is expected to be positive since greater distance among countries deters trade. In equation (5) we also include the variable representing transport infrastructure in the exporter and importer country used in the augmented log-linear gravity equation. A better transport infrastructure lowers transport costs and therefore the estimated coefficient is expected to be negative. Finally, in the augmented gravity equation we included integration dummies, which took a value of one when countries were members of an integration agreement and zero otherwise; variables representing integration agreements are included in the non-linear model by means of an exponential function. Adjacency, language, landlocked and island dummies are also included in this function. The optimisation process to estimate a non-linear model has three main parts: obtaining the starting parameter values, updating the candidate parameter vector at each interaction, and determining when we have reached the optimum. If the objective function is globally concave, there is a single maximum and any algorithm which improves the parameter vector at each iteration will eventually find this maximum. If the objective function is not globally concave, different algorithms may find different local maxima. However, all iterative algorithms suffer from the same problem of being unable to distinguish between local and global maxima. Eviews uses the Marquardt 16

17 algorithm to solve by NLS. This algorithm modifies the Gauss-Newton algorithm by adding a correction matrix to the Hessian approximation. Iterative estimation procedures require starting values for the coefficients of the model and the closer to the true values they are, the better. However, there are no general rules for selecting them. We have used the simple average of the values obtained in Croce et al. (2004) and Coe et al. (2002) for the starting values of the distance, 7 adjacency and language variables. We have conserved the values obtained in Model 3 (when we included the ArCo as the measure for technological innovation) as starting values for the landlocked, island, technological innovation and transport infrastructure variables. 8 For the CAN, CACM, MERC and NAFTA dummies, we include, as starting values, the coefficients obtained in Croce et al. (2004) and, for economic mass, the value of the coefficient obtained in Coe et al. (2002). Finally, a starting value of 1 is considered for demographic variables, CARIC and UE dummies. The estimation process achieves convergence if the maximum change in the coefficients is below the specified value. We have used a convergence criterion of 10-4 for the 62- country sample and in the estimation for the poorest countries, since when the sample size is large the use a small value for the convergence criterion might be problematic (Davidson and McKinnon, 1993). The poorest countries need a large number of iterations to achieve convergence. Convergence in these estimations is achieved if the maximum of the percentage changes in the coefficients is smaller than 0.1%. For the richest countries, the convergence criterion used is since the sample size is not very large. Table 3 shows our final results. 7 Distance is included with a positive sign because, in the non-linear specification estimated in this research work, it should be positive. 8 Transport infrastructure variables are included with a negative sign because, in the non-linear specification estimated in this research work, it should be negative. 17

18 Table 3. Determinants of international trade. Estimation results for the non-linear model in our 62-country sample and for high and low income countries. Variable Model 9 Model 10 Model 11 Model 12 Exporter s income 0.33*** 0.25*** 0.52*** 0.55*** (7.56) (3.62) (6.58) (4.39) Importer s income 0.38*** 0.37*** 0.51*** 0.49*** (8.51) (8.45) (6.76) (2.64) Exporter s population 0.73*** 0.49*** 0.74*** 0.26 (10.63) (7.38) (5.49) (0.79) Importer s population 0.86*** 0.75*** 0.79*** 0.17 (12.45) (7.42) (5.52) (0.87) Adjacency dummy *** 0.93** 1.23* (4.27) (2.17) (1.69) Island dummy *** -2.09* (1.35) (3.65) (-1.73) Landlocked dummy *** -2.21*** (-3.85) (-3.41) (-0.12) CACM dummy (0.44) (0.83) CARICOM dummy (0.03) - - MERCOSUR dummy *** (3.29) - - NAFTA dummy *** 0.63 (7.45) (0.97) - CAN dummy (0.14) - - UE dummy (0.86) (-1.39) - Distance 0.82*** 0.28*** 0.78*** 0.41 (12.87) (5.56) (2.76) (1.24) Language dummy (-0.1) (1.18) (-1.11) Exporter s ArCo 3.95*** 1.94*** 16.59*** 2.81 (6.01) (5.09) (3.81) (1.01) Importer s ArCo 6.99*** 8.82*** 19.35*** 2.35 (4.48) (3.26) (4.91) (1.56) Exporter s infrastructure 0.07* -0.24*** -0.47*** 0.01 (1.65) (-4.23) (3.48) (0.03) Importer s infrastructure *** -0.53*** (1.49) (-5.74) (-3.92) (-1.19) R-squared Adjusted R-squared Number of observations Akaike Info Criterion Number of iterations Notes: ***, **, *, indicate significance at 1%, 5% and 10%, respectively. T-statistics are in brackets. The dependent variable is exports in value (current US$). The estimation uses White s heteroscedasticityconsistent standard errors. Model 9: Determinants of international trade in the 62-country sample (not including integration, adjacency, island, landlocked and language dummies). Non-linear specification; Model 10: Determinants of international trade in the 62-country sample, including integration, adjacency, island, landlocked and 18

19 language dummies in an exponential function. Non-linear specification; Model 11: Determinants of trade in developed countries. Non-linear specification; Model 12: Determinants of trade in developing countries. Non-linear specification In Models 9 and 10, we estimate equation (5) without and with the exponential function, respectively. Our results show that income, population, distance, technological innovation, transport infrastructure (when we include the exponential function), some integration variables, adjacency and landlocked dummies are significant and have the expected sign. The inclusion of the exponential function has an important effect on the coefficients of the variables included in equation (5) and the explanatory power is higher. The coefficient elasticities are not comparable to those obtained from the log-linear model. However, a common result can be observed, namely that a greater technological innovation and transport infrastructure endowment in both the exporter and the importer country leads to higher international trade flows. In the non-linear specification, the number of observations is higher for the 62-country sample and the developing countries group, and the adjusted R-squared is always higher. In order to compare the augmented gravity and the non-linear model, the Akaike Information Criterion (AIC) is used. Smaller values of the AIC indicate that a model is preferred. According to this criterion, the linear gravity model is a better alternative, since the AIC is in Model 1 (augmented gravity model), in Model 7 (developed countries) and in Model 8 (developing countries), whereas for the non-linear specification is in Model 10 (augmented gravity model), in Model 11 (developed countries) and in Model 12 (developing countries). Finally, according to our results, there are differences in the behaviour between the richest and the poorest countries. The non-linear specification of the gravity equation 19

20 seems to be a good approach to analyse the determinants of international trade for the richest countries and, although the explanatory power is higher for the non-linear (Model 11) than for the log-linear specification (Model 7), variables included in the loglinear specification of the gravity model also have coherent elasticities and signs. Coefficients of variables included in the non-linear (Model 12) for the poorest countries are less coherent than those obtained in the log-linear specification (Model 8). Our results indicate that the linear gravity model seems a better alternative than a nonlinear one and, although one of the main criticisms against using linear gravity equations to analyse trade volumes is the failure to reflect declining trade costs (this is considered puzzling since transport costs have declined over time), it is not clear why a non-linear estimation should resolve this puzzle. For example, Anderson and van Wincoop (2004) point out that the missing globalisation puzzle may not be a real puzzle after all if one realises that since 1913 technology growth in shipping has been relatively slow in comparison to the rest of the economy Conclusions In this research, we estimate a gravity equation augmented with technological innovation and transport infrastructure variables in order to analyse the impact of these variables on trade. Geographical (distance, adjacency, being an island and being landlocked) and social variables (integration, preferential agreements among countries and sharing a language) are also considered. In the empirical model applied in this research work, all the variables included have the expected sign and are significant, excluding some integration variables. We show that distance has a considerably low explanatory power on trade compared with transport infrastructure and technological innovation. Importers technology has a lower effect on 9 Anderson and van Wincoop (2004), page

21 trade than exporters technology and a higher technology endowment in the exporter country leads to greater exports. Moreover, our results support the hypothesis that countries tend to trade more when they are closer from a technological point of view. According to our results, investing in transport infrastructure and technological innovation leads to the improvement and maintenance of the level of competitiveness. These variables can be considered as a barrier to trade for countries with lower endowment levels and, therefore, investing in them increases the participation of the poorest economies in the world economy. We also analyse whether technology has any effect on geographical distance in a more globalised and integrated world. The results indicate that the development of information technology has lowered the effect of distance on trade, since the development of technological innovation means that long distances are less important nowadays than in the past. To infer whether there is a differential behaviour among countries we divide the components of our sample according to their level of economic development. For the high-income countries, the model has a higher explanatory power than for the lowincome countries. Geographical factors are always relevant, but distance and being landlocked have higher elasticities for the poorest countries than for the richest ones. Technological and social factors also seem to be more important for the developing economies. Furthermore, technological endowment in each group of countries seems to be more important for trade flows than technological differences among the countries in the same group. A non-linear specification of the main model is estimated to account for missing trade. The non-linear coefficient elasticities are not comparable to those obtained from the loglinear model. However, a common result can be observed: greater technological 21

22 innovation and transport infrastructure endowment in both the exporter and the importer country leads to higher international trade flows. Moreover, there are different behaviours between the richest and the poorest countries. The non-linear specification of the gravity equation seems to be a good approach to analyse the determinants of international trade for the richest countries and, although the explanatory power is higher for the non-linear than for the log-linear specification, variables included in the log-linear specification of the gravity model also have coherent elasticities and signs. Otherwise, for the poorest countries the coefficients of the variables included in the nonlinear specification are less coherent than those obtained in the log-linear specification. When we compare the Akaike Information Criterion in the linear and non-linear specifications, the AIC is lower in the linear gravity specification than in the non-linear. Therefore, the linear gravity model seems to be a better alternative. An important question that remains open is the degree to which trade is beneficial for all countries in an environment where information flows, new technologies and globalisation are strengthening the interconnection and dependence among all countries. A subject for further research is to study these aspects with regard to developing countries. Finally, the performance of trading blocs and the evolution of the importance of geography and technological innovation could be analysed in an environment marked by globalisation and technological change, by extending the sample to more years and performing a panel data estimation. 22

23 REFERENCES Anderson, J. E. and van Wincoop, E. (2003), Gravity with gravitas: A solution to the border puzzle, American Economic Review, 93, Anderson, J. E. and van Wincoop, E. (2004), Trade Costs, Journal of Economic Literature, XLII, Archibugi, D. and Coco, A. (2002), A new indicator of technological capabilities for developed and developing countries (ArCo), Italian National Research Council. Bougheas, S., Demetriades, P. O. and Morgenroth, E. (1999), Infrastructure, transp ort costs and trade, Journal of International Economics, 47, Central Intelligence Agency CIA (2003), The World Factbook. Coe, D. T., Subramanian, A., Tamirisa, N. T. and Bhavnani, R. (2002), The missing globalization puzzle, IMF Working Paper. Croce, E., Juan-Ramón, V. H. and Zhu, F. (2004), Performance of Western Hemisphere Trading Blocs: A Cost-Corrected Gravity Approach, IMF Worki ng Paper No. 04/109. Cyrus, T. L. (2002), Income in the gravity model of bilateral trade: Does Endogeneity Matter?, The International Trade Journal, XVI, 2, Davidson, R. and MacKinnon, J. G. (1993) Estimation and Inference in Econometrics, Oxford University Press. Deardorff, A. V. (1995), Determinants of bilateral trade: Does gravity work in a Neo - classical word, NBER Working Paper Eaton, J. and Kortum, S. (2002), Technology, geography and trade, Econometrica, Vol. 70, Nº 5,

24 Filippini, C. and Molini, V. (2003), The determinants of East Asian trade flows: a gravity equation approach, Journal of Asian Economics, 14, Foreign Trade Information System (2003): Freund, C. L. and Weinhold, D. (2004), The effect of the Internet on international trade, Journal of International Economics, 62, Garman, G., Petersen J., and Gilliard, D. (1998), Economic integration in the Americas: , Journal of Applied Business Research, Laramine, Summer. Great circle distances between cities (2003): Helpman, E. and Krugman, P. R. (1996), Market Structure and Foreign Trade. Increasing Returns, Imperfect Competition, and the International Economy, Cambridge, MA: MIT Press. Oguledo, V. I. and Macphee, C. R. (1994), Gravity models: A reformulation and an application to discriminatory trade arrangements, Applied Economics, 26, Samuelson, P. A. (1954), The transfer problem and transport costs, The Economic Journal, 64, Soloaga, I. and Winters, L. A. (2001), Regionalism in the nineties: What effect on trade?, North American Journal of Economics and Finance, 12, Statistics Canada (2001), World Trade Analyzer. UNDP -United Nations Development Programme- (2001), Human Development Report, New York, Oxford University Press. World Bank (2001), World Development Indicators, Washington. World Bank (2003), World Development Indicators, Washington. 24

25 APPENDIX A Table A.1: Variable descriptions and sources of data. Variable Description Source X ij : Exports from i to j Nominal value of bilateral exports Statistics Canada (2001) Y i : Exporter s income Exporter s GDP, PPP (current international $) World Bank (2001) Y j : Importer s income Importer s GDP, PPP (current international $) World Bank (2001) P i : Exporter s popula tion Total population in the exporter s market World Bank (2001) P j : Importer s population Total population in the importer s market World Bank (2001) Adj ij : Adjacency dummy Dummy variable = 1 if the trading partners share a border, 0 otherwise CIA (2003) Isl i : Island dummy Dummy variable = 1 if the exporter country is an island, 0 otherwise CIA (2003) Land ij : Landlocked dummy Dummy variable = 1 if the country is landlocked, 0 otherwise CIA (2003) CACM dummy CARICOM dummy MERCOSUR dummy NAFTA dummy CAN dummy UE dummy Dist ij : Distance Lang ij : Language dummy Dummy variable = 1 if the trading partners are members of CACM, 0 otherwise Dummy variable = 1 if the trading partners are members of CARICOM, 0 otherwise Dummy variable = 1 if the trading partners are members of MERCOSUR, 0 otherwise Dummy variable = 1 if the trading partners are members of NAFTA, 0 otherwise Dummy variable = 1 if the trading partners are members of CAN, 0 otherwise Dummy variable = 1 if the trading partners are members of European Union, 0 otherwise Great circle distances between country capitals of trading partners (km) Dummy variable = 1 if the trading partners share the same official language, 0 otherwise. Foreign Trade Information System (2003) Foreign Trade Information System (2003) Foreign Trade Information System (2003) Foreign Trade Information System (2003) Great circle distances between cities (2003) CIA (2003) TAI i : Exporter s TAI Technological variable UNDP (2001), author s calculations TAI j : Importer s TAI Technological variable UNDP (2001), author s calculations ArCo i : Exporter s ArCo Technological variable Archibugi and Coco (2002) ArCo j : Importer s ArCo Technological variable Archibugi and Coco (2002) Inf i : Exporter s infrastructure Transport infrastructure variable CIA (2003), authors calculations Inf j : Importer s infrastructure Transport infrastructure variable CIA (2003), authors calculations Note: UNDP denotes United Nations Development Programme and CIA denotes Central Intelligence Agency. 25

26 Table A.2. Beta coefficients of the variables included in the augmented gravity model. Beta Coefficient Exporter s income Importer s income Exporter s population Importer s population Adjacency dummy Island dummy Landlocked dummy CACM dummy CARICOM dummy MERCOSUR dummy NAFTA dummy CAN dummy UE dummy Distance Language dummy Exporter s TAI Importer s TAI Exporter s infrastructure Importer s infrastructure

27 APPENDIX B Figure 1: Selected countries. Figure 2: Groups of countries. GDPpc High GDPpc Medium GDPpc Low GDPpc 0 Time ( ) Countries with high GDP pc: 10 Belgium-Luxembourg, United States, Norway, Iceland, Switzerland, Canada, Ireland, Denmark, Austria, Japan, Australia, Netherlands, Germany, Finland. Countries with medium GDP pc: France, Sweden, Italy, United Kingdom, Hong Kong, Singapore, Cyprus, Israel, Spain, Portugal, Republic of Korea, Greece, Czech Republic, Argentina, Slovak Republic, South Africa, Uruguay, Costa Rica, Chile, Poland, Mexico, Trinidad and Tobago, Croatia, Brazil, Turkey, Panama, Colombia, Dominican Republic, Bulgaria, Algeria. Countries with low GDP pc: Peru, Syrian Arab Republic, Paraguay, El Salvador, China, Jamaica, Egypt, Honduras, Nicaragua, India, Ghana, Pakistan, Sudan, Senegal, Nepal, Kenya, Mozambique, Tanzania. 10 GDP per capita, PPP (current intern $). Source: World Development Indicators (2003). 27

28 THE NON-LINEAR SPECIFICATION OF THE GRAVITY MODEL: AN EMPIRICAL APPLICATION ON INTERNATIONAL TRADE CELESTINO SUÁREZ-BURGUET, INMACULADA MARTÍNEZ-ZARZOSO AND LAURA MÁRQUEZ-RAMOS DEPARTAMENTO DE ECONOMÍA UNIVERSIDAD JAUME I, CASTELLÓN (SPAIN) INSTITUTO DE ECONOMÍA INTERNACIONAL Abstract In this paper, we estimate a linear and a non-linear augmented gravity model with a 62- cross-country sample. In order to analyse for the presence of heterogeneity, we also analyse bilateral trade flows for different groups of countries, classified according their level of economic development. Our results show that, in most cases, the linear gravity equation seems to be a better alternative and that there is heterogeneity in the sample. 1. Introduction Several authors focus on the specification of the model and support the view that nonlinear models explain bilateral trade better than log-linear models. For example, Coe et al. (2002) refer to the failure of declining trade costs an important aspect of globalisation to be reflected in the estimates of the standard gravity model of bilateral trade. They estimate the non-linear specification of the gravity equation and find evidence of the declining importance of geography. Moreover, the non-linear specification takes into account zero values for bilateral trade and the level of the estimated distance coefficients is more consistent with the theory. In this line, Croce et al. (2004) estimate a non-linear gravity model and find that distance has become less relevant over time. However, although the estimated coefficients have been falling over time, their values still reveal the importance of geography on trade. 1