As described earlier, the process of the integration of agri-food markets during the second half of the twentieth century was especially important among high-income countries and then, in the 1990s, so were the latest increases in South–South trade flows. We would therefore like to study here the determinants of agricultural trade, employing a disaggregated approach to trade flows for different subsamples of countries.

To analyze the factors determining the changes in the direction of agricultural trade flows during a substantial part of the second half of the twentieth century, the present article estimates the gravity equation for the bilateral volume of agricultural trade, analyzed separately in four categories of regional trade flows. We use the data for bilateral trade flows published by the United Nations Statistics Division in the UN-COMTRADE database (2003). These data were taken from the figures for bilateral exports (FOB—free on board). The sample includes trade among 30 exporters to 39 markets, whose trade flows are representative of international trade flows in agri-food products.^{Footnote 7} With regard to the representativeness of the sample employed, in the 38 years covered, this varied from 66 to 76 % of international trade in agricultural products. It largely followed the trend of the complete series of world agricultural trade (Serrano and Pinilla 2010). The representativeness of the sample exceeds 95 % in the processed foods groups, those of high-value and other processed agricultural products, while basic and plantation products represent only approximately 50 %, due to the lower presence of low-income countries specialized in this type of products.^{Footnote 8}

We constructed export flows by volume for agricultural and food products, following the system of the Standard International Trade Classification (SITC, Revision 2)^{Footnote 9} (in 1995 US$) for the period 1963–2000. Trade in agricultural and food products is that included in the SITC groups 00-04.^{Footnote 10}

The database therefore consists of four data panels comprising trade flows among the countries included in the sample and classified, following the United Nations Statistics Division, according to their level of development.^{Footnote 11} Thus, trade flows are classified into four categories, the first of which is among high-income countries (N–N). As Table 2 shows, their bilateral trade flows achieved strong growth. The second is trade flows which originate in high-income countries and are destined to low-income countries (N–S). The third is trade flows whose origins are in developing countries and are exported to the developed world (S–N); their trade in primary products was based on previous stages and grew very slowly in the study period. The final category is trade flows between low-income economies (S–S), whose growth of exchanges accelerated in the final fifteen years of the last century.

We now propose the specification of the gravity equation we shall use. The empirical approach is based on the work of Feenstra et al. (1998), Bergstrand (1985, 1989) and Anderson and van Wincoop (2003). The success of this methodological approach in explaining international trade patterns has led economists to formally develop its theoretical foundations. The empirical validations of the gravity equation, such as those performed by Helpman (1987), Hummels and Levinsohn (1995), and Evenett and Keller (2002), conclude that the equation can be derived from different theoretical models. This is an eclectic vision of trade determinants which includes, in a complementary fashion, the Hecksher–Ohlin models with specialization (Anderson 1979; Deardorff 1984; Anderson and van Wincoop 2003) and the models of the New International Trade Theory with increasing returns and monopolistic competition (Helpman and Krugman 1985), allowing the gravity equation to be better reconciled with the theoretical models.

Applying logarithms, the functional form of the equation is as follows:

$$ \begin{gathered} ln \, X_{ijt} = \, \beta_{1} + \, \beta_{2} ln \, \left( {Y_{it} } \right) \, + \, \beta_{3} ln \, \left( {Y_{jt} } \right) \, + \beta_{4} ln\left( {Ypcp_{it} } \right) \, + \, \beta_{5} ln\left( {Ypcp_{jt} } \right) \hfill \\ + \, \beta_{6} lnDist_{ij} + \, \beta_{7} lnExcvol_{ijt} + \, \beta_{8} Border_{ij} + \, \beta_{9} Lang_{ij} \hfill \\ + \, \beta_{10} Both\_in\_RTA_{ijt} + \, \beta_{11} One\_in\_RTA_{ijt} + \, \beta_{11} NRA_{ijt} \beta_{11} \hfill \\ + \, GATT_{ijt} + \delta_{ijt} + \varepsilon_{t} \hfill \\ \end{gathered} $$

(1)

where *X*_{
ijt
} represents agricultural exports flows, by volume, from country *i* to country *j* in year t, in 1995 US dollars (the series for each product group has been deflated by the respective price indices to obtain the volume series); *Y*_{
it
}**and***Y*_{
jt
} are the real GDP of both the exporting country and the importing country, in year t, in 1995 US dollars (World Development Indicators (WDI, 2012); *Ypcp*_{
i,
}*Ypcp*_{
j
} : is the per capita GDP of both the exporting and importing countries, in year t, in 1995 US dollars (WDI CD-ROM 2004); *Dist*_{
ij
} is the distance between the capitals of the countries of origin and destination (CEPII database); *Excvol*_{
ijt
}: is an indicator of exchange rate volatility in year t (estimation of the standard deviation of the first difference in the natural annual logarithm of the nominal bilateral exchange rate for the pair of countries in the ten-year preceding period t,^{Footnote 12} exchange rate data are drawn from WDI, 2012); *Border*_{
ij
} is a dummy variable which takes the value of 1 if the countries have a common border and 0 otherwise; *Lang*_{
ij
} is a dummy variable which takes the value of 1 if the countries share a common language and 0 otherwise; *Both_in_RTA*_{
ijt
} is a dummy variable which takes the value of 1 if the two countries belong to the same following regional trade agreements (EU, NAFTA, CER, APEC, MERCOSUR, ANDEAN, ASEAN, GSTP) and 0 otherwise;^{Footnote 13}*One_in_RTA*_{
ijt
} is a dummy variable which takes the value of 1 if only one country belong to the some of the following regional trade agreements (EU, NAFTA, CER, APEC, MERCOSUR, ANDEAN, ASEAN, GSTP) and 0 otherwise; *NRA*_{
ijt
} is a dummy variable which takes the value of 1 if the exporter country does not have agricultural assistance from the government and 0 otherwise; *GATT*_{
ijt
} is a dummy variable aimed at capturing the impact of the various rounds of GATT. Concretely, *GATT*_{63-94}, is a dummy variable, used if the two countries belonged to that body prior to the Uruguay Round (1994). Additionally, *GATT*_{94-05} is a dummy variable, employed if the two countries were members of GATT following the implementation of the agreements reached in the Uruguay Round of GATT (1994).

In the traditional proposal of the gravity equation, *X*_{
ijt
} represents the volume of trade flows between two countries. This depends on the geographical distance between the countries (*Dist*_{
ij
}), which is usually presented as an obstacle to trade and treated as an approximation of transport costs. It also depends on the size of their markets, which is usually approximated by the value of their income (*Y*_{
it
}*, Y*_{
jt
}), which permits us to observe that the potential of a country to offer (export) its products depends on its size, measured by GDP, while the foreign demand for these products will depend on the size and growth of the GDP of the importing country. As in the vast majority of studies, we also include multiple variables, such as geographical proximity (if the countries share a border) and cultural proximity (the existence of historical or cultural ties, such as a colonial relationship or a common language). The coefficients of all of these variables are expected to be positive.

Following Bergstrand (1989), the equation introduced countries’ per capita GDP (*Ycpc*_{
it,
}*Ycpc*_{
jt
}). The inclusion of this variable in the model allows us to describe trade in different types of goods. According to Bergstrand, the coefficient of per capita income in the exporting country may be considered an approximation of its factor endowment. This coefficient is positive in the case of capital-intensive goods and negative for labor-intensive goods. Likewise, the coefficient of per capita income in the importing country serves to define the type of good and will produce a positive sign for superior goods and a negative one for inferior goods.

Following other authors (Cho et al. 2002; Rose 2000), meanwhile, the model includes different measures of the volatility of bilateral exchange rates (*Excvol*_{
ijt
}). The objective in the present case is to examine the impact of exchange rate uncertainty on trade flows. This coefficient is expected to display a negative sign (i.e., the greater the instability of exchange rates, the lower the growth of trade between two countries).

With regard to the institutional context, the specification of the gravity equation has been refined in many studies to take account of factors that may limit or hinder trade. As in many studies, we have introduced dummy variables to analyze the effect of regional liberalization produced on the one hand, and the effects of the multilateral liberalization of international markets on the other. In the case of RTAs, we have constructed two dummy variables: Both_in_RTA is 1 if countries i and j are both members of the same RTA at time t and 0 otherwise. And One_in_RTA is 1 if the importer country i belongs to a RTA but the exporter j does not. A positive coefficient for both suggests trade creation. A coefficient which is positive for the first but negative for the second suggests trade diversion (this last case is only proposed for RTAs in the North). In the case of multilateral market liberalization, various dummy variables were included to explore the effects of membership of free trade associations, following the proposal made by Rose (2004). The aim is to examine the effects of the various rounds of the General Agreement on Tariffs and Trade (GATT). Both the result and the sign of this variable are uncertain.

In our case, we have also attempted to control for the effect of discriminatory policies, which were developed in some countries regarding export agriculture. It is very difficult to approximate these policies with a simple indicator. Nevertheless, we have attempted to do so using a dummy variable based on the Nominal Rate of Assistance (NRA) to export products. Anderson and Valenzuela (2008) estimate distortions and agricultural incentives from 1955 to 2007. We use as a proxy of distorsions the index of the Nominal Rate of Assistance to exportable agricultural goods. This dummy variable takes the value of 1 if the exporter country has a negative value higher than 0.10 and 0 otherwise. Given that for some countries and years, Anderson and Valenzuela (2008) do not provide this datum, we have assumed in these cases that its value was the same as that first existing. For this reason, we have considered it safer to establish the limit for the dummy variable at −0.10. The variable in the case of North countries is always 0, because in these countries during the whole time horizon of the study farmers were strongly subsidized (this variable always takes positive values).

Lastly, in line with the recent work by Anderson and van Wincoop (2003), the equation includes “multilateral (price) resistance terms”, which are proxied by dummy variables. The method consists of using country fixed effects for importers and exporters (Rose and van Wincoop 2001; Feenstra 2004; Baldwin and Taglioni 2006). It designates a dummy variable for a specific year and one per year. These variables reflect the effect of all the singularities of the exporting and importing nations that might affect trade between two countries and are not captured by the remaining variables specified in the empirical model. Finally, the model includes the error term (*ε*_{
t
}) which is assumed to be log-normally distributed.

With regard to the estimation technique, our aim is to overcome the limitations of previous research which has only taken into account the variations among the units of observation (cross-section analysis). The present study also examines the time variations within the observation units. The use of panel data increases the efficiency of the estimators and significantly reduces the potential problems caused by the omission of variables (Hiaso 1986). From this perspective, three types of data panel estimation are proposed: the first is the estimation of ordinary least squares (OLS) with the grouped panel; the second and third take into account the time variation, by the inclusion in the model of random effects and fixed effects, respectively.

In order to determine which of the three estimators is most efficient, the LM Breusch–Pagan test for random effects was employed; this permitted us to choose between OLS estimation of the grouped panel and estimation with random effects. Following the application of the Breusch–Pagan test, it was concluded that random effects are significant, and it is therefore preferable to use such an estimation rather than the grouped panel estimation. Similarly, to demonstrate that the inclusion of fixed effects was a more appropriate method than the other two we employed initially, various tests were performed. Firstly, the F test (Greene 2000) of the significance of fixed effects indicated that their estimations were better than when the OLS estimation of the grouped panel was employed. Secondly, the Hausman test demonstrated that the estimators of random effects and of fixed effects differ significantly and that the fixed effects model provides a better explanation of the sources of variation and is therefore more appropriate than the random effects model.

It is important to underline here that, despite having modeled temporal and spatial heterogeneity, according to a Wald test (Greene 2000) our model poses problems of heteroscedasticity and, according to the Woolridge test (Wooldridge 2001), problems of autocorrelation also exist. Lastly, the Breusch–Pagan test, used to identify problems of contemporaneous correlation in the residuals of the fixed effects model, likewise confirms the need to correct this problem. The above-mentioned problems of contemporaneous correlation, heteroscedasticity and autocorrelation can be solved jointly and were resolved by the estimation of panel-corrected standard errors (PCSEs).^{Footnote 14} On the positive side, once the problems of estimator specification were corrected, the models continued to function well. The principal variables present the expected sign and are statistically significant.

On this point, and in addition to these technical reasons, there are also theoretical motives for preferring the fixed effects estimation (Feenstra 2004, 161–163). As stated earlier, Anderson and van Wincoop (2003) derived a gravity equation specification using a model that includes the presence of “multilateral (price) resistant terms”, which was approximated using fixed effects by country pairs.^{Footnote 15} Furthermore, Baier and Bergstrand (2007) conclude that, for the analysis of trade agreements, the fixed effects approximation is best.