Economic theory and methodology 

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Economic theory and methodology

Economic theory

Gravity Model has proven itself surprisingly successful economic model over more than 50 years since its first use in Economics. The success of the Gravity Model has urged some economists to think that there should be some underlying economic theory behind this model. Anderson (1979) was the first one to derive the Gravity Model under the assumption of perfect competition. To derive the model Anderson assumes identical Cob-Douglas preference functions for all countries. He further assumes that the countries produce differentiated goods. After Anderson, it was Bergstand (1985) who derived the gravity model on the basis of the general equilibrium model of trade. In contrast, Deardoff (1998) derives the Gravity Model by the use of the Hecksher-Ohlin model. Deardoff assumes that distance can serve as a proxy to the trade barriers between countries. In his paper he shows that the Gravity Model is compatible with both Hecksher-Ohlin and Ricardian Model. Eaton and Kortum (2002) offered an alternative derivation of the model using Ricardian technology with heterogeneous productivity for all countries and iceberg trade costs.
Anderson and Van Wincoop’s (2003) paper ‘’Gravity and Gravitas’’ has become quite famous in explaining the theoretically-based Gravity Model derivation. Due to the complexity of the mathematical derivation, in this section we will present only the intuitive explanation of the model. In general, Anderson and Van Wincoop’s (2003) gravity model can be compared to a demand function. The building blocks for their gravity model are constant elasticity of substitution structure and consumer preferences. Consumers are assumed to have ‘’love for variety’’, which indicates that their consumption increases as they consume more of a particular variety or if they consume different varieties. From the production point of view, firms produce single unique product variety with increasing returns to scale. There are a large number of firms operating in an economy, which makes the firms apply constant mark-up pricing. The firms can sell their products in any country. It is further assumed that the sale in the home country doesn’t involve any transportation costs. However, if the firms sell abroad they will incur additional transportation costs. Consumers buy different product varieties from different countries but the price of imported goods is relatively higher due to the transportation costs. Firms produce both for the local and foreign markets and thus are engaged in international trade. By aggregating the firms in the economy it would be possible to derive an expression for the export which can serve as a dependent variable in the gravity model. By aggregating across the firms and applying macroeconomic identities it is also possible to derive a gravity model. What makes the Anderson and Van Wincoop’s (2003) model stand out from other authors’ derivations is the inclusion of outward and inward multilateral resistance variables. Outward multilateral resistance measures how the export from country to country depends on the trade costs to all other export markets. In contrast, the inward multilateral resistance measures how the import to country from country depend on the trade costs across all suppliers.

Model

Firstly, we use a standard model then we proceed to the extended model. We use standard gravity model suggested by Brun et al. (2005):
Bilateral trade between 2 countries is proxied by import data. and are respective GDPs of countries and and so are the population figures and . is the distance between the 2 countries. We insert quadratic time trend to the formula to the see the evolution of distance coefficient over given time. The time trend takes the quadratic form to allow for a turning point in the coefficient.
In the regression results we are mostly interested in the coefficients of the quadratic time trend. The reason we are interested in these coefficients is because they will be later used for the construction of distance index. This index will show the evolution of the distance coefficient over time. By analysing this coefficient we can deduce whether distance coefficient has increased or decreased over time. Using the values from the quadratic time trend we plot the line graph and if the line graph shows downward tendency we can deduce that elasticity of trade to distance has decreased (Brun et al. (2005)).
We expect GDP and population to have positive sign in the estimation because in general, countries with larger GDP are expected to trade more and also countries with more population will import more (Head & Mayer (2013)). Distance which serves as a proxy for transportation costs and other transactions costs should have a negative sign for the reason that countries trade more with countries closer to them and less with countries which are far away. Dummy variable of common border is expected to have a positive sign while the dummy variable of landlockedness a negative sign (Gardner et al. (2009)). Price of oil can also be expected to have a negative sign because it represents the transport cost which increases as the distance between the trading partners increases (Mario et al. (2010)).

Panel unit root and cointegration

In our research we are going to utilize panel data structure, which is a common practice among researchers working on gravity model. One of the advantages of the panel estimation is that it gives more degrees of freedom and therefore the estimates are more efficient. In addition to this, longitudinal panel data controls for the individual unobserved heterogeneity, which is usually present in the trade data (Brüderl, 2005).
It is commonly accepted that in dealing with gravity model the panel approach is superior to the cross-section approach, however, as it has been noted by Zwinkels et al. (2010), there might still be issues related to the time-series variables in the model that has to be dealt with. The problem arises when one tries to regress two or more time series variables on each other. This might lead to spurious regressions even if the variables do not have any causal relationship, the regression estimates might appear to be significant with high R square for the model (Wooldridge 2012). Although we try to avoid spurious regressions as much as we can, but some of the variables in the gravity model such as GDP, import and export tend to be usually non-stationary and integrated of order one. Moreover, these variables also tend to be co-integrated (Zwinkels et al. 2010).
In order to check whether our data suffers from the non-stationarity and the co-integration we apply panel unit root test and Pedroni cointegration test. We utilize Augmented Dickey Fuller (ADF) Fisher Chi-square statistics of the panel unit root test to determine whether the variables have unit root. ADF unit root test assumes an individual unit root as a null hypothesis. The formula of the test is:
∆   =  ₀ +            ₋₁ + ∑  ∆    _{−  +1} +
It is important to note that the t-statistics doesn’t follow the usual students’ t-distribution. The critical values of the test depend on the specification of intercept, deterministic trend or both and calculated by Dickey and Fuller (1979). The advantage of this test over other tests is that can be used for unbalanced panel, which is the case with our data. The results of the panel unit root test can be found in the table 4.

1. Introduction
1.1 Background
1.2 Previous Research
1.3 Purpose
2. Literature review 
3. Economic theory and methodology 
3.1 Economic theory
3.2 Model
3.3 Panel unit root and cointegration
3.4 Estimation method
4. Data Sources and variables 
5. Results 
5.1 Preliminary tests
5.2 Regression Results
6. Conclusion 
Reference
Appendix
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Decline in Distance Effect in International Trade