Econometric Estimation of a Gravity Model for the External Trade of Romania

The gravity model is frequently used to analyse bilateral trade statistics. In the paper we will identify, exclusively for Romania, the significant factors of influence on bilateral trade flows. As factors, we will consider the clasical gravity variables and some suplimentary dummy variables. Also, we will determine, using the estimated equation of the gravity model, the efficiency of Romanian international trade with its partners.


Introduction
The gravity model is widely used in econometric analysis of international statistics.For the foreign trade, the gravity model analyses the determinants of bilateral trade flows, the goal being the development of more precise predictions on the bilateral trade.
Newton's gravitational equation measures the maximum force between two masses that are separated in space.Trade gravity equation follows the same principle, measuring trade that may exist between two countries, mainly depending on the distance between them and their level of development, plus a few specific factors.
Literature review shows two time periods of intensive use on empirical gravity model of trade, separated by a period of theoretical foundations of the model.The first uses of gravity equations are from 1960, in 1962 when Tinbergen and then, in 1963, Pőyhőnen applied the gravity model to explain the commercial trade between two partner countries using the classical equation, in which the factors are the product of GDP's of the two countries (positive correlation) and geographical distance between the two partners (negative correlation).
After 2000, the papers are highly empirical, extending the model with a number of factors that show geographical, historical or economic relationships between the partner countries.This paper is empirical and aims to identify significant influence factors on bilateral trade flows between Romania and its trade partner countries, in order to estimate the degree of the external trade efficiency, identifying the most effective and most ineffective foreign trade partnership for Romania.The econometric model used for this purpose is not a proper gravity model, since we only used the bilateral trade flows between one reference country, Romania, and its trading partners, but it uses gravity variables as explicative factors.

Methodology and Data
The standard expression for the trade gravity ecuation is: -Fij represents the bilateral trade flows between country i and country j; -C is the constant of the equation; -GDPi is the gross domestic product for the country i; -Dij is the distance between the capitals of the two partner countries.
The equation is linearised using the logarithm function, and the gravity model of trade will have the following form: In addition to these traditional explanatory variables, the model may include a number of additional variables, dummy or not, geographical, historical or economic, relevant to explain trade between two partner countries.Glick and Rose (2002) have introduced a number of additional variables, such as the existence of common borders, a common language, a common currency and some variables showing colonial links between the two countries -a variable indicating whether one was current or past colonized by the other, and a variable showing whether the two countries have the same colonizer.Franklin, Stream and Wei (1995)

Estimation of the Econometric Trade Model
Parameters were estimated using Ordinary Least Squares method, and for the selection of the regression variables was used the stepwise method.
The parameters of the econometric model were estimated with SPSS 17.0 software.
The results show that bilateral trade flows (BTF) are explained by GDP, the distance between the two countries, the partner country's foreign direct investment in Romania and the existence of common borders between Romania and the partner country.

The positive correlation between:
-BTF and GDP shows that Romania has more intense external trade with countries that have higher GDP than with the countries with lower GDP; -BTF and FDI_dummy shows that Romania has more intensified trade activities with countries that invested more than 100 million euros, compared to countries with low or zero foreign direct investment; -BTF and BORD_dummy shows that Romania has a bigger trade volume with countries having a common border, territorial or by sea.
The negative correlation between BTF and the geographical distance shows that the greater the distance between Romania and the partner country, the lower is the trade volume between the two.Dependent Variable: BTF a.
Model errors were tested for normality and independence.The results are presented in Tables 4 and 5.The assumption that the errors are normally distributed is accepted (Sig.= 0.777> 0.05), as well as the error's independence hypothesis (Sig.= 0.64> 0.05).

Determination of Efficient and Inefficient Trade Partnerships for Romania
To analyse the efficiency of Romania's bilateral trade with a partner country, we have analysed the model error series that resulted from estimating the trade model.Negative error values shows that the real value of the BTF is below the estimated one, and positive error values indicate that the real value is greater than the estimated value.The working hypothesis is that negative error values indicate an inefficient trade, which has not reached its potential and positive error value show an effective trade, above the theoretical potential.
To determine the degree of trade efficiency or inefficiency, we calculated, for the error series, the one standard deviation interval around the mean, which is (-1, +1).If the error values are outside the range, then for positive values there is a high efficiency of bilateral trade and for negative values we have a highly inefficient trade.The result is presented in Table 6.

Concluding Remarks
In this paper we presented an external trade model, derived from a gravity model, in order to identify significant explanatory variables for bilateral trade between Romania and partner countries.Based on the obtained model error values, we determined the partners and areas to which Romania develops, efficient or inefficient, foreign trade activities.
The results for Romania confirm existing studies.Thus, bilateral trade flows (BTF) are explained on the one hand, by the GDP of the partner country, by the FDI in Romania and the existence of a common border, between which we have positive ccrrelations, and other hand, the distance between the two countries, which has a negative correlation with BTF.
Values for the model errors showed an efficient bilateral trade with EU member states and an inefficient one with the other European countries, and the best trade partnerships are with European, East and Southeast Asian countries.
The analysis was carried out for exports and imports of both goods and services, but recent studies have shown differences between the trade models of goods and the trade model of services, so a further study for the building of a sectorial model for external trade would be very useful.