Introduction
As the globe is getting smaller every day, the trade between countries is increasing every day. There was a time when each country tried to become self-sufficient to sustain on its own. Those days are gone now. Now, a country needs to be efficient in one so that it can export it to others and in return buy things from others in which they are efficient. In this way both benefit.
International trade is one of the biggest financial and economic areas for any kind of research. Economists always try to find out the factors that drive international business. Is it a fact that countries sharing good relation trade with each other more than countries far away from them. Can we say safely that if two economies are big then there is more chance of trade between them than one big and another small economy? Is total trade dependent on population of both countries? All these are questions that I will try to answer looking at the data for Canada.
Gravity Model in International Business
In 1962, Jan Tinbergen the father of gravity model put forth the concept of international trade and the influencing factors. His observation was the trade between two countries dependent on primarily two factors. The trade volume gets positively impacted by the mass of economy of the two countries and gets inversely impacted by the distance of two countries. He also identified that the attraction of trade between two countries is like the force of attraction between two heavenly bodies so his equation exactly matches the force of attraction equation of physics . His original equation is as below.
Now in this nonlinear form of the equation is not easy for prediction . forecasting as with different levels the elasticity of the constant term “G” changes making the equation different at different levels of Ms and Ds.
Or in more simplistic form
Ln(Total Trade) = Constant 1 + Constant 2*Ln(GDP of home country) +Constant3*Ln(GDP of trading partner) + Constant 4*(Distance between two countries)
Note that in our case as Constant2*Ln(GDP of Home country ) is constant as the country is Canada for us only so we will drop that part of the equation from our analysis.
We will first do a simple linear regression like below
Total trade = Constant 1+ Constant2*GDP of trading company +Constant3*Distance between two countries.
Then we will use the Gravity equation to compare it with the simple linear regression results to see if it gives us better results.
Multiple- Linear Model Analysis for Canada
First let look at the data for Linear equation. We have gathered data for Canada for the year 2010 in the following parameters:
- GDP of that country ( Millions of $)
- Population of that country ( Millions)
- Export from Canada to that country ( Millions of $)
- Import from that country to Canada ( Millions of $)
- Distance of the partner country from Canada ( Miles)
As we have data for almost 169 countries for 2010, we will try to establish if at all there is any relationship between the Total Trade of Canada (Export+ Import) and other factors (GDP, Distance and Population) of the partner country.
First, we will try to look at the Linear model and try to find out if there is any significant association between the dependent variable (Canada-Total Export) and the independent variables ( GDP, Population and Distance).
Scatter Diagram
We have plotted all three variables against Total Trade to see if they are related in some way or not to the independent variables. This also checks the randomness of the observations. It seems that there may be some relations but which are not very visible at this point of time.
Now to go one step ahead we constructed the linear equation to see if there any linear interaction between the variables.
The regression equation is as follows
Y=Total Trade = C0 + C1*GDP +C2*Population+C3*Distance
We ran the regression and found the below result.
First let us look at the significance of the test. From the F Stat we can see that F is very high (239.677) with a significance of F = 6.7 *10^(-60) , which is smaller than 0.05 so with 95% confidence level, so we can safely say that there is some interaction between the dependent variables and independent variables. Therefore, we may reject the Null Hypothesis: HO at 95 % confidence level and accept the alternate hypothesis that there is some relationship between the variables.
Then if we look at the regression statistics we can say that Adjusted R Square value is =80.99% which means the independent variables are able to explain almost 81% of the variability in Y (Total Trade) which is very significant and fits well into the model.
Now we see at the individual level statistic of the dependent variables. We see that the intercept and distance have a P value which is higher than 0.05 (0.65 for Intercept and 0.64 for Distance) and so we cannot reject the null hypothesis for those two. In fact, we have to say looking at this model that there is not much evidence that distance has any relationship with Total Trade of a country.
However, we suspect this may also occur because of some dependent variables which are connected to each other and causing the model to blow up and creating problem for other related variables. To do that, we ran a Correlation test for all the variables. We noted the following:
We can see that among the dependent variables, GDP and Population are correlated. There is 46 % correlation coefficient between the two. With this observation we can say that considering only one of those two, variables will be sufficient for our model. So we reduce our initial model to the below form now.
Y=Total Trade = C0 + C1*GDP +C2*Distance
Then we ran the regression test once again to find the result as below:
Now we can see that the F value is still high and significance of F is smaller than 0.05. This means we can reject the Null Hypothesis at 95% confidence level.
The adjusted R Square value is still very healthy 77.66% of which means it is a very good fit.
If we look at individual statistics we see that still the p value of Distance and Intercept is very high and thus we cannot reject the Null hypothesis for those two dependent parts.
After analysis we can say that if we have to construct a linear relationship between Total Trade and others then it can be best described by the below equation
Y (Total Trade) = C1*GDP =0.025666474*GDP
Gravity Model of International Trade
Let’s now look at the gravity model and we first look at the scatter plot to see if we can see any visible pattern between Ln(Total Trade) vs Ln(GDP) and Ln(Total Trade) vs. Ln(Distance)
We can see that log of GDP and Total Trade now has a very distinct positive relationship. However from the scatter plot same cannot be very strongly said for Log of distance and Total Trade. However there is a small negative correlation between the two it seems form the plot.
We will however now do a regression analysis see how far that is true.
As above we have seen that as per Gravity equation
Ln(Total Trade) = Constant 1 + Constant2*Ln(GDP of trading partner) + Constant 3*(Distance between two countries)
We have made our data as per the above equation to test regression result. Now we have the dependent variable = Ln(Total Trade)
Our regression equation result is as below
The F value is almost same as our linear equation = 280 and Significance of F is much lower than 0.05 so we can safely say that the dependent and independent variables are highly correlated and we can easily reject Null Hypothesis and accept the alternate hypothesis .
If we now look at the regression statistic we see that Adjusted R Square value is 76.9% which is extremely good and it seems the model is a very good fit. It is however still same as the linear model. At this point we can say that our current model is as good a fit as the gravity model.
If we now look at the individual statistic we see
For the intercept the p value is 0.03 so at 95% confidence level we can keep the intercept value. It was not the case in our liner equation. We could not reject the null hypothesis in case of linear equation but we could definitely reject the null hypothesis here for the intercept.
For the GDP we already had a very good relation for linear equation and in case of LOG(GDP) the interaction remains strong and the p value is low . So it remains a factor for Log(Total Trade)
In case of linear equation we had distance not found to be a good enough fit in the model and we could not reject the Null Hypothesis. However, in case of Log(Distance) the t value and the p value indicates strong interaction. Distance has a negative coefficient so it is inversely related to Total Trade.
So our final equation for Canada becomes
Ln(Total Trade) = 4.2528 + 1.0078 Ln(GDP of the partner country) -1.09126 ( Distance)
This is exactly what the gravity equation tells us. It is a much stronger relation between the two than the ordinary linear equation.
This model can be used to figure out the potential countries where Canada has trade opportunities and trade can be expanded. It can also be used to predict trade potential between a country and Canada.
This clearly shows that the Gravity model explains the international trade much better than simple regression models.
Works Cited
- Ben Shepherd , The gravity model of international trade , United Nations , Retrieved on 9th May , 2013 from http://www.unescap.org/tid/publication/tipub2645.pdf
- The Gravity Model of bilateral trade, Institute of International Economics, Retrieved on 9th May , 2013 from http://www.piie.com/publications/chapters_preview/72/4iie2024.pdf
- Global Finance, Retrieved on 9th May 2013 from http://www.gfmag.com/gdp-data-country-reports/304-canada-gdp-country-report.html#axzz2SpuoGEG3
