In physics Newton's law of universal gravitation also know as the gravity equation is given by: 

where is a gravity constant, mass one, mass two and is the distance between the two masses.
 

The equation states that the force between two objects is equal to a gravity constant times the product of

the masses divided by the square of the distance between the two masses.


 

Now the gravity model in economics or more specifically in trade theory is derived from the gravity equation in physics.  

The economic version of the gravity equation is given by:
 

where is the amount of trade between country one and two, is the GDP in country one,

is the GDP in country two, is a distance variable, and are partial trade elasticity for example

if we increase GDP in country one with one percentage point then is going to increase/decrease with percentage points.
 

We now assume that the distance variable is equal to the inverse of the actual distance between country one and 

country two represent by .  

(1)

which can be written as: 

(2)

If we take the logarithm on both sides we get: 

(3)

which can be written as: 

(4)

which is the econometric equation we are going to estimate. 

We can now load the data set set which consists of UK's Top 25 Trading Partners in the month of March 2009. 

The data has been collected from HM Revenue and Customs UK, Overseas Trade Statistics https://www.uktradeinfo.com/ 

The data set also consists of GDP which has been collected from http://en.wikipedia.org/wiki/Main_Page 

The distance data has been collected from http://www.wolframalpha.com. 

Note also that the distances has been calculated between the capital cities for all the countries.  

We start by analyzing the import data which is given by  

We now apply the logarithm and inverse transformation as discussed previously  

(5)

We can now run the regression 

	(6)

The above results tells us that if we increase the inverse of the distance with one percentage point then the the UK

import from that country is going to increase with 497.3 percentage points. Note that in order to increase we must decrease D 

which means that if we decrease the distance between UK and the exporting country with one percentage point then the the UK  

import from that country is going to increase with 497.3 percentage points.  

We can now analyze the export data which is given by  

We again apply the logarithm and inverse transformation as discussed previously  

(7)

We can now run the regression 

	(8)

The above results tells us that if we increase the inverse of the distance with one percentage point then the the UK

export to that country is going to increase with 518.2 percentage points. Note that in order to increase we must decrease D 

which means that if we decrease the distance between UK and the importing country with one percentage point then the the UK  

export to that country is going to increase with 518.2 percentage points.  

To summarize we can say that the findings are more or less in line what we initially suspected. The further the distance  

the lower is the trade flows between countries. Another interesting finding is that if we increase the distance between UK and 

and a trading country then the export flow from the UK to that country is going to decrease more than the import flow from that

country to the UK. One explanation to that might be transport costs. Finally we should not that the distance variable is only one

of many explanatory variables of trade flows and that only looking at monthly trade flows might give a distorted picture. 

The End !