Economics-QA263 Online Services

 

Problem Set : The Gravity Model

 
Recall the gravity model of international trade in which exports from country i to country j (Xij ) can be described by the following regression
 
Xij = e_0Y _1 i Y _2 j dist_ where Yi is the GDP (size) of exporter i, Yj is the GDP (size) of importer j, and distij is the distance between the two countries in kilometres. The coe_cients to be estimated are _0 (the constant), _1, _2, and _3.
 
1. Take natural logs of the above expression to convert the multiplicative gravity model to a log-linear Model .Using the data in the spreadsheet \Gravity Model Problem Set.xlsx”, take natural logs of exports, GDP, and distance. This is not the same data as we used in the tutotial. Remember to name these variables so that you can reference them later (e.g. you can name the log of exporter GDP as \l rgdp i”). Import the data into the statistical package of your choice.
 
2. Report the mean value of exporter GDP, importer GDP, the value of shipments, and distance between exporter and importer.
 
3. Plot (log) distance on the x-axis against (log) exports on the vertical axis. Include this graph in your problem set. Is a further distance between two countries correlated with more or less exports?

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4. Use ordinary least squares regression to estimate _0, _1, _2, and _3. Present the standard error and t-statistic for each coe_cient (against the null hypothesis that it is zero) to two decimal places. Can we say that each variable is significantly different from zero at the 95% level of certainty?
 
5. Suppose that we consider exports from two countries i and i0 to some country j. Assume that both i and i0, have the same GDP but i is 250km from j while i0 is 1000km away. What are exports from country i0 to j as a proportion of those from i to j? (use a calculator for this).
 
6. Now estimate the e_ect of two countries having a common colonizing country in their past.3 This can be done by estimating a regression where comcolij is a dummy variable that takes a value of if countries i and j share a common colonizer in the past.
ln(Xij) = _0 + _1ln(Yi) + _2ln(Yj) + _3ln(distij) + _4comcol
 
Present standard errors of each coefficient and the t-statistic to two decimal places. For each variable, is it significantly different from zero at the 95% level of certainty? Everything else equal, what is trade between two countries that do not have a common colonizer in their past relative to two countries that do?

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