Gravity equation data

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Homework 4 The Gravity Equation
ECO-13101 Economia Internacional I (International Trade Theory)∗



Rahul Giri. Contact Address: Centro de Investigacion Economia, Instituto Tecnologico Autonomo de Mexico (ITAM).

E-mail: rahul.giri@itam.mx

In this homework, we will depict, graphically, the central themes of the gravity equation: (i) a larger country exports and imports more than asmaller country; (ii) trade between two countries decreases as the distance between the two countries increases. We will carry out this exercise for the OECD countries (though not all of them). Download the excel file named “Homework3Data” from my website. The file has three worksheets: (i) Purchases from Home, (ii) Export Import Matrix, and (iii) Distance Matrix. In Purchases from Home you will finddata on Gross Output (denoted by Yn ) and Total Exports (denoted by En ) for the OECD countries for the year 1996. The data covers three sectors - Agriculture, Mining, and Manufacturing - since these are the commonly accepted traded goods’ sectors. The values are expressed in 1000 U.S. dollars (USD). In Export Import Matrix you will find data on bilateral imports. Each row is importing country, whileeach column is an exporting country. Value in each cell, denoted by Xni , represents the imports of country n (importer - the country for that row) from country i (exporter - the country for that column). The values are expressed in 1000 U.S. dollars (USD). Lastly, Distance Matrix gives data on the distance between trading partners. Each row is importing country, while each column is an exportingcountry. Value in each cell, denoted by τni , represents the distance between country n (importer - the country for that row) and country i (exporter - the country for that column). It is obvious that the distance between two countries is the same irrespective who the exporter or importer is, i.e. τni = τin . Distance is measured in kilometers (Km). Before we can move to plotting the data we needto construct a few important variables. 1. Start by calculating what country n purchases from its own producers. We are going to call this Home Purchases, denoted by Xnn . This is the empty column in worksheet Purchases from Home. Home Purchases are nothing but the amount of gross output of a country that is not exported. So, Xnn = Yn − En .

2

2. Fill the empty diagonal elements of thedata matrix given in worksheet Export Import Matrix with Xnn . The diagonal element represents the home purchases - how much each country buys from its own producers. 3. Calculate the total imports of each country as In =
i=n

Xni , i.e. how much each

country buys from all other countries. This is the empty column Y in worksheet Export Import Matrix. 4. Then, in the same worksheet, calculatethe total expenditure of country n on all traded goods, denoted by Xn , as the sum of expenditure on goods purchased from home producers (Xnn ) and expenditure on imports from all other countries (In ). Xn = Xnn + In . Fill this information in empty column Z . Note that this total expenditure is also referred to as total absorption or market size. Exercise 1: Imports versus Size Plot (scatter plot)total imports In against total absorption Xn , across countries. Let absorption be on the X axis and imports be on the Y axis. Label each axis carefully. This graph should (hopefully!) look similar to the graph on slide 6 of the lecture notes on Gravity Equation. Interpret the graph.

Exercise 2: Market Share and Size Plot (scatter plot) country i’s market share in each destination n, Xni /Xn(on Y axis), against country i’s total production, Yi (on X axis). Note that the figure will also include observations on country i’s penetration of its own domestic market, Xii /Xi . Choose a different symbol to represent this observation (say a + rather than a circle). This graph will, (again hopefully!), look like the one on slide 7 of the lecture notes on Gravity Equation. Interpret the graph....
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