Department of Agricultural and Resource Economics Elisabeth ...
Department of Agricultural and Resource Economics University of California at Berkeley
Elisabeth Sadoulet and Andrew Dustan Fall 2010
ENV ECON 118 / IAS 118 – Introductory Applied Econometrics Assignment 1 Due Tuesday September 14, 2010 at the beginning of class The first two exercises are based on data that I downloaded from the World Bank Indicators website on CO2 emissions and GDP per capita (http://devdata.worldbank.org/dataonline/) for 2006. To construct exercises that are manageable, I have selected some countries. But if you are interested in seeing the original data, I have made a graph that shows all the countries. You can also see the values for selected countries in the Table of exercise 1.
Source: World Development Indicators (http://devdata.worldbank.org/dataonline/)
Exercise 1. Relationship between GDP per capita and CO2 emission As you see on the graph, there is a strong association between GDP per capita and CO2 emission across countries. We will establish this relationship on a (very small) subset of 8 large countries. Data for these countries are reported in the following Table.
Table 1. GDP per capita and CO2 emissions for large countries, 2006
Country
GDP/capita (2000 US$)
Bangladesh 421 Brazil 4087 China 1612 Germany 24470 India 637 Japan 39772 Nigeria 456 United States 37674 Source: World Development Indicators
CO2/capita (tons) 0.3 1.9 4.7 9.8 1.4 10.1 0.7 19.3
(a) Draw the scatter diagram of these observations. Don’t forget to write labels and units of measurement on the axes and a title for your graph. (b) Estimate the linear relationship between GDP per capita and CO2 emission by OLS, showing all intermediate calculations as we did in the handout (you are encouraged to use Excel to create the table but you must show all the steps):
E ˆ0 ˆ1GDP / cap Interpret the value of the estimated parameters. (c) Compute the fitted values and the residuals for each observation, and verify that the residuals (approximately) sum to 0. (d) According to the estimated relation, what is the predicted E of a country with a GDP/capita of 2000US$ 3000? (e) How much of the variation in CO2 emission for these 8 countries is explained by their GDP per capita? Exercise 2. Functional forms We explore here alternative functional forms for the relationship between CO2 emission and GDP per capita (in 2000 US$). Using all the countries from the World Development Indicators database, I estimated the following equations: A linear relationship: E = 2.29 + 0.00035 GDP/cap A log linear relationship: E = -16.21 + 2.71 log(GDP/cap) A log-log relationship: log(E) = -5.90 + .845 log(GDP/cap) Interpret the parameter on GDP/cap (or log(GDP/cap)) in each of these equations. What is the predicted energy use for a country with a GDP/cap of $3000 with each of the models? Exercise 3. Importing data into Stata (a) After the Stata introduction session, you should have a folder on your computer called “EEP 118 [your name]”. Within that folder, create a subfolder called “CO2emisions”. Download the CO2 emission data from the course website and save it in your new CO2emisions folder. (b) Open Stata and change directories so that you are now in your CO2emisions folder. (c) Turn on a log file to record the following commands and output. (You will submit the log file as your answer to this exercise on the assignment.) NOTE: If you do not specify the “text” option for your log
file, Stata will default to its “.scml” format, which you will only be able to open/print on computers that have Stata installed. If you are working in the lab and need to print your log file somewhere else, be sure to specify the “text” option. (d) Show that you are in the CO2emisions subfolder of your EEP 118 folder by displaying your present working directory with the “pwd” command. (e) Load the data into Stata (use either “Import” under the File menu, or the “insheet” command). (f) Provide summary statistics on the CO2 emission variable using the “summarize” command with the “detail” option. (g) Close your log file and print it out.
Elisabeth Sadoulet and Andrew Dustan Fall 2010
ENV ECON 118 / IAS 118 – Introductory Applied Econometrics Assignment 1 Due Tuesday September 14, 2010 at the beginning of class The first two exercises are based on data that I downloaded from the World Bank Indicators website on CO2 emissions and GDP per capita (http://devdata.worldbank.org/dataonline/) for 2006. To construct exercises that are manageable, I have selected some countries. But if you are interested in seeing the original data, I have made a graph that shows all the countries. You can also see the values for selected countries in the Table of exercise 1.
Source: World Development Indicators (http://devdata.worldbank.org/dataonline/)
Exercise 1. Relationship between GDP per capita and CO2 emission As you see on the graph, there is a strong association between GDP per capita and CO2 emission across countries. We will establish this relationship on a (very small) subset of 8 large countries. Data for these countries are reported in the following Table.
Table 1. GDP per capita and CO2 emissions for large countries, 2006
Country
GDP/capita (2000 US$)
Bangladesh 421 Brazil 4087 China 1612 Germany 24470 India 637 Japan 39772 Nigeria 456 United States 37674 Source: World Development Indicators
CO2/capita (tons) 0.3 1.9 4.7 9.8 1.4 10.1 0.7 19.3
(a) Draw the scatter diagram of these observations. Don’t forget to write labels and units of measurement on the axes and a title for your graph. (b) Estimate the linear relationship between GDP per capita and CO2 emission by OLS, showing all intermediate calculations as we did in the handout (you are encouraged to use Excel to create the table but you must show all the steps):
E ˆ0 ˆ1GDP / cap Interpret the value of the estimated parameters. (c) Compute the fitted values and the residuals for each observation, and verify that the residuals (approximately) sum to 0. (d) According to the estimated relation, what is the predicted E of a country with a GDP/capita of 2000US$ 3000? (e) How much of the variation in CO2 emission for these 8 countries is explained by their GDP per capita? Exercise 2. Functional forms We explore here alternative functional forms for the relationship between CO2 emission and GDP per capita (in 2000 US$). Using all the countries from the World Development Indicators database, I estimated the following equations: A linear relationship: E = 2.29 + 0.00035 GDP/cap A log linear relationship: E = -16.21 + 2.71 log(GDP/cap) A log-log relationship: log(E) = -5.90 + .845 log(GDP/cap) Interpret the parameter on GDP/cap (or log(GDP/cap)) in each of these equations. What is the predicted energy use for a country with a GDP/cap of $3000 with each of the models? Exercise 3. Importing data into Stata (a) After the Stata introduction session, you should have a folder on your computer called “EEP 118 [your name]”. Within that folder, create a subfolder called “CO2emisions”. Download the CO2 emission data from the course website and save it in your new CO2emisions folder. (b) Open Stata and change directories so that you are now in your CO2emisions folder. (c) Turn on a log file to record the following commands and output. (You will submit the log file as your answer to this exercise on the assignment.) NOTE: If you do not specify the “text” option for your log
file, Stata will default to its “.scml” format, which you will only be able to open/print on computers that have Stata installed. If you are working in the lab and need to print your log file somewhere else, be sure to specify the “text” option. (d) Show that you are in the CO2emisions subfolder of your EEP 118 folder by displaying your present working directory with the “pwd” command. (e) Load the data into Stata (use either “Import” under the File menu, or the “insheet” command). (f) Provide summary statistics on the CO2 emission variable using the “summarize” command with the “detail” option. (g) Close your log file and print it out.
