ECOM2000: Econometric Principles ? Data Analysis Project - Economics Assignment Help

Assignment Task

1. Introduction

One of the hypotheses that have been widely discussed in the literature of development/ environmental economics is the Environmental Kuznets Curve (EKC). It states that the relationship between a country’s national income and the extent of environmental degradation is in an inverted U?shape. That is, the extent of environmental degradation increases with national income at a diminishing rate and starts decreasing as national income increases further beyond a certain level. In this project, we will test the EKC hypothesis empirically using data from the World Bank.

2. Preliminary

Data collection

To do this project, you need to download the following data from the World Bank’s (WB’s) World Development Indicators (WDI).

Data Cleaning/Formatting

Before analyzing data, you have to follow several steps to clean and rearrange it. First, opening the data file in Excel, you notice that the data downloaded from the WB are arranged as:

You see that the data are stored in rows 2?869, and below them, you see the following texts in lines 873 and 874:

Data from database: World Development Indicators

Last Updated: ##/##/2022

Please delete these two lines and save the Excel file under the same name.

Next, we need to convert the data format from a long form (data on 4 variables from 217 countries are stacked vertically in one column) into a wide form (data are stored in a table form so that the first column stores the country name and subsequent columns store the data on one variable in each column).  There are many ways to perform this transform, but one possible way is to execute the following in R:

We are familiar with the first line, which reads the Excel data into the workspace (you need to change the file path). The second line converts the data from a long form into a wide form and save the new data as “datw.”  We also want to shorten the variable names so that they are easier to handle.  We can try:

Now, a new data matrix “datw” contains the country name in the first column and the data on four variables (CO2, GDPpc, PopDen, and UrbPop) in columns 2?5.   

Two more steps we need to take before analyzing the data are: (1) convert missing values from “..” into “NA” and eliminate them from dataset, and (2) change the data type from character to numerical.  These can be done by:

The first line changes “..” into “NA” (which is the default value for missing observations in R), while the second line eliminates these missing observations from the dataset.  The remaining four lines change the data type from character into numeric for the four variables.  Now we are ready to analyze the data.   

3.  Data Analysis

Analyze the WDI data using R/RStudio and answer the following 11 questions.  

1. Create a new variable “CO2k” by converting the data on CO2 emissions from metric tons per capita into kilograms (kg) per capita (by multiplying the original data “CO2” by 1,000). Then, create a scatter plot of CO2 emissions per capita in kg (vertical axis) against per capita GDP (horizontal axis). Please label each axis clearly.

2. Under the assumption that CO2k (CO2 emissions per capita in kg) is distributed independently and identically in the population, construct a 90% confidence interval of the population mean of CO2 emissions per capita (in kg) manually (that is, using the sample mean, sample variance, and the appropriate critical values obtained from either R or statistical tables). Interpret the calculated confidence interval.

3. Estimate a multiple regression model with CO2 emissions per capita (in kg) as the dependent variable, and GDP per capita, GDP per capita squared, population density, and the share of population living in urban areas as explanatory variables. Write down the estimated sample regression equation.

4. For the regression model estimated in Question 3, interpret the reported R?squared as well as the standard error of the regression. Briefly comment on the model’s goodness of fit to the observed data.

5. For the regression model estimated in Question 3, provide interpretations of the estimated coefficients for PoPDen and UrbPop.

6. For the regression model estimated in Question 3, test if the true population coefficient for PoPDen is negative at a 10% test size, using a critical value approach. State clearly the null and alternative hypothesis.

7. For the regression model estimated in Question 3, construct a 99% confidence interval of the true population coefficient for UrbPop manually (that is, using the estimated coefficient, standard error and the appropriate critical values obtained from either R or statistical table). Interpret the obtained confidence interval.

8. Using the regression model estimated in Question 3, calculate the predicted values of CO2k for a range of GDP observed in the sample (with 1,000 increments) whilst keeping the values of PopDen and UrbPop at their respective sample means. Create a two? dimensional diagram with the predicted values of CO2k (vertical axis) is plotted against GDP (horizontal axis). Briefly describe the relationship between CO2 emissions per capita and GDP per capita as implied by the estimated regression model. Does this have the shape you expected? Explain why/why not?

9. Based on the model estimated in Question 3, find the level of GDP per capita where the effect of GDP per capita on CO2 emissions changes its sign. Briefly comment on how this relates to your answer to Question 8 above.

10. Describe how you could test a joint hypothesis that the true population coefficients for PopDen and UrbPop are both equal to zero at a 5% significance level. State the null and alternative hypothesis, and clearly present how to calculate the appropriate statistic.

11. Implement the joint hypothesis test as described in Question 10 at a 5% significance level.

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