Instruction
ECON7310: Elements of Econometrics
Research Project 2
Answer all questions following a similar format of the answers to your tutorial questions. When you use R to conduct empirical analysis, you should show your R script(s) and outputs (e.g., screenshots for commands, tables, and figures, etc.). You will lose 2 points whenever you fail to provide R commands and outputs. When you are asked to explain or discuss something, your response should be brief and compact. To facilitate tutors’ grading work, please clearly label all your answers. You should upload your research report (in PDF or Word format) via the “Turnitin” submission link (in the “Research Project 2” folder under “Assessment”) by 10:00 AM on the due date May 11, 2022. Do not hand in a hard copy. You are allowed to work on this assignment in groups; that is, you can discuss how to answer these questions with your group members. However, this is not a group assignment, which means that you must answer all the questions in your own words and submit your report separately. The marking system will check the similarity, and UQ’s student integrity and misconduct policies on plagiarism apply.
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A. Panel Data (45 points)
Background
Do citizens demand more democracy/political freedom as their incomes grow? That is, is democ- racy a normal good? To study this issue, you will explore the dataset income democracy.csv which contains a panel data set from 195 countries for the years 1960, 1965, …, 2000. A detailed data description is given in the table below.1 The dataset contains an index of democ- racy/political freedom for each country in each year, together with data on the country’s income and various demographic controls. The income and all demographic controls are lagged five years relative to the democracy index to allow time for democracy to adjust to changes in these variables.
Research Questions
1. (1 points) Is the data set a balanced panel? Explain. Hint: Look through the dataset
or use the is.pbalanced() function.
2. (6 points) The index of political democracy/political freedom is labeled dem ind.
(a) What is the value of dem ind for the United States in 2000 (1 point)? What is the average of dem ind for the United States over all years in the data set (1 points)?
(b) How many missing values are there for dem ind (1 point)? List all countries with the lowest average value of dem ind (i.e., =0) (2 points). How many countries do have the highest average value of dem ind (i.e., =1) (1 point)? Hint: You can identify
1These data were provided by of M.I.T. and were used in his paper with , , and , “Income and Democracy,” American Economic Review, 2008, 98:3, 808–842.
missing values using the is.na() function and compute sample average for each country using the aggregate() function.
3. (11 points) The logarithm of per capita income is labeled log gdppc.
(a) Regress dem ind on log gdppc using standard errors that are clustered by country. Report your estimation results in a table similar to Table 10.1 on page 378 of SW textbook without the test part (2 points).
(b) Interpret the estimated coefficient on log gdppc (1 points)? Is the coefficient statis- tically significant (1 point)?
(c) If per capita GDP in a country increases by 20%, by how much is dem ind predicted to increase (1 points)?
Construct a 95% confidence interval for the prediction (2 points)?
(d) Why is it important to use clustered standard errors for the regression (2 points)? Do the results change if you do not use clustered standard errors (2 points)?
4. (27 points) Consider panel data regressions.
(a) Suggest a variable that varies across countries but plausibly varies little (or not at all) over time and that could cause omitted variable bias in the regression in Question 3 (Q3) above (3 points).
(b) Estimate the regression in Q3, allowing for country fixed effects. Add the estimation results to the table in 3(a) (3 points). How do your answers to 3(b) and 3(c) change (2 points)?
(c) Exclude the data for Azerbaijan and re-run the regression. Do the results change (2 points)? Why or why not (2 points)?
(d) Suggest a variable that varies over time but plausibly varies little (or not at all) across countries and that could cause omitted variable bias in the regression in Q3 (3 points).
(e) Estimate the regression in Q3, allowing for both time and country fixed effects. Add the estimation results to the table in 3(a) (3 points). How do your answers to 3(b) and 3(c) change (4 points)?
(f) There are additional demographic controls in the data set. Should these variables be included in the regression? If so, re-run the regression, including these controls. Report the regression results in the table in 3(a) (3 points). How do the results change when they are included (2 points)?
A. IV Regression (55 points)
Background
To examine the quantity theory of money, Brumm (2005)2 specifies the inflation equation
inflat = β0 + β1money + β2output + u, (1)
where inflat is the growth rate of the general price level, money is the growth rate of the money supply, and output is the growth rate of national output. Economic theory suggests that β1 = 1 and β2 = −1. Four instrumental variables are proposed for the endogenous variable of output, initial = initial level of real GDP, school = a measure of the population’s educational attainment, inv = average investment share of GDP, and poprate = average population growth rate. The dataset brumm.csv consists of 1995 data on 76 countries.
Research Questions
1. (5 points) Obtain OLS estimates of the inflation equation (1) and report regression results (3 points).3 Test the economic theory using the OLS estimates (2 points). Hint: Use the lm() function.
2. (4 points) Give an intuitive explanation as to why output can be endogenous
3. (8 points) Explain why the proposed instrumental variables (IV) can be valid
4. (38 points) Consider IV regressions.
(a) Using school as an IV for output, obtain TSLS estimates of the inflation equation (1) and report regression results (3 points). Test the economic theory using the IV estimates (2 points). Is school a weak IV (1 point)? Why or why not (2 points)? Are coefficients of model (1) exactly identified, overidentified, or underidentified (2 points)? Is it possible to test the exogeneity of school as an IV (1 point)? Explain your answer (2 points). Hint: Read Section 12.3 of SW textbook.
(b) Using school and poprate as IVs, obtain TSLS estimates of the inflation equation (1) and report regression results (3 points). Test the economic theory using the IV estimates (2 points). Are coefficients of model (1) exactly identified, overidentified, or underidentified (2 points)? Does this TSLS regression suffer from weak IV problem (1 point)? Why or why not (2 points)? Test the exogeneity of school and poprate as an IV (2 points). Hint: Use the summary() function with option diagnostics = TRUE.
(c) Using all the four IVs, obtain TSLS estimates of the inflation equation (1) and report regression results (3 points). Write out the regression equation for the first stage least square estimation (3 points). Test the economic theory using the IV estimates (2 points). Does this TSLS regression suffer from weak IV problem (1 point)? Explain your answer (2 points)? Test the exogeneity of these four IVs (2 points).
2Brumm, . “Money growth, output growth, and inflation: A reexamination of the modern quantity theory’s Linchpin Prediction.” Southern Economic Journal (2005): 661-667.
3For simplicity, assume the error u in model (1) is homoskedastic.
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