ECON 7310: ELEMENTS OF ECONOMETRICS
Coordinator: Dr. Dong-Hyuk Kim
Research Project 2
Due: 4 pm, 25 Oct
Submission of your report
Your report must be single-spaced and in 12 Font size. You should give your answer to each of the
following questions following a similar format of the solutions to the tutorial problem sets. When you
are required to use R, you must show your R command and R outputs (screenshots or figures gener-
ated from R). You will lose 2 points whenever you fail to provide R commands and outputs. For each
question, when you are asked to discuss or interpret, your answer has to be brief and compact. You
will lose 2 points if your answer is needlessly wordy.
The Turnitin system may slow down as the deadline approaches due to high traffic from multiple
submissions. To avoid potential issues, submit your report well in advance. This time, late submission
penalties will be strictly based on the submission time recorded in the system. Do not email your
assignment or submit a hard copy if you miss the deadline.
This project has two research questions. You are required to investigate both of them.
Problem 1: Money, Growth, and Inflation (40 marks)
Background
To examine the quantity theory of money, Brumm (2005) [“Money Growth, Output Growth, and
Inflation: AReexaminationoftheModernQuantityTheory’sLinchpinPrediction,”SouthernEconomic
Journal, 71(3), 661–667] specifies the inflation equation
inflat = β +β money+β output+u
1 2 3
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 β = 1 and
2
β = −1. The dataset brumm.dta consists of 1995 data on 76 countries.
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Research tasks
1. It is argued that output may be endogenous. Four instrumental variables are proposed:
• inv = average investment share of GDP,
• initial = initial level of real GDP,
• school = a measure of the population’s educational attainment, and
• poprate = average population growth rate.
(a) Give an intuitive explanation as to why output can be endogenous (4 marks)
(b) Explain why the proposed IVs can be valid with no computation. (6 marks, i.e., 2 marks for
understanding of valid IVs and 1 mark for convincing story for each IV.)
2. Using inv only as an IV, obtain TSLS estimates of the inflation equation (4 marks), and test the
economic theory using the IV estimates (4 marks).
3. Using the regression above (Q2), determine whether inv is weak as an IV or not (4 marks)
4. Assuming that inv is valid, re-estimate the model using all four IVs and test if the IVs are
exogeneous (4 marks). Do you prefer the estimates here or the ones in Q2? Explain (4 marks).
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5. Modify the inflation equation above to allow the effect of output on inflat to depend on money
(4 marks). Suppose that inv is the only valid IV among the four candidates above. How many
endogenous variables your modified model has (2 marks)? Discuss how you would consistently
estimate the model coefficients (4 marks). Note: You do not need to compute the estimates.
Problem 2: Demand for Democracy (60 marks)
Background:
Do citizens demand more democracy and political freedom as their incomes grow? That is, is democ-
racy a normal good? To investigate this issue, you will explore the dataset Income Democracy.dta
which contains a panel data set from 195 countries for the years 1960, 1965, ... , 2000. A detailed
description is given in Income Democracy Description.pdf.1 The dataset contains an index of politi-
cal freedom/democracy for each country in each year, together with data on the country’s income and
various demographic controls. (The income and demographic controls are lagged five years relative to
the democracy index to allow time for democracy to adjust to changes in these variables.)
Research tasks:
1. Is the data set a balanced panel? Explain. (5 marks)
2. The index of political freedom/democracy is labeled dem ind.
(a) What is the value of dem ind for the United States in 2000? What is the average of dem ind
for the United States over all years in the data set? (4 marks) Repeat this exercise for Libya
(2 marks).
(b) List five countries with an average value of dem ind greater than 0.95; less than 0.10; and
between 0.3 and 0.7. (5 marks)
3. The logarithm of per capita income is labeled log gdppc .
(a) Regressdem indonlog gdppcusingstandarderrorsthatareclusteredbycountry(3marks).
(b) How large is the estimated coefficient on log gdppc? Is the coefficient statistically signifi-
cant? (2 marks)
(c) If per capita income in a country increases by 20%, by approximately how much is dem ind
predicted to increase? What is a 95% confidence interval for the prediction? Is the predicted
increase in dem ind large or small? Explain what you mean by large or small. (5 marks)
(d) Why is it important to use clustered standard errors for the regression? Do the results
change if you do not use clustered standard errors? (4 marks)
4. (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 above. (5
marks)
(b) Estimate the regression in Q3, allowing for country fixed effects. How do your answers to
Q3(b) and Q3(c) change? (5 marks)
(c) Exclude the data for Azerbaijan and rerun the regression. Do the results change? Why or
why not? (5 marks)
(d) Suggest a variable that varies over time but plausibly varies little–or not at all–across coun-
tries and that could cause omitted variable bias in the regression in Q3. (5 marks)
(e) Estimate the regression in Q3, allowing for time and country fixed effects. How do your
answers to Q3(b) and Q3(c) change? (5 marks)
(f) There are addition demographic controls in the data set. Should these variables be included
in the regression? If so, how do the results change when they are included? (5 marks)
1These data were provided by Daron Acemoglu of M.I.T. and were used in his paper with Simon Johnson, James
Robinson, and Pierre Yared, “Income and Democracy,” American Economic Review, 2008, 98:3, 808–842.
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