ECON7310: Elements of Econometrics 
Research Project 3 
Fu Ouyang 
October 25, 2022 
Instruction 
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 3” folder under “Assessment”) by 11:59 
AM on the due date November 7, 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. 
A. IV Regression (55 points) 
Background 
To examine the quantity theory of money, Brumm (2005)1 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. The dataset brumm.csv consists of 1995 data on 76 countries. 
Research Questions 
1. (12 points) It is argued that output may be endogenous. Four instrumental variables 
are proposed, 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. 
(a) Give an intuitive explanation as to why output can be endogenous (4 points). 
(b) Explain why the proposed instrumental variables (IV) can be valid (8 points). 
2. (5 points) Obtain OLS estimates of the inflation equation (1) and report regression 
results (3 points).2 Test the economic theory using the OLS estimates (2 points). Hint: 
Use the lm() function. 
1Brumm, Harold J. “Money growth, output growth, and inflation: A reexamination of the modern quantity 
theory’s Linchpin Prediction.” Southern Economic Journal (2005): 661-667. 
2For simplicity, assume the error u in model (1) is homoskedastic. 
1 
3. (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). 
B. Time Series Regression (45 points) 
Use the data in CONSUMP.csv to answer the questions below. 
One version of the permanent income hypothesis (PIH) of consumption is that the growth in 
consumption is unpredictable. Let gct = log(ct) − log(ct−1) be the growth in real per capita 
consumption (of non-durable goods and services). Then the PIH implies that E[gct|It−1] = 
E[gct], where It−1 denotes information known at time t− 1 (e.g., gc1, ..., gct−1); in this case, t 
denotes a year. 
(a) (5 points) Compute the first five autocorrelations of gct. 
(b) (8 points) Test the PIH by estimating gct = β0 +β1gct−1 +ut (2 points).3 Clearly state 
the null and alternative hypotheses (4 points). What do you conclude (2 points)? 
(c) (7 points) Estimate AR(p) models for p = 1, ..., 5 and report regression results (5 points). 
What lag length is chosen by the BIC (1 point)? What lag length is chosen by the AIC 
(1 point)? 
(d) (12 points) Add variables gyt−1, i3t−1, and inft−1 to the AR model you chose in (c) by 
BIC.4 Report the new regression results (4 points). Are these new variables individually 
or jointly significant at the 5% level (8 points)? 
(e) (6 points) For the regression in (d), what happens to the p-value for the t-statistic on 
gct−1 (2 points)? Does this mean the PIH hypothesis is now supported by the data (1 
point)? Explain your answer (3 points). 
(f) (7 points) For the regression in (d), what is the F -statistic and its associated p-value 
for joint significance of the four explanatory variables (3 points)? Does your conclusion 
about the PIH now agree with what you found in (b) (1 point)? Explain your answer (3 
points). 
3You do not need to compute robust standard errors for any time series regressions in this question. 
4gyt is the growth in real disposable income, i3t is the interest rate as measured by the return on three-month 
T-bill rates, and inft is the inflation rate based on the Consumer Price Index.