ECON7310: Elements of Econometrics
Final Problem Set
Ruby Nguyen
November 6, 2023
Instruction
Please answer all questions following a format similar to 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 of commands, tables, and figures). You will lose 2 points whenever you fail
to provide R commands and outputs. Please clearly label all your answers and keep your
response brief and concise. You should upload your research report (in PDF or Word format)
via the Turnitin submission link (in the “Final Problem Set” folder under “Assessment”) by
11:59 AM on the due date November 09, 2023. You are allowed to work on this assignment
in groups; however, 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 will apply.
Binary Choice Models
You want to study female labour force participation using the swiss.csv dataset, which
contains a sample of 872 women from Switzerland. The dependent variable is participation,
which is a binary variable that equals 1 if the female is in the labour force and 0 otherwise.
Explanatory variables include age, income, education (years of schooling), youngkids and
oldkids (numbers of young and older children), and foreign (=1 if not Swiss citizen).
1. (30 points) Regress participation on age, age2, income, education, youngkids,
oldkids, and foreign using a linear probability model (LPM).
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(a) (3 points) Report the regression results.
(b) (10 points) Is there evidence of a nonlinear effect of age on female labour force
participation? Do the coefficients on age have the expected sign? What is the
effect of a one-year age change from 29 to 30 years old while holding the other
variables constant?
(c) (9 points) Interpret the estimated coefficient on education. What is the effect of a
4-year increase in educational attainment, keeping other variables constant? Test
if the population coefficient is zero.
(d) (8 points) How would you modify the model to test if the effect of an additional
year of education differs for Swiss and non-Swiss females? Implement this test and
report the result.
2. (20 points) Now run a logit regression of participation on age, age2, income,
education, youngkids, oldkids, and foreign.
(a) (6 points) Report the regression results and calculate the pseudo-R2 for the logit
regression using the logLik() function (refer to the help file for usage details).
(b) (6 points) Use the logit model to compute the difference in predicted probability
between Swiss and non-Swiss females at the sample median values of all other
explanatory variables.
(c) (8 points) Use the logit model to predict the probability of being in the labour
force for a Swiss female with three young kids, no old kid, and the median age,
income, and education level of the sample. Does the result differ if you compute
this predicted probability using the LPM in 1(a)? Explain the difference (if any).
Time Series Models
The data set us macro monthly.csv contains monthly data on several macroeconomic series
for the United States. For all regressions in Questions 3 and 4 below, use the sample period
1986:M1 – 2017:M12 (that is, January 1986 through December 2017).
3. (32 points) The variable INDPRO is the Index of Industrial Production (IP), which
measures the quantity of industrial commodities produced in a given month.
Let Yt = 1200× [ln(INDPROt)− ln(INDPROt−1)].
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(a) (4 points) What does Yt measure? What are the units of Yt?
(b) (8 points) Estimate an AR(4) model for Yt. Use this AR(4) model to forecast the
value of Yt and INDPROt in January 2018.
(c) (3 points) Suppose you are worried about potential seasonal fluctuations in produc-
tion and therefore add Yt−12 to the AR(4) model. Is the estimated coefficient on
Yt−12 statistically significant?
(d) (8 points) Suppose you are worried that you might have included too few or too
many lags in the model in (b). You then estimate AR(p) models for p = 1, 2, ..., 9
over the same sample period. Use the BIC to estimate the number of lags that
should be included in the autoregression.1 Does the outcome change if you use the
AIC instead? If there is a difference, which criterion (BIC or AIC) do you favour?
Explain your answer.
(e) (9 points) Using the AR(4) model for Y with a sample period beginning in 1986:M1,
compute pseudo out-of-sample (POOS) forecasts for the IP growth beginning
in 2007:M1 and going through 2017:M12; that is, compute Y2007:M1|2006:M12,
Y2007:M2|2007:M1, ..., Y2017:M12|2017:M11. Plot these forecasts against the actual
values. How large is the root mean squared forecast error (RMSFE) of the POOS
forecasts? Is it larger than the standard error of the regression (SER, also called
residual standard error) obtained from an AR(4) model for Y estimated over the
1986:M1 – 2006:M12 sample period (the in-sample regression)?
4. (18 points) Let Xt = ∆TB3MSt, where TB3MSt is the interest rate on three-month U.S.
Treasury bills (measured in percentage points at an annual rate).
(a) (5 points) Compute the first twelve autocorrelations of Xt. Comment briefly on
these autocorrelations.
(b) (7 points) You augment your AR(4) model in Question 3(b) by adding four lagged
values of Xt. This modification leads to a specific type of model. What is the name
of this model? Does the change in interest rates help predict IP growth? Explain.
(c) (6 points) Regresses Xt on a constant, four lags of Xt, and four lags of Yt. Does IP
growth help to predict the change in interest rates? Explain.
1Hint: When you use the ts() function in R, frequency needs to be set to 12 because the data are monthly.