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ECOM30002/90002 Econometrics 2, Semester 2, 2020
ASSIGNMENT 4
Instructions and information
Submit online through LMS no later than 8am Friday, 30 October.1 assignments
submitted late (for whatever reason) incur a five-mark per (full) hour late penalty.
Assignments can be completed individually (on your own) or by a group (of up to four
students). Students in a group do not have to be from the same tutorial. Equal marks are
awarded to each group member.
Assignment groups must be formed through LMS (Canvas) before they are ‘locked’ at
10am, Tuesday, 27 October; after that, they cannot be changed. Assignments must be
submitted after groups are locked. More information on group formation to follow.
Please include on the front page the names and ID numbers of all group members. Assignments should be submitted as a fully typed document (pdf or Word). Question
numbers should be clearly indicated.
Requested regression output must be presented in clearly labelled tabular form. For questions requiring interpretation, explanation and/or discussion, concise correct
answers will be valued over lengthier unclear off-topic ones. Test any hypotheses at the 5% level unless otherwise stated.
If performing calculator-based calculations, to maximize accuracy, please do not round
intermediate results, and report final answers to four decimal places.
Notes
This assignment has two questions comprising 10 parts and will be marked out of 50 (all
question parts—(a), (b), (c) etc.—are worth five marks each).
Up to five marks in total can be deducted for not doing the following:
for parts marked (*), providing neatly tabulated regression output (e.g., from texreg or
stargazer); raw R-Studio output from the console is not sufficient;
providing your R code.
(Tables and code can be in appendices.)
1 This due date is later than originally planned because this assignment covers material included in lecture 22,
which will not be released until 22 October. (More time is being given to absorb that material.)
2
Data set: To complete this assignment, use the file WP.csv, which contains Australian
aggregate time series data from 1992 quarter 1 (1992, q1) to 2017 quarter 1 (2017,
q1), inclusive, on the following variables:
natural log of nominal wages per person employed ( , henceforth ‘log wages’)
natural log of nominal consumer prices ( , henceforth ‘log prices’)
Note: in the questions below, the following notation is used:
= log wages; = log prices.
QUESTION 1
(a) Plot and over time on the same graph and describe both variables’ main feature(s).
(b) Based on a maximum lag of eight, use VARselect (see, e.g., tutorial 10) to choose an
appropriate lag length for a VAR model for and . Report the chosen lag length.
(c) (*) Write out in equation form your chosen estimated equation for from (b) above.
(d) Use your estimated equation for to forecast log wages two periods ahead. Report
these forecasts.
(e) Based only on its residual correlogram (autocorrelation function),2 does your chosen
equation for constitute a valid forecasting model, and why (or why not)
2 Ignore any potential nonstationarity concerns for now. (We get to that it question 2.)
3
QUESTION 2
Consider the ARDL(2,2) model,
= 0 + 1 1 + 2 2 + 1 1 + 2 2 + . (2.1)
Embedded within this dynamic equation is a static one that expresses the long-run relationship
between the variables. To see this, let equilibrium be reached in the long run, and let
equilibrium be characterized by no change; i.e., = 1 = 2 = , and 1 = 2 = . Based on this characterization of equilibrium, one can derive the long-run relationship
between and implied by (2.1). This takes the form
= + , (2.1a)
where and are defined in terms of the s and s. (Note that was set to its expected value
of zero.)
(a) (*) Use your parameter estimates from (2.1) to estimate and in (2.1a) above. What
does your estimate of suggest about what was happening to equilibrium real wages
over the sample period
(b) Having used your results from (a) above to generate the linear combination
= , (2.2)
using a maximum lag of eight, test for a unit root in . Does your test result suggest
that and are cointegrated Report the relevant -value on which your decision is
based and use it to explain your answer.
(c) Using a maximum lag of eight, use suitably specified unit root tests to establish the
order of integration of each of and . Report the relevant -values on which your
decisions are based and use them to explain your answers.
(d) (*) Given your answers to (b) and (c) above, specify and estimate an appropriate time
series model for and in which the maximum levels lag is the same as that in (2.1)
above, and write out your estimated model in equation form.
(e) Use your estimated model from (d) above to forecast log wages two periods ahead.
Having reported these forecasts, compare them with those you obtained in part (d) of
question 1 above and explain why they are similar or different.