1 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: 𝐿𝐿𝐿𝐿𝑡𝑡 natural log of nominal wages per person employed (𝑤𝑤𝑡𝑡, henceforth ‘log wages’) 𝐿𝐿𝐿𝐿𝑡𝑡 natural log of nominal consumer prices (𝑝𝑝𝑡𝑡, henceforth ‘log prices’) Note: in the questions below, the following notation is used: 𝑤𝑤𝑡𝑡 = log wages; 𝑝𝑝𝑡𝑡 = log prices. QUESTION 1 (a) Plot 𝑤𝑤𝑡𝑡 and 𝑝𝑝𝑡𝑡 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 𝑤𝑤𝑡𝑡 and 𝑝𝑝𝑡𝑡. Report the chosen lag length. (c) (*) Write out in equation form your chosen estimated equation for 𝑤𝑤𝑡𝑡 from (b) above. (d) Use your estimated equation for 𝑤𝑤𝑡𝑡 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 𝑤𝑤𝑡𝑡 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, 𝑤𝑤𝑡𝑡 = 𝛽𝛽0 + 𝛽𝛽1𝑤𝑤𝑡𝑡−1 + 𝛽𝛽2𝑤𝑤𝑡𝑡−2 + 𝛿𝛿1𝑝𝑝𝑡𝑡−1 + 𝛿𝛿2𝑝𝑝𝑡𝑡−2 + 𝑢𝑢𝑡𝑡. (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., 𝑤𝑤𝑡𝑡 = 𝑤𝑤𝑡𝑡−1 = 𝑤𝑤𝑡𝑡−2 = 𝑤𝑤, and 𝑝𝑝𝑡𝑡−1 = 𝑝𝑝𝑡𝑡−2 = 𝑝𝑝. Based on this characterization of equilibrium, one can derive the long-run relationship between 𝑤𝑤 and 𝑝𝑝 implied by (2.1). This takes the form 𝑤𝑤 = 𝑎𝑎 + 𝑏𝑏𝑏𝑏, (2.1a) where 𝑎𝑎 and 𝑏𝑏 are defined in terms of the 𝛽𝛽s and 𝛿𝛿s. (Note that 𝑢𝑢 was set to its expected value of zero.) (a) (*) Use your parameter estimates from (2.1) to estimate 𝑎𝑎 and 𝑏𝑏 in (2.1a) above. What does your estimate of 𝑏𝑏 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 𝑒𝑒𝑡𝑡 = 𝑤𝑤𝑡𝑡 − 𝑎𝑎� − 𝑏𝑏�𝑝𝑝𝑡𝑡, (2.2) using a maximum lag of eight, test for a unit root in 𝑒𝑒𝑡𝑡. Does your test result suggest that 𝑤𝑤𝑡𝑡 and 𝑝𝑝𝑡𝑡 are cointegrated? Report the relevant 𝑝𝑝-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 𝑤𝑤𝑡𝑡 and 𝑝𝑝𝑡𝑡. Report the relevant 𝑝𝑝-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 𝑤𝑤𝑡𝑡 and 𝑝𝑝𝑡𝑡 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.