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1 ECON20003 Quantitative Methods

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A group of up to four students may work together and submit one set of assignment answers for the group. All members of the group must be enrolled in the same tutorial. Individuals may work alone if they wish, and submit their own assignment answers, but I urge students to work in groups.

2 Question 1 (55 marks) In this question we use a probit model, and the data set up by Ray Fair, an economist from Yale University, to predict the outcome of 2016 U.S. presidential election. Data on the outcomes of the previous presidential elections, and various variables describing the state of the economy, are stored in the file fair.wf1. The variables in this file relate to the elections held every four years from 1916 to 2012. They are: YEAR year. VOTE democratic share of presidential vote as a percentage. DEMWIN = 1 if VOTE 50.0 INCUMB = 1 if democrat incumbent; ‒1 if republican incumbent. G growth rate GDP in first three quarters of the election year. P inflation rate (GDP deflator) in the first 15 quarters of the current administration; 0 for 1920, 1944, 1948 Z number of quarters in the first 15 quarters of the current administration where real GDP per capita growth > 3.2; 0 for 1920, 1944, 1948 GROWTH = INCUMB G INFLAT = INCUMB P GOODNEWS = INCUMB Z Note that the current incumbent, Barack Obama, is a Democrat. The current candidates for the 2016 election are Hillary Clinton (Democrat) and Donald Trump (Republican). (a) Estimate a probit model for DEMWIN as a function of GROWTH, INFLAT and GOODNEWS. (b) Explain the logic behind the definitions of GROWTH, INFLAT and GOODNEWS. Why do they sometimes take on negative values. (c) What do the signs of the estimates from part (a) suggest? (d) Assuming that it is reasonable to propose one-tail tests, what coefficient estimates are significantly different from zero (i) at a 5% significance level, (ii) at a 10% significance level. (e) As of September 9, 2016, the 2016 values for the key economic variables are GROWTH 0.94 , INFLAT 1.4 and GOODNEWS 2 . Estimate the probability that Hillary Clinton will win the election. (f) How does this probability change if the growth rate had been GROWTH

3, with INFLAT and GOODNEWS remaining the same? (g) How do the probability estimates in parts (e) and (f) compare with those obtained using the linear probability model. 3 (h) Using the probit model and the values of the key economic variables specified in part (e), estimate the marginal effect of a change in the growth rate on the probability of a democratic victory. (i) Use the EViews Wald test option to find the standard error of the probability estimate found in part (e). (j) Do your results from parts (e) and (i) suggest that the probability of Donald Trump being elected could be greater than 0.5. (k) Assuming INFLAT 1.4 and GOODNEWS 2 , and using the probit model estimates from part (a), estimate the growth rate that would be required to make the probability of Donald Trump being elected greater than 0.5. Question 2 (45 marks) The file gwth.wf1 contains quarterly observations on Australian GDP growth (GWTH) from 1959Q4 to 2016Q1. (a) Graph the observations against time using EViews’ View/Graph. Comment on whether the mean and/or variance of the series appear to change over time. (b) A recession is often defined as three or more successive quarters of negative growth. Using the graph and/or the spreadsheet of observations, find the periods in which the Australian economy was in recession. (c) Find the sample autocorrelations 1

Are they significantly different from zero at a 5% level of significance? (d) Estimate an AR(2) model for GWTH. Use it to obtain forecasts and standard errors of forecast errors for growth in 2016Q2, 2016Q3, and 2016Q4. (e) Is there evidence that the residuals from the AR(2) model in part (d) are autocorrelated? If so, what are the implications of this correlation? (f) Estimate an AR(3) model for GWTH. Use it to obtain forecasts and standard errors of forecast errors for growth in 2016Q2, 2016Q3, and 2016Q4. How do these forecasts and standard errors compare with those obtained in part (d)? (g) Is there evidence that the residuals from the AR(3) model in part (f) are autocorrelated?