UNIVERSITY OF MELBOURNE DEPARTMENT OF ECONOMICS SEMESTER 1 ASSESSMENT, 2019 ECOM30001: Basic Econometrics Time Allowed: TWO Hours Reading Time: 15 minutes This examination paper contributes 60 percent to the assessment in ECOM30001. This examination consists of four (4) questions in total. You must answer ALL four questions. Each question is worth twenty (20) marks for a maximum of 80 marks. The examination paper should be inserted in the back of your answer booklet at the end of the examination. The following items are authorized in the examination room: -Casio FX-82 (any suffix) calculator This exam has 19 pages. The paper may not be removed from the exam room. Answer all questions in the examination booklet(s) provided. The examination contains a formula sheet starting on page 14. The examination contains critical values for a number of distributions starting on page 17. Page 2 of 19 Question 1 a) [5 marks] Consider the following econometric model: yi = β0 + β1Xi + εi What is meant by the term heteroskedasticity in the random error What are the con- sequences for the OLS estimator if you ignore heteroskedasticity in the random error εi Briefly outline how you would test for the presence of heteroskedasticity using White’s test. Your answer should clearly state the null and alternative hypo
theses, the test statis- tic and its distribution. b) [5 marks] Consider the following econometric model: yi = β0 + β1X i + εi Consider the following measurement equation relating the observed value for X to the ‘true’ value X : Xi = X i + υi with COV(X i , εi) = 0 and COV(υi, εi) = 0. What is meant by the term classical measurement error Clearly explain the implications for the OLS estimator of β1 if the explanatory variable X is observed with (classical) measurement error. c) [5 marks] Consider the following econometric model: yt = β0 + β1Xt + εt What is meant by the term autocorrelation in the random error Clearly explain the consequences for the OLS estimator if you ignore autocorrelation in the random error εt. Briefly outline how you would test for first order AR(1) autocorrelation in the random error. Your answer should clearly state the null and alternative hypotheses, the test statistic and its distribution. Page 3 of 19 d) [5 marks] Consider the following regression: inft = β0 + β1 inft 1 + β2 inft 1 + β3 inft 2 + β4 inft 3 + β5 inft 4 + εt where inf represents the quarterly inflation rate. This econometric model was estimated using the method of Ordinary Least Squares (OLS) for the period 1948:Q1 to 2016:Q1 and the results are presented in Figure 1.