Econ 6160-Spring 2012 Homework 3 (due 02/14) 1. Wooldri

Econ 6160-Spring 2012 Homework 3 (due 02/14) 1. Wooldridge textbook: C8.12 12.5 C12.2 C12.5 C12.10 2. In the following OLS regression HWI is help-wanted advertising index U is unemployment rate (e.g. if the unemployment rate is 7.2% U=7.2) and the data is 72 quarterly observations S1 S2 and S3 are quarterly dummy for the first second and third quarter respectively. (.11) (.27) 1 1 2 2 3 3 7.31 0.54 log( ) t t t t t HWI ? ? ? U ?? S ?? S ?? S (R2=0.96; Durbin-Watson statistic DW=3.90) a. Test at the 5% level of significance for first order autocorrelation for the error terms in the model. Based on the test can you use the above estimated model? b. If the error terms follow both regular AR(1) and seasonal autocorrelation (i.e. AR(4)) how would you estimate the model efficiently? Give details. c. If HWIt-4 is added to the model how would you test the null hypothesis that the disturbance terms are not serially correlated against the alternative that they follow a seasonal autoregressive model of AR(4) (give details)? d. With HWIt-4 added in the model and the test shows that the error terms follow AR(4) can you use OLS? Explain why? How would you estimate the model efficiently?
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