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Econ*3740 Introductory Econometrics
1. Obtain the data canadian_forest_fires_1950-2017.csv from Course Link. Using the steps in the R Tutorial Manual Section 8.4, regress the annual Number of Forest Fires on Year to estimate the trend and then construct a Breusch-Godfrey test statistic for autocorrelation of order 1 the long way. Then verify your answer using the bgtest() command (from the package). Submit your code and the value of the test statistic.

2. Using the steps in the R Tutorial section 8.7, plot the Number of Forest Fires per year against Year, and add a line showing the fitted values from Question 1. Is it possible that autocorrelation might be an indication of a mis-specified regression model? Explain.

3. Now repeat the above steps, except regress the annual Number of Fires on Year, Year2 and Year3. This is a cubic equation. If t denotes the year, your regression equation will be:

Report your results. Are the new regression coefficients significant?
Does the Breusch-Godfrey test still indicate serial correlation?

4. Following the steps in the R Tutorial section 8.5, use the data in the file rts.xls to construct a Wu-Hausman test for exogeneity of the variable TEST using the variable SF (schooling of the father) as an instrument. Do it the long way using the fitted values from a regression to construct the instrument and computing a t test, then use the ivreg() command to check your answer. Explain how the t statistic in the first stage regression confirms the Wu-Hausman score from the ivreg() command.