1 (25 points) You are interested in the impact of patents on GDP growth and have data on the number of patents filed and GDP growth in each country i in each year t. You consider the regression specification GDPGROWTHit = Bo + COUNTRY FE + BINUMPATENTSit + Eit 1. Why do you choose to include the country fixed effects? Could you also include fixed effects for the year? Why or why not? 2. Remember COUNTRYFE = y Dit where Dit = [Diit, . .., D195it] is a vector of indicator random variables (one for each country except say America to avoid colinearity). Give the OLS estimator for B = [Bo, YT, Bi]T 3. Because GDP growth over time is highly correlated, you choose to cluster the standard errors by country. Remember that VN(BOLS - B) "> N(0, E). What is your estimator for Z? 4. Show how to test Ho : B1 = 1 vs. HA : B1 1 at the 10% level (make sure to provide the test statistic, estimators for all its components, and the rejection rule)