Using the World Economic Data set, which has several variables recorded for each country for several years. 1. Provide evidence or support for whether or not the panel is completely balanced, or imbalanced. (2 Points) 2. Suppose you want to predict a country's GDP, gdp, using its expenditures on education, educationexpenditure. Use the first differences approach to control for time invariant country level factors. (3 Points) 3. Using your first difference regression from the previous problem, provide evidence for whether or not there is auto-correlation in the errors within country across time. (3 Points) 4. Instead run a fixed effects model to control for country factors that are time invariant. What is one advantage of using fixed effects compared to first differences? (2 Points) gdp = Bo+Beducationexpenditure + c + 5. Assume you found that there is autocorrelation in the error term within a country. Run the fixed effects regression, but also cluster your standard errors at the country level. What does clustering the standard errors do to the statistical significance of your estimate for ? (3 Points) 6. Run the same regression above, but instead of including fixed effects, use the approach of de-meaning the data. (3 Points) Now instead use the Birthweight data file, and run the following nave regression predicting a child's birthweight in pounds, bwghtlbs, using the family income, faminc, the mother's education, motheduc, a dummy variable for whether the child is male, male, and the mother's cigarette use, cigs: bwghtlbs =o + faminc + Bmotheduc + male + cigs + 7. Suppose you believe that there are important omitted variables that you don't have in your data set. You think that cigarette taxes could be a good instrument. Explain why cigarette taxes, cigtax, could be a good instrument for the effect of cigarette use, cigs, on the birthweight of the child in pounds, bwghtlbs. Said differently, how does the instrument of cigarette taxes satisfy the two conditions for an instrument? (3 Points) 8. Run a regression including all of the controls in the regression above, but instrument cigarette use, cigs, with cigarette taxes, cigtax, without using the ivregress command. (4 Points) 9. Run a regression using the ivregress command, including all of the controls in the regression above, but instrument cigarette use, cigs, with cigarette taxes, cigtax. Interpret the coefficient on cigarette use, cigs, and does the first stage regression suggest it is a weak instrument or not? (4 Points) 10. Performa a Durbin-Wu-Hausman test for endogeneity of cigarette use, and does it suggest you need to instrument cigarette use, cigs, with cigarette taxes, cigtax ? (3 Points)