In the previous problem sets, we have analyzed a lot of questions which investigate the relationship between education and income. Truth is, it has always been an important question for the government to determine the public spending on education. A researcher has a dataset for 79 cities in the U.S. between 1990-2010. She decides to run the following regression. incomelit = a,- + at + 51 edu_spendit+ {J'Z'popit + \"it Where edu_speno' is the education spending in city i and year t, pop is the population in city i and year t, and income10 is the average income in that same city i 10 yea rs later (i.e., in year t+10). Finally, a,- and 6am city and year xed effects. :1,- equals one for city iand is zero otherwise for all f. at on the other hand is equal to one in year t and zero for all other years for t= 1991, ..., 2010. 61990 is not included. (a) What is the purpose of excluding lggofrom the model above? (b) Name some of the factors that might be picked up by time and city xed effects here. Discuss the advantages of using panel data for this type of investigation. (c) To test for the relevance of the area fixed effects, you restrict the regression by dropping all area fixed effects and instead a single constant is added. The relevant F-statistic is 129.67. What are the degrees of freedom? What is the critical value from your F table you will want to use here? (d) What potential endogeneities remain even if we run this regression with both time and city fixed effects