3. Consider the following models where the first one is estimated using data from only 1987 and the second one is estimated using the change in variables between 1982 and 1987: CRMRTE = 128.38 - 4.16 UNEM (1987 data) (20.76) (3.42) CRMRTE 1987-CRMRTE 1982 = 15.40 +2.22 (UNEM 1987 - UNEM 1982) (4.7) (0.88)| Where CRMRTE and UNEM are crime rate and unemployment rate respectively for 46 cities. (a) Do you think the sign of the coefficient in the first model is correct? Explain your answer. (2) (b) Why does the sign of the coefficient change in the second model? Explain your answer. (3) (c) If there is data from other years, what model will you estimate that is consistent with your answer in part b? Do not forget to write the PRF of your proposed model. (2)