California intends to test if adding a $2.00 fee to each pack of cigarettes deters smoking. They randomly select 20 of 58 counties in the state to implement the fee in 2010. Data is collected on whether or not each resident smokes (Smoker) in 2008 (Before) and 2012 (After). The following table presents the fraction of residents who smoke before and after the policy is implemented in the treated counties and all other counties in California (the controls).

4. California intends to test if adding a $2.00 fee to each pack of cigarettes deters smoking. They randomly select 20 of 58 counties in the state to implement the fee in 2010. Data is collected on whether or not each resident smokes (Smoker) in 2008 (Before) and 2012 (After). The following table presents the fraction of residents who smoke before and after the policy is implemented in the treated counties and all other counties in California (the controls). 2008 Treat 0.52 Control 0.45 2012 0.34 0.41 a) We wish to estimate a single difference regression for the treated counties. Write the regression equation using values of O and l computed from the table of means above. Smoker = Bo + B1 After + u b) We wish to estimate a difference-in-differences regression. Write the regression equation using values of BO, B1, 2, and 3 computed from the table of means. Smoker = Bo + B Treat + B2 After + B3Treat * After +u c) What is the estimated effect of the policy using the single-difference method? Using the difference-in-difference method? Explain why they differ. d) The table above uses all other counties in California as control counties. We might get more accurate estimates if we carefully choose a smaller set of counties to act as the control counties. Identify three characteristics that we might wish those counties to have. 4. California intends to test if adding a $2.00 fee to each pack of cigarettes deters smoking. They randomly select 20 of 58 counties in the state to implement the fee in 2010. Data is collected on whether or not each resident smokes (Smoker) in 2008 (Before) and 2012 (After). The following table presents the fraction of residents who smoke before and after the policy is implemented in the treated counties and all other counties in California (the controls). 2008 Treat 0.52 Control 0.45 2012 0.34 0.41 a) We wish to estimate a single difference regression for the treated counties. Write the regression equation using values of O and l computed from the table of means above. Smoker = Bo + B1 After + u b) We wish to estimate a difference-in-differences regression. Write the regression equation using values of BO, B1, 2, and 3 computed from the table of means. Smoker = Bo + B Treat + B2 After + B3Treat * After +u c) What is the estimated effect of the policy using the single-difference method? Using the difference-in-difference method? Explain why they differ. d) The table above uses all other counties in California as control counties. We might get more accurate estimates if we carefully choose a smaller set of counties to act as the control counties. Identify three characteristics that we might wish those counties to have