Section 1 A country has been ravaged by a pest. The economy is struggling, with 3 of the country's 6 equally large economic sectors set to end the financial year with losses. The government is considering a reform package, but it would have heterogeneous effects on the economy. The following table characterises the potential outcomes of the reform, where Y; denotes sector i's potential profits (for Yi> 0) or losses (for Yi < 0) if it were subjected to the reform, and Yoi denotes i's potential profits or losses if it were not subjected to the reform: Sector a b C d e Yoi Yi 7.0. 16.0 -4.0 12.0 -8.0 -3.0 14.0 13.5 0.5 -4.0 -0.5 -10 Consider the following three different ways of assigning the treatment: (i) the reform applies to every sector in the economy; (ii) adoption of the reform is voluntary (assume that each sector acts as a single profit-maximising agent that has perfect information of the sector's potential outcomes); (iii) the reform only applies to sectors set to post a loss without the reform. 1. What is the average effect of the treatment on the treated (ATT) for each case (i), (ii), and (iii)? 2. Does any of the three ATTs above correspond to the average treatment effect (ATE)? Ex- plain. 3. Calculate the OLS coefficients for the regression of Y, on X; for case (iii). 4. Calculate the selection bias for case (iii), and give an intuitive explanation of why the OLS regression does or does not estimate a causal effect in this case.