Suppose that a U.S. state decides to build some new schools in 2025. It does not have enough money to build a new school in every county, so only some counties receive a new school. The following graph shows the average income for residents of counties which receive schools and those that don't. i) ii) iii) 90000 85000 80000 75000 70000 65000 60000 55000 50000 45000 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 -New school-No new school Can we use a differences-in-differences model to infer causality here? Why or why not? What does this graph tell you about which counties received new schools? Suppose that, when you control for existing education levels, the graph now looks like this: 75000 70000 65000 60000 55000 50000 45000 2020 2021 2022 2023 2024 2025 2026 2027 2028 2029 2030 -New school No new school Is this now appropriate for a diff-in-diff? What would the equation be? Suppose you would like to know how the casual effect differed for rural and urban counties. Define a variable 'urban' which equals 1 if the county has an urban area. Define the diff-in- diff-in-diff equation to estimate this effect.