Suppose we use state-level data to estimate the demand for gasoline. The outcome variable (Y ) is the gallons of gas sold per capita in 2021. Price (D) is measured as the average price paid for regular unleaded gasoline in dollars per gallon (including all taxes). We want to estimate the causal effect of D on Y . The demand equation is Yi = 0 1Di ui , where ui represents other factors that effect the demand for gasoline. Gasoline is produced by refining oil at an oil refinery. The price of gasoline varies from state to state in part due to variation in refining costs. One important factor is refining capacity in the state. Suppose we use this refining capacity (number of barrels of oil that can be refined for gasoline per day by refineries in the state) as an instrumental variable (Z). What three assumptions must be satisfied? Do you think these assumptions are plausible? What control variables might be needed to make the assumptions more plausible