Your Textbook Uses the Following Example of Simultaneous Causality Bias $\gamma _ { 0 }$

Essay

Your textbook uses the following example of simultaneous causality bias of a two equation system:
Y_i = β₀ + β₁X_i + u_i

X_i = $\gamma _ { 0 }$ + $\gamma _ { 1 }$ Y_i + v_i
To be more specific, think of the first equation as a demand equation for a certain good, where Y is the quantity demanded and X is the price. The second equation then represents the supply equation, with a third equation establishing that demand equals supply. Sketch the market outcome over a few periods and explain why it is impossible to identify the demand and supply curves in such a situation. Next assume that an additional variable enters the demand equation: income. In a new graph, draw the initial position of the demand and supply curves and label them D⁰ and S⁰. Now allow for income to take on four different values and sketch what happens to the two curves. Is there a pattern that you see which suggests that you might be able to identify one of the two equations with real-life data?