Your Textbook Uses the Following Example of Simultaneous Causality Bias

Essay

Your textbook uses the following example of simultaneous causality bias of a two
equation system: $$\begin{array} { c } Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \\\\X _ { i } = \gamma _ { 0 } + \gamma _ { 1 } Y _ { i } + v _ { i }\end{array}$$ 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 $D ^ { 0 }$ and $S ^ { 0 }$ . 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?