Your Textbook Gives the Following Example of Simultaneous Causality Bias

Essay

Your textbook gives the following example of simultaneous causality bias of a two
equation system: $$\begin{array} { c } Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \\X _ { i } = \gamma _ { 0 } + \gamma _ { 1 } Y _ { i } + v _ { i }\end{array}$$ In microeconomics, you studied the demand and supply of goods in a single market. Let the demand $\left( Q _ { i } ^ { D } \right)$ and supply $\left( Q _ { i } ^ { S } \right)$ for the $i$ -th good be determined as follows,
$$\begin{array} { c } Q _ { i } ^ { D } = \beta _ { 0 } - \beta _ { 1 } P _ { i } + u _ { i } , \\\\Q _ { i } ^ { s } = \gamma _ { 0 } + \gamma _ { 1 } P _ { i } + v _ { i }\end{array}$$
where $P$ is the price of the good. In addition, you typically assume that the market clears.
Explain how the simultaneous causality bias applies in this situation. The textbook explained a positive correlation between $X _ { i }$ and $u _ { i }$ for $\gamma _ { 1 } > 0$ through an argument that started from "imagine that $u _ { i }$ is negative." Repeat this exercise here.