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Your Textbook Gives the Following Example of Simultaneous Causality Bias

Question 37

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Your textbook gives the following example of simultaneous causality bias of a two
equation system: Yi=β0+β1Xi+uiXi=γ0+γ1Yi+vi\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 (QiD)\left( Q _ { i } ^ { D } \right) and supply (QiS)\left( Q _ { i } ^ { S } \right) for the ii -th good be determined as follows,
QiD=β0β1Pi+ui,Qis=γ0+γ1Pi+vi\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 PP 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 XiX _ { i } and uiu _ { i } for γ1>0\gamma _ { 1 } > 0 through an argument that started from "imagine that uiu _ { i } is negative." Repeat this exercise here.

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