Your Textbook Gives the Following Example of Simultaneous Causality Bias

question 20

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.

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Definitions:

Market Price

The price level at which a service or asset is being offered for sale or purchase in the market now.

Ex-dividend Date

The specific date on which a stock trades without its dividend, meaning that if you purchase the stock on or after this date, you will not receive the next dividend payment.

Date Of Record

Date on which holders of record are designated to receive a dividend.

Excess Cash

The amount of cash holdings that exceeds what a business requires for its immediate operational needs.