To Analyze the Situation of Simultaneous Causality Bias, Consider the Following

question 32

Essay

To analyze the situation of simultaneous causality bias, consider the following system of
equations: $$\begin{array} { c } Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \\\\X _ { i } = \gamma _ { 0 } + \gamma _ { 1 } Y _ { i } + v _ { i }\end{array}$$ Demonstrate the negative correlation between $X _ { i }$ and $u _ { i }$ for $\gamma _ { 1 } < 0$ , either through mathematics or by presenting an argument which starts as follows: "Imagine that $u _ { i }$ is negative."

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Definitions:

Amnion

A thin, protective membrane that surrounds the embryo in the uterus, part of the amniotic sac that contains the amniotic fluid.

Coitus Interruptus

A method of contraception where intercourse is interrupted by withdrawal of the penis before ejaculation.

Withdraw

The action of removing or taking something back, or to cease participation or membership in an activity or organization.

Ejaculation

The discharge of semen from the male reproductive tract as a result of an orgasm.