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

Essay

To analyze the situation of simultaneous causality bias, consider the following system of equations:
Y_i = β₀ + β₁X_i + u_i
X_i = $\gamma _ { 0 }$ + $\gamma _ { 1 }$ Y_i + v_i
Demonstrate the negative correlation between X_i and $\gamma _ { 1 }$ for $\gamma _ { 1 }$ < 0 , either through mathematics or by presenting an argument which starts as follows: "Imagine that u_i is negative."