Your Textbook Has Analyzed Simultaneous Equation Systems in the Case

Essay

Your textbook has analyzed simultaneous equation systems in the case of two equations, $$\begin{array} { l } Y _ { i } = \beta _ { 0 } + \beta _ { 1 } X _ { i } + u _ { i } \\\\X _ { i } = \gamma _ { 0 } + \gamma _ { 1 } Y _ { i } + v _ { i }\end{array}$$ where the first equation might be the labor demand equation (with capital stock and
technology being held constant), and the second the labor supply equation (X being the
real wage, and the labor market clears).What if you had a a production function as the
third equation $$Z _ { i } = \delta _ { 0 } + \delta _ { 1 } Y _ { i } + w _ { i }$$ where Z is output.If the error terms, u, v, and w, were pairwise uncorrelated, explain why
there would be no simultaneous causality bias when estimating the production function
using OLS.