Your Textbook Has Analyzed Simultaneous Equation Systems in the Case $\gamma _ { 0 }$

Essay

Your textbook has analyzed simultaneous equation systems in the case of two equations,
Y_i = β₀ + β₁X_i + u_i
X_i = $\gamma _ { 0 }$ + $\gamma _ { 1 }$ Y_i + v_i,
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.