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kevinh2683
kevinh2683
31.08.2020 • 
Mathematics

The true regression is given by the following equation: Y=β_0+β_1 X_1+β_2 X_2+β_3 X_3+β_4 X_4+u_1 However, you omit X1, X3, and X4 and estimate the following regression instead: Y=β_0^*+β_2^* X_2+η The relationship between the omitted variables and X2 is given by the following equations: X_1=ω_0+ω_1 X_2+u_2, X_3=γ_0+γ_1 X_2+u_3, X_4=θ_0+θ_1 X_2+u_4 a) Find the estimated values of B0* and B2* in terms of the true B’s. What is the omitted variable bias term for B0*? What is the omitted variable bias term for B2*? b) Suppose that the true effects of X1, X3, and X4 on Y are given by B1=0.4, B3= -2.4, and B4=3.1. You observe that the relationships between these three variables and X2 are given by ω1=3, γ1=0.5, and ϴ1=0. What is the predicted bias for B2*? Explain your answer as clearly as possible.

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