In a multiple regression model, the true relationship between the dependent variable (Y) and three independent variables (X1, X2, X3) is:
Y=2X1+3X2−4X3+5
However, a researcher misspecifies the model as:
Y=2X1+3X2+5
What is the omitted variable bias for the coefficient of X3 in the misspecified model?
In the true model:
Y=2X1+3X2−4X3+5
In the misspecified model:
Y=2X1+3X2+5
The omitted variable bias for the coefficient of X3 in the misspecified model is the difference between the true coefficient (−4) and the coefficient in the misspecified model (0):
Omitted Variable Bias=True Coefficient−Coefficient in Misspecified Model
Omitted Variable Bias=−4−0=−4
In the true model:
Y=2X1+3X2−4X3+5
In the misspecified model:
Y=2X1+3X2+5
The omitted variable bias for the coefficient of X3 in the misspecified model is the difference between the true coefficient (−4) and the coefficient in the misspecified model (0):
Omitted Variable Bias=True Coefficient−Coefficient in Misspecified Model
Omitted Variable Bias=−4−0=−4