Misspecification

1. Misspecification Chapter 13.4

2. Misspecification • 2 situations • Variable that belongs in the model is omitted • Variable that does not belong to the model is included • Compare two models

3. Misspecification • Gauss-Markov Theorem tells us that OLS estimators are the Best Linear Unbiased Estimators of the βj • Proper OLS estimators for the second model is

4. Misspecification • Misspecification when a relevant variable is omitted from the model • Correct model • The OLS estimator for the slope coefficient on X1 is given by γi • How these two estimators compare as estimators of β1, the true impact of X1 on Y?

5. Misspecification • Compare two sampling distributions • Because of bias, procedures of hypothesis testing and interval estimation are no longer valid

6. Misspecification EARNSi=β0+β1EDi +β2EXPi +ui β2was presumed to be positive and covariance was to be negative the omitted-variable estimator would underestimate its true impact, the estimator of a single regression would be negatively biased Sampling distribution picture

7. Misspecification • Second type of misspecification occurs when irrelevant variable is included in the estimated model • True impact of X1 on Y is given by γ1 in the simple regression • Proper OLS estimator • Instead OLS estimator Irrelevant variable estimator is inefficient

8. Specification Strategy • When relevant variable is excluded, OLS applied to the misspecified model produces biased estimators for all coefficients • When irrelevant variables are added to the misspecified model, OLS yields unbiased, but inefficient estimators • Theory suggests that variable belongs to the model but this variable is insignificant, keep it in the model