slides_Ch2_W[1]

# the smaller is var 1 jx intuition as n so does total

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 93 The Variance of the OLS Estimator - Remarks f y| x The Simple LRM under Homoschedasticity y x1 x2 E [y | x ]= β o + β1 x x3 x Melissa Tartari (Yale) Econometrics 81 / 93 The Variance of the OLS Estimator - Remarks ˆ How does Var β1 jx depend on σ2 , on the total variation in 2 fx1 , ..., xn g (denoted sx ), and on sample size n? Melissa Tartari (Yale) Econometrics 82 / 93 The Variance of the OLS Estimator - Remarks ˆ How does Var β1 jx depend on σ2 , on the total variation in 2 fx1 , ..., xn g (denoted sx ), and on sample size n? ˆ the larger σ2 the larger is Var β1 jx INTUITION: more variation in the unobservables a¤ecting y makes it more di¢ cult to precisely estimate β1 Melissa Tartari (Yale) Econometrics 82 / 93 The Variance of the OLS Estimator - Remarks ˆ How does Var β1 jx depend on σ2 , on the total variation in 2 fx1 , ..., xn g (denoted sx ), and on sample size n? ˆ the larger σ2 the larger is Var β1 jx INTUITION: more variation in the unobservables a¤ecting y makes it more di¢ cult to precisely estimate β1 2 ˆ the larger sx the smaller is Var β1 jx INTUITION: the more spread out is the sample of eVars the easier it is to trace out the relationship between E [y jx ] and x hence to estimate β1 ; if there is little variation in the xi then it can be hard to pin point how E [y jx ] varies with x Melissa Tartari (Yale) Econometrics 82 / 93 The Variance of the OLS Estimator - Remarks ˆ How does Var β1 jx depend on σ2 , on the total variation in 2 fx1 , ..., xn g (denoted sx ), and on sample size n? ˆ the larger σ2 the larger is Var β1 jx INTUITION: more variation in the unobservables a¤ecting y makes it more di¢ cult to precisely estimate β1 2 ˆ the larger sx the smaller is Var β1 jx INTUITION: the more spread out is the sample of eVars the easier it is to trace out the relationship between E [y jx ] and x hence to estimate β1 ; if there is little variation in the xi then it can be hard to pin point how E [y jx ] varies with x 2 ˆ the larger n the larger is sx and (as in b.) the smaller is Var β1 jx INTUITION: as n &quot; so does total variation in xi hence by b. it is easier to e...
View Full Document

Ask a homework question - tutors are online