slides_Ch2_W[1]

# n sa y b econometrics na n 1 n na yi i 2b 62

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: hat is the mean grade in the population of college students? Melissa Tartari (Yale) Econometrics 60 / 93 Failure of SLR.2: An Example (Questions) We will try to answer two questions with our possibly non-random sample: Q.1: what is the mean grade in the population of college students? Q.2: what is the e¤ect of attending a private high school on college grades, other things (namely, ability and drive) equal? Melissa Tartari (Yale) Econometrics 60 / 93 Failure of SLR.2: An Example (Q.1) The answer to Q.1 is E [Y ]. The problem is that E [Y ] is a function of unknown parameters hence it is itself an unknown parameter. Melissa Tartari (Yale) Econometrics 61 / 93 Failure of SLR.2: An Example (Q.1) The answer to Q.1 is E [Y ]. The problem is that E [Y ] is a function of unknown parameters hence it is itself an unknown parameter. An idea: Can we use the sample average y to estimate E [Y ]? Is the sample average an unbiased estimator of E [Y ]? Melissa Tartari (Yale) Econometrics 61 / 93 Failure of SLR.2: An Example (Q.1) The answer to Q.1 is E [Y ]. The problem is that E [Y ] is a function of unknown parameters hence it is itself an unknown parameter. An idea: Can we use the sample average y to estimate E [Y ]? Is the sample average an unbiased estimator of E [Y ]? Look at the object of interest E [Y ] and write it out using the LIE as: E [Y ] = Pr (A) E [Y jA] + Pr (B ) E [Y jB ] = fA E [ Y j A ] + ( 1 Melissa Tartari (Yale) Econometrics fA ) E [ Y j B ] 61 / 93 Failure of SLR.2: An Example (Q.1) Look at the sample average - the candidate estimator of E [Y ] - and write it out: y = = = 1 N 1 N N ∑ Yi i =1 1 ∑ Yi + N ∑ Yi i 2A NA N i 2B 1 NA = sA y A + ( 1 Melissa Tartari (Yale) ∑ Yi i 2A ! + N sA ) y B Econometrics NA N 1 N NA ∑ Yi i 2B ! 62 / 93 Failure of SLR.2: An Example (Q.1) The candidate estimator y is unbiased for E [Y ] i¤ E [y ] that is, i¤ 0 = E [ sA y A + ( 1 E [Y ] = 0, (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [y A ] + (1 sA ) E [y B ]) (fA E [Y jA] + (1 fA ) E [Y jB ]) = (sA E [Y jA] + (1 sA ) E [Y jB ]) (fA E [Y jA] + (1 fA ) E [...
View Full Document

## This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

Ask a homework question - tutors are online