# hw1_answer_econ120c_su05 - Economics 120c Name:...

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Unformatted text preview: Economics 120c Name: _________________________ Professor Yongil Jeon Summer 2005 Student ID#: _________________________ Anwer to Homework #1 (Midterm Exam, Summer 2004) 1. (a) Since i Y is a binary variable, we know i i i i i i i i i x x Y x Y x Y x Y E 1 ) | 1 Pr( ) | Pr( * ) | 1 Pr( * 1 ) | ( β β + = = = = + = = Thus, ) ( ) | ( ] | ) ( [ ) | ( 1 1 = + − = + − = i i i i i i i i x x Y E x x Y E x u E β β β β (b) We have )] | 1 Pr( 1 )[ | 1 Pr( ) | ( i i i i i i x Y x Y x Y Var = − = = )] ( 1 )[ ( 1 1 i i x x β β β β + − + = Thus, ] | ) ( [ ) | ( 1 i i i i i x x Y Var x u Var β β + − = ) | ( i i x Y Var = )] ( 1 )[ ( 1 1 i i x x β β β β + − + = (c) ) | ( i i x u Var depends on the value of i x , so i u is heteroskedastic. 2. (a) Given i YARD k ⋅ = 2 σ . Define i i YARD W ) ( 1 = . Next, multiply each variable by i W and generate i i i ice W Y Pr * ⋅ = , i i W X = * 1 , ) ln( * 2 i i i SQFT W X ⋅ = , and ) ln( * 3 i i i YARD W X ⋅ = . Then regress * i Y against * 1 i X , * 2 i X , and * 3 i X , but without constant term. (b) Since the weights are known, WLS estimates are BLUE. Hence most efficient, that is, more efficient than OLS. (c) One possible assumption is that i i i i v YARD SQFT + + + = ) ln( ) ln( 2 1 2 α α α σ (d) H is 1 = α and 2 = α (e) First regress PRICE against a constant, ) ln( i SQFT , and ) ln( i YARD and compute residuals ) ln( ˆ ) ln( ˆ ˆ Pr ˆ 2 1 i i i i YARD SQFT ice u β β β − − − = Next, estimate the auxiliary equation by regressing 2 ˆ i u against a constant, ) ln( i SQFT and ) ln( i YARD and compute test statistic such as 2 * R n , where n is the number of observations, and...
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