II. Applications [58 points total] 1 d - b Note: ad-bc-c The test statistics for a single restriction and the joint test are: s = uu/ (n - k) (RB-q), (, , -')/J F = 51 '/(n - K) t= J,x-K [R(XX) R'] A. [25 points] A demand equation for iPod is estimated for a sample of 52 observations: Q = BoI+ BP + , where P is the price and I is the income. To a certain degree, P is endogenous. Therefore, we use Archos MP3 players' price G as an instrument. Let D=[I P G], the moment matrices for all the variables are. [50 10 10 120 D'D: 10 40 20 Q'Q: 300 D'Q: 25 10 10 20 25 The critical values at 95% significant level are, Df 50 51 52 ta/2, Df: 2.00 2.00 2.00 Fa, 1Df 4.02 4.01 Fa, 2,Df 3.16 3.16 Df 1 2 Xa, DF 3.84 5.99 Zo2 = 1.96 (1) Find the OLS estimates for Bo and 1. Do coefficient estimates make sense? (2) Suppose the residual variance estimate is 0.25, test the significance of each factor in the demand equation. (3) Suppose the sum of squared error when regress Q on P only by assuming Bo= 2.5 is 12.5, test the hypothesis of Bo=2.5 using an F test. (hint: F = (RSS-RSS )/J (R-q)'[R(X'X)R'](RB-q)/J e'e/(n - K) R.S.S /(n-K) (4) Find the IV estimates for Bo and B1, along with their t-ratios. How would you interpret your results now? (hint: you can assume siv-0.73) 4.01 3.15 II. Applications [58 points total] 1 d - b Note: ad-bc-c The test statistics for a single restriction and the joint test are: s = uu/ (n - k) (RB-q), (, , -')/J F = 51 '/(n - K) t= J,x-K [R(XX) R'] A. [25 points] A demand equation for iPod is estimated for a sample of 52 observations: Q = BoI+ BP + , where P is the price and I is the income. To a certain degree, P is endogenous. Therefore, we use Archos MP3 players' price G as an instrument. Let D=[I P G], the moment matrices for all the variables are. [50 10 10 120 D'D: 10 40 20 Q'Q: 300 D'Q: 25 10 10 20 25 The critical values at 95% significant level are, Df 50 51 52 ta/2, Df: 2.00 2.00 2.00 Fa, 1Df 4.02 4.01 Fa, 2,Df 3.16 3.16 Df 1 2 Xa, DF 3.84 5.99 Zo2 = 1.96 (1) Find the OLS estimates for Bo and 1. Do coefficient estimates make sense? (2) Suppose the residual variance estimate is 0.25, test the significance of each factor in the demand equation. (3) Suppose the sum of squared error when regress Q on P only by assuming Bo= 2.5 is 12.5, test the hypothesis of Bo=2.5 using an F test. (hint: F = (RSS-RSS )/J (R-q)'[R(X'X)R'](RB-q)/J e'e/(n - K) R.S.S /(n-K) (4) Find the IV estimates for Bo and B1, along with their t-ratios. How would you interpret your results now? (hint: you can assume siv-0.73) 4.01 3.15