Download Economics Midterm Exam Questions and Solutions - Spring 2008 - Prof. David Guilkey and more Exams Introduction to Econometrics in PDF only on Docsity! Economics 771 David Guilkey Spring 2008 Midterm Exam 1. Given the following model: 1 1 1 2 2 3 3i i i iY X X X 1iβ β β= + + + ε 2i 2 1 1 2 4 3 5i i i iY Y X Xα α α= + + +ε a. Check the order condition for identification in the second equation. b. Under what conditions can you consistently estimate the second equation by OLS? Explain. c. Given the following STATA output: . regress y1 x1 x2 x3 Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 3, 996) = 447.97 Model | 1315.35878 3 438.452928 Prob > F = 0.0000 Residual | 974.843117 996 .97875815 R-squared = 0.5743 -------------+------------------------------ Adj R-squared = 0.5731 Total | 2290.2019 999 2.2924944 Root MSE = .98932 ------------------------------------------------------------------------------ y1 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .4240564 .0312679 13.56 0.000 .3626979 .4854149 x2 | .8065833 .0315655 25.55 0.000 .7446409 .8685258 x3 | -.7561827 .0318268 -23.76 0.000 -.818638 -.6937274 _cons | .4966116 .031313 15.86 0.000 .4351646 .5580587 ------------------------------------------------------------------------------ . predict error,residual . regress y2 y1 x4 x5 error Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 4, 995) = 1697.22 Model | 2537.19811 4 634.299529 Prob > F = 0.0000 Residual | 371.860097 995 .373728741 R-squared = 0.8722 -------------+------------------------------ Adj R-squared = 0.8717 Total | 2909.05821 999 2.91197018 Root MSE = .61133 ------------------------------------------------------------------------------ y2 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- y1 | .5004827 .0168964 29.62 0.000 .4673259 .5336394 x4 | .2020537 .0247587 8.16 0.000 .1534684 .250639 x5 | -.811964 .0237034 -34.26 0.000 -.8584784 -.7654497 error | .7745524 .0258443 29.97 0.000 .7238369 .8252679 _cons | .2405561 .0210031 11.45 0.000 .1993406 .2817716 ------------------------------------------------------------------------------ . ivregress 2sls y2 (y1= x1 x2 x3) x4 x5 Instrumental variables (2SLS) regression Number of obs = 1000 Wald chi2(3) = 995.30 Prob > chi2 = 0.0000 R-squared = 0.6706 Root MSE = .97884 ------------------------------------------------------------------------------ y2 | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- y1 | .4992444 .0270972 18.42 0.000 .4461349 .5523539
