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The solutions to the economics midterm exam held in spring 2008. The exam includes questions related to regression analysis, order conditions for identification, and instrumental variables. The document also includes stata output for regression analyses.

Typology: Exams

Pre 2010

1 / 2

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