exam_final_2012_solutions

X2 0074334 0017557 423 0000 003963 0109039 x1 3336331

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x2 .0074334 .0017557 4.23 0.000 .003963 .0109039 x1 .3336331 .0280586 11.89 0.000 .2781698 .3890965 y Coef. Std. Err. t P>|t| [95% Conf. Interval] Total .142504215 145 .000982788 Root MSE = .02041 Adj R-squared = 0.5761 Residual .059570665 143 .000416578 R-squared = 0.5820 Model .082933549 2 .041466775 Prob > F = 0.0000 F( 2, 143) = 99.54 Source SS df MS Number of obs = 145 . regress y x1 x2, noconst . generate x2 = kwh/kwh . generate x1 = 1/kwh . generate y = costs/kwh Answer: This is GLS with the variance of error terms modeled as KWH^2. Interpretation: the fixed costs of the plants are $333,633 on average, for each 1 billion kWh in output, costs increase by $7,433. 6. The Effect of Television Our goal is to evaluate the effects of educational television on public knowledge and attitudes. In the experiment, participants were divided into two groups: group A and group B. Group A was informed about the forthcoming PBS special on drug addiction. Group B was not given this information but they could learn about the PBS program on their own from other sources. Available data: groupA : dummy variable, equal to 1 for participants in group A. viewer : dummy variable, equal to 1 for participants who watched the program. age : person’s age educ : person’s education (number of years) gender : person’s gender, =1 for females income : person’s income test_after : the score on the test of the “knowledge of addiction”, administered after the program, measured in correct answers (0 to 8). test_before : the score on the test of the “knowledge of addiction”, administered before the program, measured in correct answers (0 to 8). Suppose we want to estimate the effect of watching the PBS program (variable viewer ) on the knowledge about the drug addiction (variable test_after ).
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5 (a) [5 points] Explain why the OLS regression of TEST_AFTER on VIEWER yields an inconsistent estimate of the effect of the PBS program. Answer: the omitted variable could be the interest in the drug addiction topic. This omitted variable can be correlated with VIEWER and prior knowledge about the drug addiction and, therefore, with TEST_AFTER. (b) [5 points] Suppose, we want to get rid of the endogeneity in regression in a) by including more explanatory variables. Which of the variables (listed above) could correct the endogeneity in a)? That is, in the model TEST_AFTER = β0 + β1 VIEWER + β2* W2 + + βk* Wk + e, (1) what are W2, …, Wk that correlate with VIEWER and have direct effects on the test results? Explain. Answer: Given the answer in (a), we can possibly get rid of the endogeneity by including TEST_BEFORE. We may also want to control for personal characteristics by including variables that affect both the likelihood that the person will watch the PBS program (which will depend on curiosity, time availability etc.) and test scores: age and education, for example. (c) [5 points] Suppose, the method above does not completely remove the correlation between VIEWER and the error term. Explain how one could estimate model (1) above by the IV with the instrument GroupA. Describe the two steps of the 2SLS (IV). Answer: Since division into groups A and B is performed randomly, GroupA is uncorrelated with the error term. Since being informed about the PBS program, most probably, increased the chances to view the program, GroupA is correlated with VIEWER. Therefore, GroupA is a strong and valid instrument. 1 Step of IV: regress VIEWER on GroupA and all of the exogenous explanatory variables and instruments.
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