PS4_solutions-2009

PS4_solutions-2009 - Department of Economics University of...

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Department of Economics Spring 2009 University of California Prof. Woroch Economics 140: Problem Set 4 SUGGESTED ANSWERS Short Questions. Answer each of the below questions about regression validity. 1. This course has two midterm exams that are used to measure your knowledge of econometrics. Suppose that your performance, and that of your fellow students, on the day of the first midterm measured knowledge imperfectly and with an error: 1 1 1 ~ i i i w X X + = where 1 ~ i X is first midterm score of student i , 1 i X is their true level of knowledge of econometrics, and 1 i w is a random error with mean zero and variance 2 w σ . For instance, w may depend on whether the student had a headache that day, whether they had an especially good night’s sleep, and so on. A similar situation holds for the second midterm: 2 2 2 ~ i i i w X X + = . What concerns would you have about internal validity of a regression of scores from the second midterm on the first midterm scores? Answer : Internal validity is violated because Measurement Error in the independent variable causes a correlation between that variable and the regression error term which, in turn, results in biased and inconsistent OLS estimate of the coefficient on that independent variable. The OLS coefficient will be attenuated (smaller in absolute value, and therefore nearer to zero). Measurement error in the dependent variable only increases the SSR and standard errors by adding additional noise to the regression error, but does not lead to biased OLSEs. 2. Assume that a simple economy could be described by the following system of Keynesian equations: 01 tt t CY u β =+ + and t I I = where C is consumption, Y is income, and I is investment. Assume the presence of the GDP identity, Y = C + I . If you estimated the consumption function, what sort of problem involving internal validity may be present? Answer : This is a case of simultaneous causality which is often also called “simultaneous equations bias” because it arises when the researcher estimates one equation involving an independent variable that is a dependent variable in another equation. The second equation here is the GDP identity in which GDP is determined by consumption plus an error term, say v. Substituting for C = Y - I from this identity into the consumption function gives an expression that can be solved for Y in terms of the two error terms, in which case the independent variable (Y) in the consumption function regression is correlated with the error term (via v). The result is biased and inconsistent OLSEs. 3. You have been hired as a consultant by building contractor, who have been sued by the owners’ representatives of a large condominium project for shoddy construction work. In order to assess the damages for the various units, the owners’ association sent out a letter to owners and asked if people were willing to make their units available for destructive testing.
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PS4_solutions-2009 - Department of Economics University of...

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