final_answersv2

final_answersv2 - Final Exam suggested solutions 1(a False...

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Final Exam: suggested solutions. 1. (a) False: Correlation among the x variables does not cause bias. As long as there isn°t perfect multicollinearity and the other MLR as- sumptions hold, OLS exists and is unbiased. The fact that the coe¢ cient is precisely estimated suggests that there is not that much multicollinearity anyway. (b) False: Under these assumptions the lagged dependent variable, y t ° 1 cannot be exogenous. For illustration purposes, suppose that the error is an AR(1) (a form of autocorrelation), then cov ( y t ° 1 ; u t ) 6 = 0 . (c) False: While it°s true that using WLS corrects for heteroskedasticity, it°s also true that the main reason to use is to get more e¢ cient estimators. It does not produce valid standard errors for the OLS estimator. If the goal is only correcting for OLS standard errors, robust standard errors should be computed. (d) True: It°s not possible to use di/erence in di/erences because we don°t have a change in policy in A or B in the time period considered. 2. (a) The model suggested has the form: ln( Gas t ) = ° 0 + ° 1 ln( p t )+ : : : + ° k ln( p t ° k +1 )+ ±t + ² 1 d 1 + ² 2 d 2 + ² 4 d 4 : (1) This equation captures the e/ect of current prices in gas consump- tion, but also takes account of the fact that gas consumption in one period is determined by prices in previous periods. For instance, if gas prices have increased during the last two years, chances are you 1
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adjust your habits, and these changes would have an impact on your current consumption decisions. That°s the reason for the inclusion of lagged prices; a linear trend is included as well as dummy variables for quarters. A quadratic trend might be needed. Seasonal dummies should be included. In the above example the omitted dummy is the 3rd quarter, so the ² 0 s measure demand relative to the 3rd quarter.
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