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hw_Fall2009 - 3 Consider the one-variable regression model...

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Econometrics : Homework 3 1 . Consider the regression model Y i 0 1 X 1 i 2 X 2 i 3 X 1 i X 2 i u i . Please show: (a) Δ Y Δ X 1 1 3 X 2 (effect of change in X 1 holding X 2 constant). (b) Δ Y Δ X 2 2 3 X 1 (effect of change in X 2 holding X 1 constant). (c) If X 1 changes by Δ X 1 and X 2 changes by Δ X 2 , then Δ Y i 1 3 X 2 Δ X 1 2 3 X 1 Δ X 2 3 Δ X 1 Δ X 2 . 2 . Using the data set TeachingRatings (Please go to the course webpage course content TeachingRatings to download the data file in the format of Excel or Stata. A detailed description is given in another file TeachingRatings_Description). Solve the following questions. (a) Estimate a regression of Course_Eval on Beauty, Intro, OneCredit, Femal, Minority, and NNEnglish. Please report all regression outputs, plot residuals vs predictor (NNEnglish) and discuss heteroskedasticity. (b) Add Age and Age 2 to the regression. Is there evidence that Age has a nonlinear effect on Course_Eval? Is there evidence that Age has any effect on Course_Eval?
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Unformatted text preview: 3 . Consider the one-variable regression model Y i 1 X i u i , and the model satisfies the least squares assumptions. Suppose that Y i is measured with error, so that the data are ̃ Y i Y i w i , where w i is the measurement error which is i.i.d. and independent of Y i and X i . Consider the population regression ̃ Y i 1 X i i , where i is the regression error using the mismeasured dependent variable, ̃ Y i . (a) Show that i u i w i . (b) Show that the regression ̃ Y i 1 X i i satisfies the assumptions of the least squares. (Assume that w i is independent of Y j and X j for all values of i and j and has a finite fourth moment.) (c) Are the OLS estimators consistent?...
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