Unformatted text preview: 3 . Consider the onevariable 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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 Spring '09
 Woutersen
 Statistics, Econometrics, Regression Analysis, regression model, Errors and residuals in statistics, onevariable regression model

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