Consider a simple regression model in which the observed regressor (x_1) contains a measurement error. The model
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- Consider a simple regression model in which the observed regressor (x_1) contains a measurement error. The model is:
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- Where the notation is an in the curriculum. x1* is the true value of the regressor, whereas e1 is the measurement error. e1 is uncorrelated with u and x1*.
- a. Suppose that the variance in x1* is 3 and that the variance in e1 is 3. Assume that the true value of β1=4. Using the result on the probability limit on the OLS estimator of β1 from the curriculum, what estimated value of the parameter will be observed in large samples?
- b. What happens to the bias if the variance in e1 is 0?
- c. What estimation method could be used to obtain a consistent estimate of β1?
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