Question: Consider a simple regression model in which the observed regressor (x_1) contains a measurement error. The model is: Where the notation is an in the

  • Consider a simple regression model in which the observed regressor (x_1) contains a measurement error. The model is:
  • y = Bo+ Bin + u x = x +
      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*.
      1. 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?
      2. b. What happens to the bias if the variance in e1 is 0?
      3. c. What estimation method could be used to obtain a consistent estimate of β1?

y = Bo+ Bin + u x = x +

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