Suppose that variable y relates to the variables x1, x2, and x3 as in the follow

Question

Suppose that variable y relates to the variables x1, x2, and x3 as in the following population regression model: y = 0 + 1x1 + 2x2 + 3x3 + u where u is the error term in the model. Also assume that the assumptions MLR.1 through MLR.5 hold in this model unless indicated otherwise. Indicate, without explanation, whether the following statements are true or false

1)Now assume that the assumptions MLR.1 through MLR.5 hold in the above model, except the assumption MLR.3. Then if you run an OLS regression of the dependent variable y on the independent variables x1, x2,and x3, the estimated coefficients on x1, x2, and x3 are not unique.

2)Now assume that the assumptions MLR.1 through MLR.4 hold. Then, the OLS estimates for 1 , 2, and 3 are LUE (linear unbiased estimator) estimates.

Explanation / Answer

1) True

MLR 3 doesn't hold means there exists multicollinearity between variables. In this case we cannot unqiuely determine individual coefficients of variables

2) True

OLS estimates continue to remain unbaised and linear. They are LUE but not BLUE

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