Question 2 A Is The Following Statement True Or False Explain Your Answer An Ordinary Least Squares Regression Of Y 1 (291.81 KiB) Viewed 30 times
Question 2 (a) Is the following statement true or false? Explain your answer. "An ordinary least squares regression of Y onto X will be internally inconsistent if X is correlated with the error term." (4 marks) (b) Consider the fitted regression in the following graph. Test score 740 720 700 F : 680 660 L 640 620 600 0 10 20 40 60 50 District income (thousands of dollars) Would this regression provide a reliable estimate of the effect of income on test scores? (4 marks) (c) A researcher sees the graph in (b) and decides to estimate the following nonlinear regression: R² = 0.561. Test Score 557.8 +36.42 ln (Income), (3.8) (1.40) Would this regression provide a reliable estimate of the effect of income on test scores? (4 marks) (d) Would the regression in (c) provide a reliable method for forecasting test scores? Explain. (4 marks) (e) The relationship between random variables Y₁, X; and W; is described by two equations, Y₁ = Bo + B₁X₁ + Ui X₂ = do + √₁Y; + √₂W₁ + Vi, where u₂ and v; are mutually independent identically distributed ran- dom variables with mean zero and where W; is not correlated with u₂ 30
and v₁. Solving this system of two equations for Y; and X₂, it can be seen that the expressions for X, and Yį are So + $130 8₂ Wi Ôi tôi Xi = 1 - 8₁3₁ + 1-8₁3₁1-8₁³₁² Bo + Soß₁ B₁8₂ Wi Y₁ = + Uji + B₁ Vi 1-8₁3₁ 1 - 8₁3₁ 1 - 8₁3₁ Which of the variables Y₁, X; and W₁ are endogenous? exogenous? Explain. Which are (3 marks) (f) Compute the covariance of X¿ and u; in the model in (e). (3 marks) (g) In the setting in (e), a researcher estimates OLS regression of X¿ on Y₁. The fitted OLS line is Ŷ; = 3, +3₁X₁. Are the estimators 3₁ and 3₁ unbiased? Are they consistent? (3 marks) + +
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