Consider estimation of the following two equation model: y1 = 1 + 1, y2 = 2x + 2. A
Chapter 14, Problem 2(choose chapter or problem)
Consider estimation of the following two equation model: y1 = 1 + 1, y2 = 2x + 2. A sample of 50 observations produces the following moment matrix: 1 y1 y2 x 1 y1 y2 x 50 150 500 50 40 90 100 60 50 100 . a. Write the explicit formula for the GLS estimator of [1, 2]. What is the asymptotic covariance matrix of the estimator? b. Derive the OLS estimator and its sampling variance in this model. c. Obtain the OLS estimates of 1 and 2, and estimate the sampling covariance matrix of the two estimates. Use n instead of (n 1) as the divisor to compute the estimates of the disturbance variances. d. Compute the FGLS estimates of 1 and 2 and the estimated sampling covariance matrix. e. Test the hypothesis that 2 = 1.
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