Consider the model Y = Bxi + U,; i = 1, 2,..., n (1) where u,...

  

Transcribed Image Text:

Consider the model Y = Bxi + U,; i = 1, 2,..., n (1) where u, a random variable with mean zero and constant variance o2. r, can be considered to be "fixed in repeated sampling". Assume that the Gauss-Markov assumptions SLR.1-SLR.5 hold. (a) Show that the estimators =1 and 3 n Dn = i=1 yi 2i=1 Fi (b) Derive the expression of Var(3) and Var(3), and show that Var(3) < Var (3). are both unbiased estimator of 3 in (1). (c) Relate the findings in (a) and (b) to the Gauss-Markov Theorem. [Hint: is the OLS estimator of 3 for model (1).] (d) Now, suppose E[u] 0. Discuss which SLR assumption is violated. Derive the bias of the estimator 3. Activate Windo Consider the model Y = Bxi + U,; i = 1, 2,..., n (1) where u, a random variable with mean zero and constant variance o2. r, can be considered to be "fixed in repeated sampling". Assume that the Gauss-Markov assumptions SLR.1-SLR.5 hold. (a) Show that the estimators =1 and 3 n Dn = i=1 yi 2i=1 Fi (b) Derive the expression of Var(3) and Var(3), and show that Var(3) < Var (3). are both unbiased estimator of 3 in (1). (c) Relate the findings in (a) and (b) to the Gauss-Markov Theorem. [Hint: is the OLS estimator of 3 for model (1).] (d) Now, suppose E[u] 0. Discuss which SLR assumption is violated. Derive the bias of the estimator 3. Activate Windo

Answer rating: 100% (QA)

a Ehatbeta1sumi1nExisumi1nxi2ight1sumi1nxi2sumi1nxiExifracsumi1nxibetasumi1nxi2beta Ehatbet... View the full answer