What does the Gauss-Markov theorem prove? Without giving mathematical details, explain how the proof proceeds. What is its importance?

What will be an ideal response?


Answer: The Gauss-Markov Theorem proves that in the class of linear and unbiased estimators the OLS estimator has the smallest variance or is BLUE. The proof first establishes the conditions under which a linear estimator is unbiased. It then derives the variance of the estimator. The smallest variance property is then established by showing that the conditional variance of any old linear and unbiased estimator exceeds that of the OLS estimator, unless they are the same. To show this it is assumed that the OLS weights and the weights of any other linear estimator differ by some amount. Substitution of this condition into the conditional variance formula for any linear and unbiased estimator then shows that the resulting variance exceeds that of the OLS estimator unless the difference in the weights is zero. Hence OLS is BLUE. The Gauss-Markov Theorem gave the major justification for the widespread use of the OLS estimator.

Economics

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A) 1 percent. B) 5 percent. C) 9 percent. D) 12 percent.

Economics

In the above figure, the initial supply of loanable funds curve is SLF0 and the initial demand for loanable funds curve is DLF0. An economic expansion that raises disposable income and the expected profit would

A) only shift the supply of loanable funds curve rightward to a curve such as SLF1. B) shift the supply of loanable funds curve rightward to a curve such as SLF1, and shift the demand for loanable funds curve rightward to a curve such as DLF1. C) only shift the demand for loanable funds curve rightward to a curve such as DLF1. D) have no effect on either the demand for loanable funds curve or the supply of loanable funds curve.

Economics

The more limited information, the _____ the new classical AS curve

a. flatter. b. steeper. c. horizontal. d. downward sloping. e. none of the above.

Economics

Unemployment was particularly high during

A. The Korean War. B. The 1980s. C. The Great Depression. D. World War II.

Economics