140_problems1 - ECON 140, Fall 2008 Alex Rothenberg...

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Unformatted text preview: ECON 140, Fall 2008 Alex Rothenberg Practice Problems for Midterm #1 Problem 1 Compare the concepts of sample mean and population mean using the notation from the textbook and lectures, the definitions, and any fitting or prediction properties. Take the notions of a random sample, population, and probability as given. { 20 min, Fall 1999 } Problem 2 For the straight line model: Y i = bX i + i , derive the formula for the least squares estimator of the slope parameter, b . (Assume that you are finding a minimum, so that the second derivative is positive.) { 10 min, Spring 2000 } Problem 3 For the straight line model: Y i = bX i + i , assume that i iidN (0 , 2 ). Show that E [ b ] = b , where b is the estimator you found in Problem 2. (Omitted Variable Bias) Now, suppose the true model is instead Y i = bX i + Z i + i . Is b still unbiased? { 15 min, ADR } 1 ECON 140, Fall 2008 Alex Rothenberg Problem 4 [Frisch-Waugh Theorem, Special Case] Suppose we have the following linear model: Y i = + X...
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140_problems1 - ECON 140, Fall 2008 Alex Rothenberg...

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