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AnswMid1

AnswMid1 - Prof Frederico Finan Econ 103 Fall 2007 Mid-term...

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Prof. Frederico Finan Econ 103 Fall 2007 Mid-term Examination #1 (1 hour and 15 minutes, 35 percent of final grade) Answer all four parts Part I. Define or explain in one or two sentences any 4 of the following 5 concepts. If you use a graph, make sure that you explain what it shows. If you use a formula makes sure you define the variables. Also please distinguish between estimates and population parameters. Do not answer more than 4 (5 points each, total of 20 points). 1. Type I error A type I error occurs when the null hypothesis is rejected when in fact is true. 2. The power of a test The power of a test is the probability that the test correctly rejects the null hypothesis when the alternative is true. 3. Heteroskedasticity The error term u i is heteroskedastic if the variance of the conditional distribution of u i given X i depends on X i . 4. The 95 percent confidence interval for a slope parameter Is an interval (or set) that contains the true value of the slope population parameter with a 95% probability when computed over repeated samples. 5. Causal effect The expected effect of a given intervention or treatment as measured in an ideal randomized controlled experiment. Part II. True or false, and very briefly explain why. Select any 4 of the following 5 statements and do not answer more than 4 (5 points each, for a total of 20 points). 6. Consider the following model: y u u 1 U u 2 x 1 U u 3 x 2 U ± . If X 1 and X 2 are highly collinear, then our estimate of u 2 will be biased. FALSE. Multicollinearity does not violate any of the CLRM assumptions so OLS will be BLUE. However, estimates of u 2 and u 3 are likely to be unstable with high standard errors. 1

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7. Imagine you regressed earnings of individuals on a constant, a binary variable (“Male”) which takes on the value 1 for males and is 0 otherwise, and another binary variable (“Female”) which takes on the value 1 for females and is 0 otherwise. Because females typically earn less than males, you would expect the coefficient for Male to have a positive sign, and for Female a negative sign. FALSE. None of the OLS estimators exist because there is perfect multicollinearity. 8. In a single regressor model, the slope estimator has a smaller standard error, other things equal, if there is more variation in the exploratory variable, X. TRUE. Under the Gauss-Markov conditions u 1 , is conditionally unbiased, and the variance of the conditional distribution of u 1 , given X is ( ) ( ) = - = n i i u n x x x x 1 2 2 1 1 , , | ˆ var σ β K The sample variance of X is given by ( ) ( ) = - - = n i i x x n X 1 2 1 1 var Therefore, as the variance of X increases the slope estimator will have a smaller standard error. 9. Consider the following regression line: TestScore
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AnswMid1 - Prof Frederico Finan Econ 103 Fall 2007 Mid-term...

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