midterm1_solutions

midterm1_solutions - Department of Economics University of...

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Department of Economics Spring 2011 University of California Prof. Woroch Economics 140 : FIRST MIDTERM EXAM SUGGESTED ANSWERS I. TRUE/FALSE/UNCERTAIN : Below are 3 statements that may be true or false, or possibly ambiguous. State which one you believe to be the case, and more importantly, give a detailed but concise explanation for your answer. Each question is worth 10 points for a total of 30. 1. Below is the Excel statistical function output for a t-test of the difference in the mean wages using a random sample of union and non-union factory workers. t-Test: Two-Sample Assuming Equal Variances NONUNION UNION Mean 28388.58723 31936.3163 Variance 129122544.4 183023030.3 Observations 146 110 Pooled Variance 152253067.9 Hypothesized Mean Difference 0 df 254 t Stat -2.277299796 P(T<=t) one-tail 0.011800069 t Critical one-tail 1.650874792 P(T<=t) two-tail 0.023600138 t Critical two-tail 1.969347483 These results lead us to accept the hypothesis that union wages are higher than non-union wages at a 2% significance level but to reject the hypothesis that wages of the two populations are the same at this same significance level. Answer : FALSE. First note that the Excel statistical function assumed equal variances of the two populations, but since the sample size is large, it would not matter if they were unequal provided the CLT assumptions hold. The first claim is about a test of a one-sided null that mean nonunion wage > mean union wage, and since the one-tail p-value is 0.0118, we reject the null at a 2% significance level, i.e., accept that union wage > nonunion wage at 2%. However, the p-value for the two-sided test is 0.23 so can not reject the null that nonunion wage = union wage at the same 2% level. 2. A simple macroeconomic consumption function relates consumption to income: i i I C 1 0 where 1 is the marginal propensity to consume. The Bureau of Labor Statistics attempts to collect data on household purchases and income by randomly sampling U.S. households, but it is known that high- income households tend to under-report their purchases (so as to not appear materialistic) while low- income households tend to over-state their purchases (to mask their lack of means). In that case, the ordinary least squares assumptions—for both the classical and robust regressions—are violated and as a result, the OLSE of the marginal propensity to consume that is biased toward zero. Answer : TRUE. The pattern described will violate the assumption that E(u i | X) = 0 which is an assumption made by both the classical and robust regressions models. As a consequence the properties of OLSE slope estimate no longer hold; in particular it is no longer unbiased. In fact,
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2 assuming that the marginal propensity to consume is positive, the OLSE of the slope is biased toward zero as this picture shows: 3. Given that the values taken by the regressor in a bivariate linear regression i X are i.i.d. random draws, an econometrician would prefer those values had a lot of variability to ensure good precision of the regression results, and yet too much variability can ruin those results altogether.
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