# assignsol - PPOL 509-03 Problem Set 6 SOLUTIONS Hypothesis...

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PPOL 509-03 Problem Set 6 SOLUTIONS Page 1 PPOL 509-03 Problem Set 6 SOLUTIONS Hypothesis Tests for a Linear Combo. Of Parameters, Review Due in class 2/22/07 1. (i) The average of prpblck is 0.113 with a standard deviation of 0.182. The average of income is 47,053.78 with a standard deviation of 13,179. It is evident that prpblck is a proportion (with values between zero and one) and that income is measured in dollars. 1. (ii) psoda = 0.956 + 0.115 prpblck + 0.0000016 income n = 401 R 2 = 0.064 If prpblck increases by 0.10 (10 percentage points), the price of soda is estimated to increase by (0.10)*(0.115)=0.0115 dollars, or 1.2 cents. Note that we have not interpreted our regression coefficient in terms of a “one unit” change. If we want to interpret the coefficient in terms of some other quantity (here we do ten percentage points, in part iv you are asked to do the same thing with 20 percentage points). While this does not seem large, there are communities with no black population and others that are almost all black, in which case the difference in psoda is estimated to be almost 11.5 cents. 1. (iii) psoda= 1.04+0.065 prpblck The simple regression estimate on prpblck is 0.065, so the simple regression estimate is actually lower. This is because prpblck and income are negatively correlated (- 0.43) and income has a positive coefficient in the multiple regression. So yes, this is what we would expect from our omitted variable bias reasoning. Sign of bias=(sign of rel. income & psoda )*(sign of rel. income & prpblck ) =(>0)*(<0)=<0 If the bias is negative, we find a lower bound in the restricted regression case. Thus, we expect that once we include income, the coefficient will be larger. Note that this is our “best case” of omitted variable bias. Our “lower bound” is greater than zero, so we can be confident that the true relationship is positive. 1. (iv) lpsoda = - 0.794 + 0.122 prpblck + 0.077 lincome n = 401 R 2 = 0.068 MAKE SURE YOU CORRECTED THE TYPO IN WOOLDRIDGE! (OR THIS ANSWER MIGHT NOT MATCH UP WITH YOUR WORK—income was on the right hand side in the text and on your handout, it should be log(income))

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PPOL 509-03 Problem Set 6 SOLUTIONS Page 2 If prpblck increases by 0.20, lpsoda is estimated to increase by 2.44% [0.2(0.122)*100 = 0.0244*100 or 2.44%] [NOTE: The interpretation of the coefficient on prpblck is a log- level interpretation, so we multiply the coefficient by 100. The interpretation of the coefficient on lincome is a log-log interpretation. In the same regression, it is possible to have more than one type of interpretation, the rules we learned on Day #2 are variable- specific.] 1. (v) β prpblck falls to 0.073 when prppov is added to the regression. Our usual omitted variable bias reasoning can explain why this coefficient fell.
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## This note was uploaded on 03/25/2012 for the course ECON 3107 taught by Professor Valentyn during the Three '11 term at University of New South Wales.

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assignsol - PPOL 509-03 Problem Set 6 SOLUTIONS Hypothesis...

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