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8. Your textbook gives the following example of simultaneous causality bias of a two equation system: Yi=0+1Xi+uiXi=0+1Yi+vi In microeconomics, you studied the demand and supply of goods in a single market. Let the demand (QiD) and supply (QiS) for the i-th good be determined as follows, QiD=01Pi+uiQiS=0+1Pi+vi where P is the price of the good. In addition, you typically assume that the market clears. The textbook explained a positive correlation between Xi and ui for 1>0 through an argument that started from "imagine that ui is negative." Repeat this exercise here and show that there is a positive correlation between Xi and ui for 1>0. ( 3 points) 9. Several authors have tried to measure the "persistence" in U.S state unemployment rates by running the following regression: uri,=0+1uri,tk+zi,t where ur is the state unemployment rate, i is the index for the i-th state, t indicates a time period, and typically k10. (a) Explain why finding a slope estimate of one and an intercept of zero is typically interpreted as evidence of "persistence." ( 2 points) (b) You collect data on the 48 contiguous U.S. states' unemployment rates and find the following estimates: ( 2 points) uri,1995=2.25+0.60uri,1970;R2=0.40,SER=0.90(0.61)(0.13) Interpret the regression results. Analyzing the accompanying figure, and interpret the observation for Maryland and for Washington. Do you find evidence of persistence? How would you test for it? (2 points) 8. Your textbook gives the following example of simultaneous causality bias of a two equation system: Yi=0+1Xi+uiXi=0+1Yi+vi In microeconomics, you studied the demand and supply of goods in a single market. Let the demand (QiD) and supply (QiS) for the i-th good be determined as follows, QiD=01Pi+uiQiS=0+1Pi+vi where P is the price of the good. In addition, you typically assume that the market clears. The textbook explained a positive correlation between Xi and ui for 1>0 through an argument that started from "imagine that ui is negative." Repeat this exercise here and show that there is a positive correlation between Xi and ui for 1>0. ( 3 points) 9. Several authors have tried to measure the "persistence" in U.S state unemployment rates by running the following regression: uri,=0+1uri,tk+zi,t where ur is the state unemployment rate, i is the index for the i-th state, t indicates a time period, and typically k10. (a) Explain why finding a slope estimate of one and an intercept of zero is typically interpreted as evidence of "persistence." ( 2 points) (b) You collect data on the 48 contiguous U.S. states' unemployment rates and find the following estimates: ( 2 points) uri,1995=2.25+0.60uri,1970;R2=0.40,SER=0.90(0.61)(0.13) Interpret the regression results. Analyzing the accompanying figure, and interpret the observation for Maryland and for Washington. Do you find evidence of persistence? How would you test for it? (2 points)