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psviiii140a - University of California Department of...

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University of California D. Steigerwald Department of Economics Economics 140A Problem Set IX 1. In a 2000 study of a sample of Californians, each person’s consumption C t is regressed on an intercept, their wage and salary income W t and their asset income A t . The OLS regression estimates are P t c = ) . ( t ) . ( t ) ( a . w . 3 3 5 2 50 3 5 200 + + R 2 = .95, t = 1,2,...,103. Residual Sum of Squares : RSS 1 = 30 . Note: The numbers in parentheses are estimated standard errors. a) Given the results above, do you think multicollinearity is present? Please explain your answer. b) If a new aggregate income regressor Y t = W t + A t replaces the individual income regressors, then the OLS regression estimates are ) (. t ) ( P t y . c 25 48 75 210 + = R 2 = .949, t=1,2,...103. Residual Sum of Squares : RSS 2 = 35 . Briefly explain how and why things may have changed compared to the previous results. c) How would you test the null hypothesis that the coefficients of W t and A t in the first regression are equal? Suppose you reject the null hypothesis, how would this affect your answers to parts a) and b) above? Can you think of an alternative procedure to the one presented in part b)? Explain. d) How would these tests you have constructed be affected if the errors are not normally distributed?
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2. Suppose output for the economy is given by the production relation (1) ln Q t = β 0 + β 1 ln L t + β 2 ln K t + U t t = 1,..., n where t indexes the time at which the observation is recorded, ln
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