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Unformatted text preview: Solutions to PS 5 * Hongyan Zhao Nov 25, 2009 Q 1 a. lnq it = E ( ln it ) + ln i + lnK it + lnL it + lnu t + ln it- E ( ln it ) b. In order to estimate using a Random effect model, we need the assumption that u t is uncorrelated with K it and L it . If not, we cannot use GLS to estimate since error term is correlated with regressors which makes the estimators inconsistent. Also, you can see this is just the null hypothesis in Hausman test. With the Hausman null hypothesis, both the fixed effect estimators and the random effect estimators are consistent, and the random effect estimators are efficient. With the Hausman alternative hypothesis, the random effect estimators are inconsistent. c. The marginal product of capital MPK it = i K - 1 it L it u t it = * q it /K it ln ( MPK it ) = ln ( ) + ln ( q it )- ln ( K it ) Thus we did fixed effect model ln ( MPK it ) = i + 1 ln ( q it ) + 2 ln ( K it ) + it We need to test the null hypothesis 1 = 2 = = I If we reject the null hypothesis, then the marginal product of capital were not com- mon across all firms. d. Like the example in the textbook, the variable p t is decided by both supply curve and demand curve. Thus it is correlated with the error term and need instrument variables. The instruments you suggest should have impacts on demand curve but not on supply curve, such as income, prices of complementary or substitute goods.on supply curve, such as income, prices of complementary or substitute goods....
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- Fall '08