solution4 - Solutions to PS 4 Hongyan Zhao Nov 1, 2009 Q1...

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Solutions to PS 4 * Hongyan Zhao Nov 1, 2009 Q1 a. Taking log, we get ln q i = ln α + β ln K i + θ ln L i + ln ε i = ln α + E (ln ε i ) + β ln K i + θ ln L i + ln ε i - E (ln ε i ) β 0 + β ln K i + θ ln L i + u i b. Under the restriction β + θ = 1 ln q i = β 0 + ( β + θ ) ln K i + θ (ln L i - ln K i ) + u i ln q i - ln K i = β 0 + ( β + θ - 1) ln K i + θ (ln L i - ln K i ) + u i = β 0 + θ (ln L i - ln K i ) + u i c. If the erros are homoskedastic, we can use homoskedasticity-only F-statistic to test the null hypothesis. Under H 0 ,the F-statistic is distributed F q,n - k - 1 . Here q=1, k=2, thus it is distributed F 1 ,n - 3 . Note: we can also use t-statistic to test the null hypothesis. The regression function can be rewritten as ln q i - ln K i = β 0 + γ 1 ln K i + θ (ln L i - ln K i ) + u i Under the null hypothesis, γ 1 = 0. Thus we can use t-statistic method. Q2 * If you find any mistake or typo, please email me hyzhao@econ.berkeley.edu 1
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Q3 (d)If we fix a=50, and run regression on the first 35observations. We get the esti-
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solution4 - Solutions to PS 4 Hongyan Zhao Nov 1, 2009 Q1...

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