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ProblemSet6Ans - ECON 3200 Introduction to Econometrics...

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ECON 3200 Introduction to Econometrics Answers for Problem Set 6 Problem 1 (Wooldridge 11.4) Assuming y 0 = 0 is a special case of assuming y 0 nonrandom, and so we can obtain the variances from (11.21): Var( y t ) = 2 e σ t and Var( y t+h ) = 2 e σ ( t + h ), h > 0. Because E( y t ) = 0 for all t (since E( y 0 ) = 0), Cov( y t , y t+h ) = E( y t y t+h ) and, for h > 0, E( y t y t+h ) = E[( e t + e t-1 + K e 1 )( e t+h + e t+h -1 + K + e 1 )] = E( 2 t e ) + E( 2 1 t e - ) + K + E( 2 1 e ) = 2 e σ t , where we have used the fact that { e t } is a pairwise uncorrelated sequence. Therefore, Corr( y t , y t+h ) = Cov( y t , y t+h )/ Var( ) Var( ) t t h y y + = t / ( ) t t h = /( t t h . Problem 2 (Wooldridge 11.6) 1. The t statistic for H 0 : β 1 = 1 is t = (1.104 – 1)/.039 2.67. Although we must rely on asymptotic results, we might as well use df = 120 in Table G.2. So the 1% critical value against a two-sided alternative is about 2.62, and so we reject H 0 : β 1 = 1 against H 1 : β 1 1 at the 1% level. It is hard to know whether the estimate is practically different from one without comparing investment strategies based on the theory ( β 1 = 1) and the estimate ( 1 ˆ β = 1.104). But the estimate is 10% higher than the theoretical value.
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