140_problems7 - ECON 140, Fall 2008 - 11/6 Alex Rothenberg...

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Unformatted text preview: ECON 140, Fall 2008 - 11/6 Alex Rothenberg Practice Problems: Serial Correlation and Panel Data Problem 1 Suppose we have the following autoregressive model for the error term (the unobservables) in a regression equation: t = t- 1 + u t (1) u t iid N (0 , 2 u ) (2) This question asks you to investigate some of the properties of this process. 1. Fixing the value of = 0, write out the first few terms of the sequence { t } in terms of the u t s. (Do this for t = 0 , 1 , 2 , 3 , 4) 2. Assuming E [ ] = 0, what is the expected value of each term? 3. Assuming that Var( t ) = 2 for all t (homoskedasticity), express 2 as a function of 2 u . 4. What is the covariance between 1 and 3 ? Between 1 and 2 ? Problem 2 Say we want to run the following time-series regression using ordinary least squares: Y t = + X t + t However, the error term in this equation is actually serially correlated: t = t- 1 + u t u t iid N (0 , 2 u ) 1. Suppose we ignore the serial correlation and just use ordinary least squares. Is still unbiased? Under what conditions will this be the case? (HINT: Remember the omitted bias formula from last time.) 2. Try to compute Var( ). What happens now that we have serial correlation?...
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140_problems7 - ECON 140, Fall 2008 - 11/6 Alex Rothenberg...

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