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Unformatted text preview: Economics 140A: FINAL Sample Test Problem 1: Coefficient interpretation and Omitted variable The following equation describes the median housing price, mea- sured in dollars, of a community in terms of amount of pollution(nox for nitrous oxide measured in parts per 100 million) and the distance between the community and the city employment center(measured in miles). log( price ) = + 1 log( nox ) + 2 log( dist ) + The above equation was estimated using data on 506 communities as log( price ) = 12 . 45- 1 . 39 log( nox )- . 04 log( dist ) a) Interpret the coefficients on log( nox ) and log( dist ) b) Suppose you unintentionally omitted the variable dist from the original model and run instead, the following model log( price ) = + 1 log( nox ) + Write down the expression for 1 . Under what conditions would the estimated coefficient on log( nox ) be biased? c) If the estimate is biased in part b , would the estimated coefficient on log( nox ) be greater or less than -1.39? Clearly explain.(Hint: discuss the possible sign of 2 and the covariance obtained in part b Problem 2: Unbiasedness and Heteroskedasticity Consider the DGP as y i = + i where E ( i ) = 0 and V ar ( i ) = 1 E ( 2 i ) = 2 . a) Derive the Ordinary Least Squares Estimator of b) Show that the OLS estimator ( OLS ) is unbiased under the as- sumptions given above c) Under Gauss-Markov assumptions, derive the variance of OLS . Show clearly the steps. d) Suppose now that for larger values of i , V ar ( i ) = 2 i for i = 1 to n . Under this assumption, is OLS still unbiased? is OLS the Best Linear Unbiased Estimator (B.L.U.E)? If not, derive an estimator that is more efficient than OLS . Problem 3: Measurement error and instrumental variable Suppose the following true regression model y i = x i + i where x i is unobserved but is the true value of the model. Suppose instead, that you observe x * i = x i + i . Assume E ( 2 i ) = 2 , E ( x i i ) = 0, E (...
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- Fall '08