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answers2003final

answers2003final - Answer key for the 2003 nal exam(econ...

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Answer key for the 2003 fi nal exam (econ 220b). 1. (a) Since we assume that C i = βY i , we can substitute for C and Y to get C i a ci = β ( Y i a yi ) and then C i = Y i + ( a ci βa yi ) . So ± i = a ci βa yi . (b) The plim of an estimator b T is the constant b (if it exists) such that, for all δ > 0 , Prob[ | b T b | > δ ] 0 as T → ∞ . For the OLS estimator, b T = ³ X Y 2 i ´ 1 X Y i C i = 1 /T X ( Y i + a yi )( C i + a ci ) . 1 /T X ( Y i + a yi ) 2 p −→ E £ ( Y i + a yi )( C i + a ci ) ¤± E £ ( Y i + a yi ) 2 ¤ = βEY 2 i ±£ EY 2 i + Ea 2 yi ¤ . Since the expected value of the OLS estimator is the product of β and a positive fraction less than one, the OLS estimator has a downward bias. (c) It is clear from part (a) that the error term is correlated with the regressor Y i . (d) i. EY i > 0 (it’s income). ii. E ( ± i ) = E ( a ci βa yi ) = 0 . (e) Regressing C i and Y i on a vector of ones gives ¯ C and ¯ Y respectively.
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