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Unformatted text preview: Problem Set 5 ECON 231W Spring 2010 Suggested Solutions 1. a)You cannot use OLS, because the equation under consideration is not of the form X 1 + X 2 + , where enters additively and the coefficients, which we estimate (in power 1), are multiplying the explanatory variables. b) You cannot compute E [ i | L i K i ] using the fact that E [ln i | L i K i ] = 0, because expectation is a linear operator and we are not given information about the whole conditional distribution of ln i (but just its first moment). In this case, you can only conclude that E [ln i | L i K i ] = 0 < ln E [ i | L i K i ] (as ln x is a concave function of x ), which implies that E [ i | L i K i ] > 1. c) You can use take the log of the right hand side and left hand side of the equation to get: ln y i = ln L i + ln K i + ln i d) In the equation above let e y ln y, e L ln L, e K ln K , e ln , so we have a convenient linear representation e y i = e L i + e K i + e i , with E [ e i | L i ,K i ] = E [ e i | e L i , e K i ] = 0, which altogether satisfies OLS Assumption 1. e) In economic terms, is the elasticity of output with respect to labor labor input, and is the elasticity of output with respect to capital. f) One way is to use a simple t-test, where: H : + = 1 H 1 : + 6 = 1 Where the standard error of b + b is q d V ar ( b ) + d V ar ( b ) + 2 d Cov ( b , b ) . An alternative method would be to re-write the equation as: ln y i = ln L i + ln K i + u i = ln L i + ln L i- ln L i + ln K i + u i = ( + )ln L i + (ln K i- ln L i ) + u i = ln L i + (ln K i- ln L i ) + u i And run a simple t-test, where: H : = 1 H 1 : 6 = 1 ....
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This note was uploaded on 04/19/2010 for the course ECO 231W taught by Professor Joshuakinsler during the Spring '10 term at Rochester.
- Spring '10