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Unformatted text preview: ARE 106 Fall 09 Problem set 2 solutions. 1. Tax and income of firms. tax i = β 1 + β 2 * income 1 + e i (1) (a) Estimate least-squares coefficients. Recall: ˆ b 2 = P 60 i =1 ( X i- ¯ X ) * ( Y i- ¯ Y ) P 60 i =1 ( X i- ¯ X ) 2 = . 2037 ˆ b 1 = ¯ Y- ˆ b 2 * ¯ X =- . 0734 (b) Estimate of the marginal tax rate for these firms. The estimated marginal tax rate is 20 . 36% for any extra dollar earned. (c) What is E ( ˆ b 2 )? What are the minimal assumptions you have to make in order to say this? If ˆ b 2 is unbiased, then E ( ˆ b 2 ) = β 2 . This requires: i. ˆ b 2 is linear in y i ii. the sum of the errors e i in (1) is zero. (d) For ˆ b 1 and ˆ b 2 to be BLUE of β 1 and β 2 respectively, the minimum required as- sumptions are SR 1 through SR 5 (please refer to the book; you need to actually list them out here for credit.) (e) Recall that (at ¯ X and ¯ Y ) = δY δX * ¯ X ¯ Y = ˆ b * ¯ X ¯ Y = . 2036 * 5 . 63 1 . 07 = 1 . 06 Then elasticity of taxes with respect to firm income, estimated at the mean, is...
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This note was uploaded on 01/20/2010 for the course ARE 106 taught by Professor Havenner during the Fall '09 term at UC Davis.
- Fall '09