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Up to now we have worked with 21 wage o 1 educ u 7 we

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Unformatted text preview: ns to the R 2 ? Melissa Tartari (Yale) Econometrics 43 / 93 Algebraic Properties: Unit of Measurement II What happens to the R 2 ? It remains unchanged (as it intuitively should). Melissa Tartari (Yale) Econometrics 43 / 93 Algebraic Properties: Unit of Measurement II What happens to the R 2 ? It remains unchanged (as it intuitively should). Let us see why: R 20 = b SSE 0 ∑n (y 0 = in=1 i0 0 SST ∑i =1 (yi Melissa Tartari (Yale) y 0) ¯ 2 y 0 )2 ¯ = Econometrics c ∑n=1 (yi b i c ∑n=1 i (yi y )2 ¯ y) ¯ 2 = SSE = R2. SST 43 / 93 Incorporating Nonlinearities We can incorporate nonlinearities by appropriately de…ning dependent and independent variables. Melissa Tartari (Yale) Econometrics 44 / 93 Incorporating Nonlinearities We can incorporate nonlinearities by appropriately de…ning dependent and independent variables. Consider for instance wage = f (educ , u ) where u = ability . Melissa Tartari (Yale) Econometrics 44 / 93 Incorporating Nonlinearities We can incorporate nonlinearities by appropriately de…ning dependent and independent variables. Consider for instance wage = f (educ , u ) where u = ability . Up to now we have worked with (2.1): wage = βo + β1 educ + u Melissa Tartari (Yale) Econometrics (7) 44 / 93 Incorporating Nonlinearities We can incorporate nonlinearities by appropriately de…ning dependent and independent variables. Consider for instance wage = f (educ , u ) where u = ability . Up to now we have worked with (2.1): wage = βo + β1 educ + u (7) We next consider three alternative functional relationships that appear often in applied work. Melissa Tartari (Yale) Econometrics 44 / 93 The Constant Percentage-E¤ect Model I The dVar appears in logarithmic form: log wage = βo + β1 educ + u Melissa Tartari (Yale) Econometrics 45 / 93 The Constant Percentage-E¤ect Model I The dVar appears in logarithmic form: log wage = βo + β1 educ + u Observe that now β1 100 gives the % change in wage given one additional year of education. ∆%wage ∆educ Melissa Tartari (Yale) d (log wage ) d (educ ) Econom...
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This note was uploaded on 02/13/2014 for the course ECON 350 taught by Professor Donaldbrown during the Fall '10 term at Yale.

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