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Unformatted text preview: think that the rela:onship looks like an exponen3al func3on Y Y X X Back to the graphs •  The age variable looks like it needs a polynomial •  The faminc variable looks like it needs to be logged •  I’ll put them in separately to isolate the effect 5 2/17/12 0 100000 200000 Residuals wrt Age 20 40 60 Age of head in 2007 Residuals 80 lowess r1 agehd 100 -100000 -50000 0 Before 50000 100000 150000 -100000 Aeer 20 40 60 Age of head in 2007 Residuals 80 100 lowess r2 agehd 100000 200000 Residuals wrt Faminc 50000 100000 150000 Total family income in 2008 Residuals lowess r1 faminc 200000 0 0 -5 Before -10 -100000 5 0 Aeer 0 50000 100000 150000 Total family income in 2008 Residuals 200000 lowess r3 faminc 6 2/17/12 A special kind of log transforma:on: Log- Linear •  Func:onal Form: ln yi = β 0 + β1 ln xi + ε i •  This form is useful when you want an elas:city of y with respect to x: e ln yi = e β0 + β1 ln x β1 Elas:city: y = e β0 e ln x = e β0 x β1 ∂y = β1e β0 x β1 −1 ∂x ∂y x x ⋅ = β1e β0 x β1 −1 ⋅ β0 β1 = β1 ∂x y ex The elas:city of income wrt age A 10% increase in age is . gen lnfaminc=log(faminc)! associated with a 1.25% increase . gen lnage=log(agehd)! . reg lnfaminc lnage $controls! in family income. ! Source | SS df MS Number of obs = 7874! -------------+-----------------------------F( 8, 7865) = 494.89! Model | 2446.92506 8 305.865633 Prob > F = 0.0000! Residual | 4860.93942 7865 .61804697 R-squared = 0.3348! -------------+-----------------------------Adj R-squared = 0.3342! Total | 7307.86448 7873 .92821853 Root MSE = .78616! ! ------------------------------------------------------------------------------! lnfaminc | Coef. Std. Err. t P>|t| [95% Conf. Interval]! -------------+----------------------------------------------------------------! lnage | .1250018 .0245474 5.09 0.000 .0768822 .1731213! black | -....
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This note was uploaded on 03/28/2012 for the course PADP 8130 taught by Professor Fertig during the Spring '12 term at LSU.

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