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Econometrics-I-19

Kids 13093 04708 2781 0054 15905 variable coefficient

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KIDS| -.13093*** .04708 -2.781 .0054 -.15905 Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Elasticity --------+------------------------------------------------------------- |LOGIT: Marginal effect for variable in probability WA| -.00804 .00521 -1.542 .1231 -.59546 WE| .05521*** .01099 5.023 .0000 1.18097 HHRS|-.74419D-04** .319831D-04 -2.327 .0200 -.29375 HA| -.00209 .00513 -.408 .6834 -.16434 HE| -.02468*** .00826 -2.988 .0028 -.53673 FAMINC| .00422** .00184 2.301 .0214 .16966 |Marginal effect for dummy variable is P|1 - P|0. KIDS| -.13120*** .04709 -2.786 .0053 -.15894 --------+------------------------------------------------------------- ™  7/29
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Part 19: MLE Applications Exponential Regression Model ™  8/29 2 1 1 2 1 1 1 1 ( | ) exp( / ), exp( ) [ | ]; [ | ] log ( | ) log log log 1 1 lo Note since [ | ], E i i i i i i i i i i i i n n i i i i i i i n n n i i i i i i i i i i i i i i i i i P y y E y Var y y LogL P y L y y L E y = = = = = = - θ θ θ = = = θ = = - θ - θ ∂θ - = = + θ = - ÷ ÷ ∂θ θ θ θ θ = x x x x x x x x β β β g L = 0 β
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Part 19: MLE Applications Variance of the First Derivative ™  9/29 1 1 1 1 ( | ) exp( / ), log 1 log Note since [ | ], E log 1 1 Var [ | ] i i i i i n i i i i i i i n n i i i i i i i i i i i P y y y L L E y L Var y = = = = - θ θ = - ÷ θ θ = = = = θ = ÷ ÷ θ θ 2 2 2 x x x 0 x x x x x X X β β β
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Part 19: MLE Applications Hessian ™  10/29 1 2 2 1 1 2 1 ( | ) exp( / ), log 1 log log because E[ | ] i i i i i n i i i i n n i i i i i i i i i i i i i i P y y y L y y L L E y = = = = - θ θ = - ÷ θ = - θ = - ÷ ÷ ∂ ∂ θ θ - = = θ ∂ ∂ x x x x x x X X, x β β β β β
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Part 19: MLE Applications Variance Estimators ™  11/29 1 1 2 Negative inverse of actual second derivatives Matrix ˆ ˆ , exp ˆ Negative inverse of expected second derivatives log Sum of outer n i i i i MLE i i i y L E - = θ = ÷ ÷ θ - = ∂ ∂ -1 x x x X X, so [X X] β β β 1 1 1 1 1 1 products of first derivatives (BHHH) 1 ˆ "Robust" estimator in wide use 1 ˆ ˆ ˆ n i i i i i n n n i i i i i i i i i i i i i i i y y y y - = - = = = - ÷ ÷ θ - ÷ ÷ ÷ ÷ ÷ ÷ θ θ θ 2 2 x x x x x x x x 1 -
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Part 19: MLE Applications Income Data Frequency HHNINC .0 0 0 .4 38 .8 7 6 1.314 1.7 5 3 2 .19 1 2 .6 2 9 3 .0 67 ™  12/29
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Part 19: MLE Applications Exponential Regression --> logl ; lhs=hhninc ; rhs = x ; model=exp $ Normal exit: 11 iterations. Status=0. F= -1550.075 ---------------------------------------------------------------------- Exponential (Loglinear) Regression Model Dependent variable HHNINC Log likelihood function 1550.07536 Restricted log likelihood 1195.06953 Chi squared [ 5 d.f.] 710.01166 Significance level .00000 McFadden Pseudo R-squared -.2970587 Estimation based on N = 27322, K = 6 --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- |Parameters in conditional mean function Constant| 1.77430*** .04501 39.418 .0000 AGE| .00205*** .00063 3.274 .0011 43.5272 EDUC| -.05572*** .00271 -20.539 .0000 11.3202 MARRIED| -.26341***
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