Econometrics-I-19 - Applied Econometrics William Greene...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
Applied Econometrics William Greene Department of Economics Stern School of Business
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Applied Econometrics 19. Two Applications of Maximum Likelihood Estimation and a Two Step Estimation Method
Background image of page 2
Model for a Binary Dependent Variable Describe a binary outcome. Event occurs or doesn’t (e.g., the democrat wins, the  person enters the labor force,… Model the probability of the event Requirements 0 < Probability < 1 P(x) should be monotonic in x – it’s a CDF
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Two Standard Models Based on the normal distribution: Prob[y=1|x] =  Φ ( β ’x ) = CDF of normal distribution The “probit” model Based on the logistic distribution Prob[y=1|x]  =  exp( β ’x )/[1+ exp( β ’x )] The “logit” model Log likelihood P(y|x) = (1-F) (1-y)  F y  where F = the cdf Log-L =  Σ i  (1-y i )log(1-F i ) + y i logF i             Σ i  F[(2y i -1)  β ’x ] since F(-t)=1-F(t) for both.
Background image of page 4
Coefficients in the Binary Choice Models     E[y|x] = 0*(1-F i ) + 1*F i   =  P(y=1|x)               = F( β ’x )      The coefficients are not the slopes, as usual       in a nonlinear model ∂E[y|x]/∂x= f( β ’x β   These will look similar for probit and logit
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Application: Female Labor Supply 1975 Survey Data: Mroz (Econometrica) 753 Observations Descriptive Statistics Variable Mean Std.Dev. Minimum Maximum Cases Missing ============================================================================== All observations in current sample --------+--------------------------------------------------------------------- LFP | .568393 .495630 .000000 1.00000 753 0 WHRS | 740.576 871.314 .000000 4950.00 753 0 KL6 | .237716 .523959 .000000 3.00000 753 0 K618 | 1.35325 1.31987 .000000 8.00000 753 0 WA | 42.5378 8.07257 30.0000 60.0000 753 0 WE | 12.2869 2.28025 5.00000 17.0000 753 0 WW | 2.37457 3.24183 .000000 25.0000 753 0 RPWG | 1.84973 2.41989 .000000 9.98000 753 0 HHRS | 2267.27 595.567 175.000 5010.00 753 0 HA | 45.1208 8.05879 30.0000 60.0000 753 0 HE | 12.4914 3.02080 3.00000 17.0000 753 0 HW | 7.48218 4.23056 .412100 40.5090 753 0 FAMINC | 23080.6 12190.2 1500.00 96000.0 753 0 KIDS | .695883 .460338 .000000 1.00000 753 0
Background image of page 6
---------------------------------------------------------------------- Binomial Probit Model Dependent variable LFP Log likelihood function -488.26476 (Probit) Log likelihood function -488.17640 (Logit) --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- |Index function for probability Constant| .77143 .52381 1.473 .1408 WA| -.02008 .01305 -1.538 .1241 42.5378 WE| .13881*** .02710 5.122 .0000 12.2869 HHRS| -.00019** .801461D-04 -2.359 .0183 2267.27 HA| -.00526 .01285 -.410 .6821 45.1208 HE| -.06136*** .02058 -2.982 .0029 12.4914
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 30

Econometrics-I-19 - Applied Econometrics William Greene...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online