Econometrics-I-19

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

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Unformatted text preview: Applied Econometrics William Greene Department of Economics Stern School of Business Applied Econometrics 19. Two Applications of Maximum Likelihood Estimation and a Two Step Estimation Method 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 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. 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 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 WHRS | 740.576 871.314 .000000 4950.00 753 KL6 | .237716 .523959 .000000 3.00000 753 K618 | 1.35325 1.31987 .000000 8.00000 753 WA | 42.5378 8.07257 30.0000 60.0000 753 WE | 12.2869 2.28025 5.00000 17.0000 753 WW | 2.37457 3.24183 .000000 25.0000 753 RPWG | 1.84973 2.41989 .000000 9.98000 753 HHRS | 2267.27 595.567 175.000 5010.00 753 HA | 45.1208 8.05879 30.0000 60.0000 753 HE | 12.4914 3.02080 3.00000 17.0000 753 HW | 7.48218 4.23056 .412100 40.5090 753 FAMINC | 23080.6 12190.2 1500.00 96000.0 753 KIDS | .695883 .460338 .000000 1.00000 753 ---------------------------------------------------------------------- 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 12.491412....
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## This note was uploaded on 11/23/2011 for the course ECON B30.3351 taught by Professor Professorw.greene during the Spring '10 term at NYU.

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

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