Lecture_18_Prof._Arkonac's_Slides_(rest_of_Ch11)

Lecture_18_Prof._Arkonac's_Slides_(rest_of_Ch11) -...

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Regression with a Binary Dependent Variable II (cont’) & III (Fall 2010) Lecture 18 Prof: Seyhan Erden Arkonac, PhD Solutions to Problem Set 6 is posted. 1

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2 Logit Regression Logit regression models the probability of Y =1 as the cumulative standard logistic distribution function, evaluated at z = 0 + 1 X : Pr( Y = 1| X ) = F ( 0 + 1 X ) F is the cumulative logistic distribution function: F ( 0 + 1 X ) = 01 () 1 1 X e  
3 Logit regression, ctd. Pr( Y = 1| X ) = F ( 0 + 1 X ) where F ( 0 + 1 X ) = 01 () 1 1 X e   . Example : 0 = -3, 1 = 2, X = .4, so 0 + 1 X = -3 + 2 .4 = -2.2 so Pr( Y = 1| X =.4) = 1/(1+ e –(–2.2) ) = .0998 Why bother with logit if we have probit? Historically, logit is more convenient computationally In practice, logit and probit are very similar

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4 STATA Example : HMDA data . logit deny p_irat black, r; Iteration 0: log likelihood = -872.0853 Later… Iteration 1: log likelihood = -806.3571 Iteration 2: log likelihood = -795.74477 Iteration 3: log likelihood = -795.69521 Iteration 4: log likelihood = -795.69521 Logit estimates Number of obs = 2380 Wald chi2(2) = 117.75 Prob > chi2 = 0.0000 Log likelihood = -795.69521 Pseudo R2 = 0.0876 ------------------------------------------------------------------------------ | Robust deny | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- p_irat | 5.370362 .9633435 5.57 0.000 3.482244 7.258481 black | 1.272782 .1460986 8.71 0.000 .9864339 1.55913 _cons | -4.125558 .345825 -11.93 0.000 -4.803362 -3.447753 ------------------------------------------------------------------------------ . dis "Pred prob, p_irat=.3, white: " > 1/(1+exp(-(_b[_cons]+_b[p_irat]*.3+_b[black]*0))); Pred prob, p_irat=.3, white: .07485143 NOTE : the probit predicted probability is .07546603
5 Predicted probabilities from estimated probit and logit models usually are (as usual) very close in this application.

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6 Example for class discussion : Characterizing the Background of Hezbollah Militants Source: Alan Krueger and Jitka Maleckova, “Education, Poverty and Terrorism: Is There a Causal Connection?” Journal of Economic Perspectives , Fall 2003, 119-144. Logit regression: 1 = died in Hezbollah military event Table of logit results:
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9 Hezbollah militants example, ctd. Compute the effect of schooling by comparing predicted probabilities using the logit regression in column (3): Pr( Y =1|secondary = 1, poverty = 0, age = 20) Pr( Y =1|secondary = 0, poverty = 0, age = 20): Pr( Y =1|secondary = 1, poverty = 0, age = 20) = 1/[1+ e –(–5.965+.281 1 – .335 0 – .083 20) ] = 1/[1 + e 7.344 ] = .000646 does this make sense? Pr( Y =1|secondary = 0, poverty = 0, age = 20) = 1/[1+ e –(–5.965+.281 0 – .335 0 – .083 20) ] = 1/[1 + e 7.625 ] = .000488 does this make sense?

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10 Predicted change in probabilities: Pr( Y =1|secondary = 1, poverty = 0, age = 20) Pr( Y =1|secondary = 0, poverty = 0, age = 20) = .000646 – .000488 = .000158 Both these statements are true: The probability of being a deceased Hezbollah militant increases by 0.0158 percentage points, if secondary school is attended. The probability of being a deceased Hezbollah militant increases by 32%, if secondary school is attended (.000158/.000488 = .32). These sound so different! what is going on?
11 Estimation and Inference in Probit (and Logit) Models (SW Section 11.3) Probit model: Pr( Y = 1| X ) = ( 0 + 1 X ) Estimation and inference How can we estimate 0 and 1 ? What is the sampling distribution of the estimators?

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This note was uploaded on 11/10/2011 for the course ECON 3142 taught by Professor Arkonac during the Spring '11 term at Columbia.

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Lecture_18_Prof._Arkonac's_Slides_(rest_of_Ch11) -...

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