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1 Regression with a Binary Dependent Variable (SW Chapter 11)

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2 Example: Mortgage denial and race The Boston Fed HMDA data set

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3 The Linear Probability Model

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5 Example: Linear Prob Model

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6 Linear probability model: HMDA data

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8 Linear probability model: Application Cattaneo, Galiani, Gertler, Martinez, and Titiunik (2009). “Housing, Health, and Happiness.” American Economic Journal: Economic Policy 1(1): 75 - 105 What was the impact of Piso Firme, a large-scale Mexican program to help families replace dirt floors with cement floors? A pledge by governor Enrique Martinez y Martinez led to State of Coahuila offering free 50m 2 of cement flooring ($150 value), starting in 2000, for homeowners with dirt floors

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9 Cattaneo et al. (AEJ:Economic Policy 2009) “Housing, Health, & Happiness” X 1 = “Program dummy” = 1 if offered Piso Firme.

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10 Cattaneo et al. (AEJ:Economic Policy 2009) “Housing, Health, & Happiness” Interpretations? X 1 = “Program dummy” = 1 if offered Piso Firme

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11 Probit and Logit Regression

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12 Probit Regression

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13 STATA Example: HMDA data

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14 STATA Example: HMDA data, ctd.

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15 Probit regression with multiple regressors

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16 STATA Example: HMDA data

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17 STATA Example: HMDA data

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18 STATA Example: HMDA data

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19 Probit Regression Marginal Effects

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20 Probit Regression Marginal Effects. sum pratio; Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- pratio | 1140 1.027249.286608.497207 2.324675. scalar meanpratio = r(mean);. sum disp_pepsi; Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- disp_pepsi | 1140.3640351.4813697 0 1. scalar meandisp_pepsi = r(mean);. sum disp_coke; Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- disp_coke | 1140.3789474.4853379 0 1. scalar meandisp_coke = r(mean);. probit coke pratio disp_coke disp_pepsi; Iteration 0: log likelihood = -783.86028 Iteration 1: log likelihood = -711.02196 Iteration 2: log likelihood = -710.94858 Iteration 3: log likelihood = -710.94858 Probit regression Number of obs = 1140 LR chi2(3) = 145.82 Prob > chi2 = 0.0000 Log likelihood = -710.94858 Pseudo R2 = 0.0930 ------------------------------------------------------------------------------ coke | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- pratio | -1.145963.1808833 -6.34 0.000 -1.500487 -.791438 disp_coke |.217187.0966084 2.25 0.025.027838.4065359 disp_pepsi | -.447297.1014033 -4.41 0.000 -.6460439 -.2485502 _cons | 1.10806.1899592 5.83 0.000.7357465 1.480373 ------------------------------------------------------------------------------

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21 Probit Regression Marginal Effects

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22 Logit Regression

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23 STATA Example: HMDA data

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24 Predicted probabilities from estimated probit and logit models usually are (as usual) very close in this application.

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25 Logit Regression Marginal Effects

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26 Comparison of Marginal Effects LPMProbitLogit Marginal Effect at Means for Price Ratio -.4008 (.0613) -.4520 (.0712) via nlcom -.4905 (.0773) via nlcom Average Marginal Effect of Price Ratio -.4008 (.0613) -.4096 (beyond eco205) -.4332 (beyond eco205) Marginal Effect at Means for Coke display dummy.0771 (.0343).0856 (.0381) via nlcom.0864 (.0390) via nlcom Average Marginal Effect For Coke display dummy.0771 (.0343).0776 (beyond eco205).0763 (beyond eco205)

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27 Probit model: Application Arcidiacono and Vigdor (2010). “Does the River Spill Over? Estimating the Economic Returns to Attending a Racially Diverse College.” Economic Inquiry 48(3): 537 – 557. Does “diversity capital” matter and does minority representation increase it? Does diversity improve post- graduate outcomes of non-minority students? College & Beyond survey, starting college in 1976

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28 Arcidiacono & Vigdor (EI, 2010)

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29 Arcidiacono & Vigdor (EI, 2010)

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30 Arcidiacono & Vigdor (EI, 2010)

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31 Logit model: Application Bodvarsson & Walker (2004). “Do Parental Cash Transfers Weaken Performance in College?” Economics of Education Review 23: 483 – 495. When parents pay for tuition & books does this undermine the incentive to do well? Univ of Nebraska @ Lincoln & Washburn Univ in Topeka, KS, 2001-02 academic year

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32 Bodvarsson & Walker (EconEduR,2004)

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33 Bodvarsson & Walker (EconEduR,2004)

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34 Estimation and Inference in Probit (and Logit) Models

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35 Probit estimation by maximum likelihood

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36 Special case: probit MLE with no X

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40 The MLE in the “no-X” case (Bernoulli distribution), ctd.:

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41 The MLE in the “no-X” case (Bernoulli distribution), ctd:

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42 The probit likelihood with one X

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43 The probit likelihood function:

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44 The Probit MLE, ctd.

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45 The logit likelihood with one X

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46 Measures of fit for logit and probit

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47 Application to the Boston HMDA Data (SW Section 11.4)

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48 The HMDA Data Set

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49 The loan officer’s decision

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50 Regression specifications

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54 Table 11.2, ctd.

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55 Table 11.2, ctd.

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56 Summary of Empirical Results

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PP Test Review Sections 6-1 to 6-6

PP Test Review Sections 6-1 to 6-6

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