Regression with a Binary Dependent Variable

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Presentation transcript:

Regression with a Binary Dependent Variable Chapter 11 Regression with a Binary Dependent Variable

Regression with a Binary Dependent Variable (SW Chapter 11)

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

The Linear Probability Model (SW Section 11.1)

The linear probability model, ctd.

The linear probability model, ctd.

Example: linear probability model, HMDA data

Linear probability model: HMDA data, ctd.

Linear probability model: HMDA data, ctd

The linear probability model: Summary

Probit and Logit Regression (SW Section 11.2)

Probit regression, ctd.

STATA Example: HMDA data

STATA Example: HMDA data, ctd.

Probit regression with multiple regressors

STATA Example: HMDA data

STATA Example, ctd.: predicted probit probabilities

STATA Example, ctd.

Logit Regression

Logit regression, ctd.

STATA Example: HMDA data

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

Example for class discussion:

Hezbollah militants example, ctd.

Predicted change in probabilities:

Estimation and Inference in Probit (and Logit) Models (SW Section 11

Probit estimation by nonlinear least squares

Probit estimation by maximum likelihood

Special case: the probit MLE with no X

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

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

The probit likelihood with one X

The probit likelihood function:

The Probit MLE, ctd.

The logit likelihood with one X

Measures of fit for logit and probit

Application to the Boston HMDA Data (SW Section 11.4)

The HMDA Data Set

The loan officer’s decision

Regression specifications

Table 11.2, ctd.

Table 11.2, ctd.

Summary of Empirical Results

Remaining threats to internal, external validity

Summary (SW Section 11.5)