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464 Chapter 11 Regression with a Binary Dependent Variable

he is subject to a workplace smoking ban. What is the effect of the
smoking ban on the probability of smoking?
ii. Repeat (i) for Ms. B, a female, black, 40-year-old college graduate.
iii. Repeat (i)–(ii) using the linear probability model.
iv. Repeat (i)–(ii) using the logit model.
v. Based on your answers to (i)–(iv), do the logit, probit, and linear
probability models differ? If they do, which results make most
sense? Are the estimated effects large in a real work sense?

A p p e n d i x

11.1 The Boston HMDA Data Set

The Boston HMDA data set was collected by researchers at the Federal Reserve Bank of
Boston. The data set combines information from mortgage applications and a follow-up
survey of the banks and other lending institutions that received these mortgage applications.
The data pertain to mortgage applications made in 1990 in the greater Boston metropolitan
area. The full data set has 2925 observations, consisting of all mortgage applications by blacks
and Hispanics plus a random sample of mortgage applications by whites.

To narrow the scope of the analysis in this chapter, we use a subset of the data for
single-family residences only (thereby excluding data on multifamily homes) and for black
applicants and white applicants only (thereby excluding data on applicants from other
minority groups). This leaves 2380 observations. Definitions of the variables used in this
chapter are given in Table 11.1.

These data were graciously provided to us by Geoffrey Tootell of the Research
Department of the Federal Reserve Bank of Boston. More information about this data set,
along with the conclusions reached by the Federal Reserve Bank of Boston researchers, is
available in the article by Alicia H. Munnell, Geoffrey M. B. Tootell, Lynne E. Browne,
and James McEneaney, “Mortgage Lending in Boston: Interpreting HMDA Data,” Amer-
ican Economic Review, 1996, pp. 25–53.

A p p e n d i x

11.2 Maximum Likelihood Estimation

This appendix provides a brief introduction to maximum likelihood estimation in the con-
text of the binary response models discussed in this chapter. We start by deriving the MLE
of the success probability p for n i.i.d. observations of a Bernoulli random variable. We then