Topic 7 Binary Outcome Models

In addition to referenced material below, please read all of SW Ch. 11

You may or may not have noticed this, but all the outcomes that we have considered so far have involved a continuous outcome. But lots of economic variables are discrete (we’ll mainly focus on binary outcomes). Examples:

• Labor force participation

• Graduating from college

The question is: Do our linear regression tools still apply to this case? In other words, does

\[ \mathbb{E}[Y | X_1, X_2, X_3] = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 \] still make sense?

We will see that, in many cases, it is more natural to use a nonlinear model when the outcome is binary. And, actually, nonlinear models are fairly common in economics. This section will thus also provide an introduction to estimating (and understanding) nonlinear models. In this section, we will not necessarily be so interested in prediction (though you can make predictions using the techniques we discuss below), but I find this a good spot to teach about binary outcome models (after we talk about prediction mainly emphasizing linear models and before we conclude the course talking about causality).

• Note: we have already included binary regressors and know how to interpret these, so this section is about binary outcomes rather than binary regressors