Binary choice models estimate the probability of an outcome that can take only two values, such as employed versus unemployed, default versus no default, or purchase versus no purchase.
Core setup
In applied econometrics, the usual idea is that a person or firm has an unobserved latent payoff:
y* = Xb + e
We do not observe y* directly. We observe only whether it crosses a threshold:
y = 1ify* > 0y = 0otherwise
That structure makes binary choice models natural for decisions where the observed result is discrete even if the underlying incentives are continuous.
Main model types
- The logit model uses a logistic cumulative distribution for the error term.
- The probit model uses a normal cumulative distribution.
- The linear probability model is simpler, but it can predict probabilities below 0 or above 1 and usually has heteroskedastic errors.
In most economics applications, logit and probit are preferred because they keep predicted probabilities in the valid 0 to 1 range.
How economists interpret them
The coefficient itself is not usually the marginal effect on probability. Instead, economists often compute:
- marginal effects,
- odds ratios in logit applications,
- predicted probabilities for representative cases.
That matters for policy work. A coefficient may show the sign of an effect, but the economically meaningful question is often: “How much does the probability change?”
Typical uses
Binary choice models are common in labor economics, public economics, finance, health economics, and industrial organization. Examples include labor-force participation, benefit take-up, loan default, entry decisions, and technology adoption.