Fairlie describes a practical method for applying the Blinder-Oaxaca decomposition when the outcome is binary and the coefficients come from a logit or probit model — a case the linear Blinder-Oaxaca formula cannot handle directly. Building on his earlier application, he explains how to compute the decomposition from logit/probit estimates, analyzes the sensitivity of the results to the parameters and matching choices, shows how to calculate standard errors, compares the estimates to the standard Blinder-Oaxaca results, and discusses a case where the linear technique is problematic.
"The Blinder-Oaxaca decomposition technique … cannot be used directly, however, if the outcome is binary and the coefficients are from a logit or probit model. I describe a relatively simple method of performing a decomposition that uses estimates from a logit or probit model."
This is the reference practitioners actually cite when they need to decompose a binary-outcome gap — employment, business ownership, benefit receipt — which is most of the interesting cases in applied labor and health economics. Its value is procedural rather than theoretical: it turns "you can't just use Blinder-Oaxaca here" into a concrete, replicable recipe with standard errors. On the wiki it fills in the Oaxaca-Blinder page's nonlinear branch alongside the Yun (2004) linearization, and its honest weaknesses — path dependence in the matching and residual nonlinearity — are exactly why the linearization approaches coexist with it rather than being displaced.