The Krinsky-Robb method is a simulation-based procedure for constructing confidence intervals around willingness-to-pay (WTP) estimates in choice modelling. It is the honest alternative to the delta-method approximation — and the only reliable choice when the price coefficient is small, uncertain, or near zero.
Why WTP intervals are hard
WTP is a ratio of two estimated utilities:
$$\mathrm{WTP} = \frac{\beta_{\text{attribute}}}{|\beta_{\text{price}}|}$$
The price coefficient sits in the denominator. When $\beta_{\text{price}}$ is well-identified, the ratio is well-behaved. When $\beta_{\text{price}}$ is small or straddles zero, the ratio explodes — a 95% CI from the standard delta method can span negative infinity to positive infinity without anyone noticing. Reporting a point WTP as if it were reliable, when the distribution is pathological, is a classical analytical failure.
How Krinsky-Robb works
Instead of linearising the ratio, Krinsky-Robb takes draws from the full joint distribution of the estimated coefficients and recomputes the ratio at each draw:
Draw $K$ (typically 1,000–10,000) samples $(\tilde{\beta}_{\text{attribute}}^{(k)}, \tilde{\beta}_{\text{price}}^{(k)})$ from the estimated multivariate normal distribution of the coefficients, respecting their covariance.
Compute $\mathrm{WTP}^{(k)} = \tilde{\beta}_{\text{attribute}}^{(k)} / |\tilde{\beta}_{\text{price}}^{(k)}|$ at each draw.
Report the empirical quantiles (2.5% and 97.5% for a 95% CI) of the resulting WTP distribution.
In a Bayesian setting, the equivalent uses posterior draws directly — no reliance on asymptotic normality, no reliance on linearisation.
When Krinsky-Robb fails loudly (and should)
The method surfaces the pathology instead of hiding it. If the price coefficient’s posterior straddles zero, the WTP distribution has infinite variance and the empirical CI will be absurdly wide — correctly signalling that the data cannot support a confident WTP. The right response is to refuse the WTP estimate rather than report an incompetent point value.
Why Ordeen uses it
Every WTP is computed via Krinsky-Robb on the posterior draws, reported with credible interval alongside the point, and refused entirely when the price coefficient is degenerate. This matches the published standard set by Hole (2007) and Daly, Hess & Train (2012). The alternative — a plain delta-method CI shipped without a sanity check — is the quickest way to an indefensible pricing recommendation.