An asymptotic threshold of sufficient randomness for causal inference

For sensitivity analysis with stochastic counterfactuals, we introduce a methodology to characterize uncertainty in causal inference from natural experiments. Our sensitivity parameters are standardized measures of variation in propensity and prognosis probabilities, and one minus their geometric mean is an intuitive measure of randomness in the data generating process. Within our latent propensity‐prognosis model, we show how to compute, from contingency table data, a threshold, , of sufficient randomness for causal inference. If the actual randomness of the data generating process is greater than this threshold, then causal inference is warranted. We demonstrate our methodology with two example applications.