Title: Robust principal scores for estimating survivor causal effects with application to analyses of litigation outcomes
Abstract: In many studies, outcomes are unobserved or undefined for some units under analysis. This is common in empirical studies of the outcomes of legal disputes where a large fraction of cases settle before a decision is rendered. Analyses that condition on settlement failure are biased for the causal effect even when the treatment of interest is randomly assigned if that treatment also affects the probability of settlement. When outcomes are truncated in this way, a valid causal quantity of interest is the treatment effect among the ``principal stratum'' of units that would fail to settle regardless of treatment. Principal score methods estimate these effects by assuming ignorability of stratum membership given observed covariates and weighting to eliminate covariate imbalances across strata. These weights are estimated using a model for principal stratum membership and can be highly sensitive to changes in model specification. I develop an estimator for principal score weights that is more robust to mis-specification of the principal score model by directly incorporating known covariate balance conditions using a generalized method-of-moments approach. I illustrate this new approach in a study of win-rates in international investor-state arbitration.