This paper presents a method for estimating the effects of a policy change on an outcome distribution that uses a comparator quantile rather than a control group and provides methods for estimating the variances of the estimators. The empirical analysis presents estimates of “spillover” effects of increases in the UK minimum wage, i.e. effects on the wages of those already above the minimum, under different counterfactual distribution shift assumptions. Evidence is presented against a simple scaled counterfactual. On the basis of the proposed counterfactual estimated spillover effects are small and in most cases do not reach above the 5th. percentile.