Taking an Extra Moment to Consider Treatment Effects on Distributions

This paper introduces Parameter Estimation by Raw Moments (PERM), a flexible method for evaluating a policy’s impact on the parameters of an outcome distribution. Such parameters include the variance (E[Y2]−E[Y]2), skewness and covariance of two outcomes. PERM simplifies distributional analysis by first separately estimating higher-order moment treatment effects (e.g., E[Y2]), then combining these to derive distribution parameter treatment effects. Two implementations are discussed: regression with controls and DiD with staggered roll-out. Applying PERM DiD to a Swedish school reform finds it reduced education inequality but increased earnings variance resulting in a lower covariance between education and earnings.