Sufficient statistics for tariff reform when revenue matters

What kinds of tariff reform are likely to raise welfare in situations where tariff revenue is important? General conditions for welfare to rise without reducing tariff revenue are opaque. We show that they can be greatly simplified using a small number of sufficient statistics, primarily the generalized mean and variance of tariffs. We present sufficient conditions for a class of linear tariff reform rules that guarantee higher welfare without a loss in revenue. The rules consist of convex combinations of (i) trade-weighted-average-tariff-preserving cuts in dispersion; and (ii) uniform tariff cuts that preserve domestic relative prices among tariff-ridden goods.