Ordinal Distributional Change and Conservative Transition Benchmarks: Measurement, Identification, and Inference

Abstract

Repeated cross-sections reveal changes in ordinal distributions but not the transitions producing them. I axiomatically characterize a probability metric for ordinal change from threshold-crossing principles. On canonical rank distributions, the resulting metric coincides with Wasserstein--1; its classical transport representation measures minimum average threshold crossings and yields conservative transition benchmarks. With missing outcomes, I derive sharp identified sets for the discrepancy and benchmark plans. I develop finite-sample-valid projection inference using randomized Monte Carlo calibration and convergent global search. Applied to Arab Barometer data, the framework documents a robust shift toward broader and more regular remittance receipt in Lebanon. The discrepancy interval remains well separated from zero after allowing for item nonresponse and sampling uncertainty, while benchmark bounds provide strong numerical evidence that least-displacement restructuring excludes movement toward less frequent receipt and requires some reassignment from nonreceipt to recurrent receipt.