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 based on threshold-crossing geometry. Its optimal-transport representation measures the minimum average number of thresholds crossed and yields conservative transition benchmarks. With missing outcomes, I derive sharp identified sets for the discrepancy and endpoint-conditioned benchmark plans. I develop finite-sample-valid projection inference using randomized Monte Carlo calibration and a convergent global-search procedure for the resulting numerical projections. Applied to Arab Barometer data, the framework documents a robust shift toward broader and more regular remittance receipt in Lebanon and a strictly positive amount of minimum ordinal restructuring after allowing for item nonresponse and sampling uncertainty. The conservative benchmarks provide strong numerical evidence that least-displacement restructuring excludes movement toward less frequent receipt and requires some reassignment from nonreceipt to recurrent receipt.