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

Abstract

Repeated cross-sections reveal changes in ordinal distributions but not the transitions that produce those changes. This paper identifies which transitions are unavoidable under least-displacement reconciliation of observed marginals. I develop a probability metric for ordinal change based on threshold geometry and aggregation, and show that its optimal-transport form measures the minimal average number of thresholds crossed, yielding conservative benchmark transition plans. For missing outcomes, I derive sharp identified sets for both the discrepancy and benchmark plans. Projection-based empirical likelihood, with Monte Carlo and Wilks calibration, ensures valid finite-sample and asymptotic inferences, respectively. Applied to Arab Barometer data, the method uncovers a robust shift toward regular remittance receipt in Lebanon and highlights the transition from nonreceipt to recurrent support as a necessary feature of benchmark reconstructions.

Substantially revised and expanded version with a new title. The paper now develops an axiomatic characterization of ordinal distributional change, conservative transition benchmarks under partial identification, and projection-based empirical likelihood inference with finite-sample Monte Carlo and Wilks calibration. The empirical application has also been substantially revised