The Penumbra program
A trade-research program on closed-loop observation problems in international trade. Theory, empirics, and a satellite-calibrated bilateral trade-cost panel.
What the program is
The Penumbra program is a multi-paper investigation of international trade settings where the official data are themselves a function of the equilibrium the researcher is trying to estimate. The intellectual problem is closed-loop in a specific sense: the cost of trade depends on the equilibrium, because the equilibrium produces the satellites, the AIS records, the customs declarations, and the third-party reconciliations that determine what trade costs look like to a researcher. The cost then determines the equilibrium. The right object to estimate is a fixed point on Wasserstein space.
The program treats this as a problem of trade theory first. The empirics, the satellite-economics applications, and the methodology contributions follow from the theory. The intermediary-selection work in domestic blended-finance settings (Helfrich 2026 on the U.S. New Markets Tax Credit) is a spinoff that applies the same decomposition logic to a different setting.
The papers
SSRN 4772016 — Unifying framework for economic equilibrium and optimal transport in infinite-dimensional Hilbert spaces. The analytical foundation: an equivalence between economic equilibrium and optimal transport on infinite-dimensional Hilbert spaces, using tensor-valued measures and nonlinear operator theory. Working draft. Used as the technical seed of the program. Paper page.
Paper 0 — Penumbra. Umbrella theory paper. Formalizes the measurement-gap problem in international trade (sanctioned crude, Sahelian gold, gray-market rare earths, illicit fishing, occupied-territory output) as a closed-loop problem on Wasserstein space. Sections 1-10 drafted; main.tex compiles. Paper page.
Paper 1 — AROE. The fixed-point theorem on the 2-Wasserstein space with a measure-dependent cost and a stochastic observation operator. Existence under standard regularity hypotheses; uniqueness with a quantitative half-order Wasserstein stability estimate under feedback contractivity. Compiled PDF in the working tree. Paper page.
Paper 2 — Russian seaborne crude empirical companion. Tests the feedback-contractivity hypothesis from Paper 1 in the corridor where the closed-loop problem is sharpest. AIS-track data, port-arrival records, the Hilgenstock-Babina-Itskhoki oil-cap monitoring infrastructure. In data-construction phase. Paper page.
Paper 5 — Effective Distance (with Dr. Elizaveta Gonchar). Satellite-calibrated bilateral trade-cost panel, 200 countries × 25 years × multiple distance variants. Validated in the Yotov et al. (2016) structural gravity framework with Weidner-Zylkin (2021) bias correction. Welfare counterfactuals on the 2021 Suez closure, the 2023 Panama Canal drought, and the 2024 Houthi Red Sea rerouting. Released CC-BY-4.0 as public-good infrastructure. Target submission Journal of International Economics. Paper page. Builds on the 2025 SSRN preprint Trade in the Spotlight (SSRN 5202676).
Joint Paper 1 — Ukraine wartime economic reorganization (with Dr. Elizaveta Gonchar). Applies the closed-loop framework to Ukrainian wartime economic reorganization, 2022-2025. Decomposes spatial reorganization across hromadas into destruction, evacuation, conscription-driven labor withdrawal, and sectoral adaptation. Produces a quarterly Ukraine Shadow-Activity Index as a public-good output. Target SSRN October 2026; journal submission target February 2027 (Journal of Development Economics or AEJ: Applied). Paper page.
The spinoff: NMTC
Helfrich (2026) on the U.S. New Markets Tax Credit is a parallel application of the program's intermediary-selection logic to a domestic-policy setting. The headline empirical result: the apparent rural-urban leverage gap in NMTC collapses once Community Development Entity fixed effects are added. The same decomposition is being extended to European blended-finance instruments (Portuguese Sociedades de Garantia Mútua, Irish SBCI on-lender structure) in collaboration with Katia Antunes.
Reading order
For the theory: SSRN 4772016 → Paper 0 → Paper 1. For the trade-cost empirics: Trade in the Spotlight (2025) → Paper 5. For the application: Joint Paper 1 (Ukraine). The NMTC paper is the cleanest stand-alone illustration of the decomposition methodology in a non-trade setting.
The full list of papers and datasets is at /research and /datasets.