WG2 — SCE Working Group on Methods, Backends & Verification

Part of the Research Program for AI as Babel Fish for Structural Economics.

Chair: Herbert Dawid (designated June 2026).

HARK integration is treated here as the primary reference backend.

Scope¶

This working group addresses the numerical solution of models specified in the language of WG1: the separation of mathematical model and numerical method; translation to multiple solver backends through Rosetta Stones; and verification that independently implemented backends agree on the solution up to stated tolerances.

Aims¶

Treat the numerical method as a separate, declarative artifact — grids, quadrature, interpolation, and solution algorithms recorded as explicit, documented choices — and ensure that a model written once in the language can be solved by any capable backend (HARK, Dynare, dolo, the VFI Toolkit, SSJ) through Rosetta Stones, with cross-backend agreement verified up to tolerance.

Scientific rationale¶

The reproducibility hurdle in structural economics often lies in numerical detail: a published result can depend on grid size, interpolation scheme, or shock discretization. Recording methods declaratively implements the program’s Υ-vs-Ρ distinction (semantic content vs. numerical representation), permits systematic robustness analysis, and allows rigorous comparison of alternative methods. If a model’s meaning is fixed in the Bellman-core (WG1), the choice of solver becomes an explicit, swappable decision, and disagreement between backends is a testable hypothesis rather than an unresolved ambiguity. HARK (Econ-ARK) serves as the primary reference implementation against which other backends are compared.

Current state (from bellman-ddsl)¶

Methodization¶

• A methodization functor: a separate methodization.yml attaches numerical schemes to operators (e.g. Gauss–Hermite for an expectation, Cartesian interpolation for representation):

  methods:
    - on: E_θ
      schemes: [{scheme: expectation, method: !gauss-hermite}]
    - on: cntn_to_dcsn_builder
      schemes:
        - {scheme: interpolation, method: !Cartesian}

• Economic parameters are separated from numerical settings; semiconjugate solve implemented end-to-end; VFI bounds (⊥) supported.

Backends and Rosetta Stones¶

• A working pipeline: translate dolo-plus → vanilla dolo “horse” → solve (global solution methods), then translate solver outputs back to ADC objects (semiconjugate path complete).

• A Rosetta Stone architecture: per-toolkit inventories of which concrete tools (dolo, HARK, ConSav, QuantEcon, SSJ, SciPy, JAX) implement each scheme, plus an LLM-assisted translator that emits pseudocode, not code. The Dolo Rosetta Stone has been executed (v0.4); HARK, Dynare, and VFI implementations are planned.

Cross-subfield interoperability¶

Reaching beyond heterogeneous-agent dynamic programming to neighboring traditions (CGE, ABM, applied IO) is, on the numerical side, an extension of the Rosetta-Stone program to subfield-standard toolkits — CGE solvers (e.g. GAMS/GEMPACK), agent-based frameworks, and structural-IO estimators and dynamic-game solvers. Two specific tasks follow:

• Equilibrium closure as a method. Composing agent decisions into market clearing (CGE, general equilibrium) is a fixed-point computation that should be a declared, swappable numerical operator rather than hard-wired — the numerical counterpart of the representational “companion structures” in WG1.

• Verifying coupled and cross-tradition models. Extending the cross-backend verification harness so that a joined model (e.g. an HA-macro block plus an applied-IO product market), or a model solved through a subfield-standard backend, can be checked against standalone reference implementations of each part.

The representational questions (what the shared/companion structures are) belong to WG1; the AI translation of subfield code and cross-subfield reproducibility belong to WG3. See prior art §6 for cross-field precedents (ASE, ESMF, OPTIMADE).

Five-year milestones¶

• Phase 1: A method registry specification (a typed catalog of method families and the operator types each can serve, validated against the Bellman-core); HARK Rosetta Stone in routine use; Dynare inventory; the Bellman-core wire format as the stable interface between specification and solution.

• Phase 2: Coverage of canonical method families with feasibility checking and accuracy/cost metadata; three or more verified backends; a cross-backend verification harness certifying agreement node-by-node up to tolerance; an aggregation/SSJ path for macro impulse responses.

• Phase 3: A standardized methods vocabulary for structural economics; a published interoperability standard; a public model-comparison database (multi-backend and method-explicit).

Open research questions¶

• Interpolation placement — where interpolation belongs in the operator chain.

• Method feasibility typing — which methods are admissible for which operator types (linked to WG1’s type system).

• Accuracy and cost metadata — recording and comparing method error and runtime; automated accuracy–cost frontiers.

• Method-equivalence certificates — conditions under which swapping a method preserves the solution up to tolerance; a natural route is to encode these conditions in the formal knowledge base and check specifications against them (joint with WG1).

• Cross-backend correctness verification — operationalizing agreement between backends on a given model up to tolerance; design of the harness and agreement metrics.

• HARK internal modeling language — replacing hand-coded HARK solution and simulation with a parser driven by the shared language (the original “narrow DML in HARK” aim).

• Back-translation; aggregation and general equilibrium (SSJ / sequence-space methods).

• Subfield-toolkit Rosetta Stones — inventories and translators for CGE (GAMS/GEMPACK), ABM frameworks, and structural-IO / dynamic-game solvers, with equilibrium closure as a declared operator and coupled-model verification against standalone implementations (cross-cutting with WG1/WG3).

Illustrative project proposals¶

Develop the method registry: a typed catalog of quadrature and interpolation schemes annotated with accuracy and cost metadata, and demonstrate automated accuracy–cost frontiers for a suite of consumption-saving and portfolio-choice models.

Build the cross-backend verification harness: define agreement metrics for value and policy functions, run canonical models through HARK, dolo, and the VFI Toolkit, and publish a benchmark suite documenting where and why backends diverge.

Indicators of progress¶

Number of method families catalogued; share of the model library with declared methodization; reproducible accuracy–cost comparisons; backends with a working Rosetta Stone; backends verified to agree on the benchmark suite; models in the public comparison database; HARK models migrated to the shared specification.

Potential funding sources¶

NSF (cyberinfrastructure / numerical methods), central banks / BIS (workhorse-model portability, pilots), FRO/Convergent, corporate sponsorship.

Foundations¶

Sargent–Stachurski / QuantEcon (method interoperability, time iteration, contraction); HARK / Econ-ARK (reference backend); SSJ (Auclert et al.) for aggregation; dolo (Winant); Backus FFP (meaning vs. representation).