A QuantFit Research Tool · Native macOS

Serious DSGE work, with a reproducible record.

Bellman DSGE is a native macOS workbench for dynamic stochastic general equilibrium models — built for economists, policy teams and universities that need every calibration, scenario and result to hold up under scrutiny.

Request access See the engine macOS 14+ · closed beta · institutional pilots open
State vector A · B · C
QZ split stable
Vintage hash 9f4c2a
FORECAST → +2 +1 0 −1 −2

Forecast fan chart — a Bellman DSGE forecast with 50%, 80% and 95% probability bands fanning from the present, in the visual idiom of the Bank of England Inflation Report.

01 · Specify
Base + modules.

Closed, small-open, or currency-union. Compose nine plug-in modules. No equation files.

02 · Solve
Klein/Sims via LAPACK.

Generalized Schur on Apple's Accelerate. Blanchard–Kahn diagnostics returned, not silently violated. Validated to 1e-7.

03 · Simulate
IRFs, forecasts, fans.

Impulse responses, variance decomposition, BoE-style fan charts at 50/80/95% confidence bands.

04 · Export
Vintage → six formats.

HTML · Excel · LaTeX · Quarto · PDF · CSV · JSON — all rendered from one canonical run-state, all hash-verified.

0
Countries calibrated
0
Plug-in modules
0
Export formats
10−7
Validation tolerance
I · The Engine

Math you can defend at the NBER.

A rational-expectations solver wired through real LAPACK, not a finite-difference shortcut.

Bellman is built natively for macOS rather than asking researchers to work through an equation-file workflow. Its numerical engine uses generalized Schur (QZ) decomposition built on Apple's LAPACK and a Sims-style rational-expectations solver. Researchers compose country models from economy bases and modules, then retain a reviewable record of every run. The validation note documents the numerical checks and their scope.

Bellman DSGE workbench — forecast fan charts, impulse responses, shock decomposition, variance decomposition, reproducibility.
Plate I The workbench, in full view — forecast, simulate, explain. Fig. 1 · Bellman DSGE
1.1

Klein/Sims QZ solver Shipping

Generalized-Schur decomposition through Apple's Accelerate framework. Blanchard–Kahn determinacy diagnostics returned as explicit variants — no silent matrix of wrong numbers when a model is on the boundary of indeterminacy. Validated against closed-form NK to 1e-7.

1.2

Sims gensys with expectational errors Shipping

Full Sims (2002) algorithm including the η-projection that absorbs shocks onto the unstable subspace. The standard reason Dynare took a decade to refine — implemented from first principles in Swift, validated end-to-end on Phillips + AR(1) with closed-form match.

1.3

Modular platform Shipping

Three economy bases (closed, small-open, currency-union) composed with nine plug-in modules — NK core, monetary policy, fiscal, financial frictions, commodity exporter, tourism services, AI-block. Configure a country by base + module set, not by editing equation files.

1.4

Bayesian estimation (SMC + MH) Roadmap

Random-Walk Metropolis-Hastings and tempered Sequential Monte Carlo posterior samplers, in the Herbst–Schorfheide tradition. Posterior draws hung off the canonical run-state so every export — fan chart, Excel, Quarto — absorbs parameter uncertainty alongside shock uncertainty.

1.5

Identification health-check Roadmap

Iskrev, Komunjer–Ng, and Qu–Tkachenko diagnostics as a traffic-light panel — not a wall of singular values. Plain-English “these two parameters cannot be told apart from the data” output.

1.6

HANK via Sequence-Space Jacobians Roadmap

Auclert–Bardóczy–Rognlie–Straub. One-asset and two-asset household blocks as drag-and-drop modules, with RANK side-by-side comparison. The math is settled; the GUI is the missing piece — Bellman is the first.

II · The Workflow

Solve. Save vintage. Diff. Export. Replicate.

The reproducibility story Dynare doesn't tell.

Every Bellman run is a vintage. Vintages carry a SHA-256 calibration hash, the solver version, the data vintage, and a complete canonical JSON of every parameter, every equation, every output. Two researchers compare six hex characters to verify they ran the same model. Open a six-month-old vintage on a different machine and reproduce every chart to the bit. The exports — HTML report with interactive uPlot fan charts, Excel with live formulas linking parameters to steady state, LaTeX bundle with siunitx tables and vector PDFs, Quarto notebook for full replication, plus CSV and JSON — all render from the same canonical JSON. They cannot disagree.

“Every Bellman vintage is a reproducible artifact. Six hex characters and the same calibration runs the same model on any machine in the world.” Bellman DSGE · Engine SOP
Bellman DSGE — reproducible by design. Versioned vintages, structured exports, transparent data tables, built-in documentation.
Plate II Vintages, hashes, exports — reproducibility is the workflow. Fig. 2 · Reproducible by design
2.1

Vintage management Shipping

SwiftData-backed Workspace → Calibration → Vintage hierarchy. Every save carries provenance: hash, timestamp, platform fingerprint, complete parameter dump. Vintages are first-class objects you query, compare, and export.

2.2

Compare any two runs Shipping

Structured diff across provenance, calibration, steady state, diagnostics, and IRF peaks. A human-readable narrative of what changed — generated, not hand-written.

2.3

Dynamic exports Shipping

HTML with interactive uPlot fan charts (80 KB, offline, browser-portable). Excel with live formulas. LaTeX with siunitx + booktabs. Quarto for full reproducibility. PDF, CSV, JSON. All rendering from the same canonical spine.

2.4

Real-data ingestion Shipping

Drag-and-drop CSV with lenient numeric parsing (percent signs, accounting parens, dollar prefixes). Map columns to model observables. Bind a dataset to a workspace so every export and fan chart overlays the right history.

III · The Frontier

The frontier Bellman is building toward.

The institutional-grade features that are on the Bellman 2026 roadmap.

3.1

NGFS Climate Studio Roadmap

Drag-and-drop NGFS short-term scenario CSVs (Net Zero 2050, Delayed Transition, Phase 2). Bellman maps trajectories onto exogenous forcing variables, recomputes the optimal Taylor rule under the new path, and produces a fan chart conditional on the climate scenario. Each saved as a vintage. The ECB stress-test toolchain, but DSGE-native.

3.2

Scenario Studio Roadmap

Pin a variable's path on the fan-chart canvas — hard pins (Waggoner–Zha) and soft constraints (Chan et al. 2025). Bellman back-solves the implied shock sequence and shows it as a sibling panel. Norges Bank does this internally; nobody ships it.

3.3

Behavioral expectations as a swappable block Roadmap

Choose the expectations operator per variable: Full-Information Rational, Gabaix Cognitive Discount, Bordalo–Gennaioli–Shleifer Diagnostic, or Maćkowiak–Wiederholt Rational Inattention. Run side-by-side IRFs. The first DSGE tool to treat expectations as a parameter.

3.4

Multi-model robust monetary policy Roadmap

Load 5–30 vintages from different model classes. For each candidate Taylor rule, compute loss across every model. Output a Pareto frontier of robust rules. Dück–Verona (CEPR 2025) did this by hand for 29 DSGEs. Bellman makes it a button.

3.5

Replication packages Roadmap

Export a zip containing every vintage, every dataset, every parameter, every chart — and a `quarto render` script that reproduces the entire paper from raw inputs. The file your referee actually wants.

3.6

Heterogeneous-Agent NK Roadmap

SSJ-based HANK as a second solver backend. Two-asset household block, sticky-wage closure, distribution-aware fan charts. The Auclert et al. methodology, finally with a GUI.

Bellman DSGE — trace every shock. Transmission analysis, explainability, transparent by design, audit-ready.
Plate III Transmission analysis, variance decomposition, audit-ready provenance. Fig. 3 · Trace every shock
IV · For

Three audiences. One workbench.

Academic research

Run the experiments, write the paper.

Solve a fully-specified Galí-Monacelli SOE for the country your paper studies — 82 countries shipped, custom calibration in two clicks. Saved vintages let you snapshot every robustness check and regenerate every IRF chart at submission time. Quarto export produces the replication archive your AEA referee asks for. Bayesian estimation with posterior fan charts on the roadmap.

Central banks & treasuries

Forecast. Brief. Stress-test.

Vintages mirror how an MPC actually works — every meeting, every Article IV, every climate stress test is a versioned, hashed artifact. NGFS scenarios as forcing variables. Scenario Studio for “what if rates hold at 4.5% for six quarters?”-style policy briefings. White-label customisation for country-specific blocks.

Universities & research teams

Same model, every desk.

Calibrations for 82 countries out of the box — Indian Ocean SIDS, Caribbean tourism economies, GCC oil exporters, currency-board members, and euro-area economies. Country-specific structural overrides stay inside the workbench. Hash-verified vintages let collaborators confirm they ran the same calibration and engine version.

V · Methodology

The intellectual lineage.

Bellman implements the canonical methods of the modern DSGE literature, faithfully and from first principles.

The solver follows Klein (2000) for the generalized Schur recovery of the stable manifold and Sims (2002) gensys for the full expectational-error projection. The HANK backend implements the Sequence-Space Jacobian framework of Auclert, Bardóczy, Rognlie and Straub (2021). Identification diagnostics combine Iskrev (2010), Komunjer and Ng (2011) and Qu and Tkachenko (forthcoming). Bayesian estimation uses the tempered Sequential Monte Carlo of Herbst and Schorfheide.

Behavioural expectations draw on Gabaix (2020) for cognitive discounting, Bordalo–Gennaioli–Shleifer for diagnostic expectations, and Maćkowiak and Wiederholt for rational inattention. Climate work is anchored on NGFS short-term scenarios v1 (2025) and integrates with the macroprudential frameworks of the European Central Bank's 2025 stress test.

Every implementation is validated against published numerical references before it ships. The replication kit shows you, line by line, that the Bellman output matches the textbook or the working paper.

  • Klein, P. · “Using the generalized Schur form to solve a multivariate linear rational expectations model”
    JEDC · 2000
  • Sims, C. A. · “Solving Linear Rational Expectations Models”
    Computational Economics · 2002
  • Auclert, Bardóczy, Rognlie, Straub · “Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models”
    Econometrica · 2021
  • Iskrev, N. · “Local Identification in DSGE Models”
    JME · 2010
  • Komunjer & Ng · “Dynamic Identification of DSGE Models”
    Econometrica · 2011
  • Gabaix, X. · “A Behavioral New Keynesian Model”
    American Economic Review · 2020
Bellman DSGE — impulse responses with confidence. Structural shocks, visual grids, policy interpretation.
Plate IV Impulse responses with confidence bands — the canonical methods, faithfully. Fig. 4 · Impulse responses with confidence
VI · Due diligence

Trust the workbench by inspecting the work.

The important claims are accompanied by documents that describe what ships, how it is validated, and where its present limits are.

A serious modelling tool should not ask for trust by assertion.

Methodology Engine SOP

Solver design, determinacy, IRFs, variance, fan charts and provenance. Read the 23-page note.

Validation Numerical validation note

Closed-form tests and explicit failure behaviour for ill-posed model configurations. Inspect the checks.

Reproducibility Citation & vintage guide

How run hashes, exports and saved vintages support a transparent research record. Read the guide.

VII · Documentation

Read it before you trust it.

Bellman ships its methodology in writing — the same documents a central-bank model-validation team would demand. Every one is free to download and meant to be read, and challenged.

Methodology · 23 pp Engine SOP The full solver methodology — linearisation, state space, Blanchard–Kahn determinacy, IRFs, variance, fan charts, and provenance. Written for peer reviewers, and honest about every approximation. Download PDF For Validation Teams Numerical Validation Note The solver core validated to 1e-8 against closed-form solutions — and the discipline of failing loudly on ill-posed models rather than returning quiet nonsense. Download PDF Getting Started Quick Start Guide From a fresh install to a solved, exported forecast in five minutes. Country-first — you pick the economy, the model assembles itself. Download PDF Coverage Country Coverage All 82 pre-calibrated economies, organised by IMF region — with deliberate depth on small open economies, commodity exporters, and island states. Download PDF Scope Scope & Roadmap Exactly what v1 ships, what it does not yet do, and the frontier the modular architecture is built to grow into. Download PDF For Authors Citation Guide How to cite Bellman DSGE in papers and policy notes, including the run-hash provenance that lets any reader reproduce your result. Download PDF Setup Installation & Requirements System requirements, install steps, and where your work is stored. Native, fully offline — your data never leaves your Mac. Download PDF Legal Licence (EULA) The end-user licence agreement governing your use of Bellman DSGE. Published by QuantFit, the software company of Andrew Esparon. Download PDF

Questions, or need clarification on the model or the methods? These documents are meant to be interrogated — reach out any time through the Support page and you'll hear back directly. An initial live discussion is available by appointment; for deeper or ongoing work, consultation can be arranged. Bellman is built by a working economist who wants this tool in as many hands as possible.

VIII · Pricing

Subscription for individuals. Customisation for institutions.

Closed beta is invitation-only. Paid self-serve subscriptions currently include the macOS 14+ beta only. A Windows version is in development.

Academic · Individual

Researcher

$49 / month

  • Full vintage management & dynamic export pipeline
  • 82 countries, all bases, all modules
  • Quarto replication packages
  • Bayesian estimation on the roadmap
  • Email & office-hours support

Available now for macOS 14+ only. Windows version is in development.

Small team · up to 5 seats

Team

$249 / month

  • Up to 5 seats included
  • Shared workspaces & vintage libraries
  • Country-team calibration overrides
  • Priority email support & office hours
  • Dedicated onboarding & methodology review
  • Need 6+ seats? Talk to Customisation →

Available now for macOS 14+ only. Windows version is in development.

Central banks · IMF · 6+ seats

Customisation

Bespoke

  • 6+ seats — institutional pricing, annual contract
  • Custom country / regime modules
  • White-label exports & reports
  • NGFS scenarios & stress-testing pipelines
  • On-premises deployment available
  • SLAs, audit logs, and procurement support
Contact sales
Closed Beta · Limited Cohort

Request access.

Bellman DSGE is currently in institutional closed beta. We onboard a small number of researchers and central bank teams each cycle, with a particular focus on practitioners whose work informs policy decisions. Tell us about yours.

What you can expect: a personal reply within 2 working days, a 30-minute methodology call to understand your model needs, and a beta build for macOS 14+.

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