Show the work.
VECTR makes three contributions to the CGE literature that, to our knowledge, have not been published elsewhere. The mathematics is documented, the code is source-available, and every coefficient is inspectable. This page is for people who will check.
Three results that are new in the literature.
Each of these emerged from the process of building VECTR and solving problems that existing approaches either avoid or handle with approximations. They are presented here for peer review.
1. CES Jacobian Diagonal Preservation
Standard CES substitution implementations compute the full Jacobian matrix, including the diagonal entries that represent a sector’s substitution of its own output. VECTR explicitly preserves these diagonal elements at their pre-shock values. The economic justification is straightforward: a sector’s use of its own intermediate output is technologically fixed — a steel mill’s use of steel in making steel is determined by the production process, not by relative prices. Treating the diagonal as substitutable introduces a systematic bias that propagates through the entire solution.
Where σ is the elasticity of substitution, sj is the cost share, pj is the input price, and P is the composite price index.
2. Resolving Dense Factorisation Limitations
Standard CGE implementations treat the Jacobian as a dense matrix, requiring $O(n^3)$ factorisation for every scenario evaluated. For an $n = 109$ sector model, this cubic cost makes exhaustive sensitivity analysis computationally prohibitive — practitioners are forced to sample a handful of parameter combinations (typically 8–16) and extrapolate via quadrature or Monte Carlo methods.
The diagonal preservation established in Contribution #1 changes this fundamentally. Because the CES adjustment modifies only the magnitudes of existing non-zero entries — never creating new ones — the augmented Jacobian inherits the sparsity structure of the underlying IO table. We prove that for the New Zealand 109-sector table, the resulting fill rate is approximately 2–5%.
where the system matrix depends only on σ and closure c — not on the shock vector
This structural sparsity is the key result: it reduces factorisation complexity from $O(n^3)$ to a function of the non-zero count, collapsing the computational barrier that forces conventional CGE models into sampled sensitivity. The consequence is that complete enumeration over the full parameter space becomes tractable where dense methods cannot follow.
The proof that sparsity is structural (determined by IO topology, invariant to CES parameterisation) and the formal complexity comparison are detailed in the VECTR technical papers.
3. Employment Multiplier Ordering Guarantee (K ≥ J ≥ N)
Under standard CGE closure rules, the employment multiplier varies depending on whether capital is mobile (Keynesian closure K), partially mobile (Johansen closure J), or fixed (Neoclassical closure N). Practitioners have long observed that K ≥ J ≥ N tends to hold empirically, but VECTR provides a closed-form proof that this ordering is guaranteed for any sector, given the standard CES production structure.
The practical implication is that when a policy team debates which closure assumption to use, the employment multiplier bounds are known a priori. The result holds regardless of the sector, the shock magnitude, or the elasticity values — which means the ordering is structural, not contingent on calibration.
Full proof available in the VECTR technical documentation. The theorem applies to the CES case; extensions to nested CES and CET structures are in progress.
What the models can actually measure.
A like-for-like comparison of CGE models across New Zealand, Australia's CoPS ecosystem, and international references. The orange line separates VECTR-only capabilities.
| Model | Est. | NZ- specific |
Dynamic | Multi- regional |
Māori / Indigenous |
Sectoral detail |
Trade / policy |
Soc. / equity |
Sequenced closure |
Self-sub. correction |
Reproducible provenance |
AGDEF compliant |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| New Zealand | ||||||||||||
VECTR v1.01 |
2024 | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |
NZTM (WP 02/07) |
2002 | ✓ | ✓ | ✗ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
C-PLAN v1.0 |
2022 | ✓ | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
| Australia — CoPS ecosystem (VU Melbourne) | ||||||||||||
ORANI / ORANI-G |
1977 | ✗ | ✗ | ◑ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
MONASH / VU-National |
1993 | ✗ | ✓ | ✓ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
MMRF / MMRF-Green |
~1996 | ✗ | ✓ | ✓ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
TERM |
~2002 | ✗ | ✗ | ✓ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
| International reference models | ||||||||||||
IFPRI Standard CGE |
2002 | ✗ | ✓ | ✓ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
Baker Institute Tax CGE |
— | ✗ | ✓ | ✗ | ✗ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ | ✗ |
Energy sector CGE |
— | ✗ | ✓ | ✗ | ✗ | ✓ | ✓ | ✗ | ✗ | ✗ | ✗ | ✗ |
The Australian CoPS models represent ~50 years of continuous institutional development. No model in the CoPS ecosystem carries indigenous disaggregation, a Social Audit Layer, sequenced closure rules, self-substitution correction, serialised reproducible provenance, or AGDEF-compliant output. ◑ = partial or prototype capability.
Direct calculation, not estimation.
VECTR is one of only two models in the world that directly calculates the New Zealand shadow economy. The other is a London-based model. Prior to these, the shadow economy for New Zealand has only been estimated using indirect methods — currency demand approaches, electricity consumption proxies, MIMIC models — or defined theoretically through IMF working papers without country-specific structural calculation.
VECTR calculates the shadow economy directly from the model's structural equations: the gap between observed economic activity and the activity implied by the formal input-output structure, accounting for tax compliance rates, informal labour markets, and unreported production. This is not an estimate layered on top of the model — it falls out of the same equilibrium solution that produces the GDP, employment, and welfare measures.
For researchers, the implication is that VECTR can answer questions about the shadow economy's response to policy shocks with the same rigour it applies to the formal economy. Tax policy changes, regulatory shifts, enforcement interventions — the model shows what happens to both the visible and invisible parts of the economy simultaneously.
22 measures. All formally specified.
Each measure has a mathematical definition, variable mapping, and implementation specification. They range from standard CGE outputs (GDP, employment) to advanced welfare and distributional measures that most models cannot produce.
How VECTR was built.
VECTR was not built by a single discipline. The development drew on expertise across eight distinct domains, with mathematics given priority because the primary objective was — and remains — the highest quality modelling platform possible. The disciplines involved, and the problems they addressed:
Advanced Mathematics
CES Jacobian structure, sparse factorisation, convergence proofs, sensitivity grid theory. The three novel contributions emerged from this work.
Economic Theory — Multiple Schools
Keynesian, Johansen, and Neoclassical closure rules. IO multiplier analysis. Welfare economics (EV, CV). Trade theory (gravity models, Armington). The model does not commit to a single school — it implements all of them and lets the user choose.
Māori Research & Well-Being Frameworks
Ethnic dimension structuring, hauora measurement, Te Reo internationalisation, iwi economic circuit design. Engagement with iwi and hapū is ongoing; version 1 reflects the team's best effort pending co-design.
Social Investment & Impact Analysis
Hauora-Efficiency measurement, distributional weighting, social welfare aggregation. The Social Auditing Layer's design requirements came from this domain.
Python & Functional Programming
Immutable data pipelines, type-safe computation chains, reproducible builds. The codebase follows FP conventions where side effects are isolated and state is explicit.
APS Data Ethics Framework
The Australian Public Service data ethics standard (Dept of Finance, 2024) is embedded programmatically in the Social Auditing Layer. Confidentiality, fairness, transparency, and accountability checks run on every output.
Front-End Engineering
Three-panel Console GUI, real-time visualisation, accessible interface design. The interface was designed for non-economists to use without training — which is a harder engineering problem than it sounds.
Back-End Engineering
DuckDB columnar storage, sparse LU pipeline, partitioned manifold indexing, sub-50ms retrieval architecture. The engineering decisions are inseparable from the mathematical ones — the sparsity enables the precomputation which enables the speed.
When your findings are rejected on assumptions.
Every CGE practitioner has experienced this: you produce a rigorous analysis, present the results, and the response is "I disagree with your elasticity assumptions" or "that closure rule doesn't reflect reality." The analysis is dismissed not because the result is wrong, but because the critic has a different prior about one parameter — and in conventional CGE workflows, testing that alternative takes weeks.
VECTR's exhaustive precomputed grid changes the dynamic. The manifold already contains the results for every combination of σ values, closure rules, and shock magnitudes that the model supports. When a reviewer objects to your assumptions, you can rerun the analysis with their exact assumptions — on the spot, in the meeting — and show them what changes. In most cases, the qualitative result holds: the sign of the impact doesn't flip, the ranking of affected sectors doesn't change, the policy recommendation survives the sensitivity test. Now you have evidence, not opinion.
In the cases where the result does change materially, that is equally valuable information: you have identified a genuine assumption sensitivity, and you can quantify exactly which parameters matter and by how much. Either way, the conversation moves forward.
Get past the question of How much?
Move on to the path to recovery.
Source-available code
Every matrix, every coefficient, every calibration parameter is inspectable. VECTR is not a black box. If you want to verify the Jacobian structure, check the sparsity pattern, or audit the SAM balancing — the code is available under commercial licence. Peer review is not just tolerated; it is invited.
API and CLI for your pipeline.
The VECTR API is RESTful and returns the full results payload for any scenario query. It can be self-hosted within your organisation's infrastructure or accessed through the Danalytics-hosted service. The response format is structured for programmatic consumption — JSON with nested measure objects, regional breakdowns, and metadata. If your research pipeline already has a data ingestion step, VECTR plugs into it.
The CLI offers the same capabilities from the command line. Script your scenarios, batch your runs, pipe the output. For practitioners who work in R, Python, or Stata environments, the CLI is the natural integration point — you call VECTR from your script and get structured output back without leaving your workflow.
Continue exploring VECTR