assembly-economics/research/ModelMatching.md

Model matching and regime flipping

Status: v0.1 (2026-10-13), ASSEMBLY-WP-0012. Matching on observed data works. Flip detection is not yet reliable (§ 4). No flip may be declared from real data until the synthetic test passes.

Code: simulations/gadm02/matching.py. Data: observed_series.json. Results: results/matching.md (observed), results/matching_synthetic.md (synthetic test).

1. Candidates and fit criterion (T01)

Candidates: band anchor B1–B4 × legitimacy loop off/on, each started from the jurisdiction's calibrated state (calibrate_data.start_state). B1 stays in the set with its misfit recorded, so a return to B1-like growth would be visible.

For each candidate, the adoption indicator is taken as proportional to K_Ω. Two values are fitted: a time offset t0 and a scale s, with log y = log s + log K_Ω(t0 + τ) + ε and ε ~ N(0, σ) (σ per series: BTOS 0.03, Eurostat 0.05). The calibrated K_Ω level range at the end of the window adds a Gaussian level term. All candidates fit the same number of values, so AIC weights reduce to likelihood weights.

The sentiment slope (Pew 2021 → 2026) is not scored yet: the points precede the model start (checkpoint 0). It is switched on once there are sentiment points after checkpoint 0.

2. Results on observed data (T02, T04)

Jurisdiction	Data	Anchor weights	Loop weights	Best
US	BTOS, 23 biweekly points 2025–2026	B1 0.00 · B2 0.38 · B3 0.44 · B4 0.18	off 1.00 · on 0.00	B3 / loop off (0.44)
EU	Eurostat 2023–2025	B1 0.00 · B2 0.38 · B3 0.62 · B4 0.00	off 0.47 · on 0.53	B3 / loop off (0.46)
DE	Eurostat 2023–2025	B1 0.00 · B2 0.73 · B3 0.27 · B4 0.00	off 0.33 · on 0.67	B2 / loop on (0.57)

Readings:

1. The data rule out B1 everywhere, and B4 for the EU and DE. The present is B2–B3, consistent with the calibration (models/Calibration.md § 3).
2. US adoption is not braked by its low sentiment. Every loop-on candidate fails for the US, because with measured US sentiment (Σ 0.285) the loop slows adoption far below the observed growth. Either adoption's elasticity to sentiment (sig_adopt) is much smaller than 1, or sentiment acts on adoption with a long lag. This is the first data-based constraint on the legitimacy loop.
3. No regime is established yet. No candidate reaches weight 0.75. Predictions v1 (P-2026-001 … 004) assume growth alignment between B2 and B3, which the matched weights bracket. No predictions v2 are needed (T04).

3. Flipping events (T03)

A flipping event is a change of the regime a jurisdiction operates under, detected when:

1. the best-weighted candidate changes, and
2. the new best holds weight ≥ 0.75 at two consecutive evaluations.

Before a first regime is established (weight ≥ 0.75), changes are not flips.

Measured flips come from the regime filter on observed data. Every quarter, each regime's dynamics run forward from the current state estimate over the last quarter, the weights are updated with a switching prior (0.02 per quarter), and the estimate advances with the best regime. Simulated flips are regime crossings inside a model run, for example the B4 boom-bust of BR-005. Flips are recorded in research/FlipRegister.md.

4. Synthetic test (T06): not yet reliable

Truth is simulated from a known candidate. In the switch cases it changes regime at t = 4. It is observed biweekly with 3 % log-noise, with level evidence as wide as the real US target. Three seeds per case (results/matching_synthetic.md).

Indicators	Correct regime at start	False flips (no-switch truth)	Switches detected
adoption only	3 of 6	3 of 6	0 of 6
adoption + annual sentiment	3 of 6	3 of 6	2 of 6 (delays 0.5 y and 3.25 y)

The design went through three stages:

1. Free re-fitting of t0 and s per window: any candidate matches any segment.
2. Alignment fixed after the first window: still path-based, so a regime change starting now is not represented.
3. A forward filter from the current state, with evidence accumulated across quarters.

Each stage reduced false flips. None of them made detection reliable.

Why: with adoption alone, neighbouring anchors (B2/B3/B4) differ by less than measurement noise over a quarter. The loop switch leaves almost no trace in adoption. In sentiment it is confounded by BR-009: the sentiment equation reverts toward neutral from the low measured level.

Requirements before flips may be declared (ASSEMBLY-WP-0017):

• more discriminating indicators: investment (L5) for self-enhancement, sentiment at least twice a year for the loop, and concentration channels (CB1) for domination dynamics;
• per-regime state tracking (one state per regime, not one shared estimate);
• the sentiment equation fixed (BR-009);
• acceptance criteria: at least 5 of 6 regimes correct at the start, no false flips in 6 no-switch runs, and at least 4 of 6 switches detected within 1.5 years.