1# WP35 — Identification: what the designs can and cannot establish23This document was written during Phase 4, before the paper. It states, for each pre-registered test, the estimand,4the assumptions under which the estimate would be causal, why those assumptions are **not** credible here, and what5the estimate therefore is: a conditional association with pre-specified direction, out-of-sample validation and6falsification tests. No causal language is used in the paper for H1 or H2.78## 1. H1 (capacity ↔ scale)9Estimand: the partial association between the capacity index K and log scale D given era, region and rival-explanation10covariates. Causal reading would require K to be as-good-as-random given covariates, which is false in both directions:11scale creates the demand for administration (Johnson 1982; Wright & Johnson 1975) and administration enables scale12(Theorems 1–4). We therefore pre-registered H1 as an association without direction, and we report the modern panel in13within-country and 50-year-difference form only to show that the association is not purely cross-sectional.14Non-independence: region fixed effects, region random intercepts, language-family clustering and Conley spatial HAC15errors (EA) address Galton's problem for inference but not for identification.1617## 2. H2-A (Seshat crisis severity)18Estimand: the association between pre-crisis coordination pressure P and the share of adverse consequences recorded for19a crisis, among polities with a CrisisDB record.20Threats, in order of seriousness:211. **Crisis selection.** CrisisDB covers 150 of 626 polities, selected because a crisis was identified by historians. The22 sample is conditioned on an outcome-related event. P is therefore tested as a predictor of *how a crisis unfolds*,23 not whether one occurs. The polity-hazard design (Y2) and the modern onset panel (Y4–Y6) are the complements.242. **Weak temporal precedence.** 93.7% of Polaris facts are undated whole-polity codes; "pre-crisis" K is mostly the25 polity's overall K. Coders who know a polity ended in collapse may also code its administration differently26 (narrative circularity). Mitigations: inferred codes dropped (sensitivity), crises starting ≥ 25 years after polity27 start (sensitivity), dated-only facts (too few to estimate; reported as not estimable).283. **Collinearity / residual interpretation.** P retains 17% of the variance of z(D)+z(K) and correlates 0.39 with D.29 A positive β_P is consistent with "scale raises severity" alone. Decisive checks: D-only and D+K baselines, and the30 placebo index built with production infrastructure instead of K. If the placebo performs as well as P, the capacity31 component is not identified as the active ingredient.324. **Omitted mechanisms.** Elite conflict, inequality, climate shocks and military pressure are only partially proxied33 (warfare technology, epidemic flag, production infrastructure). Region and era fixed effects absorb slow-moving34 confounders only.355. **Small N and clustering.** 127 crisis records in 42 regions and 10 macro-regions; cluster-robust SE with few clusters36 are anti-conservative; we report NGA-, polity- and region-clustered variants and leave-one-region-out stability.376. **Multiple outcomes.** Y1 (fractional) is primary; Y1b was declared underpowered a priori; reforms are exploratory.3839## 3. H2-B (polity duration, succession)40Polity boundaries in Seshat are coding decisions (e.g. Early vs Late Qing split at 1796), not events; the hazard of41"polity end" therefore mixes genuine breakdowns with periodization. Censoring at 1900 is a databank boundary, not a42survival boundary. Y3 (discontinuous succession) depends on the successor being in the databank (207 coded). Any43association of K or P with duration is reported with this caveat and is not evidence for or against the mechanism.4445## 4. H2-C (modern country-year panel)46Estimand: the association between P_it and any instability event in (t, t+5], conditional on development, electoral47democracy, time since last event (cubic), region and year effects; country fixed effects in the conditional logit and48LPM. Causal reading would need P_it to be exogenous to future shocks given these controls, which fails because:49(i) K is expert-coded with knowledge of subsequent events (V-Dem coders rate the whole period); (ii) population and50capacity respond to anticipated conflict; (iii) K correlates 0.75 with polyarchy, so the "capacity" interpretation51competes with "regime type", the dominant predictor in Goldstone et al. (2010). Mitigations: polyarchy control,52K-only and regime-type-free baselines, the placebo index with polyarchy in place of K, the reverse-window negative53control (past events on current P must not load more strongly than future events), forward-chaining and54leave-region-out validation, Oster (2019) and Cinelli–Hazlett (2020) sensitivity on the LPM. These bound, but do not55remove, confounding.5657## 5. What would have been a credible design and why it is not available58A natural experiment moving D or K independently (e.g. exogenous territorial accretion, or the diffusion of a record-59keeping technology for reasons unrelated to local instability) would identify the effect of mismatch. Seshat does not60code such shocks at the polity level; the modern panel has candidate instruments (printing press, railway, telegraph61diffusion) but their exclusion restrictions are implausible for instability. The paper therefore claims association,62prediction and robustness only, and explicitly declines a causal claim.63