# WP35 — Identification: what the designs can and cannot establish

This document was written during Phase 4, before the paper. It states, for each pre-registered test, the estimand, the assumptions under which the estimate would be causal, why those assumptions are not credible here, and what the estimate therefore is: a conditional association with pre-specified direction, out-of-sample validation and falsification tests. No causal language is used in the paper for H1 or H2.

# 1. H1 (capacity ↔ scale)

Estimand: the partial association between the capacity index K and log scale D given era, region and rival-explanation covariates. Causal reading would require K to be as-good-as-random given covariates, which is false in both directions: scale creates the demand for administration (Johnson 1982; Wright & Johnson 1975) and administration enables scale (Theorems 1–4). We therefore pre-registered H1 as an association without direction, and we report the modern panel in within-country and 50-year-difference form only to show that the association is not purely cross-sectional. Non-independence: region fixed effects, region random intercepts, language-family clustering and Conley spatial HAC errors (EA) address Galton's problem for inference but not for identification.

# 2. H2-A (Seshat crisis severity)

Estimand: the association between pre-crisis coordination pressure P and the share of adverse consequences recorded for a crisis, among polities with a CrisisDB record. Threats, in order of seriousness:

1. Crisis selection. CrisisDB covers 150 of 626 polities, selected because a crisis was identified by historians. The sample is conditioned on an outcome-related event. P is therefore tested as a predictor of how a crisis unfolds, not whether one occurs. The polity-hazard design (Y2) and the modern onset panel (Y4–Y6) are the complements.
2. Weak temporal precedence. 93.7% of Polaris facts are undated whole-polity codes; "pre-crisis" K is mostly the polity's overall K. Coders who know a polity ended in collapse may also code its administration differently (narrative circularity). Mitigations: inferred codes dropped (sensitivity), crises starting ≥ 25 years after polity start (sensitivity), dated-only facts (too few to estimate; reported as not estimable).
3. Collinearity / residual interpretation. P retains 17% of the variance of z(D)+z(K) and correlates 0.39 with D. A positive β_P is consistent with "scale raises severity" alone. Decisive checks: D-only and D+K baselines, and the placebo index built with production infrastructure instead of K. If the placebo performs as well as P, the capacity component is not identified as the active ingredient.
4. Omitted mechanisms. Elite conflict, inequality, climate shocks and military pressure are only partially proxied (warfare technology, epidemic flag, production infrastructure). Region and era fixed effects absorb slow-moving confounders only.
5. Small N and clustering. 127 crisis records in 42 regions and 10 macro-regions; cluster-robust SE with few clusters are anti-conservative; we report NGA-, polity- and region-clustered variants and leave-one-region-out stability.
6. Multiple outcomes. Y1 (fractional) is primary; Y1b was declared underpowered a priori; reforms are exploratory.

# 3. H2-B (polity duration, succession)

Polity boundaries in Seshat are coding decisions (e.g. Early vs Late Qing split at 1796), not events; the hazard of "polity end" therefore mixes genuine breakdowns with periodization. Censoring at 1900 is a databank boundary, not a survival boundary. Y3 (discontinuous succession) depends on the successor being in the databank (207 coded). Any association of K or P with duration is reported with this caveat and is not evidence for or against the mechanism.

# 4. H2-C (modern country-year panel)

Estimand: the association between P_it and any instability event in (t, t+5], conditional on development, electoral democracy, time since last event (cubic), region and year effects; country fixed effects in the conditional logit and LPM. Causal reading would need P_it to be exogenous to future shocks given these controls, which fails because: (i) K is expert-coded with knowledge of subsequent events (V-Dem coders rate the whole period); (ii) population and capacity respond to anticipated conflict; (iii) K correlates 0.75 with polyarchy, so the "capacity" interpretation competes with "regime type", the dominant predictor in Goldstone et al. (2010). Mitigations: polyarchy control, K-only and regime-type-free baselines, the placebo index with polyarchy in place of K, the reverse-window negative control (past events on current P must not load more strongly than future events), forward-chaining and leave-region-out validation, Oster (2019) and Cinelli–Hazlett (2020) sensitivity on the LPM. These bound, but do not remove, confounding.

# 5. What would have been a credible design and why it is not available

A natural experiment moving D or K independently (e.g. exogenous territorial accretion, or the diffusion of a record- keeping technology for reasons unrelated to local instability) would identify the effect of mismatch. Seshat does not code such shocks at the polity level; the modern panel has candidate instruments (printing press, railway, telegraph diffusion) but their exclusion restrictions are implausible for instability. The paper therefore claims association, prediction and robustness only, and explicitly declines a causal claim.