What predicts BAH 5-year growth?

What we measured

One row per Military Housing Area. Target = the 5-year compound annual growth rate of BAH (with-dependents, E5 tier) from 2021→2026, taken from DoD's annual rate releases. Features include the same MHA's Zillow rent index (ZORI) 5y CAGR, Zillow home value index (ZHVI) 5y CAGR, log troop count, years the installation has existed, latitude, longitude, and haversine distance to the nearest coastal city.

349 installations collapse to 177 unique CONUS MHA codes (many bases share an MHA — e.g. the National Capital Region has multiple installations under a single BAH rate). We drop overseas MHAs (codes starting with ZZ) because OHA, not BAH, governs them.

Read: a one-standard-deviation increase in ZHVI 5y CAGR is associated with a +0.90 percentage-point increase in BAH 5y CAGR (an MHA at mean+1σ of home-value growth grew BAH about 0.90 pp/yr faster than the average MHA). ZORI gives +0.54 pp/yr per sigma. Everything else is statistical noise.

• Supported: local rent growth and home-value growth do predict subsequent BAH growth at the MHA cross-section. The durable-rent-near-bases thesis isn't disproven.
• Caveat: the out-of-sample R² is negative. We can't quantitatively forecast a specific MHA's 5y BAH path from these features alone. Too much idiosyncratic variance.
• Surprises: coast distance is dead once rent indices are in the model. Troops have the wrong sign. ZHVI (home-value growth) is a stronger predictor than ZORI — BAH appears to track asset prices more reliably than rent indices, possibly because ZORI 5y CAGRs are noisier at the MHA level (44 % of MHAs needed ZORI imputation).
• Operationally: treat BAH growth as rent growth plus a large residual. The residual is not explained by anything we have access to in this study.

• n=177 is small. Six informative features ÷ 177 obs ≈ 30:1 obs:feature is enough for naive OLS, but partial-correlation power is modest. Any out-of-sample claim is fragile.
• Spatial autocorrelation is not corrected for. MHAs near each other are not independent draws. Reported p-values are suggestive, not confirmatory.
• H2 (income) and H4 (population) are flagged as untestable from the data we have cached. Rather than substitute weak proxies, we report them as open follow-up questions.
• H5 was tested as a level, not as a change. We only have a single recent troop-count snapshot. A panel of troop counts over the 2021–2026 window is not in the milbase dataset; that's a separate data-pipeline ticket.
• Discarded features: raw troop_count (replaced with log_troops due to heavy right tail); branch and state dummies (would have ballooned the feature count past safe levels for n=177).
• Gradient boosting was the planned supplementary nonlinear model. sklearn is not installed in the working Python environment, so the GBM result is reported as null rather than hand-rolled.
• Imputation: 77 of 177 MHAs had no market_rent_allhomes from area_econ for the 2021–2026 window. Those rows received the cohort-mean ZORI. A missingness dummy is in the panel but not in the published feature set — v2 should test whether imputed rows behave differently.
• Causation: we cannot claim it. This is observational cross-section. ZORI → BAH, shared local drivers, and even BAH → ZORI would all produce the partial correlations we see. The methodology cannot distinguish them.

The regression is one Python script. It reads projects/milbase/web/data.json, builds the MHA panel in parallel threads, fits the OLS, and writes the JSON result file. No external network calls, no hidden state.

[data] kept 294 installations after CONUS+target filter (of 454 total)
[panel] 177 MHA rows
[fit] OLS on n_train=142 features=7

=== OLS coefficient summary (standardized) ===
  const                  beta=+0.0641  t=+36.30  p=0.000
  zillow_zori_5y_cagr    beta=+0.0054  t= +2.85  p=0.005 ***
  zhvi_5y_cagr           beta=+0.0090  t= +4.73  p=0.000 ***
  log_troops             beta=-0.0024  t= -1.33  p=0.186
  years_active           beta=+0.0001  t= +0.06  p=0.949
  abs_lat                beta=+0.0015  t= +0.84  p=0.403
  lon                    beta=-0.0014  t= -0.71  p=0.479
  dist_to_coast_km       beta=-0.0003  t= -0.14  p=0.887

  R^2 train = 0.2402
  R^2 test  = -0.2716

What changed

v1 flagged H2 (income growth) and H4 (population growth) as untestable because no per-MHA ACS series were cached. The projects/zipdata/data/zip_master.json spine (31,646 ZCTAs, 13 datasets) closes that gap. v2 keeps the v1 features and adds: median HH income, total population, bachelor+ pct, ACS unemployment, BLS LAUS unemployment, IRS net migration per capita, HUD FMR 2BR, and median age — aggregated to the installation's feeder county.

Honest framing up front: zip_master holds latest cross-sectional values, not time series, for the new features. So H2/H4/H8 are tested as levels against BAH 5y CAGR, not as growth-on-growth. That's an honest re-formulation, not a re-write of the hypothesis — it is stated in the pre-registration in RESEARCH.md.

Headline

Main v2 spec adds explanatory power in-sample (R² train 0.240 → 0.289) but loses ground out-of-sample — classic overfit with k=15 features on n_train=142. The parsimonious sensitivity (only the three features with |t|≥2 in the full v2) is the cleanest out-of-sample result and still negative.

Top 5 features by |t| in the v2 spec

Hypothesis verdicts — v2

Verdict

• v1 conclusion stands. BAH growth tracks ZHVI and ZORI growth at the MHA level. Re-confirmed with the larger feature set.
• v2 does NOT beat v1 out-of-sample. Adding 8 zip_master cross-sectional features worsens held-out R² from −0.27 to −0.51 (overfit). The parsimonious version (3 features) lands at −0.13 — the cleanest out-of-sample number we have, still negative.
• Operational lesson: BAH is ZORI/ZHVI, period. Cross-sectional level features (income, unemp, education, migration, FMR, age, population) do not add usable predictive signal on a 5-year window with n=177 MHAs. The new features the data spine unlocked are mostly informative as controls, not predictors.
• Future work: the right v3 will use growth versions of the zip_master features (ACS 2018 vs 2023, HUD FMR FY21 vs FY26, BLS LAUS 2019 vs 2024). The spine doesn't hold those time series yet; that's a yellow-lane data ticket.

Sensitivity table

Two sensitivity models reported alongside the main spec, both pre-stated as robustness checks, not re-specifications:

• Joined-only: drop the 51 MHAs where the zip_master county join missed (cohort-mean imputed). On the remaining n=126 MHAs the test R² is −0.265 — basically tied with v1. So the v2 main spec's worse out-of-sample number is partly imputation drag, not a new finding.
• Parsimonious (k=3): only ZHVI 5y CAGR, ZORI 5y CAGR, log_income (the |t|≥2 features in the main spec). Test R² = −0.133, better than v1. log_income loses significance (p=0.59) when not surrounded by collinear noise — confirming the signal is rent growth, not income level.