# Food Security Fridays — Week 21: Model-Based Estimates Reproducibility Package

## "If the survey is gone, model it."

**Author:** Matthew P. Rabbitt, PhD
**Date:** June 2026
**Series:** Food Security Fridays

---

## Overview
An honest ledger on model-based food security prevalence estimates after the
CPS-FSS termination, illustrated by applying the ERR-167 macroeconomic model —
published in 2014 by researchers at USDA's Economic Research Service (Nord,
Coleman-Jensen & Gregory) — with frozen Table 1 coefficients to
2001–2024 data: excellent in its 2001–2012 estimation window (R² = 0.943,
MAE 0.34 pp), then an 8.0 pp out-of-sample miss in 2020 and wrong-side-high
through 2024 — the structural-shift problem made visible. After 2024 there
is no observed line to check it against.
Series: https://matthewpatrickrabbitt.com/food-security-fridays.html

## Files
| File | Description |
|------|-------------|
| fsf_week21_reproducibility.do | Single reproducibility file: builds the 2001–2024 panel, applies the ERR-167 Table 1 coefficients (no re-estimation), validates against ERR-167 Table 2 reference predictions (±0.05 pp), computes the in-sample fit diagnostics, and draws both figures |
| fred_UNRATE.csv | Monthly unemployment rate, SA (FRED UNRATE = BLS LNS14000000) |
| fred_CPIAUCNS.csv | Monthly CPI-U all items, NSA (FRED CPIAUCNS = BLS CUUR0000SA0) |
| fred_CPIUFDNS.csv | Monthly CPI-U food, NSA (FRED CPIUFDNS = BLS CUUR0000SAF1) |
| ers_fi_prevalence.csv | USDA-ERS published food insecurity prevalence (ERR-358 Table 1A) |
| annual_panel_and_predictions_reference.csv | Byte-identical verification target for output/annual_panel_and_predictions.csv |
| fsf_week21_README.md | This file |

Run: open `fsf_week21_reproducibility.do`, set `$projdir` to this folder
(or let your profile.do define it), and run. The file creates `output/`
with the log, both CSVs, and both figures. Verified end to end on a fresh
copy (June 12, 2026): the regenerated `output/annual_panel_and_predictions.csv`
is byte-identical to the shipped reference copy.

## Requirements
Stata 14+ only. **No API key and no internet access are required**: the four
raw input CSVs ship flat in this folder (FRED exports for UNRATE, CPIAUCNS,
CPIUFDNS, plus the USDA-ERS published prevalence series keyed to ERR-358
Table 1A and predecessors). To refresh predictors later, re-download the
three FRED series from fred.stlouisfed.org (CSV export; no key needed) and
re-run. Shipped FRED extracts were downloaded May 2026; verified June 12,
2026 that a fresh keyless download reproduces every shipped monthly value
(876/876 overlapping observations identical) and the headline predictions. All inputs are public: BLS LNS14000000 (unemployment; predictor = highest
monthly value per year), CUUR0000SA0 (CPI-U; predictor = annual-average
inflation), CUUR0000SAF1/CUUR0000SA0 × 100 (relative food price), and the
USDA-ERS published food insecurity series (ERR-358 Table 1A and predecessors).

## The model (ERR-167, Table 1)
Pred FI(y) = −50.010 + 0.523·unemp_max(y) + 0.471·inflation(y) + 0.583·relfood(y)
Estimation window 2001–2012, as published in ERR-167: R² = 0.943,
adj. R² = 0.921, MAE = 0.341 pp, largest single-year miss < 1.0 pp. With
this package's revised-vintage FRED data, the same window gives MAE 0.339
and a largest in-sample miss of 1.01 pp (2008); the reproducibility file
prints both alongside the published values. Coefficients are applied as
published; no re-estimation anywhere in the pipeline.

## Key numbers reproduced (from the CSV)
| Year | Observed | Predicted | Gap |
|---|---|---|---|
| 2019 | 10.5 | 11.8 | −1.3 |
| 2020 | 10.5 | **18.5** | **−8.0** |
| 2021 | 10.2 | 15.3 | −5.1 |
| 2022 | 12.8 | 16.7 | −3.9 |
| 2023 | 13.5 | 15.8 | −2.3 |
| 2024 | 13.7 | 15.0 | −1.3 |

Reading: the 2020–21 miss is policy structure (expanded benefits broke the
unemployment–food insecurity relationship the model learned); the 2022–24 miss runs
through the inflation term while observed increases trace to benefit
changes the model cannot see. Same frozen equation, two distinct failure
modes — and from 2025 forward, no observed series exists to reveal either.

## CSV column dictionary (annual_panel_and_predictions.csv)
| Column | Definition |
|---|---|
| year | Calendar year, 2001–2024 |
| fi_obs | Observed household food insecurity, % (USDA-ERS published) |
| unemp_max | Highest monthly SA unemployment rate in year, % (UNRATE) |
| inflation | YoY % change in annual-average CPI-U (CPIAUCNS) |
| relfood | CPI-U food ÷ CPI-U all items × 100 (CPIUFDNS/CPIAUCNS) |
| cpi_all / cpi_food | Annual-average index levels |
| fi_pred | ERR-167 Table 1 prediction (frozen coefficients) |
| resid | fi_obs − fi_pred, pp |

## Notes
- This package practices the transparency the post demands of any modeled
  product: every input ships in this folder, every assumption is in the
  reproducibility file and this README, ERR-167's in-sample prediction SE (0.513 pp;
  the chart's ±0.8 pp 90% band) quantifies the uncertainty, and every
  `fi_pred` value is labeled a prediction — never a measured rate.
- The post's ledger (advantages: full-map coverage, small-group visibility,
  cost/resilience; disadvantages: calibration dependency, shock blindness,
  binary flattening, false precision, the assistance trap) reflects the
  author's assessment of model-based prevalence estimation generally; Map
  the Meal Gap is referenced once, neutrally, as the best-known product.
- ERR-167 modeled national prevalence; small-area products add a further
  layer (covariate-based spatial interpolation) on top of the same
  calibration dependency.

## Sources
- Nord, Coleman-Jensen & Gregory (2014), ERR-167, USDA-ERS:
  https://www.ers.usda.gov/publications/pub-details?pubid=45216
- USDA-ERS food security statistics (observed series):
  https://www.ers.usda.gov/topics/food-nutrition-assistance/food-security-in-the-u-s/key-statistics-graphics
- Feeding America, Map the Meal Gap methodology:
  https://www.feedingamerica.org/research/map-the-meal-gap/how-we-got-the-map-data

## Citation

Rabbitt, Matthew P. 2026. "Food Security Fridays — If the survey is gone,
model it." Food Security Fridays series.
https://matthewpatrickrabbitt.com/food-security-fridays.html