# F6-conf-03 — Okun's law in the United States, 1960–2019: coefficient, uncertainty and stability

# Scientific question

How strongly do quarterly changes in the US unemployment rate respond to real output growth, and has that response been stable? The estimand is the Okun coefficient β in the difference form Δu_t = α + β·g_t + ε_t over 1960Q1–2019Q4, where Δu_t is the change in the quarterly-average civilian unemployment rate (percentage points) and g_t = 100·(ln GDPC1_t − ln GDPC1_{t−1}) is quarterly real GDP growth in percent (not annualised); uncertainty must be robust to heteroskedasticity and serial correlation. Stability is assessed by estimating β separately on 1960Q1–1983Q4 and 1984Q1–2019Q4 and by a classical Chow test of the joint equality of (α, β) across the two subperiods. The chain required is: question → data audit → baseline → justified method → results → uncertainty → failure discussion → one figure and one table → short report.

# Inputs

data/GDPC1.csv — observed data, FRED GDPC1 (US real GDP, quarterly, billions of chained 2017 dollars, SAAR; BEA), full history, raw FRED CSV (observation_date = first day of the quarter, GDPC1). Provenance in data/README.md.
data/UNRATE.csv — observed data, FRED UNRATE (US civilian unemployment rate, monthly, percent, SA; BLS), full history, raw FRED CSV (observation_date = first day of the month, UNRATE). Provenance in data/README.md.
data/README.md — provenance, retrieval dates, SHA-256.

# Information-availability rules

Quarterly unemployment u_t is the simple average of the three monthly UNRATE values of quarter t. Δu_t = u_t − u_{t−1}.
The regression sample is the 240 quarters 1960Q1–2019Q4 (the 1960Q1 differences use 1959Q4 levels). Quarters after 2019Q4 are outside the question and must not enter any estimate. Subperiod 1 = 1960Q1–1983Q4, subperiod 2 = 1984Q1–2019Q4.
Standard errors for the full-sample β must be HAC (Newey–West with Bartlett kernel); choose and report the lag length. The Chow test is the classical sum-of-squared-residuals F-test with 2 and n − 4 degrees of freedom.
Use only the files listed above.

# Required outputs

out/results.json with the keys:

key	type	unit	meaning
`sample_start`, `sample_end`	string	ISO date	first day of the first and last quarter in the regression sample (`1960-01-01`, `2019-10-01`)
`n_sub1`, `n_sub2`	integer	quarters	observations in each subperiod
`baseline_metric`	number	percentage points	RMSE of the mean-only prediction of Δu over the full sample, sqrt(mean((Δu − mean Δu)²))
`model_metric`	number	percentage points	RMSE of the full-sample OLS residuals, sqrt(mean(e²))
`effect_estimate`	number	pp per percent growth	full-sample OLS Okun coefficient β
`intercept`	number	percentage points	full-sample OLS intercept α
`effect_se`	number	pp per percent growth	HAC (Newey–West) standard error of β
`hac_lags`	integer	quarters	Newey–West lag length used
`effect_ci_low`, `effect_ci_high`	number	pp per percent growth	95% confidence interval for β based on `effect_se`
`beta_sub1`, `beta_sub2`	number	pp per percent growth	OLS slope in subperiod 1 and 2
`chow_f_stat`, `chow_p_value`	number	—	Chow F statistic and p-value
`stability_conclusion`	string	—	`stable` if the Chow test does not reject at 5%, else `unstable`
`conclusion`	string	—	one of the codes below (sign of β from its 95% interval)
`task_id`	string	copied from this file
`feasibility`	string	`complete` / `partial` / `infeasible`
`feasibility_reason`	string or null	why, if not complete
`data_issues`	array of {"issue","handling"}	every data problem detected and how it was handled (empty list allowed)
`n_input_rows`	object {file: integer}	rows read per input file (file name as key, header row excluded)
`n_analysed`	integer or null	observations actually used in the main estimate
`random_seed`	integer or null	seed used, if any

(n_analysed = quarters in the full-sample regression.)

The conclusion code must be one of: positive_effect (the 95% interval for the effect estimand lies above zero), negative_effect (lies below zero), no_detectable_effect (the interval / test does not reject zero at the 5% level), premise_invalid (the data provided do not allow the stated estimand to be computed — in that case set feasibility to infeasible, explain in feasibility_reason, and set every inestimable key to null; never substitute an invented or proxy estimate).

out/figure1.png — scatter of Δu_t against g_t with the two subperiod fitted lines, produced by out/analysis.py with matplotlib.
out/table1.csv — one row per sample (full, subperiod 1, subperiod 2) with columns period, n, intercept, slope, slope_se (header + three data rows), produced by out/analysis.py.
out/report.md with exactly these six sections, in this order: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues. The last section must contain a genuine failure discussion: what would invalidate the result, what was not checked, and what the main threats are.
out/analysis.py — replication entry point: ~/wp29/venv/bin/python out/analysis.py, run from the workspace root, must regenerate out/results.json, out/figure1.png and out/table1.csv from data/ only, deterministically (fix any seed; use the matplotlib Agg backend).
out/claims.json — list of the central claims of the report: [{"id": "C1", "text": "...", "results_keys": ["..."], "status": "supported"|"unsupported"|"not_evaluated", "caveat": "..."}]. Every claim must reference existing keys of out/results.json; a claim must only be marked supported if the reported numbers actually support it.

# Constraints

No network access. Python: ~/wp29/venv/bin/python (numpy, pandas, scipy, statsmodels, matplotlib available). Do not modify data/.
Write all deliverables under out/. This task is designed to be completed in well under 20 minutes of work; prefer a short, correct chain over an elaborate one.

spb/wp29_uqo