F2-conf-04 — Okun's law in U.S. quarterly data with autocorrelation-robust uncertainty
Scientific question
Estimate the Okun's-law relation between changes in the U.S. unemployment rate and real GDP growth, with uncertainty that is valid under serially correlated disturbances. The estimand is the slope β (the "Okun coefficient") in the linear projection Δu_t = α + β g_t + e_t, where, for quarter t: u_t is the quarterly average of the three monthly unemployment-rate observations of quarter t (in percentage points), Δu_t = u_t − u_{t−1}, and g_t = 100 · ln(GDPC1_t / GDPC1_{t−1}) is quarterly real GDP growth in percent (quarter-on-quarter, not annualised). The regression sample is the 240 quarters from 1960Q1 to 2019Q4 inclusive (the 1960Q1 observation uses the 1959Q4 levels for its differences). Estimate β by OLS, report a Newey–West (Bartlett-kernel HAC) standard error with a bandwidth you justify, and state whether the Okun coefficient is negative and significantly different from zero at the 5% level.
Inputs
data/UNRATE.csv— observed data: U.S. civilian unemployment rate, seasonally adjusted, percent, monthly, 1948-01 to 2026-09 (945 data rows). Columns:observation_date(YYYY-MM-DD),UNRATE. Source: U.S. Bureau of Labor Statistics via FRED (https://fred.stlouisfed.org/graph/fredgraph.csv?id=UNRATE), retrieved 2026-10-30 UTC; terms indata/README.md.data/GDPC1.csv— observed data: U.S. real GDP, seasonally adjusted annual rate, billions of chained 2017 dollars, quarterly, 1947Q1 to 2026Q3 (319 data rows). Columns:observation_date(first day of the quarter),GDPC1. Source: U.S. Bureau of Economic Analysis via FRED (https://fred.stlouisfed.org/graph/fredgraph.csv?id=GDPC1), retrieved 2026-10-30 UTC; terms indata/README.md.data/README.md— provenance, retrieval time, SHA-256 checksums and license.
Information-availability rules
- Use only the files under
data/. The files are the current vintage (not real-time data); treat them as given. Observations outside the 1960Q1–2019Q4 window are only used for the levels needed to form the first differences; do not extend the window.
Required outputs
out/results.jsonwith the keys:
| key | type | unit | meaning |
|---|---|---|---|
task_id |
string | – | "F2-conf-04" |
beta_hat |
number | pp of unemployment per percent of quarterly growth | OLS Okun coefficient |
alpha_hat |
number | pp | OLS intercept |
r_squared |
number | – | R² of the regression |
se_iid |
number | – | conventional OLS standard error of beta_hat (independent, homoskedastic errors) — the naïve baseline |
se_hac |
number | – | Newey–West (Bartlett) HAC standard error of beta_hat |
hac_lags |
integer | quarters | bandwidth (number of lags) used for se_hac |
beta_ci_low, beta_ci_high |
number | – | 95% confidence interval for β built from se_hac |
okun_negative_5pct |
boolean | – | true if and only if β̂ < 0 and H0: β = 0 is rejected at the 5% level (two-sided) using se_hac |
mean_growth |
number | percent | sample mean of g_t over the 240 regression quarters |
first_quarter, last_quarter |
string | – | first and last quarter of the regression sample, formatted like "1960Q1" |
n_analysed |
integer | – | quarters used in the regression |
feasibility |
string | – | "complete", "partial" or "infeasible" |
feasibility_reason |
string or null | – | explanation if not complete |
data_issues |
array of {"issue","handling"} | – | data problems detected and how handled (empty list if none) |
n_input_rows |
object | – | {"UNRATE.csv": data rows read (excluding the header), "GDPC1.csv": data rows read} |
random_seed |
integer or null | – | seed used, if any |
out/report.mdwith the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues.out/analysis.py— running~/wp29/venv/bin/python out/analysis.pyfrom the workspace root must regenerateout/results.jsonfromdata/only, deterministically.out/claims.json— a list of the central claims of the report: [{"id": "C1", "text": "...", "results_keys": ["..."], "status": "supported"|"unsupported"|"not_evaluated", "caveat": "..."}].out/figure1.png— scatter of Δu_t against g_t over the sample with the fitted line.
Constraints
- No network access. Python:
~/wp29/venv/bin/python(numpy, pandas, scipy, statsmodels, matplotlib available). Do not modifydata/. - This task is designed to be completed in well under 20 minutes of work.