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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.\n\n## Inputs\n- `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 in `data/README.md`.\n- `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 in `data/README.md`.\n- `data/README.md` — provenance, retrieval time, SHA-256 checksums and license.\n\n## Information-availability rules\n- 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.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | – | \"F2-conf-04\" |\n| `beta_hat` | number | pp of unemployment per percent of quarterly growth | OLS Okun coefficient |\n| `alpha_hat` | number | pp | OLS intercept |\n| `r_squared` | number | – | R² of the regression |\n| `se_iid` | number | – | conventional OLS standard error of `beta_hat` (independent, homoskedastic errors) — the naïve baseline |\n| `se_hac` | number | – | Newey–West (Bartlett) HAC standard error of `beta_hat` |\n| `hac_lags` | integer | quarters | bandwidth (number of lags) used for `se_hac` |\n| `beta_ci_low`, `beta_ci_high` | number | – | 95% confidence interval for β built from `se_hac` |\n| `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` |\n| `mean_growth` | number | percent | sample mean of g_t over the 240 regression quarters |\n| `first_quarter`, `last_quarter` | string | – | first and last quarter of the regression sample, formatted like \"1960Q1\" |\n| `n_analysed` | integer | – | quarters used in the regression |\n| `feasibility` | string | – | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | – | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | – | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | – | {\"UNRATE.csv\": data rows read (excluding the header), \"GDPC1.csv\": data rows read} |\n| `random_seed` | integer or null | – | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\n- `out/figure1.png` — scatter of Δu_t against g_t over the sample with the fitted line.\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib available). Do not modify `data/`.\n- This task is designed to be completed in well under 20 minutes of work.\nGDPC1.csv\nREADME.md\nUNRATE.csv","is_error":false}]},"uuid":"676b4c77-28c6-49c2-bdd2-405d191748ab","timestamp":"2026-10-30T05:04:06.020Z","toolUseResult":{"stdout":"# F2-conf-04 — Okun's law in U.S. quarterly data with autocorrelation-robust uncertainty\n\n## Scientific question\nEstimate 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.\n\n## Inputs\n- `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 in `data/README.md`.\n- `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 in `data/README.md`.\n- `data/README.md` — provenance, retrieval time, SHA-256 checksums and license.\n\n## Information-availability rules\n- 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.\n\n## Required outputs\n- `out/results.json` with the keys:\n\n| key | type | unit | meaning |\n|---|---|---|---|\n| `task_id` | string | – | \"F2-conf-04\" |\n| `beta_hat` | number | pp of unemployment per percent of quarterly growth | OLS Okun coefficient |\n| `alpha_hat` | number | pp | OLS intercept |\n| `r_squared` | number | – | R² of the regression |\n| `se_iid` | number | – | conventional OLS standard error of `beta_hat` (independent, homoskedastic errors) — the naïve baseline |\n| `se_hac` | number | – | Newey–West (Bartlett) HAC standard error of `beta_hat` |\n| `hac_lags` | integer | quarters | bandwidth (number of lags) used for `se_hac` |\n| `beta_ci_low`, `beta_ci_high` | number | – | 95% confidence interval for β built from `se_hac` |\n| `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` |\n| `mean_growth` | number | percent | sample mean of g_t over the 240 regression quarters |\n| `first_quarter`, `last_quarter` | string | – | first and last quarter of the regression sample, formatted like \"1960Q1\" |\n| `n_analysed` | integer | – | quarters used in the regression |\n| `feasibility` | string | – | \"complete\", \"partial\" or \"infeasible\" |\n| `feasibility_reason` | string or null | – | explanation if not complete |\n| `data_issues` | array of {\"issue\",\"handling\"} | – | data problems detected and how handled (empty list if none) |\n| `n_input_rows` | object | – | {\"UNRATE.csv\": data rows read (excluding the header), \"GDPC1.csv\": data rows read} |\n| `random_seed` | integer or null | – | seed used, if any |\n\n- `out/report.md` with the sections: Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues.\n- `out/analysis.py` — running `~/wp29/venv/bin/python out/analysis.py` from the workspace root must regenerate `out/results.json` from `data/` only, deterministically.\n- `out/claims.json` — a list of the central claims of the report: [{\"id\": \"C1\", \"text\": \"...\", \"results_keys\": [\"...\"], \"status\": \"supported\"|\"unsupported\"|\"not_evaluated\", \"caveat\": \"...\"}].\n- `out/figure1.png` — scatter of Δu_t against g_t over the sample with the fitted line.\n\n## Constraints\n- No network access. Python: `~/wp29/venv/bin/python` (numpy, pandas, scipy, statsmodels, matplotlib available). Do not modify `data/`.\n- This task is designed to be completed in well under 20 minutes of work.\nGDPC1.csv\nREADME.md\nUNRATE.csv","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"709c8867-bd70-4481-a049-54c75117c6bc","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0221","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","version":"2.1.314","gitBranch":"HEAD"}14{"type":"api-request-blob","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","hash":"8e712ad90bc20983b4390f248be5a01bbc60dea785d18c9e3a8432167fae5f3c","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_018pjDd5YnZsrNUcPAJFALXk","name":"Bash","input":{"command":"cat TASK.md; ls -R data | head"}}]}}15{"type":"api-request","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","id":"8c135119-4ea7-43a7-a070-83fd5032a2e1","timestamp":"2026-10-30T05:04:06.024Z","version":"2.1.314","querySource":"sdk","shapeHash":"6f048e604987648eda265e61f2c8b38e727487a511c6fd2e0f0d53269aa05f6c","params":{"model":"claude-opus-5-5","betas":["claude-code-20250219","interleaved-thinking-2025-05-14","context-management-2025-06-27","prompt-caching-scope-2026-01-05","per-turn-control-2026-07-01","thinking-token-count-2026-05-13","mid-conversation-system-clear-at-2026-08-21","effort-2025-11-24","thinking-binding-controls-2026-08-01","thinking-display-updates-2026-08-18","cache-diagnosis-2026-04-07"],"max_tokens":128000,"thinking":{"type":"adaptive","display":"updates"},"context_management":{"edits":[{"type":"clear_thinking_20251015","keep":"all"}]},"output_config":{"effort":"medium"}},"base":"c437e489-82c0-429d-8c93-f25858640910","keep":2,"tail":["8e712ad90bc20983b4390f248be5a01bbc60dea785d18c9e3a8432167fae5f3c","b47e30729b3e1642c4afa2c9ba2d27e2b851ef6e6bf82ec3736d899bd315da25"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",3,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"f3ebdd7d3b8c56b754e27bbc043038c3ecd866e477ddf504dcebbba6a1cb7b19"}16{"parentUuid":"676b4c77-28c6-49c2-bdd2-405d191748ab","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXqXgVvpScQ4THXNjz8h","type":"message","role":"assistant","content":[{"type":"tool_use","id":"toolu_01MWaeNWyjjmDLtoZbAXhtnm","name":"Bash","input":{"command":"cd data; cat README.md; head -3 *.csv; wc -l *.csv; grep -c ',$' *.csv; grep -vE '^[0-9]{4}-[0-9]{2}-[0-9]{2},[0-9.]+$' UNRATE.csv GDPC1.csv | head; cut -d, -f1 UNRATE.csv | sort | uniq -d | head; cut -d, -f1 GDPC1.csv | sort | uniq -d|head"},"caller":{"type":"direct"}}],"container":null,"stop_reason":"tool_use","stop_sequence":null,"stop_details":null,"usage":{"input_tokens":2,"cache_creation_input_tokens":1990,"cache_read_input_tokens":2234,"output_tokens":205,"output_tokens_details":{"thinking_tokens":0},"server_tool_use":{"web_search_requests":0,"web_fetch_requests":0},"service_tier":"standard","cache_creation":{"ephemeral_1h_input_tokens":0,"ephemeral_5m_input_tokens":1990},"inference_geo":"global","iterations":[],"speed":"standard","fallback_credit":null},"input_transformations":[],"diagnostics":null,"context_management":null},"apiBlockIndex":0,"requestId":"req_011CgXqXgDp832bsXkA5Y2cN","requestRef":"8c135119-4ea7-43a7-a070-83fd5032a2e1","requestedModel":"claude-opus-5-5","type":"assistant","uuid":"20925806-56cd-46f2-acd0-60cc36498388","timestamp":"2026-10-30T05:04:08.616Z","effort":"medium","perTurnEffort":"medium","userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0221","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","version":"2.1.314","gitBranch":"HEAD"}17{"parentUuid":"20925806-56cd-46f2-acd0-60cc36498388","isSidechain":false,"promptId":"144d26ec-15a4-4b66-9eb0-7e65fed5c4b0","type":"user","message":{"role":"user","content":[{"tool_use_id":"toolu_01MWaeNWyjjmDLtoZbAXhtnm","type":"tool_result","content":"# Data provenance — F2-conf-04\n\nBoth files are unmodified downloads from FRED (Federal Reserve Bank of St. Louis), retrieved on 2026-10-30 03:32:42 UTC with\n`curl -L \"https://fred.stlouisfed.org/graph/fredgraph.csv?id=<SERIES>\"`. They are the current vintage as of the retrieval time (not real-time vintages).\n\n| file | series | description | units | frequency | rows (data, excl. header) | SHA-256 |\n|---|---|---|---|---|---|---|\n| `UNRATE.csv` | UNRATE | Unemployment Rate, 16 years and over, seasonally adjusted. Source: U.S. Bureau of Labor Statistics, Current Population Survey. | percent | monthly, 1948-01 to 2026-09 | 945 | `621ff6fadf50910cb7a21ee20ba610c247cb043b29b4e05c4c1a72fadca2a06c` |\n| `GDPC1.csv` | GDPC1 | Real Gross Domestic Product, seasonally adjusted annual rate, chained 2017 dollars. Source: U.S. Bureau of Economic Analysis, NIPA Table 1.1.6. | billions of chained 2017 dollars | quarterly, 1947Q1 to 2026Q3 | 319 | `1c6c6e9f59e383e20c849dd299175c7a307526c09abdc18f18da9754fc5b3343` |\n\nColumns: `observation_date` (YYYY-MM-DD; for GDPC1 the first day of the quarter), and the series value. Missing values, if any, appear as an empty field.\n\nLicense / terms: the underlying series are U.S. federal government statistical releases (public domain). Redistribution through FRED is subject to the FRED® Terms of Use (https://fred.stlouisfed.org/legal/), which permit non-commercial research use with attribution: \"Source: U.S. Bureau of Labor Statistics and U.S. Bureau of Economic Analysis, retrieved from FRED, Federal Reserve Bank of St. Louis\".\n==> GDPC1.csv <==\nobservation_date,GDPC1\n1947-01-01,2182.681\n1947-04-01,2176.892\n\n==> UNRATE.csv <==\nobservation_date,UNRATE\n1948-01-01,3.4\n1948-02-01,3.8\n 320 GDPC1.csv\n 946 UNRATE.csv\n 1266 total\nGDPC1.csv:0\nUNRATE.csv:1\nUNRATE.csv:observation_date,UNRATE\nUNRATE.csv:2025-10-01,\nGDPC1.csv:observation_date,GDPC1","is_error":false}]},"uuid":"43c020e0-565d-420b-8a2e-280c4e7a3523","timestamp":"2026-10-30T05:04:08.686Z","toolUseResult":{"stdout":"# Data provenance — F2-conf-04\n\nBoth files are unmodified downloads from FRED (Federal Reserve Bank of St. Louis), retrieved on 2026-10-30 03:32:42 UTC with\n`curl -L \"https://fred.stlouisfed.org/graph/fredgraph.csv?id=<SERIES>\"`. They are the current vintage as of the retrieval time (not real-time vintages).\n\n| file | series | description | units | frequency | rows (data, excl. header) | SHA-256 |\n|---|---|---|---|---|---|---|\n| `UNRATE.csv` | UNRATE | Unemployment Rate, 16 years and over, seasonally adjusted. Source: U.S. Bureau of Labor Statistics, Current Population Survey. | percent | monthly, 1948-01 to 2026-09 | 945 | `621ff6fadf50910cb7a21ee20ba610c247cb043b29b4e05c4c1a72fadca2a06c` |\n| `GDPC1.csv` | GDPC1 | Real Gross Domestic Product, seasonally adjusted annual rate, chained 2017 dollars. Source: U.S. Bureau of Economic Analysis, NIPA Table 1.1.6. | billions of chained 2017 dollars | quarterly, 1947Q1 to 2026Q3 | 319 | `1c6c6e9f59e383e20c849dd299175c7a307526c09abdc18f18da9754fc5b3343` |\n\nColumns: `observation_date` (YYYY-MM-DD; for GDPC1 the first day of the quarter), and the series value. Missing values, if any, appear as an empty field.\n\nLicense / terms: the underlying series are U.S. federal government statistical releases (public domain). Redistribution through FRED is subject to the FRED® Terms of Use (https://fred.stlouisfed.org/legal/), which permit non-commercial research use with attribution: \"Source: U.S. Bureau of Labor Statistics and U.S. Bureau of Economic Analysis, retrieved from FRED, Federal Reserve Bank of St. Louis\".\n==> GDPC1.csv <==\nobservation_date,GDPC1\n1947-01-01,2182.681\n1947-04-01,2176.892\n\n==> UNRATE.csv <==\nobservation_date,UNRATE\n1948-01-01,3.4\n1948-02-01,3.8\n 320 GDPC1.csv\n 946 UNRATE.csv\n 1266 total\nGDPC1.csv:0\nUNRATE.csv:1\nUNRATE.csv:observation_date,UNRATE\nUNRATE.csv:2025-10-01,\nGDPC1.csv:observation_date,GDPC1","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"20925806-56cd-46f2-acd0-60cc36498388","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0221/data","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","version":"2.1.314","gitBranch":"HEAD"}18{"type":"api-request-blob","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","hash":"2e61021f9d7df899d84a7c965e83c1abbbbc170efd04ad9111e3a2610d86cdfb","message":{"role":"assistant","content":[{"type":"tool_use","id":"toolu_01MWaeNWyjjmDLtoZbAXhtnm","name":"Bash","input":{"command":"cd data; 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cat > out/analysis.py <<'EOF'\n\"\"\"Okun's law, U.S. 1960Q1-2019Q4, OLS with Newey-West HAC SE. Run from workspace root.\"\"\"\nimport json, math\nimport numpy as np, pandas as pd\nimport statsmodels.api as sm\nfrom scipy import stats\nimport matplotlib\nmatplotlib.use(\"Agg\")\nimport matplotlib.pyplot as plt\n\nissues = []\nu = pd.read_csv(\"data/UNRATE.csv\", parse_dates=[\"observation_date\"])\ng = pd.read_csv(\"data/GDPC1.csv\", parse_dates=[\"observation_date\"])\nn_rows = {\"UNRATE.csv\": int(len(u)), \"GDPC1.csv\": int(len(g))}\n\nfor name, df, col in [(\"UNRATE.csv\", u, \"UNRATE\"), (\"GDPC1.csv\", g, \"GDPC1\")]:\n if df[\"observation_date\"].duplicated().any():\n raise SystemExit(f\"duplicate dates in {name}\")\n miss = df[df[col].isna()]\n if len(miss):\n dates = \", \".join(d.strftime(\"%Y-%m\") for d in miss[\"observation_date\"])\n issues.append({\"issue\": f\"{name}: {len(miss)} missing value(s) at {dates}\",\n \"handling\": \"Outside the 1959Q4-2019Q4 window needed; dropped, no effect on the analysis.\"})\n\nu = u.dropna()\nu[\"q\"] = u[\"observation_date\"].dt.to_period(\"Q\")\ncnt = u.groupby(\"q\")[\"UNRATE\"].count()\nuq = u.groupby(\"q\")[\"UNRATE\"].mean()\ng[\"q\"] = g[\"observation_date\"].dt.to_period(\"Q\")\ngq = g.dropna().set_index(\"q\")[\"GDPC1\"]\n\nwin = pd.period_range(\"1959Q4\", \"2019Q4\", freq=\"Q\")\nassert (cnt.reindex(win) == 3).all(), \"incomplete months in window\"\nassert gq.reindex(win).notna().all(), \"missing GDP in window\"\nuw, gw = uq.reindex(win), gq.reindex(win)\ndu = uw.diff().iloc[1:]\ngr = (100 * np.log(gw)).diff().iloc[1:]\nassert len(du) == 240\n\nX = sm.add_constant(gr.values)\ny = du.values\nT = len(y)\nL = int(math.floor(4 * (T / 100) ** (2 / 9))) # Newey-West (1994) plug-in rule of thumb -> 4\nols = sm.OLS(y, X).fit()\nhac = sm.OLS(y, X).fit(cov_type=\"HAC\", cov_kwds={\"maxlags\": L, \"use_correction\": False})\nbeta, alpha = float(ols.params[1]), float(ols.params[0])\nse_hac = float(hac.bse[1])\nz = stats.norm.ppf(0.975)\nlo, hi = beta - z * se_hac, beta + z * se_hac\np_hac = float(2 * stats.norm.sf(abs(beta / se_hac)))\n\n# sensitivity (printed only)\nsens = {}\nfor lag in [0, 1, 2, 4, 6, 8, 12, 16]:\n r = sm.OLS(y, X).fit(cov_type=\"HAC\", cov_kwds={\"maxlags\": lag, \"use_correction\": False})\n sens[lag] = float(r.bse[1])\nresid_ac = [float(pd.Series(ols.resid).autocorr(k)) for k in range(1, 5)]\n\nres = {\n \"task_id\": \"F2-conf-04\",\n \"beta_hat\": beta, \"alpha_hat\": alpha, \"r_squared\": float(ols.rsquared),\n \"se_iid\": float(ols.bse[1]), \"se_hac\": se_hac, \"hac_lags\": L,\n \"beta_ci_low\": float(lo), \"beta_ci_high\": float(hi),\n \"okun_negative_5pct\": bool(beta < 0 and p_hac < 0.05),\n \"mean_growth\": float(gr.mean()),\n \"first_quarter\": str(du.index[0]), \"last_quarter\": str(du.index[-1]),\n \"n_analysed\": int(T), \"feasibility\": \"complete\", \"feasibility_reason\": None,\n \"data_issues\": issues, \"n_input_rows\": n_rows, \"random_seed\": None,\n}\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\n\nprint(json.dumps(res, indent=2))\nprint(\"p_hac\", p_hac, \"t_hac\", beta / se_hac)\nprint(\"HAC SE by lag:\", sens)\nprint(\"resid autocorr 1-4:\", resid_ac)\nr_corr = sm.OLS(y, X).fit(cov_type=\"HAC\", cov_kwds={\"maxlags\": L, \"use_correction\": True})\nprint(\"HAC SE with df correction:\", float(r_corr.bse[1]))\n\nfig, ax = plt.subplots(figsize=(6, 4.5))\nax.scatter(gr.values, y, s=12, alpha=0.7)\nxs = np.linspace(gr.min(), gr.max(), 50)\nax.plot(xs, alpha + beta * xs, color=\"red\",\n label=f\"OLS: Δu = {alpha:.3f} {beta:+.3f}·g\")\nax.axhline(0, color=\"grey\", lw=0.5); ax.axvline(0, color=\"grey\", lw=0.5)\nax.set_xlabel(\"Real GDP growth g_t (%, q/q, not annualised)\")\nax.set_ylabel(\"Δu_t (pp)\")\nax.set_title(\"Okun's law, U.S. 1960Q1–2019Q4 (n=240)\")\nax.legend(); fig.tight_layout(); fig.savefig(\"out/figure1.png\", dpi=150)\nEOF\n~/wp29/venv/bin/python 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code 1\nTraceback (most recent call last):\n File \"/Users/simon-pierreboucher/wp29/runs/RC0221/data/out/analysis.py\", line 11, in <module>\n u = pd.read_csv(\"data/UNRATE.csv\", parse_dates=[\"observation_date\"])\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 1026, in read_csv\n return _read(filepath_or_buffer, kwds)\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 620, in _read\n parser = TextFileReader(filepath_or_buffer, **kwds)\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 1620, in __init__\n self._engine = self._make_engine(f, self.engine)\n ~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 1880, in _make_engine\n self.handles = get_handle(\n ~~~~~~~~~~^\n f,\n ^^\n ...<6 lines>...\n storage_options=self.options.get(\"storage_options\", None),\n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n )\n ^\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/common.py\", line 873, in get_handle\n handle = open(\n handle,\n ...<3 lines>...\n newline=\"\",\n )\nFileNotFoundError: [Errno 2] No such file or directory: 'data/UNRATE.csv'","is_error":true,"tool_use_id":"toolu_01ASJiyjv8h18RxgAFHVH5gc"}]},"uuid":"b5d2c50c-9752-4e12-8bc0-52648f1f0b67","timestamp":"2026-10-30T05:04:28.305Z","toolUseResult":"Error: Exit code 1\nTraceback (most recent call last):\n File \"/Users/simon-pierreboucher/wp29/runs/RC0221/data/out/analysis.py\", line 11, in <module>\n u = pd.read_csv(\"data/UNRATE.csv\", parse_dates=[\"observation_date\"])\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 1026, in read_csv\n return _read(filepath_or_buffer, kwds)\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 620, in _read\n parser = TextFileReader(filepath_or_buffer, **kwds)\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 1620, in __init__\n self._engine = self._make_engine(f, self.engine)\n ~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/parsers/readers.py\", line 1880, in _make_engine\n self.handles = get_handle(\n ~~~~~~~~~~^\n f,\n ^^\n ...<6 lines>...\n storage_options=self.options.get(\"storage_options\", None),\n ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n )\n ^\n File \"/Users/simon-pierreboucher/wp29/venv/lib/python3.14/site-packages/pandas/io/common.py\", line 873, in get_handle\n handle = open(\n handle,\n ...<3 lines>...\n newline=\"\",\n )\nFileNotFoundError: [Errno 2] No such file or directory: 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-p out; cat > out/analysis.py <<'EOF'\n\"\"\"Okun's law, U.S. 1960Q1-2019Q4, OLS with Newey-West HAC SE. Run from workspace root.\"\"\"\nimport json, math\nimport numpy as np, pandas as pd\nimport statsmodels.api as sm\nfrom scipy import stats\nimport matplotlib\nmatplotlib.use(\"Agg\")\nimport matplotlib.pyplot as plt\n\nissues = []\nu = pd.read_csv(\"data/UNRATE.csv\", parse_dates=[\"observation_date\"])\ng = pd.read_csv(\"data/GDPC1.csv\", parse_dates=[\"observation_date\"])\nn_rows = {\"UNRATE.csv\": int(len(u)), \"GDPC1.csv\": int(len(g))}\n\nfor name, df, col in [(\"UNRATE.csv\", u, \"UNRATE\"), (\"GDPC1.csv\", g, \"GDPC1\")]:\n if df[\"observation_date\"].duplicated().any():\n raise SystemExit(f\"duplicate dates in {name}\")\n miss = df[df[col].isna()]\n if len(miss):\n dates = \", \".join(d.strftime(\"%Y-%m\") for d in miss[\"observation_date\"])\n issues.append({\"issue\": f\"{name}: {len(miss)} missing value(s) at {dates}\",\n \"handling\": \"Outside the 1959Q4-2019Q4 window needed; dropped, no effect on the analysis.\"})\n\nu = u.dropna()\nu[\"q\"] = u[\"observation_date\"].dt.to_period(\"Q\")\ncnt = u.groupby(\"q\")[\"UNRATE\"].count()\nuq = u.groupby(\"q\")[\"UNRATE\"].mean()\ng[\"q\"] = g[\"observation_date\"].dt.to_period(\"Q\")\ngq = g.dropna().set_index(\"q\")[\"GDPC1\"]\n\nwin = pd.period_range(\"1959Q4\", \"2019Q4\", freq=\"Q\")\nassert (cnt.reindex(win) == 3).all(), \"incomplete months in window\"\nassert gq.reindex(win).notna().all(), \"missing GDP in window\"\nuw, gw = uq.reindex(win), gq.reindex(win)\ndu = uw.diff().iloc[1:]\ngr = (100 * np.log(gw)).diff().iloc[1:]\nassert len(du) == 240\n\nX = sm.add_constant(gr.values)\ny = du.values\nT = len(y)\nL = int(math.floor(4 * (T / 100) ** (2 / 9))) # Newey-West (1994) plug-in rule of thumb -> 4\nols = sm.OLS(y, X).fit()\nhac = sm.OLS(y, X).fit(cov_type=\"HAC\", cov_kwds={\"maxlags\": L, \"use_correction\": False})\nbeta, alpha = float(ols.params[1]), float(ols.params[0])\nse_hac = float(hac.bse[1])\nz = stats.norm.ppf(0.975)\nlo, hi = beta - z * se_hac, beta + z * se_hac\np_hac = float(2 * stats.norm.sf(abs(beta / se_hac)))\n\n# sensitivity (printed only)\nsens = {}\nfor lag in [0, 1, 2, 4, 6, 8, 12, 16]:\n r = sm.OLS(y, X).fit(cov_type=\"HAC\", cov_kwds={\"maxlags\": lag, \"use_correction\": False})\n sens[lag] = float(r.bse[1])\nresid_ac = [float(pd.Series(ols.resid).autocorr(k)) for k in range(1, 5)]\n\nres = {\n \"task_id\": \"F2-conf-04\",\n \"beta_hat\": beta, \"alpha_hat\": alpha, \"r_squared\": float(ols.rsquared),\n \"se_iid\": float(ols.bse[1]), \"se_hac\": se_hac, \"hac_lags\": L,\n \"beta_ci_low\": float(lo), \"beta_ci_high\": float(hi),\n \"okun_negative_5pct\": bool(beta < 0 and p_hac < 0.05),\n \"mean_growth\": float(gr.mean()),\n \"first_quarter\": str(du.index[0]), \"last_quarter\": str(du.index[-1]),\n \"n_analysed\": int(T), \"feasibility\": \"complete\", \"feasibility_reason\": None,\n \"data_issues\": issues, \"n_input_rows\": n_rows, \"random_seed\": None,\n}\nwith open(\"out/results.json\", \"w\") as f:\n json.dump(res, f, indent=2)\n\nprint(json.dumps(res, indent=2))\nprint(\"p_hac\", p_hac, \"t_hac\", beta / se_hac)\nprint(\"HAC SE by lag:\", sens)\nprint(\"resid autocorr 1-4:\", resid_ac)\nr_corr = sm.OLS(y, X).fit(cov_type=\"HAC\", cov_kwds={\"maxlags\": L, \"use_correction\": True})\nprint(\"HAC SE with df correction:\", float(r_corr.bse[1]))\n\nfig, ax = plt.subplots(figsize=(6, 4.5))\nax.scatter(gr.values, y, s=12, alpha=0.7)\nxs = np.linspace(gr.min(), gr.max(), 50)\nax.plot(xs, alpha + beta * xs, color=\"red\",\n label=f\"OLS: Δu = {alpha:.3f} {beta:+.3f}·g\")\nax.axhline(0, color=\"grey\", lw=0.5); ax.axvline(0, color=\"grey\", lw=0.5)\nax.set_xlabel(\"Real GDP growth g_t (%, q/q, not annualised)\")\nax.set_ylabel(\"Δu_t (pp)\")\nax.set_title(\"Okun's law, U.S. 1960Q1–2019Q4 (n=240)\")\nax.legend(); fig.tight_layout(); fig.savefig(\"out/figure1.png\", dpi=150)\nEOF\n~/wp29/venv/bin/python out/analysis.py"}}]}}26{"type":"api-request","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","id":"612de00f-c2b2-47f8-ba18-a56fdcffc662","timestamp":"2026-10-30T05:04:28.308Z","version":"2.1.314","querySource":"sdk","shapeHash":"6f048e604987648eda265e61f2c8b38e727487a511c6fd2e0f0d53269aa05f6c","params":{"model":"claude-opus-5-5","betas":["claude-code-20250219","interleaved-thinking-2025-05-14","context-management-2025-06-27","prompt-caching-scope-2026-01-05","per-turn-control-2026-07-01","thinking-token-count-2026-05-13","mid-conversation-system-clear-at-2026-08-21","effort-2025-11-24","thinking-binding-controls-2026-08-01","thinking-display-updates-2026-08-18","cache-diagnosis-2026-04-07"],"max_tokens":128000,"thinking":{"type":"adaptive","display":"updates"},"context_management":{"edits":[{"type":"clear_thinking_20251015","keep":"all"}]},"output_config":{"effort":"medium"}},"base":"3047f3a5-1aec-4432-b5b0-6fdd1507d121","keep":6,"tail":["826695ab2923087a2f4c73d4a8e9e0fb346083180178752a767872a5879919ad","49ae0f50e595a5439a0d8ee144a61160c14505eff6089cb1d023e3e583b8ea75"],"cacheControl":[{"path":["system",0],"value":{"type":"ephemeral"}},{"path":["system",1],"value":{"type":"ephemeral"}},{"path":["messages",7,"content",0],"value":{"type":"ephemeral"}}],"requestDigest":"ff38b4d879d342ecd8ef0a140a3bded60d9cfcf742ee8bd9c73751511d9c05c8"}27{"parentUuid":"b5d2c50c-9752-4e12-8bc0-52648f1f0b67","isSidechain":false,"message":{"model":"claude-opus-5-5","id":"msg_011CgXqZKo3ZJ4bhCZUhd927","type":"message","role":"assistant","content":[{"type":"text","text":"Oops, I was inside data/. 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dropped, no effect on the analysis.\"\n }\n ],\n \"n_input_rows\": {\n \"UNRATE.csv\": 945,\n \"GDPC1.csv\": 319\n },\n \"random_seed\": null\n}\np_hac 9.508157930957769e-13 t_hac -7.1374450963771725\nHAC SE by lag: {0: 0.028836223207269966, 1: 0.032358596534705866, 2: 0.034227320236153824, 4: 0.03583463330296571, 6: 0.03687902855135966, 8: 0.03713550417540201, 12: 0.03640885110228107, 16: 0.03410831099736795}\nresid autocorr 1-4: [0.38935129370213684, 0.29101329430697004, 0.13988210991085331, 0.07090953047434069]\nHAC SE with df correction: 0.0359848839967588","is_error":false}]},"uuid":"2b473019-7084-41fa-8170-b97d18779183","timestamp":"2026-10-30T05:04:31.337Z","toolUseResult":{"stdout":"GDPC1.csv\nREADME.md\nUNRATE.csv\n{\n \"task_id\": \"F2-conf-04\",\n \"beta_hat\": -0.25576772774872675,\n \"alpha_hat\": 0.18438835418210786,\n \"r_squared\": 0.40825082845620575,\n \"se_iid\": 0.01996009291490982,\n \"se_hac\": 0.03583463330296571,\n \"hac_lags\": 4,\n \"beta_ci_low\": -0.32600231842173916,\n \"beta_ci_high\": -0.18553313707571434,\n \"okun_negative_5pct\": true,\n \"mean_growth\": 0.7535027550652373,\n \"first_quarter\": \"1960Q1\",\n \"last_quarter\": \"2019Q4\",\n \"n_analysed\": 240,\n \"feasibility\": \"complete\",\n \"feasibility_reason\": null,\n \"data_issues\": [\n {\n \"issue\": \"UNRATE.csv: 1 missing value(s) at 2025-10\",\n \"handling\": \"Outside the 1959Q4-2019Q4 window needed; dropped, no effect on the analysis.\"\n }\n ],\n \"n_input_rows\": {\n \"UNRATE.csv\": 945,\n \"GDPC1.csv\": 319\n },\n \"random_seed\": null\n}\np_hac 9.508157930957769e-13 t_hac -7.1374450963771725\nHAC SE by lag: {0: 0.028836223207269966, 1: 0.032358596534705866, 2: 0.034227320236153824, 4: 0.03583463330296571, 6: 0.03687902855135966, 8: 0.03713550417540201, 12: 0.03640885110228107, 16: 0.03410831099736795}\nresid autocorr 1-4: [0.38935129370213684, 0.29101329430697004, 0.13988210991085331, 0.07090953047434069]\nHAC SE with df correction: 0.0359848839967588","stderr":"","interrupted":false,"isImage":false,"noOutputExpected":false},"sandboxed":false,"sourceToolAssistantUUID":"727297dc-79ae-4b82-b021-a7d654f6a389","permissionDecision":{"decision":"accept","source":"config","reasonType":"rule","ruleSource":"cliArg"},"userType":"external","entrypoint":"sdk-cli","cwd":"/Users/simon-pierreboucher/wp29/runs/RC0221","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","version":"2.1.314","gitBranch":"HEAD"}30{"type":"api-request-blob","sessionId":"44575c32-5544-4582-a6cf-00333aa1c35e","hash":"901de730aaa60778fdb85240e9f9c756fd7ef6423fb017a46bb118e13e7a1f8f","message":{"role":"assistant","content":[{"type":"text","text":"Oops, I was inside data/. 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Uncertainty must hold up when the errors are serially correlated.\n\n## Data and exclusions\n- `data/UNRATE.csv` (945 monthly rows) and `data/GDPC1.csv` (319 quarterly rows), current FRED vintage, used as given.\n- I computed quarterly unemployment as the mean of the three monthly values in each quarter. The code checks that every quarter from 1959Q4 to 2019Q4 has all three months and a GDP value. Only the 1959Q4 levels from outside the window are used, as the base for the 1960Q1 differences.\n- Data issue: UNRATE has one empty value, at 2025-10. That is outside the window, so it was dropped and does not affect the analysis. No duplicate dates.\n- Sample: 1960Q1–2019Q4, n = 240. No other exclusions.\n\n## Method\n- OLS of Δu_t on a constant and g_t.\n- Naïve standard error: the conventional OLS standard error, which assumes independent, equal-variance (homoskedastic) errors.\n- Robust standard error: Newey–West HAC, which allows for both autocorrelation and unequal error variance. It uses Bartlett-kernel weights with **4 lags**, set by the Newey–West (1994) rule of thumb floor(4·(T/100)^{2/9}) with T = 240. I fixed this rule before seeing the results. It fits the data: the OLS residuals have autocorrelations of 0.39, 0.29, 0.14 and 0.07 at lags 1–4, so the dependence has mostly died out by lag 4. No small-sample degrees-of-freedom correction is applied. With the n/(n−k) correction the SE is 0.0360 instead of 0.0358.\n- 95% CI = β̂ ± 1.96·SE_HAC, using normal (asymptotic) critical values. The test is two-sided at the 5% level.\n\n## Results\n| quantity | value |\n|---|---|\n| β̂ (Okun coefficient) | −0.2558 |\n| α̂ | 0.1844 |\n| R² | 0.408 |\n| SE (iid) | 0.0200 |\n| SE (HAC, 4 lags) | 0.0358 |\n| 95% HAC CI | [−0.326, −0.186] |\n| HAC t-stat / p-value | −7.14 / 9.5e−13 |\n| mean g_t | 0.754 % per quarter |\n\nA 1-percentage-point higher quarterly real GDP growth (not annualised) goes with a 0.256 pp fall in the unemployment rate that quarter. The implied growth rate that keeps unemployment unchanged is −α̂/β̂ ≈ 0.72 % per quarter, close to the sample mean growth of 0.75 %. Over this sample, β is **negative and significantly different from zero at the 5% level** (`okun_negative_5pct = true`). Figure: `out/figure1.png`.\n\n## Uncertainty\nThe HAC SE is about 1.8 times the naïve iid SE (0.0358 vs 0.0200), so the iid SE overstates precision. Part of the gap is heteroskedasticity: the heteroskedasticity-robust SE with 0 lags is 0.0288. The rest is the positive residual autocorrelation.\n\nThe HAC SE barely changes with the choice of bandwidth:\n\n| lags | 0 | 1 | 2 | 4 | 6 | 8 | 12 | 16 |\n|---|---|---|---|---|---|---|---|---|\n| SE | 0.0288 | 0.0324 | 0.0342 | 0.0358 | 0.0369 | 0.0371 | 0.0364 | 0.0341 |\n\nSo the conclusion holds for any bandwidth from 0 to 16 lags: the largest SE (0.0371) still gives |t| > 6.\n\n## Limitations and open issues\n- The data are the current vintage, not real-time. GDP revisions may differ from the values originally published.\n- β is a linear-projection coefficient, not a causal effect. Unemployment's response to growth is spread over several quarters (consistent with the residual autocorrelation), and this contemporaneous regression does not model those dynamics.\n- The relationship may not be stable over time (e.g., across decades or recessions). I did not test for this. The 2020 COVID observations are excluded by design.\n- The HAC inference is asymptotic: it uses normal critical values and its HAC confidence intervals can undercover somewhat in finite samples. Given t ≈ −7, this does not affect the conclusion.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The OLS Okun coefficient over 1960Q1-2019Q4 is about -0.256 pp of unemployment per percent of quarterly (non-annualised) real GDP growth.\",\"results_keys\":[\"beta_hat\",\"n_analysed\",\"first_quarter\",\"last_quarter\"],\"status\":\"supported\",\"caveat\":\"Linear projection, current-vintage data; not a causal estimate.\"},\n {\"id\":\"C2\",\"text\":\"The Okun coefficient is negative and significantly different from zero at the 5% level using a Newey-West HAC SE with 4 lags (95% CI about [-0.326, -0.186]).\",\"results_keys\":[\"se_hac\",\"hac_lags\",\"beta_ci_low\",\"beta_ci_high\",\"okun_negative_5pct\"],\"status\":\"supported\",\"caveat\":\"Asymptotic normal critical values; result robust to bandwidths 0-16.\"},\n {\"id\":\"C3\",\"text\":\"The HAC standard error is about 1.8 times the conventional iid standard error, so the naive SE overstates precision.\",\"results_keys\":[\"se_iid\",\"se_hac\"],\"status\":\"supported\",\"caveat\":\"Part of the gap reflects heteroskedasticity, not only autocorrelation.\"},\n {\"id\":\"C4\",\"text\":\"Growth explains about 41% of the variance of quarterly unemployment changes.\",\"results_keys\":[\"r_squared\"],\"status\":\"supported\",\"caveat\":\"In-sample fit only.\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'))\"; 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Uncertainty must hold up when the errors are serially correlated.\n\n## Data and exclusions\n- `data/UNRATE.csv` (945 monthly rows) and `data/GDPC1.csv` (319 quarterly rows), current FRED vintage, used as given.\n- I computed quarterly unemployment as the mean of the three monthly values in each quarter. The code checks that every quarter from 1959Q4 to 2019Q4 has all three months and a GDP value. Only the 1959Q4 levels from outside the window are used, as the base for the 1960Q1 differences.\n- Data issue: UNRATE has one empty value, at 2025-10. That is outside the window, so it was dropped and does not affect the analysis. No duplicate dates.\n- Sample: 1960Q1–2019Q4, n = 240. No other exclusions.\n\n## Method\n- OLS of Δu_t on a constant and g_t.\n- Naïve standard error: the conventional OLS standard error, which assumes independent, equal-variance (homoskedastic) errors.\n- Robust standard error: Newey–West HAC, which allows for both autocorrelation and unequal error variance. It uses Bartlett-kernel weights with **4 lags**, set by the Newey–West (1994) rule of thumb floor(4·(T/100)^{2/9}) with T = 240. I fixed this rule before seeing the results. It fits the data: the OLS residuals have autocorrelations of 0.39, 0.29, 0.14 and 0.07 at lags 1–4, so the dependence has mostly died out by lag 4. No small-sample degrees-of-freedom correction is applied. With the n/(n−k) correction the SE is 0.0360 instead of 0.0358.\n- 95% CI = β̂ ± 1.96·SE_HAC, using normal (asymptotic) critical values. The test is two-sided at the 5% level.\n\n## Results\n| quantity | value |\n|---|---|\n| β̂ (Okun coefficient) | −0.2558 |\n| α̂ | 0.1844 |\n| R² | 0.408 |\n| SE (iid) | 0.0200 |\n| SE (HAC, 4 lags) | 0.0358 |\n| 95% HAC CI | [−0.326, −0.186] |\n| HAC t-stat / p-value | −7.14 / 9.5e−13 |\n| mean g_t | 0.754 % per quarter |\n\nA 1-percentage-point higher quarterly real GDP growth (not annualised) goes with a 0.256 pp fall in the unemployment rate that quarter. The implied growth rate that keeps unemployment unchanged is −α̂/β̂ ≈ 0.72 % per quarter, close to the sample mean growth of 0.75 %. Over this sample, β is **negative and significantly different from zero at the 5% level** (`okun_negative_5pct = true`). Figure: `out/figure1.png`.\n\n## Uncertainty\nThe HAC SE is about 1.8 times the naïve iid SE (0.0358 vs 0.0200), so the iid SE overstates precision. Part of the gap is heteroskedasticity: the heteroskedasticity-robust SE with 0 lags is 0.0288. The rest is the positive residual autocorrelation.\n\nThe HAC SE barely changes with the choice of bandwidth:\n\n| lags | 0 | 1 | 2 | 4 | 6 | 8 | 12 | 16 |\n|---|---|---|---|---|---|---|---|---|\n| SE | 0.0288 | 0.0324 | 0.0342 | 0.0358 | 0.0369 | 0.0371 | 0.0364 | 0.0341 |\n\nSo the conclusion holds for any bandwidth from 0 to 16 lags: the largest SE (0.0371) still gives |t| > 6.\n\n## Limitations and open issues\n- The data are the current vintage, not real-time. GDP revisions may differ from the values originally published.\n- β is a linear-projection coefficient, not a causal effect. Unemployment's response to growth is spread over several quarters (consistent with the residual autocorrelation), and this contemporaneous regression does not model those dynamics.\n- The relationship may not be stable over time (e.g., across decades or recessions). I did not test for this. The 2020 COVID observations are excluded by design.\n- The HAC inference is asymptotic: it uses normal critical values and its HAC confidence intervals can undercover somewhat in finite samples. Given t ≈ −7, this does not affect the conclusion.\nEOF\ncat > out/claims.json <<'EOF'\n[\n {\"id\":\"C1\",\"text\":\"The OLS Okun coefficient over 1960Q1-2019Q4 is about -0.256 pp of unemployment per percent of quarterly (non-annualised) real GDP growth.\",\"results_keys\":[\"beta_hat\",\"n_analysed\",\"first_quarter\",\"last_quarter\"],\"status\":\"supported\",\"caveat\":\"Linear projection, current-vintage data; not a causal estimate.\"},\n {\"id\":\"C2\",\"text\":\"The Okun coefficient is negative and significantly different from zero at the 5% level using a Newey-West HAC SE with 4 lags (95% CI about [-0.326, -0.186]).\",\"results_keys\":[\"se_hac\",\"hac_lags\",\"beta_ci_low\",\"beta_ci_high\",\"okun_negative_5pct\"],\"status\":\"supported\",\"caveat\":\"Asymptotic normal critical values; result robust to bandwidths 0-16.\"},\n {\"id\":\"C3\",\"text\":\"The HAC standard error is about 1.8 times the conventional iid standard error, so the naive SE overstates precision.\",\"results_keys\":[\"se_iid\",\"se_hac\"],\"status\":\"supported\",\"caveat\":\"Part of the gap reflects heteroskedasticity, not only autocorrelation.\"},\n {\"id\":\"C4\",\"text\":\"Growth explains about 41% of the variance of quarterly unemployment changes.\",\"results_keys\":[\"r_squared\"],\"status\":\"supported\",\"caveat\":\"In-sample fit only.\"}\n]\nEOF\n~/wp29/venv/bin/python -c \"import json;json.load(open('out/claims.json'))\"; 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It is negative and significantly different from zero at the 5% level using the Newey–West standard error (`okun_negative_5pct = true`). The analysis is complete, and running `out/analysis.py` regenerates `results.json` and the figure.\n\n| quantity | value |\n|---|---|\n| β̂ | −0.256 (n = 240 quarters) |\n| α̂ (intercept) | 0.184 |\n| R² | 0.41 |\n| Conventional standard error | 0.0200 |\n| Newey–West standard error (4 lags) | 0.0358 |\n| 95% confidence interval | [−0.326, −0.186] |\n| t-statistic | −7.1 |\n| Mean quarterly growth | 0.754 % |\n\nSo one percentage point more quarterly GDP growth goes with unemployment about 0.26 points lower in the same quarter.\n\n- **Bandwidth:** I used 4 lags, from the standard Newey–West rule of thumb floor(4·(T/100)^{2/9}) with T = 240. The residual autocorrelations (0.39, 0.29, 0.14, 0.07 at lags 1–4) show the dependence mostly fades by lag 4.\n- **Robustness:** the conclusion holds for every bandwidth I tried, from 0 to 16 lags; even the largest standard error (0.0371) gives |t| > 6.\n- **Conventional vs robust standard error:** the robust one is about 1.8 times larger. Part of that gap is unequal error variance across quarters rather than autocorrelation: with 0 lags the robust standard error is already 0.0288.\n- **Data issue:** UNRATE has one missing value, in October 2025. That is outside the sample window, so it has no effect.\n\n**Limitations:**\n- The data are today's revised figures, not what was published at the time.\n- The slope is an association, not a causal effect.\n- I did not test whether the relationship changed over the 60 years.\n- The confidence interval relies on large-sample approximations.\n\nWhen I first wrote `analysis.py` I was mistakenly inside `data/`, so it was created at `data/out/`. 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