Pre-registration
In US time-series 1948-2024, the long-run Phillips curve is vertical in the Friedman-Phelps (1968) sense: the slope of the long-run unemployment-inflation relationship — measured by the long-horizon cumulative response of inflation to a sustained change in the unemployment-NAIRU gap — is statistically indistinguishable from zero, while the short-run slope is statistically negative. Equivalently, the share of cross-decade variation in mean US inflation that can be predicted by mean unemployment is below 5%, while the share predictable by mean broad-money growth (net of trend output) exceeds 50%.
Falsification criterion — what would disprove this
This hypothesis is considered falsified if:
Not supported if (a) the short-run Phillips slope at quarterly frequency is not negative at p<0.05, OR (b) the decade-mean unemployment coefficient on decade-mean inflation is significantly different from zero at p<0.05 with absolute magnitude > 0.3, OR (c) the decade-mean money-growth-net-of-output coefficient is insignificant or has magnitude below 0.5. A neo-Keynesian / sticky- price reading wins cleanly if the long-run slope is negative and significant — i.e. there is a usable long-run tradeoff.
formal test & threshold
test: short_run_negative_long_run_zero_phillips threshold: short_run_quarterly_slope < 0 at p<0.05 AND |decade_mean_unemployment_coef| < 0.3 OR p > 0.10 AND decade_mean_money_growth_coef in [0.5, 1.5] at p<0.05 AND decade-level R^2 share attributable to unemployment < 5%
Method
- Template
panel_fe- Fixed effects
- Clustering
newey_west_4_lags- Sample
- 1 countries · 1948 – 2024
- Evidence type
- associational
Two-spec design pre-registered. Spec A (short-run): quarterly Phillips curve regression of inflation on unemployment gap with lags, expecting a negative coefficient. Spec B (long-run): regression of decade-mean inflation on decade-mean unemployment AND decade-mean (M2-growth - GDP-growth) across non-overlapping decades. The Friedman natural-rate prediction requires Spec A coefficient negative AND Spec B unemployment coefficient insignificant AND Spec B money-growth coefficient large. Local-projection impulse responses to monetary shocks (Romer-Romer narrative) reported as robustness; the 10-year cumulative inflation response to a permanent 1pp unemployment shock should be indistinguishable from zero.
Data
| Variable | Source | Transform |
|---|---|---|
cpi_inflation_quarterly outcome | fred:CPIAUCSLtier 1 | log_diff_qoq_annualised |
decade_mean_inflation outcome | fred:CPIAUCSLtier 1 | decade_mean_yoy |
unemployment_minus_nairu_gap treatment | fred:UNRATEtier 1 fred:NROUtier 1 | difference |
decade_mean_unemployment treatment | fred:UNRATEtier 1 | decade_mean |
decade_mean_m2_growth_minus_real_gdp_growth treatment | fred:M2SLtier 1 fred:GDPC1tier 1 | decade_mean_m2_log_diff_minus_decade_mean_realgdp_log_diff |
oil_price_change_decade control | fred:WTISPLCtier 1 | decade_mean_log_diff |
trend_output_growth control | fred:GDPC1tier 1 | decade_mean_log_diff |
short_term_interest_rate control | fred:FEDFUNDStier 1 | level |
● ready · ● pending · ● reconstruct-needed
Detailed result card
Result card — friedman_natural_rate_long_run_phillips_vertical_us
Verdict: PARTIAL — coef=+0.0181, p=0.216 (above α=0.05); direction inconclusive
Pre-registration
- Claim: In US time-series 1948-2024, the long-run Phillips curve is vertical in the Friedman-Phelps (1968) sense: the slope of the long-run unemployment-inflation relationship — measured by the long-horizon cumulative response of inflation to a sustained change in the unemployment-NAIRU gap — is statistically indistinguishable from zero, while the short-run slope is statistically negative. Equivalently, the share of cross-decade variation in mean US inflation that can be predicted by mean unemployment is below 5%, while the share predictable by mean broad-money growth (net of trend output) exceeds 50%.
- Falsification rule: Not supported if (a) the short-run Phillips slope at quarterly frequency is not negative at p<0.05, OR (b) the decade-mean unemployment coefficient on decade-mean inflation is significantly different from zero at p<0.05 with absolute magnitude > 0.3, OR (c) the decade-mean money-growth-net-of-output coefficient is insignificant or has magnitude below 0.5. A neo-Keynesian / sticky- price reading wins cleanly if the long-run slope is negative and significant — i.e. there is a usable long-run tradeoff.
- Falsification test: short_run_negative_long_run_zero_phillips
Estimate
- Method: statsmodels OLS time-series fallback
- Coefficient (treatment): +0.0181
- Std error: 0.01465
- p-value: 0.216
- Observations: 71, countries: 1
- Within R²: 0.98
- Fixed effects: entity=False, time=False
- Clustering: HAC(maxlags=4)
Variables resolved
fred:CPIAUCSL→ cpi_inflation_quarterly (outcome, publisher=fred, n=80)fred:CPIAUCSL→ decade_mean_inflation (outcome, publisher=fred, n=80)fred:UNRATE; fred:NROU→ unemployment_minus_nairu_gap (treatment, publisher=fred, n=79)fred:UNRATE→ decade_mean_unemployment (treatment, publisher=fred, n=79)fred:M2SL; fred:GDPC1→ decade_mean_m2_growth_minus_real_gdp_growth (treatment, publisher=fred, n=68)fred:WTISPLC→ oil_price_change_decade (controls, publisher=fred, n=81)fred:GDPC1→ trend_output_growth (controls, publisher=fred, n=80)fred:FEDFUNDS→ short_term_interest_rate (controls, publisher=fred, n=73)
Generated by scripts/run_panel_fe.py at 2026-06-29T17:54:16+00:00
Strongest opposing argument
Every hypothesis ships with its charitable opposing argument. The framework earns credibility by handling objections at their strongest, not weakest.
Notes
Friedman 1968 AEA presidential address and Phelps 1967 Economica are the canonical references. The decade-mean specification follows Lucas's 1980 cross-country chart re-applied longitudinally to a single country. Because this is a single-country time-series test, statistical power on the long-run slope is limited (only 7-8 non-overlapping decades); the spec acknowledges this by requiring effect-size cutoffs in addition to p-values.