Replication — Gertler & Karadi (2015)¶

The canonical proxy-SVAR application: Gertler and Karadi identified a monetary policy shock in a monthly four-variable VAR from high-frequency fed funds futures surprises, and found that modest policy-rate movements produce large credit-cost responses and a real-activity decline. This page replicates the paper on its own data with proxy_svar — reproducing its first-stage strength numbers verbatim — and then runs the modern audit the subsequent literature demanded: valid moving-block bands (Jentsch-Lunsford), the Montiel Olea-Pflueger effective F with its honest thresholds (proxy_first_stage), weak-instrument-robust Anderson-Rubin sets (proxy_ar_sets), and the Doko Tchatoka-Haque post-1984 subsample where identification measurably weakens.

.venv/bin/python docs/examples/replication_gertler_karadi.py

The data is the paper's own AEJ replication dataset: 396 months (1979:7–2012:6) of the 1-year Treasury rate, 100·log CPI, 100·log industrial production, the Gilchrist-Zakrajšek excess bond premium, and the published FOMC-surprise instrument series. It is committed at fixtures/gertler_karadi.csv (vendored verbatim from the Plagborg-Møller & Wolf svma_iv mirror and cross-checked column-by-column against the independent VAR-Toolbox mirror — agreement to float-print precision), so the replication runs fully offline.

The specification¶

GK's baseline, exactly: VAR(12) in levels with a constant on (1-year rate, log CPI, log IP, EBP) over the full 1979:7–2012:6 sample; the external instrument is the three-month-ahead fed funds futures surprise (FF4) in a 30-minute window around FOMC announcements, used over 1991:1–2012:6 (258 months). The VAR's lag coefficients are estimated on the full sample and the instrument enters only the identification moments — tsecon's NaN-masked proxy handles the two samples natively:

pr = tsecon.proxy_svar(data, proxy,          # proxy is NaN before 1991:1
                       lags=12, horizon=48, norm_var=0, unit=0.2)

unit=0.2 is the unit-effect normalization: the shock raises the 1-year rate by exactly +20bp on impact, the size of the "representative" surprise in the paper's Figure 1.

The first stage: the paper's numbers, verbatim¶

statistic (FF4 on the 1-year-rate residual)	published	tsecon
classical first-stage F	21.55	21.55
heteroskedasticity-robust F	~17.5	17.50
effective observations	258	258

The robust F is the Montiel Olea-Pflueger effective F in this just-identified case, and the new proxy_first_stage diagnostic supplies the thresholds the number should be judged against — which is where the replication stops being a victory lap:

	effective F	MOP τ=10% bar	certified worst-case bias	folklore F>10
baseline 1979–2012	17.50	23.11	15.5%	passes
post-1984 subsample	13.82	23.11	23.3%	passes

GK's instrument clears the Stock-Wright-Yogo folklore bar with room to spare — as the paper says — and still falls short of the MOP τ=10% bar. The data certify worst-case relative bias below 15.5%, not below 10%. That is not a refutation of the paper (its F is honestly reported and its result was corroborated by Montiel Olea-Stock-Watson's weak-IV-robust re-analysis); it is the demonstration that "F > 10" was never the test, and it is why the Anderson-Rubin sets below are reported alongside every band.

The impulse responses¶

To a +20bp policy surprise (responses in percent; rate/EBP in percentage points; point estimates, full sample):

h (months)	1-yr rate	CPI	IP	EBP
0	+0.200	−0.034	+0.030	+0.116
6	+0.132	−0.020	−0.139	+0.068
12	+0.066	−0.030	−0.302	+0.020
18	−0.037	−0.070	−0.400	+0.022
24	−0.086	−0.095	−0.425	+0.013
36	−0.069	−0.135	−0.337	−0.006
48	−0.007	−0.134	−0.190	−0.013

Against the paper's stated shapes (Fig. 1 and text):

the 1-year rate "increases roughly 20 basis points on impact and then reverts back to trend after roughly a year" — here +20bp exact (the normalization) and below +7bp by month 12, negative by month 18;
industrial production shows "a significant and fairly rapid drop … that begins after several months and reaches a trough after roughly 18 months" — here the response turns negative in month 4 and troughs at −0.43% in month 25, with month 18 already within 0.03% of the trough (the trough is a plateau across months 18–30, not a spike);
the CPI "declines steadily, though this decline is not significant" — here a slow drift to −0.13% by month 48, never significant below;
the excess bond premium "increases eight basis points on impact and remains at that level for roughly eight months" — here +12bp on impact, then a ~6bp plateau through month 8, positive through month 31. The impact size differs because the normalizations differ (the paper's representative surprise is its one-standard-deviation shock, not an exact +20bp); the sign, timing and the credit-channel excess (a 20bp rate move producing a disproportionate spread response) reproduce.

The bands: GK's wild bootstrap vs the valid moving block¶

GK computed 95% bands with the wild proxy bootstrap — the method Jentsch & Lunsford (2019, AER) later proved is not asymptotically valid for proxy SVARs (a common Rademacher draw leaves the identifying moment bit-identical across replications). tsecon ships both: bands="wild" reproduces the paper's method (and self-reports asymptotically_valid: False), bands="moving_block" is the Jentsch-Lunsford bootstrap whose validity is proven. Significant horizons at 95% (Efron percentile bands, 2000 draws, seed 0):

response	wild (GK's method, invalid)	moving block (valid)
IP < 0	h = 7…40 (34 of 49)	h = 25…29 (3 of 49)
EBP > 0	h = 0…8 (9 of 49)	h = 0…3 (2 of 49)
CPI < 0	h = 30…48 (19 of 49)	none

The wild bands reproduce the paper's significance pattern; the valid bands are materially wider, and most of the published IP significance does not survive the correction at 95% (at 90%, IP remains significant over h = 16…40). The credit-cost impact response is what survives at every level. This is the measured, on-this-data form of the Jentsch-Lunsford warning, and the reason proxy_svar_bands defaults to the moving block.

Both bootstraps report n_failed: 0 — no draw was lost to a near-zero denominator, consistent with a first stage of this strength.

Post-1984: identification weakens, output effects dissolve¶

Doko Tchatoka & Haque (2024, Economic Record) re-ran GK excluding the Volcker disinflation and found that post-1984, monetary policy shocks show no significant output effects under weak-identification-robust inference, despite large credit-cost movements. Reproduced here: the VAR re-estimated on 1984:1–2012:6 (same FF4 1991:1+ instrument), with 95% Anderson-Rubin sets (reduced-form uncertainty propagated) from proxy_ar_sets:

h	IP set, full sample	IP set, post-1984
6	[−0.68, +0.34]	[−0.88, +0.57]
12	[−1.05, +0.21]	[−1.39, +0.51]
18	[−1.18, +0.10]	[−1.62, +0.50]
24	[−1.15, +0.06]	[−1.73, +0.44]
36	[−0.91, +0.09]	[−1.63, +0.38]
48	[−0.60, +0.15]	[−1.19, +0.45]

the effective F falls from 17.50 to 13.82, the certified worst-case bias bound rises from 15.5% to 23.3% — the new diagnostic flags the weakening before any band is drawn;
every AR set stays bounded in both samples (the relevance statistic clears its χ²₁ critical value: 10.0 and 8.7 vs 3.84), but the post-1984 IP sets are a median 1.80× wider;
the EBP impact response excludes zero in both samples (post-1984 at h = 0, 2, 4, 6) while no IP set excludes zero in either — under fully robust inference the credit-cost channel is the finding that survives, and post-1984 the output response is unambiguously indistinguishable from zero. Exactly the Doko Tchatoka-Haque conclusion.

(That the full-sample IP sets also straddle zero pointwise is not a contradiction of the table above: the AR sets add weak-instrument robustness and reduced-form-coefficient uncertainty on top of a 95% level — they are the most conservative object on this page, by design.)

Sensitivities, and what matches what¶

Instrument window. Starting the instrument at its 1990:1 availability instead of the paper's 1991:1 moves the effective F from 17.50 to 17.58 — nothing changes.
HAC first stage. A Newey-West (5-lag) effective F is 20.36 vs the HC1 17.50 — the FF4 surprise's score is close to serially uncorrelated, as a surprise series should be.
The other published GK instruments (first stage on the 1-year rate, same 1991:1–2012:6 window): mp1_tc F = 16.36; the eurodollar surprises ed2/ed3/ed4_tc F = 6.97 / 4.66 / 4.16 — every one of them below the MOP τ=10% bar, the eurodollars below the folklore bar too. The paper's choice of FF4 as the baseline is visibly the strongest available instrument.
What is deliberately not claimed: agreement with figure pixels (the paper's figures were not digitized — every pinned claim comes from the paper's text and tables); the paper's Cholesky comparison column; and its GSS-decomposition/forward-guidance extensions (Section IV), which need the full futures term structure, not the four instruments vendored here.

Known deviations, stated plainly. (i) The IRF normalization is unit-effect (+20bp exact) where the paper plots a one-standard-deviation surprise (≈20bp) — shapes are invariant, impact magnitudes of the non-normalized variables scale accordingly. (ii) tsecon's bands re-estimate the VAR inside every bootstrap draw with no Kilian bias correction; GK's wild implementation differs in that detail as well as in validity. (iii) GK report first-stage statistics for several instrument sets; the 21.55 / 17.5 comparison is their FF4-on-the-1-year-rate entry, the baseline identification. (iv) The published robust F is quoted at the paper's printed precision ("17.5"); tsecon's 17.50 matches it at that precision.

The regression test (test_replication_gk.py) pins the dataset vintage, the verbatim first-stage numbers, the IRF shape facts, the wild-vs-moving-block significance contrast, and the post-1984 weakening, all offline.

Citations. Gertler, M. & Karadi, P. (2015), "Monetary Policy Surprises, Credit Costs, and Economic Activity," AEJ: Macroeconomics 7(1):44–76 — please cite the paper if you use the data. Jentsch, C. & Lunsford, K.G. (2019), AER 109(7):2655–2678 (wild-bootstrap invalidity) and (2022), JBES 40(4):1876–1891 (moving-block validity). Montiel Olea, J.L. & Pflueger, C. (2013), JBES 31(3):358–369 (effective F). Montiel Olea, J.L., Stock, J.H. & Watson, M.W. (2021), J. Econometrics 225(1):74–87 (SVAR-IV inference). Doko Tchatoka, F. & Haque, Q. (2024), Economic Record 100(329):234–259 (post-1984). Gilchrist, S. & Zakrajšek, E. (2012), AER 102(4):1692–1720 (the excess bond premium). Data mirrors: Plagborg-Møller & Wolf's svma_iv repository; Cesa-Bianchi's VAR-Toolbox.

See also. proxy_svar model card · proxy_first_stage for why 23.11 (not 10) is the bar · proxy_ar_sets for what an honest confidence statement looks like when instruments weaken · the interval-coverage audit, which measured on synthetic data the same folklore-threshold failure this page demonstrates on published data.