Replication — Ramey & Zubairy (2018)¶

Every other page in this gallery runs on synthetic data, where the truth is known because we built it. This one runs on the authors' own data and aims at a published number.

Ramey & Zubairy (2018) estimate US government-spending multipliers from historical data using Ramey's military-news series as the identifying shock. Their headline finding is that the integral multiplier is roughly 0.6–0.8 — crucially below one, meaning a dollar of government spending buys less than a dollar of output.

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

The data is Ramey & Zubairy's public replication file, committed to the repository at fixtures/ramey_zubairy.csv (564 quarters, 27 series, 1875Q1–2015Q4), so this runs fully offline — tsecon ships no data loaders. The script reads it with a dozen lines of csv.

The result¶

Full historical sample, 1890Q1–2015Q4 (n = 504)

h (quarters)	cumulative ΔY	cumulative ΔG	multiplier	SE	first-stage F
2	0.280	0.382	0.735	0.115	10.9
4	0.647	1.018	0.635	0.057	15.2
8	1.813	2.758	0.657	0.039	16.8
12	3.250	4.641	0.700	0.033	13.5
16	4.219	5.973	0.706	0.048	11.7
20	4.767	6.413	0.743	0.057	12.0

Across horizons 4–20 the multiplier sits in 0.64 to 0.74 — inside RZ's published 0.6–0.8 range, and comfortably below one at every horizon (the 95% band at h = 8 is 0.58 to 0.73). The central economic claim replicates.

Postwar subsample, 1947Q1–2015Q4 (n = 276)

h	cumulative ΔY	cumulative ΔG	multiplier	SE	first-stage F
2	0.085	0.082	1.032	0.377	17.0
4	0.232	0.297	0.783	0.184	56.2
8	0.509	0.856	0.594	0.129	112.9
12	0.841	1.419	0.592	0.122	117.2
16	0.943	1.789	0.527	0.125	65.6
20	1.288	2.077	0.620	0.140	39.6

The postwar point estimates land lower, and their standard errors are roughly three times the full-sample ones — at h = 2 the multiplier is not distinguishable from anything between 0.3 and 1.8. That is the same point RZ themselves make: the identifying variation in the military-news series is overwhelmingly pre-1950, which is precisely why their headline estimates use the long historical sample.

How the multiplier is constructed¶

Normalisation (Gordon-Krenn). Real quantities are divided by CBO potential output rather than logged:

g = (ngov / pgdp) / rgdp_potcbo     # real government spending / potential
y = rgdp / rgdp_potcbo              # real GDP / potential
newsy = news / lag(pgdp * rgdp_potcbo)

Dividing rather than logging is what makes the estimate a multiplier — dollars of output per dollar of spending — instead of an elasticity.

The integral multiplier is one call:

r = tsecon.lp_multiplier(y, g, newsy, horizons=20, n_lag_controls=4)
r["multiplier"]      # extra dollar of output per extra dollar of spending
r["se"]              # standard error OF THE MULTIPLIER
r["first_stage_f"]   # weak-instrument diagnostic

lp_multiplier runs the one-step Ramey-Zubairy regression at each horizon:

sum_{j=0..h} y_{t+j} = m_h * sum_{j=0..h} g_{t+j} + c
                     + sum_{l=1..p} (phi_l y_{t-l} + psi_l g_{t-l}) + u

with the cumulated spending instrumented by the contemporaneous news shock. Because the multiplier is a single 2SLS coefficient rather than a ratio of two separately estimated responses, se is the standard error of the number being reported — not a delta-method approximation and not one leg's SE relabelled. The two reduced-form legs are returned as cumulative_outcome and cumulative_impulse for transparency; by the just-identified IV algebra their ratio equals multiplier to numerical precision, which is exactly the identity the tables above display.

A trap worth naming

It is tempting to reach for lp_iv(y, g, newsy, cumulative=True) and read the coefficient as the multiplier. It is not. cumulative=True (also spelled cumulative="outcome") cumulates only the outcome, so the coefficient is output per unit of contemporaneous spending. Its numerator accumulates and its denominator does not, so it inherits the growth of the spending path rather than measuring anything per-dollar: on this data it runs 7.4 at h = 4 and 48.7 by h = 20, with a first-stage F of 1.68 into the bargain.

That flag still exists and still means what it always meant — a cumulative impulse response is a perfectly good object. It is simply not a multiplier. A multiplier needs both sides accumulated, which is why the library now gives it its own entry point rather than a flag you have to know to set correctly. If you want the both-sides cumulation without the multiplier's control set you can also ask for it directly: lp_iv(..., cumulative="both").

(Earlier versions of this page worked around the gap by running two cumulative lp calls and dividing. That ratio used a different control set in each leg — lags of y in the numerator, lags of g in the denominator — which is not any single well-defined IV estimator. The one-step version moves the h = 4..20 estimates from 0.66–0.71 to 0.64–0.74; the largest change is +0.037 at h = 20 and the economic conclusion is unchanged.)

What this is, and is not¶

This reproduces RZ's headline integral multiplier using their data, their instrument, and their normalisation. It is not a line-by-line port of their Stata code: their published tables involve sample splits, lag choices, and standard-error conventions this script does not reproduce exactly. The standard errors reported here are the library's kernel-HAC ones for the one-step multiplier regression, not RZ's own convention.

The claim being checked is the one that carries the economics — that the multiplier is well below one, and stable across horizons in the long sample — not bitwise equality with a published table. Where the subsample results are ugly, they are printed as they came out.

Citation. Ramey, V. A. & Zubairy, S. (2018), "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data," Journal of Political Economy 126(2):850-901. The replication archive is distributed by the authors; please cite the paper if you use the data.

See also. lp / lp_iv model card · yield-curve recession replication · frontier Monte Carlo, which measures what LP-IV does when the instrument is weak.