P01 · Recover the Basic LP Estimator

Replication lab REP01, Stata problem set STA01, and the Shock-to-Response Explorer handoff

What we are building

A Stata project that rebuilds the levels curve of Jordà and Taylor’s first Monte Carlo example one regression at a time, reproduces the published benchmark once the number of draws matches, and then carries the same moves from the twelve rows of Lecture 01’s hand table to a century of quarterly data on military news. When it runs clean you can say what each point on a response graph is: which regression produced it, from which rows, averaged over what, and what it has not yet shown. The complete lab project contains the starter do-files, the solved problem set, the data with provenance, and automated checks. The instructor build is the executed version.

The question

Lecture 01 asked how a regression coefficient becomes one point on an impulse-response function, and answered in an economy where the answer is known. If y_t=\rho\,y_{t-1}+\theta_0 s_t+v_t with an observed shock s_t, the regression of y_{t+h} on a constant, s_t, and y_{t-1} has population coefficient \theta_0\rho^h. A published local-projection result rests on the same arithmetic, but the arithmetic sits inside someone else’s do-file, behind their variable names, their loop, and their choice of what to store. So the practicum asks:

Can you rebuild a published local-projection result one regression at a time, and say exactly what each number in it measures?

Part A answers the question for the smallest published target in the course readings, the levels curve in Figure 1a of Jordà and Taylor (2025). Its economy is the lecture’s AR(1) with \rho=0.95 and T=100, so the true response is known and every gap between the curve and the truth can be read. Part B repeats the moves on the lecture’s own anchors: the hand table, one simulated draw, a Monte Carlo experiment, and the military-news data of Ramey and Zubairy (2018). Part C reruns in Stata what you predicted and computed in the browser.

How to use the lab project

Download and unzip the lab project. It unzips to a folder called lab-project. Set Stata’s working folder to it and run the master file:

cd "lab-project"
do master.do          // checks, REP01, your problem set, the handoff check

master.do runs four files in order and stops at the first check that fails:

tests/checks.do confirms, without a network connection, that the shipped data, benchmark, and vendor files have the SHA-256 values recorded in data/PROVENANCE.md and vendor/jel-code/SOURCE.md, that the simulated data follow their rules, that data/raw/make_sim_data.do regenerates them byte for byte, and that the helper programs in helpers/lp_helpers.do behave as documented;
replication/rep01.do rebuilds the REP01 target and compares it with three references;
starter/pset.do runs your problem set;
handoff/check_handoff.do reruns what the Shock-to-Response Explorer computed for you.

Everything lands in output/: master.log and one log per step, assertions.csv with every check and its result, rep01-benchmark.csv, and the two REP01 figures. The problem set writes its deliverables to output/pset/. Two globals change the work. global R sets the number of Monte Carlo draws, 200 by default (editor decision D2), and global AUTHOR_CHECK 0 skips the run of the authors’ own script. With the defaults, the checks and REP01 take about 30 seconds in StataNow/SE 19.5, and a completed problem set about 30 seconds more, the download in Task 5 included; the instructor build, with R=500, took 137 seconds from start to MASTER COMPLETE. No user-written commands are needed.

While you work on the problem set, run do starter/pset.do on its own from the same folder; keep the master file for the final record. The archive also holds the solved problem set, solution/pset_solution.do, and do master.do solution runs it in place of the starter. Open it after you have attempted every task.

Part A · Replication lab REP01

The target

Field	Value
Paper and version	Jordà and Taylor (2025), Journal of Economic Literature 63(1), 59–110. Replication package `ojorda/JEL-Code`, commit `655696c1c576b7537c5a939d2c261f0a111ae663` (CC0); the four files REP01 needs ship in `vendor/jel-code/`, with only the authors’ two `cap cd` folder paths commented out
Exact target	Figure 1a, the levels curve: the Monte Carlo mean of \hat\beta_h from reg f`h'.y vy l.y, h=0,\dots,10, with an intercept and without the lagged difference, in an AR(1) with \rho=0.95 and T=100 after 500 burn-in periods, seed 12345
Kind	Statistical reproduction. The published figure averages 10,000 draws; the instructor build averages 500 and the student default 200 (D2). At a matched draw count the reproduction is exact
Data and vintage	None external: the script simulates its data. Package frozen on 2026-09-13
Original code	`Example1_LongDifferences/SSBias_IntcpYLagdiffN_95.do` (the authors’ file, SHA-256 `07116508…4682a1e7e2`; `vendor/jel-code/SOURCE.md` records the shipped copy’s): settings, lines 20–27; seed, line 39; simulated data, lines 45–63 (intervention `vy` on line 52, disturbance `e` on line 56, recursion on line 59, burn-in dropped on line 62); levels regressions, lines 84–90 (line 87); stored draws, lines 125–128; Monte Carlo means, lines 139–140; true response, lines 156–168. Driver `all-simulate.do`, lines 18–19 (`nobs 100`, `nreps 10000`)
Benchmark	The course benchmark `REP01-levels-lp.csv`: the authors’ script at 500 draws in Stata/SE 18.5, from 1.00175750 at h=0 to 0.43152007 at h=10. Two further references: the same script at 200 draws in StataNow/SE 19.5 (0.99686521 to 0.42771590) and the authors’ shipped 10,000-draw means (0.99697095 to 0.42890212). The instructor build reproduces the 500-draw benchmark with a largest absolute difference of 4\times10^{-8}
Tolerance	Absolute 10^{-6} on every mean when the draw counts match. Against the 10,000-draw means, \lvert z\rvert<3, where z is the difference divided by \mathrm{sd}_R\sqrt{1/R+1/10{,}000}
Deliberate departures	Draws reduced from 10,000 (D2). The course code leaves out the authors’ `$a*l.d.y` term, which is zero in this variant (line 57 sets `a` to 0.00), stores each draw as `double` where the authors store `float`, and records T_h from `e(N)`, which the authors do not keep. The long-difference, cumulative-difference, and AR(1) curves of the same figure belong to REP02. The authors’ `cap cd` lines, commented out in the shipped copy so that the archive holds no absolute path, and their Palatino font setting have no effect in batch
Runtime	Instructor build (R=500): Monte Carlo 15.1 s, authors’ script 46.4 s, the whole REP01 file 63.7 s. Student default (R=200): 26.6 s for the REP01 file, 18.6 s of it in the authors’ script

Reconstruct the specification

replication/rep01.do rebuilds the target in five steps, and a sixth step is yours. The blocks below follow that file. To run them yourself, start Stata in the project’s top folder, type do helpers/lp_helpers.do, which loads lp_assert and lp_close, and then run the blocks of Steps 2 to 5 in order in the same session.

Step 1 · Read the authors’ simulation

The whole target comes from about twenty lines of the authors’ script. Read them before running anything.

* SSBias_IntcpYLagdiffN_95.do, lines 39-62 (blank lines removed, indentation normalized)
set seed 12345
qui forvalues i = 1(1)$nreps{
    noi disp "`i'," , _continue
    preserve
    clear
    set obs  $tobs
    gen t = _n
    sort t, stable
    tsset t
    *** Generate data from the model
    gen vy  = rnormal()
    gen y   = 0
        *!!! add noise and lagdiff
        gen e=rnormal()
        global a 0.00
    replace y = $rho * l.y + $a * l.d.y + vy + e    if _n > 2
    *** Drop the burn-in sample
    drop if _n <= $burn

* lines 83-90
    *** Estimate the LP in levels
    forvalues h = 0/$hmax{
*       reg f`h'.y y
*       local b_level_`h' = _b[y]
        reg f`h'.y vy l.y /*l.d.y*/  // cons and N lag diff
        local b_level_`h' = _b[vy]
        }

Read the result. In the lecture’s notation vy is the intervention s_t and e the disturbance v_t; both are standard normal, and all 600 values of vy are drawn before any value of e. Line 59 is y_t=0.95\,y_{t-1}+s_t+v_t, so \theta_0=1 and the true response is \theta_h=0.95^h, which lines 156–168 store as rt. The first two periods stay at zero, and the 500 periods dropped on line 62 make that start irrelevant. Line 87 is the local projection of the lecture’s smallest model with \mathbf w_t=y_{t-1} and p=1. After the burn-in the sample has T=100 periods; l.y is missing in the first of them and fh’.y` in the last h, so the regression at horizon h uses T_h=99-h rows. The authors keep the coefficient and nothing else: no row count and no standard error.

Checkpoint. Before restore, the loop also fits an AR(1), long differences, and cumulated differences. Say why none of those regressions can change the draws that the levels regression sees.

Step 2 · One realization, one horizon

Rebuild the first draw outside the loop and run the h=0 regression.

local rho  = 0.95
local burn = 500
local tobs = 600
clear
set seed 12345
set obs `tobs'
generate t = _n
tsset t
generate vy = rnormal()           // line 52: the intervention s_t, drawn first
generate y  = 0                   // line 53: stored as float, as in the authors' code
generate e  = rnormal()           // line 56: the disturbance v_t, drawn second
replace y = `rho'*L.y + vy + e if _n > 2      // line 59; the term in a is zero
drop if _n <= `burn'              // line 62: keep the last 100 periods
replace t = _n
tsset t
regress F0.y vy L.y
lp_assert "REP01 step 1: the h = 0 regression has T_0 = 99 rows" : e(N) == 99
lp_close _b[vy] 1.06035137, tol(1e-6) label(REP01 step 1: draw 1 at h = 0)

Read the result. The first draw gives \hat\beta_0=1.060351 on 99 rows, 0.06 above \theta_0=1. The block keeps the authors’ storage of y as a float, so this is their first draw, not a draw like it. The check’s target, 1.06035137, is the coefficient as the authors’ float variable holds it: display %11.8f float(_b[vy]) prints it after the regression. The build’s double copy, 1.06035143, differs from it by 6\times10^{-8}.

Checkpoint. Both checks pass. Explain the 99 without running anything: which row is lost, and why.

Step 3 · The same draw at every horizon

tempfile draw1
tempname D
postfile `D' h double b_draw1 T_draw1 using `draw1'
forvalues h = 0/10 {
    quietly regress F`h'.y vy L.y
    post `D' (`h') (_b[vy]) (e(N))
}
postclose `D'
use `draw1', clear
list, clean noobs
lp_assert "REP01 step 2: T_h = 99 - h in draw 1" : T_draw1 == 99 - h

Read the result. Rounded to six decimals, draw 1 gives 1.060351, 0.999817, 0.596461, 0.555731, 0.403161, 0.213559, 0.088265, −0.148038, −0.282293, −0.250712, and 0.243100 at h=0,\dots,10. The true response never falls below 0.95^{10}=0.599. This sample says the response turns negative seven periods out and recovers by the tenth, and neither statement is true of the economy that produced it. Posting e(N) with the coefficient keeps each point attached to its rows, and rep01.do checks all eleven values against the authors’ stored ones at 10^{-6}.

Checkpoint. In the second figure of the instructor build, find the horizons at which draw 1 lies outside the middle 90 percent of the 500 draws. Use the lecture’s section on the residual to explain why those horizons sit next to each other.

Step 4 · The Monte Carlo

capture mkdir output
if "$R" == "" global R 200            // the student default (D2); master.do sets it
tempname M
postfile `M' rep h double b T_h using "output/rep01-draws.dta", replace
set seed 12345                        // once, before the loop, as on line 39
quietly forvalues r = 1/$R {
    clear
    set obs 600
    generate t = _n
    tsset t
    generate vy = rnormal()
    generate y  = 0
    generate e  = rnormal()
    replace y = 0.95*L.y + vy + e if _n > 2
    drop if _n <= 500
    replace t = _n
    tsset t
    forvalues h = 0/10 {
        regress F`h'.y vy L.y
        post `M' (`r') (`h') (_b[vy]) (e(N))
    }
}
postclose `M'
use "output/rep01-draws.dta", clear
lp_assert "REP01: every draw has T_h = 99 - h rows" : T_h == 99 - h
collapse (mean) mean_R=b (sd) sd_R=b, by(h)

Read the result. With R=500 the instructor build reproduces the benchmark at every horizon. Six of the eleven rows, rounded as shown:

h	\theta_h	Benchmark, 500 draws, Stata 18.5	This build, 500 draws, StataNow 19.5	Monte Carlo SE
0	1.0000	1.00175750	1.00175746	0.0047
2	0.9025	0.86787397	0.86787396	0.0103
4	0.8145	0.73754936	0.73754938	0.0135
6	0.7351	0.62550861	0.62550860	0.0159
8	0.6634	0.51882571	0.51882570	0.0177
10	0.5987	0.43152007	0.43152008	0.0178

The benchmark column is the file as import delimited using "replication/benchmark/REP01-levels-lp.csv", clear varnames(1) encoding(utf8) reads it, the line rep01.do runs before it compares; asdouble returns the same eight decimals. The two columns never differ by as much as 5\times10^{-8}, and what difference there is comes from storage: the authors average float draws and the course averages double draws. The mean lies below \theta_h at every horizon from h=1 on, by 0.025 at h=1 and by 0.167 at h=10, which is 9.4 Monte Carlo standard errors. That gap belongs to the estimator in samples of 100 periods with \rho=0.95, not to the reproduction; Lecture 2 explains it.

Checkpoint. At the default R=200 your means must equal the authors’ own 200-draw run, replication/benchmark/REP01-author-R200-v195.csv, at 10^{-6}, and rep01.do also checks them against the 500-draw benchmark within three nested Monte Carlo standard errors. If every draw returns the same estimate, set seed has moved inside the loop.

Step 5 · Two cross-checks

The first runs the authors’ script itself at the same number of draws; the second compares the build with the 10,000 draws of the published figure.

tempfile summary author10000
save `summary'                        // the means and standard deviations of Step 4

* the authors' script at the same R, from a folder of its own
local here = c(pwd)
capture mkdir "output/rep01-author"
quietly cd "output/rep01-author"
global nobs = 100
global nreps = $R
quietly do "`here'/vendor/jel-code/SSBias_IntcpYLagdiffN_95.do"
quietly cd "`here'"
keep t rl                             // rl: the authors' mean of the levels estimates
rename (t rl) (h author_R)
merge 1:1 h using `summary', nogenerate assert(match)
lp_assert "REP01 cross-check: the authors' script and Step 4 agree at every h (1e-6)" : abs(author_R - mean_R) < 1e-6

* the published figure's means, treated as an independent stream of 10,000 draws
preserve
use "vendor/jel-code/SSBias_IntcpYLagdiffN_95.dta", clear
keep t rl
rename (t rl) (h author_10000)
save `author10000'
restore
merge 1:1 h using `author10000', nogenerate assert(match)
generate double se_10000 = sd_R*sqrt(1/$R + 1/10000)
generate double z_10000  = (mean_R - author_10000)/se_10000
format mean_R author_R author_10000 %11.8f
format z_10000 %6.2f
list h mean_R author_R author_10000 z_10000, clean noobs
lp_assert "REP01 statistical: |z| < 3 against the 10,000-draw means at every h" : abs(z_10000) < 3

Read the result. At R=500 the authors’ script and rep01.do agree at every horizon within 4\times10^{-8}. The authors’ shipped 10,000-draw means differ from the 500-draw means by at most 0.018, at h=2, where z=1.71, and no horizon comes near \lvert z\rvert=3. The published figure is reproduced as a statistical object; the 500-draw curve is the authors’ own curve at that draw count.

Checkpoint. Explain why the comparison with the 10,000-draw means cannot be exact, and why its standard error adds 1/10{,}000 to 1/R rather than subtracting it.

Step 6 · Write the construction note

In about 150 words, write down what REP01 reproduces for a reader who has only Figure 1a: which variable is s_t and how it is drawn, which rows enter the regression at horizon h and how many, what the curve averages and over how many draws, and what the authors’ output does not contain. Add one sentence on the gap between the curve and 0.95^h that describes it without explaining it.

Checkpoint. Someone else should be able to rerun the target from your note and vendor/jel-code/ alone.

Discrepancy guidance

When your number differs, record it before you change anything. A row of the discrepancy log has six fields: the object (which mean, at which horizon, at which R), the published value and its source, the reproduced value, the class (data, specification, software, inference, or presentation), a diagnosis, and a status (resolved, accepted as a departure, or open). For this target the likely causes are few, and each leaves a recognizable trace.

What you see	Most likely cause	Class
Every mean within 10^{-7} of the reference but not identical to it	`float` versus `double` storage of the draws or of `y`	software
Every mean off by more than 10^{-6} but by less than three Monte Carlo standard errors	a different random stream: `e` drawn before `vy`, another seed, or another `set obs`	specification
A standard deviation of zero across draws	`set seed` inside the loop	specification
T_h=599-h	the burn-in was never dropped	specification
T_h=100-h	`L.y` left out of the regression, which also changes the estimate	specification
Your means match the 200-draw file but not the 500-draw benchmark	a different R: compare with the reference for your draw count	specification
A curve with a different shape or level everywhere	another variant of the script: `IntcpN` drops the intercept, `LagdiffY` adds \Delta y_{t-1} (REP02)	specification
A difference between Stata 18.5 and StataNow 19.5 beyond 10^{-6}	a software change (D1); the instructor build found none	software

Part B · Stata problem set STA01

The problem set runs the lecture’s argument in the order construct, estimate, diagnose, interpret. starter/pset.do gives the data steps, the files to write, and the checks; the lines marked TASK are yours. The checks are the lp_assert and lp_close lines at the end of each task. Each prints pass or FAIL, and the first failure stops the file. They test what a machine can test; the captions in Tasks 4 and 5 and the paragraph in Task 5 are read by a person against the slots and sentences listed below. The tasks follow Exercises 3, 4, 6, 7, and 9 of the Lecture 01 exercises, whose hints apply here. A worked answer ships as solution/pset_solution.do, and the instructor build shows it task by task with its output; read either after your own attempt.

Task 1 · Construct the rows for h=0,1,2

Read the hand table (data/raw/hand_table.csv, or the copy that the Explorer’s Lab 2 exports) and, for each horizon, mark the rows of the regression of y_{t+h} on s_t and y_{t-1} without running it: the lead y_{t+h}, the rows with t\ge2 and a lead that exists, and their counts.

Deliverable. output/pset/results_hand.dta with h, T_h, n1 (intervention rows), n0 (comparison rows), first, and last.
Checks. T_h=11-h; every row is an intervention row or a comparison row; the rows run from t=2 to t=12-h; three intervention rows at h=0 and two at h=1 and h=2.

Task 2 · Estimate the slopes from the rows

On the same rows, compute the group means \bar y_1 and \bar y_0, compute the slope by hand as \sum_t(s_t-\bar s)\,y_{t+h}/\sum_t(s_t-\bar s)^2, confirm it with regress, and add y_{t-1} on the same rows.

Deliverable. The means and the three slopes, added to results_hand.dta.
Checks. The slope by hand equals \bar y_1-\bar y_0 within 10^{-6}; regress returns the same slope; both regressions use exactly the rows of Task 1; the slopes are 0.617322, −0.983356, and 2.050024 without the control and 0.575667, −1.050405, and 2.153022 with it.

Task 3 · A response in a loop

On onedraw_rho09_seed2.csv, the T=200 sample that Lab 3 displays, regress y_{t+h} on a constant, s_t, and y_{t-1} for h=0,\dots,12, posting each coefficient with its e(N).

Deliverable. output/pset/results_onedraw.dta with h, beta_h, and T_h.
Checks. T=200; T_h=199-h; \hat\beta_0=0.878940 and \hat\beta_{12}=-0.293297 within 10^{-6}; the estimate lies below \theta_h=0.9^h at all thirteen horizons.

Task 4 · Many draws, one graph, a caption with four slots

Write the Monte Carlo loop of Exercise 7: seed 3 set once for each \rho\in\{0.5,0.9\}, 300 periods with all of s drawn before any v, the first 100 dropped, and at each horizon the slope with and without y_{t-1}. The given code summarizes the first 200 samples. Then draw Task 3’s estimates against 0.9^h with the simulated 5–95 percent band. Fill the caption’s four slots before you draw: what one unit of the intervention is, the outcome’s units, the horizon unit, and what a value of zero is compared with.

Deliverable. output/pset/mc_draws.dta, mc_R200_summary.dta, fig-sta01-one-draw.svg and .png, and fig-sta01-one-draw-caption.txt.
Checks. 199-h rows with the control and 200-h without; with R=200, at \rho=0.9 and h=8, a mean of 0.370337 and a standard deviation of 0.211226 within 10^{-6}; without the control a larger spread at every horizon when \rho=0.9; all four caption slots filled; the graph exported. The caption is read for the four slots.

Task 5 · Military news: the response, its variation, one episode

data/raw/get_rz.do downloads Ramey and Zubairy’s February 2018 package from the authors’ link and verifies its SHA-256, or prints the manual steps; the course does not redistribute the workbook (D5, D35). The starter reads it with import excel using "data/raw/RZDAT.xlsx", sheet("rzdat") firstrow clear. Trend GDP is Ramey and Zubairy’s rgdp_pott6, the series they call potential GDP and estimate as a sixth-degree polynomial trend in real GDP. Build y_t=\texttt{rgdp}_t/\texttt{rgdp\_pott6}_t and the news as a fraction of the previous quarter’s nominal trend GDP, estimate the response for h=0,\dots,20, compute each quarter’s share of \sum_t(s_t-\bar s)^2 in the h=8 sample, re-estimate h=8 without 1950Q3, and write the caption and a five-sentence paragraph headed “What has not yet been argued.”

Deliverable. output/pset/first_contact.dta, sta01-news-shares.csv, fig-sta01-first-contact.svg and .png, the caption file, and not-yet-argued.txt.
Checks. 508 consecutive quarters; the news recorded in 504 of them; the news in 1950Q3 equal to 0.600073; T_h=504-h; \hat\beta_8=0.361906 and \hat\beta_{10}=0.404210, with the peak at h=10; 1941Q4 and 1950Q3 the two largest shares, 0.261211 and 0.195838; without 1950Q3, 0.433969 on 495 rows; with Ramey and Zubairy’s controls, 0.29376385 at h=10 on 490 rows, the linear GDP response in the course’s REP04 benchmark. The paragraph is read for one sentence each on units, controls, identification, uncertainty, and dependence on a few episodes.

Part C · The browser-lab handoff

The “Transfer to Stata” section of the Shock-to-Response Explorer writes three files: l01-explorer-handoff.json, hand_table.csv, and the draw file chosen in Lab 3. Put them in the project’s handoff/ folder, replacing the sample there; handoff/README.md in the archive lists every key of the record.

Explorer lab	What the record holds	Where Stata uses it
Lab 2	`hand_table.csv`; the chosen h, control, and single-episode setting; the browser’s T_h and slope	Tasks 1–2 read the file when its SHA-256 equals the shipped copy’s; `check_handoff.do` reruns the regression
Lab 3	The draw file, T, the control choice, and thirteen slopes and row counts	Task 3 reads the draw when its values equal the shipped copy’s; `check_handoff.do` reruns all thirteen regressions
Lab 4	Your hypothesis about the h=8 coefficient without 1950Q3, and the stored estimate for your settings	Task 5 prints the hypothesis beside its own estimate; `check_handoff.do` re-estimates the stored coefficient and sets the hypothesis against it

Lab 4 displays only estimates computed in Stata from the Ramey–Zubairy data, never data rows (D33), so its part of the check waits until Task 5 has downloaded the workbook. The hypothesis is read for a direction (raise, lower, or unchanged) and a number, and the verdict goes to output/handoff-check.csv without a grade. The sample record shipped with the project predicts that dropping 1950Q3 lowers the estimate to about 0.30. The estimate rises, from 0.361906 to 0.433969, and the check records the prediction as refuted.

Submission package

Deliverable	Required contents
Replication record	The target (Figure 1a, levels curve, h=0,\dots,10), the package commit, the draw count you ran, `output/rep01-benchmark.csv`, a sentence comparing your StataNow run with the Stata 18.5 benchmark at your draw count, the construction note of Step 6, and any discrepancy-log rows
Stata submission	The project folder with your `starter/pset.do`; `output/master.log` ending in `MASTER COMPLETE`; `output/assertions.csv`; the `output/pset/` files listed under each task; the REP01 figures
Interpretation record	For Task 5: the estimand \theta_h and the assumptions under which \beta_h=\theta_h, the units of the news and of GDP relative to trend, the absence of standard errors, and the “not yet argued” paragraph
Lab record	Your `l01-explorer-handoff.json` with its four predictions, `output/handoff-check.csv`, and one paragraph on what the chain of four labs showed you

Mastery requirement

The practicum is done when you can say, with the numbers from your own run and without notes:

Each point of the levels curve is the coefficient on s_t in a regression of y_{t+h} on a constant, s_t, and y_{t-1} over 99-h rows, averaged over the draws; at 500 draws it reproduces the published benchmark to within 10^{-6}, and it lies below 0.95^h for a reason Lecture 2 explains. In the military-news data the same regression averages over every quarter with news, weighted by (s_t-\bar s)^2, so two war quarters carry 46 percent of its variation and dropping one of them moves the estimate at h=8 by 0.07. It is not yet the causal response to the news: its units, controls, identification, and uncertainty are still to be argued.

References

Jordà, Òscar, and Alan M. Taylor. 2025. “Local Projections.” Journal of Economic Literature 63 (1): 59–110. https://doi.org/10.1257/jel.20241521.

Ramey, Valerie A., and Sarah Zubairy. 2018. “Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data.” Journal of Political Economy 126 (2): 850–901. https://doi.org/10.1086/696277.