The dynamic path of the park effect
A park is not a switch — its effect on nighttime light builds for ~5 years. The event study normalizes every coefficient to the year before opening (k = −1): the four pre-opening leads should hug zero (the parallel-trends signature), then the post-opening path rises. Drag the post-horizon slider to reveal years one at a time, and simulate a noisy draw to see why only 17 treated woredas make late-year estimates wobble.
The three takeaways of this lab
- A flat pre-trend, then a rising effect to a +0.48 plateau. Pre-opening leads run −0.027 to −0.001 (largest |t| = 2.17); the effect jumps to +0.115 at k = 0 and climbs to +0.484 by k = 4 — which is why the naive 2×2 (+0.201) understates the long-run ATT.
- Modern estimators agree with TWFE — the staggered-bias problem is empirically negligible here. TWFE, Sun-Abraham, Borusyak/Gardner and Callaway-Sant'Anna all land in 0.21–0.30 because 95.4% of the TWFE weight is "clean" treated-vs-never comparisons.
- The average hides the story — women gain where the pooled effect is null. Non-ag employment is +0.091 (ns) overall but +0.140*** for women and ≈ 0 for men; empowerment and household welfare follow the jobs.
How many post-opening years to show (k = 0 … this). Pre-opening leads are always shown.
The real study had only 17 — fewer treated units make the simulated path wobble more.
Add a slope to the pre-opening leads to break parallel trends (the true study's is ≈ 0).
Orange = the post's published IHS-light coefficients (teal markers = significant post-opening, grey = not). Steel dashed = your simulated draw. The shaded left band is the pre-trend region. Move a slider to redraw.
Key concepts
Event-study / dynamic DiD
Instead of one "after" coefficient, estimate a separate effect for each year relative to opening (event time k). The leads (k < 0) test the parallel-trends assumption; the lags (k ≥ 0) trace the build-up of the effect.
Parallel trends (the identifying assumption)
Absent the park, treated and control woredas would have followed the same light path. It is untestable, but flat pre-opening leads are suggestive support. Here the largest pre-period |t| is just 2.17.
ATT — average treatment effect on the treated
The effect on the woredas that actually got a park, under parallel trends. Every estimator in this lab targets the same ATT; this is an observational setting (parks are not randomly placed), so the FE design does confounding control, not precision-only adjustment.
Why the naive 2×2 understates the effect
Collapsing the staggered design at the median opening year (2017) gives a 2×2 DiD of +0.201. Because the effect ramps up over 5 years, averaging the small early post-years with the large late ones pulls that blended number below the long-run ATT.
Forbidden comparisons & negative weights
Under staggered timing, two-way fixed effects quietly uses already-treated units as controls for later-treated ones. When effects grow over time these "forbidden" comparisons get negative weights and can bias — even flip — the estimate. Here they carry just 1.2% of the weight, so the bias is negligible.
Repeated-cross-section DiD
When each survey round samples different households (no panel key), you cannot use unit fixed effects. The effect is identified off district × round group means, absorbing district and region × round fixed effects — used here for the DHS welfare and employment outcomes.
Conley spatial-HAC standard errors
Because the 17 treated woredas cluster in space, a regional shock hits several at once, so errors are not independent draws. Conley errors let a district's errors correlate with nearby districts in the same year; here the SE inflates 2.43× (0.033 → 0.080) yet the effect stays significant.
Four estimators, one estimand — and the Goodman-Bacon teaching moment
Under staggered timing, two-way fixed effects (TWFE) can use already-treated units as controls — the "forbidden comparisons" that can flip its sign. Three modern estimators avoid them. Here all four land in the same 0.21–0.30 band. The Goodman-Bacon decomposition shows why: toggle the forbidden comparisons to see how little weight they carry.
TWFE vs Sun-Abraham vs Borusyak/Gardner vs Callaway-Sant'Anna ATT on IHS night-light, with 95% intervals. The teal band marks the 0.21–0.30 agreement zone. Hover for the SE and method note.
Clean weight (treated vs never)
95.4%
avg 2×2 = +0.271
Clean weight (earlier vs later)
3.4%
avg 2×2 = +0.337
Forbidden weight (later vs earlier)
1.2%
avg 2×2 = +0.014
Each bubble is one of the 64 underlying 2×2 comparisons; bubble size ∝ its Goodman-Bacon weight. Teal = clean treated-vs-never, steel = clean earlier-vs-later, orange = forbidden later-vs-earlier. The dashed line is the TWFE coefficient (+0.270).
What to look for
- The four estimator intervals overlap heavily — a spread of only 0.046 IHS units across methods that can diverge sharply in other settings.
- The big teal bubbles (treated vs never) sit near the TWFE line and carry 95.4% of the weight — they are the headline.
- Toggle the highlight: the orange forbidden bubbles are tiny (1.2% of weight) and near zero, so they barely move TWFE. The negative-weights problem is real in principle but empirically negligible whenever a large never-treated pool dominates.
Location fundamentals: the effect fades with distance, roads amplify it
A park does not lift every woreda equally. The implied effect on raw light fades the farther a woreda lies from an economic center and is amplified by denser roads. Pick a moderator, then drag the marker along the axis to read the marginal effect — and find where it crosses zero.
Effect at the marker
—
raw-light units
Interaction slope
—
per unit of moderator
Significance
—
Implied marginal park effect = main treatment + interaction × moderator. Drag the steel marker (or click the line) to move along the axis. Orange line = a negative (fading) slope; teal = a positive (amplifying) slope.
What to look for
- All three distance interactions are negative — the effect fades with distance. Distance-to-nearest-city is the steepest (−0.0335***): the implied effect crosses zero by roughly 105 km out.
- Both road interactions are positive — denser roads amplify the effect — but only paved-road density is significant (+0.669**); primary-road density is correctly signed yet borderline (+0.326, ns).
- With only 17 treated woredas, the mutually-correlated moderators cannot all be precise at once — direction is on target everywhere; precision is what the small treated sample cannot fully deliver.
Who benefits? Welfare rises, and the gender split is the story
The satellite light effect is real — but who actually gains? Households near a park gain durables, housing, and wealth. Then the analytical climax: non-agricultural employment is null on average yet large and significant for women, and the empowerment cascade (decision power, savings, falling acceptance of domestic violence) follows the jobs.
ATT with 95% intervals. Teal = significantly positive, orange = significantly negative, grey = not significant. A bar crossing the dashed zero line is indistinguishable from "no effect". Hover a row for the SE, CI, and base rate.
Employment — full sample
+0.091
t = 1.57 · NULL
Employment — women
+0.140
t = 3.00 · ***
Employment — men
+0.018
t = 0.19 · ≈ 0
Repeated-cross-section phase event studies: household durables (orange) and women's non-ag employment (teal). Both have flat pre-phases and jump at phase 0 — the RCS analogue of a clean pre-trend.
What to look for
- Welfare rises broadly: durables +0.229***, housing +0.248***, wealth +0.383*** — adding controls barely moves them, confirming the FE design absorbs the main confounding.
- The pooled employment bar straddles zero (+0.091, ns) — read alone it would say "parks don't move jobs". Switch to "by sex": the +0.140*** female gain is diluted by the ≈ 0 male effect. The split is the finding.
- Empowerment follows: decision power +0.110***, savings +0.315*** (enormous off a 6.3% base), and acceptance of domestic violence falls −0.210*** — economic agency translating into bargaining power and shifting norms.