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Driscoll-Kraay and clustered standard errors for a panel local projection

Clustering by entity is the reflex. On a panel hit by a common shock it is the wrong reflex, and it does not fail loudly — it fails by making your standard errors smaller. tsecon.panel_lp exposes the choice as se_type, and this recipe shows what each one is actually correcting.

The recipe

import numpy as np, tsecon

rng = np.random.default_rng(5)
N, T = 30, 120                                       # 30 countries, 120 quarters
shock = rng.standard_normal(T)                       # ONE common shock, same for everyone
common = rng.standard_normal(T)                      # an unobserved common factor
alpha = rng.normal(0, 1, N)                          # entity fixed effects
y = np.zeros((N, T))                                 # outcome is N x T
for i in range(N):
    for t in range(1, T):
        y[i, t] = (alpha[i] + 0.5 * y[i, t - 1] + 0.8 * shock[t]
                   + 0.9 * common[t] + rng.standard_normal())

for se in ("nonrobust", "cluster", "driscoll_kraay"):
    r = tsecon.panel_lp(y, shock, horizon=6, n_lag_controls=2, se_type=se)
    band = " ".join(f"{s:.3f}" for s in r["se"][:4])
    tstat = r["irf"][2] / r["se"][2]
    print(f"{se:>15}   se(h=0..3) {band}   t at h=2 {tstat:6.2f}")

      nonrobust   se(h=0..3) 0.026 0.032 0.033 0.034   t at h=2   9.31
        cluster   se(h=0..3) 0.021 0.022 0.022 0.023   t at h=2  14.18
 driscoll_kraay   se(h=0..3) 0.086 0.142 0.142 0.128   t at h=2   2.18

Reading it

The point estimates are identical across all three rows — only the uncertainty changes. What changes is dramatic:

  • cluster made things worse. Clustering by entity allows arbitrary correlation within a country over time, and assumes independence across countries. This panel violates exactly that assumption: a common factor hits every country in the same quarter. The t-statistic goes up, from 9.3 to 14.2. Nothing warns you.
  • driscoll_kraay is four to six times wider and drops the t-statistic to 2.2. It clusters by time and applies a HAC kernel across periods, so it absorbs both the cross-sectional dependence and the serial correlation the local projection guarantees.

When the regressor is a single common shock — one number per period, shared by every unit — the effective sample size is closer to T than to N × T. Driscoll-Kraay is the estimator that knows this. Reach for cluster when your shock varies across entities and cross-sectional dependence is genuinely implausible.

Building the band

r = tsecon.panel_lp(y, shock, horizon=6, n_lag_controls=2, se_type="driscoll_kraay")
for h in range(7):
    lo = r["irf"][h] - 1.96 * r["se"][h]
    hi = r["irf"][h] + 1.96 * r["se"][h]
    print(f"h={h}   {r['irf'][h]:+.3f}   [{lo:+.3f}, {hi:+.3f}]")

h=0   +0.731   [+0.563, +0.899]
h=1   +0.515   [+0.237, +0.794]
h=2   +0.310   [+0.032, +0.588]
h=3   +0.239   [-0.012, +0.490]
h=4   +0.140   [-0.141, +0.421]
h=5   +0.226   [-0.084, +0.535]
h=6   +0.125   [-0.129, +0.380]

Under Driscoll-Kraay the response is significant through h=2 and indistinguishable from zero afterwards. Under clustered standard errors every horizon would have looked significant.

Gotchas

  • Shapes. outcome is N × T (entities by time); shock is length T. tsecon.panel_fe takes the same outcome plus regressors as k × N × T and offers the same se_type menu.
  • bandwidth sets the Driscoll-Kraay kernel width. Like any HAC bandwidth it moves the answer; report it.
  • jackknife=True applies the Dhaene-Jochmans half-panel correction for Nickell bias — worth using when T is short and lagged dependent variables are in the controls.
  • cumulative=True switches to the Ramey-Zubairy cumulated-outcome convention.
  • Slopes genuinely heterogeneous across units? A pooled estimator is the wrong model, not the wrong standard error — see tsecon.panel_mean_group and tsecon.panel_pmg.

See also