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Get HAC (Newey-West) standard errors on a regression

Serially correlated errors do not bias OLS coefficients — they wreck the standard errors. In tsecon the whole robust ladder is one keyword on tsecon.ols: se_type="nonrobust", "hc0", "hc1", or "hac". The HAC rung is the Bartlett-kernel Newey-West estimator and matches statsmodels' cov_type="HAC" to 1e-10.

The recipe

import numpy as np, tsecon

rng = np.random.default_rng(1)                     # persistent regressor, persistent errors
n = 300
x = np.zeros(n)
e = np.zeros(n)
for t in range(1, n):
    x[t] = 0.8 * x[t - 1] + rng.standard_normal()
    e[t] = 0.7 * e[t - 1] + rng.standard_normal()
y = 1.0 + 0.5 * x + e                              # true slope = 0.5
X = np.column_stack([np.ones(n), x])               # add your own constant column

for se in ("nonrobust", "hc1", "hac"):
    r = tsecon.ols(y, X, se_type=se)
    print(f"{se:>9}   beta {r['params'][1]:.4f}   se {r['bse'][1]:.4f}   t {r['tvalues'][1]:5.2f}")

nonrobust   beta 0.5298   se 0.0423   t 12.53
      hc1   beta 0.5298   se 0.0441   t 12.02
      hac   beta 0.5298   se 0.0681   t  7.78

Reading it

Three things to internalise, all visible in three lines of output.

  1. The coefficient never moves. Robust standard errors reweight uncertainty, not estimates. If a package changes your point estimate when you change se_type, something else is going on.
  2. hc1 does almost nothing here. White-type corrections fix heteroskedasticity and assume independent errors. On time series data they are just as overconfident as nonrobust. Reaching for "robust standard errors" out of cross-sectional habit is the single most common inference mistake in applied time series.
  3. HAC is 60% wider, and the t-statistic falls from 12.5 to 7.8. In a borderline case that is the difference between a published finding and a null.

tsecon.ols returns params, bse, tvalues, and the echoed se_type — no p-values, deliberately, because the right reference distribution depends on the inference you are doing. 2 * scipy.stats.norm.sf(abs(t)) is the usual normal approximation if you want one.

Choosing the bandwidth

maxlags=None (the default) uses the Newey-West rule of thumb. Set it explicitly when you know the persistence in your data outruns the rule:

print("Newey-West rule of thumb :", round(tsecon.ols(y, X, se_type="hac")["bse"][1], 4))
print("maxlags=12               :", round(tsecon.ols(y, X, se_type="hac", maxlags=12)["bse"][1], 4))

Newey-West rule of thumb : 0.0681
maxlags=12               : 0.0756

Widening the window raises the standard error by another 11%. That sensitivity is real and it is why a HAC standard error without its kernel and bandwidth is not a reportable number — say "Newey-West, Bartlett kernel, 12 lags" in the table note. When you replicate someone else's HAC t-statistic and it does not match, the bandwidth is the first suspect, not the estimator.

Gotchas

  • x is used exactly as given. tsecon.ols adds no constant; build the design matrix yourself with np.column_stack([np.ones(n), ...]).
  • use_correction toggles the small-sample \(n/(n-k)\) factor. Packages differ on this default; it is another reason two HAC numbers can disagree.
  • HAC undercovers in small samples even when the bandwidth is right — see the coverage experiment and the fixed-b / EWC discussion in the guide chapter below.
  • Estimating a long-run variance on its own rather than a regression? That is tsecon.long_run_variance.

See also