Two-way clustered covariance of the panel models can have negative variances
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调研方向
Start with the reproducer in the issue: PooledOLS(...).fit(cov_type='clustered', cluster_entity=True, cluster_time=True) yields a negative diagonal in res.cov. Read the clustered covariance code path that fit reaches, where the one-way covariances are summed and the intersection term is subtracted, and where std_errors takes the square root. Done means a maintainer-chosen behaviour (eigenvalue clipping by default or as an option, or a named warning) and a test that covers the small-panel case. The default-versus-option decision is still open, so confirm it before writing code.
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描述
The two-way clustered covariance of the panel models (cluster_entity=True, cluster_time=True, or two cluster variables) is the sum of the two one-way clustered covariances minus the covariance clustered by their intersection (Cameron, Gelbach and Miller, 2011). It is not guaranteed to be positive semi-definite. In small panels a variance can be negative, and std_errors is then NaN, with a RuntimeWarning from np.sqrt:
import numpy as np
import pandas as pd
from linearmodels.panel import PooledOLS
rng = np.random.default_rng(4)
idx = pd.MultiIndex.from_product([range(6), range(5)], names=["entity", "time"])
df = pd.DataFrame({"x": rng.standard_normal(30), "y": rng.standard_normal(30)}, index=idx)
df["const"] = 1.0
res = PooledOLS(df.y, df[["const", "x"]]).fit(
cov_type="clustered", cluster_entity=True, cluster_time=True
)
print(np.diag(res.cov)) # [-0.005253 0.019529]
print(res.std_errors) # const is NaN, RuntimeWarning: invalid value encountered in sqrt
Options:
- Replace the negative eigenvalues of the covariance with zero, as Cameron, Gelbach and Miller (2011) suggest and as Stata's
reghdfeandvcemwaydo. This needs a decision on whether it is the default or an option, and on how to report that it happened. - Keep the covariance, and say clearly that a variance is negative (a warning naming the parameters) instead of a numpy RuntimeWarning.
Deferred from 7.1.
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