FamaMacBeth kernel covariance over-rejects in short panels
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调研方向
Start by running the reproduction script in the issue, which fits FamaMacBeth with cov_type="kernel" and counts rejections of the x coefficient at the 5% level. Then read the cov_type handling in FamaMacBeth.fit and the f_statistic_robust method, along with the docstrings the issue says describe the problem. The issue leaves the fix open between fixed-b critical values and a cosine estimator, so the work needs a maintainer decision first. Done means the kernel-covariance tests reach roughly nominal size at T = 10 and T = 40.
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描述
With cov_type="kernel", the t-tests of FamaMacBeth reject a true null far more often than their nominal level, even when the cross-sectional estimates are independent.
import numpy as np
import pandas as pd
from linearmodels import FamaMacBeth
rng = np.random.default_rng(0)
n, t, reps = 100, 10, 2000
idx = pd.MultiIndex.from_product([range(n), range(t)])
rejections = 0
for _ in range(reps):
data = pd.DataFrame(
{"y": rng.standard_normal(n * t), "x": rng.standard_normal(n * t), "const": 1.0},
index=idx,
)
res = FamaMacBeth(data.y, data[["const", "x"]]).fit(cov_type="kernel")
rejections += res.pvalues["x"] < 0.05
print(rejections / reps) # 0.174
The 5% test rejects in 17.4% of the samples with T = 10 and in about 12% with T = 40. With cov_type="unadjusted" both are about 5%. The joint test in f_statistic_robust is worse with more parameters: about 37% with 3 parameters and T = 10.
A kernel estimate of the long-run variance from T estimates is much noisier than the sample variance, and the t(T - 1) and F reference distributions ignore this. The docstrings describe the problem as of 7.1.
Deferred from 7.1. Possible fixes are fixed-b critical values (Kiefer and Vogelsang, 2005) or an equal-weighted cosine estimator with t and F reference distributions (Lazarus, Lewis, Stock and Watson, 2018).
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