FixedEffectsOLS

Within-estimator for high-dimensional fixed effects

Code 
from _api_doc_utils import *

1 Where it fits

Group: Regression

FixedEffectsOLS partials out one or more categorical fixed effects, then runs least squares on residualized variables:

\[ M_F y = M_F X\beta + M_F u. \]

The fixed-effect matrix fe is a 2D uint32 array of zero-based category codes, one column per fixed-effect dimension.

2 Python API

Constructor: cm.FixedEffectsOLS

Call fit(x, fe, y) or fit_weighted(x, fe, y, sample_weight). There is no predict() because the class is estimation-first and does not materialize fixed-effect coefficients. summary() supports the same covariance options as the other linear estimators and reports absorbed_df, residual_df, and absorbed_df_method. Rank is exact for one- and two-way fixed effects; three or more dimensions use a labeled conservative count.

Code 
print(inspect.signature(cm.FixedEffectsOLS))
Code 
cls = cm.FixedEffectsOLS
display(HTML(html_table(["Public method"], public_methods(cls))))

3 Minimal example

Code 
rng = np.random.default_rng(3)
n = 300
x = rng.normal(size=(n, 2))
worker = rng.integers(0, 30, size=n, dtype=np.uint32)
firm = rng.integers(0, 12, size=n, dtype=np.uint32)
fe = np.column_stack([worker, firm]).astype(np.uint32)
y = x @ np.array([0.8, -0.5]) + rng.normal(size=30)[worker] + rng.normal(size=12)[firm] + rng.normal(scale=0.2, size=n)
model = cm.FixedEffectsOLS()
model.fit(x, fe, y)
print(model.summary(vcov='cluster', clusters=worker.astype(np.int64)))

4 summary() contract

The table below is generated by fitting the live class in this repository and then inspecting summary(). Shapes are shown because most values are plain NumPy arrays or scalars.

Code 
rng = np.random.default_rng(103)
n = 100
x = rng.normal(size=(n, 2))
g = rng.integers(0, 10, size=n, dtype=np.uint32)
h = rng.integers(0, 5, size=n, dtype=np.uint32)
fe = np.column_stack([g, h]).astype(np.uint32)
y = x @ np.array([0.8, -0.5]) + rng.normal(size=10)[g] + rng.normal(size=n) * 0.2
model = cm.FixedEffectsOLS()
model.fit(x, fe, y)
summary = model.summary()
display(HTML(html_table(["summary() key", "shape"], summary_shape_rows(summary))))