linearmodels.panel.model.FamaMacBeth

class FamaMacBeth(dependent, exog, *, weights=None, check_rank=True)

Pooled coefficient estimator for panel data

Parameters:

dependentarray_like

Dependent (left-hand-side) variable (time by entity)

exogarray_like

Exogenous or right-hand-side variables (variable by time by entity).

weightsarray_like

Weights to use in estimation. Assumes residual variance is proportional to inverse of weight to that the residual time the weight should be homoskedastic.

Notes

The model is given by

\[y_{it}=\beta^{\prime}x_{it}+\epsilon_{it}\]

The Fama-MacBeth estimator is computed by performing T regressions, one for each time period using all available entity observations. Denote the estimate of the model parameters as \(\hat{\beta}_t\). The reported estimator is then

\[\hat{\beta} = T^{-1}\sum_{t=1}^T \hat{\beta}_t\]

While the model does not explicitly include time-effects, the implementation based on regressing all observation in a single time period is “as-if” time effects are included.

Parameter inference is made using the set of T parameter estimates with either the standard covariance estimator or a kernel-based covariance, depending on cov_type.

Attributes:

formula

Formula used to construct the model

has_constant

Flag indicating the model a constant or implicit constant

not_null

Locations of non-missing observations

Methods

fit([cov_type, debiased, bandwidth, kernel])	Estimate model parameters
from_formula(formula, data, *[, weights, ...])	Create a model from a formula
predict(params, *[, exog, data, context])	Predict values for additional data
reformat_clusters(clusters)	Reformat cluster variables

Properties

formula	Formula used to construct the model
has_constant	Flag indicating the model a constant or implicit constant
not_null	Locations of non-missing observations