linearmodels.panel.covariance.DriscollKraay¶

class linearmodels.panel.covariance.DriscollKraay(y: ndarray, x: ndarray, params: ndarray, entity_ids: ndarray, time_ids: ndarray, *, debiased: bool = False, extra_df: int = 0, kernel: str | None = None, bandwidth: float | None = None)[source]¶

Driscoll-Kraay heteroskedasticity-autocorrelation robust covariance estimation

Parameters:¶

y: ndarray¶

(entity x time) by 1 stacked array of dependent

x: ndarray¶

(entity x time) by variables stacked array of exogenous

params: ndarray¶

variables by 1 array of estimated model parameters

entity_ids: ndarray¶

(entity x time) by 1 stacked array of entity ids

time_ids: ndarray¶

(entity x time) by 1 stacked array of time ids

debiased: bool = False¶

Flag indicating whether to debias the estimator

extra_df: int = 0¶

Additional degrees of freedom consumed by models beyond the number of columns in x, e.g., fixed effects. Covariance estimators are always adjusted for extra_df irrespective of the setting of debiased.

kernel: str | None = None¶

Name of one of the supported kernels. If None, uses the Newey-West kernel.

bandwidth: float | None = None¶

Non-negative integer to use as bandwidth. If not provided a rule-of- thumb value is used.

Notes

Supported kernels:

• “bartlett”, “newey-west” - Bartlett’s kernel

• “quadratic-spectral”, “qs”, “andrews” - Quadratic-Spectral Kernel

• “parzen”, “gallant” - Parzen kernel

Bandwidth is set to the common value for the Bartlett kernel if not provided.

The estimator of the covariance is

$$n^{-1}{\hat{\mathrm{\Sigma }}}_{xx}^{-1}\hat{S}{\hat{\mathrm{\Sigma }}}_{xx}^{-1}$$

where

$${\hat{\mathrm{\Sigma }}}_{xx}=n^{-1}{X}^{\prime }X$$

and

$$\begin{array}{rl}{\xi }_t& =\sum _{i=1}^{n_t}{ϵ}_i{x}_i\\ {\hat{S}}_0& =\sum _{i=1}^t{\xi }_t^{\prime }{\xi }_t\\ {\hat{S}}_j& =\sum _{i=1}^{t-j}{\xi }_t^{\prime }{\xi }_{t+j}+{\xi }_{t+j}^{\prime }{\xi }_t\\ \hat{S}& =(n-df{)}^{-1}\sum _{j=0}^{bw}K(j,bw){\hat{S}}_j\end{array}$$

where df is extra_df and n-df is replace by n-df-k if debiased is True. $K(i,bw)$ is the kernel weighting function.

Methods

deferred_cov()

Covariance calculation deferred until executed

Properties

ALLOWED_KWARGS
DEFAULT_KERNEL
cov	Estimated covariance
eps	Model residuals
name	Covariance estimator name
s2	Error variance