linearmodels.panel.covariance.DriscollKraay¶

class linearmodels.panel.covariance.DriscollKraay(y: ndarray[tuple[int, ...], dtype[float64]], x: ndarray[tuple[int, ...], dtype[float64]], params: ndarray[tuple[int, ...], dtype[float64]], entity_ids: ndarray[tuple[int, ...], dtype[integer]], time_ids: ndarray[tuple[int, ...], dtype[integer]], *, 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[tuple[int, ...], dtype[float64]]¶

(entity x time) by 1 stacked array of the dependent variable.

x: ndarray[tuple[int, ...], dtype[float64]]¶

(entity x time) by variables stacked array of the exogenous variables.

params: ndarray[tuple[int, ...], dtype[float64]]¶

Variables by 1 array of estimated model parameters.

entity_ids: ndarray[tuple[int, ...], dtype[integer]]¶

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

time_ids: ndarray[tuple[int, ...], dtype[integer]]¶

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

debiased: bool = False¶

Flag indicating whether to debias the estimator. The default is False.

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. The default is 0.

kernel: str | None = None¶

Name of the kernel. If not provided, “newey-west”, which is the Bartlett kernel, is used. The names are not case sensitive. Supported kernels are:

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

• ”parzen”, “gallant” - Parzen’s kernel

• ”qs”, “quadratic-spectral”, “andrews” - Quadratic spectral kernel

bandwidth: float | None = None¶

Non-negative bandwidth to use. It must be below the number of time periods. The Bartlett and Parzen kernels use its integer part. If not provided a rule-of-thumb value is used.

Raises:¶

• ValueError – If the bandwidth, or the default bandwidth if none is given, is not below the number of time periods. It is also raised if the model has no residual degrees of freedom: the number of observations less extra_df, and less the number of regressors if debiased is True, is not positive.

• UnknownOptionError – If kernel is not one of the supported names. It is both a ValueError and a KeyError.

Notes

Bandwidth is set to the common value for the Bartlett kernel if not provided, \(\lfloor 4 (T / 100)^{2/9} \rfloor\) where \(T\) is the number of time periods.

The estimator of the covariance is

\[n^{-1}\hat{\Sigma}_{xx}^{-1}\hat{S}\hat{\Sigma}_{xx}^{-1}\]

where

\[\hat{\Sigma}_{xx} = n^{-1}X'X\]

and

\[\begin{split}\xi_t & = \sum_{i=1}^{n_t} \epsilon_i x_{i} \\ \hat{S}_0 & = \sum_{i=1}^{t} \xi'_t \xi_t \\ \hat{S}_j & = \sum_{i=1}^{t-j} \xi'_t \xi_{t+j} + \xi'_{t+j} \xi_t \\ \hat{S} & = (n-df)^{-1} \sum_{j=0}^{bw} K(j, bw) \hat{S}_j\end{split}\]

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

The sums \(\xi_t\) of the scores of the \(T\) time periods have autocovariances up to lag \(T-1\), so the bandwidth must be below \(T\). The bandwidth is checked when the estimator is created, so that the fit method of a model raises the error.

Changed in version 7.1: A bandwidth that is not below the number of time periods raises a ValueError. Earlier versions raised “Length of w is larger than the number of elements in z” with the Bartlett and Parzen kernels, when the covariance was first used. The quadratic spectral kernel, which has no truncation, returned a covariance without an error. With a large bandwidth the weights of all of the lags are close to one, and the sum of the scores over all of the periods is zero in a regression, so that the covariance was close to zero.

Changed in version 7.1: A kernel that is not one of the supported names raises an UnknownOptionError when the estimator is created, so that the fit method of a model raises. Earlier versions raised it when the covariance was first used, for example when std_errors of the results was read, so that fit returned results that raised when the covariance was used.

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.