linearmodels.iv.model.IVLIML

class IVLIML(dependent, exog, endog, instruments, *, weights=None, fuller=0, kappa=None)

Limited information ML and k-class estimation of IV models

Parameters

dependentarray_like

Endogenous variables (nobs by 1)

exogarray_like

Exogenous regressors (nobs by nexog)

endogarray_like

Endogenous regressors (nobs by nendog)

instrumentsarray_like

Instrumental variables (nobs by ninstr)

weightsarray_like, default None

Observation weights used in estimation

fullerfloat, default 0

Fuller’s alpha to modify LIML estimator. Default returns unmodified LIML estimator.

kappafloat, default None

Parameter value for k-class estimation. If None, computed to produce LIML parameter estimate.

See also

IV2SLS, IVGMM, IVGMMCUE

Notes

kappa and fuller should not be used simultaneously since Fuller’s alpha applies an adjustment to kappa, and so the same result can be computed using only kappa. Fuller’s alpha is used to adjust the LIML estimate of \(\kappa\), which is computed whenever kappa is not provided.

The LIML estimator is defined as

\[\begin{split}\hat{\beta}_{\kappa} & =(X(I-\kappa M_{z})X)^{-1}X(I-\kappa M_{z})Y\\ M_{z} & =I-P_{z}\\ P_{z} & =Z(Z'Z)^{-1}Z'\end{split}\]

where \(Z\) contains both the exogenous regressors and the instruments. \(\kappa\) is estimated as part of the LIML estimator.

When using Fuller’s \(\alpha\), the value used is modified to

\[\kappa-\alpha/(n-n_{instr})\]

Todo

• VCV: bootstrap

Methods

estimate_parameters(x, y, z, kappa, float])	Parameter estimation without error checking
fit(self, \*, cov_type, debiased, \*\*cov_config)	Estimate model parameters
from_formula(formula, data, \*, weights, …)	Parameters
predict(self, params, …)	Predict values for additional data
resids(self, params)	Compute model residuals
wresids(self, params)	Compute weighted model residuals

Properties

formula	Formula used to create the model
has_constant	Flag indicating the model includes a constant or equivalent
isnull	Locations of observations with missing values
notnull	Locations of observations included in estimation