linearmodels.iv.model.IVLIML¶
- class IVLIML(dependent, exog, endog, instruments, *, weights=None, fuller=0, kappa=None)[source]¶
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
- fuller
float
,default
0 Fuller’s alpha to modify LIML estimator. Default returns unmodified LIML estimator.
- kappa
float
,default
None
Parameter value for k-class estimation. If None, computed to produce LIML parameter estimate.
Notes
kappa
andfuller
should not be used simultaneously since Fuller’s alpha applies an adjustment tokappa
, and so the same result can be computed using onlykappa
. Fuller’s alpha is used to adjust the LIML estimate of \(\kappa\), which is computed wheneverkappa
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
- Attributes
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
Methods
estimate_parameters
(x, y, z, kappa)Parameter estimation without error checking
fit
(*[, cov_type, debiased])Estimate model parameters
from_formula
(formula, data, *[, weights, ...])- Parameters
predict
(params, *[, exog, endog, data, eval_env])Predict values for additional data
resids
(params)Compute model residuals
wresids
(params)Compute weighted model residuals
Properties
Formula used to create the model
Flag indicating the model includes a constant or equivalent
Locations of observations with missing values
Locations of observations included in estimation