linearmodels.iv.model.IVGMM¶

class linearmodels.iv.model.IVGMM(dependent: IVData | ndarray | DataArray | DataFrame | Series, exog: IVData | ndarray | DataArray | DataFrame | Series | None, endog: IVData | ndarray | DataArray | DataFrame | Series | None, instruments: IVData | ndarray | DataArray | DataFrame | Series | None, *, weights: IVData | ndarray | DataArray | DataFrame | Series | None = None, weight_type: str = 'robust', **weight_config: Any)[source]¶

Estimation of IV models using the generalized method of moments (GMM)

Parameters:¶

dependent: IVData | ndarray | DataArray | DataFrame | Series¶

Endogenous variables (nobs by 1)

exog: IVData | ndarray | DataArray | DataFrame | Series | None¶

Exogenous regressors (nobs by nexog)

endog: IVData | ndarray | DataArray | DataFrame | Series | None¶

Endogenous regressors (nobs by nendog)

instruments: IVData | ndarray | DataArray | DataFrame | Series | None¶

Instrumental variables (nobs by ninstr)

weights: IVData | ndarray | DataArray | DataFrame | Series | None = None¶

Observation weights used in estimation

weight_type: str = 'robust'¶

Name of moment condition weight function to use in the GMM estimation

**weight_config

Additional keyword arguments to pass to the moment condition weight function

Notes

Available GMM weight functions are:

• “unadjusted”, “homoskedastic” - Assumes moment conditions are homoskedastic

• “robust”, “heteroskedastic” - Allows for heteroskedasticity by not autocorrelation

• “kernel” - Allows for heteroskedasticity and autocorrelation

• “cluster” - Allows for one-way cluster dependence

The estimator is defined as

\[\hat{\beta}_{gmm}=(X'ZW^{-1}Z'X)^{-1}X'ZW^{-1}Z'Y\]

where \(W\) is a positive definite weight matrix and \(Z\) contains both the exogenous regressors and the instruments.

Todo

• VCV: bootstrap

See also

linearmodels.iv.model.IV2SLS, linearmodels.iv.model.IVLIML, linearmodels.iv.model.IVGMMCUE

Methods

estimate_parameters(x, y, z, w)	param x: Regressor matrix (nobs by nvar)
fit(*[, iter_limit, tol, initial_weight, ...])	Estimate model parameters
from_formula(formula, data, *[, weights, ...])	param formula: Formula modified for the IV syntax described in the notes
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	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