# linearmodels.iv.model.IVGMM¶

class IVGMM(dependent, exog, endog, instruments, *, weights=None, weight_type='robust', **weight_config)[source]

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

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

weight_typestr, default “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

Methods

 estimate_parameters(x, y, z, w) Parameters fit(self, \*, iter_limit, tol, …) 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