# linearmodels.iv.model.IVGMM¶

class linearmodels.iv.model.IVGMM(dependent: , exog: , endog: , instruments: , *, weights: = None, weight_type: str = 'robust', **weight_config: Any)[source]

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

Parameters:
dependent:

Endogenous variables (nobs by 1)

exog:

Exogenous regressors (nobs by nexog)

endog:

Endogenous regressors (nobs by nendog)

instruments:

Instrumental variables (nobs by ninstr)

weights: = 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

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