def _endogeneity_setup(self, vars=None):
"""Setup function for some endogeneity iv"""
if vars is not None and not isinstance(vars, list):
vars = [vars]
nobs = self.model.dependent.shape[0]
e2 = self.resids.values
nendog, nexog = self.model.endog.shape[1], self.model.exog.shape[1]
if vars is None:
assumed_exog = self.model.endog.ndarray
aug_exog = c_[self.model.exog.ndarray, assumed_exog]
still_endog = empty((nobs, 0))
else:
assumed_exog = self.model.endog.pandas[vars].values
ex = [c for c in self.model.endog.cols if c not in vars]
still_endog = self.model.endog.pandas[ex].values
aug_exog = c_[self.model.exog.ndarray, assumed_exog]
ntested = assumed_exog.shape[1]
from linearmodels.iv import IV2SLS
mod = IV2SLS(self.model.dependent, aug_exog, still_endog,
self.model.instruments)
e0 = mod.fit().resids.values[:, None]
z2 = c_[self.model.exog.ndarray, self.model.instruments.ndarray]
z1 = c_[z2, assumed_exog]
e1 = proj(e0, z1)
e2 = proj(e2, self.model.instruments.ndarray)
return e0, e1, e2, nobs, nexog, nendog, ntested
def wooldridge_overid(self):
r"""
Wooldridge's score test of overidentification
Returns
-------
t : WaldTestStatistic
Object containing test statistic, p-value, distribution and null
Notes
-----
Wooldridge's test examines whether there is correlation between the
model residuals and the component of the instruments that is
orthogonal to the endogenous variables. Define :math:`\tilde{z}`
to be the residuals of the instruments regressed on the exogenous
variables and the first-stage fitted values of the endogenous
variables. The test is computed as a regression
.. math ::
1 = \gamma_1 \hat{\epsilon}_i \tilde{z}_{i,1} + \ldots +
\gamma_q \hat{\epsilon}_i \tilde{z}_{i,q}
where :math:`q = n_{instr} - n_{endog}`. The test is a
:math:`n\times R^2 \sim \chi^2_{q}`.
The order of the instruments does not affect this test.
"""
from linearmodels.iv.model import _OLS
exog, endog = self.model.exog, self.model.endog
instruments = self.model.instruments
nobs, nendog = endog.shape
ninstr = instruments.shape[1]
if ninstr - nendog == 0:
import warnings
warnings.warn(
'Test requires more instruments than '
'endogenous variables', UserWarning)
return WaldTestStatistic(0,
'Test is not feasible.',
1,
name='Infeasible test.')
endog_hat = proj(endog.ndarray, c_[exog.ndarray, instruments.ndarray])
q = instruments.ndarray[:, :(ninstr - nendog)]
q_res = annihilate(q, c_[self.model.exog.ndarray, endog_hat])
test_functions = q_res * self.resids.values[:, None]
res = _OLS(ones((nobs, 1)), test_functions).fit('unadjusted')
stat = res.nobs * res.rsquared
df = ninstr - nendog
null = 'Model is not overidentified.'
name = 'Wooldridge\'s score test of overidentification'
return WaldTestStatistic(stat, null, df, name=name)
