def test_debiased(self, data):
wm = HomoskedasticWeightMatrix(debiased=True)
weight = wm.weight_matrix(data.x, data.z, data.e)
z, e, nobs, nvar = data.z, data.e, data.nobs, data.nvar
s2 = (e - e.mean()).T @ (e - e.mean()) / nobs
scale = nobs / (nobs - nvar)
assert_allclose(weight, scale * s2 * z.T @ z / nobs)
def test_config(self, data):
wm = HomoskedasticWeightMatrix()
z, e, nobs = data.z, data.e, data.nobs
weight = wm.weight_matrix(data.x, z, e)
s2 = (e - e.mean()).T @ (e - e.mean()) / nobs
assert_allclose(weight, s2 * z.T @ z / nobs)
assert wm.config['center'] is False
assert wm.config['debiased'] is False
def test_homoskedastic(self, data):
c = IVGMMCovariance(data.x, data.y, data.z, data.params, data.i, 'unadjusted')
s = HomoskedasticWeightMatrix().weight_matrix(data.x, data.z, data.e)
x, z = data.x, data.z
xzwswzx = x.T @ z @ s @ z.T @ x / data.nobs
cov = data.xzizx_inv @ xzwswzx @ data.xzizx_inv
cov = (cov + cov.T) / 2
assert_allclose(c.cov, cov)
assert c.config['debiased'] is False
def test_defaults(self, data):
wm = HomoskedasticWeightMatrix()
z, e, nobs = data.z, data.e, data.nobs
weight = wm.weight_matrix(data.x, z, e)
s2 = (e - e.mean()).T @ (e - e.mean()) / nobs
assert_allclose(weight, s2 * z.T @ z / nobs)
def test_center(self, data):
wm = HomoskedasticWeightMatrix(True)
weight = wm.weight_matrix(data.x, data.z, data.e)
z, e, nobs = data.z, data.e, data.nobs
s2 = (e - e.mean()).T @ (e - e.mean()) / nobs
assert_allclose(weight, s2 * z.T @ z / nobs)