BUG: Exclude implicit intercepts from IV model F tests

linearmodels/iv/model.py

@@ -564,6 +564,16 @@ def _f_statistic(
     ) -> WaldTestStatistic | InvalidTestStatistic:
         const_loc = find_constant(self._x)
         nobs, nvar = self._x.shape
+        if self.has_constant and const_loc is None:
+            # Under the null, the coefficients are proportional to the vector
+            # that produces an intercept. Test its orthogonal complement rather
+            # than dropping an arbitrary dummy or testing the intercept itself.
+            scale = abs(self._x).max(axis=0)
+            intercept = pinv(self._x / scale) @ ones((nobs, 1))
+            basis, _ = qr(intercept, mode="complete")
+            restriction = basis[:, 1:].T * scale
+            params = restriction @ params
+            cov = restriction @ cov @ restriction.T
         return f_statistic(params, cov, debiased, nobs - nvar, const_loc)
 
     def _estimate_kappa(self) -> float:

linearmodels/iv/results.py

@@ -337,6 +337,11 @@ def f_statistic(self) -> WaldTestStatistic:
         This version of the F-statistic directly uses the model covariance
         estimator and so is robust against the same specification issues.
 
+        For IV estimators, if the regressors span a constant without an explicit
+        constant column, the null is that the fitted values are constant. For
+        example, with a dummy for every group, the group coefficients must be
+        equal and all other coefficients must be zero.
+
         An ``InvalidTestStatistic`` is returned if the model has no non-constant
         exogenous terms, or if the covariance of the parameters is singular, e.g.,
         the dependent variable is all zero, so that the model fits exactly.

linearmodels/tests/iv/test_implicit_constant_f_statistic.py

@@ -0,0 +1,39 @@
+"""The IV model F test excludes an intercept spanned by dummy columns."""
+
+import numpy as np
+from numpy.testing import assert_allclose
+import pytest
+
+from linearmodels.iv import IV2SLS, IVGMM, IVLIML
+
+
+@pytest.mark.parametrize("model", [IV2SLS, IVLIML, IVGMM])
+@pytest.mark.parametrize("debiased", [False, True])
+@pytest.mark.parametrize("cov_type", ["unadjusted", "robust"])
+@pytest.mark.parametrize("weighted", [False, True])
+@pytest.mark.parametrize("scales", [(1.0, 1.0), (-2.0, 5.0)])
+def test_model_f_statistic_with_implicit_constant(
+    model, debiased, cov_type, weighted, scales
+):
+    rng = np.random.default_rng(0)
+    nobs = 200
+    group = np.arange(nobs) % 2
+    x = rng.standard_normal(nobs)
+    z = rng.standard_normal((nobs, 2))
+    endog = z @ np.array([0.8, 0.4]) + rng.standard_normal(nobs)
+    y = 1.0 + 0.3 * group + 0.2 * x + 0.4 * endog + rng.standard_normal(nobs)
+    exog = np.column_stack([scales[0] * (group == 0), scales[1] * (group == 1), x])
+    weights = rng.uniform(0.5, 2.0, nobs) if weighted else None
+    res = model(y, exog, endog, z, weights=weights).fit(
+        cov_type=cov_type, debiased=debiased
+    )
+    # A constant fitted value requires equal group effects and zero slopes.
+    restriction = np.array([[scales[0], -scales[1], 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
+    expected = res.wald_test(restriction).stat / (3 if debiased else 1)
+    assert res.f_statistic.df == 3
+    assert_allclose(res.f_statistic.stat, expected, rtol=1e-10)
+    explicit = model(
+        y, np.column_stack([np.ones(nobs), group, x]), endog, z, weights=weights
+    ).fit(cov_type=cov_type, debiased=debiased)
+    assert_allclose(res.f_statistic.stat, explicit.f_statistic.stat, rtol=1e-10)
+    assert_allclose(res.f_statistic.pval, explicit.f_statistic.pval, rtol=1e-10)