diff --git a/linearmodels/system/model.py b/linearmodels/system/model.py
index ca59e5697a..5c765b5806 100644
--- a/linearmodels/system/model.py
+++ b/linearmodels/system/model.py
@@ -1653,8 +1653,8 @@ def multivariate_iv(
         dependent_ivd = IVData(dependent, var_name="dependent")
         if exog is None and endog is None:
             raise ValueError("At least one of exog or endog must be provided")
-        exog_ivd = IVData(exog, var_name="exog")
         nobs = dependent_ivd.shape[0]
+        exog_ivd = IVData(exog, var_name="exog", nobs=nobs)
         endog_ivd = IVData(endog, var_name="endog", nobs=nobs)
         instr_ivd = IVData(instruments, var_name="instruments", nobs=nobs)
         for col in dependent_ivd.pandas:
diff --git a/linearmodels/tests/system/test_multivariate_iv.py b/linearmodels/tests/system/test_multivariate_iv.py
new file mode 100644
index 0000000000..b202a40558
--- /dev/null
+++ b/linearmodels/tests/system/test_multivariate_iv.py
@@ -0,0 +1,76 @@
+"""
+Tests of IV3SLS.multivariate_iv with only some of the exogenous, endogenous and
+instrumental variables
+
+The documentation requires at least one of exog and endog, so endog and instruments
+without exog is a valid specification.
+"""
+
+import numpy as np
+from numpy.testing import assert_allclose
+import pandas as pd
+import pytest
+
+from linearmodels.iv import IV2SLS
+from linearmodels.system import IV3SLS
+
+NOBS = 200
+NDEP = 2
+
+
+@pytest.fixture(scope="module")
+def data():
+    rng = np.random.default_rng(0)
+    instruments = rng.standard_normal((NOBS, 3))
+    shocks = rng.standard_normal((NOBS, NDEP + 1))
+    endog = (
+        instruments @ np.array([[1.0, 0.5], [0.5, 1.0], [0.2, 0.2]])
+        + 0.5 * shocks[:, [0]]
+        + rng.standard_normal((NOBS, 2))
+    )
+    dependent = endog @ rng.standard_normal((2, NDEP)) + shocks[:, 1:]
+    exog = rng.standard_normal((NOBS, 2))
+    return dependent, exog, endog, instruments
+
+
+@pytest.mark.parametrize("kind", ["array", "frame"])
+def test_endog_and_instruments_without_exog(data, kind):
+    dependent, _, endog, instruments = data
+    if kind == "frame":
+        index = pd.date_range("2000-1-1", periods=NOBS)
+        dependent = pd.DataFrame(dependent, columns=["y0", "y1"], index=index)
+        endog = pd.DataFrame(endog, columns=["x0", "x1"], index=index)
+        instruments = pd.DataFrame(instruments, columns=["z0", "z1", "z2"], index=index)
+    mod = IV3SLS.multivariate_iv(dependent, endog=endog, instruments=instruments)
+    res = mod.fit()
+    assert len(res.equations) == NDEP
+    # The equations share the regressors and the instruments, so 3SLS is 2SLS
+    # in each equation
+    dep = np.asarray(dependent)
+    for i, label in enumerate(res.equation_labels):
+        expected = IV2SLS(dep[:, i], None, np.asarray(endog), np.asarray(instruments))
+        assert_allclose(
+            res.equations[label].params, expected.fit().params, rtol=1e-8, atol=1e-10
+        )
+        assert len(res.equations[label].params) == 2
+
+
+def test_exog_only_and_with_exog_are_unchanged(data):
+    dependent, exog, endog, instruments = data
+    only_exog = IV3SLS.multivariate_iv(dependent, exog=exog)
+    assert only_exog.fit().params.shape[0] == NDEP * exog.shape[1]
+    full = IV3SLS.multivariate_iv(dependent, exog, endog, instruments).fit()
+    assert full.params.shape[0] == NDEP * (exog.shape[1] + endog.shape[1])
+    # endog without instruments: nothing identifies the endogenous variables
+    with pytest.raises(ValueError, match=r"endogenous variables"):
+        IV3SLS.multivariate_iv(dependent, endog=endog)
+
+
+def test_wrong_number_of_observations(data):
+    dependent, _, endog, instruments = data
+    with pytest.raises(ValueError, match=r"observations"):
+        IV3SLS.multivariate_iv(dependent, endog=endog[:-1], instruments=instruments)
+    with pytest.raises(ValueError, match=r"observations"):
+        IV3SLS.multivariate_iv(
+            dependent, exog=instruments[:-5], endog=endog, instruments=instruments
+        )