diff --git a/tests/estimation/test_msm_weighting.py b/tests/estimation/test_msm_weighting.py
index c15375a59..c87fd7a56 100644
--- a/tests/estimation/test_msm_weighting.py
+++ b/tests/estimation/test_msm_weighting.py
@@ -22,7 +22,7 @@ def expected_values():
 cov_np = np.diag([1, 2, 3])
 cov_pd = pd.DataFrame(cov_np)
 
-test_cases = itertools.product([cov_np, cov_pd], ["diagonal", "optimal"])
+test_cases = itertools.product([cov_np, cov_pd], ["diagonal", "optimal", "identity"])
 
 
 @pytest.mark.parametrize("moments_cov, method", test_cases)
@@ -38,7 +38,11 @@ def test_get_weighting_matrix(moments_cov, method):
         assert calculated.columns.equals(moments_cov.columns)
         calculated = calculated.to_numpy()
 
-    expected = np.diag(1 / np.array([1, 2, 3]))
+    if method == "identity":
+        expected = np.identity(cov_np.shape[0])
+    else:
+        expected = np.diag(1 / np.array([1, 2, 3]))
+    
     aaae(calculated, expected)