From 04eba89abeac273cf4d529562c6f3e509c6b098b Mon Sep 17 00:00:00 2001
From: Brock <jbrockmendel@gmail.com>
Date: Fri, 29 Jul 2022 13:32:42 -0700
Subject: [PATCH] BUG: preserve _id in MultiIndex.copy(deep=False)

---
 pandas/core/indexes/multi.py            |  5 +++++
 pandas/tests/indexes/multi/test_copy.py | 12 ++++++++++++
 2 files changed, 17 insertions(+)

diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index fd6b6ba63d7e0..b4b576df9918e 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1190,6 +1190,7 @@ def copy(
         This could be potentially expensive on large MultiIndex objects.
         """
         names = self._validate_names(name=name, names=names, deep=deep)
+        keep_id = not deep
         if levels is not None:
             warnings.warn(
                 "parameter levels is deprecated and will be removed in a future "
@@ -1197,6 +1198,7 @@ def copy(
                 FutureWarning,
                 stacklevel=find_stack_level(),
             )
+            keep_id = False
         if codes is not None:
             warnings.warn(
                 "parameter codes is deprecated and will be removed in a future "
@@ -1204,6 +1206,7 @@ def copy(
                 FutureWarning,
                 stacklevel=find_stack_level(),
             )
+            keep_id = False
 
         if deep:
             from copy import deepcopy
@@ -1225,6 +1228,8 @@ def copy(
         )
         new_index._cache = self._cache.copy()
         new_index._cache.pop("levels", None)  # GH32669
+        if keep_id:
+            new_index._id = self._id
 
         if dtype:
             warnings.warn(
diff --git a/pandas/tests/indexes/multi/test_copy.py b/pandas/tests/indexes/multi/test_copy.py
index 9a0e4bc0996be..2b64845c919cf 100644
--- a/pandas/tests/indexes/multi/test_copy.py
+++ b/pandas/tests/indexes/multi/test_copy.py
@@ -104,3 +104,15 @@ def test_copy_deprecated_parameters(deep, param_name, param_value):
         idx_copy = idx.copy(deep=deep, **{param_name: param_value})
 
     assert [list(i) for i in getattr(idx_copy, param_name)] == param_value
+
+
+def test_copy_deep_false_retains_id():
+    # GH#47878
+    idx = MultiIndex(
+        levels=[["foo", "bar"], ["fizz", "buzz"]],
+        codes=[[0, 0, 0, 1], [0, 0, 1, 1]],
+        names=["first", "second"],
+    )
+
+    res = idx.copy(deep=False)
+    assert res._id is idx._id