BUG: MultiIndex.set_levels with emtpy levels

doc/source/whatsnew/v0.21.0.txt

@@ -325,6 +325,7 @@ Other API Changes
 - Compression defaults in HDF stores now follow pytable standards. Default is no compression and if ``complib`` is missing and ``complevel`` > 0 ``zlib`` is used (:issue:`15943`)
 - ``Index.get_indexer_non_unique()`` now returns a ndarray indexer rather than an ``Index``; this is consistent with ``Index.get_indexer()`` (:issue:`16819`)
 - Removed the ``@slow`` decorator from ``pandas.util.testing``, which caused issues for some downstream packages' test suites. Use ``@pytest.mark.slow`` instead, which achieves the same thing (:issue:`16850`)
+- func:`pandas.MultiIndex.set_levels()` now allows the setting of empty levels and, when `level` is a list-like object, each element of levels is confirmed to be list-like (:issue:`16147`)
 - Moved definition of ``MergeError`` to the ``pandas.errors`` module.
 - The signature of :func:`Series.set_axis` and :func:`DataFrame.set_axis` has been changed from ``set_axis(axis, labels)`` to ``set_axis(labels, axis=0)``, for consistency with the rest of the API. The old signature is deprecated and will show a ``FutureWarning`` (:issue:`14636`)
 - :func:`Series.argmin` and :func:`Series.argmax` will now raise a ``TypeError`` when used with ``object`` dtypes, instead of a ``ValueError`` (:issue:`13595`)

pandas/core/indexes/multi.py

@@ -229,16 +229,28 @@ def set_levels(self, levels, level=None, inplace=False,
                    labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
                    names=[u'foo', u'bar'])
         """
-        if level is not None and not is_list_like(level):
-            if not is_list_like(levels):
-                raise TypeError("Levels must be list-like")
-            if is_list_like(levels[0]):
-                raise TypeError("Levels must be list-like")
+
+        level_list_like = level is None or is_list_like(level)
+        levels_list_like = (is_list_like(levels) and
+                            all(is_list_like(x) for x in levels) and
+                            levels != [] )
+
+        if level_list_like:
+            # level is a list-like object of scalars
+            levels_error = ("`levels` and `level` are incompatible. "
+                            "When `level` is list-like, `levels` must be a "
+                            "list-like object containing list-like objects")
+            if not levels_list_like:
+                raise TypeError(levels_error)
+        elif not level_list_like:
+            # level is a scalar
+            levels_error = ("`levels` and `level` are incompatible. "
+                            "When `level` is a scalar, `levels` must be a "
+                            " list-like object of scalars.")
+            if levels_list_like:
+                raise TypeError(levels_error)
             level = [level]
             levels = [levels]
-        elif level is None or is_list_like(level):
-            if not is_list_like(levels) or not is_list_like(levels[0]):
-                raise TypeError("Levels must be list of lists-like")
 
         if inplace:
             idx = self

pandas/tests/indexing/test_multiindex.py

@@ -428,6 +428,50 @@ def test_xs_multiindex(self):
         expected.columns = expected.columns.droplevel('lvl1')
         tm.assert_frame_equal(result, expected)
 
+    def test_set_level_checkall(self):
+
+        idx = MultiIndex.from_tuples([(1, u'one'), (1, u'two'),
+                                     (2, u'one'), (2, u'two')],
+                                     names=['foo', 'bar'])
+        result = idx.set_levels([['a', 'b'], [1, 2]])
+        expected = MultiIndex(levels=[[u'a', u'b'], [1, 2]],
+                              labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
+                              names=[u'foo', u'bar'])
+        tm.assert_index_equal(result, expected)
+
+        result = idx.set_levels(['a', 'b'], level=0)
+        expected = MultiIndex(levels=[[u'a', u'b'], [u'one', u'two']],
+                              labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
+                              names=[u'foo', u'bar'])
+        tm.assert_index_equal(result, expected)
+
+        result = idx.set_levels(['a', 'b'], level='bar')
+        expected = MultiIndex(levels=[[1, 2], [u'a', u'b']],
+                              labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
+                              names=[u'foo', u'bar'])
+        tm.assert_index_equal(result, expected)
+
+        result = idx.set_levels([['a', 'b'], [1, 2]], level=[0, 1])
+        expected = MultiIndex(levels=[[u'a', u'b'], [1, 2]],
+                              labels=[[0, 0, 1, 1], [0, 1, 0, 1]],
+                              names=[u'foo', u'bar'])
+        tm.assert_index_equal(result, expected)
+
+        # setting empty levels are allowed
+        idx = MultiIndex(levels=[['L1'], ['L2']], labels=[[], []],
+                         names=['a', 'b'])
+        result = idx.set_levels([], level='a')
+        expected = MultiIndex(levels=[[], ['L2']], labels=[[], []],
+                              names=['a', 'b'])
+        tm.assert_index_equal(result, expected)
+
+        idx = MultiIndex(levels=[['L1'], ['L2']], labels=[[], []],
+                         names=['a', 'b'])
+        result = idx.set_levels([[], []], level=['a', 'b'])
+        expected = MultiIndex(levels=[[], []], labels=[[], []],
+                              names=['a', 'b'])
+        tm.assert_index_equal(result, expected)
+
     def test_multiindex_setitem(self):
 
         # GH 3738