Add pandas-dev#16147 fix to whatsnew

Author: leej3

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`)