BUG: fix convert_dtypes to handle empty df

doc/source/whatsnew/v1.3.0.rst

@@ -625,6 +625,7 @@ Other
 - Bug in :class:`Styler` where multiple elements in CSS-selectors were not correctly added to ``table_styles`` (:issue:`39942`)
 - Bug in :meth:`DataFrame.equals`, :meth:`Series.equals`, :meth:`Index.equals` with object-dtype containing ``np.datetime64("NaT")`` or ``np.timedelta64("NaT")`` (:issue:`39650`)
 - Bug in :func:`pandas.util.show_versions` where console JSON output was not proper JSON (:issue:`39701`)
+- Bug in :meth:`DataFrame.convert_dtypes` incorrectly raised ValueError when called on an empty DataFrame (:issue:`40393`)
 
 
 .. ---------------------------------------------------------------------------

pandas/core/generic.py

@@ -6322,7 +6322,10 @@ def convert_dtypes(
                 )
                 for col_name, col in self.items()
             ]
-            return concat(results, axis=1, copy=False)
+            if len(results) > 0:
+                return concat(results, axis=1, copy=False)
+            else:
+                return self.copy()
 
     # ----------------------------------------------------------------------
     # Filling NA's

pandas/tests/frame/methods/test_convert_dtypes.py

@@ -26,3 +26,8 @@ def test_convert_dtypes(self, convert_integer, expected):
             }
         )
         tm.assert_frame_equal(result, expected)
+
+    def test_convert_empty(self):
+        # Empty DataFrame can pass convert_dtypes, see GH#40393
+        empty_df = pd.DataFrame()
+        tm.assert_frame_equal(empty_df, empty_df.convert_dtypes())