BUG: loc misbehaves when Period is at start of 3-level MultiIndex

(#20684)

If `MultiIndex` nlevel is 3 and first level index is `PeriodIndex`,
`.loc` would raise exception with a miss match key

Author: proost

doc/source/whatsnew/v1.0.0.rst

@@ -174,7 +174,7 @@ Missing
 MultiIndex
 ^^^^^^^^^^
 
--
+- If `MultiIndex` nlevel is 3 and first level index in `MultiIndex` is `PeriodIndex` , `.loc` could not raise exception when key is not matched (:issue:`20684`)
 -
 
 I/O

pandas/_libs/tslibs/parsing.pyx

@@ -251,10 +251,8 @@ def parse_time_string(arg, freq=None, dayfirst=None, yearfirst=None):
     -------
     datetime, datetime/dateutil.parser._result, str
     """
-    if not isinstance(arg, (str, unicode)):
-        # Note: cython recognizes `unicode` in both py2/py3, optimizes
-        # this check into a C call.
-        return arg
+    if not isinstance(arg, str):
+        raise TypeError
 
     if getattr(freq, "_typ", None) == "dateoffset":
         freq = freq.rule_code

pandas/tests/indexes/period/test_period.py

@@ -617,6 +617,21 @@ def test_insert(self):
             result = period_range("2017Q1", periods=4, freq="Q").insert(1, na)
             tm.assert_index_equal(result, expected)
 
+    def test_contains_raise_error_if_first_level_index_is_period_index(self):
+        # issue 20684
+        df = DataFrame(
+            {
+                "A": [Period("2019"), Period("2018")],
+                "B": ["x1", "x2"],
+                "C": ["y1", "y2"],
+                "V1": [1, 2],
+                "V2": [10, 20],
+            }
+        ).set_index(["A", "B", "C"])
+        msg = r"Period\('2019', 'A-DEC'\), 'foo', 'bar'"
+        with pytest.raises(KeyError, match=msg):
+            df.loc[(Period("2019"), "foo", "bar")]
+
 
 def test_maybe_convert_timedelta():
     pi = PeriodIndex(["2000", "2001"], freq="D")

pandas/tests/tslibs/test_parsing.py

@@ -209,3 +209,13 @@ def test_try_parse_dates():
 
     expected = np.array([parse(d, dayfirst=True) for d in arr])
     tm.assert_numpy_array_equal(result, expected)
+
+
+def test_parse_time_string_check_instance_type_raise_exception():
+    # issue 20684
+    with pytest.raises(TypeError):
+        parse_time_string((1, 2, 3))
+
+    result = parse_time_string("2019")
+    expected = (datetime(2019, 1, 1), datetime(2019, 1, 1), "year")
+    assert result == expected