BUG: concat warning when joining with empty and columns have different dtype

[rhshadrach]

The warning is due to #39122

pd.set_option("infer_string", True)
df = pd.DataFrame({"a": "x", "b": ["y", "z"]}).set_index(["a", "b"])
df.columns = pd.Index([], dtype="int")
ser = pd.DataFrame({"b": ["y", "z"], "value": [1, 2]}).set_index("b")["value"]
df.join(ser, on="b")
# FutureWarning: The behavior of array concatenation with empty entries is deprecated...

In the above code, we hit

pandas/pandas/core/reshape/merge.py

Line 1134 in 82fa271

result = concat([left, right], axis=1)

with left having no columns but of int64 dtype and right having columns with str dtype. Both before and after the deprecation we get str dtype for the columns. The call to pandas.core.dtypes.concat.concat_compact does result in object dtype, but then we wrap this with Index._with_infer(...) in Index._concat giving str again.

Should we be inferring dtype after the concat index is determined?

In merge, it seems to me we should skip calling concat with axis=1 if left or right has empty columns but perhaps still call concat if both are empty.

cc @jbrockmendel @jorisvandenbossche

[jbrockmendel]

If you want to suppress the warning on 2.3.4 i won't complain.

Should we be inferring dtype after the concat index is determined?

IIRC that code path is the same one as for Index.append, where we have pretty good consensus about deprecating the _with_infer call in #60159.

In the example you explicitly set df.columns.dtype to int. If you hadn't, one long-term solution would be to have Void Dtype, which would be ignored in the concat.

[rhshadrach]

If you want to suppress the warning on 2.3.4 i won't complain.

Do you think we shouldn't just avoid calling concat from join in the case left or right is has no columns (but not both)?

[Fahad-Alam-Jamal]

Can you assign this issue to me

[jbrockmendel]

Do you think we shouldn't just avoid calling concat from join in the case left or right is has no columns (but not both)?

My knee-jerk is that this constitutes value-dependent behavior that we should try to avoid. But I don't feel all that strongly about this case.