Pairs of base tables that have at least two columns with the same names and data types

WITH tables AS (SELECT C.table_schema, C.table_name, C.column_name, C.data_type || coalesce(C.character_maximum_length::text, C.numeric_precision ||'.'|| C.numeric_scale, '0') AS data_type
FROM information_schema.columns C INNER JOIN information_schema.tables T USING (table_schema, table_name)
INNER JOIN information_schema.schemata S ON T.table_schema = S.schema_name
WHERE T.table_type = 'BASE TABLE' AND (T.table_schema = 'public' OR S.schema_owner<>'postgres'))

SELECT T1.table_schema AS T1_schema, T1.table_name AS T1_name, T2.table_schema AS T2_schema, T2.table_name AS T2_name, Count(*) AS number_of_common_columns
FROM tables AS T1, tables AS T2
WHERE T1.column_name=T2.column_name AND T1.data_type=T2.data_type 
AND (T1.table_name>T2.table_name)
GROUP BY T1.table_schema, T1.table_name, T2.table_schema, T2.table_name
HAVING Count(*)>1
ORDER BY number_of_common_columns DESC, T1.table_schema, T1.table_name, T2.table_schema, T2.table_name;