You cannot create a date datatype that stores only the year and month component. There's no such option available at the data type level.
If you want to to truncate the day component to default it to start of month, you may do it. This is as good as having only the month and year component as all the dates will have day = 1 and only the month and year would change as per the time of running insert
.
For Eg:
create table t ( id int, col1 text,
"date" date default date_trunc('month',current_date) );
insert into t(id,col1) values ( 1, 'TEXT1');
select * from t
d col1 date
1 TEXT1 2019-05-01
If you do not want to store a default date, simply use the date_trunc('month,date)
expression wherever needed, it could either be in group by
or in a select
query.