[big_whack]

Postgres pads tuples to 8 bytes alignment so an indexed single-column int takes the same space as an indexed bigint. That's the usual case for indexed foreign keys.

Differences can appear in multicolumn indexes because two ints takes 8 bytes while two bigints takes 16, however the right layout of columns for an index is not always the layout that minimizes padding.

[sgarland]

Postgres doesn't necessarily pad to 8 bytes; it depends on the next column's type. EDB has a good writeup on this (https://www.2ndquadrant.com/en/blog/on-rocks-and-sand/), but also here's a small example:

  CREATE TABLE foo
    (id INT GENERATED ALWAYS AS IDENTITY PRIMARY KEY, iid INT NOT NULL);

  CREATE TABLE bar
    (id INT GENERATED ALWAYS AS IDENTITY PRIMARY KEY, iid BIGINT NOT NULL);

  CREATE TABLE baz
    (id BIGINT GENERATED ALWAYS AS IDENTITY PRIMARY KEY, iid BIGINT NOT NULL);

  -- fill each with 1,000,000 rows, then index

  CREATE INDEX {foo,bar,baz}_iid_idx ON {foo,bar,baz}(iid);

  SELECT table_name,
         pg_size_pretty(pg_table_size(quote_ident(table_name))) "table_size",
         pg_size_pretty(pg_indexes_size(quote_ident(table_name))) "index_size"
  FROM information_schema.tables
  WHERE table_schema = 'public';

   table_name | table_size | index_size
  ------------+------------+------------
   foo        | 35 MB      | 43 MB
   bar        | 42 MB      | 43 MB
   baz        | 42 MB      | 43 MB

`foo` has an INT followed by an INT, and its table size is 35 MB. `bar` has an INT followed by a BIGINT, and its table size is 43 MB; this is the same size for `baz`, despite `baz` being a BIGINT followed by a BIGINT.

[big_whack]

You seem to think you're disagreeing with me but afaict you're just demonstrating my point, unless your point is just about how (int, int) will get packed. That's what I meant about the column order of indexes. If you have two ints and a bigint, but you need to index it like (int, bigint, int), then you aren't gaining anything there either.

As your example shows, there is no benefit in index size (e.g for supporting FKs) in going from int to bigint for a single key. You end up with the same index size no matter what, not twice the size which was what I took your original post to mean.

[sgarland]

I misunderstood your post, I think. I re-ran some experiments with a single-column index on SMALLINT, INT, and BIGINT. I'm still not sure why, but there is a significant difference in index size on SMALLINT (7.3 MB for 1E6 rows) vs. INT and BIGINT (21 MB for each), while the latter two are the exact same size. I could get them to differ if I ran large UPDATEs on the table, but that was it.