Calculate the inventory in kardex table

create table product(productId serial primary key);
create table kardex(
  id serial,
  pId int,
  in_inventory int,
  out_inventory int,
  createdAt timestamp default now(),
  primary key(pid, id),
  constraint fk_product
    foreign key(pId)
      references product(productId)
);

# insert dummy data
insert into product values (12);
insert into product values (13);
insert into kardex values(default, 12, 12, 0);
insert into kardex values(default, 12, 0, 6);
insert into kardex values(default, 13, 10, 0);
insert into kardex values(default, 13, 0, 3);

# the previous query. This query does not work correctly. because it just uses the previous row not the whole previous records.
with cte as (
  select *, in_inventory - out_inventory as inventory
  from kardex
  where pId = 12
) select
  id,
  pId,
  in_inventory,
  out_inventory,
  lag(inventory, 1) over (order by createdAt) as prev_inventory,
  lag(inventory, 1) over (order by createdAt) - out_inventory as inventory
from cte;

# this query fetch the final inventory
select pId, sum(in_inventory - out_inventory) from kardex where pId = 12 group by pId;

# the correct query. these queries had the same result
select *, sum(in_inventory - out_inventory) over (order by createdAt) as inventory from kardex where pId = 12 order by createdAt;
select *, SUM(in_inventory - out_inventory) over (order by id) as inventory from kardex where pId = 12;