Is it possible to define global variables in postgresql

Postgresql does not support global variables on the DB level. Why not add it:

CREATE TABLE global_variables (
  key text not null PRIMARY KEY
  value text
);

INSERT INTO global_variables (key, value) VALUES ('error_code_for_spaceship_engine', '404');

If different types may be the values, consider JSON to be the type for value, but then deserialization code is required for each type.

Postgres does not have global variables. However you can define custom configuration parameters. To keep things clear define your own parameters with a given prefix, say glb.

This simple function will make it easier to place the parameter in queries:

create or replace function glb(code text)
returns integer language sql as $$
    select current_setting('glb.' || code)::integer;
$$;

set glb.user_not_found to -1;
set glb.user_does_not_have_permission to -2;

select glb('user_not_found'), glb('user_does_not_have_permission');

User-defined parameters are local in the session, therefore the parameters should be defined at the beginning of each session.

You can use a trick and declare your variables as a 1-row CTE, which you then CROSS JOIN to the rest. See example:

WITH
variables AS (
    SELECT 'value1'::TEXT AS var1, 10::INT AS var2
)
SELECT t.*, v.*
FROM
    my_table AS t
    CROSS JOIN variables AS v
WHERE t.random_int_column = var2;

Building on @klin's answer, there are a couple of ways to persist a configuration parameter beyond the current session. Note that these require superuser privieges.

To set a value for all connections to a particular database:

ALTER DATABASE db SET abc.xyz = 1;

You can also set a server-wide value using the ALTER SYSTEM command, added in 9.4. It only seems to work for user-defined parameters if they have already been SET in your current session. Note also that this requires a configuration reload to take effect.

SET abc.xyz = 1;
ALTER SYSTEM SET abc.xyz = 1;
SELECT pg_reload_conf();

Pre-9.4, you can accomplish the same thing by adding the parameter to your server's postgresql.conf file. In 9.1 and earlier, you also need to register a custom variable class.