Controlling the log_min_error_statement will prevent the statements being logged in the log_destination file. Essentially, you are logging all messages of FATAL and PANIC levels when this parameter is set to 'FATAL'.
Here is the excerpt from Postgresql Documentation https://www.postgresql.org/docs/9.5/static/runtime-config-logging.html
log_min_error_statement (enum) Controls which SQL statements that cause an error condition are recorded in the server log. The current SQL statement is included in the log entry for any message of the specified severity or higher. Valid values are DEBUG5, DEBUG4, DEBUG3, DEBUG2, DEBUG1, INFO, NOTICE, WARNING, ERROR, LOG, FATAL, and PANIC. The default is ERROR, which means statements causing errors, log messages, fatal errors, or panics will be logged. To effectively turn off logging of failing statements, set this parameter to PANIC. Only superusers can change this setting.To effectively turn off logging of failing statements, set this parameter to PANIC. Only superusers can change this setting.
1. log_min_error_statement='error'
Terminal 1
postgres=# show log_min_error_statement;
log_min_error_statement
-------------------------
error
(1 row)
postgres=# DO $$
BEGIN
RAISE LOG 'Justin Is Awesome';
END $$;
DO
Terminal 2
-bash-4.1$ tail -f pg_log/postgresql-2016-07-13_112940.log
2016-07-13 11:50:01 PDT LOG: Justin Is Awesome
2016-07-13 11:50:01 PDT STATEMENT: DO $$
BEGIN
RAISE LOG 'Justin Is Awesome';
END $$;
2. log_min_error_statement='fatal'
Terminal 1
postgres=# set log_min_error_statement='FATAL';
SET
postgres=# DO $$
BEGIN
RAISE LOG 'Justin Is Awesome';
END $$;
DO
Terminal 2:
-bash-4.1$ tail -f pg_log/postgresql-2016-07-13_112940.log
2016-07-13 11:51:15 PDT LOG: Justin Is Awesome