Postgres trigger after insert accessing NEW

I have a pretty simple trigger:

CREATE OR REPLACE FUNCTION f_log_datei()
RETURNS TRIGGER AS $$
BEGIN
  INSERT INTO logs (aktion, tabelle, benutzer_id) VALUES(TG_OP, 'dateien', NEW.benutzer_id);
END; $$ LANGUAGE 'plpgsql';

CREATE TRIGGER log_datei AFTER INSERT OR UPDATE OR DELETE
ON dateien
FOR EACH STATEMENT
EXECUTE PROCEDURE f_log_datei();

My table logs is the following:

CREATE TABLE logs(
    id int PRIMARY KEY DEFAULT NEXTVAL('logs_id_seq'),
    zeit timestamp DEFAULT now(),
    aktion char(6),
    tabelle varchar(32),
    alt varchar(256),
    neu varchar(256),
    benutzer_id int references benutzer(id)
);

After inserting something in dateien I get the following error:

ERROR:  record "new" is not assigned yet
DETAIL:  The tuple structure of a not-yet-assigned record is indeterminate.
CONTEXT:  SQL statement "INSERT INTO logs (aktion, tabelle, benutzer_id) VALUES(TG_OP, 'dateien', NEW.benutzer_id)"
PL/pgSQL function "f_log_datei" line 3 at SQL statement

Why did I get this error? I looked into the documentation and it seems they use new in the same way I do.