Well, two things to correct here. You're using single quotes, and variables aren't parsed inside them. Also, you're using $PHP_SELF, which you should hope does not exist. If it does, you're using register_globals, which you shouldn't, unless you know what you're doing (and in that case, you'd probably just turn it off). You should instead be using $_SERVER['PHP_SELF'] as TheDefender pointed out.
However, the line he gave you should give you a parse error. Instead, concatenate the variable with the echoed string:
'<form id="keyword_input" method="post" action="' . $_SERVER['PHP_SELF'] . '">'
But, if we look up echo, it takes multiple arguments. Thus, we can simply:
echo '<form id="keyword_input" method="post" action="', $_SERVER['PHP_SELF'], '">';
Voila.