javascript change value but inside onchange event listener not firing

I wrote a simple script to count words while typing in form
My question is why by changing the value of the word_count field when typing;
The EventListener of word_count is not fired

document.getElementById('subject').addEventListener('change', function() {
    var string = this.value
    string = string.replace(/s+/g, " ");
    var words = string.split(/s+/).length;
    document.getElementById('word_count').value = words;
}, false);
document.getElementById('subject').addEventListener('keypress', function() {
    var string = this.value
    string = string.replace(/s+/g, " ");
    var words = string.split(/s+/).length;
    document.getElementById('word_count').value = words;
}, false);
document.getElementById('word_count').addEventListener('change', function() {
    alert('change fired');
}, false);

<form>
   <div> <label for="story">string:</label>
      <textarea   id="subject" name="subject"></textarea>
   </div>
   <div>  <label for="story">count:</label>
      <input id="word_count">
   </div>
</form>