Hide Emacs echo area during inactivity

The echo area is the line at the bottom of Emacs below the mode line:

                     ~                       ~
                     |                       |
                     +-----------------------+
                     |-U:--- mode-line       |
                     +-----------------------+
                     | M-x echo-area         |
                     +-----------------------+

Now the mode line is highly customizable while the echo area is more rigid (and unused a lot of the time). The question is pretty simple: is it possible to hide the echo area during inactivity and redisplay it once it needs your attention:

  ~                       ~             ~                       ~
  |                       |             |                       |
  |                       |             +-----------------------+
  |                       |             |-U:--- mode-line       |
  +-----------------------+             +-----------------------+
  |-U:--- mode-line       |             | M-x echo-area         |
  +-----------------------+             +-----------------------+

          Inactive                                Active

This is similar to the way Google Chrome displays URLs when you hover your mose over a link and the Firefox addon Pentadactyl where the command-line is hidden by default.