I think Chris is right. Besides you get more leverage when you pick using your whole arm as opposed to mainly using your wrist and fingers. Your picking movement should feel natural. If your shaking your wrist back and forth frantically in an effort to pick faster, chances are you're going to feel pretty uncomfortable in a short period of time and tire out quickly. I would also suggest focusing not so much on what your arm and wrist are doing and focusing more on the efficiency of which direction your pick hits the string in the course of your playing. For example, if you are moving from, let's say, the 6th string to the 5th string in the course of playing a piece of music, you can make that move with the least amount of effort by using two down strokes instead of alternate picking a down and then an up stroke. Incorporating that idea really lessens a lot of unnecessary picking movement and helps to improve your speed with very little extra exertion on your part. It's a little tricky to apply throughout at first, but once you get the hang of it, it becomes something you do unconsciously.