I've my own little software enterprise and I'm both the programmer and project manager, so I can give you both points of view.

Your initial assumption is not true. Let me write it down:

Project Management & Software Analysis =

Creating documentation or even creating Gantt chart and asking progress to programmers.

If you really think that's all Project Management and Software Analysis is about, it's no wonder that you think that programming is harder.

But that's a ridiculing, unfair and non-realistic way to define those professions. It concentrates on merely visual aspects, as if the they didn't give value.

How would you feel about this other definition?

Programming =

Sitting in front of a computer and punching keys.

If programming is defined like that, PM & SA look much more difficult, even by your definition (which isn't correct).

Those professions are better paid because they are, indeed, more difficult than programming.

1. They involve dealing with people, not machines. People are vastly more difficult to work with, given their non-deterministic nature. The subset called clients is specially troublesome.
2. Others have said it, but let me repeat it: responsibility. If a programmer screws up, it's up to the PM to solve the problem. Not just to report it, to solve it. It might involve delaying a launch for 2 weeks. Or skipping one feature.
3. The amount of multi-tasking one PM has to do is usually staggering. It's a constant exercise in balance between the team, management, the clients, and the budget. It is not easy.
4. It also involves communication "the other way around" - Not only the programmer must report to the PM on the status; the PM is in charge of properly communicating expectations, risks and goals. If some cases they're also in charge of training.
5. Have I mentioned dealing with clients?

If the project managers that you work with just do powerpoints, they are not doing their jobs correctly. And that's sad.

I think you will not really understand why project managers earn more than programmers until you meet a good project manager.