Peter left a comment saying that he didn't believe changes in the monetary base caused anything, and I thought I'd promote my response to a post. I said:
... I disagree that the monetary base doesn't cause anything and a different thought experiment shows how it works. Let's say I give you 900 € (and you live in the EU). You'd do one of three things: nothing, deposit some of it in your bank (which gets lent out), or spend part of it. Since we are all complicated individuals with our own motivations I can't say exactly what you'd do. The least informative prior says you'd spend 300 €, put 300 € in the bank and let 300 € sit in your wallet. On average, you'd do something with it. Very few people would just let the 900 € sit under their mattress.
Did giving you 900 € cause you to deposit the money or spend it? Well, that's philosophical. Personally, I like to say the 900 € opened up your consumption state space and you took your own path through it ... and on average people do wander through part of it.
[I used € because dollar signs will collide with mathjax.]
The key thing to understand the state space opened up by the 900 €. Does it include higher prices (inflation)? Increased output (NGDP = N)?
This blog says yes to both if the 900 € is physical currency M and the ratio of the naive (least informative prior) information in revealing a dollar of output (log N) to the information in revealing a dollar of physical currency (log M) is greater than one (this is the information transfer index k).  If k is close to one (allocating a dollar of output has the same information as allocating a dollar of currency), then there is output growth but not inflation. Inflation measures widget information ; money measures widgets. Output is a mix of both.
 There's a bit of nuance to that statement, but it's a good elevator pitch version. See here and here for more.
 See the draft paper for more.