Every other macro blogger seems to be taking a crack at this question. I like what they have to say. But I have a much simpler theory.
Let's suppose you wanted to design an experiment to test the effects of monetary and fiscal policy. And suppose you had the power to do whatever you wanted, and couldn't care less about getting clearance from the Research Ethics Board. What experiment would you design?
Probably something like: get 100 countries, then for each country toss two dice, one for monetary policy, the other for fiscal policy, then watch what happens for a couple of decades. That should settle the question.
Now, just for a laugh, imagine you wanted the worst possible experiment design. An experiment design so bad that no researcher would ever be able to figure out the effects of monetary and fiscal policy by looking at the data. What would you do?
Probably something like: make monetary policy negatively correlated with fiscal policy, and negatively correlated with any other shocks you observed hitting the economy. So it would be impossible for the researcher to disentangle the effects of monetary policy, fiscal policy, and any other observed shocks. If you were feeling really mean, you would do your best to try to set monetary policy and/or fiscal policy so that nothing ever did happen to the economy. So all the researcher would ever observe would be a few small fluctuations in the economy due to shocks you didn't observe (and he probably can't observe either), plus a few small fluctuations because you over-compensated or under-compensated for the shocks you did observe, and even here the researcher won't be able to figure out even the sign of the effect of monetary policy because he won't know whether tight money caused inflation or whether you just didn't tighten monetary policy enough in response to an inflationary shock.
That's the world we live in. We live in something very close to the worst possible experiment design for testing macroeconomics. We live in a house controlled by Milton Friedman's Thermostat. It's sometimes a wonky thermostat, that under- or over-compensates for the shocks it can see, but it's still a thermostat. For all its faults, it does not play dice with the amount of oil going into the furnace. Even if it did play dice, you could never be sure that it was playing dice, or just responding as best it could to some shock it sees that you don't see.
You want us macroeconomists to figure stuff out better? Sure. No problem. Just lend us 100 countries for a couple of decades, and let us play dice with monetary and fiscal policy.