Since I updated the US model of the real world in part 1, I thought I would show what the counterfactual world would look like in three scenarios: no ARRA ("the $787 billion fiscal stimulus"), no QE (quantitative easing) as well as neither QE nor ARRA. This is partially in response to a back and forth on "monetary offset" in the comments on this Yglesias post. The key point is that one needs a model to extract counterfactuals; a graph of NGDP on its own shows nothing of the effect of monetary or fiscal policy.
First we'll look at the price level (or rather the change in the price level) due to ARRA and QE:
The ARRA had a small effect on the price level; QE -- a much larger effect. Next we'll look at the effect on NGDP:
Here we can see the effect of QE was about twice as big as the ARRA. Additionally, if we compare the "sticker price" of the ARRA (green curve) to the effect the ARRA on NGDP (blue curve), we get a "fiscal multiplier" of 1.25 (somewhat less than the 1.5 used to estimate the effect of the stimulus, but near the 1.3 estimated by the IMF, or between 0.9 and 1.7). However, if we look at the effect of the ARRA without the monetary stimulus (the difference between the purple and red curves) we get a multiplier of only 1.07. A failure of monetary policy would have reduced the multiplier by about 15%; that gives a us scale of how much monetary offset we might expect.
Next we look at the effect of the ARRA and QE on interest rates. In this case the effect is almost entirely monetary:
We can see a small deviation raising interest rates on the order of 20 basis points due to the ARRA (one could imagine this is the scale of "crowding out"), but monetary policy dominates the change.
In the final graph we look at the labor markets, in particular the unemployment rate (calculated by looking at the change in employment in the labor model P:NGDP→L from part 1):
One thing that immediately appears is how misguided claims that the fiscal stimulus "failed" based on the original estimates of the effect of the ARRA. Those estimates were predicated on a particular counterfactual world that was actually a much rosier picture than was even known at the time. Here we see that the size fo the effect of the ARRA was pretty much as predicted, reducing the unemployment rate from a peak of 13% to a peak of 10% (as opposed to reducing a peak of 9% to a peak of 7%).
And that's why model-based counterfactuals are important.