Why Obama's recovery won't match up to Reagan's

Growth was consistently much higher during the Reagan recovery than in the Obama recovery but exceeded it by a lot more during the phase when government spending increased equally than when spending rose in the Reagan recovery compared to the Obama recovery.

Paul Krugman claims, both in his latest column and in a recent blog post, that because government spending rose a lot more during the first 10 quarters of the Reagan recovery than the Obama recover that the Obama recovery would have been just as strong if only government spending had increased equally.
His proof? Well, he argues that this is the case because Keynesian models show that with the multiplier effect from these purchases growth would have been just as strong. But that of course assumes that we buy into the legitimacy of these models, something that Krugman and others have failed to do on a theoretical basis.

But doesn't the empirical fact that the stronger Reagan recovery was associated with a higher increase in government spending prove the accuracy of these models? No, because first of all, you can't establish the legitimacy of theoretical models with such simple comparisons as there are so many other factors involved. And secondly, if you look closer at the chart (below) you'll see that for the first five quarters government spending increased equally.

Yet during those five quarters when government spending increased equally, average annualized GDP growth was 3.1% during Obama and 7.8% during Reagan. During the following five quarters of the recovery when spending increased during Reagan and fell during Obama growth was 1.8% during Obama and 3.7% during Reagan.

So the facts are the following: growth was consistently much higher during the Reagan recovery than in the Obama recovery but exceeded it by a lot more during the phase when government spending increased equally than when spending rose in the Reagan recovery compared to the Obama recovery. If really government spending had the strong effect Krugman imagined we would have expected at the very least that the gap would have been smaller during the period when spending increased equally.

Note also that compared to GDP, government spending fell more during Reagan even for the 10 quarter period as a whole. Government spending may have risen 7 percentage points (3% versus 10%) less during Obama,  but the gap in cumulative GDP growth was 9 percentage points (6% versus 15%).