Do Government Spending Cuts Reduce Growth?

We can test this proposition using the stimulus wind-down over the past couple of quarters. The blue squares in the chart below are measures of actual inflation-adjusted government spending growth and real GDP growth. It looks like the economy grew more as government spending was cut after the stimulus peaked.

(For an explanation of the red and green hypotheticals shown in the chart, click here).

You might argue that government spending cut back only when the economy began to recover for other reasons, but I see two problems with that argument:

• the wind-down of the ARRA "stimulus" was set two years ago when the law was passed. By what miracle did the stimulus designers get the timing exactly correct, while at the same time were wildly off on how deep the recession would ultimately prove to be?
  
• If you believe that government spending really does increase GDP, what exactly is helped the economy endure the end-of-stimulus spending cuts by actually growing faster that it did a year ago when stimulus spending was peaking?