The graph above shows the % growth in real total government expenditures (federal,state and local) compared to the % growth in real private GDP. The median growth rate is subtracted from each to more easily see the pattern (when the graph is above 0 it is growing faster than the median value).
In this case 80.49% of the time government spending and private GDP are on opposite sides of 0. If the line is headed up the growth rate is increasing. The lines are headed in opposite directions 72.5% of the time.
There are many factors at play which complicate the pattern so the curves aren't exactly mirror images. Worldwide economic factors have an influence as do government policies that impact the economy but don't change spending, advances in technology, etc. For more info check the new page.