This is illustrated in Graph 1.
The red dots are data points from 1954 through Q1 '62. The yellow dots are from Q1 '62 on. The blue dots are the three low St Dev points from 1957, and the pink dots represent the transitions in and out of the 1957 blue dot data and the tumble down from Q2 '62 to Q4 ''63. The original blue trend line is retained. Note that removing these three blue and 8 transitional data points from the pre-1964 data set causes the negative correlation of that period to completely evaporate.
This might seem a bit arbitrary; but now we can observe a more tightly packed red data set, and the behavior of the pink data points does seem to be unusual. The string of high side outliers in the yellow data set occur in 1971-2, and are associated with the 1970-71 recession.
This piqued my curiosity, so I took a look at the bigger picture - all 253 quarterly data points from Q1 1950 through Q1 2013, shown in Graph 2.
I see the great majority of these points clustering or stringing out along upward sloping lines that suggest coherent data sets, and a relatively small number of points [39, or 15.4% of the total] where the data is in transition between sets.
I parsed it out as shown in graph 3.
The 112 green dots represent the most common subset and also the lowest Std Dev to CARC relationship. There are 42 blue points, representing an intermediate relationship, and 50 yellow points representing a high relationship. The purple dots at the top are ultra-high. Each of these subset exhibits a very respectable R^2 value. The 32 pink dots occur in discrete short periods when Std Dev rises or falls sharply.
This is an unusual way of looking at GDP data, but I feel pretty good about it, because the linear subsets sort themselves out quite reasonably, and to my eye do not look contrived. Also, the data points along each line follow the lines pretty closely, and are robust along the time span of the entire FRED data set. Now that I squint at it a little harder, it might be that the green set is further divisible.
To bring this back into the real world, Graph 3 shows the 12 period CARC average from 1950 to 2013, with the CARC data points color coded to correspond with graph 2.
The yellow points occur, unsurprisingly, when recessions are clustered, as in the 50's, or especially severe. The blue points occur during and following less severe recessions. The pink points occur duirng transitions in or out of recessions. The dark purple line is at the far left and results from the economic instability in the aftermath of WW II. The green points represent the quasi-normality of non-recessionary times.
Note that each of these data sets is coherent, irrespective of the inflationary environment. It is the presence or absence of recessions that dominates the realm in which the Std Dev of CARC falls. In each of the three recessionary/non-recessionary environments described, the Std Dev of CARC is strictly linear with CARC.
When not following one of these lines, the CARC - Std Dev relationship is transitional, moving into and out of recessions.
What strikes me is that I simply eyeballed straight lines through this scatter of data, and it wound up making some sort of coherent sense.
Now - the big question in my mind is this: how can NGDP targeting be expected to lead to controlled, relatively stable economic growth at any desired level, unless you can accurately predict not only what the underlying rate of inflation will be, but also which Standard Deviation realm you end up in?
For anyone who's curious, Graph 4 shows the CARC - Std Dev scatter, color coded by decade.
Red - 1950-59
Yellow - 1960-69
Light Blue - 1970-79
Purple - 1980-89
Orange - 1990-99
Green - 2000-09
Blue - 2010-13
Note two things. 1) As the data moves across time, when it gets to one of the realms described by Graph 2, it tends to linger there. These realms have traction. 2) Since 1980 there has been a choppy by relentless migration to lower and lower NGDP growth. We are now stuck in the worst recovery on record, and the lowest growth period ever to occur outside of a recession.
Whether fiscal policy, monetary policy, or trade policy is to blame, this is economic failure on a scale unprecedented in the post WW II period.