Recession daters decoded

Mahalanobis distance tells use whether one set of M samples is from the M dimensional distribution, or another distribution. The four dimensions seems to be:

• Industrial Production (one-year percentage change, measured monthly) 
• Nonfarm Payrolls (one-year percentage change, measured monthly)
• Return of the Stock Market (one-year return, measured monthly) 
• Slope of the Yield Curve (10-year rate minus the Federal Funds Rate) 

We define recessions as those periods identified as recessions by the NBER. We define periods as robust growth as months in which the year-over-year percentage change in industrial production ranked above the 75th percentile relative to the prior 10 years. This tail of the growth distribution is approximately proportional to the recession tail. For the first five years of our sample we use a threshold of 5% annual growth in industrial production. 

The assumption is that all are equilibrium with Dr. Gauss.   The measure is coincident because of the relative weighting, the less sharp of the distributions weighted less by having the covariance appear in the denominator. 

The Gaussian assumption mostly holds if we are there, already. The slope is going straight up, I interpret this to mean the recession daters have been meeting in secret. Nice work, actually. No cause and effect determined, just the bare facts.