Accurate Characterization of Yield-Curve and Recession Probabilities
There has been massive propaganda by Federal Reserve System (FRS) and the financial media to downplay the Inversion of the Yield-Curve. One part of the propaganda was a report by New York Fed: (http://www.newyorkfed.org/research/current_issues/ci2-7.pdf) which produced fraudulent table for probability of recession as a function of 10Y-3M-YD (US Treasury 10-Year Note minus 3-Month Bill Yield Differential). John Maudlin, who recently made use of the table, is justifying it based on "math" model used to compute the probabilities despite observably false data. Some others have supported my data and arguments presented in Ref.  and .
Our goal here is to demystify the "math" so that even a college dropout can see for himself, or herself, what the true probabilities of recession are based on any given Target Level (TL) of 10Y-3M-YD. For example, a Target Level of zero, or just below zero, would correspond to the Inversion of the Yield-Curve. In order to compute probability one has to define carefully what are valid independent observations and even more carefully what are outcomes for each observation.
If our goal is to find the probability of a recession within 12 months after the 10Y-3M-YD reaches a certain TL, the universe of observations is to be defined as all those instances in time when the 10Y-3M-YD first reaches the TL from a higher level, or on the downside, when the economy is NOT in a recession already. The next observation must not begin for at least 12 months. There are only two outcomes to be examined once the observation has been triggered - was there a beginning of a recession within 12 months or not? By dividing the total number of recessions triggered by the total number of observations we get the probability of a recession within 12 month for the given TL. By feeding the data into a "math," or statistical, model, without careful selection of observations and outcomes what one would get is GIGO (garbage in garbage out) and that is what the Fed study produced. Whether it was deliberate fraud or not one can hide behind the model unless one can clearly show the timings of the observations and outcomes in a figure and a table so that one can count for himself, or herself, and be satisfied that indeed the recessions did occur within 12 months of 10Y-3M-YD reaching the given TL.
I have expanded the data period to 50 years, 1956-2005, from the 36 years, 1960-1995, used in the Fed study. I have chosen to start in 1956 because the last time the US had deflation, on YoY basis, was in 1955. So, the data covers only the inflationary period, because I have reasons to believe that the results would not be good forecast for a deflationary period. This is because in an outright deflationary period the Fed can never take the real Fed Funds rate to negative. This means that even at 0% Fed Funds rate the Fed Policy could be too tight! I also believe that for inflation rate much higher than that achieved in 1980, e.g., 20%, the forecast based on 10Y-3M-YD and the current data would not be very good. The longer period also gives more accurate probabilities because the US had 8 recessions during this period compared to only 5 in the Fed study.
As it turns out it is not necessary to wait for the Inversion of the Yield-Curve for one to start worrying about a recession. There is a significant probability, e.g., 25%, of a recession once the 10Y-3M-YD has hit +0.5%. The normal range is +1.0-1.5%.
Fig. 1 shows how the probability should be computed at the TL of +0.32%. In yellow we show the instances when the 10Y-3M-YD hits 0.32%, or below, on monthly data basis, on the downside, when the economy is not already in a recession and there was no such instance within the last 12 months. There were a total of 10 such instances for the 50-year period of our study. For these 10 instances, there were 5 recessions within 12 months. THIS IMPLIES THAT THE PROBABLITY OF A RECESSION AFTER THE 10Y-3M-YD HITS +0.32% IS 50%! Results are summarized below in Table 1.
|Observations||Date TL = +0.32%
Within 12 Months
Within 20 Months
With experiments as summarized in Table 1 we reach the following results:
In 12 Months
|0.16% & Above||66.70%||6||1|
|0.0% & Above||77.78%||7||1|
|-0.16% & Above||88.89%||8||1|
|-0.32% & Above||100.00%||8||0|
Fig. 2 gives the full picture of 10Y-3M-YD and recessions over the 50 years.
As it turns out once the 10Y-3M-YD hits -0.16%, it has predicted all the eight recessions (it missed no recession) and there was one false alarm (no recession occurred within 12 months). The Inversion of the Yield-Curve has predicted 7 of the 8 recessions, within 12 months of Inversion, over the past 50 years and there was only one false alarm when the economy came very close to a recession. The only inference that can be drawn from a very negative level of 10Y-3M-YD is about the severity of the coming recession, but nothing affecting the probability once 10Y-3M-YD had cracked -0.32%. As things stand, probability of recession in 2006 is already at 50%, regardless of what happens to 10Y-3M-YD from now onwards!, and will go higher by the month if 10Y-3M-YD continues to go further down.
It would be interesting to see if Mr. Mauldin remains committed to defending the fraudulent results in the Fed study because the fraud, whether deliberate or due to incompetence, is bullish for the economic outlook. People are very afraid to talk about something with the best record of forecasting that indicates a higher than 50% probability in 2006. The "muddle thru" economy, Mr. Mauldin's forecast, may not be able to muddle thru much longer in that case. There are some people in the gallery who are watching to see how Mr. Mauldin deals with all the evidence that I have provided and hides behind the "math" that he does not understand and certainly can't explain as I have explained my math. I wonder what would have happened to the Fed study had it made the error in the opposite direction, i.e., grossly over stated the probabilities of recession.
There is no guarantee that there will be a recession in 2006, but if 10Y-3M-YD reaches -0.25% over the next two months the odds will be overwhelming. Continuing bad news on housing will do it.