The present US economic expansion has been one of the weakest on record and also one of the longest. From the progress to date on the headline unemployment rate, and from recent Fed moves to increase short interest rates from their 0 rate floor, we can readily see that we are now entering late-cycle conditions. So the question arises - how late are we in the present cycle, and how likely is it that the actual end of the cycle could occur in a short period ahead, say the next 12 months?

To answer this question, I start from a standard conception of the business cycle and its underlying causes. That standard conception predicts movements in certain macroeconomic indicators as being causally related to the end of an expansion period and the onset of recession. I will briefly describe that model and those variables below. Here I just want to emphasize that the selection of variables used is not based on statistical patterns or a search for anything that might correlate with recessions; it is driven by a believed causal logic. The three key indicators this approach picks out are the spread between longer- and shorter-term interest rates ("the yield curve" for short), the unemployment rate, and the rate of inflation.

Having identified these measures as likely to show a definite pattern just prior to the end of expansions, I next train a simple statistical model to predict recessions in the following 12 months. This means the training algorithm is allowed to assign weights to these factors, and that statistical measures can tell us whether they are statistically significant predictors of the outcome we are aiming at, in the context of the information provided by each of the others. All the indicators do have that character, in some cases after suitable smoothing or transformation. The model details will be given below. The result of the model is a simple mathematical function of the 3 indicator variables that returns a single number - a sort of recession risk score. I provide a plot of that recession risk score versus its actual training variable below, which helps us to interpret those scores. Simple threshold levels of the score can then serve as recession warning indicators.

What is the underlying cycle model that selects these indicators? The stylized cycle sees higher profits and business expansion for future rather than immediate output, funded by expanding credit and producing a progressive increase in supply and increases in factor incomes. Eventually, this new supply reaches the market and reduces relative pricing power of business, while stretched use of labor and capital raises wages and (with a lag to the previous) interest paid to capital.

These twin forces downward on selling prices and upward on costs reduce the profits to business of the new activities just funded, leading some of them to regret investments made at previously prevailing prices. When they retrench, the expansion process partially reverses. This capsule model of the cycle therefore predicts that labor must get tight and broad prices rise before the late-cycle top is reached, and that interest rates moving significantly higher is the final act of the drama. On this reasoning, the indicators chosen are not merely temporally correlated with the cycle but are coupled to it as causes, and therefore cannot be separated from it.

Please note that this model is not trying to predict movements of stock prices or of interest rates (and therefore, bond prices). It is strictly trying to give us warning, at least a year ahead of time, of a contraction in real US GDP. I think we all know already that such economic events are associated with weak periods for stocks, and that is practical motivation enough. Operationally, when the recession risk indicator exceeds a certain level, it would counsel reduction of one's stock allocation. No backtest of that rule is provided here, but from the results it is clear that it would in the past have worked reasonably well as a stock market timer. Naturally, that may be "overfitting" to a short period of the past, and the next period could follow its own patterns etc.

In the first chart above, the orange shaded areas are the periods we are training to spot. They are defined by real GDP recessions but precede those recession periods themselves by 12 months. Specifically, the target vector for our predictor model is 1 if the US economy was in recession at any point within 12 months after that date, and 0 otherwise. The blue line shows the risk level the model predicts at that point in time for the level of economic indicators prevailing then. A perfect predictor would go "on" like a light switch in the orange regions, while being 0 outside of those regions. You can see from the plot that ours ticks up before recessions, exceeds a value of about 0.3 reliably just before the year ahead time threshold is crossed, and gives values in the 0.30s or higher (sometimes much higher) in the periods at least a year ahead of the recessions themselves.

The chart below shows the values of the indicators used by the predictor function. The source data for all 3 come from the Fred II databases from the St. Louis Fed, with different degrees of pre-processing and smoothing. For example, the inflation data is based on year-over-year changes in the CPI, then further smoothed with a 6-month moving average. The unemployment rate is a 3-month moving average of the headline civilian unemployment rate. The yield curve is defined as the constant maturity rate on 10-year Treasuries minus the constant maturity rate on 2-year Treasuries - T10-2 for short - and that is also smoothed with a 12-month moving average. Note that these pre-processing steps have also been used to "align" the different indicators in the time domain with what they are trying to predict, and to deal with the differing levels of noise seen in each type of data.

A few factual items about those indicators - the mean of the unemployment rate over the period covered is 6.35%, the mean of the inflation rate is 3.66%, and the mean of the yield curve spread is 0.96%. The present levels of the same 3 indicators are 4.5%, 2.3%, and 1.034% respectively, showing the unemployment rate well below its long-run full-cycle average but the yield curve measure pretty much right at normal, though trending down.

If you look back at the last portion of the first graph at the top of the page, you can see the blue line rising from its previous near-zero level, signaling the onset of late-cycle conditions. That stems from the tightening of the yield curve measure and from the low and falling level of the unemployment rate. But notice, it is still well below the levels that actually predict recession within the next 12 months.

Here is a parameter table of the details of the model, which is a logistic regression against the recession timing vector:

Notice that all of the p-values are statistically significant at the 5% level and all but the inflation rate at much higher levels of significance. The inflation measure is frankly weakened by the much larger rate of inflation seen in the recessions at the end of the 1970s and beginning of the 1980s. The signs of the estimate values are telling us that higher inflation, lower unemployment, and a lower yield curve are all associated with a higher risk of recession in the next 12 months. The size of the estimates is telling us that the yield curve measure is by far the most powerful, for each unit of 1% that is, with 1% of yield curve "worth" 2.5% of unemployment rate, and inflation coming in a distant third with 5% points of it needed to match the importance of a 1% lower unemployment rate. When all figures are near their means, the recession chance is 0.015, which is basically 0. For their current values, the risk measure comes back as 0.052.

We can then ask, what would need to happen for this model to return 0.3 or higher and a significant risk of recession in 12-15 months? The basic answer comes back that the yield curve would need to tighten to around 0.5% if, in the meantime, the unemployment rate fell to around 4% and the inflation rate climbed to around 3%.

Basically, the model is telling us that as long as the yield curve keeps its present positive slope of 1% difference between the 10-year and 2-year Treasury, the risk of recession is low, even at these levels of the unemployment rate or a bit lower. The strongest recession signal is a flat or inverted yield curve; when that accompanies an unemployment rate as low as it is today or lower, recession in the next 12 months is nearly assured.

The whole exercise tells us that recession is not right around the corner, that the next 12 months should be free of recession, but that we need to watch the yield curve carefully from here forward. If the Fed continues its campaign of tightening but the 10-year rate moves up in parallel, the expansion is likely to continue.

I hope this is helpful, and comments are welcome.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure: **Long US stocks, real estate, and corporate bonds.