John H. Welch
Research for Emerging Markets
5 August 2024
· The Fed of St. Louis estimates the natural unemployment is somewhere around 4.5%; we are currently at 4.3%.
· The CBO estimates the output gap is a positive 0.4%, above full employment.
· Suddenly, the Sahm rule indicates that we may already be in a recession.
· Claudia Sahn developed the rule (of thumb) for the fiscal policy purposes not for predictions and looks at changes and not levels.
· That is, the data tells us that we are going somewhere but not where we are going, where we will end up, or when we arrive.
· If we are at high employment and we have a natural slowing of employment growth combined with increased labor force participation, this change really does not indicate a recession true.
· This may merely reflect a movement back towards a more normal level of unemployment regardless of the inflation rate.
· Using a more a stronger methodology (cointegration)than moving averages, we find that this is exactly what is happening.
Suddenly, investors have gone into a panic over the change in the unemployment rate breaking the so-called Sahm Rule, developed by Claudia Sahm to trigger budget for automatic stabilizer such as increased unemployment payments and lower tax revenues. But the Sahm Rule is based upon changes in unemployment with no reference to where the economy is in levels. [1] On Bloomberg surveillance today, Dr. Sahm stated so and the rule was created for a US economy already in recession. As best it gives us some direction for the economy but does not give any indications of location, that it, a recession.
In contrast the St. Louis Fed’s estimate of natural unemployment is somewhere around 4.5%; we are currently at 4.3% (chart 1). The CEO's estimate of the output gap is less than a positive 0.4%, above full employment (chart 2). If the measurements are right, the economy cannot operate above potential or full employment for ever. Inflation or macroeconomic policies will bring the economy back to full employment and will necessarily involve a decrease in output and job creation and an increase in the unemployment rate. Increases in labor market participation ss the pandemic-led exodus reverses and growing salaries makes the path nonlinear. Simpe smoothing filters and linear extrapolation may give us direction but do not give us a clear idea of where we end up.
Source: FRED
Source: CBO
Suddenly the Sahm rule indicates that we may already be in a recession.
The simple Sahm rule posits that the three-month moving average of the national unemployment rate is at least 0.5 percentage-points above the low of the prior twelve months, we are in the early months of recession. The rule uses only a simple smoothing filter is useful when putting together budget changes to accommodate transfers and lower tax revenue.
Hence if we are at high employment and we have a slowing of employment growth and an increase in labor force participation this change really does not indicate a recession true.
This movement in the employment and unemployment numbers may merely reflect a movement back towards a more normal level of unemployment regardless of the inflation rate.
Using a more sophisticated methodology than moving averages, we find that this movement is exactly a return to normality or mean reversion that is stronger than just moving averages (cointegration).
The gaps calculated above mean reverting by construction with a 0% average. But what about the underlying data? Simple tests (Augmented Dickey Fuller) shows that the unemployment and natural rates of unemployment are random walks (integrated of order 1).[1]
Consider two random walks: a drunk walking his dog (see cartoon below).[2] They have some leeway to wander in whatever direction they want. These are the changes in the Sahm Rule. This goes on until they hit the leash, and the leash brings them back in. If there is no leash or is some slack, predicting the next step of each of them is difficult. Hence, they can go in any direction. But at some point, the leash holds their juxtaposition although both are moving.
In this case, the fast-moving variable, the unemployment rate, will eventually achieve and usually surpass the slow-moving variable with average deviations around the natural unemployment rate equal to zero. The difference estimated the dynamics of the movement of the unemployment rate back to full employment. These estimates also show the two series as cointegrated of order 1. [3] Chart 3 sows this relationship which looks very much like the output gap figures from the CBO. These reflect that my simple bivariate model does not capture all of what is in the CBO’s model. But the message is the same.
Source: FRED, REM, Inc.
The changes of a moving average compared to a level observed twelve months ago may signal a strong move in one direction or another, but it does not show the location the distance from the ultimate target, The Sahm Rule shows direction but by our gauge, the economy is still far from recession.
[1] See, for example, Sahm, Claudia (2019-05-16). "Direct stimulus payments to individuals". Brookings. Retrieved 2020-12-20.
[2] Null Hypothesis: UNEMP has a unit root
[3] Analogy taken from Michael P. Murray (1994): “A Drunk and Her Dog: AN Illustration of Cointegration and Error Correction,” The American Statistician, Vol.48 No. 1.
[4] Date: 08/05/24 Time: 15:32
[5] They are different because I estimated the coefficients instead of setting them equal to 1 and -1. Here are the estimated ones.
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