User:Stevelihn/sandbox/Unemployment momentum

The unemployment momentum $U_{1y}(t)$ is defined in Lihn (2019) as the 12-month difference of logarithm of the unemployment rate in the U.S.:

$U_{1y}(t)=\log {\text{UNRATE}}(t)-\log {\text{UNRATE}}(t-1),$

where ${\text{UNRATE}}(t)$ is the U.S. civilian unemployment rate published by the Federal Reserve, and $t$ is measured by year.

The unemployment acceleration $A_{6m}(t)$ is defined as the 6-month rate of change of $U_{1y}(t)$:

$A_{6m}(t)=2(U_{1y}(t)-U_{1y}(t-0.5)).$

Applications

In the real-time recession probability model developed in Lihn (2019), $U_{1y}(t)$ has two states - normal state and crash state - in the Hidden Markov Model (HMM), and $A_{6m}(t)$ has three states - acceleration, middle (or normal), deceleration. The composite HMM can decode the NBER recession indicator, USREC, since 1960 with reasonable precision. It shows that positive momentum in unemployment kicks off a recession. The momentum accelerates during the recession. And eventually the rapid deceleration marks the end of it.