In our previous note on WorkWhile’s American Labor Utilization Rate (ALUR), we introduced ALUR as a real-time gauge of whether active workers keep earning on our platform. We showed that ALUR is a timely, high-frequency signal that helps nowcast labor-force dynamics, and – crucially – that it co-moves with employment continuation (the share of workers employed last month who are still employed this month). With simple, transparent regressions, ALUR demonstrated explanatory power for predicting officially reported labor market flows, giving policymakers and analysts an early read on the direction of official prints.

The two-step bridge: ALUR → continuation → unemployment

Ignoring monthly changes in labor force participation, the unemployment rate can be decomposed into flow components – continuation and hiring – via the following identity:

\[
u_t=1 - e_{t-1}c_t - h_t
\]

where:

• $c_t$ = continuation rate
• $e_{t-1}$ = last month’s employed share of the labor force
• $h_t$ = this month’s hires as a share of the labor force
  
  

Holding hiring $h_t$ fixed (which in general won’t be true):

\[
\Delta u_t = - e_{t-1}\Delta c_ t
\]

Let \(\hat{\beta}\) be the estimated one-unit effect of a change in ALUR on employment continuation rates. Then we get:

\[
\Delta u_t = - e_{t-1} \hat{\beta} \,\Delta \text{ALUR}_t
\]

This gives a simple, approximate way to translate an ALUR delta into an unemployment delta.

A small, concrete example

• $e_{t-1} = 0.96$
  
  
• As estimated in our previous note, ALUR impact on employment continuation $c_t$ is $= 0.1$ (i.e., $+10$ basis point ALUR change ≈ $1$ basis point continuation rate change)
  
  
• ALUR change: $–0.5$

Computation:

\[
\Delta u_t \approx - 0.96 \times 0.1 \times (-0.5) = 0.048 \approx 0.05
\]

Interpretation: a half-point deterioration in ALUR implies roughly a $5$ basis point upward pressure on the unemployment rate through reduced continuity alone.

Why tiny ALUR moves matter

Monthly labor prints turn on flows – who stays or leaves and who gets hired. ALUR gives a timely read on who stays. Even small drifts (e.g., $+0.3$ to $+0.5$ p.p.) translate into basis-point-scale tilts in unemployment, sharpening directional views before the official release.

What this method doesn’t (yet) capture

1. Hiring dynamics held fixed.
   The identity isolates the continuation channel. Monthly changes in labor force participation and hiring are critical components excluded from this simplified methodology.
   
   
2. Empirical, not structural elasticities.
   The ALUR→continuation coefficient should be estimated for the relevant sector mix, window, and refreshed over time.

Until those extensions land, this continuation-only bridge offers a clear first pass – when ALUR ticks up, unemployment pressure via persistence tilts down. Even small ALUR changes are meaningful monthly signals.

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