Underemployment Risk (CPS)

Composite stress indicator based on U‑6 underutilization and median weeks unemployed. Outputs include robust z‑scores, optional percentile ranks, EMA smoothing, 0–100 scaling, and categorical regimes.

Why: Elevated U‑6 and longer unemployment durations reflect slack and scarring in the labor market that often precede demand weakness.

Abstract

We build a monthly underemployment risk signal from CPS series capturing broad slack (U‑6) and job‑loss persistence (median unemployment duration). Each series is standardized using robust rolling z‑scores; the composite is their average. We also report full‑sample percentile ranks for interpretability, apply EMA smoothing, scale to 0–100, and classify regimes.

1. Data (BLS CPS Identifiers)

LNS13327709 — U‑6: Alternative measure of labor underutilization (%)
LNS13008276 — Median weeks unemployed

Inputs are monthly. We enforce presence of date, series_id, and value, and align data to a month‑start grid with bounded forward‑fill (ffill(limit=2)).

2. Data Handling & Validation

Types & dates: Coerce numeric values; normalize dates to month‑start timestamps.
Pivot & grid: Wide pivot by series_id, align to asfreq('MS').
Fail‑fast: raise if either series is fully missing after pivot.

3. Measures & Diagnostics

U‑6 underutilization rate (higher = more slack)

Median weeks unemployed (higher = longer job‑finding frictions)

Diagnostics: 3‑month momentum for both inputs (diff(3)).

4. Standardisation (Robust Rolling z‑scores)

Each series is scaled with a median/MAD z‑score using an adaptive window.

z_t(x) = (x_t − median_W(x)) / (1.4826·MAD_W(x)),\ W = min(36, max(8, ⌊0.8·N_valid⌋))

5. Composite Construction

We take an equal‑weight average of the two z‑scores (both are bad when high):

Underemployment_z = 0.5·z(U‑6) + 0.5·z(Median Weeks)

For interpretability, we also compute full‑sample percentile ranks for each input and average them: Underemployment_Composite_pctRank.

6. Smoothing, Scaling & Regimes

Headline smoothing: 3‑period EMA on the composite z‑score.
Score (0–100): min–max scaling over observed history; NaN if the series is flat.
Regimes: thresholds on the unsmoothed composite z‑score.

HOT (stress ↑): > +0.75
NEUTRAL: −0.75 to +0.75
COOL (stress ↓): < −0.75

7. Output Panel

[
  "u6_underutilization_rate","median_weeks_unemployed",
  "u6_pct_rank_fullsample","weeks_pct_rank_fullsample",
  "Underemployment_Composite_pctRank",
  "u6_z","weeks_z","Underemployment_z",
  "Underemployment_0_100","Underemployment_Smoothed","Underemployment_Regime",
  "u6_mom_3m","weeks_mom_3m"
]

8. Implementation Notes (Python)

# Expect columns: date, series_id, value (monthly)
# Align to MS grid; ffill(limit=2); pivot to wide; compute z-scores, pct-ranks,
# composite, EMA smoothing, 0–100 scaling, regime classification as detailed above.

9. Interpretation & Use

A HOT underemployment regime indicates broad slack and elongated job‑finding, often consistent with cooling demand and softer wage pressure. A COOL regime reflects easing stress and faster re‑employment dynamics.