# Step 280: how much of a labour-cost saving reaches prices? European industries, 2000–2023

**Why.** The third referee report noted that the empirical part informs no model parameter. Pass-through
is one of the model's main factors, and the grid sets it at 0, 0.5 or 1 by assumption. This step
estimates it.

**What the model's pass-through means.** In the model, P = 1 − π × s × (1 − w/e): firms pass a share π
of the saving in labour cost to prices, where s is the labour share. The empirical counterpart is the
elasticity of an industry's price to its unit labour cost, weighted by the labour share:

    Δln P_ict = γ × s_ic × Δln ULC_ict + country-year fixed effects + industry fixed effects + e

- P is the value-added deflator.
- ULC is compensation of employees divided by real value added.
- γ estimates π. γ = 1 means a fall in unit labour cost reaches the industry's price in full; γ = 0
  means it stays in margins.
- Country-year fixed effects remove each country's aggregate inflation, so γ is the pass-through to
  **relative** prices.

**Data.** Eurostat `nama_10_a64`, with value added at current prices and in chain-linked volumes, and
compensation of employees. Coverage: 15 countries, 50 market industries (NACE A\*64), 2000–2023, giving
17,686 country-industry-years. The data were downloaded in GitHub Actions by
`scripts/passthrough_v280.py` (workflow `eurostat-passthrough-v280.yml`). The panel, estimates and
source manifest are archived in `data/processed/passthrough_*_v280.*`.

**Inference.** Standard errors are clustered by country (15) and by country-industry (739). The p-value
comes from a wild cluster bootstrap by country (Webb weights, null imposed, 4,999 replications).
Descriptive; not causal.

## Results

| Specification | γ (pass-through) | 95% CI (country clusters) | Bootstrap p (γ = 0) | Observations |
|---|---:|---|---:|---:|
| Annual changes | 0.63 | 0.50 to 0.76 | 0.0002 | 16,843 |
| 5-year changes | 1.03 | 0.83 to 1.22 | 0.0002 | 3,651 |
| 5-year, manufacturing | 1.57 | 1.25 to 1.90 | | 1,397 |
| 5-year, services and other | 0.78 | 0.61 to 0.96 | | 2,254 |

Reduced form: a 1% rise in an industry's real value added is associated with a relative price fall of
0.42% within the year and 0.63% over five years. The median labour share is 0.55, which implies a
pass-through of productivity gains of 0.76 within the year and 1.14 over five years.

## Caveats

- **Division bias.** Real value added appears in both the deflator and unit labour cost. Measurement
  error in it biases γ upwards. This is the likely reason γ exceeds 1 in manufacturing.
- **Instrumenting does not settle it.** I tried the lagged change in unit labour cost as an
  instrument, but it is too weak (first-stage F of 3.9 for annual changes and 0.3 for 5-year changes).
  The resulting estimates (0.19 and 2.48) are uninformative.
- **Relative prices only.** The estimate is the pass-through to relative prices. Whether the aggregate
  price level falls depends on monetary policy. Under inflation targeting it does not, and the gain
  appears as higher real wages (the model's "gain to wages" regime, steps 272 and 281).

## What it means for the model

- The data reject no pass-through. They suggest that most of a labour-cost saving reaches relative
  prices within a year and roughly all of it within five years, with an upward bias of unknown size.
- The empirically relevant part of the grid is therefore π between about 0.6 and 1. Under the revised
  central specification (step 281), that corresponds to preservation of 51%–69% of cases, against 73%
  with no pass-through.
- Whether this harms the displaced through deflation depends on what happens to the aggregate price
  level, not on the industry evidence.
- **Thesis.** The empirical chapter now has two parts. This estimate sets the model's pass-through. The
  AI-adoption association (steps 192–270) becomes a short motivating section that reports a null.