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

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.