# Step 270: further checks on the European AI-adoption regression

**Why.** The second referee report raised three points about step 251:

- Occupation fixed effects absorb the level of AI exposure, but not exposure-specific trends.
- The placebo was judged by eye ("a relation of the same size a year earlier") rather than tested.
- The placebo sample (809 cells) differs from the main sample (848).

Generated by `scripts/empirical_v270.py`; archived in `data/processed/empirical_v270.json`. Panel and
inference as in step 251. The panel has 13 countries, 39 occupations and the years 2024–2025. The
wild cluster bootstrap is by country, with Webb weights, the null imposed and 9,999 replications. With
13 clusters its p-value is the one to read. Descriptive; not causal.

## Fixed effects for exposure-specific trends

Coefficient on exposure × change in AI adoption, with 95% CI from country-clustered SE and the
bootstrap p-value:

| Fixed effects | Unweighted | Employment-weighted |
|---|---|---|
| Country × year, occupation (step 251) | −0.54 [−1.65, 0.56], p = 0.39 | −1.21 [−1.86, −0.55], p = 0.015 |
| + exposure × year | −0.30 [−1.43, 0.83], p = 0.65 | −1.12 [−1.85, −0.40], p = 0.012 |
| + exposure × country | −1.83 [−2.57, −1.10], p = 0.077 | −0.71 [−1.20, −0.23], p = 0.32 |
| Step 251, on the 809 placebo cells | −0.76 [−2.05, 0.53], p = 0.33 | −1.33 [−2.00, −0.66], p = 0.010 |

With exposure × country fixed effects, the coefficient is identified only from the change in a
country's adoption between 2024 and 2025. The unweighted estimate is then large, but the bootstrap
does not confirm it (p = 0.077; the clustered SE alone would give p < 0.001).

**What it shows.** The weighted association survives a common trend by exposure. It does not survive
country-specific exposure trends. The unweighted estimate stays insignificant.

## A formal placebo test

The outcome in the placebo is employment growth one year earlier; the regressor is unchanged. Both
coefficients are estimated on the same 809 cells in one stacked regression with separate fixed
effects. The test asks whether they are equal:

| | Main, same cells | Placebo | Difference | 95% CI | Bootstrap p |
|---|---:|---:|---:|---|---:|
| Unweighted | −0.76 | −0.66 | −0.10 | −3.07 to 2.86 | 0.94 |
| Weighted | −1.33 | −1.49 | +0.16 | −1.95 to 2.26 | 0.90 |

**What it shows.** The data cannot tell the main coefficient from the placebo. Nor can they tell the
placebo from zero (weighted p = 0.27, step 251). The test has little power: the confidence interval for
the difference is wider than the main estimate itself. The weighted relation cannot be attributed to
the timing of AI adoption. Equally, the data do not show that it is a pre-existing trend.

## Wording for the text

"The employment-weighted association is robust to a common trend by exposure but not to
country-specific trends, and a placebo one year earlier is statistically indistinguishable from it,
though the placebo test has little power. The evidence does not support reading the association as an
effect of AI adoption."