# Step 251: inference, weighting and placebo tests for the European regression; Israel by year

**Why.** The European regression (step 192: 848 observations, 13 countries, 39 occupation groups,
annual changes ending 2024 and 2025) clusters standard errors by occupation, but the adoption change
is a country-year variable. It is unweighted, has no placebo or pre-trend test, and its "54 robustness
checks" are 13 leave-one-country-out and 39 leave-one-occupation-out estimates plus two others. In
Israel, averaging 2023 and 2024 hides the 2024 value for clerical workers.

Generated by `scripts/empirical_inference_v251.py` (numpy; the step-192 panel is rebuilt from the
archived inputs); archived in `data/processed/empirical_inference_v251.json`. Wild cluster bootstrap by
country with the null imposed, Webb six-point weights, 9,999 replications.

## Main estimate

| Specification | beta | SE occupation | SE country | SE two-way | Wild bootstrap p (country) |
|---|---:|---:|---:|---:|---:|
| Unweighted (step 192) | -0.545 | 0.543 | 0.562 | 0.299 | 0.391 |
| Weighted by employment | -1.208 | 0.518 | 0.334 | 0.518* | 0.016 |

\* the two-way variance estimate was negative; the larger one-way estimate is reported.

- The unweighted estimate is reproduced exactly; with country clustering or the wild bootstrap it
  stays far from significance (p = 0.33-0.39). The two-way SE is smaller, not larger, so occupation
  clustering was not the problem.
- **Weighted by employment the estimate doubles and becomes significant** (p = 0.016 by wild
  bootstrap). Large occupation groups drive a negative association.

## Placebo: earlier employment growth on the later adoption change

| Outcome | beta | Wild bootstrap p | Observations |
|---|---:|---:|---:|
| Growth one year earlier, unweighted | -0.655 | 0.563 | 809 |
| Growth one year earlier, weighted | **-1.486** | 0.271 | 809 |
| Growth two years earlier, unweighted | 0.144 | 0.944 | 404 |
| Growth two years earlier, weighted | -1.503 | 0.738 | 404 |

**The weighted placebo is as large as the weighted estimate.** Employment in exposed occupations was
already growing more slowly, a year before, in the countries whose adoption later rose most. The
placebo is not significant, but its size means the significant weighted estimate cannot be read as an
effect of adoption: it is at least as consistent with pre-existing trends.

**Conclusion for the text.** The European evidence does not show an effect of AI adoption: the
unweighted estimate is a wide null under every inference method, and the weighted estimate, which is
significant, fails a placebo test. The data are uninformative rather than reassuring.

## Israel: relative risk of unemployment by year

| Group (ILO exposure) | 2017 | 2018 | 2021 | 2022 | 2023 | 2024 |
|---|---:|---:|---:|---:|---:|---:|
| Clerical support (0.55) | 1.36 | 1.34 | 1.60 | 1.61 | 1.26 | **1.42** |
| Professionals (0.40) | 0.57 | 0.67 | 0.56 | 0.64 | 0.72 | **0.83** |
| Managers (0.36) | 0.81 | 0.84 | 0.75 | 0.74 | 0.66 | 0.80 |
| Technicians (0.35) | 0.94 | 1.00 | 1.11 | 0.92 | 0.93 | 0.92 |
| Service and sales (0.24) | 1.41 | 1.28 | 1.37 | 1.20 | 1.23 | 1.11 |
| Skilled trades and operators (0.20) | 0.97 | 0.97 | 1.10 | 1.25 | 1.18 | 1.05 |
| Elementary (0.15) | 1.72 | 1.64 | 1.48 | 1.79 | 1.82 | 1.53 |

Clerical over-representation in 2024 (1.42) is above 2017-18 and below the COVID-affected 2021-22
values; averaging 2023 and 2024 (1.34) understated it. Professionals rise steadily, from 0.57 to 0.83.
Two post-AI years in seven groups, with the war in both, are not a test.

## Limits

- 13 countries: wild bootstrap p-values with few clusters are approximate.
- Placebo samples are smaller (fewer earlier pairs pass the quality filter).
- Weights are start-year employment; the outcome is still growth of employment counts.