# Statistical appendix

All estimates are descriptive. The retained CSV files contain unrounded coefficients, confidence intervals, p-values and sample sizes.

## Pre-period and holdout diagnostics

| sector | specification | adf_residual_p | holdout_rmse | last_month_benchmark_rmse | n_train | training_end |
| --- | --- | --- | --- | --- | --- | --- |
| C | No trend | 0.002097 | 1.231 | 1.386 | 114 | 2019-12 |
| C | Linear trend | 0.004211 | 1.398 | 1.386 | 114 | 2019-12 |

Full dataset: `data/clean/model-diagnostics.csv`.

## Manufacturing known-date joint tests

| sector | date | chow_f | chow_p | hac_wald_p | n_pre | n_post | short_post | hac_p_holm |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| C | 2018-01 | 1.828 | 0.1094 | 0.0003648 | 89 | 103 | False | 0.01605 |
| C | 2020-01 | 1.553 | 0.1758 | 0.002623 | 113 | 79 | False | 0.09444 |
| C | 2022-02 | 1.811 | 0.1128 | 8.232e-05 | 138 | 54 | False | 0.003951 |
| C | 2023-01 | 1.987 | 0.08256 | 9.693e-06 | 149 | 43 | False | 0.0004944 |
| C | 2025-01 | 0.941 | 0.4557 | 1.901e-05 | 173 | 19 | True | 0.0009507 |

Full dataset: `data/clean/structural-break-tests.csv`.

## Manufacturing change in summed order coefficient

| sector | date | order_slope_change | lower | upper | p | n | p_holm |
| --- | --- | --- | --- | --- | --- | --- | --- |
| C | 2018-01 | -0.1503 | -0.4338 | 0.1333 | 0.2989 | 192 | 1 |
| C | 2020-01 | -0.16 | -0.4448 | 0.1247 | 0.2706 | 192 | 1 |
| C | 2022-02 | -0.007621 | -0.2727 | 0.2575 | 0.9551 | 192 | 1 |
| C | 2023-01 | 0.02591 | -0.2352 | 0.287 | 0.8458 | 192 | 1 |
| C | 2025-01 | 0.1845 | -0.06526 | 0.4343 | 0.1476 | 192 | 1 |

Full dataset: `data/clean/order-slope-change-tests.csv`.

## Manufacturing global segmentation alternatives

| sector | segments | bic | rss | break_dates | n | min_segment | bic_selected |
| --- | --- | --- | --- | --- | --- | --- | --- |
| C | 1 | 415.6 | 1458 | nan | 192 | 30 | False |
| C | 2 | 414.2 | 1229 | 2020-05 | 192 | 30 | False |
| C | 3 | 372.3 | 838.1 | 2017-10/2020-05 | 192 | 30 | True |
| C | 4 | 381 | 744.1 | 2017-10/2020-05/2023-03 | 192 | 30 | False |

Full dataset: `data/clean/multiple-break-search.csv`.

## Energy exposure cross section

| sector | model | term | coefficient | lower | upper | p | n | adj_r2 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Matched sectors | Cross section HC3 | const | -19.99 | -50.6 | 10.63 | 0.2007 | 14 | 0.3335 |
| Matched sectors | Cross section HC3 | log_energy | 1.83 | -9.771 | 13.43 | 0.7572 | 14 | 0.3335 |
| Matched sectors | Cross section HC3 | pretrend_pct | 0.6073 | -0.4962 | 1.711 | 0.2808 | 14 | 0.3335 |

Full dataset: `data/clean/energy-cross-section-model.csv`.

## GIERI level/change and investment tests

| sector | model | term | coefficient | lower | upper | p | n | adj_r2 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| Manufacturing | GIERI | const | 1.03 | -0.07793 | 2.137 | 0.06845 | 64 | 0.5595 |
| Manufacturing | GIERI | GIERI | 3.713 | 3.15 | 4.277 | 3.868e-38 | 64 | 0.5595 |
| Manufacturing | GIERI / differences | const | 0.07338 | -0.3353 | 0.4821 | 0.7249 | 63 | 0.1321 |
| Manufacturing | GIERI / differences | GIERI | 2.968 | -0.8031 | 6.739 | 0.1229 | 63 | 0.1321 |
| Manufacturing | Without capacity | const | 1.207 | 0.01193 | 2.402 | 0.04776 | 64 | 0.4943 |
| Manufacturing | Without capacity | GIERI_ex_capacity | 3.347 | 2.53 | 4.163 | 9.515e-16 | 64 | 0.4943 |
| Manufacturing | Without capacity / differences | const | 0.1388 | -0.2773 | 0.5549 | 0.5132 | 63 | -0.007743 |
| Manufacturing | Without capacity / differences | GIERI_ex_capacity | 0.6653 | -0.3781 | 1.709 | 0.2114 | 63 | -0.007743 |
| Manufacturing | Energy double weight | const | 1.211 | 0.05368 | 2.369 | 0.04028 | 64 | 0.5242 |
| Manufacturing | Energy double weight | GIERI_energy_double | 3.425 | 2.78 | 4.069 | 2.053e-25 | 64 | 0.5242 |
| Manufacturing | Energy double weight / differences | const | 0.09729 | -0.281 | 0.4756 | 0.6142 | 63 | 0.06026 |
| Manufacturing | Energy double weight / differences | GIERI_energy_double | 2.139 | -0.6543 | 4.933 | 0.1334 | 63 | 0.06026 |
| Manufacturing | Politics half weight | const | 1.289 | 0.06238 | 2.515 | 0.03943 | 64 | 0.5163 |
| Manufacturing | Politics half weight | GIERI_politics_half | 4.03 | 3.402 | 4.659 | 3.466e-36 | 64 | 0.5163 |
| Manufacturing | Politics half weight / differences | const | 0.08961 | -0.3155 | 0.4948 | 0.6646 | 63 | 0.143 |
| Manufacturing | Politics half weight / differences | GIERI_politics_half | 3.107 | -0.8557 | 7.07 | 0.1244 | 63 | 0.143 |
| Manufacturing | Components | const | 0.498 | -0.3712 | 1.367 | 0.2614 | 64 | 0.6286 |
| Manufacturing | Components | Energy | 0.8855 | 0.03938 | 1.732 | 0.04025 | 64 | 0.6286 |
| Manufacturing | Components | Logistics | -0.3842 | -1.533 | 0.7651 | 0.5124 | 64 | 0.6286 |
| Manufacturing | Components | Politics | 1.175 | 0.5943 | 1.757 | 7.354e-05 | 64 | 0.6286 |
| Manufacturing | Components | Financing | -1.186 | -3.184 | 0.8111 | 0.2444 | 64 | 0.6286 |
| Manufacturing | Components | Capacity | 1.16 | 0.09398 | 2.226 | 0.03294 | 64 | 0.6286 |
| Manufacturing | Components / differences | const | 0.07134 | -0.4396 | 0.5823 | 0.7844 | 63 | 0.3506 |
| Manufacturing | Components / differences | Energy | 0.5362 | -0.2361 | 1.308 | 0.1736 | 63 | 0.3506 |
| Manufacturing | Components / differences | Logistics | -0.0614 | -0.5936 | 0.4708 | 0.8211 | 63 | 0.3506 |
| Manufacturing | Components / differences | Politics | 0.1759 | -0.3542 | 0.706 | 0.5154 | 63 | 0.3506 |
| Manufacturing | Components / differences | Financing | -0.7787 | -2.133 | 0.576 | 0.2599 | 63 | 0.3506 |
| Manufacturing | Components / differences | Capacity | 2.26 | 1.581 | 2.938 | 6.789e-11 | 63 | 0.3506 |
| Total economy | Uncertainty → investment association | const | 0.4638 | 0.06959 | 0.858 | 0.02111 | 63 | 0.02029 |
| Total economy | Uncertainty → investment association | Politics | -0.1578 | -0.2728 | -0.04291 | 0.007106 | 63 | 0.02029 |

Full dataset: `data/clean/risk-models.csv`.

## Interpretation gate

A low p-value for a joint parameter break does not identify the source of the break. The slope-change tests target the sum of the order coefficients directly and retain their intervals and multiplicity adjustment. Statistical significance in levels does not protect a risk-index regression against shared trends or endogenous utilization. The publication does not assign causal percentages.