---
title: AI CNAE Incidence Matrix Analysis
url: https://www.emergentmind.com/topics/ai-cnae-incidence-matrix
type: topic
---

# AI CNAE Incidence Matrix Analysis

The AI CNAE incidence matrix is a quantitative construct designed to evaluate the potential exposure of Spanish employment sectors to artificial intelligence, particularly generative models. Centered on the CNAE-2009 national classification, which organizes economic activities into 99 two-digit sectors, the matrix provides sector-specific incidence factors reflecting the intensity of AI applicability. The methodology integrates occupational structure, sectoral mapping, task-level weights, and generative-model usage data. By applying this construct to provincial employment data and further disaggregating by gender, it enables an empirically grounded assessment of structural AI exposure across Spain, supporting data-driven policy design and routine monitoring [2512.23059].

## 1. Formal Definition of the AI CNAE Incidence Matrix

The construction begins with the assignment of an incidence factor $m_c$ to each CNAE sector $c$. For $S=99$ sectors, the incidence vector is defined as:

$$
\mathbf{m} = (m_1, m_2, \ldots, m_S)^{\mathsf{T}}
$$

Each factor is

$$
m_c = \sum_{o \in O} \phi_{c,o} \, \alpha_o = \sum_{t=1}^{T} w_t \, \phi_{c,t}, \qquad c=1,\ldots,S
$$

where

- $O$: set of occupations (SOC/ESCO groups)
- $\phi_{c,o}$: employment share of occupation $o$ within sector $c$
- $\alpha_o$: AI applicability score for occupation $o$ (per Tomlinson et al., 2025)
- $w_t$: task-level AI generative applicability weight (from generative-model usage)
- $\phi_{c,t}$: intensity of task $t$ in sector $c$

The resulting incidence factors have observed bounds $0.06 \leq m_c \leq 0.30$, aggregating occupational exposure at the sectoral level. The diagonal incidence matrix is thus

$$
M = \mathrm{diag}(m_1, m_2, \ldots, m_S) \in \mathbb{R}^{S \times S}
$$

## 2. Data Sources and Sectoral Classification

Core data components for the incidence analysis include:

- **CNAE System**: The 2009 National Classification of Economic Activities (CNAE-2009), structuring Spanish sectors from "01 Agricultura" to "99 Organismos extraterritoriales".
- **Employment Microdata**: INE Censo anual de población ocupada, series 69960–, for 2021 and 2022, with breakdowns by province ($p$), sex, and CNAE sector ($c$).
- **AI-task Identification**: Occupational AI applicability scores ($\alpha_o$) derived from Copilot/Bing usage data covering 200,000+ interactions ("Working with AI", Tomlinson et al., 2025).
- **Expert Mapping**: Integration of SOC/ESCO profiles to CNAE through expert judgement, incorporating evidence of sectoral digitalization and generative-model adoption.

## 3. Methodological Workflow

The methodology encompasses conceptual mapping and quantitative aggregation:

**Step 1: Occupation-to-sector mapping**
- For each sector $c$, determine $\phi_{c,o}$ using labor structure surveys and SOC/ESCO correspondence.

**Step 2: Sector incidence factor assignment**
- Calculate $m_c$ for each sector; typical ranges by sector type:

  | Sector Type              | $m_c$ Range    |
  |-------------------------|:--------------:|
  | Primary/extractive      |   0.06–0.08    |
  | Traditional manufacturing| 0.11–0.17     |
  | Construction & utilities| 0.095–0.17     |
  | Commerce & logistics    | 0.11–0.305     |
  | Business/ICT/finance    | 0.24–0.30      |

**Step 3: Matrix construction**
- Assemble $M$ as above.

## 4. Application to Provincial and Gender-Disaggregated Employment

For each province $p$, let $\mathbf{E}_p = (E_{p,1}, \ldots, E_{p,S})^{\mathsf{T}}$ denote sectoral employment. The AI-adjusted employment vector is

$$
\mathbf{E}^{\mathrm{AI}}_p = M \mathbf{E}_p \quad \left[ (\mathbf{E}^{\mathrm{AI}}_p)_c = m_c E_{p,c} = \text{IA\_empleo}(p, c) \right]
$$

Provincial AI exposure share:

$$
\mathrm{IA\_share}(p) = \frac{\sum_{c=1}^S [\mathbf{E}^{\mathrm{AI}}_p]_c}{\sum_{c=1}^S E_{p,c}} = \frac{\sum_c E_{p,c} m_c}{E_{p,\mathrm{total}}}
$$

Extending to gender disaggregation (with $E^{(f)}_{p,c}$ and $E^{(m)}_{p,c}$ for female and male employment):

$$
\mathrm{IA\_share}^{(f)}(p) = \frac{\sum_c E^{(f)}_{p,c} m_c}{\sum_c E^{(f)}_{p,c}}, \qquad
\mathrm{IA\_share}^{(m)}(p) = \frac{\sum_c E^{(m)}_{p,c} m_c}{\sum_c E^{(m)}_{p,c}}
$$

The gender gap:

$$
\Delta_{\mathrm{gender}}(p) = \mathrm{IA\_share}^{(f)}(p) - \mathrm{IA\_share}^{(m)}(p)
$$

Empirical analyses indicate $\Delta_{\mathrm{gender}}(p) \approx 1.5\text{–}3.0\,\mathrm{pp}$, with the gap present in all provinces.

## 5. Empirical Results: Territorial and Gender Patterns

The AI CNAE incidence matrix reveals stable, sector-anchored exposure patterns:

| Province      | $E_{\mathrm{total}}$ | $E^{\mathrm{IA}}$ | $\mathrm{IA\_share}$ |
|---------------|---------------------|------------------|----------------------|
| Madrid        | 3,014,953           | 653,696          | 0.2168               |
| Barcelona     | 2,475,590           | 517,127          | 0.2089               |
| Las Palmas    | 386,306             | 81,422           | 0.2108               |
| Soria         | 39,124              | 7,052            | 0.1803               |

By gender (2022):

| Province      | $\mathrm{IA\_share}^{(f)}$ | $\mathrm{IA\_share}^{(m)}$ |
|---------------|---------------------------|---------------------------|
| Madrid        | 0.2194                    | 0.2118                    |
| Barcelona     | 0.2150                    | 0.2032                    |
| Soria         | 0.1944                    | 0.1683                    |

Key structural patterns:

- Average national AI-share: 18–22% of employment (stable 2021–2022)
- Territorial polarization: Madrid–Barcelona–Valencia–Málaga–Illes Balears–Canarias above 20%; interior provinces (Soria, Teruel, Zamora) around 17–18%
- Metropolitan/island economies concentrate sectors with high $m_c$ (finance, ICT, services, commerce)
- Rural/industrial provinces concentrate sectors with low $m_c$ (agriculture, manufacturing, construction)
- Consistent gender gap: In every province, $\mathrm{IA\_share}^{(f)} > \mathrm{IA\_share}^{(m)}$, attributed to female overrepresentation in education, health, admin, commerce

## 6. Policy Implications and Monitoring

The AI CNAE incidence matrix is validated as a robust tool for structural analysis, not forecasting job displacement but identifying where AI and generative models are likely to reshape task and skill demands. Key policy recommendations include:

- Targeted reskilling and upskilling programs for high-exposure provinces (Madrid, Barcelona, islands)
- Gender-sensitive training, particularly in administrative and service sectors, to avoid amplifying labor-market inequities
- Strategic support for peripheral provinces to diversify toward higher-value services
- Replicable, scalable method for annual monitoring (INE microdata, ENIA, PERTE evaluation)

The framework’s integration into policy and planning supports evidence-based strategies for AI readiness across Spain’s territories and social groups [2512.23059].

Source: https://www.emergentmind.com/topics/ai-cnae-incidence-matrix