AI CNAE Incidence Matrix Analysis

• AI CNAE Incidence Matrix is a quantitative framework that assesses sector-specific AI exposure in Spain using CNAE-2009 classifications.
• It integrates occupational data, task-level AI applicability, and employment microdata to reveal regional and gender disparities in AI risk.
• The methodology supports evidence-based policy design by identifying high-risk sectors and informing targeted reskilling programs.

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 (Mestre et al., 28 Dec 2025).

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 (Mestre et al., 28 Dec 2025).