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Augmented Human Capital: A Unified Theory and LLM-Based Measurement Framework for Cognitive Factor Decomposition in AI-Augmented Economies

Cristian Espinal Maya

Abstract

This paper proposes a decomposition of human capital into three orthogonal components -- physical-manual (H^P), routine-cognitive (H^C), and augmentable-cognitive (H^A) -- and develops a production function in which AI capital interacts asymmetrically with these components: substituting for routine cognitive work while complementing augmentable cognitive work through an amplification function phi(D). I derive a corrected Mincerian wage equation and show that the standard specification is misspecified in AI-augmented economies. Using LLM-generated measures of occupational augmentability for 18,796 O*NET task statements mapped to 440 Colombian occupations, merged with household survey microdata (N = 105,517 workers), I estimate the augmented Mincer equation. The wage return to H^A increases with AI adoption in the formal sector (beta_2 = +0.051, p < 0.001), while informal workers cannot capture augmentation rents (beta_2 = -0.044). A triple interaction confirms formality as the binding mechanism (beta_{AHC x D x Formal} = +0.272, p < 0.001). The augmentation premium is strongest for experienced workers (ages 46-65) and in health and education sectors. These results provide the first developing-country evidence of cognitive factor decomposition in AI-augmented labor markets and demonstrate that the binding constraint on human-AI complementarity in the Global South is not technology access but labor market institutions.

Augmented Human Capital: A Unified Theory and LLM-Based Measurement Framework for Cognitive Factor Decomposition in AI-Augmented Economies

Abstract

This paper proposes a decomposition of human capital into three orthogonal components -- physical-manual (H^P), routine-cognitive (H^C), and augmentable-cognitive (H^A) -- and develops a production function in which AI capital interacts asymmetrically with these components: substituting for routine cognitive work while complementing augmentable cognitive work through an amplification function phi(D). I derive a corrected Mincerian wage equation and show that the standard specification is misspecified in AI-augmented economies. Using LLM-generated measures of occupational augmentability for 18,796 O*NET task statements mapped to 440 Colombian occupations, merged with household survey microdata (N = 105,517 workers), I estimate the augmented Mincer equation. The wage return to H^A increases with AI adoption in the formal sector (beta_2 = +0.051, p < 0.001), while informal workers cannot capture augmentation rents (beta_2 = -0.044). A triple interaction confirms formality as the binding mechanism (beta_{AHC x D x Formal} = +0.272, p < 0.001). The augmentation premium is strongest for experienced workers (ages 46-65) and in health and education sectors. These results provide the first developing-country evidence of cognitive factor decomposition in AI-augmented labor markets and demonstrate that the binding constraint on human-AI complementarity in the Global South is not technology access but labor market institutions.

Paper Structure

This paper contains 29 sections, 3 theorems, 7 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Decomposition of Human Capital
  4. Production Function with Amplification
  5. Equilibrium Wages and Key Propositions
  6. Measurement with LLMs
  7. The Measurement Challenge
  8. Occupational Crosswalk
  9. LLM Scoring Protocol
  10. AHC Index Construction
  11. Validation
  12. Data
  13. GEIH Microdata
  14. AI Adoption Proxy
  15. Identification Strategy
  16. ...and 14 more sections

Key Result

Proposition 1

From the firm's first-order conditions, when $D_f > 0$: The marginal product of augmentable human capital exceeds that of routine cognitive capital by a factor $\phi(D_f) \cdot D_f > 1$. $\blacktriangleleft$$\blacktriangleleft$

Figures (5)

  • Figure 1: Augmentable Human Capital (AHC) score by sector. Sectors above the median (blue) are $H^A$-intensive; sectors below (gray) are $H^P$- or $H^C$-intensive. Education, professional services, and public administration rank highest.
  • Figure 2: AHC score vs. Frey--Osborne automation probability at the occupation level ($n = 430$). The strong negative correlation ($r = -0.79$) confirms that augmentation and automation are opposing dimensions. Bubble size proportional to employment.
  • Figure 3: External validation: correlation of the AHC index with seven existing AI exposure indices. Green bars indicate convergent validity (AHC correlates positively with measures of AI-relevant cognitive content); red bars indicate discriminant validity (AHC correlates negatively with measures of automation/robotization risk).
  • Figure 4: Heterogeneity of the augmentation premium ($\beta_2$: AHC$\times$D interaction) across subgroups. Blue bars: significant positive premium. Red bars: significant negative. Gray: not significant. The formal/informal split and the age gradient are the strongest patterns.
  • Figure 5: Augmentation premium across the wage distribution. Left: AHC level effect ($\beta_1$), which turns positive above the median. Right: AHC$\times$D interaction ($\beta_2$), which is 19 times larger at $\tau = 0.90$ than at $\tau = 0.10$, indicating that AI augmentation is inequality-increasing.

Theorems & Definitions (5)

  • Definition 1: Augmented Human Capital Decomposition
  • Definition 2: Amplification Function
  • Proposition 1: Differential Returns to Cognitive Components
  • Proposition 2: Augmented Mincer Equation
  • Proposition 3: Formality as Binding Constraint