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.