A Note on Aggregating Human Capital Across Heterogeneous Cohorts

The objective of this paper is to add to the the criticisms of the "macro-Mincer" approach by emphasizing two important theoretical points, not addressed so far in the literature. First, we show that the "macro-Mincer" relationship between aggregate human capital and average years of schooling is generally lost upon aggregation. More precisely, we find that even if the cross-sectional "micro-Mincer" relationship does hold at the level of individuals, the "macro-Mincer" equation can be obtained only in very special cases. We proceed to explain that these cases are inconsistent with heterogeneity, insofar they require the aggregated individuals to have an equal number of years of schooling. We also demonstrate an important difference in aggegation results whether human capital stocks in the whole population or in the labor force are considered. In particular, the "macro-Mincer" relationship can only be obtained (under additional restrictions) for the latter case but not for the former. We solve the aggregation problem formally, based on a general framework for computing the aggregate human capital stock under heterogeneity across cohorts, building on Growiec (2010). The building blocks of the framework are: (a) the human capital accumulation equation at the individual level, (b) the demographic survival law, (c) assumptions regarding the allocation of time between schooling and work. The Mincer equation between the human capital stock and years of schooling is preserved upon aggregation (when going from the "micro-Mincer" to the "macro-Mincer" equation) only if: (a) all working individuals have the same number of years of schooling, or (b) the survival law is consistent with Blanchard's (1985) "perpetual youth" assumption, and a certain additional restriction holds. Otherwise, the loglinear Mincerian relationship is lost upon aggregation. NOTE: The attached paper is a preliminary and incomplete version, please do not circulate.