Structural change, elasticity of substitution, and growth

This paper investigates structural change driven by sectoral differences in the elasticity of substitution (ES). While existing literature successfully replicates empirical patterns using complex numerical simulations, the underlying mechanisms often remain opaque. To provide clear theoretical insights, we develop an analytically tractable two-sector model, strategically using linear and Cobb-Douglas production functions for the agricultural and non-agricultural sectors respectively. This model helps analyze how the primary aspects of structural shift from the agricultural to non-agricultural sector change over time. The model demonstrates how standard monotonic shifts of labor and value-added shares from agriculture to non-agricultural sectors coexist with non-monotonic dynamics: the capital share of the non-agricultural sector and the macro ES follow U-shaped paths, while the aggregate capital income share follows an inverted U-shaped trend. We elucidate the mechanisms that lead to these non-monotonic changes while showing that our results are largely consistent with empirical findings.
The income ratio of capital to labor shows an inverted U-shaped trend.
The capital share of the non-agricultural sector shows a U-shaped trend.
The elasticity of substitution between capital and labor shows a U-shaped trend.
We use two types of production functions: linear and Cobb-Douglas.