Work in progress

1. Optimal Growth with Threshold-Activated Automation: A Filippov System Approach  (since 2025)

Motivation: The role of automation in economic growth has received increasing attention in recent macroeconomic research. Prettner (2019), for instance, examines the implications of automation for aggregate growth in a Solow-type framework, emphasizing its effects on long-run capital accumulation and labor substitution. In this paper, we extend Prettner’s analysis by embedding automation into an optimal growth model with forward-looking agents. Whereas the original study considers the case in which automation is always active, our framework introduces a more general setting in which automation is triggered only once capital per head surpasses a critical threshold. This feature generates a piecewise-defined, two-dimensional dynamical system in capital and consumption per head. The discontinuous nature of the dynamics challenges standard analytical methods and necessitates alternative approaches to fully characterize the equilibrium behavior of the economy. 

To address this, we employ the Filippov system framework, which allows us to rigorously analyze sliding modes and discontinuous trajectories in the phase space. This approach captures the qualitative features of the growth path under automation adoption, including potential multiple regimes and threshold-driven transitions.

Contribution (Potential): The contribution of this paper is threefold. First, we provide a theoretical extension of Prettner (2019) by integrating automation into an optimal growth model, highlighting the implications of capital thresholds on long-run dynamics. Second, we introduce a Filippov system approach to the macroeconomic growth literature, offering a rigorous tool to handle piecewise-smooth dynamics arising from threshold-driven automation adoption. Third, we complement our analytical results with numerical simulations, illustrating phase diagrams, sliding modes, and the economic implications of switching regimes. These findings provide insights into the policy relevance of automation adoption thresholds and their effects on consumption and growth trajectories. 

Reference

Prettner, K. (2019). A note on the implications of automation for economic growth and the labor share. Macroeconomic Dynamics, 23(3), 1294-1301.