Research

AI labs are increasingly using AI itself to accelerate AI research, creating a feedback loop that could potentially lead to an "intelligence explosion". We develop a general semi-endogenous growth model with an innovation network, where research and automation in one sector increases the productivity of research in other sectors, and derive a clean analytical condition under which growth becomes super-exponential ("explosive"). The key intuition is that automation of research both offsets diminishing returns to research and increases cross-sectoral research spillovers, making explosive growth more likely. Applying this model to a calibrated, AI-integrated economy, we demonstrate that the growth effects of automation may be slow initially but compound rapidly. In our benchmark calibration, the level of automation needed to double the long-run growth rate already achieves well over half of the automation level needed to generate explosive growth.

In this note I consider an economy with two factor inputs, one growing exponentially and one growing hyperbolically. I derive the conditions under which aggregate output is growing super exponentially vs subexponentially. In the case where the slow growing factor is in fact fixed, I get a closed form solution for the date at which the growth regime changes from super to subexponential.

This note derives conditions under which an endogenous automation frontier eliminates task bottlenecks in a CES task-based model, despite complementarities across tasks. An expanding AI task share can offset the drag from unbalanced factor growth, and the key condition admits a clean form: automation scales without bottleneck so long as the slope of the AI productivity gradient is less than the elasticity of substitution between AI and labour.