Determine the steepness of the agentic AI adoption S-curve

Determine the true steepness parameter k of the logistic adoption function V(r, τ) used to model agentic AI deployment across regions and years in the Agentic Task Exposure (ATE) framework, using empirical data to quantify how quickly adoption progresses and thereby resolve the dependence of displacement timing and scale on this parameter.

Background

The ATE framework models regional deployment of agentic AI via a logistic (S-curve) function V(r, τ) characterized by parameters k (growth rate), τ0 (inflection), and L (saturation). The sensitivity analysis shows that the timing and magnitude of displacement risk are highly sensitive to k, with large differences in threshold crossings under conservative versus aggressive values.

A discrepancy exists between the calibrated Tier 1 k (0.85) and a much lower k (~0.13) derived from AI job-posting data, motivating the need for direct empirical estimation of k from suitable deployment indicators to resolve this uncertainty and refine displacement projections.