Description of the Full Takeoff Model


The Full Takeoff Model (FTM) is an endogenous economic growth model developed by Tom Davidson. It is meant to illustrate the future trajectory of Artificial Intelligence, the economy and associated factors. In particular, it helps us answer how long it will take to go from a partial automation of the economy to a total automation of the economy.

This model combines features from the biological anchors' AI timelines framework by Ajeya Cotra, and previous macroeconomic models of automation, e.g. the one by Aghion, Jones and Jones.

This section details a succinct mathematical description of the Full Takeoff Model (FTM). This will be helpful to mathematically oriented readers who want to see all the dynamics of the model written down in a single place.

Readers who want to understand the model's conclusions would be better served reading the short summary of Tom's report. Readers who want to understand why the model is built the way it is will be better-served reading the report. Justifications for the best-guess parameter values are described below. If you want to play with the model, you can do so in the playground.

Overview of the model

The core of the FTM is three CES production functions that govern the production of goods and services (G&S), hardware research, and software research.

Each of these functions takes as input an amount of capital (K), labour (L), effective compute (C), a level of automation (A), and the total factor productivity (TFP). Their output is used to estimate the amount of capital, compute and automation available in the next timestep, while labour and the TFP vary exogenously.

The rest of the model determines how the output of the production functions translates to improvements to the efficiency of hardware and software, how the different input factors are split up across the production functions and what is the current level of automation.

Population growthInvestmentCapitalLabourEffective computeProductionGross World ProductHardware R&D InputSoftware R&D InputR&DHardware efficiencySoftware efficiencyCapitalLabourEffective compute(Re) investmentAutomationBiggest training runG&S automationR&D automation

(Click on the different parts of the model to understand how each one works)

We aim to use this framework to estimate 1) when we'll develop AI that could fully automate cognitive labour and 2) how much earlier we'll have AI could that could automate 20% of cognitive labour (with tasks weighted by their share of output in 2020).

Through a Monte Carlo analysis, we show that this model and our choices of parameters lead to a median date of AGI of 2045, and a median takeoff duration of 3.6 years (conditional on AGI happening before 2100). You can read more about the model's results in the short summary, and browse the results of the different analyses in the reports section.

Distribution of the year when AI could readily automate all cognitive labour, and when people "wake-up" to the economic potential of AI and start upping their investments in the area. Also shown the distribution of TAI from Ajeya Cotra's bioanchors.
Distribution of the takeoff length, measured as the time between AI that could readily automate 20% of the cognitive tasks needed for producing goods and services, and 100%.