Saving for the Machines

gist

Jesús Fernández-Villaverde models automation as a task-based growth boom whose size depends on how much households save. In his calibration, the same technology path that yields 11.7% annual growth when the saving rate is chosen optimally delivers only 2.2% when it stays at the U.S. 2025 rate of 23%. Task complementarity shapes how long the boom lasts and how wages move, while a rising capital share, not thrift, drives the higher saving rate; the ten-year real yield jumps from 5.1% to as high as 13.6% on impact.

ideas

• Capital supply sets boom size; tasks set duration. With full automation by 2045 and constant machines, optimal saving produces limit growth of 21.9%, 14.8%, and 11.6% for task elasticities σ = 1, 0.5, and 0.2, while a fixed 23% saving rate yields only 6.5%, 3.5%, and 2.2% in 2045.
• Saving rises with the capital share. The saving rate climbs to about 54–57% of GDP under full automation with constant machines, mainly because automation moves tasks to capital rather than because households become thriftier.
• Wages fall hard under full automation, then can recover if some tasks stay human. With constant machines, wages settle at 46%, 34%, and 28% of trend for σ = 1, 0.5, and 0.2; under partial automation with σ = 0.2 they later rebound to about 7.5 times trend by 2065.
• Hand-to-mouth households lose a lot; compensating them is cheap relative to output. They lose the equivalent of about 40–65% of consumption, while a temporary transfer to keep them on trend peaks at about 4–20% of GDP and a capital-income tax cuts growth by at most a few points.
• Long yields price the boom immediately. On impact the ten-year real yield jumps from 5.1% to 13.6% (σ = 1) or 9.3% (σ = 0.2), while the short rate does not move because the machine stock is fixed.

quotes