Saving for the Machines
“Saving for the Machines” (Jesús Fernández-Villaverde, PIER Working Paper 26-018, October 2026) asks who funds the physical capital — data centers, power plants, the machines themselves — that an automation transition requires, and what happens when saving falls short. Its claim: capital supply, and not the technology alone, governs the size of the growth boom.
The mechanism
The production side is the Acemoglu–Restrepo task framework: output aggregates tasks, each performed by labor or machines, and automation moves tasks from labor to machines. That raises the capital share of output — from one-third toward one under full automation in the calibration — while ordinary productivity growth leaves the capital share roughly unchanged. Saving is the capital share times the ratio of investment to capital income; with an optimizing representative household the second ratio barely moves (0.69 to about 0.55 as the return climbs from 11% to 52%), so the saving rate rises because machines earn more of output, and households respond to higher returns rather than to any change in thrift. 1
Quantitative results
Holding the automation path fixed (every task automatable between 2025 and 2045 in the benchmark), the economy grows at 11.7% per year with optimal saving and at 2.2% with the saving rate frozen at its calibrated 2025 value of 23%. Slow observed growth can therefore reflect insufficient capital accumulation rather than a technological bottleneck. The optimizing household eventually saves more than half of output (54% in the limit at the benchmark intertemporal elasticity of substitution; 93% with log utility); the fixed rate only clears the boom threshold under high task complementarity. Long yields price the boom: the ten-year real yield jumps from 5.1% to 13.6% on impact. The gains are uneven: wages stay between a quarter and a half of trend under common comparative advantage (labor cannot earn more than the machines that replace it), and hand-to-mouth households lose the equivalent of two-fifths to two-thirds of their consumption; keeping them on trend temporarily costs at most a fifth of GDP. With continuously improving machine productivity, the capital share and saving rate fall toward zero in the long run — better machines make capital cheap. 2
The fiscal back-of-envelope: adopters and bystanders
In a public summary circulated with the paper (quoted in full by Cowen), Fernández-Villaverde runs the debt arithmetic for an AI-adopting economy (the U.S. in his example) and a “bystander” integrated into world capital markets but not adopting (his deliberately extreme case: Spain). Both pay the higher world interest rate; only the adopter gets the growth. With unit elasticity across tasks the real rate rises to 42% by 2040 while growth lags it; on a balanced primary budget, debt reaches 296% of GDP in 2040 and 907% in 2045, and holding debt at 100% of GDP requires primary surpluses of 10% of GDP in 2035 rising to 24% afterward — coverable in the adopter’s case by a flat tax on net capital income (which grows to about 88% of GDP) at 36%, though the tax slows growth. The bystander needs surpluses of 44% of GDP forever, which no tax system raises, and its capital flows abroad to the machines in any case. The named exits: default, inflation, or financial repression — capital controls keeping domestic savers from investing in machines abroad. Repricing of long yields front-loads the same bill on any Treasury that rolls its debt. He adds a policy kicker: a government convinced of transformative AI should term out its debt now — fifty-year bonds — while long real yields remain low. Cowen, hosting the summary, pushes back on the zero-adoption assumption (ideas are public goods Spain can benefit from — see knowledge-problem) and on the assumed inelasticity of long-run capital supply. 3
Historical precedent: financial repression
The financial-repression exit has a worked twentieth-century precedent. Reinhart and Sbrancia document how post-WWII advanced economies liquidated high public debt through negative or below-market real interest rates — interest-rate caps, directed lending to government by captive domestic audiences (pension funds, banks), and cross-border capital controls — a transfer from savers to the government. Real interest rates were negative about half of the time across advanced economies during 1945–1980, average annual interest-expense savings ran about 1 to 5 percent of GDP for their twelve-country sample, and the mechanism worked best when paired with inflation. They suggest financial repression may rejoin the toolkit as public debt surged again after 2008. 4
Related
- ai-economic-growth-complementarity — the AI growth-model comparison; this paper’s capital-supply margin cuts across all of them
- knowledge-problem — ideas as public goods (Cowen’s caveat), and price signals generally
- technological-unemployment-history — the labor-side history of machine displacement
- lifecycle-wealth-accumulation — the household side of saving behavior: identical saving rules plus compounding generate steep age-wealth profiles
Sources
- Jesús Fernández-Villaverde 2026 — Saving for the Machines
- Tyler Cowen 2026 — Will bystander economies be able to finance their governments?
- Carmen M. Reinhart and M. Belen Sbrancia 2015 — The Liquidation of Government Debt