Saving for the Machines

When machines can perform a growing share of tasks, growth depends on two margins: how the task structure affects the returns to accumulating machines, and how strongly capital accumulation responds to those returns. I argue that, in a standard task model, capital supply governs the size of the growth boom associated with automation, while the task structure sets the duration of this growth boom and the evolution of wages. I document how the same technology path that generates 11.7% annual growth when households choose their saving rate optimally delivers only 2.2% when the saving rate is fixed at the calibrated U.S. 2025 level of 23%. Therefore, slow growth might reflect too little capital accumulation instead of a technological bottleneck. Also, the saving rate rises mainly because automation raises the capital share, not because households become thriftier. Long yields price the growth boom: the ten-year real yield jumps from 5.1% to 13.6% on impact. In my benchmark calibration, hand-to-mouth households lose the equivalent of two-fifths to two-thirds of their consumption, while keeping them on trend temporarily costs at most a fifth of GDP.