Cristóbal Ruiz-Tagle C.

Everyone talks about what AI will do. But almost nobody asks who will pay for the machines. Taking advantage of AI will require an extraordinary amount of capital, from data centers to new power plants. Will that capital be around? I try to address that question in the first draft of my new paper “Saving for the Machines.” To show how important capital is to fuel the transition to an AI-based economy, 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 remains fixed. In other words, if we experience slow growth over the next few years despite fast improvements in AI, this slow growth may reflect too little capital accumulation instead of a technological bottleneck. The key to this result is that AI raises the capital share by moving tasks from labor to machines, which requires that those machines are built. In comparison, ordinary technical progress makes labor and existing machines better at the tasks they already perform. To inspect the mechanism, I start from an accounting identity: the saving rate is the capital share times the ratio of investment to capital income. If I take the evolution of the capital share as given, I can ask how much the latter ratio moves in response to that evolution. Crucially, with an optimizing household, this ratio barely moves. As machines take over tasks and the return to capital rises, the household responds by letting consumption grow faster, by the intertemporal elasticity of substitution times the rise in the return. To pay for that faster consumption, capital must also grow faster by the same amount. So, the household keeps investing about the same fraction of what the machines earn. And since machines earn a larger share of output, the saving rate also goes up. With a fixed saving rate, the same accounting identity tells me the opposite: the ratio falls in proportion as the capital share rises. Will the U.S. and other advanced economies then generate enough capital? For many reasons, I doubt it. We might end up in a situation where many of the opportunities offered by AI are left on the table. This is particularly important for all who think that AI might get us out of many problems, such as fiscal troubles (like in France) or ultra-low fertility. We need to save for the machines, and it is not clear we can do that. Anyway, this paper has been long in the making (many months of hard work), but I have learned much from it. In particular, working through the model changed my mind about many issues related to AI. Again and again, my intuition said X, but the math said Y. And math always won in the end. That is why we write formal models. A nice example is Proposition 5, whose proof is the one I like the most in the paper. With improving machines and strong task complementarity, there is no fixed balanced growth path because the target itself keeps moving. The nice part of the proof is to realize that, after the right normalization, the moving target becomes a fixed point, and the saddle gets steeper as machines improve. So instead of falling behind, the economy tracks the moving BGP more and more closely. A fair amount of ODE work to get there, but a very simple economic idea underneath it once you get it. The paper is here: sas.upenn.edu/~jesusfv/Savin… and the slides are here: sas.upenn.edu/~jesusfv/Slide…