Will AI poison the public finances of many modern states? There is a real risk that it will. Yesterday, I circulated a new paper, “Saving for the Machines,” which makes a simple point. Building the AI transformation will require enormous investment. The only way to induce agents to save for that investment is through a large increase in the real interest rate. For instance, in my benchmark scenario, the ten-year real yield jumps from 5.1% to 13.6% on impact. But that means government borrowing will become much more expensive. Here is a back-of-the-envelope calculation. Take a government that owes 100% of GDP in 2025 (a typical case in Western Europe) and runs a balanced primary budget from then on (not so typical but never mind; I want to build an optimistic scenario). That means the debt ratio changes only with the gap between the real interest rate and growth. I input the interest rate and the growth rate for my benchmark transition to full automation, and I roll over the debt at the short rate. I consider two economies. The first economy is an AI adopter, for example, the U.S., which experiences an AI boom at home. The government pays the new interest rate but also enjoys faster growth. The second economy is a bystander, for example, Spain. This economy lives in an integrated financial market but does not adopt AI (this is an extreme case of zero adoption, just to make the exercise transparent): it pays the same world interest rate and continues growing at its old 1.6% trend. Let’s first consider the adopter. With an intertemporal elasticity of substitution of one-half, the Euler equation implies that consumption growth is about half the real interest rate. Hence, the gap between the interest rate and growth does not close during the AI-driven growth boom. Instead, it widens. For example, with a unit elasticity of substitution among tasks, the real rate rises from 5.1% to 42% by 2040, while growth increases only from 1.6% to 22%. Debt doubles by 2038, reaches 296% of GDP in 2040, and 907% in 2045. To hold the ratio at 100%, the government needs a primary surplus of 10% of GDP in 2035 and 24% from 2045 onward. With a low elasticity of substitution of 0.2, the numbers are milder, but the pattern is the same: 204% in 2040, 397% in 2045, and a stabilizing surplus of 13% of GDP. But the adopter has a way out. The capital share goes to one, so net capital income is about 88% of GDP, and a flat tax on it can cover the surplus. A 36% tax on net capital income holds the debt at 100% of GDP in the limit with unit elasticity, and a 20% tax does so with strong complementarity across tasks. The tax is above the gap because it slows growth, from 21.9% to 13.6% with unit elasticity and from 11.7% to 9.1% with an elasticity of 0.2, while it does nothing to the rate the Treasury pays, which technology pins at the machines' net return. Painful, but the boom survives and the adopter can pay its debt. The grim news is that the bystander economy has no way out. Its capital income is still a third of GDP, which grows at 1.6%, and the surplus it needs is 11% of GDP in 2030, 26% in 2035, and 44% forever with unit elasticity (18% and 24% with an elasticity of 0.2). On a balanced primary budget, its debt doubles by 2033 and triples by 2035. No tax system raises that. Two more bad pieces of news for the bystander. First, long yields jump on impact, so a Treasury that issues ten-year debt pays more, and sooner, than rolling over at the short rate assumes: it is the same bill but front-loaded. Second, the bystander’s own capital flows to the machines abroad, so its GDP and tax base fall below trend. One relief is that households can save for other people’s machines and get rich on the returns, which the bystander’s government can tax to some extent. This back-of-the-envelope calculation is a benchmark, not a forecast of what is to come. But the arithmetic is simple, and it runs counter to the hope that an AI-fueled growth boom will take care of public debt, because growth comes with an interest rate that is twice as high. Not a pretty future for most of Western Europe. Due to AI, the choice is between default, inflation, or, most likely, financial repression: capital controls that keep domestic savers from investing in machines abroad. Let me close with a practical implication. If you believe in the transformative effects of AI, you disagree with the bond market, since today’s long real yields have not risen nearly as much as they should in that scenario. Therefore, the time to term out the debt is now, before repricing, because every year of coupon locked in at today’s rates is a transfer from today’s bondholders to taxpayers. A treasury that believes in transformative AI should be issuing fifty-year bonds; one that is shortening its maturity is betting the other way.

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…