# Speculative Growth and the AI "Bubble" # Speculative Growth and the AI "Bubble" Ricardo J. Caballero (MIT and NBER), July 15, 2026. First draft Dec 17, 2025. Source PDF: https://economics.mit.edu/sites/default/files/2026-07/speculative_growth_AI_public.pdf Extracted with pdftotext -layout. Math sections (2-4) and appendices A-D omitted; abstract, introduction, and conclusion retained. --- Speculative Growth and the AI “Bubble” Ricardo J. Caballero∗ July 15, 2026 Link to the latest version Abstract High valuations of AI-related firms are usually read in binary terms: either they reflect fundamentals or they are a bubble. This paper develops a third possibility: an optimistic valuation can have a permanent real legacy even when the valuation later corrects. AI capital expands productive capacity and shifts income toward high-saving capital owners. Over time, this wealth-saving feedback lowers the interest rate and can generate multiple steady states, including a self-sustaining high-capital economy. But rational pricing from the low-capital state does not take the economy there. The transition requires a temporary belief-supported valuation: investors perceive high returns, valuation rises, investment accelerates, and the interest rate rises during the transition. If enough capital has been installed before learning removes the wedge, the economy lands in the high-capital state, where the long-run interest rate is lower. If learning arrives too soon, the transition fails. The technology can be real, peak valuations can be unsustained, and the capital installed during the boom can remain. Workers receive higher wages at the high-capital destination despite a lower worker share, while capitalists finance the investment surge and are exposed to the correction in belief-supported prices. JEL Codes: E21, E22, E24, E44, O33, O41. Keywords: AI, speculative growth, Bayesian learning, investment transition, multiple steady states, real rates, labor share, wealth-in-utility, saving glut, market capitalization. ∗ MIT and NBER. Email: caball@mit.edu. I thank Andrei Shleifer, Alp Simsek, Ludwig Straub, and Luohan Academy seminar participants for their comments, and Kei Uzui for research assistance. First draft: December 17, 2025. 1 1 Introduction “While some part of the investment which was going on in the world at large was doubtless ill-judged and unfruitful, there can, I think, be no doubt that the world was enormously enriched by the constructions of the quinquennium from 1925 to 1929; its wealth increased in these five years by as much as in any other ten or twenty years of its history.” —Keynes (1931) The recent increase in AI-related valuations raises a familiar question: do high prices reflect fundamentals, or are they a bubble? The question takes the fundamentals as given and asks only whether the market has them right. But investment responds to valuation, and the capital installed during a boom changes the economy that later prices it. Once prices shape the fundamentals against which they are judged, the two answers are no longer exhaustive: a valuation can be unsustainable and still leave a permanent real legacy. This paper develops that third possibility. A temporary overvaluation raises investment; if enough capital is installed before the valuation corrects, the economy is left permanently with a larger capital stock, higher wages, and a lower interest rate. The mechanism is fragile: the legacy survives only if the correction arrives late enough. The paper therefore separates three objects that the bubble question runs together: whether the technology is productive, whether peak valuations are sustained, and whether the capital financed at those valuations remains. AI provides the economic environment for the mechanism. AI capital performs tasks previously done by labor. As it accumulates, productive capacity expands and income shifts toward capital owners, who have a stronger saving motive. The resulting increase in saving capacity lowers the interest rate associated with a larger installed capital stock. This feedback can generate multiple steady states: a low-capital state and a high-capital state that is self-sustaining once enough capital has been installed. The transition mechanism is separate from the destination. The model starts from the low-capital state; an ongoing AI episode can be interpreted as an economy already inside the transition. From that initial condition, rational pricing selects the low-capital path even though a high-capital steady state exists. A temporary overvaluation supplies the missing transition force. It raises perceived returns, pushes up valuation, accelerates investment, and moves capital toward the region where the high-capital economy can sustain itself. During this phase, investment demand raises the interest rate. The long-run effect is different: once installed capital has changed the distribution of income and the supply of saving, the high-capital steady state has a lower interest rate. The overvaluation eventually corrects. The key question is whether the correction comes after enough capital has been installed. If it does, valuation can fall back to the high-capital rational path and the capital remains. If it comes too early, the perceived high-capital path disappears and the transition collapses back to the low-capital path. The same distinction between the transition and the destination also shapes incidence. Workers benefit because AI deployment is accompanied by conventional capital deepening: workers operate with a larger conventional capital stock and wages rise even as the worker share falls. The capitalists who finance the investment boom carry the valuation exposure: they invest at prices supported by beliefs that later correct, and they compress their own consumption to finance it. 2 The model has three blocks. Investment follows a 𝑞-theory specification, so asset prices affect real accumulation. Capitalists have wealth-in-utility preferences. This generates a rising propensity to save with wealth, as in the non-homothetic structure in Straub (2019), and makes the interest cost of capital fall as capitalist wealth rises. Beliefs are Bayesian: investors estimate a persistent excess return from a noisy signal, use the posterior mean to value capital, and revise the posterior as evidence arrives. The baseline path is an optimistic-prior path that is not confirmed by subsequent data; equivalently, it can be read as an adverse ex-post realization under genuine uncertainty about a new technology. Valuation moves accumulation, wealth lowers required returns, and temporary beliefs supply a transition force that fades when the data do not confirm it. The contribution is to show that a temporary belief wedge on productive capital can have permanent real effects when the capital it finances moves the economy into a self-sustaining high-capital steady state. The current AI cycle motivates this mechanism. Market capitalization has concentrated in AI-related firms, while announced data-center, power, and computing investment points to large real capital accumulation (Fortune, 2025; Goldman Sachs Global Institute, 2025; Van Nieuwerburgh, 2026; McKinsey, 2025). Review of the literature. The closest antecedent is the speculative-growth mechanism of Caballero et al. (2006, henceforth CFH), in which asset values, funding conditions, and accumulation reinforce one another. This paper keeps the funding-feedback logic but changes both the technology and the source of optimism. AI provides the technological source: task substitution expands effective labor, shifts income toward capital owners, and lowers the eventual interest rate through the wealth-saving channel. Optimism comes instead from Bayesian learning: capitalists temporarily perceive an excess return to AI-related capital, and an optimistic posterior valuation can move capital across the separatrix before the posterior is revised down. The technological environment follows the task-based view that advanced AI changes which tasks reproducible capital can perform. Acemoglu and Restrepo (2018) provide a canonical task-based formalization of automation and factor shares. Moll, Rachel, and Restrepo (2022) study how automation raises returns to wealth and increases income and wealth inequality. In the present model, automation also shifts income toward capital owners; because capitalists have a stronger wealth-saving motive, this redistribution lowers the destination real interest rate. Related work studies AGI and AI transition scenarios (Restrepo, 2025; Korinek and Suh, 2024) and broader macroeconomic implications of transformative AI (Trammell and Korinek, 2023; Acemoglu, 2024; Aghion and Bunel, 2024; Jones and Tonetti, 2026; Brynjolfsson et al., 2025). The wealth-saving feedback draws on work connecting inequality, saving, and low interest rates. The wealth-in-utility specification reproduces the saving behavior generated by non- homothetic preferences in Straub (2019): richer households have lower marginal propensities to consume. It also relates to Mian, Straub, and Sufi (2020) on the saving glut of the rich. AI here provides an endogenous source of the concentration that drives the channel. The transition trigger uses learning-driven valuation. Pástor and Veronesi (2009) show how learning about a new technology can generate high prices that later fall even when the technology is real. The additional force here is the wealth-saving feedback: learning-driven valuation affects capital accumulation, and installed capital can move the economy to a different steady state. The belief-to-investment link is related to evidence on expectations and investment in Gennaioli, Ma, and Shleifer (2016). Historical evidence from the late-1920s stock market provides a useful 3 overvaluation benchmark: De Long and Shleifer (1991) use closed-end fund premia to measure investor sentiment. Because investment responds to valuation, a temporary belief wedge has real effects: it raises capital accumulation before valuation returns to rational pricing. The paper is also related to rational-bubble models (Tirole, 1985; Martin and Ventura, 2012; Farhi and Tirole, 2012). These models study self-referential price components in overlapping- generations or liquidity-friction environments. The object here is different. The wedge is a perceived excess return on productive capital. When learning removes it, the price returns to the rational capital-claim valuation; the real legacy survives only if enough capital has already been installed to make the high-capital continuation available. Models of speculation with heterogeneous beliefs and resale motives (Scheinkman and Xiong, 2003; Simsek, 2013) study trade and pricing when investors disagree. In the representative-capitalist model here, all capitalists share the same belief, so the wedge reallocates resources intertemporally rather than across investors. Finally, the paper is related more broadly to work on takeoff dynamics and multiple long-run outcomes. Big-push and coordination-failure models provide a benchmark for expectation-driven takeoff and multiple long-run outcomes (Rosenstein-Rodan, 1943; Murphy, Shleifer, and Vishny, 1989; Cooper and John, 1988; Azariadis and Drazen, 1990; Matsuyama, 1991). Here, multiplicity is in steady states rather than rational continuations from a fixed initial capital stock: the high-capital state is self-sustaining once reached, while the transition requires a belief-supported valuation that raises investment until the wealth-saving feedback generated by installed AI capital can sustain the high-capital outcome. The remainder of the paper proceeds as follows. Section 2 builds the technology, saving, and valuation blocks. Section 3 develops the rational benchmark: AI deployment and the wealth- saving feedback generate multiple steady states, while the inherited capital stock selects a unique rational continuation. Section 4 studies the speculative transition: a temporary valuation wedge can move the economy toward the high-capital state, but the outcome depends on whether enough capital is installed before the wedge disappears. Section 5 concludes. The appendices collect the technology details, the wealth-in-utility derivation, the equilibrium system, the steady-state and local-geometry proofs, the Bayesian foundation for the belief wedge, the remaining transition proofs, and the illustrative numerical example behind the figures. ## 5 Conclusion 5 Conclusion A temporary overvaluation can leave a real legacy when valuation affects investment. In the model, a belief wedge raises valuation and compresses current capitalist consumption relative to investment; the real interest rate rises during the transition even though realized capital returns can be low. The installed AI capital then changes the economy it enters: it substitutes for labor tasks, shifts income toward capital owners, deepens the pool of saving, and lowers the interest rate consistent with a larger capital stock. 24 This feedback creates a high-capital steady state that is self-sustaining once reached. Rational pricing from the low-capital state remains on the low-capital path, so the transition relies on a temporary overvaluation. The mechanism is fragile because the overvaluation must correct. If enough capital has been installed before the correction, valuation lands on the high rational arm and the capital remains. If learning removes the perceived high branch too soon, valuation crashes to the low arm and the transition collapses. The distributional implication follows from the same logic. Workers benefit from the installed capital stock through higher wages at the high-capital destination. Capitalists finance the belief-supported valuation; their realized return reflects the high-capital destination gain, the compressed consumption, and the price correction required to get there. The broader lesson is that an asset-price boom should be judged not only by whether current prices are justified by current fundamentals, but also by whether the boom finances the capital accumulation that can make the high-valuation outcome self-sustaining.