arXiv subjects

Alexis Akira Toda

Publications and source records attributed to Alexis Akira Toda.

At least 19 recordsLinked to original sources

arXiv2026

Leverage, Endogenous Unbalanced Growth, and Asset Price Bubbles

We develop a macro-finance model in which leverage creates a positive feedback loop between capital investment and land prices. When leverage is below a threshold, land prices equal the present value of rents. Relaxing leverage lowers the productivity of the marginal investor and the interest rate until the fundamental value diverges. The economy then undergoes a phase transition to unbalanced growth. Demand for a store of value makes land prices grow faster than rents, so a bubble necessarily emerges. When the upper tail of the productivity distribution is sufficiently thick, this regime can prevail at arbitrarily high leverage.

econ.TH↗

arXiv2026

Conditional Impatience and Concavity of Consumption Functions

Concave consumption functions imply a marginal propensity to consume that falls with wealth. I characterize the utility functions that guarantee this property in finite-horizon optimal saving problems with stochastic discounting, returns, income, and borrowing limits. Under conditional impatience---the conditional expected discounted gross return does not exceed one---consumption functions are always concave if and only if inverse absolute prudence, $-u''/u'''$, is concave. When no conditional-impatience restriction is imposed, hyperbolic absolute risk aversion (HARA) is necessary and sufficient for uniform concavity. Thus conditional impatience permits declining marginal propensities to consume for a preference class strictly larger than HARA.

econ.TH↗

arXiv2026

Self-Fulfilling Prophecies, Quasi Nonergodicity, and Wealth Inequality: A Comment

Bouchaud and Farmer (2023) argue that self-fulfilling beliefs generate a realistic wealth distribution. Their reported Gini coefficient, quantiles, and Pareto exponent are computed from dynasty-level wealth averaged over 250 dates, not from a cross section. Correcting the estimand strengthens their qualitative result: with $N=1{,}000{,}000$ dynasties, the terminal cross-sectional Gini is 0.883 rather than 0.7, and median wealth is 0.0052 rather than 0.39 of average wealth. The model therefore generates more inequality, but not the reported quantitative fit. Appendix F analyzes a different process and does not establish the claimed Pareto tail or exponent.

econ.GN↗

arXiv2026

Robust Asset-Liability Management

Financial institutions often cannot replicate long-dated liabilities with available bonds, especially when leverage and collateral constraints bind. We characterize the feasible portfolio that minimizes, to first order, the worst equity loss over a prespecified set of yield curve changes. The solution accommodates general deterministic liabilities and portfolio constraints and includes duration and convexity matching as special cases. The minimized loss measures the economic capital buffer needed to absorb the specified interest rate stress. Under an $\ell^2$ stress set, the portfolio is a constrained generalized least squares projection. A portfolio representation shows how additional stress directions can reduce reliance on unstable exact hedges. In U.S. Treasury applications, robust immunization delivers the best or nearly best funding performance for most liabilities and constraints. Simulated and historical dynamic exercises also show modest leverage, turnover, and transaction costs.

q-fin.RM↗

arXiv2026

Linearity, Geometry, and Substitution in Aggregate Production

We study aggregate production under efficient input allocation across heterogeneous production units. With constant returns to scale, every profit-maximizing allocation generates a cone on which the aggregate production function is linear, whose dimension is the rank of active units' input vectors. Under concavity, the maximal cone at a supporting price is generated by component-technology contact sets. Higher-dimensional cones exist exactly when the pointwise maximum of strictly concave component technologies is nonconcave on the unit simplex. As an application, coexistence of land-using and land-free activities implies infinite aggregate elasticity of substitution at sufficiently high nonland-to-land ratios.

econ.TH↗

arXiv2026

General-Purpose Technologies and Stock Market Bubbles

We develop a macro-finance model linking stock price bubbles to a general-purpose technology (GPT), such as information technology and artificial intelligence. Knowledge spillovers differ across production factors, generating unbalanced growth and causing stock prices to outgrow dividends. Under our conditions, the unique equilibrium contains a bubble on dividend-paying stocks even though agents share common beliefs and rationally anticipate its collapse. The probability that spillovers persist affects the bubble's duration but not its existence. When spillovers equalize as the technology matures, the economy reaches balanced growth and the bubble collapses. Through IPO proceeds, the bubble can increase R\&D employment, while accumulated knowledge remains productive afterward. More broadly, balanced growth is a knife-edge property: the restrictions used to obtain it make stock prices and dividends grow at the same rate, thereby ruling out rational bubbles on dividend-paying assets by construction.

econ.TH↗

arXiv2026

Wealth Preferences and the Upper Tail of Consumption

We develop a theory of optimal saving when wealth enters utility. Relative curvatures of consumption and wealth utility, $γ$ and $δ$, govern the upper-tail behavior. When $δ<γ$, wealth preferences generate a vanishing asymptotic marginal propensity to consume and power-law consumption, $c(w)\sim w^{δ/γ}$, yielding a thinner upper tail for consumption than for wealth. When $δ=γ$, they lower the positive limiting propensity to consume; when $δ>γ$, they become asymptotically irrelevant. The framework encompasses joy-of-giving/warm-glow bequests under random mortality. A calibrated model shows that the asymptotic characterization is accurate at observed wealth levels and reproduces wealthy households' high saving rates.

econ.TH↗

arXiv2026

Global Characterization of Equilibria in Tirole's (1985) Model with a Dividend-Paying Asset

We revisit Tirole's classic paper "Asset Bubbles and Overlapping Generations" (1985, Econometrica) in the case of a dividend-paying asset. Recently, Pham and Toda (2026) constructed a counterexample to Proposition 1(c), showing that Tirole's equilibrium classification is incorrect as stated and that long-run outcomes can depend on initial capital. This paper characterizes the entire set of equilibrium initial asset prices under capital over-accumulation. Exactly one of three regimes occurs: (i) a unique bubbleless equilibrium with capital converging to zero (capital collapse), (ii) a unique asymptotically bubbly equilibrium converging to a positive steady state (bubble necessity), or (iii) a continuum of equilibria with different long-run bubble behavior (indeterminacy). We further derive a threshold for initial capital under the bubble necessity condition, establish preference-free sufficient conditions for capital collapse, and show that the continuum in the pure bubble model survives sufficiently small dividend perturbations. Closed-form examples illustrate the possible long-run outcomes.

econ.TH↗

arXiv2026

A Theory of Saving under Risk Preference Dynamics

Empirical evidence shows that wealthy households have substantially higher saving rates and markedly lower marginal propensity to consume (MPC) than other groups. Existing theory cannot account for this pattern without jointly imposing restrictive assumptions on returns, discounting, and preferences. In this paper, we develop a general theory of optimal savings with preference shocks and identify a novel mechanism through which stochastic risk preferences reshape the asymptotic consumption and saving behavior. Specifically, the mere possibility of becoming less risk averse next period raises the value of carrying wealth forward, since future selves may be more willing to convert wealth into consumption. Unlike the classical precautionary saving motive, which typically arises from resource risks and weakens as wealth increases, this force remains operative even at arbitrarily high wealth levels, generating a persistent incentive to defer consumption and driving the asymptotic MPC to zero (i.e., a 100% asymptotic saving rate). As a result, vanishing MPCs emerge as a generic implication of risk preference dynamics, rather than an artifact of restrictive assumptions, offering a theoretically robust and empirically consistent account of the persistently high saving rates and low MPCs observed among wealthy households.

econ.TH↗

arXiv2026

Can AI Refute Economic Theory? Evidence from Beyond the Knowledge Cutoff

Can artificial intelligence (AI) refute economic theory? I document experiments in which I asked several AI models (Gemini, Refine, Claude, and ChatGPT) to check the correctness of four published papers in economic theory, each containing an error that I helped identify or correct. ChatGPT Pro performed best, occasionally constructing counterexamples and corrected proofs, while other models fared worse. However, no model located a true error without substantial human guidance, and data contamination complicates interpretation. I argue that a competent human paired with a frontier model can outperform current peer review, but AI cannot yet refute economic theory on its own.

econ.GN↗

arXiv2026

Reducible Markov modulation, pole order, and tail behavior in random growth models

Recent work on random growth models with light-tailed Markov-modulated additive shocks has shown that irreducible modulation yields tail behavior resembling an exponential distribution. We show that with reducible modulation the tail behavior more generally resembles an Erlang distribution. Our main technical contribution is a theorem on the order of a real pole of the inverse of a holomorphic matrix-valued function with reducible Metzler structure. In a special affine case, the theorem recovers the Rothblum index theorem. Applying this result together with a Tauberian theorem, we characterize the Erlang shape parameter in two models of Markov-modulated random growth.

math.PR↗

arXiv2026

Comment on 'Asset Bubbles and Overlapping Generations'

Tirole (1985) studied an overlapping generations model with capital accumulation and showed that the emergence of asset bubbles solves the capital over-accumulation problem. His Proposition 1(c) claims that if the dividend growth rate is above the bubbleless interest rate (the steady-state interest rate in the economy without the asset) but below the population growth rate, then bubbles are necessary in the sense that there exists no bubbleless equilibrium but there exists a unique bubbly equilibrium. We show that this result (as stated) is incorrect by presenting an example economy that satisfies all assumptions of Proposition 1(c) but its unique equilibrium is bubbleless. We also restore Proposition 1(c) under the additional assumptions that initial capital is sufficiently large and dividends are sufficiently small. We show through examples that these conditions are essential.

econ.TH↗

arXiv2025

Land and Infinite Debt Rollover

Since McCallum (1987), it is well known that in an overlapping generations (OLG) economy with land, the equilibrium is Pareto efficient because with balanced growth, the interest rate exceeds the economic growth rate ($R>G$), which rules out infinite debt rollover (a Ponzi scheme). We show that once we remove knife-edge restrictions on the production function and allow unbalanced growth, under some conditions an efficient equilibrium with land bubbles necessarily emerges and infinite debt rollover becomes possible, which is a markedly different insight from the conventional view derived from the Diamond (1965) landless economy. We also examine the possibility of Pareto inefficient equilibria.

econ.TH↗

arXiv2025

Rational Bubbles Attached to Real Assets

A rational bubble is a situation in which the asset price exceeds its fundamental value defined by the present discounted value of dividends in a rational equilibrium model. We discuss the recent development of the theory of rational bubbles attached to real assets, emphasizing the following three points. (i) There exist plausible economic models in which bubbles inevitably emerge in the sense that all equilibria are bubbly. (ii) Such models are necessarily nonstationary but their long-run behavior can be analyzed using the local stable manifold theorem. (iii) Bubbles attached to real assets can naturally and necessarily arise with economic development. We illustrate these three points in various settings attesting that bubbles may necessarily emerge for aggregate stocks, land, and other assets.

econ.TH↗

arXiv2025

Optimal taxation and the Domar-Musgrave effect

This article concerns the optimal choice of flat taxes on labor and capital income, and on consumption, in a tractable economic model in which agents are subject to idiosyncratic investment risk. We identify the tax rates which maximize welfare in stationary equilibrium while preserving tax revenue, finding that an increase in welfare equivalent to a permanent increase in consumption of nearly 7% can be achieved by only taxing capital income and consumption. The Domar-Musgrave effect explains cases where it is optimal to tax capital income. We characterize the dynamic response to the substitution of consumption taxation for labor income taxation.

econ.GN↗

arXiv2025

Housing Bubbles with Phase Transitions

We analyze how equilibrium housing prices are determined in the process of economic development within an overlapping generations model with perfect housing and rental markets. We characterize the rent growth rate in all equilibria. The economy exhibits a two-stage phase transition: as incomes of home buyers rise, the equilibrium regime changes from fundamental to bubble possibility, where fundamental and bubbly equilibria coexist. With even higher incomes, fundamental equilibria disappear and housing bubbles become a necessity. We also discuss extensions and refinements such as equilibrium uniqueness, multiple savings vehicles, welfare implications, credit- and expectation-driven bubbles, and testable implications of our theory.

econ.TH↗

arXiv2024

Unbalanced Growth and Land Overvaluation

Historical trends suggest the decline in importance of land as a production factor but its continued importance as a store of value. Using an overlapping generations model with land and aggregate uncertainty, we theoretically study the long-run behavior of land prices and identify economic conditions under which land becomes overvalued on the long-run trend relative to the fundamentals defined by the present value of land rents. Unbalanced growth together with the elasticity of substitution between production factors plays a critical role. Around the trend, land prices exhibit recurrent stochastic fluctuations, with expansions and contractions in the size of land overvaluation.

econ.TH↗

arXiv2024

Equilibrium Selection in Pure Bubble Models by Dividend Injection

Rational pure bubble models feature multiple (and often a continuum of) equilibria, which makes model predictions and policy analyses non-robust. We show that when the interest rate in the fundamental equilibrium is below the economic growth rate ($R<G$), a bubbly equilibrium with $R=G$ exists. By injecting dividends to the bubble asset that grow slower than the aggregate economy, we can eliminate the fundamental steady state and resolve equilibrium indeterminacy. We show the general applicability of dividend injection through examples in overlapping generations and infinite-horizon models with or without production or financial frictions.

econ.TH↗