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Alexis Akira Toda

Publications and source records attributed to Alexis Akira Toda.

At least 37 records · Page 2Linked to original sources
arXiv2024

Pareto's Limits: Improving Inequality Estimates in America, 1917 to 1965

American income inequality, generally estimated with tax data, in the 20th century is widely recognized to have followed a U-curve, though debates persist over the extent of this curve, specifically regarding how high the peaks are and how deep the trough is. These debates focus on assumptions about defining income and handling deductions. However, the choice of interpolation methods for using tax authorities' tabular data to estimate the income of the richest centiles -- especially when no micro-files are available -- has not been discussed. This is crucial because tabular data were consistently used from 1917 to 1965. In this paper, we show that there is an alternative to the standard method of Pareto Interpolation (PI). We demonstrate that this alternative -- Maximum Entropy (ME) -- provides more accurate results and leads to significant revisions in the shape of the U-curve of income inequality.

econ.GN↗
arXiv2024

Incentivizing Hidden Types in Secretary Problem

We study a game between $N$ job applicants who incur a cost $c$ (relative to the job value) to reveal their type during interviews and an administrator who seeks to maximize the probability of hiring the best. We define a full learning equilibrium and prove its existence, uniqueness, and optimality. In equilibrium, the administrator accepts the current best applicant $n$ with probability $c$ if $n<n^*$ and with probability 1 if $n\ge n^*$ for a threshold $n^*$ independent of $c$. In contrast to the case without cost, where the success probability converges to $1/\mathrm{e}\approx 0.37$ as $N$ tends to infinity, with cost the success probability decays like $N^{-c}$.

econ.TH↗
arXiv2024

Rational Bubbles: A Clarification

"Rational bubble", as introduced by the famous paper on money by Samuelson (1958), means speculation backed by nothing. The large subsequent rational bubble literature has identified attaching bubbles to dividend-paying assets in a natural way as an important but challenging question. Miao and Wang (2018) claim to "provide a theory of rational stock price bubbles". Contrary to their claim, the present comment proves the nonexistence of rational bubbles in the model of Miao and Wang (2018). We also clarify the precise mathematical definition and the economic meaning of "rational bubble" in an accessible way to the general audience.

econ.GN↗
arXiv2024

Bubble Necessity Theorem

Asset price bubbles are situations where asset prices exceed the fundamental values defined by the present value of dividends. This paper presents a conceptually new perspective: the necessity of bubbles. We establish the Bubble Necessity Theorem in a plausible general class of economic models: with faster long-run economic growth ($G$) than dividend growth ($G_d$) and counterfactual long-run autarky interest rate ($R$) below dividend growth, all equilibria are bubbly with non-negligible bubble sizes relative to the economy. This bubble necessity condition naturally arises in economies with sufficiently strong savings motives and multiple factors or sectors with uneven productivity growth.

econ.TH↗
arXiv2024

On Equilibrium Determinacy in Overlapping Generations Models with Money

This paper provides a detailed analysis of the local determinacy of monetary and non-monetary steady states in Tirole (1985)'s classical two-period overlapping generations model with capital and production. We show that the sufficient condition for local determinacy in endowment economies provided by Scheinkman (1980) does not generalize to models with production: there are robust examples with arbitrary utility functions in which the non-monetary steady state is locally determinate or indeterminate. In contrast, the monetary steady state is locally determinate under fairly weak conditions.

econ.TH↗
arXiv2023

Bubble Economics

This article provides a self-contained overview of the theory of rational asset price bubbles. We cover topics from basic definitions, properties, and classical results to frontier research, with an emphasis on bubbles attached to real assets such as stocks, housing, and land. The main message is that bubbles attached to real assets are fundamentally nonstationary phenomena related to unbalanced growth. We present a bare-bones model and draw three new insights: (i) the emergence of asset price bubbles is a necessity, instead of a possibility; (ii) asset pricing implications are markedly different between balanced growth of stationary nature and unbalanced growth of nonstationary nature; and (iii) asset price bubbles occur within larger historical trends involving shifts in industrial structure driven by technological innovation, including the transition from the Malthusian economy to the modern economy.

econ.GN↗
arXiv2023

Unbounded Markov Dynamic Programming with Weighted Supremum Norm Perov Contractions

This paper shows the usefulness of the Perov contraction theorem, which is a generalization of the classical Banach contraction theorem, for solving Markov dynamic programming problems. When the reward function is unbounded, combining an appropriate weighted supremum norm with the Perov contraction theorem yields a unique fixed point of the Bellman operator under weaker conditions than existing approaches. An application to the optimal savings problem shows that the average growth rate condition derived from the spectral radius of a certain nonnegative matrix is sufficient and almost necessary for obtaining a solution.

math.OC↗
arXiv2023

'Ergodicity Economics' is Pseudoscience

In a series of papers, Ole Peters and his collaborators claim that the 'conceptual basis of mainstream economic theory' is 'flawed' and that the approach they call 'ergodicity economics' gives 'reason to hope for a future economic science that is more parsimonious, conceptually clearer and less subjective' (Peters, 2019). This paper argues that 'ergodicity economics' is pseudoscience because it has not produced falsifiable implications and should be taken with skepticism.

q-fin.GN↗
arXiv2023

Tuning Parameter-Free Nonparametric Density Estimation from Tabulated Summary Data

Administrative data are often easier to access as tabulated summaries than in the original format due to confidentiality concerns. Motivated by this practical feature, we propose a novel nonparametric density estimation method from tabulated summary data based on maximum entropy and prove its strong uniform consistency. Unlike existing kernel-based estimators, our estimator is free from tuning parameters and admits a closed-form density that is convenient for post-estimation analysis. We apply the proposed method to the tabulated summary data of the U.S. tax returns to estimate the income distribution.

econ.EM↗
arXiv2022

Optimal Epidemic Control in Equilibrium with Imperfect Testing and Enforcement

We analyze equilibrium behavior and optimal policy within a Susceptible-Infected-Recovered epidemic model augmented with potentially undiagnosed agents who infer their health status and a social planner with imperfect enforcement of social distancing. We define and prove the existence of a perfect Bayesian Markov competitive equilibrium and contrast it with the efficient allocation subject to the same informational constraints. We identify two externalities, static (individual actions affect current risk of infection) and dynamic (individual actions affect future disease prevalence), and study how they are affected by limitations on testing and enforcement. We prove that a planner with imperfect enforcement will always wish to curtail activity, but that its incentives to do so vanish as testing becomes perfect. When a vaccine arrives far into the future, the planner with perfect enforcement may encourage activity before herd immunity. We find that lockdown policies have modest welfare gains, whereas quarantine policies are effective even with imperfect testing.

econ.TH↗
arXiv2022

Fixed-k Tail Regression: New Evidence on Tax and Wealth Inequality from Forbes 400

We develop a novel fixed-k tail regression method that accommodates the unique feature in the Forbes 400 data that observations are truncated from below at the 400th largest order statistic. Applying this method, we find that higher maximum marginal income tax rates induce higher wealth Pareto exponents. Setting the maximum tax rate to 30-40% (as in U.S. currently) leads to a Pareto exponent of 1.5-1.8, while counterfactually setting it to 80% (as suggested by Piketty, 2014) would lead to a Pareto exponent of 2.6. We present a simple economic model that explains these findings and discuss the welfare implications of taxation.

econ.GN↗
arXiv2022

Capital and Labor Income Pareto Exponents in the United States, 1916-2019

Accurately estimating income Pareto exponents is challenging due to limitations in data availability and the applicability of statistical methods. Using tabulated summaries of incomes from tax authorities and a recent estimation method, we estimate income Pareto exponents in U.S. for 1916-2019. We find that during the past three decades, the capital and labor income Pareto exponents have been stable at around 1.2 and 2. Our findings suggest that the top tail income and wealth inequality is higher and wealthy agents have twice as large an impact on the aggregate economy than previously thought but there is no clear trend post-1985.

econ.GN↗
arXiv2022

Robust Comparative Statics for the Elasticity of Intertemporal Substitution

We study a general class of consumption-savings problems with recursive preferences. We characterize the sign of the consumption response to arbitrary shocks in terms of the product of two sufficient statistics: the elasticity of intertemporal substitution between contemporaneous consumption and continuation utility (EIS), and the relative elasticity of the marginal value of wealth (REMV). Under homotheticity, the REMV always equals one, so the propensity of the agent to save or dis-save is always signed by the relationship of the EIS with unity. We apply our results to derive comparative statics in classical problems of portfolio allocation, consumption-savings with income risk, and entrepreneurial investment. Our results suggest empirical identification strategies for both the value of the EIS and its relationship with unity.

econ.TH↗
arXiv2022

Determination of Pareto exponents in economic models driven by Markov multiplicative processes

This article contains new tools for studying the shape of the stationary distribution of sizes in a dynamic economic system in which units experience random multiplicative shocks and are occasionally reset. Each unit has a Markov-switching type which influences their growth rate and reset probability. We show that the size distribution has a Pareto upper tail, with exponent equal to the unique positive solution to an equation involving the spectral radius of a certain matrix-valued function. Under a non-lattice condition on growth rates, an eigenvector associated with the Pareto exponent provides the distribution of types in the upper tail of the size distribution.

econ.EM↗
arXiv2021

Perov's Contraction Principle and Dynamic Programming with Stochastic Discounting

This paper shows the usefulness of Perov's contraction principle, which generalizes Banach's contraction principle to a vector-valued metric, for studying dynamic programming problems in which the discount factor can be stochastic. The discounting condition $β<1$ is replaced by $ρ(B)<1$, where $B$ is an appropriate nonnegative matrix and $ρ$ denotes the spectral radius. Blackwell's sufficient condition is also generalized in this setting. Applications to asset pricing and optimal savings are discussed.

econ.TH↗
arXiv2021

Capital and Labor Income Pareto Exponents across Time and Space

We estimate capital and labor income Pareto exponents across 475 country-year observations that span 52 countries over half a century (1967-2018). We document two stylized facts: (i) capital income is more unequally distributed than labor income in the tail; namely, the capital exponent (1-3, median 1.46) is smaller than labor (2-5, median 3.35), and (ii) capital and labor exponents are nearly uncorrelated. To explain these findings, we build an incomplete market model with job ladders and capital income risk that gives rise to a capital income Pareto exponent smaller than but nearly unrelated to the labor exponent. Our results suggest the importance of distinguishing income and wealth inequality.

econ.EM↗
arXiv2021

Unbounded Dynamic Programming via the Q-Transform

We propose a new approach to solving dynamic decision problems with unbounded rewards based on the transformations used in Q-learning. In our case, the objective of the transform is to convert an unbounded dynamic program into a bounded one. The approach is general enough to handle problems for which existing methods struggle, and yet simple relative to other techniques and accessible for applied work. We show by example that many common decision problems satisfy our conditions.

math.OC↗