# Research

I am a mathematical economist with strong interests in applications. The topics I have worked on include

- the impossibility of canonical macroeconomic models to explain wealth inequality,
- a simple explanation for the saving behavior of the rich that does not rely on ad hoc utility functions,
- a computational algorithm for solving macroeconomic models with realistic wealth distributions,
- simple formula and mathematical foundation for Pareto exponents that arise in random multiplicative processes in Markovian environments,
- verification of the random multiplicative process to explain the spread of COVID-19,
- wealth inequality and stock market returns,
- determination of academic salaries,
- implication of financial development to international capital flows and welfare,
- efficient discretization of non-linear, non-Gaussian Markov processes,
- optimal epidemic control when testing and government enforcement are imperfect,

among others.

Below is the complete publication list. My best papers are indicated with đź‘Ť.

## Refereed research articles

- â€śRobust Comparative Statics for the Elasticity of Intertemporal Substitutionâ€ť, with
*Joel P. Flynn and Lawrence D. W. Schmidt*,**Theoretical Economics**18(1):231-265 (2023) WP version BibTeX

(Theory) Robust comparative statics for the elasticity of intertemporal substitution; sign- and point-identification of EIS minus 1. - đź‘Ťâ€ťPareto Extrapolation: An Analytical Framework for Studying Tail Inequalityâ€ť, with
*Ă‰milien Gouin-Bonenfant*,**Quantitative Economics**14(1):201-233 (2023) WP version Code BibTeX

(Power law, Numerical method, Macro) Analytical framework designed to solve and analyze heterogeneous-agent models that endogenously generate fat-tailed wealth distributions. - â€śTail Behavior of Stopped LĂ©vy Processes with Markov Modulationâ€ť, with
*Brendan K. Beare and Won-Ki Seo*,**Econometric Theory**38(5):986-1013 (2022) WP version BibTeX

(Power law, Theory) Characterize tail behavior of Markov-modulated LĂ©vy processes that are stopped at state-dependent Poisson rates; application to wealth distribution. - đź‘Ťâ€ťDetermination of Pareto Exponents in Economic Models Driven by Markov Multiplicative Processesâ€ť, with
*Brendan K. Beare*,**Econometrica**90(4):1811-1833 (2022) WP version Slides BibTeX

(Power law, Mathematics) Provide simple formula and mathematical foundation for Pareto exponents of stationary Markov multiplicative processes. - â€śCapital and Labor Income Pareto Exponents across Time and Spaceâ€ť, with
*Tjeerd de Vries*,**Review of Income and Wealth**68(4):1058-1078 (2022) LIS Working Paper 794 arXiv Code BibTeX

(Power law, Empirical) Estimate capital and labor income Pareto exponents across 475 country-year observations and document that capital income inequality is higher than labor income inequality (median Pareto exponents 1.46 and 3.35 respectively) and the two inequalities are uncorrelated, suggesting importance of distinguishing the two. - â€śUnbounded Dynamic Programming via the Q-Transformâ€ť, with
*Qingyin Ma and John Stachurski*,**Journal of Mathematical Economics**100:102652 (2022) WP version BibTeX

(Theory) Simple operation that often transforms an unbounded dynamic programming problem into a bounded one. - â€śAsymptotic Linearity of Consumption Functions and Computational Efficiencyâ€ť, with
*Qingyin Ma*,**Journal of Mathematical Economics**98:102562 (2022) WP version Code BibTeX

(Theory, Numerical method) Prove asymptotic linearity of policy functions when marginal utility is regularly varying; follow-up of Ma & Toda (2021). - đź‘Ťâ€ťOptimal Epidemic Control in Equilibrium with Imperfect Testing and Enforcementâ€ť, with
*Thomas Phelan*,**Journal of Economic Theory**206:105570 (2022) WP version Slides Code BibTeX

(Theory) Study a behavioral SIR model with imperfect testing and government enforcement and show that equilibrium action is approximately static efficient in the sense that the laissez faire equilibrium allocation is close to the optimal short-term lockdown policy, implying that short-term lockdown policies are redundant. - â€śThe Effect of Social Distancing on the Reach of an Epidemic in Social Networksâ€ť, with
*Gregory Gutin, Tomohiro Hirano, Sung-Ha Hwang, and Philip R. Neary*,**Journal of Economic Interaction and Coordination**16:629-647 (2021) WP version Code BibTeX

(Network) Simulation study of the evolution of an epidemic disease on social networks; the effectiveness of social distancing greatly depends on network structure. - đź‘Ťâ€ťA Theory of the Saving Rate of the Richâ€ť, with
*Qingyin Ma*,**Journal of Economic Theory**192:105193 (2021) WP version Slides Code BibTeX

(Theory, Macro) Prove asymptotic linearity of policy functions when preferences are homothetic; show that asymptotic marginal propensities to consume can be zero, implying a large saving rate of the rich. - â€śData-based Automatic Discretization of Nonparametric Distributionsâ€ť,
**Computational Economics**57:1217-1235 (2021) WP version Code BibTeX

(Numerical method) Automatic discretization method of nonparametric distributions using Gaussian quadrature. - đź‘Ťâ€ťNecessity of Hyperbolic Absolute Risk Aversion for the Concavity of Consumption Functionsâ€ť,
**Journal of Mathematical Economics**94:102460 (2021) WP version BibTeX

(Theory) That HARA utility implies concave consumption functions is well-known, but the converse is also true. - â€śPerovâ€™s Contraction Principle and Dynamic Programming with Stochastic Discountingâ€ť,
**Operations Research Letters**49(5):815-819 (2021) WP version BibTeX

(Mathematics) Show the usefulness of Perovâ€™s contraction principle (which is a generalization of Banachâ€™s contraction principle) for solving certain dynamic programming problems. - â€śEfficient Minimum Distance Estimation of Pareto Exponent from Top Income Sharesâ€ť, with
*Yulong Wang*,**Journal of Applied Econometrics**36(2):228-243 (2021) WP version Code BibTeX

(Power law, Econometrics) How to efficiently estimate Pareto exponents when only certain top income shares are observable. - â€śIs Gibratâ€™s â€śEconomic Inequalityâ€ť Lognormal?â€ť, with
*Sherzod Akhundjanov*,**Empirical Economics**59(5):2071-2091 (2020) Code BibTeX

(Power law, Empirical) The majority of data sets analyzed by Gibrat and claimed to be lognormal are actually closer to Pareto-type distributions. - đź‘Ťâ€ťOn the Emergence of a Power Law in the Distribution of COVID-19 Casesâ€ť, with
*Brendan K. Beare*,**Physica D: Nonlinear Phenomena**412:132649 (2020) WP version Code BibTeX

(Power law, Empirical) Size distribution of COVID-19 cases across US counties as of March 2020 obeys the power law; empirical Pareto exponent is consistent with the estimated growth rate and age distributions. - â€śThe Income Fluctuation Problem and the Evolution of Wealthâ€ť, with
*Qingyin Ma and John Stachurski*,**Journal of Economic Theory**187:105003 (2020) WP version Code BibTeX

(Power law, Theory) Establish existence and uniqueness of a solution to a general income fluctuation problem; characterize tail behavior of stationary wealth distribution. - đź‘Ťâ€ťThe Equity Premium and the One Percentâ€ť, with
*Kieran James Walsh*,**Review of Financial Studies**33(8):3583-3623 (2020) WP version BibTeX

(Finance, Theory, Empirical) In general equilibrium model with heterogeneous risk aversion and/or beliefs, the wealth distribution predicts excess stock returns, which we confirm in data using estate tax rate change as instrument. - â€śPublications, Citations, Position, and Compensation of Economics Professorsâ€ť, with
*Yifei Lyu*,**EconJournalWatch**16(2):239-257 (2019) Code BibTeX

(Empirical) Publications (Top 5/Non-top 5) and job rank explains over 80% of variations in salaries among economics professors in the UC system; no evidence of gender gap. - â€śSecuritized Markets, International Capital Flows, and Global Welfareâ€ť, with
*Gregory Phelan*,**Journal of Financial Economics**131(3):571-592 (2019) WP version Code BibTeX

(Finance, Theory) With collateral constraints, financial integration may hurt the less constrained country. - đź‘Ťâ€ťAn Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneityâ€ť, with
*John Stachurski*,**Journal of Economic Theory**182:1-24 (2019) WP version Slides BibTeX Corrigendum

(Power law, Theory, Macro) Prove the impossibility for the canonical Bewley-Huggett-Aiyagari model to generate heavier-tailed wealth than income. - â€śWealth Distribution with Random Discount Factorsâ€ť,
**Journal of Monetary Economics**104:101-113 (2019) WP version Code BibTeX

(Power law, Theory, Macro) Formal proof that the Krusell-Smith (1998) random discount factor trick generates power law tails; Pareto exponent is sensitive to the calibration of discount factor process. - đź‘Ťâ€ťDiscretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Momentsâ€ť, with
*Leland E. Farmer*,**Quantitative Economics**8(2):651-683 (2017) WP version Matlab code Julia code BibTeX

(Numerical method, Finance) Approximates Markov processes by finite-state Markov chains using maximum entropy discretization of Tanaka & Toda (2013, 2015); applications to solving asset pricing models. - â€śGrowth Effects of Annuities and Government Transfers in Perpetual Youth Modelsâ€ť, with
*Yoshiyuki Miyoshi*,**Journal of Mathematical Economics**72:1-6 (2017) Code BibTeX

(Theory, Macro) In perpetual youth models, introduction of government transfer crowds out annuity market and increases growth. - â€śA Note on the Size Distribution of Consumption: More Double Pareto than Lognormalâ€ť,
**Macroeconomic Dynamics**21(6):1508-1518 (2017) WP version Online appendix Code BibTeX

(Power law, Empirical) Cross-sectional household consumption is well-approximated by double Pareto-lognormal distribution. Formerly a section of Toda & Walsh (2015). - â€śHuggett Economies with Multiple Stationary Equilibriaâ€ť,
**Journal of Economic Dynamics and Control**84:77-90 (2017) WP version Code BibTeX

(Theory, Macro) Closed-form solution to a Huggett (1993) economy with non-Gaussian VAR(1) dynamics and general examples of multiple stationary equilibria. - â€śEdgeworth Box Economies with Multiple Equilibriaâ€ť, with
*Kieran James Walsh*,**Economic Theory Bulletin**5(1):65-80 (2017) WP version Code BibTeX

(Theory) Many general examples of multiple equilibria in Edgeworth box economies. - â€śFat Tails and Spurious Estimation of Consumption-Based Asset Pricing Modelsâ€ť, with
*Kieran James Walsh*,**Journal of Applied Econometrics**32(6):1156-1177 (2017) WP version Code BibTeX

(Power law, Econometrics, Finance) Monte Carlo study of spurious inference caused by power law. Formerly a section of Toda & Walsh (2015). - â€śDiscretizing Distributions with Exact Moments: Error Estimate and Convergence Analysisâ€ť, with
*Kenâ€™ichiro Tanaka*,**SIAM Journal on Numerical Analysis**53(5):2158-2177 (2015) WP version BibTeX

(Numerical method, Mathematics) Convergence and error analysis of maximum entropy discretization of Tanaka & Toda (2013). - â€śAsset Prices and Efficiency in a Krebs Economyâ€ť,
**Review of Economic Dynamics**18(4):957-978 (2015) WP version BibTeX

(Theory, Macro, Finance) Asset pricing and optimal taxation in a class of tractable dynamic general equilibrium models. Formerly a section of Toda (2014). - â€śBayesian General Equilibriumâ€ť,
**Economic Theory**58(2):375-411 (2015) BibTeX

(Theory) Walrasian equilibrium is a special limiting case of statistical equilibrium. Extension of Toda (2010). - đź‘Ťâ€ťThe Double Power Law in Consumption and Implications for Testing Euler Equationsâ€ť, with
*Kieran James Walsh*,**Journal of Political Economy**123(5):1177-1200 (2015) WP version Slides Code BibTeX

(Power law, Econometrics, Empirical) Power law in cross-sectional household consumption data causes spurious inference. - â€śIncomplete Market Dynamics and Cross-Sectional Distributionsâ€ť,
**Journal of Economic Theory**154:310-348 (2014) WP version BibTeX

(Power law, Theory) Class of tractable dynamic general equilibrium models that generates power law in size distributions. One of my dissertation chapters at Yale. - â€śRadii of the Inscribed and Escribed Spheres of a Simplexâ€ť,
**International Journal of Geometry**3(2):5-13 (2014) BibTeX

(Mathematics) Generalization to an \(n\)-simplex of the fact that the sum of the reciprocals of the radii of escribed circles of a triangle equals the reciprocal of the radius of the inscribed circle. I obtained those results in 1998 when I was freshman. - â€śDiscrete Approximations of Continuous Distributions by Maximum Entropyâ€ť, with
*Kenâ€™ichiro Tanaka*,**Economics Letters**118(3):445-450 (2013) BibTeX

(Numerical method) Simple maximum entropy method to discretize probability distributions. - â€śLearning Curve for Paramedic Endotracheal Intubation and Complicationsâ€ť, with
*Junko Toda and Johji Arakawa*,**International Journal of Emergency Medicine**6:38 (2013) BibTeX

(Medicine, Empirical) You need to practice at least 30 times to intubate a patient consistently. - â€śThe Impact of Media Reports on the 2008 Outbreak of Hydrogen Sulfide Suicides in Japanâ€ť, with
*Mitsuhiro Nakamura, Hideo Yasunaga, Toru Sugihara, and Tomoaki Imamura*,**International Journal of Psychiatry in Medicine**44(2):133-140 (2012) BibTeX

(Medicine, Empirical) The media coverage during the 2008 outbreak of hydrogen sulfide suicides in Japan caused more suicides. - â€śThe Double Power Law in Income Distribution: Explanations and Evidenceâ€ť,
**Journal of Economic Behavior and Organization**84(1):364-381 (2012) BibTeX

(Power law, Empirical) A certain mean-reverting income process generates a stationary double Pareto distribution. My third-year empirical paper at Yale. - â€śIncome Dynamics with a Stationary Double Pareto Distributionâ€ť,
**Physical Review E**83(4):046122 (2011) BibTeX

(Power law, Empirical) A certain mean-reverting income process generates a stationary double Pareto distribution. An abridged version of my third-year empirical paper at Yale. - â€śOperator Reverse Monotonicity of the Inverseâ€ť,
**American Mathematical Monthly**118(1):82-83 (2011) BibTeX

(Mathematics) Simple proof of the equivalence \(A \ge B\) if and only if \(B^{-1} \ge A^{-1}\) for positive definite matrices based on convex conjugate functions. - â€śExistence of a Statistical Equilibrium for an Economy with Endogenous Offer Setsâ€ť,
**Economic Theory**45(3):379-415 (2010) BibTeX

(Theory) Generalizes Foleyâ€™s (1994) statistical equilibrium model when offer sets are endogenous. My master thesis at U of Tokyo. Further generalized in Toda (2015).

## Conference proceedings

- â€śError Estimate and Convergence Analysis of Moment-Preserving Discrete Approximations of Continuous Distributionsâ€ť, with
*Kenâ€™ichiro Tanaka*, in Robert K. Niven, Brendon Brewer, David Paull, Kamran Shafi, Barrie Stokes eds.**Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings**1636:30-36 (2014) - â€śAxiomatization of Maximum Entropy without the Bayes Ruleâ€ť, in Philip Goyal, Adom Giffin, Kevin H. Knuth, Edward Vrscay eds.
**Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings**1443:7-13 (2012)

## Other publications

- â€śCorrigendum to â€śAn Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity [Journal of Economics Theory 182 (2019) 1-24]â€ť, with
*John Stachurski*,**Journal of Economic Theory**188:105066 (2020) - â€śSusceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impactâ€ť,
**Covid Economics, Vetted and Real-Time Papers**1 (2020) arXiv Slides VoxEU Fortune

## Working papers

- â€śCollateralized Loans, Pooling, and Maximum Leverageâ€ť, revise and resubmit at
**Theoretical Economics**PDF - â€śZipfâ€™s Law: A Microfoundationâ€ť PDF
- â€śFixed-\(k\) Tail Regression: New Evidence on Tax and Wealth Inequality from Forbes 400â€ť, with
*Ji Hyung Lee, Yuya Sasaki, and Yulong Wang*PDF - â€śTuning Parameter-Free Nonparametric Density Estimation from Tabulated Summary Dataâ€ť, with
*Ji Hyung Lee, Yuya Sasaki, and Yulong Wang*PDF - â€śCapital and Labor Income Pareto Exponents in the United States, 1916-2019â€ť, with
*Ji Hyung Lee, Yuya Sasaki, and Yulong Wang*PDF Slides - â€śIncentivizing Hidden Types in Secretary Problemâ€ť, with
*Longjian Li*PDF Slides - â€śNecessity of Rational Asset Price Bubbles in Two-Sector Growth Economiesâ€ť, with
*Tomohiro Hirano and Ryo Jinnai*PDF