# Research

I am an “applied general equilibrium theorist”, meaning that I am a theorist interested in general equilibrium theory and its applications (typically in finance and macroeconomics). In addition to papers in mathematical economics and finance, I have written many papers on power law, which naturally emerges in dynamic general equilibrium models with heterogeneous agents. I have also written several papers on numerical methods (discretization of probability distributions and stochastic processes), which are useful for numerically solving models (see the discretization page). Below is the complete publication list.

## Refereed research articles

1. “Tail Behavior of Stopped Lévy Processes with Markov Modulation”, with Brendan K. Beare and Won-Ki Seo, accepted at Econometric Theory WP version
(Power law, Theory) Characterize tail behavior of Markov-modulated Lévy processes that are stopped at state-dependent Poisson rates; application to wealth distribution.
2. The Effect of Social Distancing on the Reach of an Epidemic in Social Networks”, with Gregory Gutin, Tomohiro Hirano, Sung-Ha Hwang, and Philip R. Neary, Journal of Economic Interaction and Coordination WP version Code
(Network) Simulation study of the evolution of an epidemic disease on social networks; the effectiveness of social distancing greatly depends on network structure.
3. A Theory of the Saving Rate of the Rich”, 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.
4. Data-based Automatic Discretization of Nonparametric Distributions”, Computational Economics 57:1217-1235 (2021) WP version Code
(Numerical method) Automatic discretization method of nonparametric distributions using Gaussian quadrature.
5. Necessity of Hyperbolic Absolute Risk Aversion for the Concavity of Consumption Functions”, 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.
6. Efficient Minimum Distance Estimation of Pareto Exponent from Top Income Shares”, 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.
7. Is Gibrat’s “Economic Inequality” Lognormal?”, 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.
8. On the Emergence of a Power Law in the Distribution of COVID-19 Cases”, 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.
9. The Income Fluctuation Problem and the Evolution of Wealth”, 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.
10. The Equity Premium and the One Percent”, 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. One of my best papers.
11. Publications, Citations, Position, and Compensation of Economics Professors”, 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.
12. Securitized Markets, International Capital Flows, and Global Welfare”, 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.
13. An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity”, 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. One of my best papers.
14. Wealth Distribution with Random Discount Factors”, 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.
15. Discretizing Nonlinear, Non-Gaussian Markov Processes with Exact Conditional Moments”, 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. One of my best papers.
16. Growth Effects of Annuities and Government Transfers in Perpetual Youth Models”, 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.
17. A Note on the Size Distribution of Consumption: More Double Pareto than Lognormal”, 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).
18. Huggett Economies with Multiple Stationary Equilibria”, 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.
19. Edgeworth Box Economies with Multiple Equilibria”, 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.
20. Fat Tails and Spurious Estimation of Consumption-Based Asset Pricing Models”, 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).
21. Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis”, with Ken’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).
22. Asset Prices and Efficiency in a Krebs Economy”, 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).
23. Bayesian General Equilibrium”, Economic Theory 58(2):375-411 (2015) BibTeX
(Theory) Walrasian equilibrium is a special limiting case of statistical equilibrium. Extension of Toda (2010).
24. The Double Power Law in Consumption and Implications for Testing Euler Equations”, 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.
25. Incomplete Market Dynamics and Cross-Sectional Distributions”, 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.
26. Radii of the Inscribed and Escribed Spheres of a Simplex”, International Journal of Geometry 3(2):5-13 (2014) BibTeX
(Mathematics) Generalization to an $n$-simplex of the fat 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.
27. Discrete Approximations of Continuous Distributions by Maximum Entropy”, with Ken’ichiro Tanaka, Economics Letters 118(3):445-450 (2013) BibTeX
(Numerical method) Simple maximum entropy method to discretize probability distributions.
28. Learning Curve for Paramedic Endotracheal Intubation and Complications”, 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.
29. The Impact of Media Reports on the 2008 Outbreak of Hydrogen Sulfide Suicides in Japan”, 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.
30. The Double Power Law in Income Distribution: Explanations and Evidence”, 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.
31. Income Dynamics with a Stationary Double Pareto Distribution”, 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.
32. Operator Reverse Monotonicity of the Inverse”, 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.
33. Existence of a Statistical Equilibrium for an Economy with Endogenous Offer Sets”, Economic Theory 45(3):379-415 (2010) BibTeX
(Theory) Generalizes Foley’s (1994) statistical equilibrium model when offer sets are endogenous. My master thesis at U of Tokyo. Further generalized in Toda (2015).

## Conference proceedings

1. Error Estimate and Convergence Analysis of Moment-Preserving Discrete Approximations of Continuous Distributions”, with Ken’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)
2. Axiomatization of Maximum Entropy without the Bayes Rule”, 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

1. Corrigendum to “An Impossibility Theorem for Wealth in Heterogeneous-agent Models with Limited Heterogeneity [Journal of Economics Theory 182 (2019) 1-24]”, with John Stachurski, Journal of Economic Theory 188:105066 (2020)
2. Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact”, Covid Economics, Vetted and Real-Time Papers 1 (2020) arXiv Slides VoxEU Fortune

## Working papers

1. “Collateralized Loans, Pooling, and Maximum Leverage”, revise and resubmit at Theoretical Economics PDF
2. “Zipf’s Law: A Microfoundation” PDF
3. “Bad News and Robust Comparative Statics for the Elasticity of Intertemporal Substitution”, with Lawrence Schmidt, revise and resubmit at Theoretical Economics PDF
4. “Geometrically Stopped Markovian Random Growth Processes and Pareto Tails”, with Brendan K. Beare, revise and resubmit at Econometrica PDF Slides
5. “Pareto Extrapolation: An Analytical Framework for Studying Tail Inequality”, with Émilien Gouin-Bonenfant PDF Code
6. “Asymptotic Linearity of Consumption Functions and Computational Efficiency”, with Qingyin Ma PDF
7. “Capital and Labor Income Pareto Exponents across Time and Space”, with Tjeerd de Vries, revise and resubmit at Review of Income and Wealth LIS Working Paper 794 arXiv
8. “Unbounded Dynamic Programming via the Q-Transform”, with Qingyin Ma and John Stachurski PDF
9. “Contraction Mapping Theorem for the Cartesian Product of Complete Metric Spaces”, revise and resubmit at Operations Research Letters PDF
10. “Optimal Epidemic Control in Equilibrium with Imperfect Testing and Enforcement”, with Thomas Phelan PDF
11. “Tax Progressivity and Wealth Inequality: Evidence from Forbes 400”, with Ji Hyung Lee, Yuya Sasaki, and Yulong Wang PDF