Letter of recommendation
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My policy for writing letters of recommendation
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My policy for writing letters of recommendation
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Discretizing probability distributions and stochastic processes
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Advices on applying to economics Ph.D. programs
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Email writing tips for undergraduate students
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List of my coauthors
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Resources on LaTeX
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Places that I have visited
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How this website was created
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After my 2022 ECMA paper got accepted in January 2022, I got burnt out. I stopped doing research and spent most of my time playing tennis. I became a captain of a USTA 7.0 mixed doubles team (I had just become 4.0), and my wife and I recruited strong players, organized practices, and advanced to sectionals twice. In one of the Southern California sectionals, we narrowly lost in the semifinal.
My coauthor Jim Rauch was the recruitment chair when I got hired at UCSD in 2013. He was also the department chair from 2013 to 2016, so I had a lot of interaction with him. When we chatted in June 2022, he mentioned he was interested in a project to animate the contraction mapping theorem to help build intuition. We knew it had zero career benefit but it sounded fun, so I wrote up some pedagogical material and Matlab codes and Jim made the video.
We tried to publish this in journals on economic education but we got desk-rejected each time and the paper became dormant. Later, I was asked to review a paper at Qeios. Because I had never heard of that journal, I thought it was a predatory journal, but upon inspection its business model seemed interesting: they publish anything, but reviews are open and (to prevent abuse) not anonymous. So we posted our paper there, and we are happy that our paper and video have been well received.
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In May 2023, I read something about Ergodicity Economics, and I thought it was a completely nonsense pseudoscience promoted by failed self-proclaimed physicists. Although it had zero career benefit, to contribute to the public good to prevent the spread of pseudoscience, I spent a few days to write this critique. The paper got desk-rejected from Physical Review Letters, Physical Review E, and Chaos, and became dormant. After my pleasant experience at Qeios, I published the paper there.
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Short description of portfolio item number 1
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Short description of portfolio item number 2
Published in Economic Theory, 2010
(Theory) Generalize Foley’s (1994) statistical equilibrium model when offer sets are endogenous; my master thesis at U of Tokyo; further generalized in Toda (2015).
Published in American Mathematical Monthly, 2011
(Mathematics) Simple proof of reverse monotonicity of the inverse of positive definite matrices based on convex conjugate functions.
Published in Physical Review E, 2011
(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.
Published in International Journal of Psychiatry in Medicine, 2012
(Medicine, Empirical) The media coverage during the 2008 outbreak of hydrogen sulfide suicides in Japan caused more suicides.
Published in Journal of Economic Behavior and Organization, 2012
(Power law, Empirical) A certain mean-reverting income process generates a stationary double Pareto distribution; my third-year empirical paper at Yale.
Published in Economics Letters, 2013
(Numerical method) Simple maximum entropy method to discretize probability distributions.
Published in International Journal of Emergency Medicine, 2013
(Medicine, Empirical) You need to practice at least 30 times to intubate a patient consistently.
Published in International Journal of Geometry, 2014
(Mathematics) High-dimensional generalization 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; obtained those results in 1998 when I was freshman.
Published in Journal of Economic Theory, 2014
(Power law, Theory) Class of tractable dynamic general equilibrium models that generates power law in size distributions; one of my dissertation chapters at Yale.
Published in Economic Theory, 2015
(Theory) Walrasian equilibrium is a special limiting case of statistical equilibrium; extension of Toda (2010).
Published in SIAM Journal on Numerical Analysis, 2015
(Numerical method, Mathematics) Convergence and error analysis of maximum entropy discretization of Tanaka & Toda (2013).
Published in Journal of Political Economy, 2015
👍(Power law, Econometrics, Empirical) Power law in cross-sectional household consumption data causes spurious inference.
Published in Review of Economic Dynamics, 2015
(Theory, Macro, Finance) Asset pricing and optimal taxation in a class of tractable dynamic general equilibrium models; formerly a section of Toda (2014).
Published in Economic Theory Bulletin, 2017
(Theory) Many general examples of multiple equilibria in Edgeworth box economies.
Published in Quantitative Economics, 2017
👍(Numerical method, Finance) Approximate Markov processes by finite-state Markov chains using maximum entropy discretization of Tanaka & Toda (2013, 2015); applications to solving asset pricing models.
Published in Journal of Applied Econometrics, 2017
(Power law, Econometrics, Finance) Monte Carlo study of spurious inference caused by power law; formerly a section of Toda & Walsh (2015).
Published in Macroeconomic Dynamics, 2017
(Power law, Empirical) Cross-sectional household consumption is well-approximated by double Pareto-lognormal distribution; formerly a section of Toda & Walsh (2015).
Published in Journal of Mathematical Economics, 2017
(Theory, Macro) In perpetual youth models, introduction of government transfer crowds out annuity market and increases growth.
Published in Journal of Economic Dynamics and Control, 2017
(Theory, Macro) Closed-form solution to a Huggett (1993) economy with non-Gaussian VAR(1) dynamics and general examples of multiple stationary equilibria.
Published in Journal of Financial Economics, 2019
(Finance, Theory) With collateral constraints, financial integration may hurt the less constrained country.
Published in Journal of Monetary Economics, 2019
(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.
Published in Journal of Economic Theory, 2019
👍(Power law, Theory, Macro) Prove the impossibility for the canonical Bewley-Huggett-Aiyagari model to generate heavier-tailed wealth than income.
Published in Econ Journal Watch, 2019
(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
Published in Journal of Economic Theory, 2020
(Power law, Theory) Establish existence and uniqueness of a solution to a general income fluctuation problem; characterize tail behavior of stationary wealth distribution.
Published in Review of Financial Studies, 2020
👍(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.
Published in Empirical Economics, 2020
(Power law, Empirical) The majority of data sets analyzed by Gibrat and claimed to be lognormal are actually closer to Pareto-type distributions.
Published in Physica D: Nonlinear Phenomena, 2020
👍(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.
Published in Journal of Applied Econometrics, 2021
(Power law, Econometrics) Efficient estimation of Pareto exponents when only certain top income shares are observable.
Published in Journal of Economic Interaction and Coordination, 2021
(Network) Simulation study of the evolution of an epidemic disease on social networks; the effectiveness of social distancing greatly depends on network structure.
Published in Journal of Economic Theory, 2021
👍(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.
Published in Computational Economics, 2021
(Numerical method) Automatic discretization method of nonparametric distributions using Gaussian quadrature.
Published in Journal of Mathematical Economics, 2021
👍(Theory) That HARA utility implies concave consumption functions is well-known, but the converse is also true.
Published in Operations Research Letters, 2021
(Mathematics) Show the usefulness of Perov’s contraction principle (which is a generalization of Banach’s contraction principle) for solving certain dynamic programming problems.
Published in Journal of Mathematical Economics, 2022
(Theory, Numerical method) Prove asymptotic linearity of policy functions when marginal utility is regularly varying; follow-up of Ma & Toda (2021).
Published in Journal of Mathematical Economics, 2022
(Theory) Simple operation that often transforms an unbounded dynamic programming problem into a bounded one.
Published in Econometrica, 2022
👍(Power law, Mathematics) Provide simple formula and mathematical foundation for Pareto exponents of stationary Markov multiplicative processes.
Published in Econometric Theory, 2022
(Power law, Theory) Characterize tail behavior of Markov-modulated Lévy processes that are stopped at state-dependent Poisson rates; application to wealth distribution.
Published in Journal of Economic Theory, 2022
👍(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.
Published in Review of Income and Wealth, 2022
(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.
Published in Quantitative Economics, 2023
👍(Power law, Numerical method, Macro) Analytical framework designed to solve and analyze heterogeneous-agent models that endogenously generate fat-tailed wealth distributions.
Published in Theoretical Economics, 2023
(Theory) Robust comparative statics for the elasticity of intertemporal substitution; sign- and point-identification of EIS minus 1.
Published in Journal of Econometrics, 2024
(Econometrics) Just like what the title says, for example estimation of income distributions from tax returns data.
Published in 👍Journal of Mathematical Economics, 2024
👍(Theory, Macro, Finance) Self-contained review of the theory of asset price bubbles.
Published in Accepted at Economic Theory Bulletin, 2024
(Theory) Combine weighted supremum norm and Perov contraction theorem for solving unbounded dynamic programming problems.
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Undergraduate, UCSD, 2015
This course covers some topics in operations research, such as convex analysis, nonlinear programming, and dynamic programming. I do not currently teach this course.
Graduate, UCSD, 2016
This course trains third year Ph.D. students to conduct research, write papers, and make presentations.
Graduate, UCSD, 2017
This course covers topics in finance theory. I do not currently teach this course.
Graduate, UCSD, 2023
This course covers mathematical topics that are essential for economics, very quickly but rigorously.
Undergraduate/Graduate, UCSD, 2023
This course covers the classical Arrow-Debreu theory of general equilibrium. The undergraduate course (Econ 113) meets 3 hours per week for 10 weeks and covers about 2/3 of the lecure notes. The graduate course (Econ 200A) meets 3 hours per week for 5 weeks and covers the entire lecture notes plus additional topics on mathematical economics.
Undergraduate, UCSD, 2024
This course covers some institutional details on the financial markets, bond pricing (including duration analysis), optimal portfolio problem, mutual fund theorem, Capital Asset Pricing Model, and option pricing (including bounds on option prices, suboptimality of early exercise of American call options, put-call parity, and binomial option pricing).
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