arXiv subjects

Qingyin Ma

Publications and source records attributed to Qingyin Ma.

12 recordsLinked to original sources

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

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

Optimal Savings under Transition Uncertainty and Learning Dynamics

This paper studies optimal consumption and saving decisions under uncertainty about the transition dynamics of the economic environment. We consider a general optimal savings problem in which the exogenous state governing discounting, capital returns, and nonfinancial income follows a Markov process with unknown transition probability, and agents update their beliefs over time through Bayesian learning. Despite the added endogenous state from belief updating, we establish the existence, uniqueness, and key structural properties of the optimal policy, including monotonicity and concavity. We also develop an efficient computational method and use it to study how transition uncertainty and learning interact with precautionary motives and wealth accumulation, highlighting a dynamic mechanism through which uncertainty about regime persistence shapes consumption dynamics and long-run household wealth.

econ.TH↗

arXiv2024

Interest Rate Dynamics and Commodity Prices

In economic studies and popular media, interest rates are routinely cited as a major factor behind commodity price fluctuations. At the same time, the transmission channels are far from transparent, leading to long-running debates on the sign and magnitude of interest rate effects. Purely empirical studies struggle to address these issues because of the complex interactions between interest rates, prices, supply changes, and aggregate demand. To move this debate to a solid footing, we extend the competitive storage model to include stochastically evolving interest rates. We establish general conditions for existence and uniqueness of solutions and provide a systematic theoretical and quantitative analysis of the interactions between interest rates and prices.

econ.TH↗

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↗

arXiv2021

Asymptotic Linearity of Consumption Functions and Computational Efficiency

We prove that the consumption functions in optimal savings problems are asymptotically linear if the marginal utility is regularly varying. We also analytically characterize the asymptotic marginal propensities to consume (MPCs) out of wealth. Our results are useful for obtaining good initial guesses when numerically computing consumption functions, and provide a theoretical justification for linearly extrapolating consumption functions outside the grid.

econ.GN↗

arXiv2021

A Theory of the Saving Rate of the Rich

Empirical evidence suggests that the rich have higher propensity to save than do the poor. While this observation may appear to contradict the homotheticity of preferences, we theoretically show that that is not the case. Specifically, we consider an income fluctuation problem with homothetic preferences and general shocks and prove that consumption functions are asymptotically linear, with an exact analytical characterization of asymptotic marginal propensities to consume (MPC). We provide necessary and sufficient conditions for the asymptotic MPCs to be zero. We calibrate a model with standard constant relative risk aversion utility and show that zero asymptotic MPCs are empirically plausible, implying that our mechanism has the potential to accommodate a large saving rate of the rich and high wealth inequality (small Pareto exponent) as observed in the data.

econ.TH↗

arXiv2020

The Income Fluctuation Problem and the Evolution of Wealth

We analyze the household savings problem in a general setting where returns on assets, non-financial income and impatience are all state dependent and fluctuate over time. All three processes can be serially correlated and mutually dependent. Rewards can be bounded or unbounded and wealth can be arbitrarily large. Extending classic results from an earlier literature, we determine conditions under which (a) solutions exist, are unique and are globally computable, (b) the resulting wealth dynamics are stationary, ergodic and geometrically mixing, and (c) the wealth distribution has a Pareto tail. We show how these results can be used to extend recent studies of the wealth distribution. Our conditions have natural economic interpretations in terms of asymptotic growth rates for discounting and return on savings.

econ.TH↗

arXiv2019

Dynamic Programming Deconstructed: Transformations of the Bellman Equation and Computational Efficiency

Some approaches to solving challenging dynamic programming problems, such as Q-learning, begin by transforming the Bellman equation into an alternative functional equation, in order to open up a new line of attack. Our paper studies this idea systematically, with a focus on boosting computational efficiency. We provide a characterization of the set of valid transformations of the Bellman equation, where validity means that the transformed Bellman equation maintains the link to optimality held by the original Bellman equation. We then examine the solutions of the transformed Bellman equations and analyze correspondingly transformed versions of the algorithms used to solve for optimal policies. These investigations yield new approaches to a variety of discrete time dynamic programming problems, including those with features such as recursive preferences or desire for robustness. Increased computational efficiency is demonstrated via time complexity arguments and numerical experiments.

math.OC↗

arXiv2019

Dynamic Optimal Choice When Rewards are Unbounded Below

We propose a new approach to solving dynamic decision problems with rewards that are unbounded below. The approach involves transforming the Bellman equation in order to convert an unbounded problem into a bounded one. The major advantage is that, when the conditions stated below are satisfied, the transformed problem can be solved by iterating with a contraction mapping. While the method is not universal, we show by example that many common decision problems do satisfy our conditions.

econ.TH↗

arXiv2018

The Income Fluctuation Problem with Capital Income Risk: Optimality and Stability

This paper studies the income fluctuation problem with capital income risk (i.e., dispersion in the rate of return to wealth). Wealth returns and labor earnings are allowed to be serially correlated and mutually dependent. Rewards can be bounded or unbounded. Under rather general conditions, we develop a set of new results on the existence and uniqueness of solutions, stochastic stability of the model economy, as well as efficient computation of the ergodic wealth distribution. A variety of applications are discussed. Quantitative analysis shows that both stochastic volatility and mean persistence in wealth returns have nontrivial impact on wealth inequality.

econ.TH↗

arXiv2017

Optimal Timing of Decisions: A General Theory Based on Continuation Values

Building on insights of Jovanovic (1982) and subsequent authors, we develop a comprehensive theory of optimal timing of decisions based around continuation value functions and operators that act on them. Optimality results are provided under general settings, with bounded or unbounded reward functions. This approach has several intrinsic advantages that we exploit in developing the theory. One is that continuation value functions are smoother than value functions, allowing for sharper analysis of optimal policies and more efficient computation. Another is that, for a range of problems, the continuation value function exists in a lower dimensional space than the value function, mitigating the curse of dimensionality. In one typical experiment, this reduces the computation time from over a week to less than three minutes.

math.OC↗