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Working Paper
Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics
In this paper we explore some of the benefits of using the finite-state Markov chain approximation (MCA) method of Kushner and Dupuis (2001) to solve continuous-time optimal control problems. We first show that the implicit finite-difference scheme of Achdou et al. (2017) amounts to a limiting form of the MCA method for a certain choice of approximating chains and policy function iteration for the resulting system of equations. We then illustrate the benefits of departing from policy function iteration by showing that using variations of modified policy function iteration to solve income ...
Working Paper
The Optimal Taxation of Business Owners
Business owners in the United States are disproportionately represented among the wealthy and are exposed to substantial idiosyncratic risk. Further, recent evidence indicates that business income primarily reflects returns to the human capital of the owner. Motivated by these facts, this paper characterizes stationary efficient allocations and optimal linear taxes on income and wealth when business income depends on innate ability, luck, and the past effort of the owner. I first show that in stationary efficient allocations, more productive entrepreneurs typically bear more risk and the ...
Journal Article
Modeling Behavioral Responses to COVID-19
Many models have been developed to forecast the spread of the COVID-19 virus. We present one that is enhanced to allow individuals to alter their behavior in response to the virus. We show how adding this feature to the model both changes the resulting forecast and informs our understanding of the appropriate policy response. We find that when left to their own devices, individuals do curb their social activity in the face of risk, but not as much as a government planner would. The planner fully internalizes the effect of all individuals’ actions on others in society, while individuals do ...
Working Paper
On the Optimality of Differential Asset Taxation
How should a utilitarian government balance redistributive concerns with the need to provide incentives for business creation and investment? Should they tax business profits, the (risk-free) savings of owners, or some combination of both? To address this question, this paper presents a model in which the desirability of differential asset taxation emerges endogenously from the presence of agency frictions. I consider an environment in which entrepreneurs hire workers and rent capital to produce output subject to privately observed shocks and have the ability to both divert capital to private ...
Journal Article
Two Approaches to Predicting the Path of the COVID-19 Pandemic: Is One Better?
We compare two types of models used to predict the spread of the coronavirus, both of which have been used by government officials and agencies. We describe the nature of the difference between the two approaches and their advantages and limitations. We compare examples of each type of model—the University of Washington IHME or “Murray” model, which follows a curve-fitting approach, and the Ohio State University model, which follows a structural approach.
Working Paper
The Art of Temporal Approximation An Investigation into Numerical Solutions to Discrete and Continuous-Time Problems in Economics
A recent literature within quantitative macroeconomics has advocated the use of continuous-time methods for dynamic programming problems. In this paper we explore the relative merits of continuous-time and discrete-time methods within the context of stationary and nonstationary income fluctuation problems. For stationary problems in two dimensions, the continuous-time approach is both more stable and typically faster than the discrete-time approach for any given level of accuracy. In contrast, for convex lifecycle problems (in which age or time enters explicitly), simply iterating backwards ...
Working Paper
Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics
In this paper we explore some benefits of using the finite-state Markov chain approximation (MCA) method of Kushner and Dupuis (2001) to solve continuous-time optimal control problems in economics. We first show that the implicit finite-difference scheme of Achdou et al. (2022) amounts to a limiting form of the MCA method for a certain choice of approximating chains and policy function iteration for the resulting system of equations. We then illustrate that, relative to the implicit finite-difference approach, using variations of modified policy function iteration to solve income fluctuation ...
Journal Article
The Evolution of Student Debt 2019–2022: Evidence from the Survey of Consumer Finances
In recent years, economists and policymakers have been interested in the burden of student debt across socioeconomic groups. In this Economic Commentary, we use the two most recent waves of the Survey of Consumer Finances, collected in 2019 and 2022, to study changes in the joint distribution of student debt and two measures of “ability-to-pay,” income and net worth. We find that between 2019 and 2022, both the fraction of families with student debt and real student debt per family were essentially unchanged, and aggregate student debt fell as a fraction of aggregate income and net worth. ...
Journal Article
Student debt incidence: recent data and conceptual issues
In recent years, the rising level of student debt has led to calls for increased government assistance in the form of partial or full student debt cancellation. In this Commentary, we use the 2019 Survey of Consumer Finances (SCF) to study the incidence of student debt and cancellation benefits along quantiles of household income, net worth, and our estimate of lifetime wealth. We show that student debt is highly concentrated among households with low net worth, but much more evenly distributed across income and lifetime wealth. We then highlight several challenges in using such statistics to ...
Working Paper
Time Use and the Efficiency of Heterogeneous Markups
What are the welfare implications of markup heterogeneity across firms? In standard monopolistic competition models, such heterogeneity implies inefficiency even in the presence of free entry. We enrich the standard model with heterogeneous firms so that preferences are non-separable in off-market time and market consumption and show that this changes the welfare implications of markup heterogeneity. In this context, homogeneity of markups is neither necessary nor sufficient for efficiency. The marginal cost of the marginal firm is weakly inefficiently high when off-market time and market ...