This paper introduces the probabilistic formulation of continuous-time economic models: forward stochastic differential equations (SDE) govern the dynamics of backward-looking variables, and backward SDEs capture that of forward-looking variables. Deep learning streamlines the search for the...

This paper develops a dynamic programming method when the one-stage deviation principle in the sense of mechanism design literature doesn’t hold. The commonly used dynamic programming method is valid only if the one-stage deviation principle in the sense of mechanism design literature is...

Epidemiological models assume gravity-like interactions of individuals across space without microfoundations. We combine a simple epidemiological frame-work with a dynamic model of individual location choice. The model predicts that flows of people across space obey a structural gravity...

We embed a lockdown choice in a simplified epidemiological model and derive formulas for the optimal lockdown intensity and duration. The optimal policy reflects the rate of time preference, epidemiological factors, the hazard rate of vaccine discovery, learning effects in the health care...

Twelve percent of the Malawian population is HIV infected. Eighteen percent of sexual encounters are casual. A condom is used a third of the time. To analyze the Malawian epidemic, a choice-theoretic general equilibrium search model is constructed. In the developed framework, people select...

I present a stylized suspected-infected-recovered (SIR) model of COVID-19, with symptomatic versus asymptomatic patients, and social distancing intervention. The optimal suppress strategy has low-infection rates, enabling assumptions that support closed-form solutions. The model predicts high...

We estimate the causal effects of a pandemic-era wage subsidy program in Canada on job losses and business closures. Our estimates use administrative microdata and a regression discontinuity strategy to estimate the effects of marginal changes in the wage subsidy rate. The estimated net wage...

We propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including stiff differential equations and systems giving rise...

Subjective evaluations are widely used, but call for different contracts from traditional moral-hazard settings. Previous literature shows that contracts require payments to third parties, which real-world contracts rarely use. I show that the implicit assumption of deterministic contracts makes...

This paper defines isomorphism for network formation that is not mathematically isomorphic. Once the pattern of network formation is characterized, one can test for (i) location fixed effects, (ii) heterogeneity, (iii) private information allowing for long-term contracts. The paper provides...