A nonlinear programming formulation is introduced to solve infinite horizon dynamic programming problems. This extends the linear approach to dynamic programming by using ideas from approximation theory to avoid inefficient discretization. Our numerical results show that this nonlinear...

There is great uncertainty about future climate conditions and the appropriate policies for managing interactions between the climate and the economy. We develop a multidimensional computational model to examine how uncertainties and risks in the economic and climate systems affect the social...

There is great uncertainty about the impact of anthropogenic carbon on future economic wellbeing. We use DSICE, a DSGE extension of the DICE2007 model of William Nordhaus, which incorporates beliefs about the uncertain economic impact of possible climate tipping events and uses empirically...

Continuous time is a superior representation of both the economic and climate systems that Integrated Assessment Models (IAM) aim to study. Moreover, continuous-time representations are simple to express. Continuous-time models are usually solved by discretizing time, but the quality of a...

Maximum likelihood estimation of structural models is often viewed as computationally difficult. This impression is due to a focus on the Nested Fixed-Point approach. We present a direct optimization approach to the general problem and show that it is significantly faster than the NFXP approach...

Beginning with Mirrlees, the optimal taxation literature has generally focused on economies where individuals are differentiated by only their productivity. In this pa- per we examine models with discrete types where individuals are differentiated by two or more characteristics. For example, we...

We study computational aspects of moral-hazard problems. We consider deterministic contracts as well as contracts with action and/or compensation lotteries, and formulate each case as a mathematical program with equilibrium constraints (MPEC). We investigate and compare solution properties of...

Numerical dynamic programming algorithms typically use Lagrange data to approximate value functions over continuous states. Hermite data is easily obtained from solving the Bellman equation and can be used to approximate value functions. We illustrate this method with one-, three-, and...

Numerical methods for dynamic programming often use value function iteration and interpolation. We present a novel shape-preserving rational spline approximation method that improves value function iteration in terms of both stability and accuracy compared to more common methods.

Dynamic programming is the foundation of dynamic economic analysis and often requires numerical solution methods. Standard methods are either slow or unstable. These instabilities are avoided when one uses modern methods from numerical optimization and approximation. Furthermore, large dynamic...