GPU-Accelerated Value Function Iteration in Julia: Faster Macroeconomic Modeling

Among the many computational techniques that economists, and more specifically macroeconomists use to solve models, value function iteration (VFI) is probably the most commonly used. VFI is simple to implement, conceptually very close to the theoretical results of dynamic programming and works over a wide range of models, especially if these entail complex stochastic elements. Unfortunately, VFI algorithms are computationally very taxing even for modern machines, usually requiring long times (in the order of hours) to converge to a solution. To address this problem, much in the footsteps laid down by the paper by Aldrich, Fernandez-Villaverde,Gallant and Rubio-Ramirez “Tapping the Supercomputer under your Desk: Solving Dynamic Equilibrium Models with Graphics Processors” , I would like to present how it is almost trivial to use Julia, OpenCL, and the packages GPUArrays.jl and CLArrays.jl to run VFI algorithms orders of magnitude faster, using only a consumer (integrated) graphics card and without loosing appreciable precision. We focus our attention on the following topics:

• Introduction to Dynamic Programming and why VFI is so common …Many problems in macroeconomic are usually posed, or can be posed in the form of dynamic programming: this usually entails writing the so-called Bellman equation of the problem. We introduce the Value Function Iteration algorithm in the context of the super simple Real Business Cycle model.
• VFI in Julia …Value function iteration is easy to implement in Julia, but can be very slow: this is because the algorithm explicitly requires a maximization step. Because of the so called “curse of dimensionality” this approach does not scale well as we increase the number of points. This effectively creates a “physical” barrier between the researcher and exploring the model features with ease by changing parameters and studying the resulting solution.
• Leveraging the GPU …We first port the VFI algorithm for the RBC using OpenCL.jl and writing a simple OpenCL kernel. This approach however is cumbersome and may be unfeasible. Then, we discuss how the packages GPUArrays.jl and CLArrays.jl allow to make this transition much, much simpler.
• More complex models and GPU superiority …Finally, we expand the GPU value function iteration algorithm used for the RBC model to two more articulate settings: and RBC model with uncertainty; and an Overlapping Generations Model, for which the GPU implementation cuts the solution time from more than 40 minutes to less than 30 seconds, with a speed gain of around 150x.

Speaker's bio

I am an M.SC in Economics student in my second and last year at Konstanz University, Germany, in a double degree program with the University of Rome Tor Vergata. I have an undergraduate degree in Mathematics (which is and will be my secret passion), even thought I’ve now turned to Macroeconomics. My passions are: programming, tennis, pasta all’amatriciana and listening to music during long car trips. I don’t have to write code, but it gives me much joy.