This is a collection of code files that solve various economic models using dynamic programming. It is intended as a reference for economists who are getting started with solving economic models numerically.
The code is written in MATLAB, a programming language developed by MathWorks. MathWorks sells a piece of software (also called MATLAB) for writing and running MATLAB code, and most economics departments will have licenses for it. However, to run the code included in this collection you do not need to have a MATLAB license. All the code is written to be compatible with GNU Octave, a free software alternative to MATLAB. Where certain MATLAB features are not implemented in Octave, I provide alternative files with the suffix "_octave".
cakeeating.m
Code for solving an infinite horizon non-stochastic cake-eating problem with log utility. This problem can be solved analytically, so the code is redundant from the point of view of finding the solution. However, since the true solution is already known, we can use the code to verify that the value function iteration approach works. Starting from an arbitrary guess for the value function and repeatedly applying the Bellman operator, the code does indeed get very close to the true value function. Note that this cake-eating problem is just a special case of the Ramsey model with u(c)=log(c), f(k)=0 and delta=0.
cakesearch.m
With log utility, considering zero consumption causes an error in the value function iteration: the value of a cake of size zero is negative infinity, and with each iteration of the Bellman operator this value spreads to the next-smallest cake size. cakeeating.m works around this problem by replacing zero consumption values with a very small number. cakesearch.m finds the value of this small number that minimises the difference between the numerical solution and the analytical solution.
cakeloss.m
An auxiliary function used by cakesearch.m. For any given number, it performs value function iteration as in cakeeating.m, replacing zero consumption values with that number. It then takes the resulting numerical value function and the analytical value function, and calculates the sum of squared residuals.
ramsey_fulldep_logutil.m
Code for solving an infinite horizon non-stochastic Ramsey model with full depreciation and log utility. As with cakeeating.m, this model has an analytical solution, so we can compare this with our numerical result to verify that the value function iteration approach works.
ramsey.m
A more general script file for solving non-stochastic Ramsey models. The depreciation rate (delta) can be changed, as can the production and utility functions.
ramseyprod.m
Production function for ramsey.m.
ramseyutil.m
Utility function for ramsey.m.
Copyright (c) 2012 Andrew Gimber
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