Estimating The Accuracy Of Numerical Solutions To Dynamic Optimization Problems

The paper provides a method to measure the accuracy of numerical solutions to stochastic dynamic optimization problems. The theorems proven in the paper provide, first, a tight upper bound on the loss in the value function that comes from using the numerical solution rather than the exact solution. The loss is computed at a given point of the state space, using the Euler residuals along simulated paths of the model. Second, they allow to compute an unbiased estimate of the error in the policy function at such a point. However, estimating the error in the policy function requires a higher computational effort than obtaining the value function error. Both measures can be obtained without knowing the exact solution.The measures are applied to several variants of the neoclassical growth model, some of them highly nonlinear. It is shown that the method provides indeed tight estimates of the error, which are helpful to evaluate numerical solution techniques according to their accuracy.