A Framework for Solving Non-Linear DSGE Models

We propose a framework to solve non-linear DSGE models combining approximation and estimation techniques. Instead of relying on a fixed grid, we use Monte Carlo methods to draw samples from the state space, which are used to estimate an approximation for the value or policy functions of interest. By using estimators from high-dimensional statistics we can attenuate the curse of dimensionality while maintaining flexibility, theoretical guarantees for convergence and upper bound for the errors. In particular, we propose two different methods: a regularized projection and a support vector machine algorithm. To illustrate these solution procedures, we apply the first algorithm to solve a standard growth model, which has a known linear solution, and show that it achieves good accuracy, correctly shrinking the coefficients of a polynomial basis. Moreover, we use the support vector machine algorithm to solve a New Keynesian model with a Zero Lower Bound (ZLB) and compare our results with the ones from the Smolyak Method, which is widely used in the literature. We show that the latter overestimate the impact of the ZLB in the economy, achieving a lower accuracy than the one from our solution.