Using Nonlinear Model Predictive Control for Dynamic Decision Problems In Economics

Abstract

This paper presents a new approach to solve dynamic decision models in economics. The proposed procedure, called Nonlinear Model Predictive Control (NMPC), relies on the iterative solution of optimal control problems on finite time horizons and is well established in engineering applications for stabilization and tracking problems. Only quite recently, extensions to more general optimal control problems including those appearing in economic applications have been investigated. Like Dynamic Programming (DP), NMPC does not rely on linearization techniques but uses the full nonlinear model and in this sense provides a global solution to the problem. However, unlike DP, NMPC only computes one optimal trajectory at a time, thus avoids to grid the state space and for this reason the computational demand grows much more moderately with the space dimension than for DP. In this paper we explain the basic idea of NMPC, give a proof concerning the accuracy of NMPC for discounted optimal control problems, present implementational details, and demonstrate the ability of NMPC to solve dynamic decision problems in economics by solving low and high dimensional examples, including models with multiple equilibria, tracking and stochastic problems.

Cooperative Monetary and Fiscal Policies in the Euro Area

“…These variables have then been contrasted with counterfactual simulated paths, where we assume cooperative behavior of the central bank and the fiscal authorities. These simulated paths are obtained by a numerical procedure, nonlinear model predictive control, as presented in Grüne, Semmler, and Stieler (). Our results in section 4 suggest that a cooperative solution is capable of providing superior results compared with the noncooperative scenario, reducing the danger of a break‐up of the euro area via decentralized, but coordinated fiscal policies in combination with a centralized monetary authority.…”

“…The data‐series will then be contrasted with counter‐factual simulations where we assume some cooperative behavior of the central bank and fiscal authorities. We trace the path of the above variables as suggested by cooperative behavior, and the cooperative solution is obtained by nonlinear model predictive control (NMPC), as described in Grüne, Semmler, and Stieler ().…”

Interaction of Labour and Credit Market in Growth Regimes: A Theoretical and Empirical Analysis

“…The parameters of the matching functions are assumed to be: and Applying the NMPC procedure of Grüne et al . () gives us solution paths such as those depicted in Figure .…”

“…The high dimensionality of the problem precludes a closed‐form analytical solution, however. We first solve the model variants numerically using a new method called nonlinear model predictive control (NMPC, see Grüne et al ., ) that allows for approximately accurate solutions in finite horizon models. NMPC is a finite horizon solution method that can be applied to large scale macro systems and the dynamics can be explored on a finite horizon assuming limited information agents.…”

Demand and supply effects of bargaining power shocks

“…This case constitutes an alternative mechanism to expectation formation. Existing alternative treatments of expectations include the heterogeneous agent literature (Brock and Hommes, 1997;Chiarella, 1992;De Grauwe and Kaltwasser, 2012) or nonlinear model predictive control methods (Ernst and Semmler, 2013;Gruene et al, 2013) for instance.…”