THE IMPULSE RESPONSES OF CAPITAL, CONSUMPTION, AND PRICES IN THE STOCHASTIC RAMSEY MODEL WITH AN INFINITE TIME HORIZON EMPLOYING VALUE FUNCTION ITERATION AND LINEAR INTERPOLATION

Abstract

In this paper, we use value function iteration and linear interpolation to solve an example of a stochastic, infinite-horizon Ramsey model, which is one kind of dynamic general equilibrium (DGE) model. To obtain an approximation of the policy function’s solution, we pick a grid of capital investments for each period, set the starting value of the value function, build an iterative loop to compute the new value using interpolation, and establish the selection criteria and stop conditions. We model transient shocks to total factor productivity (TFP) and capture the impulsive reactions of consumption, capital, and factor pricing, with the algorithm anticipated to converge in “x” iterations. This concept is helpful and inspiring for assessing financial risk avoidance and dealing with and better comprehending potential shocks.