The Effectiveness of Parametric Approximation: A Case of Main- frame Computer Investment

Abstract

The general method to solve the fixed point problem is a discretization of observed state variables. When the observed state variable is continuous, the required fixed point is in fact an infinite dimensional object. Therefore, in order to solve the fixed point problem, it is necessary to discretize the state space so that the state variable takes on only finitely many values. But there are limits regarding this method: (ⅰ) “curse of dimensionality”; (ⅱ) the limits it places on our ability to solve high-dimensional DP problems. Despite these limits, this method have been used in many literature. However, The discretization method may not be applicable to computer replacement research to solve the fixed point problem, because of the aforementioned problems. Using a detailed data set on computer holdings by one of the world’s largest telecommunication companies, this paper shows the effectiveness of Parametric Approximation procedure by comparison with the discretization method, which converts the contraction fixed-point problem into a nonlinear least squares problem with combining maximum likelihood estimation method to estimate the unknown parameters.