An Empirical Model of Mainframe Computer Replacement∗

This paper formulates a stochastic optimal stopping model for the replacement of mainframe computer systems in the telecommunications industry. It describes the replacement behavior by focusing on unique features of computer systems, which are associated with technological development. The optimal stopping rule is the solution of a stochastic dynamic programming model that specifies the system administrator’s objective to maximize profits through three choices: ‘keep’, ‘upgrade’, or ‘replace’. The model depends on unknown parameters which govern both the profit structures of the task level of the company and the system administrator’s expectation of the future values of the state variables. Using a detailed data set on computer holdings by one of the world’s largest telecommunication companies, I investigate the stylized facts of computer replacement and estimate the model with the nested fixed point algorithm. The estimation requires two procedures: (i) a parametric approximation procedure which converts the contraction fixed-point problem into a nonlinear least squares problem; (ii) maximum likelihood estimation method to estimate the unknown parameters. The estimation supports the observed stylized facts of the data in general, allowing for better understanding of the replacement behavior in the era of rapidly growing computer technology. I also show the effectiveness of the parametric approximation method in comparison with the discretization method. ∗I give special thanks my to advisor, John Rust for invaluable advice and encouragement. I also thank Steven Berry and Martin Pesendorfer. I am indebted to the provider of the computer data who wishes to remain anonymous. I have greatly benefitted from discussions with Janryoul Kim. All errors are my own. †Contact information: e-mail [email protected], homepage http://www.econ.yale.edu/~sungjcho, phone (203) 432-3559, fax (203) 432-5779