Industrial organization
Applied econometrics
Microeconomics
Applied microeconomics

Industrial Organization
Econometrics
Microeconomics

1997 (Orals): Econometrics, Industrial Organization
1996 (Writtens): Microeconomics and Macroeconomics theory

Empirical Models of Mainframe Computer Replacement

Professor John Rust
Professor Steven Berry
Professor Martin Pesendorfer

Summer 2001

M.Phil., Yale University, 1998
M.A., Yale University, 1997
B.A., Northwestern University, 1995

Yale University Dissertation Fellowship, Fall 1999
Yale University Graduate Fellowship
The fellowship granted from the Assembly of Koryoung region, Korea
Graduated with Highest Distinction Honor at Northwestern University

Teaching Assistant, Econometrics and Data Analysis, Fall 2000, Fall 1997
Teaching Assistant, Introduction to Economics (Microeconomics) Spring, 1999
Teaching Assistant, Introduction to Probability and Statistics, Fall 1998
Teaching Assistant, The Structure of American Industry, Spring 1998

"Finite Horizon Case of Computer Maintenances in Korea Telecom", mimeo, Yale University, 1999.

"Collusive Pricing Behavior of Oligopoly with Volatile Demand Shock", mimeo, Yale University, 1998

Despite the importance of computers in the "information economy", comparatively little is known about the factors affecting upgrade and replacement decisions. In the face of rapid technological progress and steadily declining costs, consumers and firms must decide whether to upgrade or replace an existing computer now, or wait to purchase a faster/cheaper system in the future.

This paper presents a dynamic programming model of a firm's decision of whether to keep, upgrade, or replace an existing computer subject to uncertainty over the timing and magnitude of future cost reductions for computer systems. I estimate and test this model using a detailed data set on computer holdings by one of the world's largest telecommunications companies. The data include brands of mainframe computers, costs, capacity choices, and dates of upgrade and replacement for the mainframe computers of the company. A number of "stylized facts" are evident from an initial analysis of these data. First, the durations between successive upgrades or replacements have become shorter during the last two decades, possibly reflecting the increased rate of technological progress in computing equipment during this time period. Second, computer replacements occurred roughly at a 6-year cycle at the beginning of the sample period, decreasing to 5-year cycle at the end of the period. Third, I show that when increases on demand for the services of the computer begin to exceed its processing capacity, the firm is more likely to expand its capacity via an upgrade of the existing computer rather than a purchase of a new computer if the existing computer is relatively new, but more likely to replace the computer as its age approaches the length of the replacement cycle.

I develop a stochastic dynamic programming model to see whether these stylized facts of replacement and upgrade behavior could be rationalized as an optimal investment strategy for this firm. In the model the firm has three possible actions at each time period: keep, upgrade, or replace. The state variables include the processing capacity of the current system, the level of demand for this processing capacity, the age of the current system, and the current market price of a standardized unit of processing capacity. The technological depreciation and the relative performance of each computer system are measured by composite measures of all four state variables in the model. The model depends on the unknown primitive parameters that specify the firm's profit function and its expectation of future values of the state variables, with its expectation of future reductions in the price of computing capacity playing a critical role in the model's predictions of the optimal length of the replacement cycle.

I show via simple calibration and simulation exercise that the model is capable of accounting for the key stylized facts I observe in the data. In particular, the likelihood of an upgrade or replacement increases with the age of the current system, and decreases with the current price of computing capacity. These results imply that the durations between successive replacements or upgrades tend to decline over time as the cost of computing decreases.

I use a parametric approximation method to solve the DP problem. This greatly reduces the computational burden involved in solving the infinite-horizon version of model where decisions are taken at monthly intervals and the three key state variables, current capacity, current demand, and the price per unit of new capacity are allowed to assume a continuum of possible values. The parametric approximation procedure converts the contraction fixed-point problem into a nonlinear least squares problem. I show that this latter problem can be solved much more rapidly than standard methods based on discretization of state space. The speed up in solution time is sufficiently large to make it feasible to estimate the unknown parameters of the model by maximum likelihood.