Industrial Organization
Applied Econometrics
Microeconomics
Applied Microeconomics

Industrial Organization
Econometrics
Microeconomics

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

An Empirical Model of Mainframe Computer Investment

Professor John Rust
Professor Steven Berry
Professor Martin Pesendorfer

May 2002

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
Phi Betta Kappa, Northwestern University, 1995

Teaching Assistant, Microeconomics with Environmental Applications, Fall 2001
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

"Multiple Equilibria of the Macro Cycles in R&D Expenditure and Mainframe Computer Investment," work in progress.

"An Empirical Model of Mainframe Computer Investment," mimeo, Yale University, 2001.

"Finite Horizon Case of Computer Maintenances in Telecommunication Company," manuscript, Yale University, 1999.

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

Applied Microeconomics Workshop, November 2001, upcoming (Yale University).
Applied Microeconomics Workshop, December 2000 (Yale University).

"An Empirical Model of Mainframe Computer Investment," Southern Economic Association’s 71st Annual Conference, Nov 2001, upcoming

"An Empirical Model of Investment Decision of Mainframe Computer Maintenance," 2001 North American Summer Meetings of the Econometric Society, June 2001.

Journal of Applied Econometrics [2 articles]

Econometric Society, KAEA (The Korea America Economic Association)

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 in 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 main possible actions at each time period: keep, upgrade, or replace. Contingent on replacement decision, there are n sub-choices of capacities. 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.

The paper is the first to apply a combination of the Nested fixed point algorithm and the Parametric approximation method (NLS-NFXP) to a high dimensional fixed point problem as an estimation technique. Parametric approximation method which is used to solve the DP problem 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. I also show the effectiveness of the parametric approximation method in comparison with the discretization method.

The estimation results are consistent with the stylized facts observed from the data in general, allowing for better understanding of the replacement behavior in an era of rapidly evolving computer technology. 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. Capacity and timing choices of replacement depend on the expectation of future demand and future cost per capacity.

Simulations of the estimated model show how the model is able to account for the key features of the data. The model allows us to separate the effects of decreases in the cost of computing equipment and the demand for services on the firm's overall investment expenditures in computing equipment. We show that on balance, the reduction in the cost of mainframe computers during the last two decades has had a bigger effect on investment expenditures than growth in demand. The simulated total expenditure and the actual total expenditure of the firm behave similarly and do not increase over time, even though capacities of the computer systems increase tremendously over time. This phenomenon confirms the conjecture that decreasing effect of real cost per capacity (technological progress) surpasses increasing effect of capacity of computer systems.

Several policy experiments forecast how changes in various environments of the model or structural parameters affect the timing and frequency of mainframe computers replacement and upgrade. The experiments also show the versatility of the model. As a result, the model confirms that the firm does not use an arbitrary rule of thumb in deciding to upgrade and replace its mainframe computers so rapidly, but rather the firm appears to have a very sophisticated understanding of the impact of technological progress resulting from Moore's Law and is taking advantage of this progress to significantly reduce its operating costs and provides better service to its customers.