PART C: APPLICATIONS OF FORECASTING

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1 PART C: APPLICATIONS OF FORECASTING

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3 FORECASTING WITH INNOVATION DIFFUSION MODELS: A LIFE CYCLE EXAMPLE IN THE TELECOMMUNICATIONS INDUSTRY John F. Kros ABSTRACT Production operations managers have long been concerned about new product development and the life cycle of these products. Because many products do not sell at constant levels throughout their lives, product life cycles (PLCs) must be considered when developing sales forecasts. Innovation diffusion models have successfully been employed to investigate the rate at which goods and/or services pass through the PLC. This research investigates innovation diffusion models and their relation to the PLC. The model is developed and then tested using modem sales from June 4 to May INTRODUCTION Generation of new product opportunities has been a major area of study in production and operations management for decades. Products are born, Advances in Business and Management Forecasting, Volume, 68 Copyright r 2008 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 4-400/doi:0.06/S4-400(0)0020-

4 60 JOHN F. KROS they live, and then many die. This cycle is generally referred to as the product life cycle (PLC). Examination of products as they move through their life cycle is crucial to a firm s success. Within the operations discipline the PLC and forecasting can be linked using what is called innovation diffusion theory. 2. BACKGROUND AND LITERATURE REVIEW Innovation diffusion theory has received considerable attention since it inception in the 60s. The diffusion of innovation can be defined as the process by which an innovation is imparted on members of society through certain channels over time (Rogers, 8). Seminal works in the area of technological change and rates of imitation were completed by Fourt and Woodlock (60) and Mansfield (6). The work by Fourt and Woodlock (60) and Mansfield (6) are the basis for research in diffusion modeling by Bass (6). The Bass model for new product growth and innovation diffusion has been used to forecast numerous products in many different industries (for examples see Akinola, 86; Bass, 6; Dodds, ; Henderson & Lentz, 6; Kalish & Lilien, 86; Lancaster & Wright, 8; Lawton & Lawton, ; Nevers, 2; Tigert & Farivar, 8). Mahajan and Muller () and Mahajan, Muller, and Bass (0) provide a review of the contributions to this literature through the 0s and on into the 80s. Young () provides an excellent article comparing nine growth and innovation diffusion models including Mansfield s and Bass models. Grover, Segars, and Fiedler (8) and Harrison, Mykytyn, and Riemenschneider () discuss the influence of information technology diffusion on large and small businesses. This work proposes a novel extension to the original Mansfield model applied to the technology industry. The model is developed and then tested using modem sales from mid-4 to mid The model is applied to each successive generation of modem innovation: 4.4 k, 28.8 k, 6 k, and broadband.. NEW PRODUCT GROWTH AND INNOVATION DIFFUSION MODELS A number of different new product growth and innovation diffusion models exist. However, the logistic growth model is the cornerstone to many of

5 Forecasting with Innovation Diffusion Models 6 these models. The logistic growth model can be described by the following equation: L Y t ¼ þ ae ðbtþ () where Y t is the cumulative level of sales at a given time, t,l is a measure of the upper limit of market sales or the total market capacity, and a and b are parameters that define how quickly a product diffuses into a market. Specifically, a defines how disperse the PLC is or the product s position in its life cycle, whereas b describes how peaked the product s life cycle or what the rate of change over time is of the product s diffusion into the market. Larger values of a characterize products in the early phases of their PLCs and larger values of b characterize more peaked life cycles and faster rates of change over time. These parameters, a and b, must be estimated. This model is very similar to Mansfield s original model which is described by the following equation: Y t ¼ þ e ð ðaþbtþþ (2) However, in comparing the logistic model with Mansfield s, two differences exist. First, Mansfield does not specify an upper limit on market sales, L. Second, Mansfield s model functionally employs a and b parameters in a different manner. Instead of using a to modify the output from the exponential calculation, Mansfield uses a in a linear combination with b. This allows Mansfield s model to be represented as a linearized version of the logistic model. Although Mansfield s model can be estimated using linear regression there are drawbacks including the validity of the linear regression variance assumption and the concern that L, the upper market limit, must be known to perform complete analysis. For these reasons, this work chooses to employ the logistic growth model as the underlying functional form. 4. CUMULATIVE NATURE OF THE LOGISTIC GROWTH MODEL The underlying logistic growth model is cumulative in nature. Y t is defined as the absolute or cumulative level of diffusion at time t. The logistic curve

6 62 JOHN F. KROS in its cumulative form takes on an S-shape. However, many operations managers without formal training in logistic forecasting models would be unable to glean critical information from this function such as: time to peak sales, sales at future time t, and overall shape of the diffusion curve. Additionally, if data such as per period sales numbers were being collected, the cumulative nature of the S-shaped function does not lend itself to easy interpretation or forecasting. Therefore, this paper proposes an approach to analyzing the logistic growth diffusion model. In order to portray the data in a manner that most operations managers can identify with, this research proposes taking a first derivative of Y t to obtain the non-cumulative form of the logistic growth diffusion model. In doing so, critical information that operations managers seek peak time to sales, sales at future time t, and the overall shape of the diffusion curve will become more apparent. The non-cumulative form (i.e., first derivative) of the logistic growth diffusion model is as follows: Y t ¼ able ðbtþ ð þ ae ðbtþ Þ 2 () The logistic curve in its non-cumulative form takes on a bell shape and is symmetrical. With this representation it is clear at what time peak diffusion occurs, where sales at future time t occur, and what the overall shape of the diffusion curve is. Diminished diffusion is characterized as the time when diffusion falls below a pre-defined market sales level. From (), Y t is the non-cumulative penetration of a product in a given time t, (i.e., what percentage of the total sales sales over its life span came in the first period, what percentage came in the second period, and so on). L is a measure of the upper limit of market sales, the total market capacity, or the long run market saturation level. L is expressed in various ways, but most commonly in total number of units or percentage penetration into the overall market. The parameters a and b define how quickly a product diffuses into a market. Specifically, a describes when the peak penetration into its product s life cycle occurs. Parameter b is defined as the amount of time a product spends in the introduction phase of the PLC and is commonly referred to as the delay factor. A larger value of a implies that product is in its early phase of its PLC, and a larger value of b implies that a product will approach the market saturation level at a faster rate. Values for a and b differ based on a number of variables such as technology type and relative price. For this model, the range of b is between 0 and inclusive. Generally, for very new technology values of b tend to be less than 0.0,

7 Forecasting with Innovation Diffusion Models 6 Table. Parameter Estimates for a and b for Various Products. Parameter Clothes Dryers Product Refrigerators Lawn Mowers a b whereas for more established technology such as consumer goods, the values of b tend to be greater than 0.0 and may be as high as 0.. The parameter a has no such high and low range, but past research has shown that for established technologies values of a tend to be in the range of 20 0, whereas for newer technology values of a tend to be in the range of Examples of values for a and b estimated for consumer goods such as refrigerators, lawn mowers, and dryers are given in Table.. APPLICATION OF LOGISTIC GROWTH DIFFUSION MODEL The original Mansfield model has been used to forecast industrial products, high technology products, and administrative innovations (Mansfield, 6). Since the original Mansfield model relies on an underlying logistic diffusion model, a logical extension was made that the non-cumulative logistic diffusion model would also be highly useful in forecasting technological product innovation... Methodology To perform the experimentation required to test the non-cumulative logistic diffusion model, data sets were gathered. The data sets consisted of modem equipment percentage penetration for 4.4 k, 28.8/.6 k, 6 k, and broadband modems from June 4 to May The data was complied using The Bandwidth Report (2006). All data sets were categorized as noncumulative and in percentage penetration values. One data set was also defined by an unknown upper limit. For each data set a non-linear estimation procedure was employed to estimate the parameters of interest and model fit of each non-linear estimation procedure was reported by mean absolute error (MAD). Ex post forecasts, peak diffusion locations, and

8 64 JOHN F. KROS periods of diminishing diffusion were also investigated. These results are presented in the next section..2. Results The non-cumulative logistic diffusion model requires the estimation of three parameters, a, b, and L. Table 2 contains the parameter estimates using the modem data resulting from the non-linear regression procedure. All parameter estimates are positive and they are all plausible. The parameter b estimates are discussed first as they are considered to be the most interesting (Bass, 6; Nevers, 2) followed by discussion of the parameters a and L. AU :.2.. Parameter b Estimates Norton and Bass (86) discuss the magnitude of the parameter estimate for b. They comment that for a given technology class, the behavioral process for adoption of advancing generations could be expected to be similar. It is seen from Table 2 that the magnitude of b is on average 0.04 within a range of This not only adds validity to Norton and Bass claim, it is very interesting since the estimates of b were made independently of each other (i.e., four separate non-linear regression procedures) Parameter a Estimates Investigating the parameter a also leads to some interesting conclusions. The parameter a characterizes how disperse the PLC is or the product s position in its life cycle. Larger values of a characterize products in the early phases of their PLCs. Over the past decade, the progression of modem technology has been as follows from earliest to latest: 4.4 k, 28.8 k, 6 k, and broadband. The values for a logically follow this progression: a 4.4 k =0.68, a 28.8 k =6., a 6 k =2., and a broadband =48.. In other words, the 4.4 k modem technology is late in its PLC, whereas the broadband technology is early in its PLC. Table 2. Parameter Estimates for Non-Cumulative Logistic Function. Parameter 4.4 k 28.8 k 6 k Broadband L a b R

9 Forecasting with Innovation Diffusion Models Parameter L Estimates The estimates for the parameter L are all fall between 2 and 0. L is described as a measure of upper market sales level. The estimates appear to be explaining that the overall market for any modem technology, no matter what generation it falls in, has an upper limit on market sales or in this case penetration. The parameter estimates of L in Table 2 validate the underlying concept of the PLC and the introduction of successive, newer generations of modem technology into the market. As successive generations of newer technology are being introduced penetration of older technology that at one time dominated the marketplace, must peak and then decline. The estimates show that for any of the modem technologies introduced in this example an almost constant upper limit of market penetration appears Model Fit Statistics Table 2 also displays the fit of the model to the data for modems. The R 2 values are all high, the lowest being greater than 0.4. The degree of R 2 for each model augments the Norton and Bass (86) belief that the rate of adoption should be similar for advancing generations of similar technology. From the R 2 statistics it is apparent that there exists a close association between the model and the actual data... Forecasts The principal use of the non-cumulative diffusion growth model is for operations managers to make more detailed and accurate forecasts of new products and successive technology. Therefore, ex post forecasts are made via each model for one-step-ahead time periods, peak diffusion locations, and periods of diminishing diffusion are also investigated. Table displays the one-step-ahead forecasts for each modem technology. The one-step-ahead forecasts in Table depict the near future of modem technology market penetration. Broadband and 6 k modems make up the bulk of the market, approximately % of the market, with 28.8 k modems making up just.4% and 4.4 k modems almost completely pushed out by the newer technology. Peak diffusion locations are listed in Table by time t, date, and diffusion percentage. The time t, to peak diffusion varies slightly from successive generation to successive generation. For example, peak to peak diffusion time between 28.8 k and 6 k modems and peak to peak diffusion time

10 66 JOHN F. KROS Table. Non-Cumulative Diffusion Growth Model Forecasts. Results 4.4 k 28.8 k 6 k Broadband Forecast One-step-ahead Peak location Time t Date Mar May Mar 2002 Jan 200 Diffusion %.6 6 Diminishing diffusion Time t Date Feb 200 May 2004 Nov 200 Dec 204 between 6 k and broadband modems are relatively constant, 8 months. These peak to peak diffusion times differ from the peak to peak diffusion time for 4.4 k and 28.8 k modems which is 8 months. The longer peak to peak diffusion time is most likely attributable to the long debates surrounding the adoption of a 6 k modem standard in the high-tech industry (for details see Agreement reached on 6 k modem standard, 8) and limited access to cable and DSL broadband connectivity for parts of the United States. For operations managers, the most interesting numbers from Table are the peak diffusion location for broadband modems and the diminishing diffusion points for 6 k and broadband modems. The peak diffusion location for broadband modems is estimated to be around time period of January 200 and one could expect market penetration of approximately %. The diminishing diffusion point characterizes the point where a technologies market share falls below the % penetration level. Broadband modems can expect to reach a diminishing diffusion point around December 204 and that a newer generation of technology will begin to make inroads into the high-speed Internet delivery market in roughly five years. 6. CONCLUSIONS The life of a most products travel through a birth death cycle referred to as the PLC. This work researchers the rate of diffusion for one product s life cycle. The unique contribution of this work to the area of production operations is linking the concepts of PLC and forecasting using what is

11 Forecasting with Innovation Diffusion Models 6 called innovation diffusion theory. Data for modem market penetration are in very good agreement with the underlying modified Mansfield model. Parameter estimates derived from non-linear regression analysis when used in concert with the model provide accurate descriptions of modem market penetration for successive product generations. REFERENCES Agreement reached on 6 k modem standard. (8). International Telecommunication Union press release. Retrieved February 2, 2004, from press_releases/8/04.html Akinola, A. (86). An application of the Bass model in the analysis of diffusion of cocospraying chemicals among Nigerian cocoa farmers. Journal of Agricultural Economics, AU :2 (). Bass, F. M. (6). A new product growth for model consumer durables. Management Science, (), 2. Dodds, W. (). An application of the Bass model in long-term new product forecasting. Journal of Marketing Research, 0, 08. Fourt, L. A., & Woodlock, J. W. (60). Early prediction of market success for new grocery products. Journal of Marketing, 26(2). Grover, V., Segars, J. T. A., & Fiedler, K. (8). The influence of information technology diffusion and business process change on perceived productivity: The IS executive s perspective. Information & Management, 4. Harrison, D. A., Mykytyn, P. P., & Riemenschneider, C. K. (). Executive decision about adoption of information technology in small business: Theory and empirical tests. AU : Information Systems Research, 8(2). Henderson, J. C., & Lentz, C. M. A. (6). Learning, working, and innovation: A case study in the insurance industry. Journal of Management Information Systems, 2(). Kalish, S., & Lilien, G. L. (86). A market entry timing model for new technologies. Management Science, 2, Lancaster, G. A., & Wright, G. (8). Forecasting the future of video using a diffusion model. European Journal of Marketing, (2), 0. Lawton, S. B., & Lawton, W. H. (). An autocatalytic model for the diffusion of educational innovations. Educational Administration Quarterly,,. Mahajan, V., & Muller, E. (). Innovation diffusion and new product growth models in marketing. Journal of Marketing, 4, 68. Mahajan, V., Muller, E., & Bass, F. M. (0). New product diffusion models in marketing: A review and directions for research. Journal of Marketing, 4, 26. Mansfield, E. (6). Technical change and the rate of imitation. Econometrica, (4). Nevers, J. V. (2). Extensions of a new product growth model. Sloan Management Review,, 8. Norton, J. A., & Bass, F. M. (86). A diffusion theory model of adoption and substitution for successive generations of high-technology products. Management Science, (). Rogers, E. M. (8). Diffusion of innovations (rd ed.). New York: The Free Press.

12 68 JOHN F. KROS The Bandwidth Report. (n.d.). Retrieved October, 2006, from com/bw/ Tigert, D., & Farivar, F. (8). A Bass new product growth model: A sensitivity analysis for a high technology product. Journal of Marketing, 4, 8 0. Young, P. (). Technological growth curves. Technological Forecasting and Social Change, 44, 8.

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