Forecasting telecommunication service subscribers in substitutive and competitive environments

International Journal of Forecasting 18 (2002) 561–581 www.elsevier.com / locate / ijforecast

Forecasting telecommunication service subscribers in substitutive and competitive environments a, b c d e Duk B. Jun *, Seon K. Kim , Yoon S. Park , Myoung H. Park , Amy R. Wilson a

Graduate School of Management, Korea Advanced Institute of Science and Technology ( KAIST), 207 -43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130 -012, South Korea b Samsung Electronics Co., Ltd., San [24 Nongseo-Ri, Giheung-Eup, Yongin-City, Gyeonggi-Do 449 -711, South Korea c Department of Business Administration, Chonbuk National University, 664 -14 1 Ga Duckjin-dong Duckjin-gu Jeonju Chonbuk 561 -756, South Korea d Department of Industrial Engineering, Hansung University, 389 Samsun-dong, Sungbuk-gu, Seoul, South Korea e Division of Health Services Research and Policy, School of Public Health, University of Minnesota, 420 Delaware Street SE, MMC 729, Minneapolis, MN 55455, USA

Abstract The telecommunications market is expanding rapidly and becoming more substitutive and competitive. In this environment, demand forecasting is very difficult, yet important for both practitioners and researchers. In this paper, we adopt the modeling approach proposed by Jun and Park [Technological Forecasting and Social Change 61 (1999)]. The basic premise is that demand patterns result from choice behavior, where customers choose a product to maximize their utility. We apply a choice-based substitutive diffusion model to the Korean mobile telecommunication service market where digital service has completely replaced analog service. A choice-based competitive diffusion model is also formulated and applied to the case where two digital services compete. In comparison with Bass-type models, these two models provide superior fitting and forecasting performance. Finally, we suggest a new choice-based diffusion model to describe an environment in which substitution and competition occur simultaneously and show the application results. The choice-based model is useful in that it enables the description of such complicated environments and provides the flexibility to include marketing mix variables such as price and advertising in the regression analysis.  2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved. Keywords: Marketing—new products, price, advertising; Comparative methods—choice-based multigeneration diffusion model, diffusion models

* Corresponding author. Tel.: 182-2-958-3634; fax: 182-2-958-3604. E-mail addresses: [email protected] (D.B. Jun), [email protected] (S.K. Kim), yspark@ business.chonbuk.ac.kr (Y.S. Park), mhpark@hansung. ac.kr (M.H. Park), [email protected] (A.R. Wilson).

1. Introduction While forecasting sales of a new product is very difficult, it is critical to market success. This is especially true when other products have a highly positive or negative influence on the

0169-2070 / 02 / $ – see front matter  2002 International Institute of Forecasters. Published by Elsevier Science B.V. All rights reserved. PII: S0169-2070( 02 )00067-5

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product because of substitution or competition effects. Many formerly monopolistic markets have become more competitive, and in recent years, these transformations have occurred more frequently and quickly. The telecommunication service market is typical of this phenomenon. Sales patterns have become more complicated because of the market entry of many competing and advanced services / products. The models proposed in this paper will incorporate the interrelationships among products in demand forecasts. Early applications of diffusion models primarily addressed durable goods markets. The best-known first-purchase diffusion models for new products in marketing are those of Bass (1969), Fourt and Woodlock (1960), Mansfield (1961), Easingwood, Mahajan and Muller (1983), etc. Although these models had early success in fitting diffusion processes for a number of industries, they possessed a potential conceptual limitation. As noted by Peterson and Mahajan (1978), they were single-product models concerned only with the forecasting of sales growth for a single product. New products are not introduced in a vacuum, however, nor do they exist in isolation. The existence of other products may influence, positively or negatively, the sales of a new product. A number of models have been proposed to overcome the limitations of single-product models. Norton and Bass (1987), Mahajan and Muller (1996) and Jun and Park (1999) proposed multigeneration diffusion models that simultaneously capture the diffusion and substitution patterns for each successive generation of a durable technological innovation. While Norton and Bass (1987) and Mahajan and Muller (1996) extended the form of the Bass model, Jun and Park (1999) proposed a diffusion model for multiple generations of products based on a representation of customer choice behavior. Cross-brand or competitive influence was first discussed in the marketing literature by Peterson

and Mahajan (1978). As Parker and Gatignon (1994) note, the optimal strategy for various marketing mix variables has been an integral part of most models of brand-level or competitive market behavior; these models included price (Rao & Bass, 1985; Dockner & Jorgensen, 1988), advertising (Teng & Thompson, 1983; Horsky & Mate, 1988), and both price and advertising (Thompson & Teng, 1984). In recent years, much interest has focused on developing aggregate diffusion models in a competitive environment. Mahajan, Sharma and Buzzell (1993) proposed a diffusion modeling approach for assessing the impact of entry by a new competitor into a market previously served by a single firm. Parker and Gatignon (1994) investigated diffusion at the brand level, i.e. in the context of products or firms that compete in a new market. Allison (1982), Hedstrom (1994), and Oren and Rothkopf (1984) etc. used multinomial logit model in a diffusion context. To represent the processes generating events in discrete-time units, Allison (1982) specified a discrete-time hazard rate as a function such as logit model, which depends on time and the explanatory variables. The method is to break up each individual’s event history into a set of discrete time units in which an event either did or did not occur. Hedstrom (1994) also estimated the hazard rate using the logit model based on the discrete-time event history approach. These studies had focused on modeling the hazard rate with the logit model and explaining the diffusion based on each individual’s history. Jun and Park (1999) advocated studying the utility-maximizing choice behavior of customers to understand the sales patterns of new products and to develop sales forecasting models for multiple generations of products. In this paper, we expand the modeling approach to the competitive case and suggest a choice-based diffusion model to describe an environment where substitution and competition occur simultan-

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eously. While applications of diffusion models to services are also possible, little research has taken place in this area. In this paper, we first study digital service, which has completely replaced analog service, in the Korean mobile telecommunication service market. We apply the multigeneration diffusion model of Jun and Park (1999) to the substitutive case, and call this the choice-based substitutive diffusion model. In Section 2, we show the results of the model’s application to the analog and digital mobile telecommunication service market in Korea. In Section 3, we develop a choice-based competitive diffusion model and report empirical results for digital cellular and PCS services in Korea. For both model applications, we compare the fitting and forecasting performance of our proposed models with those of other models. Finally, in Section 4, we suggest a new choicebased substitutive and competitive model to more realistically and fully describe overall market. Then, we show the results of this model’s application, which includes marketing mix variable data such as price and advertising expenditure, to analog, digital cellular and PCS services in Korea.

2. A choice-based substitutive diffusion model for forecasting analog and digital services subscribers in Korea

2.1. A choice-based substitutive diffusion model In this section, we apply the choice-based substitutive diffusion model of Jun and Park (1999) to forecasting the number of subscribers to both analog and digital services. Fig. 1a depicts the number of cumulative subscribers for each service in Korea. Since the introduction of digital service, the number of analog service subscribers has declined. Digital service has

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completely replaced analog service in Korea where analog service was withdrawn from the market in December 1999. Let t1 be the time of introduction for analog service, and t2 be that for digital service (t2 . t1 ). When t , t2 , a potential customer need only decide whether to subscribe to analog service. When t $ t2 , digital service is also available and two different choice situations arise. First, a potential customer must decide whether to subscribe and if so, to which service. Second, a subscriber already using analog service must decide whether to upgrade to digital service. As shown in Fig. 1b, price for digital service has decreased continuously since the introduction of higher quality digital service and the ensuing competition between the providers (in Fig. 1b, some price and advertising data observations are missing because they are not available). Thus, analog subscribers have naturally turned to digital service. Both potential customers and analog subscribers select the alternative that maximizes their utility with limited resources. Note that we can include the alternative of abandoning the service in our model. However, because the subscribers who subscribed to the services in spite of initial high price must have had significant need for mobile telecommunications, there is little possibility that subscribers turn to non-subscribers. For these reasons, we do not consider it in the models. Define the utility that the i-th potential customer (i.e. non-subscriber) would obtain by choosing not to subscribe or by subscribing to a service at time t as: ) ) U (0,k 5V (0,k 1 ´ (0,k) , k 5 0, 1, 2 ti t ti

(1)

where k50, k51 and k52 indicate nonsubscription, analog and digital service subscription, respectively. In the superscript, the first term represents the subscription status of the individual just before the choice, and the second term represents the choice made at time t. Thus, the superscript (0,0) means that the i-th

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Fig. 1. Analog and digital services in Korea. (a) The cumulative number of subscribers for analog and digital services. (b) The net number of subscribers for analog and digital services and the price and advertising expenditures for digital service (Price unit: Won; advertising expenditure unit: 310,000 Won).

non-subscriber remains a non-subscriber. The superscripts, (0,1) and (0,2) indicate that he chooses analog and digital service at time t. In

the equation, V and ´ denote the deterministic term and the error term of the utility. Jun and Park (1999) assume that the deterministic term,

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V, is independent of the individual customer and is related only to the attributes (e.g. price, advertising, design, etc.) of each service; the error term, ´, is stochastic and captures both random taste variation across the population and model specification error. These assumptions make it possible to aggregate across individuals. In the second choice situation, the i-th analog subscriber at time t must decide whether to upgrade. The utility that the i-th analog subscriber would obtain by choosing a specific alternative at time t is defined as follows: ) ) U (1,k 5V (1,k 1 ´ (1,k) ti t ti

k 5 1, 2

(2)

The superscript (1,1) means that the i-th analog subscriber remains an analog subscriber and (1,2) that he upgrades to digital service. To capture the diffusion and substitution dynamics for successive generations of products as well as for a single generation, Jun and Park (1999) specify the deterministic terms of the utility as follows: V (0,0) 5 c (0,0 ) t

(3)

V t( j,k ) 5 q ( j,k )st 2 tk 1 1d 1 b ( j,k ) X t(k) , j 5 0, 1, k 5 1, 2

ple, with time, more advertising, sales promotion, word-of-mouth, etc., result in an increase in product recognition. Furthermore, the time variables may capture most of the effects of the unavailable attributes (or exogenous variables). While some attributes, such as price, are easily available, others are not easy to quantify or to observe even if they have a significant influence on the decision process of consumers. In such situations, the time variables may explain the effect of factors such as design, sales promotion. In Eq. (4), if the values of the time coefficients for digital service are greater than those for analog service (q ( j,2 ) . q ( j,1) , j 5 0,1), the choice utility for digital service increases more quickly with time than does that for analog service. Thus, digital service replaces analog service. When we assume that the error terms, ´ (0,k) , follow independent and identically ti Gumbel (or type I extreme value) distribution (for justification of this assumption, refer to Ben-Akiva and Lerman (1985)), the probability that a customer, i, subscribes to analog or digital service at time t is: P

(4)

Eq. (3) indicates the assumption that the deterministic part of the non-subscription utility is constant. In Eq. (4), X denotes the attributes including installed base influencing the customer utility. A vector of coefficients, b, determines the effect of these attributes on the utility. The time variables account for the diffusion effects related to multiple generations of products. As time passes, a consumer’s valuation of a product’s attributes usually increases when the product succeeds in the market. When a new product is introduced into the market, information about the product is uncertain and insufficient. As more information becomes available to consumers, however, they can achieve higher levels of utility. For exam-

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(0,k ) t

expsV t(0,k )d 5 ]]]]]]]]]]] ) , expsV t(0,0 )d 1 expsV (0,1) d 1 expsV (0,2 d t t

k 5 1, 2

(5)

where the subscript, i, is omitted because the choice probability in Eq. (5) is the same for all individuals under the assumption that the deterministic terms are independent of the individual. Note that the choice probability for service k depends on the attributes related to the other service available during the time period as well as on those related to the service itself. Similarly, the probability that an analog subscriber upgrades to digital service at time t is the same for all individuals: P

(1,2 ) t

expsV (1,2) d t ]]]]]]] 5 (1,1) ) expsV t d 1 expsV (1,2 d t

(6)

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Define the total market potential of the choicebased model at time t, Mt , as: Mt 5 Mk , tk # t , tk 11

(8)

Then the expected number of new subscribers for service k is: ) E f Z (0,k , k 5 1, 2 g 5sMt 2 Yt21d P (0,k) t t

(9)

Now if we define the number of subscribers for analog service at time t 2 1 as Y (1) t21 , then the number of new upgraders to digital service at time t, Z (1,2) , among those analog service t subscribers is a random variable following the binomial distribution with purchase probability, ) P (1,2 , under the assumption of independent t (1) behavior among Y t21 . Thus: ) (1,2) Z (1,2) | BinsY (1 d t t 21 , P t

(10)

Then the expected number of new upgraders to digital service at time t is: (1,2 )

E fZ t

g 5 Y t(121) P t(1,2 )

E fS

expsV t d g 5sM1 2 Yt 21d]]]]]]] (0,0) ) expsV t d 1 expsV (0,1 d t

(7)

where tk is the introduction time for service k. It is possible that the market potential may be unchanged throughout the time period. We denote the total number of subscribers to analog and digital services at time t 2 1 as Yt 21 . Then the total number of non-subscribers at time t is (Mt 2 Yt21 ). The number of new subscribers for service k at time t, Z (0,k) , among these nont subscribers is a random variable following the multinomial distribution with purchase probability, P (0,k) , under the assumption of indepent dent behavior among non-purchasers. Thus: ) ) ) , Z (0,2 , P t(0,2 )d sZ (0,1 d | MNsMt 2 Yt21 , P (0,1 t t t

(0,1 )

(1) t

(11)

Using the above results, we can develop a net subscribers model for both analog and digital services. Before the introduction of digital service (t1 # t , t2 ), the expected net number of subscribers at time t for analog service can be defined as:

(12) After the introduction of digital service (t $ t2 ), the expected net number of subscribers at time t for each service can be defined as: expsV 9t (0,1)d E f S (1) t g 5 sM2 2Yt21d]]]]]]] (0,0) expsV t9 d1expsV 9t (0,1)d1expsV 9t (0,2)d (1,2)

expsV t9 d (1) ]]]]] 2Y t21 expsV t9 (1,1)d1expsV t9 (1,2)d expsV t9 (0,2)d E f S (2) t g 5 sM2 2Yt21d]]]]]]] (0,0) expsV t9 d1expsV 9t (0,1)d1expsV 9t (0,2)d

(13)

expsV 9t (1,2)d 1Y (1) t21 ]]]]] expsV 9t (1,1)d1expsV t9 (1,2)d (k )

(k )

(k )

where Y t 5 Y t21 1 S t , k 5 1,2, and Yt 5 Y (1) 1 Y t(2) 5 Yt 21 1 S (1) 1 S (2) t t t . In Eq. (13), V 9t (0,0 ) and V t9 (0,1 ) may differ from V t(0,0) and V (0,1) in Eq. (12). This indicates that the t customers’ utilities may differ before and after the introduction of digital service, as represented by changes in the coefficients and variables in the utilities.

2.2. Analog and digital mobile telecommunications service market in Korea Mobile telecommunications services in Korea can be classified as either analog or digital. Analog service was introduced in April 1984 (t1 5 1) and digital service in April 1996 (t2 5 145). We applied the choice-based substitutive model to the data describing the number of subscribers from December 1988 to December 1999; these data consist of 133 monthly observations for analog service, and 45 for digital service. We reserved the last six observations to perform an out-of-sample evaluation of the forecasting performance. To estimate the coefficients of a system of equations for successive generations, we used the nonlinear least squares (NLS) method of the

Table 1 Estimation results for analog and digital services in Korea Model

Norton and Bass model Before Y (1) t 5 F1st 2 t1d M1 After (2) Y (1) t 5 F1st 2 t1d M1 f 1 2 F2st 2 t2dg , Y t 5 F2st 2 t2df M2 1 F1st 2 t2d M1 g 1 2 exps 2s pk 1 qkdst 2 tk 1 1dd Fkst 2 tkd 5 ]]]]]]]] qk 1 1 ]exps 2s pk 1 qkdst 2 tk 1 1dd pk Mahajan and Muller model Before (1) (1) S (1) t 5s p1 1 q1 Y t21 /M1dsM1 2 Y t21d After (1) (2) (1) (2) (2) (1) S (1) t 5 (1 2 a ) h p1 1 q1sY t21 1 Y t21d /M2 jsM2 2 Y t21 2 Y t21d 2 as p2 1 q2 Y t21 /M2d Y t21 (2) (1) (2) (1) (2) (2) (1) S t 5 a h p1 1 q1sY t21 1 Y t21d /M2 jsM2 2 Y t21 2 Y t21d 1 as p2 1 q2 Y t21 /M2d Y t21

Estimate

Approx. S.E.

Approx. Prob. . utu

c (0,0) r (0,1) (0,0) c9 q 9 (0,1) q 9 (0,2) b (0,2) p q 9 (1,1) (1,2) q9 (1,2) bp b (1,2) a M1 M2

6.3674 1.68E26 2.5709 20.0136 0.0589 28.63E26 0.0126 0.0220 21.15E26 1.36E27 5,376,957 21,920,707

2.6130 9.4E27 0.6825 0.0052 0.0229 1.162E26 0.0022 0.0107 3.856E27 2.766E28 14,991,842 1,943,758

0.0163 0.0765 0.0003 0.0100 0.0112 0.0001 0.0001 0.0418 0.0036 0.0001 0.7205 0.0001

p1 q1 p2 q2

8.3549E28 0.1081 0.0021 0.1455

6.8891E28 0.0072 0.0001 0.0024

0.2275 0.0001 0.0001 0.0001

M1 M2

2,298,449 19,017,608

55,469 283,653

0.0001 0.0001

p1 q1 p2 q2 a M1 M2

0a 0.0906 0a 1.1086 0.7592 3,604,203 28,595,534

– 0.0059 – 0.1416 0.0343 600,941 2,152,148

– 0.0001 – 0.0001 0.0001 0.0001 0.0001

R2 Analog

Digital

Total

Choice-based substitutive diffusion model Norton and Bass model Mahajan and Muller model

0.8172 0.7424 0.7089

0.7556 0.5887 0.5687

0.8933 0.8219 0.8126

a

These restrictions are required considering the convergence and the expected sign of estimates.

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Model

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Choice-based substitutive diffusion model V (0,0) 5 c (0,0) t (0,1) V t 5 r (0,1) Y (1) t21 (0,0) (0,0) v 9t 5 c9 (0,1) (0,1) v 9t 5 q 9 st 2 t1 1 1d (0,2) (0,2) (0,2) (2) v 9t 5 q 9 st 2 t2 1 1d 1 b p x tp (1,1) (1,1) v t9 5 q 9 st 2 t1 1 1d (1,2) (1,2) (1,2) (2) (1,2) (2) v t9 5 q 9 st 2 t2 1 1d 1 b p x tp 1 b a x ta (2) x tp : price (Won) of digital service x (2) ta : advertising expenditures (31000 Won) of digital service

Parameter

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procedure MODEL, available as a part of the Statistical Analysis System (SAS). Table 1 summarizes the estimation results for the proposed model, the Norton and Bass model, and the Mahajan and Muller model. We included exogenous variables such as price and advertising expenditure, which were not considered in the Bass-type models. Most estimates for the choice-based model were significant at the 10% level except for one parameter. The time coefficient values for digital service were greater than those for analog service, that is, q 9 (0,2 ) . q 9 (0,1) and q 9 (1,2) . q 9 (1,1 ) . This indicates that digital service replaces analog service. The estimate of

q 9 (0,1 ) was negative, which means that nonsubscribers’ utility for analog service decreases with time because of the presence of digital service. For comparison, we also estimated Bass-type multigeneration models proposed by Norton and Bass (1987), and Mahajan and Muller (1996). With an exception, most estimates for these models were also significant at the 5% level. As shown in Table 1, the parameters, p1 and p2 , of the Mahajan and Muller model were set to be zero. These restrictions are required because their estimates were negative or did not converge without these assumptions. In the Norton and Bass model, the values of the

Table 2 Forecasting results for analog and digital services in Korea (a) MAD and MAPE for out-of-sample from July 1999 to December 1999 Choice-based model

Norton and Bass model

Mahajan and Muller model

Analog

MAD MAPE

11,664 41.09

13,276 78.98

34,586 125.67

Digital

MAD MAPE

449,779 45.48

610,090 54.23

489,045 43.33

(b) Tests for out-of-sample forecast encompassing P-values on u1 from: En t 5 u0 1 u1 Fv t 1 ht Forecast Fv t from:

Analog

Digital

Choice-based model

Norton and Bass model

Mahajan and Muller model

Forecast error En t

Choice-based model

–

0.5422

0.2550

from

Norton and Bass model

0.4907

–

0.5874

Mahajan and Muller model

0.3410

0.0312**

–

Forecast error En t

Choice-based model

–

0.4117

0.4091

from

Norton and Bass model

0.0102**

–

0.3798

Mahajan and Muller model

0.0041***

0.1798

–

* P,0.10, ** P,0.05, *** P,0.01.

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innovation and imitation coefficients for digital service were greater than those for analog service. To compare the fitting results, we calculated R 2 using estimated coefficients for the three models. As shown in Table 1, the choice-based substitutive diffusion model exhibited the best fitting performance for both services. We also estimated the choice-based substitutive model not including exogenous

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variables and compared its performance with those of the Bass-type models. Though the comparison result was omitted in the paper, our model was superior in fitting performance to others. To compare forecasting performance among the models, the mean absolute deviation (MAD) and mean absolute percent error (MAPE) from one-step- to six-step-ahead forecasts for each

Fig. 2. Net subscribers for analog and digital services in Korea (Observed, fitted and predicted values for the choice-based substitutive diffusion model). (a) Analog service. (b) Digital service.

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model are reported in Table 2a. The choicebased model produced the lowest MAD and MAPE values. We also compared models using the encompassing test. This test formalizes the intuition that model n should be preferred to model v, if model n can explain what model v cannot explain without model v being able to explain what model n cannot explain (refer to Donaldson & Kamstra, 1996). The tests for encompassing involve testing for significance of the u1 parameter in the following regressions: En t 5 u0 1 u1 Fv t 1 ht and Ev t 5 u 09 1 u 19 Fn t 1 h t9 , where En t and Ev t are model n and v ’s prediction errors, respectively, and Fn t and Fv t are model n and v ’s predicted values, respectively. If the estimate of the u1 coefficient, uˆ 1 , is not significant, but uˆ 91 is significant at some predetermined level, then we say that model n encompasses model v, or vice versa. If both estimates are significant or insignificant, however, then we cannot infer anything about the relationship between the models. Table 2b contains P-values associated with the t-statistics for u1 for all possible n 2 v comparisons. The P-value of 0.0102 in the Norton and Bass model row and choice-based model column for digital service reveals that the choice-based model can explain what the Norton and Bass model cannot explain at the 5% level. Conversely, the P-value of 0.4117 in the Norton and Bass model column and choice-based model row reveals that the Norton and Bass model does not explain what the choice-based model cannot explain at the 5% significance level. From these two P-values, one can conclude that the choice-based model encompasses the Norton and Bass model at the 5% level. As a result, we can conclude that the choice-based substitutive diffusion model is statistically preferred to other models for digital service. For analog service, however, the estimated coefficients in the choice-based model column are statistically insignificant. Fig. 2 plots the observed, fitted and predicted values for the net number of subscribers from the

choice-based substitutive diffusion model (We omit the figures for the other models due to space limitations). It is well known that obtaining stable and robust estimates with Bass or other diffusion models requires sufficient data. For example,

Fig. 3. Estimates at different levels of right censoring for the choice-based substitutive diffusion model. (a) Variation ( 0,1 ) ( 0,2 ) ( 0,2 ) ( 0,1 ) of the estimates of q 9 and q 9 (q 9 . q9 ). (b) ( 1,1 ) ( 1,2 ) ( 1,2 ) Variation of the estimates of q 9 and q 9 (q 9 . ( 1,1 ) q9 ). (c) Variation of the estimate of M1 and M2 (M2 . M1 ).

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the NLS estimates of the Bass model coefficients were biased and they changed systematically as the number of observations used

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in the estimation increased, a phenomenon identified by Van den Bulte and Lilien (1997). These authors also identified the cause of these

Fig. 4. Digital cellular and PCS services in Korea. (a) The cumulative number of subscribers for digital cellular and PCS services. (b) The net number of subscribers, the price and advertising expenditures for digital cellular service. (Price unit: Won; Advertising expenditure unit: 310,000 Won). (c) The net number of subscribers, the price and advertising expenditures for PCS service. (Price unit: Won; Advertising expenditure unit: 310,000 Won).

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estimation problems to be the lack of richness in the data as compared to the complexity of the model and is common to all diffusion models including our own. In Fig. 3, we graph our model estimates of time coefficients and market potential for different levels of right censoring (those of the other parameters were omitted due to space limitations); this graph shows how the estimates vary as we add one observation to the estimation sample. The horizontal axis shows the date of the most recent observation added to the sample. Although the estimates are sensitive to the estimation sample size, the inequalities q 9 (0,2 ) . q 9 (0,1) and q 9 (1,2) . q 9 (1,1) are maintained. The market potential also increases as the number of observations increases.

3. A choice-based competitive diffusion model for forecasting digital cellular and PCS service subscribers in Korea

3.1. A choice-based competitive diffusion model In this section, we develop a choice-based

competitive diffusion model to forecast the number of subscribers for two competing services. We also assume that subscribers do not abandon either service. Let t1 and t2 be the entry-to-market time of services 1 and 2, respectively. Unlike the substitutive case, in a competitive situation, the time variable is not adequate to specify the utility function because one service does not completely replace the other. We define the utility that the i-th potential customer would obtain by choosing an alternative at time t as follows: ) ) U (0,0 5V (0,0 1 ´ ti(0,0 ) 5 c (0,0 ) 1 ´ ti(0,0 ) ti t

(14)

) ) U (0,k 5V (0,k 1 ´ (0,k) ti t ti ) (0,k ) (k ) 5 r (0,k) Y (0,k X t 1 ´ (0,k) , t21 1 b ti

k 5 1, 2

(15)

where the superscript (0,0) indicates that the potential customer chooses not to subscribe. The superscript (0,1) and (0,2) indicate the choice of one of the two competing services. In Eq. (15), X represents the available exogenous variables (k ) and Y t21 the cumulative number of subscribers

Fig. 4. (continued)

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for service k at time t 2 1. Bass (1969) emphasized that ‘word-of-mouth’ from previous purchasers significantly influences the sales growth for a new product. Katz and Shapiro (1985) called this effect a network externality. In this paper, we assume that the customer’s choice utility is a linear function of the number of cumulative subscribers and the marketing activities. As with the substitutive model, we derive the probability that a potential customer, i, subscribes to service k at time t on the assumption that the error terms follows the Gumbel distribution. Though we cannot observe switching demand separately, it is possible for subscribers to switch between the two services. Our competitive model reflects new subscription among non-subscribers and switching behavior to the other service. Therefore, the proposed net subscribers model is as follows: Before the introduction of the new competing service (t1 # t , t2 ), the expected net number of subscribers at time t for service 1 can be defined as: E fS

(1) t

) expsV (0,1 d t g 5sM1 2 Yt 21d]]]]]]] (0,0) ) expsV t d 1 expsV (0,1 d t

(16) After the entry of the competing service (t $ t2 ), the expected net number of subscribers at time t for each service can be defined as: expsV 9t (0,1)d E f S t(1) g 5 sM2 2Yt21d]]]]]]] expsV 9t (0,0)d1expsV 9t (0,1)d1expsV 9t (0,2)d (1,2)

(2,1)

expsV t9 expsV t9 d d (1) ]]]]] 2Y t21 1Y (2) t21 ]]]]] expsV t9 (1,1)d1expsV t9 (1,2)d expsV t9 (2,1)d1expsV t9 (2,2)d (0,2)

expsV t9 d E f S t(2) g 5 sM2 2Yt21d]]]]]]] expsV t9 (0,0)d1expsV 9t (0,1)d1expsV 9t (0,2)d (2,1)

(1,2)

expsV 9t expsV t9 d d (2) ]]]]] 2Y t21 1Y (1) t21 ]]]]] expsV 9t (2,1)d1expsV t9 (2,2)d expsV t9 (1,1)d1expsV t9 (1,2)d

(17) (k ) (k) where Y (k) t 5 Y t 21 1 S t , k 5 1, 2, and Yt 5 Y t(1) 1 Y t(2) 5 Yt 21 1 S (1) 1 S (2) t t . (0,0 ) (0,1 ) 9 In Eq. (17), V t and V t9 represent the

573

possibility of changes in the utilities before and after the entry of a competing service.

3.2. Digital cellular and PCS services market in Korea In this section, we apply the choice-based competitive model to the digital service market in Korea where digital cellular and PCS services compete. Fig. 4a plots the number of cumulative subscribers for each service in Korea’s competitive environment. Since the entry of PCS service in October 1997, we see that the total number of subscribers for the two services has increased dramatically. There has been keen competition, spawning marketing efforts such as price incentives and increased advertising by the service providers as shown in Fig. 4b and c (some price and advertising data observations are missing because they are not available). In the figures, we see that the number of new subscribers to each service increases as price decreases, and it increases in proportion to the advertising effort of each provider. Digital cellular service was introduced in April 1996 (t1 5 1) and PCS service in October 1997 (t2 5 19). The data consist of monthly observations of the number of subscribers from April 1996 to June 2000, with 51 values for digital cellular service, and 33 for PCS service. The last six observations were used for an out-of-sample comparison. Table 3 shows the estimation results for the models. The same estimation method was used as in the substitutive case. We included exogenous variables such as price and advertising expenditures in the choice-based competitive model (but did not include them in the Basstype models). Although there was Parker and Gatignon’s model considering the impact of competitive marketing mix variables, it was impossible to obtain converging estimates. All of the estimates in Eq. (17) were also not converged because of the increase in the number of parameters. In case of telecommunica-

D.B. Jun et al. / International Journal of Forecasting 18 (2002) 561–581

574

Table 3 Estimation results for digital cellular and PCS services in Korea Model

Parameter

Estimate

Approx. S.E.

Approx. Prob. . utu

Choice-based competitive diffusion model V (0,0) 5 c (0,0) t (0,1) (0,1) (1) Vt 5r Y t21 (0,0) (0,0) V t9 5 c9 (0,1) (0,1) (1) (0,1) (1) V 9t 5 r 9 Y t21 1 b p x tp (0,2) (0,2) (2) (0,2) (2) V t9 5 b p x tp 1 b a x ta (1) x tp : price (Won) of digital service (2) x tp : price (Won) of PCS service (2) x ta : advertising expenditures (31,000 Won) of PCS service

c (0,0) (0,1) r (0,0) c9 (0,1) r9 b (0,1) p b p(0,2) b (0,2) a M1 M2

3.8505 1.1581E26 2.9789 1.3155E27 26.2275E26 28.8912E26 3.6682 3,853,085 29,077,088

0.3141 3.3027E27 0.2749 2.5454E28 7.4525E27 9.7683E27 8.1550E28 615,902 1,839,399

0.0001 0.0012 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

p1 q1 p2 q2 c1 c2 M1 M2

0.0028 0.0636 0.0261 0.0647 0.0055 a 0 37,408,563 13,307,723

0.0026 0.0273 0.0065 0.0409 0.0110 – 34,555,726 2,869,167

0.3013 0.0248 0.0002 0.1211 0.6213 – 0.2853 0.0001

p1 q1 p 19 q 91 p2 q2 M1 M2

0.0014 0.1254 a 0 0.0633 0.0728 0.0102 47,731,531 4,900,978

0.0012 0.0368 – 0.0083 0.0671 0.0053 20,830,388 5,161,678

0.2449 0.0015 – 0.0001 0.2844 0.0612 0.0271 0.3479

p1 q1 p 19 q 91 p2 q2 c1 c2 M1 M2

0.0064 0.1899 0a 0.0106 0.0098 0.0384 a 0 20.0263 7,560,576 42,920,220

0.0075 0.1215 – 0.0129 0.0042 0.0654 – 0.0657 8,439,878 17,876,142

0.3955 0.1257 – 0.4124 0.0255 0.5597 – 0.6910 0.3756 0.0210

Digital cellular

PCS

Total

0.7495 0.4464 0.5099 0.5129

0.7026 0.0509 0.0478 0.0309

0.7370 0.2895 0.3215 0.3156

Peterson and Mahajan model Before (1) (1) (1) S t 5s p1 1 q1 Y t21 /M1dsM1 2 Y t21d After (1) (1) (2) (1) S t 5s p1 1 q1 Y t21 /M1 2 c 1 Y t21 /M2dsM1 2 Y t21d (1) (2) S t(2) 5s p2 1 q2 Y (2) t21 /M2 2 c 2 Y t21 /M1dsM2 2 Y t21d

Mahajan, Sharma and Buzzell model Before (1) (1) S t(1) 5s p1 1 q1 Y t21 /M1dsM1 2 Y t21 d After (1) (1) (1) (2) S t 5s p 91 1 q 91 Y t21 /M1dsM1 2 Y t21d 1 c (1,2)sY (1) t21 /M1dsM2 2 Y t21d (2) (2) (2) (2,1) (2) (1) S t 5s p2 1 q2 Y t21 /M2dsM2 2 Y t21d 1 c sY t21 /M2dsM1 2 Y t21d (1,2) (2,1) q 19 5 c and q2 5 c

Parker and Gatignon model Before (1) (1) (1) S t 5s p1 1 q1 Y t21 /M1dsM1 2 Y t21d After (1) (1) (2) (1) (1) (2) S t 5s p 91 1 q 91 Y t21 /M1 1 c 1 Y t21 /sM1 1 M2 2 Y t21ddsM1 1 M2 2 Y t21 2 Y t21d (2) (2) (1) (2) (1) (2) S t 5s p2 1 q2 Y t21 /M2 1 c 2 Y t21 /sM1 1 M2 2 Y t21ddsM1 1 M2 2 Y t21 2 Y t21d

Model

Choice-based competitive diffusion model Peterson and Mahajan model Mahajan, Sharma and Buzzell model Parker and Gatignon model a

R2

These restrictions are required considering the convergence and the expected sign of estimates.

D.B. Jun et al. / International Journal of Forecasting 18 (2002) 561–581

tions services, there is little switching demand because the subscribers are obliged to pay initial high prices again in order to switch to competing service. Therefore, our choice-based competitive model was estimated without the switching terms. According to the estimation results, the market potential increased after the

575

entry of PCS service. In the model, all estimated coefficients were significant, even at the 1% level. We also estimated Bass-type competitive models proposed by Peterson and Mahajan (1978), Mahajan et al. (1993), and Parker and Gatignon (1994). In the Mahajan et al. model and the Parker and Gatignon model, we as-

Table 4 Forecasting results for digital cellular and PCS services in Korea (a) MAD and MAPE for out-of-sample from January 2000 to June 2000 Choice-based model

Peterson and Mahajan model

Mahajan, Sharma and Buzzell model

Parker and Gatignon model

Digital cellular

MAD MAPE

353,400 79.37

433,030 110.34

433,371 110.51

427,480 108.09

PCS

MAD MAPE

164,017 54.47

209,190 59.24

205,095 54.99

211,400 66.22

(b) Tests for out-of-sample forecast encompassing P-values on u 1 from: E nt 5u 0 1u 1 F vt 1h t Forecast Fv t from:

Digital cellular

PCS

Forecast error En t from

Forecast error En t from

Choice-based model

Peterson and Mahajan model

Mahajan, Sharma and Buzzell model

Parker and Gatignon model

Choice-based model

–

0.4837

0.4887

0.6392

Peterson and Mahajan model

0.0805*

–

0.2594

0.3837

Mahajan, Sharma and Buzzell model

0.0815*

0.2582

–

0.3867

Parker and Gatignon model

0.0842*

0.2642

0.2679

–

Choice-based model

–

0.1538

0.1440

0.1435

Peterson and Mahajan model

0.0328**

–

0.0587*

0.0583*

Mahajan, Sharma and Buzzell model

0.0359**

0.0720*

–

0.0647*

Parker and Gatignon model

0.0316**

0.0622*

0.0560*

–

* P,0.10, ** P,0.05, *** P,0.01.

576

D.B. Jun et al. / International Journal of Forecasting 18 (2002) 561–581

sumed that the coefficients before and after the introduction of PCS differed. Comparing this case with the case assuming equal coefficients before and after the introduction, we reported the better of the two. As shown in Table 3, the parameters, c 2 of the Peterson and Mahajan model and p2 of the Mahajan et al. model and the Parker and Gatignon model were set to be zero because their estimates were negative or did not converge without these assumptions. The parameter, c 1 of the Parker and Gatignon

model was also assumed to be zero. This restriction is required because of the sign of its estimate. The choice-based competitive diffusion model produced the highest R 2 value (We also estimated our competitive model without exogenous variables and compared the fitting result with others. Our model was superior in fitting performance to the Bass-type models). The MAD, MAPE and encompassing test results are reported in Table 4. Our choicebased model produced the lowest MAD and

Fig. 5. New subscribers for digital cellular and PCS services in Korea (Observed, fitted and predicted values for the choice-based competitive diffusion model). (a) Digital cellular service. (b) PCS service.

D.B. Jun et al. / International Journal of Forecasting 18 (2002) 561–581

MAPE values. According to the encompassing test, the choice-based model is statistically preferred to other models. All the P-values in the choice-based model column were statistically significant at the 10% level. Thus, we conclude that the choice-based model forecasts comparatively outperformed forecasts from the other models. Fig. 5 shows the observed, fitted and predicted values for new subscribers estimated by the proposed choice-based competitive diffusion model. As with the substitutive model, the estimates of parameters were sensitive to the sample size. However, as we expected, the signs of estimates did not change (We omit the details in the paper).

4. A choice-based diffusion model for substitutive and competitive environments Fig. 6 shows the cumulative number of subscribers in Korea to three mobile telecommunication services: analog, digital cellular, and PCS. The graph shows that substitution and

577

competition occurred simultaneously in the market. The modeling approach above proves very useful in trying to describe such a complicated environment. In this section, we suggest a new choice-based substitutive and competitive diffusion model that incorporates the interrelationships among analog, digital cellular and PCS services. All previous models treat interrelationships such as substitution or competition as independent phenomena. For this reason, no existing model is comparable to the model proposed in this section and we do not compare its performance with that of other models. Let t1 , t2 and t3 be the entry-to-market time of analog, digital cellular and PCS services, respectively, and t4 the withdrawal time of analog service. Prior to the introduction of digital cellular service (t1 # t , t2 ), the expected number of net subscribers is defined as: ) expsV (0,1 d t E f S t(1) g 5sM1 2 Yt 21d]]]]]]] (0,0) ) expsV t d 1 expsV (0,1 d t

Fig. 6. The cumulative number of subscribers for analog, digital cellular and PCS services in Korea.

(18)

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578

During the substitutive period of analog and digital cellular service (t2 # t , t3 ), the expected number of net subscribers at time t is defined as: expsV 9t (0,1)d ]]]]]]]]] E f S (1) 5 M 2Y g s 2 t21d t expsV 9t (0,0)d1expsV 9t (0,1)d1expsV 9t (0,2)d expsV t9 (1,2)d ]]]]]] 2Y (1) t21 expsV 9t (1,1)d1expsV 9t (1,2)d

expsV t9 (1,2)d ]]]]]] 1Y (1) t21 expsV 9t (1,1)d1expsV 9t (1,2)d

During the coexistence period of analog, digital cellular and PCS service (t3 # t , t4 ), the expected number of net subscribers at time t is defined as: expsV t99 (1,2)d E f S t(1) g 5 2Y (1) t21 ]]]]]]]] (1,1) expsV t99 d1expsV t99 (1,2)d1expsV t99 (1,3)d expsV 99t (1,3)d 2Y (1) t21 ]]]]]]]] (1,1) expsV 99t d1expsV t99 (1,2)d1expsV t99 (1,3)d (0,2)

expsV 99t d E f S t(2) g 5 sM3 2Yt21d]]]]]]]] expsV 99t (0,0)d1expsV t99 (0,2)d1expsV t99 (0,3)d (1,2)

expsV t99 d 1Y (1) t21 ]]]]]]]] expsV t99 (1,1)d1expsV t99 (1,2)d1expsV t99 (1,3)d (2,3)

s 99

s 99 d d s 99

expsV t999 (0,3)d E f S t(3) g 5 sM4 2Yt21d]]]]]]]] (0,0) expsV t999 d1expsV 999t (0,2)d1expsV 999t (0,3)d (2,3) expsV 999 expsV t999 (3,2)d d t (2) (3) ]]]]] ]]]]] 1Y t21 2Y t21 (2,2) (2,3) (3,2) expsV 999 expsV 999 d1expsV 999t d d1expsV t999 (3,3)d t t

(19)

expsV t9 (0,2)d E f S g 5 sM2 2Yt21d]]]]]]]]] (0,0) expsV 9t d1expsV 9t (0,1)d1expsV 9t (0,2)d

expe V t (3,2) 1Y (3) t21 ]]]]] exp V t (3,2) 1exp V t (3,3)

expsV t999 (2,3)d expsV t999 (3,2)d (2) (3) ]]]]] ]]]]] 2Y t21 1Y t21 (2,2) (2,3) (3,2) expsV t999 expsV 999 d1expsV 999t d d1expsV t999 (3,3)d t

(21)

(2) t

expsV t99 d (2) ]]]]] 2Y t21 expsV t99 (2,2)d1expsV t99 (2,3)d

(0,2) expsV 999 d t E f S t(2) g 5 sM4 2Yt21d]]]]]]]] (0,0) (0,2) expsV t999 d1expsV 999t d1expsV 999t (0,3)d

(20)

d

(0,3)

expsV 99t d E f S t(3) g 5 sM3 2Yt21d]]]]]]]] expsV 99t (0,0)d1expsV t99 (0,2)d1expsV t99 (0,3)d (1,3)

expsV t99 d 1Y (1) t21 ]]]]]]]] expsV t99 (1,1)d1expsV t99 (1,2)d1expsV t99 (1,3)d expsV t99 (2,3)d (2) ]]]]] 1Y t21 expsV t99 (2,2)d1expsV t99 (2,3)d expsV 99t (3,2)d (3) ]]]]] 2Y t21 expsV 99t (3,2)d1expsV t99 (3,3)d

After the withdrawal of analog service (t $ t4 ), the expected number of net subscribers at time t is defined as:

As indicated by the utility superscripts and the market potential subscripts, the customers’ utilities and the market potential may change with the market environment. As in previous sections, we assume that subscribers do not abandon services. During the period in which the three services coexist, analog subscribers upgrade to digital cellular or PCS service and non-subscribers choose between digital cellular and PCS services. The last six observations from January 2000 to June 2000—after the withdrawal of analog service—were used for an out-of-sample comparison. We estimated the coefficients from Eqs. (18)–(20) and summarized the results in Table 5a. Note that the time variable coefficients for the competing services were set to be equal to each other, that is, q (1,2 ) 5 q (1,3) because one competing service does not completely replace the other one (as explained in Section 3). These coefficients may be deleted in the case where they are not significantly estimated, which means both coefficients are set to be zero. In this overall model, all the estimates were significant, even at the 1% level. We can see the effects of the substitutive relationship in that the time coefficient values for digital service are much greater than those for analog service. The market potential greatly increased after the introduction of PCS service and the nonsubscribers did not choose the older analog service after the introduction of PCS service. In fact, the market was expanded due to aggressive marketing efforts stemming from the competi-

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579

Table 5 Estimation and forecasting results of the choice-based substitutive and competitive diffusion model for analog, digital cellular and PCS services in Korea (a) Estimation results of the choice-based substitutive and competitive diffusion model for estimation sample from December 1988 to December 1999 Choice-based substitutive and competitive diffusion model

Parameter

( 0,0 ) ( 0,0 ) ( 0,0 ) Vt 5V t9 5c ( 0,1 ) ( 0,1 ) ( 0,1 ) Vt 5V t9 5q st 2 t1 1 1d ( 0,2 ) ( 0,2 ) V 9t 5q st 2 t2 1 1d ( 1,1 ) ( 1,1 ) ( 1,1 ) V t9 5V t99 5q st 2 t1 1 1d ( 1,2 ) ( 1,2 ) ( 1,2 ) 9 99 Vt 5V t 5q st 2 t2 1 1d ( 1,3 ) ( 1,3 ) V 99 5q st 2 t3 1 1d t ( 0,0 ) ( 0,0 ) V 99 5 c 99 t ( 0,2 ) ( 0,2 ) ( 2 ) ( 0,2 ) ( 2 ) V t99 5r Y t 21 1 b p x tp ( 0,3 ) ( 0,3 ) ( 3 ) ( 0,3 ) ( 3 ) V 99 5 b p x tp 1 b a x ta t x (tp2 ) : price (Won) of digital cellular service x (tp3 ) : price (Won) of PCS service x (ta3 ) : advertising expenditures (31,000 Won) of PCS service

c q ( 0,1 ) q ( 0,2 ) q ( 1,1 ) q ( 1,2 ) 5 q ( 1,3 ) c 99 ( 0,0 ) ( 0,2 ) r b (p0,2 ) b p( 0,3 ) b (a0,3 ) M1 M2 M3

( 0,0 )

Estimate

Approx. S.E.

Approx. Prob. .utu

9.2914 0.0408 0.5200 0.0225 0.0437 2.8920 1.507E27 27.42E26 29.67E26 3.92E27 4,015,957 5,348,951 28,465,886

0.5920 0.0428 0.0468 0.0011 0.0099 0.1622 1.534E28 4.599E27 6.029E27 4.796E28 393,056 146,649 956,987

0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

R2 Analog

Digital cellular

PCS

Total

0.7828

0.7720

0.7156

0.9008

(b) Forecasting results (MAD and MAPE) of the choice-based substitutive and competitive diffusion model for out-ofsample from January 2000 to June 2000 Digital cellular

MAD MAPE

349,889 77.74

PCS

MAD MAPE

159,845 49.24

tion among the service providers. MAD and MAPE of the model are reported in Table 5b. Comparing Table 5b with Table 4a, we find that the forecasting performance of the choice-based substitutive and competitive model is superior to that of the choice-based competitive model. Thus we can conclude that it is helpful to consider all the mobile telecommunication services in the model though their interrelationships are complicated.

5. Conclusion The telecommunication service market is changing markedly. Monopolistic markets are becoming more competitive and substitutive, and the tendency is for these transformations to occur more quickly and frequently. To demonstrate and forecast the complicated demand patterns in a quickly changing telecommunication market, models must address the interrela-

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tionships among services and / or products. Much effort in recent years has focused on developing aggregate diffusion models incorporating these interrelationships. One of the purposes of this paper was to develop such a diffusion model and apply it to the telecommunication market. In this paper, we focused on the modeling approach proposed by Jun and Park (1999). In this model, customers choose the particular service that maximizes their utility and efficiently uses their limited resources; they adopt new services whenever doing so will maximize their utility. That model, based on customer choice behavior, captures the diffusion and the substitution processes for a multigeneration product. The choice-based diffusion models differ from the Bass-type models in that the relationships among choice probabilities, the substitution / competition process and the marketing mix variables are derived by modeling the choice behavior of the customer. In the Korean mobile telephone service market, digital service is completely replacing analog service. We applied the choice-based multigeneration model proposed by Jun and Park (1999) to the market, and compared the fitting and forecasting performance with other Bass-type models including the Norton and Bass (1987) and the Mahajan and Muller (1996) model. We also developed a choice-based competitive diffusion model and applied it to the digital cellular and PCS service markets in Korea. The results were compared with other Bass-type models including those proposed by Peterson and Mahajan (1978), Mahajan et al. (1993), Parker and Gatignon (1994). Finally, expanding on the choice-based modeling idea, we developed a new choice-based diffusion model to describe an environment, such as the Korean mobile telephone service market, where substitution and competition occur simultaneously. As shown in the fitting and forecasting results, our model was superior to other models.

The choice-based diffusion model is expected to be very useful for analyzing complicated phenomena such as the substitutive and competitive diffusion process. The model also provides the flexibility to include marketing mix variables as in the regression analysis, and we believe it will provide useful for both researchers and practitioners.

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Institute of Science and Technology (KAIST). He received his doctorate from University of California, Berkeley in 1985. His research interests include time series modeling, structural changes, adaptive forecasting, business cycle forecasting, and forecasting telecommunication services and new products. He has published in Journal of Forecasting, Technological Forecasting and Social Change, Marketing Letters, Telecommunication Systems, and other journals. Seon K. KIM is a manager at Samsung Electronics. She received her doctorate from KAIST in 2002. Her research interests include new product forecasting, telecommunications forecasting, and time series models. Yoon S. PARK is a full-time lecturer in the Department of Business Administration at the Chonbuk National University. He received his doctorate from KAIST in 2000. His research interests include new product forecasting, telecommunications forecasting, and time series models. Myoung H. PARK is a professor in the Department of Industrial Engineering at the Hansung University. He received his doctorate from KAIST in 1993. His research interests include telecommunications forecasting and new product forecasting. He has published in Telecommunication Systems, Computers and Operations Research, and other journals Amy R. WILSON is an assistant professor in the Division of Health Services Research and Policy at the University of Minnesota. She received her doctorate from the University of California, Berkeley in 2000. Her research interests include modeling decision making under uncertainty, allocation of resources to health care interventions, and targeting of health care interventions.