9 APPLICATIONS INNOVATION DIFFUSION OF MODELS IN MARKETINGgarylilien.info/publications/37 - Applications of innovation....pdf · INNOVATION DIFFUSION MODELS IN MARKETING Shlomo Kalish

APPLICATIONS OF 9 INNOVATION DIFFUSION MODELS IN MARKETING Shlomo Kalish and Gary L. Lilien

Many recent books and articles stress that one key to long-term orga- nizational health is a systematic process of new product design, development, and introduction. Innovation is accompanied by costs and risks, both of which can be controlled through a well-conceived program of new product development. A key ingredient in such a program should be the use of sound, explicit models for planning and forecasting new product sales.

In this chapter we focus on the application of explicit guanlira- five dflusion modeis to aid in new product planning and decision making.

1 . Application. While there have been a number of theoretical in- vestigations about the diffusion of new products and technologies, the number of reported applications is relatively small. By application, we mean the use of the model, by a decision maker, to provide actionable information. The demonstration that a model fits data, retrospectively, falls outside this definition of application.

2. Quanfitotive dirnsion models. Our focus is on diffusion models representing the sales growth of a new product or process. Quanti- tative diffusion models specify mathematical relationships between quantifiable variables and include parameters that allow the model to be customized for a specific product situation.

3. Product p/anning. The applications we refer to are in the product planning area. The models may be used

to describe the rate of diffusion, so that an understanding of the past sales history is provided; to predict the future sales trajectory, so that growth may be planned for; to control the future sales trajectory (normative use) to provide input into pricing, advertising and product development decisions.

Descriptive models often have little need for controllable variables (price, for example), especially if the levels of those variables have not changed significantly. While these models are of intellectual interest, we will not deal with them here as they are considered in other chapters of this book.

Predictive models should incorporate controllable variables, especially those variables that are likely to change. Here, functional relationships are sought that are stable within the expected range of data variation. The information from such models is most important for providing input into production, inventory control, and financial decisions and plans.

Most of our attention will focus on those models that aim to control the future sales trajectory, normative models, Such models should have causal link between the control variable and sales, so that alternative advertising policies, pricing policies, and the like may be evaluated. To be most useful, the variables these models include should match up well with the marketing and product planning decisions that the organization faces.

Our view here is that there is no best, single, applied diffusion model. The problem, the data available and the specific characteristics of the situation combine to suggest the most cost effective approach. The examples we develop here were chosen because of the range of applications they represent and because each has been applied. We con- clude with a series of suggestions (or lessons) for those who wish to make use of these models.

MODELING DIFFUSION OF INNOVATIONS

A diffusion process in our context is the spread of a new idea or product from its source of creation to its ultimate users or adopters over

APPLICATIONS OF INNOVATION DIFFUSION MODELS 237

time. A d~flusion model, the mat hematical representation of the process of diffusion, is therefore appropriate in many circumstances. We consider several ways of classifying new product situations and the degree to which diffusion models have been used to model those phenomena. We classify these situations by product newness, repurchasability, homogeneity of market, and type of product or market.

Product Newness

We distinguish three categories of new products. At one extreme we have the true new product innovation, a product new to the company and to the market. An example is the digital computer when it was first developed. A second category is a product new to the company, perhaps, but not to the market whose potential adopters recognize the brand as part of an established product class. A third category is the new model, where the product is immediately recognizable as an extension of the company's product line. Most diffusion models deal with the generic new product -the product that defines a new industry. Cases 1 and 5, however, are examples of how diffusion models can be applied to a new brand in a new market.

Product Repurchasability

We distinguish products according to their repurchase cycle: products that are purchased once, products purchased occasionally, and products purchased frequently.

Consider the first type of product -a new book, for example. In a population of a given size, once all the potential buyers have bought a product in a product class, there are no more sales: the sales rate grows at the beginning and later falls until no potential buyers remain.

Products that are purchased occasionally (such as appliances) ex- hibit replacement cycles, dictated either by their physically wearing out or by changing styles and tastes. Initial purchase sales are frequently estimated separately from replacement sales, which can be related to the age distribution of existing goods and product mortality data.

The sales of frequently purchased new products (such as consumer packaged goods) are often analyzed via a t wo-s tage process: trial and repeat. Models for product trial often are related to advertising and

promotional effects (how well the product is perceived). Models for repeat sales often are most closely associated with how well the prod. uct satisfies needs, given its price.

Most diffusion model applications deal with first purchase only and hence are most appropriate for products most likely to be bought once or occasionally. In cases 1 and 5 we show how to deal with the repurchase phenomenon in a diffusion model framework.

Since the interpurchase cycle for frequently purchased goods is short, a detailed understanding of early sales dynamics is less important than analyzing steady state performance. Several models have centered on forecasting those steady state results from early Iabo- ratory or test-market data. Several of those models incorporate the dynamics of awareness and trial, and therefore could be classified as diffusion models. We present one such model (case 5 ) , and show how it relates to more classical diffusion models. (See also Mahajan, Muller, and Sharrna, 1984, for a comparison of the awareness parts of a range of models.)

Homogeneity o f Market

If market sales can be modeled as if there were a single (relatively) homogeneous population of adopters, the diffusion process is frequently modeled with a single equation or interrelated set of equa- tions. Most of the classical, early diffusion models are of this type (Mahajan and Peterson, 1985, provide a review). Often, however, a market may be sufficiently heterogeneous so that several or many segments exist, all of which value the product differently. For example, in 1967 Gould Inc, introduced an electrostatic printer aimed at the market for computer line printers. No safes were recorded for that appiication after two years in that market; the product was then re- positioned for the printer-plotter market and became successful there. Case 3 describes how a product or market can be divided into homogeneous segments, a diffusion model built for each, and the results combined.

Type o f Product-Market

Diffusion phenomena exist for consumer products and industrial products. While the general modeling approach is not conceptually different between these product or market categories, the elements included


in the models frequently differ. Consumer product markets often differ along taste dimensions and, therefore, the "value" of the product to the individual (and his or her degree of receptivity to early adoption) may be related to taste or individual-specific variables. Industrial products, used in producing other outputs, are frequently evaluated more quantitatively as substitutes that must show a specific return on investment (ROI) to justify adoption. While the models for these sectors may not differ in structure, the sources of data are often dissimilar, with consumer market models calibrated with attitudinal or survey data industrial models calibrated with engineering studies related to customers' value in use associated with adoption. For industrial market models, segmenting the market along this dimension is essential. Cases 1, 2 and 5 are consumer products; cases 3 and 4 are industrial.

THE STATE OF PRACTICE

As other chapters in this book indicate, many results that are of both theoretical and descriptive value have been developed in this area. Yet, by almost any standard, the level of application is Iow. The reasons for this low rate of application will form a bridge to understanding why the applications reviewed here have occurred.

First, consider some of the problems associated with applying explicit form (single-equation) diffusion modeis:

1. A market may have several segments; that is, it may be heterogeneous. A single equation, aggregating effects across segments, is unlikely to be completely satisfactory.

2. A diffusion model is most useful very early in a product's life. At that time, very little data is available. Hence (1) parameter estimates (especially of the adopting population size as in Horsky and Simon 1983, and Lilien, Rao, and Kalish 1981), tend to be unstable and (2) other sources of data (surveys, judgment) may need to be incorporated in the estimation procedure.

3. While many models (Bass 1969, for example, and related models) may be useful predictive tools, their lack of marketer controls make policy analysis difficult.

A number of models have appeared that incorporate marketing variables (see Kalish and Sen, Chapter 5). Most models have looked

240 APPLICATIONS

at advertising or price. The models incorporating advertising include those of Gould (1970), Horsky and Simon (1983) and Kalish (1985). The papers on pricing have mainly looked at pricing policies over time in a monopoly. They include the models of Bass (1980), Bass and Bultez (1982), Dolan and Jeuland (1981), Jeuland and Dolan (1982), and Jeuland (1981a), Kalish (1983a, 1985), Clarke, Darrough, and Heineke (1982), and Robinson and Lakhani (1975). None of these models, however, report on application as we defined it in the intro- ductory section.

Disaggregare models -those aimed at heterogeneous adopting population - have seen a little application success. Their development has been heaviest in the alternative energy field; their weakness has been their failure to incorporate sound diffusion principles. Warren (1979), in a review of the most widely known solar energy market penetration models (MITRE 1977; SRI International 1978; Arthur D. Little 1977; Midwest Research Institute 1977; and Energy and Environmental Analysis 1978) concludes that they rely on overly simplified represen- tations of diffusion phenomena, exogenously specifying (and arbi- trarily calibrating) an S-curve for diffusion. Issues such as information levels, possible negative feedback, distribution, technical risk, and esthetics are not considered in any of the models,

The development and application of a disaggregate model whose calibration was tied to a field data collection procedure is reported in Lilien (1982).

In a review of applications of several types, aimed primarily at the power-utility industry, Bodington and Quinn (1982) report a large gap between practice and the state of the art.

We found that in all industries there is a large gap between the methods of analyzing market penetration which are frequently used and the state- of-the-art of these methods, as published in the academic literature. Of 20 interviews in 6 industries (airline; appliance manufacturers; automobile manufacturers; gas and electric utilities; and the heating ventilation, and air conditioning (HVAC) equipment manufacturers), nearly all rely primarily on expert judgment and a simple time series model when forecasting the sales of a particular product. (p, S-6)

We identified several reasons for the slow adoption of many methods of analyzing market penetration. For example, we found a general lack of awareness of many methods. Also, the assumptions underlying many methods are viewed with considerable skepticism. The complete lack of, or poor quality of, the necessary data, and the difficulty associated with

APPLICATIONS OF INNOVATION DIFFUSION MODELS 24 1

communicating the methods and results to others in the organization, were also found to inhibit the usefulness and practicality of many methods. (P. S-7)

As the quotation shows, the reasons for the low rate of implementation are the usual ones: lack of awareness, complexity, communication, data difficulties.

VALIDATION AND USEFULNESS OF APPLIED DIFFUSION MODELS

We mentioned earlier that we will be focusing on applied diffusion models here, models that are developed to support managerial decisions. Those models must then conform to the specific context and problem-situation in which they are being applied. The situation may impose certain restrictions on data availability, theory and even on the receptivity of decision makers to model based analysis. Even under this restricted set of circumstances, there may be several or many models that will work equally well. This should not be of concern to us; indeed, our view is that no model is best in an absolute sense and that models should be as situation-specific as the problems they will help to solve (Lilien and Kotler 1983, p. 39).

Nevertheless, we suggest that, in selecting an applied diksion model it is useful to keep three criteria in mind.

Principle I : Parameterizability. Diffusion models have parameters that must be estimated and these estimates can be developed in several ways. I f sales data are available, these historical data can be used to estimate the parameters statistically. In most applications these data will not be available and it is necessary to calibrate the model using survey or judgmental data (case 2, below). Finally, the product may, in some way, be "like" another; in other words, an analogue may exist and the sales history of a similar product or market can be used. The work of Mansfield (1961). Blackrnan et al. (1973) and Black- man (1974) provides a way of parameterizing a diffusion model when little more than the product's economic value to a potential adopter is known (case 3). A broad range of analogies may lead to more formal modeling of appropriate analogies (case 4). These approaches may be combined -historical data, judgment, and analogies -in a Bayesian framework (see Lilien, Rao, and Kalish 1981).

242 APPLICATIONS

Principle 2: Ability to incorporate Appropriare Controls. As we focus on managerial use, the decisions facing the decision maker (product quality, market entry timing, advertising, price, distribution) should be explicitly incorporated in the model. Other controls may be included (price, for example) even if they are not under direct inves- tigation, if their values change over time and also affect the rate of diffusion.

Principle 3: Appropriuteness to Problem. Here the usual principles apply, depending on case: logical consistency, robustness, understand- ability, parsimony, and so on (Little 1970, for example). The idea is to incorporate as many important phenomena with as few parameters as possible.

In choosing between models that meet all of these criteria, we suggest three selection criteria:

1. Descriptive value. Does the model fit well (better than others?) 2. Predictive value. Does the model predict well (better than others?) 3. Normative value. Does the model yield more sensible policy im-

plications than others?

The specific application will dictate the relative importance of these three values.

In the next five sections we describe cases of applied diffusion models. All the models have been implemented and used. Each illustrates different types of problems, modeling approaches, and lessons for implementing diffusion models.

CASE 1: A CONSUMER DURABLE MODEL WITH PRICE, ADVERTISING AND REPLACEMENT (Kalish 1985)

The product class dealt with here is a consumer durable, with an average life time of seven to ten years. The product was relatively new, having been introduced seven years previously and had experienced consistent growth during that period. The diffusion curve was level- ing off, and the question facing management was what future sales were going to look like.


Historical growth had been accompanied by a price decline and a competitive entry into the market, factors that needed to be addressed. In addition, the product was in a stage where replacement sales were important. Advertising was considered a major sales influence by management. Consequently, competition, price, and advertising had to be included in the model.

The problem was decomposed into an aggregate product class sales model and a market share model for the different competitors and brands (see Lilien and Kotler 1983, pp. 91-96), Market share was structured as a nested logit model. The product class sales model was formulated as a diffusion equation, incorporating replacement, price, and advertising.

Product Class Sales Model

All competing products provide a comparable service, so we consider the total number of units sold. We specify the potential market for the number of products demanded to be a function of price. If we subtract the number already purchased from total demand, we get the net potential demand. The speed at which this potential demand is met depends both on advertising and on word of mouth. The result is as follows:

Y ( t ) = X ( t ) - X ( t - 1) = [ N ( P ) - X ( t - I ) ] f [ADV, WOM], ( I )

where f ( . , ) , the probability of purchase in the period, is increasing in both arguments. ADV is the cumulative discounted advertising effect, and WON is quality adjusted word of mouth, X ( t ) = cumulative number of adopters by time t , Y ( t ) = new adopters in period t , N ( P ) = market potential as a function of price P, and P ( t ) = price at time t .

However, replacement purchases have to be considered here. The approach taken is as follows: Let f ( i ) be a product survival curve, which gives the percentage of products of age ( i ) still in use. The total stock is then given by summing the sales Y ( t ) over time multiplied by the survival percentage:

Assuming that repeat buyers are similar to new buyers, we then get

244 APPLICATIONS

f

- 2 Y(t - 0- f (i) f [ADV, WOM]. r = l I - -- (3) total existing stock portion

potential purchasing this period

Note that this model is similar to stock adjustment models. If we had a direct measurement of existing stock, then the model becomes

Y(t) = [N(P( t ) ) - Stock(t)] .f(ADV, WOM). (4) Thus, we have a stock adjustment model with the adjustment speed

a function of advertising and word of mouth.

The model was parameterized as foflows.

Price. The total number of units demanded as a function of price is

N,(r) is the total number of units that would be in use if price is very low and d and c are constants. (For refrigerators, for example, No(t ) should be approximated by the number of households.) In this application No( t ) was all individuals over fifteen years of age. The term exp(-dP(t) '], is the fraction that find price acceptable. This functional form can deal with many types of population heterogeneity with respect to price (Weibull distribution).

Survival Curve. The percent of units of age i that are still opera- tional is specified as

7 is a half-life parameter (that is, the age where half the products still survive), and F is a shape parameter, and the higher it is, the higher the percentage of products that fail at an age close to T. (See Figure 9- 1 .)

Probability of Adoption

The proportion of potential buyers that will actually buy in a time period is modeled as

APPLICATIONS OF INNOVATION DIFFUSION MODELS

where e is a parameter that gives the percentage who buy at introduction (with no advertising and word of mouth), and a and b are the advertising effectiveness and word-of-mouth effectiveness, respectively. This functional form exhibits diminishing returns to scale, as expected. ADV is the discounted cumulative effect of recent advertising, specified as

1 8 ADV = -A(t) + C A(t - i ) *0 .6 ' ,

2 i = I

where A ( t ) is advertising level in quarter t . Equation (8) assumes that only half of current period advertising has actually reached consumers, since some have bought early in the period. The carryover effect of advertising is 0.6 per quarter over eight quarters, which is consistent with previous studies (Clarke 1976). These forgetting parameters were set because the model already had many parameters, and sensitivity analysis showed that the model results and implications were relatively insensitive to the specific values chosen.

The word-of-mouth effect was modeled similarly, as the discounted sum of past buyers. The sum is discounted because recent buyers are more likely to inform and influence current nonbuyers. In addition, in this case product usage declines with time. The discount coefficient for word of mouth was chosen to be 0.8, and since there was no significant quality change over the planning period this has resulted in the following relationship.

The resulting model is summarized as follows:

Total market sales( t )

X e + a . A D V + b : WOM I + U * A D V + ~ . W O M '


Market Share Model

Following Bell, Keeney, and Little (1975) most consistent models of market share are of the attraction form: US/(US +THEM). While intuitively appealing, these models suffer from the assumption of inde- pendence of irrelevant alternatives. This means that each brand is assumed to capture share from other brands in proportion to that other brand's market share. This assumption is violated in product classes where the brands break down into subcategories (luxury versus economy cars, for example).

One way around this problem within the context of attraction models is the nested logit (generalized extreme value) model, ( McFadden 1980). Here the market is represented as a tree structure, with each brand ending in a standard (logit) market share model. Managerial judgment suggested that the market structure for this product class was as follows. First, the market is separated by three types of product: expensive, medium priced, low priced; then by firm, and then by the different models of the products. Here the low-price models offered by company 1 compete directly and a standard attraction model of logit form is appropriate. This segment competes as a group against a similar offering by company 2. No alternative market structure was tested against the one suggested by managemens and applied here, al- though, in general, when time and resources permit, alternative structures should be considered.

SpecificalIy, let I be the set of brands (classes) competing directly as branches of the same tree, and let P, and X,, be the prices, and other features that describe the particular brand, with index j re- ferring to the features. For example, if the product is a wristwatch, a particular brand is described by whether or not it has an alarm, dual time, a stop watch, etc. The net value (utility) for product i is: U, = q - P, + C C J . X,, + r, where ? and C, I are importance weights for price and features, respectively. The market share (MS) for brand k (under suitable assumptions on E , ) .

This formulation, defined in terms of product features, aliows us to evaluate and simulate the performance of new products.

248 APPLICATIONS

Equation (1 1) is the steady-state market share. Since there is diffusion at the brand level as well, the actual model used is

where M, is actual market share, and a is the diffusion speed. The estimation of the market shares at the higher branches of the

tree is done similarly, where the attributes defined at the higher levels are used (e.g., advertising at the company level), along with a term called inclusive value, a summary of the utility of all brands that are descended from that branch (see Kalish, 1983b; McFadden, 1980). (See Figure 9-2.) This term enters at the next level as an additional attribute, with the log of the denominator of (11) as the attribute's value.

This model now allows estimation of product sales as Product sales = Total market sales x Market share. (13)

Estimation

The product class sales model was estimated using quarterly data, from introduction until the most recent time period. Dummy variables for seasonality (QRTI, QRTZ, QRT3) were introduced in a multiplic- ative fashion. The price chosen was the deflated price of the least expensive unit. This assumes that the least expensive brand determines the market potential while other prices were used to determine relative market share.

The model is nonlinear in the parameters and we used a nonlinear least squares estimation procedure (TROLL 1979). The shape parameter, F, was exogenously determined to be 2, using mortality curves estimated independently from a market research study of product owners.

The model fit the data quite well. (See Table 9- 1 .) The percentage of variance expiained is 99.5 percent (partly because of seasonality), and all the parameters except e and a are statistically significant. This suggests, perhaps, that advertising was not very effective in creating product class sales (but it was significant in the share model). The Durbin-Watson test indicates no serial correlation, and the standard error of the residuals is small when compared with the actual sales level. (See Figure 9-3 for fit versus actual sales.)

The market share model was estimated using the actual market shares, prices, distribution penetration, advertising expenditures, and

APPLICATIONS OF INNOVATION DIFFUSION MODELS

250 APPLICATIONS

Table 9-1, Regression Results for Market Sales Model.

RSQ = 0.996 GRSQ = 0.995 F(8/18) = 733.8 DW(0) = 2.05

Coeficient Value Standard Error t-S fatisic

a b QRT2 QRT3 QRT 1

features of the existing and past brands. The market share model was estimated using linear regression, after appropriate data transforma- tions and the fit, again, was quite good. The signs of the coefficient for the features turned out as expected, with price, advertising, and distribution statistically significant.

Assessment

The model was implemented as an interactive, on line decision support system. The user specifies control variables (price and advertising), as well as the exogenous variables (population size, gross national product, and price deflators). The model then creates quarterly and yearly forecasts. In addition, the user can insert different vaiues for the parameters and coefficients in order to test the sensitivity of the forecasts.

The model has been in use for three years. Two yearly forecasts were produced that turned out to be more accurate than what could be expected from the standard errors of the estimates (by luck). Similarly, the market share model's predictions have been very good. It forecast sales prior to launch for two new products. The two new products had a new characteristic whose value was judged to be similar to an existing characteristic that we had estimated previously. The model


predicted that the higher priced product would have a larger market share than the second new product, because the added characteristic was valued more than the price difference. This was in contrast to a sales forecast produced elsewhere in the company, that predicted equal shares. The model's prediction turned out to be accurate, evi- denced by stockouts of the first product, and large inventories of the second. The company subsequently increased the price of the first product.

The model system has yet to be adopted as a standard part of the planning process, however. There are several possible reasons. One is that for both years the forecasts have shown a decline in sales. Al- though in retrospect these forecasts turned out to be correct, it is difficult to accept bad news (the "kill the messenger" syndrome). Second, the organizationai conditions for adoption of such a system were not in place. No one in the operating group fully understood the model. Little (1979) suggests that one of the factors for success of such a system is to have an in-house marketing science intermediary to adapt, interpret, and "sell" the idea.

An interesting lesson here is that, with a sophisticated diffusion analysis system like this, it may be better to provide the forecasts directly rather than to provide them in the form of a (potentially intim- idating) decision support system.

This case illustrates how diffusion models can be adapted to deal with brand sales, through separate models of product class sales and market share. The product class sales model shows how price and advertising can be incorporated into the model and how replacement sales can be dealt with. It also illustrates some of the challenges associated with implementation of such sophisticated diffusion models.

Similar applications in this area are reported by Oren, Rothkopf, and Srnallwood (1980), and Wauser, Roberts, and Urban (1983). Both these papers report using direct customer measurement prior to launch, as opposed to our approach here, using sales data.

Oren, Rothkopf, and Smallwood (1980), and Oren and Rothkopf (1984), report on a model applied to forecast the market penetration of the Xerox 9700 computer printer. They implemented a direct measurement approach, that is, they have interviewed potential customers and have measured the value for adopting the product directly by comparing the cost savings for the installation to the price. The probability of adoption is modeled by a logit formulation, as here. The dynamics of adoption are modeled as a function of several production, distribution, and sales force factors, incorporating an exog-

enousiy imposed penetration curve. The parameters of the dynamic model are set subjectively by management. The authors report a successful implementation: The model's predictions were instrumental in reversing a tentative no-go for a product that turned out to be a major commercial success. The limitations of their model are in its

imposed penetration curve, and in the fact that there is no account of the existing stock of printers.

Roberts (1984), and Hauser, Roberts, and Urban (1983) report a pretest market measurement model for new automobiles. Their model is composed of total market sales and brand market shares. Total market sales are not of interest here as theirs is a mature market. New brand market share is modeled as a diffusion process.

In their model, information regarding the value of the new brand is diffused by word of mouth. This information updates prior beliefs about the product for potential buyers. The new beliefs will typically have a lower uncertainty, and thus, if the expectation level is not changed, the value of the product increases, due to reduced risk aver- sion by customers.

The utilities of the different competing brands then determine the probability of choice using a nested logit model.

The authors develop and implement a comprehensive measurement procedure, where prospective buyers are shown the new automobile, test drive it, go through simulated word-of-mouth recommendations, and undergo several other measurements. Information diffusion effects are estimated, and market shares are forecast. The authors report a successful initial implementation at the firm.

This application and the other two use a logit or nested logit approach to model market share as a function of consumer utilities. This model is calibrated using sales data, and thus does not require external data gathering. The other two have developed customized measurement procedures that allow their use prior to obtaining sales data. This more costly approach may be the only available alternative in the absence of sales data; the existence of sales data in our case Permitted the econometric parameterization discussed here.

CASE 2: A PROGRAM TIMING MODEL (Kalish and Litien 1986)

In 1980 the U.S. Department of Energy's photovoltaic (PV - solar bat- teries) program was reviewing a proposal to build, with government

support, 100 photovoltaic homes in a cluster in the southwest. A!. though this proposal was a welcome initiative from a private sector developer, DOE expressed concern that the technology might not be far enough along to demonstrate it in this way. The question was: when should such a demonstrative program begin?

The Timing Model

A natural way to incorporate technological uncertainty in an explicit form diffusion model is by operationalizing the word-of-mouth efFect as a perceived product-quality feedback term. In addition, the impact of price on diffusion adds realism to the model. Consider the following model-specification:

New Adopters = X ( t + 1 ) - X ( t )

where X ( t ) = cumulative number of adopters by time t , N= market potential when price = 0, p = price,

h ( p ) = fraction of market potential, N, that finds price, p, acceptable,

A( t ) = "information level" in the market place (advertising and demonstration program communication effect),

Q( t ) = perceived product quality at time t , weighted by the impact of past adopters,

R , ( . ) = relative market response at r to A ( [ ) , R , ( . ) = relative market response to Q ( t ) .

Note that the Bass (1969) model is a special case of (14) with R, = a, R,= bXand h ( p ) = l .

Let us interpret this in the framework of photovoltaics and then operationalize it. N in this model is the stock of homes with roofs that could physically accommodate photovoltaics. The function h is the fraction of the owners of those homes who would consider buy- ing P V and who find it potentially cost effective at price p.

Consider A ( & ) the demonstration-program effect - the sum total of market impacts in terms of awareness and the like that the P V market development activity has on potential buyers. Note that R, (.) = 0 prior to demonstration or mass communications.


Let P ( t ) be the expected perceived quality of the equipment in- stalled at time I. Let i index the possible performance of the system, (from best to worst). Then the expected perceived quality is

where ei is the impact of performance level i on quality perception and z , ( t ) is the likelihood of equipment sold at t giving that level of performance. The quality impact on the remaining population should decay with time (newer installations having greater perceptual impact). With this in mind, we model

where X ( t ) - X ( t - 1 ) represents the sales in the most recent period and r is a forgetting factor.

As defined in (16), the product-quality effect at any time is a weighted average of the quality of the product at any time in the past.

Now consider using this model for analyzing the timing of demonstration programs. Suppose that at time f, z , (? ) is high where the sub- script 1 refers to a failure and e, is also high and negative. In this case, the term R, may be negative, and negative market feedback may be said to be occurring. Clearly, the product should not be introduced then.

But some probability of failure always exists -and a market introduction (or demonstration program) should not be delayed indefinitely. The likelihood of failure for the product is declining in time, due to continued research and development, and the delayed introduction should allow diffusion to proceed more rapidly.

In order to deal with the optimal timing issue, we need to specify an objective function. In our application the objective was to maximize penetration by some target year, T (the stated objective of the government's photovoltaic program). We look then at the following problem: find the product introduction time, t , to

maximize X ( T) (1 7 )

subject to equation (14) plus certain initial conditions.

Using the Model

For this application, the following model forms were used.

h ( p ) = e-dJ' where d is a parameter to be estimated.

0 before the beginning of the demonstration program, a after (a! is a parameter to be estimated).

In order to assess "quality" levels, we worked closely with staff at Massachusetts Institute of Technology's Lincoln Laboratories, the organization under contract with DOE for technical evaluation, in. stallation, and monitoring of photovoltaic experimental and demonstration programs. Lincoln Laboratories' staff identified three categories of PV system failure: (1) lowered array output due to panel degradation, (2) system breakdown, primarily due to power conditioning unit malfunction, and (3) damage to residence through fire resulting from short circuit. Lincoln Laboratories also provided estimates for the current rate of incidence of these failure categories along with technological forecasts of how those likelihoods would change by 1986. In our analysis we assumed that the likelihood-of-failure category would change linearly over time from the 1980 numbers to the 1986 estimates and would remain constant at the 1986 figures after 1986.

We performed a telephone survey of fifty-two builders in the North- east to assess their perception of the impact on the marketplace (the relative weights, e,) of each of these types of futures relative to the positive effect of a perfectly running demonstration.

In order to estimate other model parameters we used the results of a model developed for DOE (PV 1 : Lilien and Wolfe 1980) run under the assumption that pho tovoltaics work . This model was a planning model developed for DOE, and it assumed that the PV market begins in 1981. While the use of such simulated data may be questioned, it was the best available consistent with the application-objectives. Note that PVl assumed that product uncertainty was large enough that essentially no private sector sales would occur until a demonstration program proved viability. Our analysis assumed that here.

The form of the model that was used for calibration is as foilows:

where r , the forgetting factor was taken to be 0.1 (and varied as a parameter in sensitivity analysis later) and N ( t ) , the market potential, war taken as 25 percent of the stock of single family homes (according to

Table 9-2. Parameter Estimation of Base Case Diffusion Model.

Coeficien t Value Standard Error t-Statistic

Nore: R 2 = 0.952; Corr R * = 0.939; F(2/7) = 70.4.

a DOE rule of thumb). N ( t ) was derived from the Citibank data base and the stock of homes was assumed to increase at 2 percent per year over the planning horizon. This model now has three parameters, d , a, and f l , that need to be estimated. Assuming good quality as a base case (e , = 0, i = 1,2,3), we estimated a, 6, and d using the National Bureau of Economic Research's TROLL system's nonlinear estimation procedure. Table 9-2 gives the results; the fit is good and the parameters have correct signs, good significance levels, and proper magnitudes.

Next we used the calibrated model, together with assumptions about possible negative effects of degrees of PV system failures to simulate the effect of a demonstration program at any time t from 1980 on. Starting a demonstration program at t has the following effects on our model: (1) it switches on R, from 0 to a and (2) it adds installations to the installation base. For the purpose of this analysis, we have assumed that when the demonstration program begins, a total of twenty-five homes are built in that and subsequent years as PV demonstrations (that the demonstrations are phased in).

The year 1990 was the target year for penetration evaluation; it is T in equation (17). Figure 9-4 graphs the relative effect of introduction at any time t relative to introduction in 1980. Called the delay eflecr, this is

X(1990; introduce at t ) Deiay effect ( t ) =

X(1990; introduce in 1980) ' (19)

Sensitivity analysis also showed that the model implication - wait until 1986 to introduce -was relatively robust with respect to the in- tensity of the demonstration and market entry program, the forgetting factor and the target year (with the target year sensitivity displayed in


Figure 9-4). Clearly, given these results, a case can be made for de- laying a demonstration program until the technology is better developed.

Partly on the basis of this analysis, funding for the demonstration program was nor granted; the developed was asked to wait several years until the technology was more technically proven.

Assessment

This case shows how an explicit form diffusion model was developed and calibrated, incorporating product quality improvement (and possible negative word of mouth), to aid in the decision of when to introduce the technology. As such, its normative value is best judged, first, by the robustness of its results, and, second, by its use. With respect to (1) no sensitivity analyses run with this model were able to lead to a recommendation to introduce earlier than 1985 (Kalish and Lilien 1986); therefore the model seems robust. Judging by its use, the model was indeed used as input into the evaluation of the 1980 proposal and provided quantitative support for a decision to delay the demonstrative program. Given the nature of the problem faced here, a mode! was developed that could deal with the issue of entry timing and could incorporate both positive and negative feedback. In addition the model shows how historical data, judgmental data, and survey data can be combined in calibrating a diffusion model prior to market entry.

Other attempts to incorporate negative feedback are included in the models of Midgley (1977) and Mahajan, Muller, and Kerin (1984). All these models required more data and inctuded many more parameters than were required for this relatively parsimonious model.

The issue of entry timing under a situation of improving product quality is discussed in Yoon and Lilien (1984). Our model differs in that it focuses on a new technology while Yoon and Lilien (1984) focus on a second or later product entering a market facing diffusion.

CASE 3: MARKET ASSESSMENT FOR ACTIVE SOLAR COOLING (Johnston and Litien 1982)

In 1981, the U.S. Department of Energy was evaluating whether or not (or at what level) to subsidize an active solar cooling industry in

260 APPLICATIONS

the United States. Solar-powered air conditioning represents a technology that could meet some of the anticipated space cooling needs of the 1980s and the 1990s (Warren and Wahlig 1982). Market penetration had been hampered by a number of factors, primarily the high first cost of solar relative to conventional space cooling equipment. For example, Warren and Wahlig estimate the current cost of a 25- ton solar system with enough collector area to operate at half-peak load, to be about $110,000. This compares to $18,000 to $25,000 for a conventional 25-ton unit. Major cost reductions during the next two decades may reduce this gap somewhat.

This application tried to determine the combination of fuel escalation assumptions, solar cost decline assumptions and federal incen- tives (subsidies) that would be required to make solar cooling viable by the year 2000.

Assumptions and Approaches

Several assumptions drive this analysis, including the following.

1. Solar cooling is an investment in hearing, ventilation, and air conditioning (NVAC). The technology is novel, but the need (space cooling) is not. Solar cooling is expected to share existing demand in the cooling marketplace. Therefore, a diffusion model is appropriate for estimating substitution rates.

2. The major solar market wilf develop in commercial buildings in census regions 3, 4, 6, 7, and 9. Commercial buildings are most appropriate for solar cooling for technical reasons (lack of fea- sible, residential technology) as well as due to their large cooling loads. The noted census regions cover the sunbelt -areas with much sun, high economic growth and long cooling seasons.

3 . The total cooling market is assumed to be all new construction plus 5 percent (assuming a t wenty-year life) of exisring equipment.

Data required to support this analysis here inciuded projected cooling energy use by region and building type, projected fuel costs (and ranges), projected costs of conventional cooling equipment, insolation (sunshine) rates, and cooling season lengths by region. In addition, a range of assumptions about current and projected cost declines for solar cooling are included.


The approach taken here is to model penetration as

penetration = Annual potential Percentage substitution . (20) In order to determine the annual potential, information from a

survey by Lilien and Johnston (1980) was used. That survey showed, for example, that 35 percent of industriai or commercial HVAC decision makers require a five-year or faster payback on HVAC equipment. That survey provided a complete set of data for determining market potential as a function of market size, economic life, warranty period, land availability, and payback offered.

For percentage substitution we rely on a form of the Fisher-Pry (1971) model. The underlying concept of that model is that, when a new product or process replaces an older one the rate of adoption is proportional to the interaction of the fraction of the older one still in use and the current level of penetration. Mathematically, this relationship can be expressed as follows:

where f = fraction of potential market having adopted the new technology,

b = a constant, characterizing the speed of switching to the new technology,

or, in discrete form F2-F, = b(1- F,)F, ,

where F2 = penetration percentage at time 2, F, = penetration percentage at time 1.

The work of Blackman et al. (1973) and Blackrnan (1974), building upon the work of Mansfield (1961, 1968), provided a means of estimating the constant b from exogenous data. Mansfieid argued that 6 should be higher when the relative profitability associated with the new product is high, and when the initial investment is low. In studies of diffusion in disparate industriai sectors including railroads, coal, steel, and breweries, he found an empirical expression for b as

b = Z + .53I?- .027S, (23)

where Z = an industry specific constant, I?= estimated rate-of-return associated with the innovation

divided by the minimum rate-of-return for investment (the hurdle rate).

262 APPLICATIONS

S = initid investment in the innovation x 100 divided by the total assets of an average firm adopting the innovation.

A critical term in this expression is still 2. The contribution of Blackman et al. (1973) was to relate the industrial innovation coeficient Z to more general industry coefficients. They create an industry coefficient index (I) which is derived as follows:

1. They create a matrix of eight general measures of industry inno- vativeness -such as R&D expenditures, current and planned, new product sales as percent of total, value added - for each of a dozen industrial sectors.

2. They factor-analyze this matrix to obtain a set of factor scores for each industry.

3. They regress the score for the first factor (I) against the value of Z to obtain the following equation.

The t-statistic for the coefficient of I is 3.38 and the coefficient of determination is 0.85; in general, the fit appears quite good. Table 9-3 Lists the value of the innovation index in a number of industrial sectors. We took here, as a value for Z in equation (24), an average industry

Table 9-3. Ranking of Industrial Sectors According to Value of Their Innovation Index.

Industrial Sector Innovation Index

Aircraft and missiles Electrical machinery and communication Chemicals and allied products Autos and other transportation equipment Food and kindred products Professional and scientific instruments Fabricated metals and ordinance Petroleum products Stone, clay, and glass Paper and allied products Textile mill products and apparel Rubber products


Figure 9-5. Market Penetration Methodology.

(a) Assumprrons: Solar technology/performance

* Subsidy level Fuel cost scenario

(d) D~flusion model merhodology: Est~mate substitution:

Prior year's substitutron Current relatrve payback/ ROI

Penetration = Potential x Substitutron 070 Summed over census region

9

innovation rate = 0. We modeled rI as the median acceptabie payback period (four years, Lilien and Johnston 1980), divided by the actual payback. We assumed that S is smail enough ( 0 ) so that it can be ignored. This provided a best-base situation for solar cooling.

The analytic approach taken here is outlined in Figure 9-5.

Estimate market potential as Economic life, warranty, Land availability, Payback acceptability

I I

(b.2) Dara base:

Building rates Insolation etc.

Box (a) Provides the assumptions for solar technology/performance, subsidy level, and fuel cost escalation for each run of the model.

r a

(c) Market potenrial assessmenr:

rn >

Boxes (b) Incorporate the data outlined above (b.2) in a payback or return-on-investment (ROI) calculation for an

(b. I ) Payback estimation: foreachr,1980to2000, each census region

4

264 APPLICATIONS

investment in solar cooling for each year from 1980 to 2000.

Box (c) Is market potential assessment as a function of economic life, warranty period, land availability, and payback acceptability.

Box (d) Is the diffusion model methodology, estimating the substitution percentage as a function of the prior year's substitution and the current relative payback or ROI.

Box (e) Estimates penetration (sales) as potential times substitution percentage.

Note that the analysis is run separately for each census region under study.

Results

Table 9-4 gives the results of a few sample analyses, for the "best guess" oil price increase scenario. Only two extremes (optimistic and pessimistic) cost decline scenarios are presented. Even for the most

Table 9-4. "Best Guess" Oil Price Scenarios: Year 2000 Results.

Energy Government Case Savings Cost a Subsid-v Unitsb ShclreC Cost x $ 1 o6

Nil Nil Nil Nil Nil 0.02 quad 0.06 quad 0.12 quad

aCost decline assumption A = No price decline (pessimistic), E = 50 percent cost decline (opr~mistic).

b~quivaIent 25-ton systems Share in year 2000

optimistic cost decline scenario, without federal subsidy (case 51, solar cooling can only expect to see 2 percent of the market in the year 2000. Other cases are similarly pessimistic; a rather high level of subsidy (20 percent in case 6) only increases that year 2000 share to 9.6 percent.

The conclusions and recommendations from that study were as follows.

Based on the results of the solar cooling penetration analysis we see that only under very optimistic cost-reduction assumptions coupled with significant levels of government subsidy will a market for solar cooling de- veiop in the commercial sector. For the market to persist, the subsidy would have to be continued indefinitely; if the subsidy were to be discon- tinued the market would essentially disappear. World oil prices will have an effect on the market, but even under the most pessimistic outlook for oil price escalation soiar air conditioning would have to be subsidized to attain and hold a significant market share. . . I t thus appears that only for non-economic reasons should solar cooling technology be supported by subsidy at this time. Indeed, only if research efforts propose to meet or exceed the most optimistic cost-reduction assumptions used in this analysis does it appear that funds for development should be allocated to a solar cooling program. (Johnston and Lilien 1982, pp. 54-55)

Partly on the basis of this analysis, DOE decided not to provide special subsidies for soiar powered cooling.

Assessment

This case illustrates a situation where a heterogeneous diffusion model is most appropriate. Each census region has a different level of insolation and fuel costs, leading to different economic performance projection for solar cooling. It shows how model calibration can be ac- complished with an analogue approach. (The next case develops a more sophisticated form of analogue.) The focus of the analysis here was the allocation of public funds to support a new technology. The case shows that diffusion models are appropriate tools for evaluating the appropriateness of federal industrial support policies; the difference between sales projections with and without subsidies provides the 'benefit' measure to compare with program costs. (See Kalish and Lilien 1983 for an analysis of the appropriate form of price subsidy policies.) The approach is dependent on a data set that is over twenty

266 APPLICATIONS

years old, however, pointing out the need for an analogue-update, as discussed in the next case.

CASE 4: FORECASTING SALES PRIOR TO PRODUCT LAUNCH (Choffray and Lilien 1986)

In 1982, the Arjomari Company, a leading European paper producer, was dissatisfied with the judgment-based sales forecasts for its new products. Its management hoped to be able to reduce forecasting error and lower the rate of new product failure due to market misassess- ment. They began searching for "lookalike" product market situations, hoping that the way a new product is accepted in the marketplace would be close to the way similar products were accepted.

The analysis team quickly found that the determination of an appropriate analogue was difficult. Through the French Ministry of In- dustry, they became aware of a study that produced results that they could use.

The Study

In 1980 the Center for Research in Management Science at Ecole Su- perieure des Sciences Economiques et Commerciales (ESSEC) in con- junction with the French Ministry of Industry and the Novaction Company, a French consulting firm, launched a project to provide the basis for developing analogues for sales growth patterns for new industrial products. The approach built on the work of Mansfield (1968) who studied variations in the rate of adoption of twelve innovations.

Mansfield's work (which also provides the basis of the application reported in case 3) was both dated and devoid of detailed guidance on market strategy alterations. Based on this evaluation, it was decided to develop a data base of individual new products, including information on the development process, the marketing strategy and the rate of market penetration for a five-year period.

For each of the 112 products included in the data base, over 500 pieces of information were collected in three categories.

* R&D process. Cost structure, financing, duration, methods of evaluation, types of protection, etc.


Market introduction strategy. Bases for decision, success or failure, evaluation criteria, initial marketing mix, etc. Rate of product penetration. Sales volume and dollar sales for the new product and its prime competitors, market structure, changes in the marketing mix, etc.

Market penetration information was collected on a quarterly basis over a five-year period after market introduction. Other data included managerial judgments about how the new product performs relative to competition, information on the objectives set for the new product, the way these objectives evolved over time, and how they were achieved.

The objective of the project was to identify and quantify the deter- minants of sales growth for new industrial products. The first step of the analysis was the measurement of two rates.

The initial rate of penetration. The percentage of total industry demand that the new product captured during its first year of com- mercialization, and

* The rate of dtmsion. The speed with which the new product pen- etrated the market over time. (See Figure 9-6.)

For total industry demand, the cumulative volume of sales for all products in the market during the five years of observation was used. Following Mansfield (1961), Fisher and Pry (1971), and Blackman (1974), the diffusion rate of each product was then computed assuming a logistic diffusion curve of the form

where p,, = fraction of industry demand captured at time t by new product i ,

,i3, = diffusion rate of product i over the observed period, cri = initial market penetration level, M = maximum attainable market share of product i (as esti-

mated by respondent).

For each product i ordinary least square estimates of the a, parameter over the three to five years of available observations were developed. The fit of the model was good, with R~ averaging 0.87, and with an

APPLICATIONS


average standard deviation of 0.08. A predictive test on a holdout sample of 15 products yielded an R' of 0.77.

Two models were then developed to relate the initial penetration rate (p,,) and the speed of diffusion ( P , ) , to a set of key descriptive variables (Novaction 1983 ; Yoon 1984).

Initial Penetration Rate Model

Logit (initial penetration rate) = Function of

(product design and development process descriptors (X,,)), and

(target market structure descriptors c

K J

In(p,;/(l-p,j)) = a+ s @kXki f C ?,TI* k = 1 . J = I

0 c p,, c 1.0 (26)

Definitions of the X and V descriptors are provided in Table 9-5 along with standardized importance weights representing constants for [ a,

and IY,I.

Diffusion Rate Model

Diffusion rate = Function of (entry strategy descriptors), and

(descriptors of changes in the competitive environment)

where Yk refers to ratio-scaled descriptors of the firm's entry strategy, W, refers to binary descriptors of changes in the environ-

mental after market introduction.

Model (27) was linearized, taking logs, prior to parameter estimation. Definitions of the Y and W variables, along with standardized importance weights representing (b, j and { c, 1 are given in Table 9-5.

APPLICATIONS


These results were incorporated in a microcomputer based decision support system (called BEII) that can be used for forecasting sales and evaluating launch strategies prior to new industrial product introduction.

BEII is a menu-driver, user-friendly system, programmed in Apple- soft Basic on an Apple IIe. The system requires the user to specify the characteristics of the product's development process and the competitive structure of its target market. Assumptions are also introduced into the computer about planned entry strategy and anticipated changes in the firm's competitive environment.

Figure 9-7 gives the general structure of the BEII Decision Sup- port System. It comprises three modules:

1 . Sales forecusting module. (Our focus here) asks fifteen questions about market structure, entry strategy and the development process and transiates them into a four-year sales projection.

2. Product cost module. Based on experience curve and economy of scale concepts, this module projects annual production, marketing, and distribution costs for the product.

3. ProBtabilify module. Takes cost, and volume projections and translates then into financial projections for the product.

Assessment

After using the system, Arjomari reports that they are pleased with the results, giving them cumulative sales projections with Iess than a 30 percent discrepancy bet ween actual and forecast sales ( Virolleaud 1983).

This system has been used in several other situations. In a recent experiment conducted at Viejlle Montagne, a world leader in zinc production and associated technologies, the system was used to simulate the time growth of cumulative sales for a new product introduced five years ago. Discrepancy with the actual sales rate was less than 15 percent over that horizon. Subsequently, the approach was used to heip plan entry strategy for a line of new products.

Other firms such as Ciments et Betons France, have used it too, evaluate the effect of alternative strategies aimed at accelerating the diffusion of new lines of products.

This sample of system users, however, does not provide definite


evidence of the external validity of the analogue approach to building a diffusion model for new industrial product sales forecasting. Ex- perience to date is encouraging, however.

This case illustrates several important points. First, the analogue approach can be used to parameterize a diffusion model prior to market introduction and the consequent collection of sales data. Second, that diffusion model can be used for forecasting, providing results that are superior to a previous (judgmental) approach. Third, the incor- poration of the results into a user-friendly DSS, when properly introduced to appropriate firm-employees, can enhance the likelihood of model acceptance and use.

CASE 5: A CONSUMER PACKAGED GOODS MODEL (Blattberg and Golanty 1978)

Our last case deals with a frequently purchased goods. Applications of this type have not traditionally been classified as diffusion models. We take one model from this class and show how it relates to more traditional diffusion models.

This class of models are test-market or pretest market models, where early sales results, combined with some measurements at the individual level are used to predict eventual penetration or market share of the product. The purpose of the Tracker model is to predict year end, test market sales using survey data. The model has three components; awareness, trial, and repeat. The first two components provide the model dynamics that incorporate product diffusion. At a reported cost of about $15,000 per use it provides an inexpensive way to estimate these dynamics within a test-market environment.

Awareness Model

Total brand awareness is developed as

where A, = awareness at t , U R = unaided recall of new brand, AR = aided recall of new brand given lack of unaided recall,

N = sample size.

274 APPLICATIONS

The model relates the change in awareness at r to advertising spend. ing as

Newly aware= A,-A,-, = (1 -A,-,)-(1-exp[a- b*(GRP,)]). (29)

where GRP, = gross-rating points of advertising at t , a, I j = parameters.

Note that the equation shows diminishing returns to advertising spending and that, without advertising, awareness may be stable (a= 0), it may grow (a < 0), or it may dedine (a > 0). Thus, a captures the net effect of forgetting and free publicity. The parameter b is a rnea- sure of the awareness response to advertising: the greater b, the greater the advertising effectiveness is.

Blattberg and Golanty estimate A,, the initial awareness level, and a and b by regressing previous introductions in the same product class against advertising spending. This assumes that relationship (30) is the same for all products in the product category.

This awareness model structure is similar to those in other models. The Fourt and Woodlock (1961) model has the same basic structure but no advertising effects, Models by Stigler (1961), Dodson and Mul- ler (1978), Horsky and Simon (1983), and Kalish (1985), include advertising effects or forgetting effects. These latter models include word- of-mouth communications as well.

Trial Model

In this model, trial rates are estimated within two separate popula- tions: the newly aware and those aware for more than one period. In particuiar, the authors specify trial rates as

T, -T , - ,=c (A , -A ,_ , )+d(A , - , - T,-l) for O < d c C < 1, - - (3 1) Newly Past aware but aware not yet trying

where T, = cumulative percentage of triers by period t , A, = percentage aware in period t ,

c = probability of trial by consumers who became aware this period,

d = probability of trial by consumers aware last period or earlier but who have not yet tried.

Here the model postulates a greater conversion rate among the newly aware.

The trial rate in this equation is adjusted for relative price:

where RP, = relative price at t ct = price-elasticity parameter

Similarly, an error term is added to the equation for estimation; it is both autocorrelated and heteroscedastic (where the heteroscedasticity is related to relative price). Parameters of the model are assumed constant in a product class and are estimated by a nonlinear procedure, pooling data for a number of products in the class.

The trial model has the same basic dynamic structure as the awareness mode1 where the rate of new trials is proportional to the difference between the aware individuals (market potential), and those who have tried already. The conditional probability of trial is a function of price. Similar structures have been incorporated in diffusion models, such as those of Robinson and Lakhani (1975), Dodson and Muller (1978), and Kalish (1985). Again, diffusion models usually incorporate the added effect of word-of-mouth communications.

Repeat Model and Projection Model

The projection model for market share or sales is based on tracing the percentage of triers who become first-time users, second-time users, and so on. Triers or repeat users who discontinue use are classified as nonusers. Triers are assumed to have a constant, average purchase rate, TU, and repeaters are assumed to have a different use rate, R U . Total sales per potential trier is then given as

where TS, = total sales during period f, T, = new triers during period t ,

TU = trial use rate, RU = repeat use rate,

UC,, = new triers in period i who are still users during period t .

To model UC,, , the authors use a depth-of-repeat model. For simplicity it is assumed that

that is, that the percentage (r) of triers who repeat at least once is independent of time. The rest of the structure of UC,, develops as follows:

UC,,,+,+,= k,(UC,,,+l) (35)

where ki is the percentage of triers in period t who continue to purchase after period t + i. Note that the [k,] are also assumed independent of time.

According to Blattberg and Golanty, r and RU are estimated with telephone surveys, while the [k,] are estimated subjectively with product-satisfaction data from the questionnaires; the trial rate TU is set equal to one by definition. The reason for the subjective estimation of the [k, ] is that no quantitative, long-term, depth-of-repeat information is available; this problem exists in all cases where a short purchase history is used to project future sales.

If sampling is instituted during the test market, the model must be replicated for the sampled and nonsampled potential customers.

Assessment

Blattberg and Goianty report eleven new-product inrroductions evaluated with Tracker. The predictions appear reasonable, being within 10 to 15 percent of actual in eight of the cases. In two of the other cases the model predicted an early failure.

The model provides a practical structure that is apparently being applied with success in evaluating test markets. Its weaknesses are that numerous parameters (the [k,], for example) are subjectively estimated and based on little data. In addition, the estimation procedures are somewhat ad hoe; for example, the awareness model often will not discriminate between company and brand identification. Furthermore,


parameters are often estimated partially from related products; this feature limits the model's use in cases where a product is unique.

This case illustrates how the dynamics of new product adoption (both awareness and trial) can be modeled in a test-market environment for frequently purchased packages. It ties a conceptually simple yet relatively complete model structure together with a set of associated measurements needed for model calibration. It includes advertising and (relative) price and therefore has normative value beyond simply forecasting test market results.

A number of other models aimed at evaluating test-market or pretest -market performance for frequently purchased packaged goods are reviewed in Assmus (1981), Narasimhan and Sen (1983), Robinson (1981), Urban and Hauser (1980), and Wilson and Pringle (1981).

CONCLUSION

A diffusion model's applied value is determined by its ability to help managers analyze, plan, and control the process of introducing and managing a new product. It is difficult to project and control sales growth with little or no sales data and where the competitive structure of the market is uncertain. Diffusion models can help in these tasks if they are used appropriately. They are not meant to replace management judgment; rather they should be used to aid that judgment, to help run sensitivity anaIyses and to compare market scenarios.

In what follows we group suggestions for applying diffusion models in two categories: those dealing with model structure and those dealing with model use.

Model Structure

Market Potential. For goods with a long lifetime, market potential is a key factor affecting the model's predictive value. Market potential for the product class should be modeled as a function of price, population changes over time, and other marketing variables.

Con~rol Viriabtes. The model should incorporate relevant control variables: price, advertising and quality for exampIe. Without those variables, the model may not be useful for policy and sensitivity analyses. A model with control variables can evaluate different marketing

programs, and study the evolution of the market under different price scenarios.

Competition. Many past models ignored competitive effects, which are of vital managerial concern. A way to incorporate competition is to model product class sales using the diffusion model, and brand share using a market share model (see case 1).

Quality and Risk. Individuals perceive new products as riskier than established ones due to uncertainty about product performance. Prod- uct quality and reliability may indeed change over time. The issues of uncertainty, information diffusion, and perceived and actual product quality should be considered in the model.

Replacement Sales. Replacement sales become a major issue later in the life cycle. It is important to model replacement explicitly, par- ticularly for products that are extensions of a product line and not completely new.

Model Use

Early Calibration. The model is likely to be most needed before the product is introduced. At that time no sales data are available. Thus the model should be parameterized in such a way that the parameters have an intuitive interpretation, and the model can be calibrated using a combination of survey data and managerial judgment. Methods for updating the parameters once sales data are available should be provided. Alternatively, suitable analogues should be sought and a procedure for calibrating models using those analogues developed.

Simplicity and Robustness. The model structure should be made simple and intuitive so that the manager can understand it and be comfortable with it. it should also be robust. Otherwise, i t will not be used.

On net, diffusion models can be valuable and can be used. They are much more flexible and widely applicable than their use to date would indicate. The challenge is not so much to buid better diffusion models, as it is to customize models using existing concepts and to

make them work. To meet this challenge we must provide means to estimate model parameters credibly, to explain the concepts to management, and make the model-manager interface efficient, so these models can provide a net positive value to the user.

Documents

9 APPLICATIONS INNOVATION DIFFUSION OF MODELS IN MARKETINGgarylilien.info/publications/37 - Applications of innovation....pdf · INNOVATION DIFFUSION MODELS IN MARKETING Shlomo Kalish