Modelling and forecasting the diffusion of innovation – A 25-year review

Abstract

The wealth of research into modelling and forecasting the diffusion of innovations is impressive and confirms its continuing importance as a research topic. The main models of innovation diffusion were established by 1970. (Although the title implies that 1980 is the starting point of the review, we allowed ourselves to relax this constraint when necessary.) Modelling developments in the period 1970 onwards have been in modifying the existing models by adding greater flexibility in various ways. The objective here is to review the research in these different directions, with an emphasis on their contribution to improving on forecasting accuracy, or adding insight to the problem of forecasting.

The main categories of these modifications are: the introduction of marketing variables in the parameterisation of the models; generalising the models to consider innovations at different stages of diffusions in different countries; and generalising the models to consider the diffusion of successive generations of technology.

We find that, in terms of practical impact, the main application areas are the introduction of consumer durables and telecommunications.

In spite of (or perhaps because of) the efforts of many authors, few research questions have been finally resolved. For example, although there is some convergence of ideas of the most appropriate way to include marketing mix-variables into the Bass model, there are several viable alternative models.

Future directions of research are likely to include forecasting new product diffusion with little or no data, forecasting with multinational models, and forecasting with multi-generation models; work in normative modelling in this area has already been published.

Introduction

The modelling and forecasting of the diffusion of innovations has been a topic of practical and academic interest since the 1960s when the pioneering works of Fourt and Woodlock (1960), Mansfield (1961) Floyd (1962), Rogers (1962), Chow (1967) and Bass (1969) appeared. The interest excited by these papers can be judged by the numbers of citations for these papers on ISI Web of Science (in April 2005) which were 119, 428, 10, 988, 58 and 582 respectively. Two papers, Fourt and Woodlock, and Bass, use ‘new product’ rather than technology in their titles. Although the approach to modelling the diffusion of a technology or a new consumer durable is very similar, in recent years, new product applications in marketing have tended to dominate in the overall diffusion literature.

The phenomenon of innovation diffusion is shown in a stylised form in Fig. 1. Cumulative adoption and period-by-period adoptions are shown, but which of these two representations is of greater importance depends on the application. For example, in the diffusion of mobile phones, a service provider is concerned about the demand on the infrastructure and is thus concerned with cumulative adoptions; a handset supplier is concerned with meeting demand and will thus want to model and forecast period by period adoptions. In this example, the service provider will want to know the level of adoption at a particular time and the eventual number of adopters; the handset provider will want to know the rate of adoption at a given time, the timing of peak demand and the magnitude of peak demand. As a counterpoint to the smooth curves of Fig. 1, Fig. 2 shows the comparable information for the diffusion of residential telephones in the United Kingdom. The period-by-period adoptions depart fairly drastically from the bell-shaped curve. The difficulties in forecasting are also demonstrated, as in 1975, period-by-period demand appears to have peaked; decisions to expand production may have been cancelled or postponed; however, in 1979, a 43% higher peak is reached.

The main models used for innovation diffusion were established by 1970; of the eight different basic models listed in the Appendix, six had been applied in modelling the diffusion of innovations by this date. The main modelling developments in the period 1970 onwards have been in modifying the existing models by adding greater flexibility to the underlying model in various ways.

The main categories of these modifications are listed below, and in each case, the citations of a pioneering paper are quoted as a proxy for research activity in this area:

• the introduction of marketing variables in the parameterisation of the models; Robinson and Lakhani (1975)

• generalising the models to consider innovations at different stages of diffusions in different countries; Gatignon, Eliashaberg and Robertson (1989)

• generalising the models to consider the diffusion of successive generations of technology; Norton and Bass (1987).

It is fair to say that in most of these contributions, the emphasis has been on the explanation of past behaviour rather than on forecasting future behaviour. To quantify this comment and the previous comment about the preponderance of marketing studies, the references used in this study are classified by their journals into the following categories in decreasing order in Table 1. There is little difference between the disciplines in terms of the freshness of their contributions; the average age of the marketing, forecasting and OR/management science references is 15 years, the average age of the business/economics reference is 19 years.

During the last 25 years, there have been several reviews of diffusion models. These include Meade (1984); Mahajan and Peterson (1985), Mahajan et al., 1990, Mahajan et al., 1993, Baptista (1999), Mahajan et al., 2000a, Mahajan et al., 2000b and Meade and Islam (2001). Meade emphasised several criteria for good practice in the use of growth curves for forecasting market development. These included:

• model validity: the product should be adoptable rather than consumable (i.e. there should be an obvious upper bound to the saturation level)

• statistical validity: the estimation of model parameters should be subject to significance tests

• demonstrable forecasting ability and validity: the forecast should be contextually plausible and the forecast should be accompanied by some measure of uncertainty, ideally a prediction interval.

As we will see, (a) it is still relatively easy to find applications where the model validity is dubious, (b) the application of significance tests is widespread but not ubiquitous, (c) when forecasting is included explicit discussion of uncertainty occurs in a minority of cases.

Baptista's review takes an economic viewpoint; he focuses on the diffusion of process between firms and the roles that geography and inter-firm networks play in knowledge transfer.

Mahajan, Muller and Bass offer a research agenda for the development of sounder theory for diffusion in a marketing context and more effective practice (this agenda included several topics that were currently underway). Their agenda included:

• increasing the understanding of the diffusion process at the level of the individual

• exploiting developments in hazard models as a means of incorporating marketing mix variables

• investigating the nature and effect of supply and distribution constraints

• modelling and predicting product take-off

• empirical comparisons with ‘other sales forecasting’ models.

Of these items, the empirical comparisons have received least attention. In this review, we shall look at modelling the diffusion of a single innovation in a single market; then the diffusion of an innovation in several (national) markets at the same time; then the diffusion of successive generations of the same innovative technology. The length of each section obviously depends on the amount of work done on the topic discussed; thus, as the latter topics are newer and less researched, the relevant sections are shorter. Within each of these topics, we shall look at issues of modelling including the introduction of explanatory variables, estimation and forecasting accuracy. The most often encountered diffusion models are described in the Appendix; we will refer to these models where necessary and keep further equations within the text to a minimum.