FormalPara Definition

Diffusion is the process by which innovations spread across potential adopters over time. Adoption takes time and may take place at different levels of aggregation: within a firm (i.e., intra-firm diffusion), at the industry level (i.e., inter-firm diffusion), at the economy level (i.e., inter-industry diffusion).

The Main Stylized Fact

The main stylized fact about innovation diffusion is that the dynamics over time of the adoption of an innovative product (i.e., the percentage of market penetration) is S-shaped, indicating: (1) an initial slow increase in the rate of diffusion; (2) a phase of acceleration; (3) a subsequent phase in which market penetration still increases but a decreasing rate; (4) a final phase in which the curve flattens out (Stoneman 2002) (Fig. 1).

Innovation Diffusion, Fig. 1
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The S-shaped innovation diffusion curve

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Explanations of the Pattern of Diffusion

Several explanations of this S-shaped pattern have been proposed, generating alternative approaches to innovation diffusion.

The Spread of Information

The Static ‘epidemic’ Approach: Information from Adopters

According to this approach, the major constraint to innovation diffusion is the lack of information about the existence of the innovation itself. The adoption mechanism is the spread of information about the existence of the innovation, which is made available by new adopters to potential adopters who, in turn, contribute to spreading the information further by becoming adopters. This is the so-called ‘contagion model’ (Griliches 1957; Mansfield 1961). In this context, diffusion is understood as the outcome of a sequence of adoptions which has an upper limit (equilibrium) constituted by the total number of adopters within the population. While the basic approach assumes that diffusion depends on demonstration effects and learning from the experience of others, interpersonal contact (i.e., word of mouth) is generally assumed to be the mechanism for spreading information. However, in many cases, information may reach potential adopters through other channels.

Diversity in the Sources of Information

One series of contributions has focused on the role of the diversity in the sources of information. These approaches (Bass 1969; Lekvall and Wahlbin 1973) distinguish between internal and external sources. Internal information sources are those concerned with the transmission of information through social interaction and/or the mere observation of the usage of a new product. They are dependent on the mass of previous adopters. External information sources are those from ‘public and constant’ sources such as mass media, salesmen and specialized trade press. These sources convey information which is not necessarily dependent on the experience of previous adopters but may instead reach all the potential adopters uniformly.

User Learning and the ‘dynamic’ Epidemic Approach

Epidemic models are static to the extent that they assume both the absence of further improvements in the innovations once introduced in the market and the existence of a fixed population of adopters (Thirtle and Ruttan 1987). Mansfield (1968) elaborates on the basic contagion model to investigate the speed of response of individual adopters to the appearance of an innovation. In his model, learning plays an important role in determining the timing of adoption. Learning impinges upon the extent of use of the innovation, which reduces, over time, the overall uncertainty about the fixed profitability of the new technology and leads to an increase in the proportion of new adopters. The emphasis on risk, uncertainty and learning is the main driving force behind diffusion.

Changes in Expected Benefits

Reduction of uncertainty alone can induce a self-propagating pattern of diffusion typical of epidemic models only when the expected profitability of the new technology is not changing. However, if adopters change their estimates of expected benefits as they collect information, it is the interplay between changing estimates and reduction of uncertainty rather than the latter effect alone which influences the decision to adopt. This interplay is the focus of the so-called mean-variance approach to innovation diffusion (Stoneman 1981), which represents adoption as a portfolio choice based upon an evaluation of both the expected returns and the variance of innovation.

The Heterogeneity of Adopters

The equilibrium approach to innovation diffusion assumes that adopters have perfect information about both the existence and the nature of the innovation. As a consequence, the spread of information to potential users cannot be the mechanism explaining heterogeneity of diffusion rates. Two broad types of equilibrium models can be identified, according to the mechanism they embody.

Heterogeneity in Some Objective Characteristics

Probit models assume that potential adopters differ according to some ‘objective’ characteristics, which directly influence the benefits deriving from innovation adoption (David 1966; Hannan and McDowell 1984; Colombo and Mosconi 1995). The basic characteristic of probit models is the possibility of identifying each potential adopter by means of an ‘ordering’ variable (e.g., a firm’s size) which governs the adoption decision. Adoption occurs if, at a certain point in time, the individual value of this variable exceeds a critical threshold level. Within this framework, the probability to observe an adoption at a certain point in time can be determined as the probability to find a potential adopter whose level of the variable exceeds the critical level. Two crucial assumptions are made that both the distribution of the variable and the threshold level over the population of potential adopters are independent of each other. The main consequence of these assumptions is that the applicability of probit models is restricted to innovations which do not entail the possibility of expanding productive capacity far beyond the existing (pre-adoption) level, and which impact mainly on the costs and not on the benefits that adopters may receive from the exploitation of the innovation itself.

Heterogeneity and Changes in the Benefits and Cost of Adoption

Stock models address this limitation. Stock models assume that different rates of diffusion across different adopters or differences in the individual propensity derive from differentials in the benefits that the adoption of the innovation has created through its impact on the price of the final product (Reinganum 1981). For stock models the timing of adoption may be influenced by the benefits that the innovation will generate ex post. When such dependence is acknowledged, provided that a suitable specification for the future pattern of adoption costs is put forward, the sequence of adoption is influenced by the intertemporal evaluation of the pattern of costs vis-à-vis the speed of change in the benefits from adoption. When both costs and benefits of adoption fall over time but benefits fall faster than costs, it may be in the interest of potential adopters to wait for adoption costs to decrease and let their rivals precede them in adoption. Stock models employ game theory to model this strategic interaction as a ‘waiting contest’ among the potential adopters.

Improvements in the Original Innovation or Truncated Diffusion Processes

The basic versions of these models have been extended to cases in which innovations undergo a series of improvements which impact on the timing of adoption either through expectations of further improvements and/or price reductions (Rosenberg 1976; Balcer and Lippman 1984) or through changes in the supply of innovation (Stoneman and Ireland 1983). Other models take into account the emergence of a radically new product that substitutes the product that is undergoing diffusion, and therefore truncates the diffusion curve.

Evolutionary Models of Diffusion

Evolutionary models of diffusion are disequilibrium ones. They are usually divided into two groups: selection models and density-dependent models. The two types differ in the determinants of adoption behaviour and in the impact on individual decisions of the possibility that the available best practice technique may change over time. Selection models take technological change explicitly into account and explain diffusion as a result of a process in which innovators displace traditional firms as they are progressively selected out of the market (Silverberg et al. 1988; Metcalfe 1994). Density-dependent models are concerned with the issue of payoff interdependencies (i.e., network effects) which affect the decisions of adopters (Farrell and Saloner 1985; Katz and Shapiro 1986; Arthur 1989).

See Also