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Article Excerpt
Standard diffusion models capture social contagion only coarsely and do not allow one to operationalize different contagion mechanisms. Moreover, there is increasing skepticism about the importance of contagion and, as has long been known, S-shaped diffusion curves can also result from heterogeneity in the propensity to adopt. We present hypotheses about conditions under which specific contagion mechanisms and income heterogeneity are more pronounced, and test these hypotheses using a meta-analysis of the q/p ratio in applications of the Bass diffusion model. The ratio is positively associated with the Gini index of income inequality in a country, supporting the heterogeneity-in-thresholds interpretation. The ratio also varies as predicted by the Gamma-Shifted Gompertz diffusion model, but the evidence vanishes after controlling for national culture. As to contagion, the q/p ratio varies with the four Hofstede dimensions of national culture--for three of them in a direction consistent with the social contagion interpretation. Furthermore, products with competing standards have a higher q/p ratio, which is again consistent with the social contagion interpretation. Finally, we find effects of national culture only for products without competing standards, suggesting that technological effects and culturally moderated social contagion effects might not operate independently from each other.
Key words: diffusion of innovations; social contagion; income heterogeneity; national culture; meta-analysis
History: This paper was received July 30, 2003, and was with the authors 1 month for 1 revision; processed by Gary Lilien.
1. Introduction
How new products gain market acceptance has long been of great interest to marketers. It is commonly accepted that new product diffusion is often driven by social contagion, i.e., that actors' adoptions are a function of their exposure to other actors' knowledge, attitudes, or behaviors concerning the new product. Researchers have offered different theoretical accounts of social contagion, including social learning under uncertainty, social-normative pressures, competitive concerns, and performance network effects (Van den Bulte and Lilien 2001).
Although these contagion mechanisms are conceptually distinct, their expressions in diffusion data of a single innovation are often indistinguishable, making it impossible to identify the exact nature of the contagion at work. So, although diffusion models often describe new product diffusion patterns over time quite well, it is unclear what kind of contagion process, if any, is being captured in the equations. This has long frustrated marketing researchers (Gatignon and Robertson 1986, Solder and Tellis 1998, Parker 1994).
Some have noted an even more fundamental theoretical issue in diffusion research: S-shaped diffusion curves need not stem from social contagion at all but can result from heterogeneity in the intrinsic tendency to adopt. Many of the popular diffusion models can be derived mathematically from both contagion and heterogeneity assumptions (e.g., Bemmaor 1994, Chatterjee and Eliashberg 1990). Consequently, it is impossible to unambiguously interpret the model parameters of any single diffusion curve as reflecting social contagion or heterogeneity in the propensity to adopt.
The difficulty in identifying which of the many possible mechanisms is at work in the diffusion of a single innovation has led skeptics such as Stoneman (2002) to deem diffusion model parameters to be more informative as data summary devices than as evidence of any specific process. Although using model parameters as mere summary devices can lead to substantive insights (e.g., Bayus 1992, Griliches 1957, Van den Bulte 2000), the nature of the process matters for marketing strategy recommendations. For instance, a price penetration strategy might be optimal only when contagion exists: A low price can help to get the endogenous feedback process going and the firm can increase its price once the feedback momentum is strong enough (Horsky 1990). When the S-shaped diffusion curve stems only from heterogeneity in reservation prices, in contrast, this rationale for price penetration vanishes and skimming clearly seems the better strategy. Another strategy decision affected by the strength of contagion is whether to enter multiple markets sequentially or simultaneously. The benefits of sequential entry depend in part on the strength of contagion across markets (Kalish et al. 1995). Knowing that contagion is at work is not enough. The nature of the process also matters. Depending on the type of contagion that is at work, advertising and sales calls should convey product information and reduce perceived risk, emphasize social-normative expectations, or play on fear of being outpaced by more innovative competitors. Also, the decision on whom to focus one's early viral marketing efforts will depend on the nature of contagion. For social norms and social learning direct ties are important, and an astute marketer will focus on well-connected actors. This need not be a good choice when contagion is driven by competition for status (Burt 1987). So, it is important to know not only the shape of diffusion paths, but also what contagion process, if any, is at work.
The key idea underlying the present study is that, although fitting the popular Bass (1969) model to any single diffusion data series cannot empirically identify which process is at work, one can draw inferences from patterns of variation across multiple diffusion paths (compare Taibleson 1974). Specifically, while several contagion processes as well as heterogeneity can result in the Bass model and fit the diffusion path of any single innovation equally well, different mechanisms have different implications about how the q/p ratio will vary across multiple diffusion paths, such as the diffusion of the same product in different countries.
Our research strategy consists in developing hypotheses about conditions under which different contagion mechanisms and heterogeneity are more pronounced, and testing these hypotheses using a meta-analysis of the q/p ratio in applications of the Bass diffusion model to consumer durables. For heterogeneity, we assume that income is an important dimension, and develop hypotheses about the relationship between income heterogeneity and the shape of the diffusion curve as reflected in the q/p ratio. For social contagion, we develop hypotheses about the relationship between Hofstede's (2001) dimensions of national culture and the q/p ratio. Following work on technologically induced endogenous feedback, we also develop hypotheses about the relationship between the presence of competing standards and the q/p ratio. Through these hypotheses we are able to assess empirically the different types of mechanisms that might result in sigmoid diffusion curves.
Our contribution consists of six findings. First, the Gini index of income inequality, capturing the shape of the income distribution, is positively related to the q/p ratio capturing the shape of the diffusion curve. This is consistent with income threshold models of diffusion. Second, the q/p ratio varies as predicted by Bemmaor's (1994) Gamma-Shifted Gompertz (G/SG) model, assuming that the tendency to postpone adoption is inversely related to income. The evidence, however, vanishes once we control for national culture. Third, several methodological choices affect the estimated q/p ratio, increasing the risk of spurious evidence of contagion. Fourth, even after controlling for income heterogeneity and method artifacts, the q/p ratio varies systematically with the four Hofstede dimensions of national culture--for three of them in a direction consistent with the social contagion interpretation. Because the different dimensions of national culture are related to different contagion processes, our results also shed some light on the nature of contagion. Specifically, we find evidence consistent with contagion being fueled by both status concerns and social-normative pressures, but inconsistent with contagion being driven by social learning under uncertainty. Fifth, products with competing standards have a higher q/p ratio, which is again consistent with the social contagion interpretation. Sixth, the presence of competing standards drastically dampens the effects of culture and income inequality. This indicates that social contagion and the fear to adopt a losing technology do not operate independently from each other (Choi 1997).
Our study provides evidence on two fundamental issues in diffusion theory: the nature of contagion and the relevance of income heterogeneity. Because we analyze how diffusion trajectories vary as a function of the income distribution and national culture across 28 countries, we also provide new insights into international diffusion patterns.
We first discuss how diffusion through social contagion implies variations in the q/p ratio across national cultures and between products with and without competing standards, and then discuss how diffusion driven by heterogeneity implies variations in the same ratio as a function of the shape and scale of the income distribution. Next, we describe the data, analysis method, and results. The paper concludes with a discussion of implications and limitations.
2. Social Contagion
The contagion explanation for S-shaped diffusion curves has long dominated the marketing literature. The Bass (1969) model specifies the rate at which actors who have not adopted yet do so at time t (more precisely, in the time interval It, t + dt] where dt [right arrow] O) as r(t) = p + qF(t), where F(t) is the cumulative proportion of adopters in the population, parameter p captures the intrinsic tendency to adopt, and parameter q captures social contagion, be it coarsely. Because the proportion of the population that adopts at time t can be written as dF(t)/dt = r(t)[1 - F(t)], one obtains
(1) dF(t)/dt = [p + qF(t)][1 - F(t)].
Whereas this equation clearly conveys social contagion--F(t) affects future changes in F(t)--how F(t) varies over time is better reflected in the solution of the differential Equation (1). Assuming that one starts with zero adoptions (F(0) = 0), the solution is
(2) F(t) = [1 - [e.sup.-(p+q)t]/[1 + (q/p)[e.sup.-(p+q)t]. (2)
The curve is S-shaped when q > p, and more pronouncedly so as the q/p ratio increases. This ratio summarizes the shape of the curve and can be interpreted as a shape parameter (Chatterjee and Eliashberg 1990).
The model does not specify the nature of the contagion process, such as social learning under uncertainty, social-normative pressures, competitive concerns, or performance network effects. Additional theoretical detail must be provided for one to obtain refutable hypotheses pertaining to each process separately. One can do so by specifying observable contingency factors for each type of contagion. Our research strategy therefore consists in testing, not the contagion explanation in general, but the narrower claim that culture and competing standards affect diffusion in a particular way if contagion is indeed a driver. Because the heterogeneity models we investigate provide testable implications for q/p but not for p and q separately we limit our hypotheses about social contagion to the same ratio which, according to the contagion interpretation, reflects the relative importance of imitative and innovative tendencies.
2.1. Social Contagion and National Culture
Since their introduction in 1980, Hofstede's (2001) four dimensions of national culture have become important elements in studying consumer behavior across countries. Several researchers have recognized the value of these dimensions when seeking to explain adoption behavior (Jain and Maesincee 1998, Sundqvist et al. 2004, Steenkamp et al. 1999, Tellis et al. 2003, Yaveroglu and Donthu 2002). Building on prior research and introducing some additional arguments from sociology, we hypothesize how the q/p ratio should vary across these four dimensions if social contagion affects diffusion. The hypothesis relating individualism to q/p is based on social-normative pressure, and that relating uncertainty avoidance to q/p is based on social learning under uncertainty. The...
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