A Flexible Class of Purchase Incidence Models

Purchase incidence models estimated on household scanner panel data typically assume the household's decision interval to be one week. However, it is well known in the econometrics literature that discrete-time models are highly sensitive to the assumed time interval of decision-making. In this study we investigate the consequences of endogenizing the household's decision interval, instead of restricting it to be one week. We characterize the household's random utility maximization problem, and therefore its purchase likelihood function, as a function of the household's decision interval. Such a flexible purchase incidence model is then used to explicitly estimate households' decision intervals in addition to their response to marketing activity and their baseline hazard functions. The proposed model of purchase incidence not only nests traditionally used choice models (such as the binary logit model) and hazard models (such as the discrete hazard model), but also allows for a gamut of more flexible parametric specifications. We estimate the proposed model across four category-level scanner panel datasets and find that the traditional assumption of restricting the household's decision interval to be one week may be too restrictive. We find that households are not only quite heterogeneous in their decision intervals but often have decision intervals longer than a week. From a managerial perspective, we show that estimated price elasticities are systematically understated if one does not allow for the effects of decision intervals. We demonstrate, using a fourth product category, that the results obtained from the category-level analyses generalize to the context of a full model of purchase incidence and brand choice.Decision intervals, Purchase incidence models, Choice models, Logit, Hazard ,

Multinational Diffusion Models: An Alternative Framework

The literature on cross-national diffusion models is gaining increased importance today due to the needs of present day managers. New product sales growth in a given nation or society is affected by many factors (Rogers 1995), and of these, sociocontagion (or word of mouth) has been found to be the most important factor that characterizes the diffusion process (Bass 1969, Moore 1995). Hence, it is interesting and perhaps challenging to analyze what would happen if a new product diffuses in parallel in two neighboring but culturally different countries. Not only will we expect the diffusion process in the two countries to be different, but we will also expect some interaction among them, especially if the two societies mingle with each other. There are two streams of research in cross-national diffusion. The first type focuses on exploring the differences between diffusion processes in two countries and finding out whether those differences can be attributed to social and cultural differences between the countries involved. Examples of this type of research are found in Takada and Jain (1991), Gatignon et al. (1989), Helsen et al. (1993), and Kumar et al. (1998). These studies did find some relationship between the cultural differences of the countries studied and the differences in the diffusion process. The second stream of research focuses on modeling explicitly the interaction between the diffusion processes in two countries. The interaction is typically captured through lead-lag effect (Eliashberg and Helsen 1996, Kalish et al. 1995), where the sales process in the lead country (i.e., the country where the product was first introduced) is modeled to affect the sales process in the lag country (i.e., the country where the product was introduced a few years later). Another method to study the interaction among the diffusion processes in two countries was suggested by Putsis et al. (1997), who used a “mixing model” to empirically explore the existence of such interactions. These studies basically observed that, when a new product is introduced early in one country and with a time lag in subsequent countries, the consumers in the lag countries learn about the product from the lead country adopters, resulting in a faster diffusion rate in the lag countries. Ganesh and Kumar (1996) formulized this effect as the learning effect and, subsequently, Ganesh et al. (1997) found this learning effect to be influenced by country-specific factors (cultural similarity, economic similarity, and time lag elapsed between the lead and the lag countries) and product-specific factors (continuous vs. discontinuous innovation and the presence or absence of a standardized technology). A careful analysis of the extant literature on the second stream of research would reveal that neither the learning effect model nor the mixing model can be modified to accommodate the other model. Our contribution to the literature exactly addresses this point. In this paper, an alternative framework is proposed that has two unique features. First, the framework is flexible enough to not only account for the lead country affecting the lag countries and vice versa, but also to accommodate the simultaneous interaction among countries in explaining the diffusion processes in the countries concerned. Using multiple product categories and a variety of new product introduction situations, we empirically demonstrate the flexibility and efficiency of our proposed framework. We found strong evidence of all types of interactions, namely, lead lag, lag lead, and simultaneous, which evidence suggests that one cannot afford to omit any of the interactions. The second unique feature of our paper is the estimation procedure that we used. Because statistical estimation of a dynamic process that includes lead-lag, lag-lead, and simultaneous types of causality within a single framework is not straightforward, we suggest an iterative estimation procedure for the estimation. This new procedure not only proved to be flexible in accommodating different types of interaction, but also converged rather quickly in all of the cases that we empirically tested. Noting that the statistical properties of these estimators are not generally available, we carried out a simulation exercise that clearly revealed the efficiency of the proposed estimation procedure. After analyzing the interaction, we went further and showed that the magnitude of the cross-national influences is affected by certain country-specific and product-specific factors. The flexibility of the proposed method over the existing methods is demonstrated through obtaining superior forecasts with the proposed method. Several interesting insights for managers concerned with formulating international marketing strategies are offered.Multinational Diffusion, Iterative Estimation, Lead-Lag, Lag-Lead, and Simultaneous Effects, International Marketing Strategy

Evolutionary Estimation of Macro-Level Diffusion Models Using Genetic Algorithms: An Alternative to Nonlinear Least Squares

In this paper, we provide theoretical arguments and empirical evidence for how Genetic Algorithms (GA) can be used for efficient estimation of macro-level diffusion models. Using simulations we find that GA and Sequential Search-Based-Nonlinear Least Squares (SSB-NLS) provide comparable parameter estimates when the data including peak sales are being used, for a range of error variances, and true parameter values commonly encountered in the literature. From empirical analyses we find that the forecasting performance of the GA estimates is better than that of SSB-NLS, Augmented Filter, Hierarchical Bayes, and Kalman Filter when only pre-peak sales data is available for estimation. When sales data until the peak time period are available for estimation, SSB-NLS is able to obtain parameter estimates when the starting values provided are the estimates from using GA. The estimates from GA are not biased and do not change in a systematic fashion when post-peak sales data are used, whereas the estimates from SSB-NLS are biased and change in a systematic fashion. Summarizing, we find that GA may be better suited for diffusion model estimation under the three conditions where SSB-NLS has been found to have problems.Bass model, starting values, systematic change and bias, closed-form solution, nonlinear least squares, genetic algorithms, pre-peak sales forecasting

Modeling the demand and supply in a new B2B-upstream market using a knowledge updating process

Business-to-Business (B2B) services companies invest heavily in acquiring very expensive assets that they hire out to serve their clients (e.g. UPS buys huge warehouses and hires them out to companies), and hence they engage in careful long-term planning and forecasting, especially when it concerns a new market. It is interesting to note that the client-firms, on the other hand, decide to hire those assets based mostly on the prevailing short-term market forces. Hence, it is important for the companies which provide the assets for hire to also build the prevailing short-term market trends into their long-term forecasting and planning. In this paper, we develop a model for tracking these two simultaneously evolving and interacting patterns, namely the asset-availability (i.e. supply) and utilization (i.e. demand) patterns, in order to better understand the underlying processes, and thereby provide a basis for better forecasting. We test our models using three sets of data collected from the oil drilling industry, and find the proposed model to provide a good fit and forecasting efficiency.Marketing B2B service Knowledge updating Demand and supply Oil drilling

Why the Bass Model Fits without Decision Variables

Over a large number of new products and technological innovations, the Bass diffusion model (Bass 1969) describes the empirical adoption curve quite well. In this study, we generalize the Bass model to include decision variables such as price and advertising. The generalized model reduces to the Bass model as a special case and explains why the Bass model works so well without including decision variables. We compare our generalized Bass model to other approaches from the literature for including decision variables into diffusion models, and our results provide both theoretical and empirical support for the generalized Bass model. We also show how our generalized Bass model can be used for product planning purposes.diffusion, marketing mix, new product research, pricing research