Knowledge that Transforms

People are frequently exposed to potentially attractive events that are subsequently and unexpectedly reversed and to potentially painful events, which are also unexpectedly reversed. In the process of being returned to the initial asset position, does the sequence in which the positive and negative events occur matter? This issue of the combined effect of pleasurable and painful stimuli has received scant theoretical or empirical attention. We attempt to fill this lacuna in the literature by studying the retrospective evaluation of surprises that return individuals to their original economic state. Although such surprises do not change an individual's original economic state, we argue that the individual's psychological state changes, and the final affective state is, among other things, a function of the sequence in which the events occur. From a theoretical standpoint, several perspectives can be brought to bear on the issue. For instance, one reading of mental accounting, based on prospect theory's value function, would predict that losses should dominate gains, and therefore, regardless of sequence, people should be unhappy when exposed to two economically equivalent outcomes of different signs. Conversely, the literature on intertemporal choice would suggest that a series that ends on an up note is preferred to a series that ends on a down note, because people like to defer gratification so that they may savor positive outcomes. Similarly, people apparently have a preference for "happy endings." Finally, the extant literature on "recency effects" would predict that the last event in a series should have a disproportionate influence on overall affect. Our model relies on a shift in the reference point to explain how a surprising reversal of an event will lead to a nonzero evaluation of the sequence. We suggest that people's reference points shift immediately but imperfectly after a stimulus is presented. Intuitively, this implies that the first stimulus will shift the reference point in its direction, as a result of which the evaluation of a sequence of events in which an initial event is unexpectedly reversed will be more favorable if the first event is a loss than if it is a gain. This model captures the unanticipated nature of the second event (i.e., the surprise element) by allowing the first event to move the reference point. Consequently, by the time the next event occurs the reference point has been updated, as a result of which the zero economic outcome of the sequence yields nonzero utility. We further posit that the magnitude of the reference point shift should be affected by the time elapsed between the two stimuli. Specifically, the reference point shifts gradually with time, until it is fully updated. Consequently, the final affective state of the sequence is also a function of the temporal distance between the two events. The main predictions of the model were empirically supported first in a survey using a mall-intercept sample. Subsequently, we conducted a study of student subjects involving a coin-tossing game in which real money was at stake and in which subjects in one condition experienced the second outcome after a two-day delay. Our results from this second study supported the model's prediction regarding the impact of the elapsed time between the events. The experimental tasks involved surprising reversals of initial outcomes, thus ensuring that "savoring/dread" types of explanations (which require that subjects anticipate the second event) could not be operating. Finally, in a series of three follow-up studies, we tested the claim that the magnitude of outcomes would have an impact on observed affect, and consistent with our theory and contrary to recency predictions, we observed similar results across different magnitudes. While theoretically interesting, we should also note that our research is of potential pragmatic significance. People's reactions to a series of events is of considerable interest to marketers desirous of generating enhanced attitude, affect, purchase intention, and the like without offering economic inducements such as rebates, coupons, or other costly discounts. Additionally, public policy officials may be interested in protecting people from being manipulated into purchasing a product simply because of changes in the sequence in which a series of offers is made by the merchant.

We examine the retailer's store brand positioning problem. Our game-theoretic model helps us identify a set of conditions under which the optimal strategy for the retailer is to position the store brand as close as possible to the stronger national brand. In three empirical studies, we examined whether market data are consistent with some of the implications of our model. In the first study, using observational data from two US supermarket chains, we found that store brands are more likely to target stronger national brands. Our second study estimated cross-price effects in 19 product categories, and found that only in categories with high-quality store brands, store brand and the leading national brand compete more intensely with each other than with the secondary national brand. In a third product perception study, we found that although explicit targeting by store brands influenced consumer perceptions of physical similarity, it had no influence on consumers' perceptions of overall or product quality similarity. While it appears that retailers do follow a positioning strategy consistent with our model, it changes buying behavior in the intended fashion only if the store brand offers quality comparable to the leading national brands.

Assessment of accurate market size and early adoption patterns is essential to strategic decision making of managers involved in new-product launches. This article proposes methodology that explains changes in parameter estimates of the Bass model, p (coefficient of innovation), q (coefficient of imitation), and c (market penetration rate) by direction of "extra-Bass" skew in the data, or equivalently, by underlying heterogeneity of the population. This research shows significantly opposite patterns of these parameter estimates, depending on skew of the diffusion curve detected by a generalized model, i.e., the gamma/shifted Gompertz (G/SG) model, which embeds the Bass model as a special case. The G/SG model originally presented in Bemmaor (1994) is based on two assumptions: (1) Individual-level times to first purchase are distributed shifted Gompertz and (2) individual-level propensity to buy follows a gamma distribution across the population. We assume that the scale parameter of the shifted Gompertz distribution is constant across consumers. The advantage the G/SG model has over alternative diffusion models such as the nonuniform influence model is that its cumulative distribution function takes a closed-form expression. In line with Van den Bulte and Lilien (1997), we analyze these opposite patterns from simulated data using the G/SG model as the true model and 12 real adoption data sets. The patterns are: (1) as the level of censoring decreases, the estimates of p and c decrease and those of q increase when data exhibit more right skew than the Bass model and (2) the estimates of p and c increase and those of q decrease when data exhibit more left skew than the Bass model. For the simulated data, we manipulated four dimensions: (1) "extra-Bass" skew in the data, (2) ratio q/p, (3) speed of diffusion, and (4) error variance. Both results of the simulated data and the real adoption data sets confirm the existence of two opposite patterns of parameter estimates of the Bass model depending on "extra-Bass" skew. When the model is correctly specified with simulated data, estimates of c increase and those of q decrease for both the Bass and the G/SG models. The estimates of p increase as one adds data points only for the G/SG model. No significant tendency in parameter estimates of p was detected for the Bass model. As for ill-conditioning issues, systematic changes in the parameter estimates of the G/SG model can be substantially larger in some cases than those obtained with the Bass model, even though the data were generated by taking the G/SG model as the true one. Therefore, model complexity can aggravate the tendency for parameters to change systematically as one adds data points. The forecasting results from the simulated data show the supremacy of the G/SG model. It provides more accurate results than the Bass model in the one-step ahead, two-step ahead, and three-step ahead forecasts. With the real data set, the G/SG model provides more accurate one-step ahead forecasts than the Bass model, but the model's forecasting performance deteriorates more rapidly than the Bass model when one shifts to two-step ahead and three-step ahead forecasts. The systematic changes in parameter estimates are larger for the more complex model. Our research shows that the G/SG model is a flexible model used to analyze the systematic changes in parameter estimates when specification error and ill-conditioning occur. As our findings incorporate two possible types of parameter estimate bias, compared to the previous single-direction view, they can provide essential information to enhance forecasting accuracy of products and services using new technological innovations. Our forecasting results of simulated and real adoption data raise a question about the optimal horizon of forecasting in applying flexible models of diffusion. The G/SG model also provides grounds to investigate jointly "the speed of takeoff" and "the diffusion speed after takeoff".