Endogeneity and Heterogeneity in a Probit Demand Model: Estimation Using Aggregate Data

The Influence of Consumer Goals and Marketing Activities on Product Bundling

Demand analysis is a key element of economics. It has the attractive feature of being important in theory as well as in application. Its purpose is to explain consumer behavior in the market place, i.e., demand analysis is designed to explain what commodities the consumer will purchase and in what quantities and how the consumer can be expected to respond to changes in commodity prices and income. Since the parameters of demand functions can be extremely valuable for both public and private decision makers, it is important to obtain concise and accurate estimates of them. Public policy makers must have reliable estimates of demand parameters for the scientific study of economic growth and development and for the rational formulation of economic policies. Farm policies directed towards commodity programs like price supports, production controls, and payment programs for the major farm crops, would no doubt benefit from more accurate information in regard to market demand functions. Private business models for forecasting future markets, planning merchandising and advertising, and devising promotional programs can be improved with demand analysis. Traditionally, most of the estimates of demand parameters in empirical analysis were based on single equation least squares approach. Theoretically, however, the estimation of demand parameters calls for the complete set of demand functions to be considered as a whole. One of the major reasons for the relatively few studies devoted to the estimation of the full set of demand parameters is the existence of a gap between demand theory and empirical analysis, i.e., the classical theory of consumer behavior has not provided workable relationships for estimation purposes due to the fact that available data is insufficient for the estimation of a large number of the required parameters. Recent studies of the theory of consumer behavior have provided a number of empirically useful hypotheses concerning the separability of the consumers utility functions. These hypotheses imply certain empirically meaningful conditions on the parameters of demand functions. More specifically, these conditions reduce the number of parameters to be estimated in a complete system of demand functions and thus make estimation of all the parameters more feasible. In this study an attempt is made to examine consumer behavior in the United States for the period 1929-1969, by assuming an additive preference specification and by using a complete system of demand functions. Briefly, the plan of this study is as follows: a historical note on demand analysis is given below. In Chapter II a review of the classical theory of consumer demand is presented. The assumptions of additivity and separability are then introduced and examined in terms of their consequences for estimation. Chapter III provides a statistical model for obtaining estimates of demand parameters under the assumption of an additive preference specification. Chapters IV, V, and VI contain the main results of this study. In Chapter IV estimates of demand elasticities (price and income) for major commodity groups, e.g., food, clothing, etc. are reported. Chapter V contains estimates of price and income elasticities of demand for food and non-food commodity groups. The statistical information available is then used to obtain estimates of demand elasticities (price and income) for nine food groups. The empirical evidence which suggests that the demand for food at retail level is becoming more elastic is examined in Chapter VI. Concluding remarks are offered in Chapter VII.

In this paper we develop a general class of dynamic brand choice models, called Lightning Bolt (LB) models, which are consistent with the theory of random utility maximization of consumer choice behavior. The underlying random utility process is Markov, and the inter-temporal evolution of the (utility-maximizing) brand choice process is also Markov. The models permit parsimonious parameterizations of the random utility process in brand choices with the resulting switching probabilities being functionally related to explanatory variables. The model allows for structural state dependence (feedback), habit persistence (inertia), and unobserved heterogeneity. The theoretical development shows that several well known stochastic brand choice models can be deduced from random utility maximization theory. From a managerial perspective, the usefulness of the proposed model stems from its ability to separate out the effects of habits, state dependence and heterogeneity. Strong state dependence effects imply incentives for inducing trial of a brand (e.g., product sampling). In contrast with state dependence, a strong habit persistence effect may be indicative of buyer behavior where inducement of trial of a different brand may not be sufficient to maintain a (sustained) defection of the consumer from the habitually purchased brand to the trial brand. Failure to distinguish between these two effects has important implications. For example, a model that only accounts for state dependence effects would, in the presence of only habit persistence, incorrectly attribute it to state dependence. Based on this the manager could decide to embark on an expensive sampling program that might prove ineffective due to the absence of state dependence. It is also important to distinguish between the effects of unobserved heterogeneity and state dependence. In the absence of true state dependence, failing to account for unobservable variations across households (such as differences in price sensitivities), results in the temporally persistent unobservable elements showing up as state dependence in the model. Hence, a manager may incorrectly opt for sampling as the appropriate marketing action, whereas, a couponing or price promotion strategy should have been preferred. We estimate the model parameters using the AC Nielsen household scanner panel data set on catsup purchases. Further, we investigate empirical techniques for overcoming the “initial conditions” problem that affects many dynamic models of brand choice. Through simulation analysis using the estimated parameters, we show that the calculated profitability of a promotion must take into account the multi-period impact due to state dependence. Further, we demonstrate how ignoring heterogeneity can result in spurious state dependence, thereby making marketing tactics such as product sampling appear far more attractive than they actually are. Specifically, the model that accounts only for habit persistence and state dependence effects predicts a share increase of 2.4% points through sampling for one of the brands in the empirical analysis. Once the effects of unobserved heterogeneity are accounted for, however, this number drops precipitously to 0.3%. While even this low number might fulfill the objectives of the brand manager, it ensures that expectations are not eight times that number. It is important to note that this paper is a first attempt at analyzing the three fundamental dimensions of dynamic brand choice behavior. Our formulation represents a “reduced form” approach as opposed to a “structural” approach. Other limitations of the model include our focus on time-invariant choice sets. Extensions of the model to situations where choice sets vary over time are possible, but are difficult. Another limitation is the dependence on multivariate extreme value distributions. An alternative would be to use multivariate normal distributions, i.e., a probit-like structure which has certain useful properties. A comparison of the two approaches would be useful. Empirical extensions of the model to allow for higher-order processes and nested logit type model structures could also be fruitful. Explicitly incorporating variety-seeking behavior in the model would further enrich the theoretical framework proposed in this paper.

Patterns of customer purchases are often modeled as discrete behavioral events following some probability law. These stochastic models have been applied separately to the phenomena of product class purchase incidence and brand choice (conditional on the products being purchased). Most of these models are probability mixture models where the parameters of an individual customer model vary across the population according to some distribution. This paper proposes a simple model of purchase behavior at the individual level, Poisson (λ) product purchases and Bernoulli (p) brand choices, so that λ and p characterise each customer. However, λ and p may vary jointly across the population in an arbitrary fashion. Therefore, purchase incidence and brand choice are treated together making no assumptions about the dependence between them. This generality is obtained at the cost of efficiency but enables us to focus on the individual behavior. Estimators (with known asymptotic properties) are developed for predicting future purchasing behavior of individuals conditional on their past purchasing behavior. These predictions of future purchases, at brand and product levels, are of interest to marketing managers. For example, what is the expected number of brand (or product) purchases in period 2 for the group of customers that made x brand and n product purchases in period 1? Apart from the basic insights provided by such predictions, they are particularly useful in evaluating the impact of marketing efforts. The model and the estimation results are applied to a frequently purchased product and compared with other stochastic approaches. While this paper focuses on buying behavior, the model is applicable to accidents, direct mail purchases and other random events.

Community preferences for deriving aggregate consumption de- mand has been used in international trade theory for many years. Authors like Samuelson [12], Gorman [5], Muellbauer [8], Milne [7], and others, have investigated the problem: under what conditions can individual preferences be aggregated so that there exists a community preference map from which an aggregate de- mand function can be derived. Eisenberg [3] has shown that if the individuals' preferences are homothetic and the distribution of income is fixed, then the aggregate demand function can be derived from a homogeneous and concave utility function. In relationship to E i s e n b e rg's results, Chipman [1] published an article demonstrating that also in terms of the integrability theory, using an approach pioneered by Samu- elson and perfected by Hurwicz and Uzawa, the aggregation of individual demand functions is possible so that the community de- mand function acts as if it were derivable from a single preference ordering. As a basic assumption, Chipman also requires that the consumers' preferences are homothetic. This paper is concerned with the aggregation of individual de- mand functions in terms of the revealed preference analysis. Based on hypotheses according to Uzawa [11], we want to show that if consumers' demand functions are linearly homogeneous in income

PurposeThis study evidences the influence that sales promotion has on brand choice behaviour. Establishments wish to influence consumers' buying behaviour, and thus they launch strong promotional campaigns or introduce changes in their price policies, among other actions. However, they are not always capable of achieving their goal, since, although they may reach their objective in the short term, when the longer term is considered there are undesirable consumer actions.Design/methodology/approachThe problem of consumer brand choice can be adequately described with logit models that allow the use of discrete dependent variables. The probability that the consumer chooses a brand depends directly on the capacity of satisfaction that the brand holds for him/her. In this case, the dependent variable is the brand, and the independent variables are price, reference price, losses and gains, and the different types or techniques of sales promotion. With the aim of obtaining the necessary information for the present study, a regional consumer panel was used.FindingsThe results show that it is necessary to consider the product's promotional state at the moment of purchase as an explanatory element of the process. Promotion is a tool that can help manufacturers and/or retailers in the achievement of their objectives (try the brand, help to decide what brand to buy, etc.). Immediate price reduction is the technique that exerts greatest influence on the brand choice process. It is possible that the consumer perceives a promotion, for example, coupons or rebates, but does not modify his or her behaviour. In this case, manufacturers and/or retailers will be investing their resources in promotional actions that do not have any effect on the consumer.Originality/valuePresents a regional consumer panel that has been elaborated and planned by the authors. Because of this, the information collected is just what was necessary for this study. On the other hand, the paper shows that is very important to know the consumer's preferences and the actions that influence his or her behaviour. Considering the results, it seems that promotions based on price have the greatest effectiveness.

Retail research has highlighted how the presence of others can affect consumers' brand evaluations, purchase intentions, and choice behavior. This field study investigated whether the presence (vs. absence) of peers and other consumers, respectively, could influence consumers' propensity to purchase popular brands (i.e., a market leader) within a given product category. Consumers at a supermarket were observed when standing in front of a spice shelf and their choices were analyzed as a function of whether they shopped alone or in the presence of peers versus other consumers. The results revealed that peer presence, but not the mere presence of other consumers, increased consumers' inclination to make popular brand choices, and that this effect was mediated by their stated familiarity with the chosen brand. As such, peer presence seems to increase consumers’ reliance on heuristics and the accessibility of concepts linked to popularity, leading to congruent popular brand choices. Moreover, consumers shopping in the presence of others generally took a longer time before choosing a brand and touched slightly more products in the presence of other consumers. Taken together, these results contribute to theory refinement in social influence from ecologically valid conditions and offer a set of implications for companies, store managers, and people working in the food industry.

The authors examine the long-term effects of promotion and advertising on consumers’ brand choice behavior. They use 8 1/4 years of panel data for a frequently purchased packaged good to address two questions: (1) Do consumers’ responses to marketing mix variables, such as price, change over a long period of time? (2) If yes, are these changes associated with changes in manufacturers’ advertising and retailers’ promotional policies? Using these results, the authors draw implications for manufacturers’ pricing, advertising, and promotion policies. The authors use a two-stage approach, which permits them to assess the medium-term (quarterly) effects of advertising and promotion as well as their long-term (i.e., over an infinite horizon) effects. Their results are consistent with the hypotheses that consumers become more price and promotion sensitive over time because of reduced advertising and increased promotions.

As populations around the world age, brand choice behaviour by older customers becomes an increasingly important issue for marketers. This is especially the case in Japan, which has the largest older customer segment as a proportion of the population of any country. Our study measures brand choice behaviour of the older customer segment in Japan in fast-moving consumer goods categories. We employ an 11-point purchase probability scale, the Juster, to calculate brand performance measures such as penetrations, buying frequency and sole buying for three age-based customer segments. The Juster output is used as input into a mathematical model, the Dirichlet, for benchmarking the brand performance measures. The findings here reveal new insights into the brand purchase behaviour of older customers. There are more similarities than differences between the brand purchase of younger and older customers in most categories analysed here. The results have practical implications for understanding and creating appropriate marketing strategies for the older customer segment. Our study also demonstrates a novel method for analysis of brand choice data collected via a survey instrument, as compared to the traditional consumer panel data. The research framework in our study is recommended for further empirical research in other regions where demographic changes are presenting challenges to marketers, and where panel data are often not easy to obtain.

We propose a structural model to investigate the impact of forgetting on consumers' brand choice decisions in frequently purchased products. Forgetting results in consumers imperfectly recalling their prior brand evaluations when making a purchase decision in the category. We conceptualize the imperfect recall by positing that consumers recall their prior evaluations with noise. Based on prior research in the behavioral area, we characterize the extent of forgetting as an increasing and concave function of time. Our framework generates analytical results on the impact of forgetting on consumers' brand evaluations and their consequent purchase behavior. We calibrate our model using scanner panel data for liquid detergents. Furthermore, we obtain insights into the consumers' extent of forgetting in the category, extent of learning, predicted price elasticities and implications on state dependence and habit persistence. Our results underscore the importance of modeling consumers' ability to recall only imperfectly.

We propose a model to analyze the impact of advertising media plans and point-of-purchase marketing variables on a brand's market performance. Our model integrates brand choice, purchase incidence, and exposure behavior within a nonstationary stochastic framework. Moreover, it considers various aspects of consumer heterogeneity including individual differences in loyalty levels, purchase rates, and exposure probabilities for a population of consumers. The integrated model provides a relationship of advertising exposures from media plans, and other marketing variables, to measures of a brand's performance that include market share, penetration and depth of repeat patterns over time. In this paper, we focus on a multi-brand model formulation and stress its application to the analysis of advertising media plans. Based on single-source UPC scanner panel data for a frequently purchased product category, we provide an empirical test of the model. In this context, our analyses show that the model provides a good fit to the empirical data as well as accurate forecasts in hold-out predictive tests.

Artificial neural networks can be seen as nonlinear generalizations of conventional Statistical or econometric models. This paper studies goodness-of-fit and forecasting Performance of neural networks with one hidden layer. The central dependent variables regarded are purchase incidence and brand choice within the context of consumer non-durables. The connectionist models are compared to the well-known NBD and conditional logit models. Models are estimated on the basis of household panel data. On the whole, the neural models achieve better results than their conventional counterparts. Influence of predictors is interpreted using a distribution of elasticities or change rates.

This paper examines demand elasticities using an integrated framework proposed by Hanemann [Hanemann, M. W. 1984. Discrete/continuous models of consumer demand. Econometrica 52(3) 541–561], which models the incidence, brand choice, and quantity decisions of a consumer as an outcome of her utility maximization subject to budget constraints. Although the Hanemann framework has been the mainstay of earlier efforts to examine these decisions jointly, empirical researchers who have used the it to study purchase behavior have often found that the quantity elasticities are around −1, regardless of the brand or category. We attempt to uncover the underlying reasons for this finding and propose approaches to get as close to the “true” quantity elasticities as possible. We do this by (i) analytically demonstrating how assumptions on the distribution of the brand-specific econometrician's errors imply certain restrictions that in turn force quantity elasticities to −1, (ii) discussing how these restrictions can be alleviated by considering a suitable specification of unobserved parameter heterogeneity, and (iii) using scanner data to empirically illustrate the impact of the restrictions on quantity elasticities and the relative efficacy of multiple specifications of unobserved heterogeneity in easing those restrictions. We find that the specification of unobserved heterogeneity crucially influences estimates of quantity elasticities and that the mixture normal specification outperforms the alternatives.

A substantial body of research evidence has now accumulated in the reference price literature. One stream of research has identified the antecedents of reference price and has assessed their effects through experimentation. Others have calibrated a variety of reference price models on panel data and reported the effects on brand choice and other purchase decisions. In this article, the authors review the published literature on reference price in both the behavioral and modeling streams. They offer an integrative framework to review prior research on (1) the formation of reference price, (2) retrieval and use of reference price, and (3) influences of reference price on various purchase decisions and evaluations. In doing so, the authors examine the influences of consumers' prior purchase history and contextual moderators, such as specific purchase occasions, promotional environment of the store, and product category characteristics. They summarize the key findings, identify the unresolved issues, and offer an agenda for further research, which includes a set of testable propositions. They also identify the methodological challenges that face reference price research. In the concluding section, the authors discuss the managerial implications of reference price research.

Government-subsidized theatres in Russia aim to increase both revenue and number of tickets sold. Achievement of such a goal is closely connected with study of theatre tickets demand function focusing on the estimation of price elasticity of demand. Previous papers studied price elasticity of demand for theatrical performances provide controversial results. Estimates of price elasticity varies with countries, theatres, segments of theatre audience and even with level of data aggregation. Ticket sales and price data aggregation at the national level or theatre level typically does not allow to control for the differences in produced cultural goods quality. Incorrect control or ignoring of a theatre, performances and seats quality leads to a problem of omitted variables and bias in price elasticity estimates. In this paper we employ disaggregated ticket sales data for four seasons of Perm opera and ballet theatre and estimate the price effect on the theatrical demand for various performance types and seats in the hall. We use censored quantile regression to estimate the parameters of theatre demand function. We reveal the weak elasticity of demand for Perm opera and ballet theatre. We also show that ignoring the limited capacity of the theatre hall, characteristics of performances and seats quality leads to biased estimates of demand function parameters.