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This paper presents a framework for organizing and discussing factors influencing consumer choice dynamics, how these factors may be incorporated into models of buyer behavior and problems that may arise in estimating such models. The paper identifies research issues and delineates possible approaches.

In 1964, Palda published the results of the first application of lagged-variable regression models to the question of advertising's sales effectiveness. In doing this he supplied the first empirically supported quantification of the salesadvertising relationship. The purpose of this paper is to reexamine some of the issues which have been raised subsequent to Palda's research and to focus directly on some of the structural issues associated with the class of models examined by Palda (see Schmalensee 1972). As such this paper will focus on these issues by comparing results from the following models: (1) Palda's (1964) original distributed-lag model; (2) a current-effects model (Clarke and McCann 1973); (3) an extension of the above model utilizing a second-order autoregressive structure; (4) a brand-loyalty model, structured after early work by Kuehn (1961); and (5) several Pascal lag distributions (see Kmenta 1971).

The authors briefly review the literature associated with the autocorrelated current effects model and present a simple procedure that recovers its parameters from time-aggregated data when the level of aggregation is known. The procedure is based partly on the estimation of a first-order autocorrelation coefficient. The procedure is illustrated and its properties are compared with those of a GLS procedure by means of a Monte Carlo experiment. In many of the tested cases, there is good recovery of the microparameters with aggregated data.

This article reports the findings of an empirical investigation into the movement of competitive market share. Palda's cumulative advertising model is adapted to include a price variable, and the analysis is extended to a multibrand market. The statistical methodology employed in the investigation overtly recognizes the competitive interdependence of the brands studied and exploits this interdependence in its estimation procedures.

Griliches’ test is not completely adequate for discriminating among several popular models of advertising effectiveness and, as a result, its use by several researchers in that area has produced inconclusive results. The authors review some past applications of Griliches’ test and develop a testing procedure which will properly discriminate between models of current and cumulative advertising effects. Finally, an empirical example of the proposed procedure is presented.

The authors investigate the measurement of the sales-advertising relationship with temporally aggregated data. Previous work has produced encouraging results for recovering micro-level parameters of the brand loyal model from data aggregated over time, but the Koyck model has not been studied in this context. The authors develop methods for recovering micro parameters of the Koyck model and extend the results for the brand loyal model. The results are supported by simulation experiments examining both asymptotic and small-sample properties.

The purpose of this report is to discuss, explain, and position the more notable literature on logically consistent market share demand models. More specifically, the report explains and provides examples for the analysis by McGuire et al., discusses the recent paper by Naert and Bultez, and comments on a recent related article by Beckwith.

This article reports the results of a demand analysis investigating the underlying structure and price responsiveness of a consumer product market. The analysis employs a non-linear demand model arising directly from recent empirical research on individual consumer behavior and is concerned with the determinants of market share in a competitive environment. The empirical investigation focuses on the form of the relationship relating price and adverstising expenditures to market share, and in this interest a number of linear models relating these variables were fitted to provide a reference for the results obtained with the non-linear model. Finally, the results of the study were put into perspective and related to the relevant literature.

The purpose of this paper is to develop a procedure to estimate the parameters for a class of distributed lag models by making use of data aggregated over time. The general problem of aggregating economic relations over time has already received considerable attention in the literature. Theil (1954) explained the difficulties of obtaining the correct aggregate relation when lagged variables appeared in the micro relationship, but he did not consider the role of the disturbance term. Mundlak (1961) studied the effects of aggregation over time on the partial adjustment model and developed the relationship between the parameters of the micro relation and those of the mispecified (to accommodate aggregate data) time-aggregated macro model. Mundlak was also unconcerned with the full role of the disturbances in such circumstances. Morigouchi (1970). taking account of disturbances, was able to quantify both the estimation bias and the loss of efficiency resulting from temporal aggregation for certain cases of the independent variable .X (t). More recently, Rowe (1976) has demonstrated the effect of temporal aggregation on regression t-ratios and R 2s. All of these studies are similar in that they did not devise an estimation procedure to correct the bias arising from temporal aggregation. In a later secThis paperdevelops an iterative generalized least-squar-es (GILS) procedul-e for estimating the par-ameters of certain economic relations characterized by first-order autocorrelated diSturbances (!1 hxt + Et, et = /) Et-l + IIt) when the available dclata have been aggregated over time. The estimation procedlure is conditional on knowledge of the level of aggregation (the number of subilltervals) making up the aggregate data interval. An example of the estimation procedure is provided using a set of annual sales-advertising data.

The authors analyze the impact of data collection period on the coefficient of the lagged dependent variable in 69 econometric studies of the sales-advertising relationship. The null hypothesis that the coefficient is independent of data collection period is not rejected. Reasons for this result are offered and discussed.

Many annual data series for the sales of branded consumer goods exhibit marked autocorrelation which provides significant fits with lagged-variable advertising sales response models. Concern continues to be expressed that the source of such autocorrelation is not advertising efforts but spurious effects from temporal data aggregation, and some researchers have criticized advertising studies using annual data as being misleading. The authors investigate the source of autocorrelation in annual series and show that temporal data aggregation is unlikely to be the primary cause of upwardly biased estimates of the coefficient (λ) of the lagged dependent variable. Sampling and specification error are more likely causes. The authors develop the aggregate form of the brand loyal model for data aggregated over time and derive a formula to calculate the amount of autocorrelation that is induced by aggregation. They present a new estimation approach which takes into account the impact of aggregation on estimates of coefficients and the error terms of such models. They compare the effects of specification error on the estimate of λ for two well known approximations to the aggregate function as well as for the approximation developed here.

We would like to agree with most of Meyer and Rothkopf's comments but take exception to their misleading assertion that certain of our assertions were misleading. Meyer and Rothkopf seem to be more upset by what we did not assert than by what we did. They do not seem to object to our statement that, "The power of direct search rests (1) in its built-in strategy for deciding where on the response surface to search next for improvements and (2) the speed of the data processing equipment used." Rather they are concerned that we did not point out that variants of Newton's method could be implemented on digital computers. We did not intend to imply that pattern search was a panacea for all nonlinear optimization problems but attempted to present an overview of the direct search techniques along with an application. In closing, we would like to point out that when "properly applied" most of the search techniques will produce "reliable results." However, "proper applicaion" probably embodies the art form in empirical research. The results from any application of a methodology must be a function of the researcher's familiarity with the problem as well as his applied experience with the methodology. * Theodore A. Van Wormer is Vice President with CiMS Group, Inc., Pittsburgh, Pennsylvania. Doyle L. Weiss is Associate Professor of Industrial Management, Purdue University.

Empirical validation and testing of simulation models have been hampered by the problems associated with estimating parameters for their nonlinear structures. This article discusses direct search techniques as a methodology for fitting parameeters of models too complex for linear regression analysis.