Doyle L. Weiss

Determinants of Market Share

The economic well-being of a business firm can often be summarized in terms of its market share. Market share responds to price, advertising expenditures, retail availability, and product character...

An Iterative GLS Procedure for Estimating the Parameters of Models with Autocorrelated Errors Using Data Aggregated over Time

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 Periodic Pain of Lydia E. Pinkham

In 1964, Palda published the results of the first application of lagged-variable regression models to the question of advertisings 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 Paldas 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) Paldas (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).

Robustness of linear models in dynamic multivariate predictions

Linear aggregation models employing unit and equal weights have been shown to be superior to human decisions in a surprising range of decision situations. In addition, decisions based on these models have often been found to be superior to those based on linear regression models (LRMs). This general issue was explored for repetitive decisions in production planning. The problem considered differs in several aspects from the types of problems investigated previously: (1) the problem is dynamic rather than static; (2) a set (or vector) of interactive decisions dependent on previous decisions is required to be made, where a decision in stage t, the dependent variable, becomes an independent variable in stage t + 1; and (3) the criterion function is cost with a quadratic loss function (rather than the correlation measure of R2). Moreover, since repetitive decisions were involved, the parameters of the models were estimated using past human decisions. These were used to predict specific values of the decision variables (rather than rank order), which in turn were employed recursively to predict values of the decision variables at subsequent stages. While decisions from equal weighting rules were found to be superior to human decisions and not greatly inferior to decisions from linear regression models, decisions from unit weighting rules performed poorly. The rationale for such performance is discussed, indicating that previous theoretical and empirical research on linear weighting models is not generally applicable to dynamic, multivariate interactive decisions problems with lagged variables.