Because the number of brands is often large in relation to the number of observations (up to 2500 brands with no more than 200 observations) there are insufficient degrees of freedom to begin with the second or third steps involving multiple regressions over all other brands.
The procedures developed by Sims to extract a set of competing brands which he felt would certainly include the most important competitors (but by no means only the most important) were easily represented by rules and, though implemented declaratively, could have been implemented procedurally as well since they are, in fact, procedural.
Effectively, the first cut at the competitive set was to include all brands for which all of the relevant regression coefficients were of the correct sign with t-statistics greater than 5 in magnitude. The relevant coefficients were the OLS coefficients on price with focus-brand value share as the dependent variable and, where these were of appropriate sign and magnitude, the coefficient on the focus brand price with the competing brand's value share as the dependent variable. The point here is to ensure that the competition goes both ways even if the cross-price elasticities are not symmetrical.
The second cut used similar criteria but in an OLS regression of the value share of the focus brand against a log transform of all of the price variables in the first-cut competitive set. Brands were winnowed out of this set one at a time either because in the regressions their coefficients had the wrong sign (indicating that they were complements rather than competitors) or, if all coefficients were of the appropriate sign, because their coefficients were the least significant.
At this stage, it is usual for some surprising brands to be left in the competitive set. If the set has been cut down too far, some brands that the domain experts would expect to be in the competitive set are left out. Since we want to be sure that no actual competitors are left out of further consideration, we typically make the second-cut competitive set rather larger that the size of the set we intend to end up with. In general, the marketing professionals are interested in the half-dozen or so most important competitors. If we leave 15 to 20 brands in the second-cut competitive set, then they have some confidence that that set will include all of the most important six to eight competitors.
The reason that inappropriate brands are left in the second-cut competitive set is that some ephemeral strategy has brought them temporarily into competition with the focus brand. Usually, this will be because of some special offer which increases their sales while the offer remains in force but does not lead to a long-term increase in market share. the problem here is that the assumption of a linear relation between market share and competitors' prices may yield a spurious result in which a few large and systematic fluctuations in volumes and prices are averaged out over all observations and make the constant coefficients and t-statistics larger and apparently more significant than would be the case without those few fluctuations.
In order to identify the brands which should be in the competitive set but might not be captured by linear regressions and their interpretations as well as those that should not be captured, we employ a non-linear technique called local regression which is a generalization of linear regression. This procedure produces a regression coefficient for each observation and each regressor. The user selects the value of a parameter called "span" which determines the number of data points to be considered in the regressions for each observation point. Data values corresponding to points further from the point for which the coefficients are being calculated are given smaller weights than those which are closer to the current point. The pattern of values of these weights is determined by two more parameters. the greater the span, the smoother will be time pattern of local regression coefficients for each regressor. The combination of values of the span and weighting parameters is chosen by trial and error to yield the best t statistics or some other measure of significance for the patterns of coefficients.*2
The interpretation of the time patterns of local regression coefficients is determined by rules and is entirely declarative. The rules "look" at the patterns of levels and first and second differences in the coefficients on each regressor over the data period. The coefficients of interest are those on the price variables where the dependent variable is the focus brand's value share. These will be significant and positive for competing brands and insignificant or negative for non-competing brands. A positive coefficient indicates that the focus brand will lose (resp. gain) share if the price of another brand falls (resp. rises). Because the price variable used is a log transform of the actual price, the coefficient is the elasticity of focus-brand value share with respect to the price of the other brand. Thus, a high coefficient value indicates a high elasticity and, therefore, more competitiveness.
The aim of the rulebase in this regard is to identify brands which are consistently strong competitors of the focus brand and to include brands which become competitors over the data period and to eliminate from consideration those which have ceased to be competitors during the data period. The time pattern of the local regression price coefficients identifies which brands fall into these various categories. There are, naturally enough, a number of considerations involved in identifying brands in each of these groups. Moreover, some of these considerations are more important than others and, in addition, some make a potentially competing brand more interesting to consider and some considerations make such brands less interesting to consider.
In order to capture the weight and nature of the implications of these various considerations and how they apply to individual brands, we applied an endorsement procedure developed by Moss (1995) on the basis of a suggestion and implementation by Cohen (1985). In Moss's procedure, there are a variety of individual endorsement schemes, each defined by a base and a list of endorsement tokens and corresponding endorsement values. Usually, an endorsement scheme is devised for each type of object in the model that is endorsed. In the model reported here, two types of objects are endorsed: dates and brands. The former are endorsed in order to identify interesting episodes during the data period. The latter are endorsed in order to identify members of the competitive set and to exclude brands from the competitive set as well as to focus attention on brands which are more interesting (or threatening) than others.
The endorsements and their values for the dates endorsement scheme is given in Table 1. The first column is the token, the second the value of the endorsement and the third is a description of the conditions in which the endorsement is applied. The basis of the endorsement scheme is 2 which means that the total endorsement value of a date is the
where E is the total endorsement value of the date (or other object) and
is the value of the ith endorsement of the date. These endorsements are used not only to identify dates or brands in which it is recommended that the user take especial interest, but also to identify objects which the rulebase considers further for special purposes and also to explain to the user why a special interest should be taken in a date or sequence of dates or set of brands.
In the two sections following, we show how these procedures work in practice.
No Title - 23 AUG 96 [Next] [Previous] [Top] [Contents]
Generated with CERN WebMaker