MANAGEMENT SCIENCE
`Vol. 32, No. 6, June 1986
`Printed in U.S.A.
`
`MARKET SHARE REWARDS TO PIONEERING BRANDS:
`AN EMPIRICAL ANALYSIS
`AND STRATEGIC IMPLICATIONS*
`
`GLEN L. URBAN, THERESA CARTER, STEVEN GASKIN
`AND ZOFIA MUCHA
`Alfred P. Sloan School of Management, Massachusetts Institute of Technology,
`Cambridge, Massachusetts 02139
`International Business Machines, Greensboro, North Carolina 27407
`Information Resources Inc., Waltham, Massachusetts 02254
`McKinsey & Co., New York, New York 10022
`
`An empirical analysis indicates that the order of entry of a brand into a consumer product
`category is inversely related to its market share. Market share is modeled as a log linear
`function of order of entry, time between entries, advertising, and positioning effectiveness. The
`coefficients of the entry, advertising, and positioning variables are significant in a regression
`analysis on an initial sample of 82 brands across 24 categories. These findings are confirmed
`by predictions on 47 not previously analyzed brands in 12 categories. Managerial implications
`for pioneers and later entrants are identified.
`(MARKETING; COMPETITION; NEW PRODUCTS)
`
`Introduction
`
`One strategy for new product development is based on innovation and the creation
`of new markets. It is expensive and risky to be a pioneering brand (Urban and Hauser
`1980). The costs of development are often large and the first firm in a market must
`allocate funds to make consumers aware of its product and convenience them to buy
`it. The risk of failure is high because the potential demand is not known with certainty.
`An alternative strategy is based on being the second (or later) entrant into the market.
`The costs may be lower since the innovator has created the primary demand and the
`basic product design exists; the risk also may be less because a proven demand exists.
`If an equal market share can be gained, this strategy could be more profitable. If, on
`the other hand, as a result of being the first entrant in a market, a dominant market
`share is achieved and maintained, the innovation strategy may be superior. The
`purpose of this paper is to investigate the market share effects of being a pioneering
`brand.
`If the market grants a long-run market share reward to early entrants, this would
`encourage innovation. From a public policy point of view, this would serve a similar
`function to that of patents by providing an additional reward to innovators. Although
`patents sometimes provide protection, in many cases they are ineffective because of
`difficulties of establishing and protecting the rights and the ability of other firms to
`"invent around" the patent as technology advance (von Hippel 1982). This difficulty
`of protecting an innovation is compounded by the fact that imitators generally take
`less time and require fewer funds to copy the innovation (Mansfield, Schwartz, and
`Wagner 1981). If pioneering brands earn a long-run market share advantage, the
`effectiveness of patent protection may be less critical in providing incentives for
`innovation and firms may be more willing to innovate without patent protection.
`
`* Accepted by John R. Hauser; received February 8, 1984. This paper has been with the authors 3 months
`for 1 revision.
`
`645
`
`0025-1909/86 /3206 / 0645$01.25
`Copyright 1986, The Institute of Management Science
`
`

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`646 (cid:9)
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`G. L. URBAN, T. CARTER, S. GASKIN AND Z. MUCHA
`
`Several authors have argued on theoretical grounds that such long lived advantages
`can exist. Early ideas by Bain (1956) indicated that existing products can have an
`advantage accruing from fundamental consumer traits that lead to stable preference
`patterns. If an experience curve is present, production costs for the pioneer may be
`lower because its cumulative production is likely to be greater than later entrants
`(Abell and Hammond 1979). If the pioneer can not only gain a cost advantage but
`also erect barriers to entry (Porter 1980), sales advantages may be even greater.
`Recent theoretical work by Schmalensee (1982) is based on the fundamental notion
`that once buyers use the first entrant's product, they will be willing to pay more for it,
`if it works, because they are not certain the second product will work. Based on a
`number of assumptions (e.g., products either work or do not work, second entrant
`objectively equal to first, no response by pioneer to new entrant, and no advertising
`effects) he shows that a long-run price advantage can persist for the pioneering brand.
`In this model, the second entrant must offer a price reduction to persuade consumers
`to try and learn about the product. This can imply higher profits for the pioneer. Lane
`and Wiggins (1981) also assume that consumers only know the exact quality of the
`products they have used. Their model is similar to Schmalensee's but includes
`advertising and some response by the pioneer to later entrants. After examining profit
`maximizing strategies they find "even with entry, the first entrant's advantage persist
`in the form of higher demand and profitability" (p. 3).
`Hauser and Shugan (1983) have formulated a defensive strategy model which uses
`the product positioning of the new entrant to determine share. In this model, the
`persistence of the sales levels of pioneering brands depends on how well the pioneer
`designed the product attributes to meet heterogeneous consumer preferences. If the
`"best" positioning was chosen by the first firm, later entrants may have lower market
`shares because, if they want to differentiate, they must adopt an inferior position.
`However, if the first brand to enter did not fully understand consumer preferences, the
`second entrant could get a preferential positioning advantage and earn a greater share.
`These theoretical models show the possibility of long-run market share rewards for
`pioneering brands and indicate these rewards also will be a function of the product
`positioning and pricing strategies of the new and old products.
`A limited amount of empirical analysis on the benefits of early entry has been
`reported. Biggadike (1976) studied 40 industrial product entries into new markets
`represented by large firms in the PIMS project. He found that after four years the
`average share of these entrants was 15 percent while the share of the largest existing
`competitor in each of the 40 businesses decreased from 47 percent to 28 percent when
`new entrants came on the market. These data suggest that although the share of the
`pioneering brand decreases as a result of subsequent entry, shares may not equalize.
`Robinson and Fornell (1985) studied the PIMS data for 371 consumer goods
`business units that were in the mature phase of their life cycle. In this sample firms
`designated themselves as "pioneers, early followers, or later entrants." "Pioneers" had
`an average share of 29 percent while "early followers" had 16 percent share and "later
`entrants" had 11 percent market share. The authors conducted an econometric
`analysis to uncover the mechanisms underlying the share differences. They found that
`pioneers tended to have higher quality products and a broader product line. In
`convenience goods, market pioneers gained additional advantages due to distribution
`effects. Pioneers also benefited in markets with low price and low purchase frequency.
`This cross-sectional study provides evidence of order of entry effects at the business
`unit level.
`Two longitudinal industry studies have been conducted which have information
`relevant to entry effects. The first is by Bond and Lean (1977) and reflects a study of
`two related prescription drugs (diuretics and antiaginals). A historical review and time
`
`

`
`MARKET SHARE REWARDS TO PIONEERING BRANDS (cid:9)
`
`647
`
`series regression analysis of the sales, entry and promotion in each of these markets led
`the authors to conclude for these prescription drugs that "the first firm to offer and
`promote a new type of product received a substantial and enduring sales advantage"
`(p. vi). Neither heavy promotional outlays nor low price dislodged the pioneers.
`However, later entrants that offered therapeutic novelty did achieve substantial sales
`volumes when backed by heavy promotional expenditures. They found that "large
`scale promotion of brands that offer nothing new is likely to go unrewarded" (p. vi).
`Another interpretative study of trends in seven cigarette submarkets by Whitten
`(1979) led to the finding that the "first entry brand received a substantial and enduring
`sales advantage" in six of the seven cigarette market segments (p. 41). She found,
`however, that later entry brands which were early in a growing market or which were
`significantly differentiated could gain a substantial share in the market or even
`dislodge the first entry brand from its dominant position.
`These theoretical and empirical analyses suggest order of entry may affect the
`market share potential of later entries and that this effect may be modified by the
`entrant's positioning, quality, pricing, and marketing strategy. This paper enlarges the
`body of empirical knowledge by a cross product analysis over many categories of
`frequently purchased brands of consumer goods. It includes effects of order of entry as
`well as advertising and product positioning. We begin by describing the data base and
`specifying the statistical model. Then we describe its fit to an initial data base of 82
`brands, assess its predictive ability on a new sample of 47 brands, and present a
`re-estimation of the model parameters based on the pooled data. We consider the
`strategic implications of our findings and close with a discussion of future research
`needs.
`
`Data
`
`Pre-test market assessment procedures have been widely used in the markets for
`frequently purchased brands of consumer products. One such system, called ASSES-
`SOR (Silk and Urban 1978), provides a rich data base for the study of order of entry
`effects. In this procedure, data on existing products are collected first and then new
`product response is measured. We are concerned here with only the data on existing
`products. Studies were carried out in the 1979-82 period. In each category studied, 300
`(or more) respondents were interviewed to determine their evoked set of brands, their
`preferences for these brands (constant sum paired comparisons across each consumer's
`evoked set), the last brand they purchased, and ratings of selected evoked brands on
`product attribute scales.' These data allow market shares to be estimated by the
`fraction of the sample which last purchased the brand. The preference and ratings data
`supply a basis of determining product positioning and differentiation. An initial
`sample of 24 categories was selected for exploratory analysis. 82 major brands existed
`across these categories. After the collection and analysis of the initial sample, data for
`47 different brands were made available. This second sample became the data for
`predictive testing. The products in these samples represented tightly defined categories
`of frequently purchased goods (e.g., liquid detergent, instant freeze dried coffee, fabric
`softener, anti-dandruff shampoo). The categories were well established. The average
`time in the market for second entrants was 25.9 years, third entrants 20.5 years, fourth
`entrants 15.2 years, fifth entrants 8.9 years, and sixth entrants 6.2 years. These data
`
`The respondents were intercepted at a shopping mall, screened for category usage, and interviewed if
`they were within the age and demographic quotas established in the stratified sampling plan for each study.
`The evoking is based on positive unaided response to one of the following conditions: now using, ever used,
`on hand, would consider using, or would not consider using. Approximately 90% of evoking is associated
`with use experience.
`
`

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`648 (cid:9)
`
`G. L. URBAN, T. CARTER, S. GASKIN AND Z. MUCHA
`
`were supplemented by advertising expenditures obtained from the Leading National
`Advertisers published media audits. Although these audits may not report 100 percent
`of each brand's spending, they are useful in comparing advertising expenditures if we
`assume no biases in relative advertising. Since the brands considered had been on the
`market at least two years, these spending levels represent post-introductory expendi-
`tures.
`The order of entry was determined by identifying the time of national introduction
`for each brand. This was done by personally calling the firms which market each of
`these products and determining when it was introduced. In the few cases where the
`firms were not willing to provide this data, at least two competitors were asked to
`provide an estimate of the entry time and their average response was utilized.
`These data provided a cross sectional data base for the investigation of order effects.
`At the time of each study, the shares for the existing brands, the year of each product's
`entry into the market, the brand's recent advertising spending, and the relative product
`preferences are known.
`
`Statistical Model
`
`The dependent variable in this study is the ratio of the market share of the nth
`(second, third, fourth . . . ) brand to enter the market to that of the first product to
`enter. Since the number of brands in each category varies, the absolute shares also
`vary; the ratio allows a meaningful comparison of relative relationships of brands
`within and across categories. Brands are included in the analysis if they were
`advertised at a significant level (greater than one million dollars per year) and a
`reasonable share estimate could be obtained (at least 30 respondents reporting a
`specific brand as last brand purchased).
`The order of entry (first, second, third . . . ) is used as an independent variable. This
`variable can empirically reflect the theoretical long lived share advantages of pioneer-
`ing brands argued by Schmalensee (1982) and Lane and Wiggins (1981). If, as
`theorized, the early entrant becomes the standard of comparison and subsequent
`brands require consumers to make additional investments in learning, the order of
`entry variable will be negatively correlated to the share index. This variable is
`supplemented by another which is defined as the number of years between the nth
`entry and the one which immediately preceded it. Being the second brand in the
`category may have a different share effect if the lag between the pioneer is one year
`rather than two, three, or four years, Whitten (1979) stressed the importance of a firm
`being early after a new trend is established. Advertising is represented by the total
`advertising expenditure over the last three years by the nth brand to enter the category
`divided by that of the pioneering brand. This variable reflects the sustaining level of
`advertising spending and allows the order of entry effect to be modified by the
`application of marketing resources.
`Differential product positioning has been identified as another moderator of the
`effect of order of entry. The Bond and Lean (1977) and Whitten (1979) studies stress
`its significance. Robinson and Fornell (1985) and Hauser and Shugan (1983) also
`argue for its importance. One method of constructing a positioning variable is by
`combining the product attribute ratings to estimate the utility for a brand. (See Urban
`and Hauser (1980) or Shocker and Srinivasan (1979) for a review.) Many procedures
`exist and they usually reproduce stated preferences or choices well. Another method is
`to use stated preferences directly. This has the advantage of avoiding variance due to
`lack of fits between the attributes and preferences, but has the disadvantage of not
`linking the attributes to preferences. Because our primary purpose is to use the
`positioning variable as a covariate of order of entry in explaining share rather than
`
`

`
`MARKET SHARE REWARDS TO PIONEERING BRANDS
`
`649
`
`supporting the design of new products, we choose to use preference to construct the
`positioning variable. The constant sum preferences supplied by respondents over their
`evoked set reflect their overall evaluations of the brand's price and features. After
`scaling the preferences by least square procedures (see Silk and Urban 1978), we
`obtain a preference value for each evoked brand j, respondent i and category c
`We define a relative preference for a brand for each consumer and average over all
`individuals who evoke the brand:
`
`R
`
`=
`
`/./c (cid:9)
`
`Ye
`k
`
`( 1)
`
`VJc = preference value for respondent i and brand j in category c,
`lie = number of respondents in category c who evoke brand j,
`ac = scale parameter for category c,
`R = relative preference of brand j in category c.
`The value of Ric is a measure of the consumers' evaluation of the product given that it
`is evoked. It reflects consumers' preferences that result from a specific multiattribute
`positioning. In most cases evoking occurs by use of the brand. If it performs well and
`price is low, Ric will be high; if it does not perform well and price is high, Rie will be
`low. The scale parameter fic is estimated by logit procedures (see Silk and Urban 1978,
`for details) and it empirically has values in the range of 1 to 3 with a median of about
`2. This scaling of preferences results in Ric approximating the probability of purchase
`of the brand given that it is evoked. The driving forces behind Ric are the measured
`preferences across the evoked set, but this scaling must be remembered when the
`statistical analysis is interpreted (see below).
`Another aspect to emphasize is that Ric is conditioned by evoking. The same market
`share (e.g., 10%) for a brand could be due to high preference conditioned on evoking
`and low evoking (e.g., 50% preference given evoking and 20% evoking), low condi-
`tioned preference and high evoking (e.g., 20% preference and 50% evoking) or
`moderate levels of both (e.g., 33% preference and 33% evoking). The variable Ric is not
`necessarily correlated to share. Before 1974, Tylenol had a low share, but pre-test
`market evaluations indicated high preference by those who had used it. After Tylenol
`advertised and promoted its product, its share increased dramatically as the fraction of
`the population evoking it increased.
`In our model we are interested in the positioning quality of later entrants relative to
`the pioneer, so we define the ratio of Ric for the nth brand to Ric for the first brand to
`enter as the variable to represent the relative preference given evoking. If the later
`entrant is superior, the ratio is greater than one, and if less desirable, the ratio is less
`than one.
`The form of the model is nonlinear to reflect the hypothesis that the impact of the
`second brand to enter on the pioneer will be greater than the third or fourth brand.
`Considerable precedent exists for modeling a nonlinear response to advertising (Little
`1979). Bond and Lean (1977) indicate an interaction between order, position, and
`marketing promotion and this can be captured in an elasticity function. Formally for
`brand n in category c:
`
`Snc = Enac'Pnc2Anc3Lnc4 (cid:9)
`
`(2)
`
`Snc = ratio of the market shares of the nth brand to enter category c to the market
`share of the first brand to enter the category,
`Enc = order of entry of nth brand in category c (n = 1,2,3, 4 . . . ),
`Pnc = ratio of preference given evoking for nth brand to preference for first brand
`
`(cid:9)
`(cid:9)
`

`
`650 (cid:9)
`
`G. L. URBAN, T. CARTER, S. GASKIN AND Z. MUCHA
`
`given evoking,
`Pnc = Rnc Ric where
`Ric = preference for jth brand in category c conditioned by evoking (see Equation
`1),
`Anc = ratio of the last 3 years advertising for nth brand to enter to the last three
`years advertising for first brand,
`L„,.= number of years between n and n — 1 brand entry plus one (Lnc = 1 if entry is
`in the same year).
`This model captures some major theoretical phenomena. If a is negative and
`significant, it supports the notion of an enduring share advantage for early entrants. If
`a2 is positive and significant, it confirms the notion that the order of entry effect can
`be moderated by a product which is superior in price and features as reflected in the
`preferences of those who have it in their evoked set. If a3 is positive and significant, it
`suggests advertising may modify the effect of later entry. If a4 is negative and
`significant it would indicate a larger penalty for the nth entrant the later it arrives in
`the market. If the positioning (Pnc) and advertising (A ,,c) indices have a value of one to
`reflect parity and entry is in the same year (L,„ = 1), equation (2) predicts the share
`ratio to be only a function of the order of entry. If Enc is equal to two to reflect the
`second product in the market, in this case the ratio of its share to the first (Sm) is 2a3.
`Note that in equation (2) the share ratio takes a value of one when the first brand is
`considered (n = 1).
`Statistical analysis is based on a log transform of equation (2):
`al E,:c + a2P,:c + a3ALe + a414,e (cid:9)
`
`(3)
`
`where the primes denote the logs of the respective variables defined in equation two.
`Note that this is a linear regression with no additive constant term (a,3). The constant
`would confound the interpretation of the magnitude of a's because with an additive
`constant in equation (3), the share index would not equal one for the first brand in the
`market as is required for logical consistency.
`
`Fitting
`
`The first application of the model is to the initial sample of 82 brands across 24
`categories. Regression is used to estimate the parameters in equation (3). These
`regression procedures are based on 58 data points because the first brand is not
`appropriate for inclusion in relative share formulation given in Equation (3) (i.e., all
`first brand variables would have values of 0).2 The resulting F(4, 54) is 58.0 and it is
`significant at the one percent level. The t values also are significant at the one percent
`level (see Table 1) for order, positioning, and advertising. The order coefficient (a1 ) is
`negative as hypothesized indicating that subsequent entrants are associated with
`reduced shares relative to the pioneering brand. The positioning effect (a2) is positive,
`indicating good positioning is associated with larger shares. In this log-linear model the
`positioning effect increases share proportionately at each entry point. Therefore share
`for the nth entrant is reduced by the order effect (a1 ) and modified by the positioning
`effect (a2). It is possible for the nth entrant to earn a dominant share when its
`positioning is sufficiently superior to overcome the order effect penalty. The relative
`advertising coefficient (a3) is also positive and reflects another correlate to increased
`
`2 An alternate approach is to include the additive constant in equation (3) and regress over the first and
`later entrants. This is not as theoretically attractive a procedure but the a0 is driven toward zero by the
`number of first brands. Empirical application of this procedure led to an a0 that was not significantly
`different from zero at the 10 percent level (a0 = 0.12, t = 1.2).
`
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`MARKET SHARE REWARDS TO PIONEERING BRANDS
`
`651
`
`TABLE 1
`Statistical Fitting Results
`
`Variable
`
`Parameter
`
`Value
`
`t Statistic
`
`Order of Entry (E)
`Position (P)
`Advertising (A)
`Lag Between Entry (L)
`
`al
`a2
`a3
`a4
`
`— 0.48
`1.14
`0.27
`0.04
`
`—4.5*
`6.8*
`5.5*
`0.6
`
`*Values significant at 1% level. Critical value with 55 degrees of freedom
`and two tail test is t = 2.7.
`
`share when a brand is a late entrant. Superior positioning and aggressive advertising
`spending would be the most likely correlates of dominance in a category by a later
`entrant. The parameter reflecting the time between entry (a4) is not significantly
`different from zero.
`Appendix 1 shows the actual and predicted values for the share indexes plotted
`versus the order of entry variable for three representative categories along with the
`unadjusted order effect EnT . Recall the predictions are obtained from our multivariate
`model so any deviation from the declining effect of order of entry (a1) reflects
`positioning and/or advertising effects. For example the third entry in the antacid
`market (Rolaids) achieved a predicted share higher than the second entrant due to
`higher advertising and positioning values (Anc of 1.6 and positioning value P„, of 2.1).
`This more than compensated for the order of entry decline and the resulting predicted
`share is greater than the share of Digel or Tums.
`In assessing these fits, we calculate R 2 at 76 percent.3 Another measure of goodness
`of fit is to determine the proportion of the cases where the model prediction corre-
`sponds to the turns in the actual data exemplified in Appendix 1. There are 58 turns
`and the direction of actual and fitted values agrees for 45 turns or 78 percent of them.
`Multicollinearity among the independent variables is low; five out of six of the
`pairwise correlations are less than 0.25 in absolute value. The sixth is the correlation
`between order of entry and the time between subsequent entries. In this data there is a
`moderate negative correlation of — 0.37 indicating some tendency for shorter intervals
`between entrants as more brands enter the market. The parameter estimates are quite
`stable as variables are added to the regression. The order effect parameter is — 0.61
`(t = —5.1) when it is the only independent variable, —0.53 (1 = —5.9) when the
`positioning variable (P) is added, —0.43 (t = —5.7) when the advertising variable (A)
`also is appended, and — 0.48 (t = — 4.5) with all the variables.
`Examination of the residuals indicate that they are not significantly different from a
`normal distribution.4 Heteroscedasticity was not evident. The standard deviation in the
`residuals was not significantly different for second and third or later entrants.'
`
`3 We calculate R 2 in this case of regression with no constant by following the procedure suggested by
`Judge et al. (1980 p. 253):
`
`R 2 = (cid:9)
`
`E <Pi — Yi)2
`Yi2
`where Y, = actual values of dependent variable and Pi = predicted value.
`4The residuals were rank ordered and divided into six approximately equally sized classes. The chi-
`squared statistic was calculated based on the actual frequency and the frequency expected from a normal
`distribution of the same mean and variance. x2 = 0.455, df = 3. This implies a 99 percent chance of
`observing a value this high or higher from a normal distribution.
`5The standard deviation of the residuals for brands of order of entry two was 0.537 and for order three
`0.54. These are not significantly different at the 10 percent level F(24, 15) = 1.01. Similarly, for second
`versus fourth or greater F(24, 32) = 1.5.
`
`(cid:9)
`

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`652 (cid:9)
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`G. L. URBAN, T. CARTER, S. GASKIN AND Z. MUCHA
`
`The estimates have been reviewed for adverse effect from the leverage of outlying
`data points (Belsley, Kuh and Welsh 1980). Three data points were identified as
`having high leverage (Tegrin, Datril and Ocean Blend Cat Food), but when they were
`removed, the significant parameters (a t , a2, a3) changed less than 15 percent from
`their original values and the t's remained significant at the one percent level.
`A number of alternative forms (e.g., linear and exponential) and variable specifica-
`tions (e.g., advertising as a percentage of category spending and order of entry and lag
`time combined as one variable to reflect years from first to nth entry) were evaluated
`in the statistical analysis, but none were theoretically or empirically superior to the
`results reported here.
`In reviewing the regression results (see Table 1), the positioning variable is most
`significant followed by the advertising and order of entry parameters. A stepwise
`regression shows the relative explanatory power of the order of entry variable. If the
`order of entry variable is the first to be included, 32 percent of the variation is
`explained. Adding positioning increased the R 2 to 62 percent and including the
`advertising variable raised it to 76 percent. In each case the incremental variance
`explained was significant at the 10 percent level.
`Some care must be exercised in interpretation of the advertising and positioning
`coefficients. Although the advertising index (A) correlates highly with the share index,
`this may not be due to advertising causing share changes. In fact if advertising budgets
`were set by a rule such as "advertising equals X% of sales," the causal relationship is
`one of advertising being dependent on sales. Although the interpretation of the
`advertising coefficient must be cautious, we assume our procedure removes a compo-
`nent of covariance and does not affect the interpretation of the order of entry
`coefficient (a1). We observe that the variables have relatively small intercorrelations
`and one may consider order as a significant explanatory variable of the residual
`variance.
`The positioning variable reflects the relative preference of brands given they were
`evoked. Such relative preferences when scaled by fi through logit procedures provide
`good estimates of the probability of purchase conditioned by evoking (see equation
`(1)). Since past choices among evoked brands are used to estimate 13 and the market
`shares are estimated based on the unconditional fractions of past purchases, there is a
`danger that the correlation would be inflated. However, this threat would be greater if
`the scaling parameter /3 were fit along with the a's in equation (2) by non-linear
`estimation procedures. The conservative view is to consider the positioning variable as
`removing a component of the variance due to correlation of unconditioned market
`share and probability of purchase conditioned by evoking. The positioning variable
`(P) has a small correlation to the order variable (0.21), so the threat to the construct
`validity of the order effects (a1) is low. The overall interpretation we draw from the
`fitting is that the order of entry effect is significant after considering the effects of
`advertising and product positioning.
`
`Predictive Testing
`
`The above results are encouraging, but they should be viewed with some caution
`because many regressions were run to find them. In order to gain more confidence in
`these results, predictions were made on a new sample of data that became available
`after the fitting analysis. This data set contained 47 new brands across 12 categories.6
`
`6Two of the categories were in the fitting exercise, but predictions were made on five new entrants in these
`two categories.
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`MARKET SHARE REWARDS TO PIONEERING BRANDS
`
`653
`
`The parameter estimates (a's) reported in Table 1 and the observed independent
`variables for the new sample are used in equation (3) to predict the new share ratios.
`Appendix 2 shows a representative set of the actual and predicted share ratios. The
`correlation between actual and predicted values for all the prediction sample is 0.85
`(the corresponding value in the fitting is 0.81). The predicted turns correspond with 73
`percent of the actual turns (the corresponding value in the fitting is 78). The root mean
`squared error in the raw share data (e.g. not transformed by logs) is 0.47; the
`corresponding value in the fitting data is 0.60. The predictive results are similar to the
`statistical fitting results and the samples are not systematically different.'
`We can gain insight into the nature of the errors in prediction by examining Theil's
`U2 measure (Theil 1966, p. 28; Bliemel 1973):
`
`u2 —
`
`E ,{P — Yi)2
`yi2
`
`where (cid:9)
`
`(4)
`
`= predicted observation i,
`= actual observation i.
`U2 represents the sum of the squared deviations as a proportion of the sum of squares
`of the actual values. In this application it has an additional interpretation. Consider a
`revised U2 where Po reflects the null hypothesis of no order of entry effects or a share
`index of 1.0:
`
`z (cid:9)
`- Yo2
`u2 - ' ze(Po YO2
`
`(4A)
`
`Recall we are using log transforms for all values and note Po = ln(1.0) = 0.
`Equation (4A) reduces to equation (4) in this case. Therefore, we can interpret the U2
`in equation (3) as the sum of squares of the error in prediction as a fraction of the sum
`of squares of the deviation of the new data from the null hypothesis values reflecting
`no order of entry effect. In our application the U2 value is 0.21 and reflects good
`prediction.8
`Finally, the ninety percent confidence intervals for the prediction of the share
`indices were calculated (Theil 1971, pp. 122-1