Incorporating Competitor Data into CRM:



Incorporating Competitor Data into Customer Relationship Management

Doug Walker

Doctoral Student

University of Houston

Dissertation Proposal

June 12, 2007

Committee Chairman

James D. Hess

Committee Members

Michael Ahearne

Niladri B. Syam

Christian J. Murray

TABLE OF CONTENTS

Abstract 3

Introduction 4

Literature Review 14

Competitor Data in CRM 15

Pharmaceutical Sales 16

Missing Data 17

Database Augmentation 19

Data 21

Model 23

Demand for Products in a Category 23

General Model 26

Misspecifications of the General Model 32

Firm Demand Model 35

Category Demand Model 35

Brand Demand Model 37

Firm Demand with Effort Model 38

Category Demand with Effort Model 38

Brand Demand with Effort Model 39

Analysis of Research Questions 39

Econometric Challenges 45

Endogeneity 46

Heterogeneity 48

Data Augmentation 50

Customer Acquisition, Development and Retention 50

Contributions 51

Dissertation Schedule 53

References 54

ABSTRACT

Fueled by technological innovation, customer relationship management (CRM) research and practices have been driven primarily by the exponential growth in customer transaction data held by firms. Consideration of the competition has largely been lost in this flood of firm-focused data. CRM seems to have strayed from its market orientation roots.

Academic leaders in the field of CRM have called for research incorporating competitor data. This research intends to answer that call. Using a dataset particularly rich in competitor data relating to the firm’s customers, we will address questions relevant to researchers and practitioners alike. How biased are the firm’s estimates of the impact their marketing efforts have on sales when competitor sales and marketing efforts are ignored? Is share-of-wallet, an aggregate competitive measure, adequate? How important is endogeneity, augmented data, and cross-sectional versus panel data in accurately estimating the impact of marketing effort on sales?

1. INTRODUCTION

Customers commonly divide their total category demand across brands. For example, customers may purchase certificates of deposit from several different banks over time. Consider the brand shares for a particular customer in a three brand market, represented using a unit simplex as shown in Figure1. Brand C enjoys the largest share for this customer. To some extent, the brand shares for each customer are determined by attributes of the respective brands that are essentially fixed. For example, a main ingredient in products in the category may vary over brands.

Figure 1: Market Share Simplex

However, many aspects of the marketing mix are not fixed. Each of the three firms represented in Figure 2 would like to manipulate their marketing mix as it applies to the customer in such as way as to move the “point” and increase their share of the customer’s purchases. For example, Brand A desires to move the “point” that serves to trisect the triangle upward above the horizontal line. Of course, the firm has more than one customer and a limited marketing budget, so they must decide which “points” to push and how hard.

Figure 2: Brand “A” Share Can Be Increased by Moving “Point” Upward

Several relevant factors that will impact those decisions are readily apparent. All else equal, the firm prefers large customers to small customers. All else equal, a customer where the firm has a small share has more potential for growth than does one where the share is large. Of course, all else will not be equal. The question of where and how hard to push also depends on the competition. Where and how hard are they pushing?

Ideally, the firm will know the share for each brand as well as the respective brand marketing efforts for all customers. If the firm has this level of data, a distinction can be made between customers even if their total category demand and brand shares are identical, as shown in Figure 3. The thick arrow associated with Brand C indicates that Brand C has expended more marketing effort relative to Brands A and B to achieve their share for Customer 1 than they have for Customer 2. Therefore, an equivalent increase in effort for Brand A targeted at both customers would have a greater impact on the relative marketing effort for Customer 2 than it would for Customer 1. This information could prove valuable to the firm. But what if competitor effort is unknown by the firm? Now, the customers in Figure 3 are indistinguishable.

Even without data on competitor marketing effort, the firm can distinguish between the customers in Figure 4 because they know the relative brand shares. Obviously, brand share is more dispersed for Customer 2 than for Customer 1, suggesting the effectiveness of an incremental increase in marketing effort by Brand A would differ for the two customers. But what if the firm does not know brand shares, but only their own firm’s share of each customer’s total category demand (i.e. share-of-wallet)? Now, the customers in Figure 4 are indistinguishable to the firm. In fact, any customers where the “point” lies on the horizontal line that results in a constant share for Brand A would be indistinguishable to the firm, as shown in Figure 5.

Similarly, even without data on competitor marketing effort or brand shares, the firm can distinguish between the customers in Figure 6 because they know their share-of-wallet for both customers. They know the actual “points” lie somewhere on the horizontal lines. Their sales to

Figure 3: Brands Shares with Variation in Marketing Effort Across Customers

Figure 4: Brand “A” Share Constant, Other Brands’ Share Variable Across Customers

Figure 5: Brand “A” Share Constant for All Points on Horizontal Line

Figure 6: Brand “A” Sales Same Across Customers

both customers may be equivalent, but Customer 1 clearly has more potential for sales growth than does Customer 2. But what if the firm doesn’t know share-of-wallet? Now, given Brand A sales are the same for both customers, the two customers are indistinguishable to the firm, as shown in Figure 7.

Obviously, the more competitor data available to the firm the clearer the picture they will have of the customer, leading to better informed decisions. But customer relationship management (CRM) research has focused primarily on the use of firm-specific data (Boulding et al. 2005). The reason is clear – firm-specific data, primarily transactional, can be collected easily and inexpensively. Firms have embraced technological advancements to collect and store more of this type of customer data than ever before. Data related to a firm’s marketing efforts are also plentiful. On the other hand, collecting competitor data on shared or prospective customers commonly proves to be difficult and costly, at best.

Unfortunately, orchestrating CRM activities considering only firm-specific customer data can be dangerous if the structure of customer brand shares or competitor marketing effort influence customers’ response to the firm’s marketing activities, conditions that almost certainly are the case. Firms in most industries engage in fierce competition for customers. CRM initiatives are prevalent. Firms act both unilaterally and responsively, based on the information they have, in an attempt to attract and retain the best customers. Firms committed to a market orientation cannot ignore the competition.

Numerous studies, concentrating only on firm-specific data, demonstrate CRM can enhance firm profits, at least in the short run (e.g. Cao and Gruca 2005; Ryals 2005). It is an open debate whether these programs provide a true competitive advantage or whether they reflect nothing more than a firm’s operational effectiveness (Porter 1996). Regardless, fully

Figure 7: Brand “A” Sales Same Across Customers, Share-of-Wallet Unknown

utilizing the informational value in the data held by the firm is critical to the performance of the firm. CRM’s firm-specific data focus has resulted in processes capable of incorporating the inherent information found in that data into the firm’s CRM decision making, but what about competitor data?

Firms desire reliable estimates of response to various types of marketing effort. Market response research is certainly not new. In fact, Hanssens, Parsons and Schultz (2001, pg. xi) state “something remarkable has happened to market response research: it has become practice.” However, fueled by an ever increasing flood of firm-specific data, CRM has struggled to maintain a market orientation, despite its evolution from that school of thought. Although firms are experienced in considering market response using primarily firm-specific data, research on the incorporation of competitor data into CRM, and perhaps even more importantly, the value of incorporating that data into decision making, has been largely ignored (Boulding et al. 2005).

Researchers have conceptualized that knowing the firm’s share-of-wallet can be of value in segmenting a firm’s customers (e.g. Reinartz and Kumar 2003). The basic premise, which is quite intuitive, is that the firm should focus on customers with substantial category demand, but of which the firm has a small share (Anderson and Narus 2003). There is some empirical support for this approach (Reinartz, Thomas, and Kumar 2005). This stream of research suggests, as would be expected, that there is value in having some competitor data. But is the payoff gained from acquiring this information worth the cost of doing so? If knowing share-of-wallet is valuable, wouldn’t knowing each competitor’s share of that wallet be even more valuable? And what about the competitions’ marketing efforts? How valuable would competitor effort data be to the firm? Is brand share data more valuable than competitor effort data? If you have one, do you need the other?

Firms in a few industries (e.g. ethical drugs) do have access to some competitor data. Avenues are available for the collection of competitor data for most firms. The lack of CRM research that considers the competition suggests several important questions that we will address in this study. The richness of our data will allow us to investigate these questions. First, how biased is the estimated impact of the firm’s marketing efforts on sales when competitor sales volume is aggregated, or even ignored? Second, how biased is the estimated impact of the firm’s marketing efforts on sales when competitor marketing efforts are ignored? Third, how does ignoring simultaneity bias impact the parameter estimates in the models? Fourth, how does the use of augmented competitor marketing effort data for some customers, rather than measured competitor marketing effort data for all customers, impact the parameter estimates in the models? Fifth, how does the use of cross-sectional data rather than panel data impact the parameter estimates in the models? Sixth, how much is competitor data worth?

2. LITERATURE REVIEW

In this section, we will consider several research streams that are relevant to this research. First, we will discuss the few papers in the vast CRM literature that incorporate competitor data. Second, since the context of this study involves the marketing of a category of ethical drugs, we will review relevant papers in the pharmaceutical sales literature. Third, since the exclusion of competitor data when estimating response can be thought of as a missing data issue, we will look at topics in that literature that are relevant to this study. Finally, we will discuss applicable data augmentation methods.

Competitor Data in CRM

CRM researchers are not ambivalent to the importance of considering the competition when making CRM decisions. Boulding and colleagues (2005, pg. 161) state that “a failure to integrate competition into a firm’s CRM activities potentially puts it at serious risk.” Bell and his co-authors (2002) concur, emphasizing that the learning gained from examining a firm’s own customers is incomplete without considering prospective customers. Their comments seem relevant to shared customers where the firm enjoys varying shares of those customers’ total category requirements.

The firm’s share-of-wallet for each customer is one competitor-oriented measure that has received some attention from CRM researchers. Share-of-wallet has commonly been conceptualized as a measure of customer loyalty and used as a proxy for competitor effort (e.g. Bowman and Narayandas 2004; Reinartz et al. 2005). Share-of-wallet has been found to positively impact customer profitability (Reinartz et al. 2005) and has been theorized to mediate the effect of customer retention on profits (Zeithaml 1985).

Several papers have taken the findings that share-of-category requirements are predictive of customer profitability as incentive to devise methods to estimate the share-of-wallet for a firm’s customers. The underlying assumption, of course, is that knowing this information will result in better informed CRM decisions. Bhattacharya et al. (1996) looked at the relationship between share-of-category requirements and the marketing mix. They found a small but significant relationship, but cautioned against making causal claims. Du, Kamakura and Mela (2007) prescribe a larger investment in large category-demand, low category-share customers, and propose a database augmentation method that estimates share-of-wallet.

There are limitations in using share-of-wallet in CRM decision making. First, although knowing the share-of-wallet provides the equivalent information to knowing the total wallet as long as the firm knows their own sales by customer, incorporating share-of-wallet into a decision-making model without using total wallet can be problematic. For example, a large share of a large wallet is different in important ways from a large share of a small wallet. Second, it is unclear from the work that has been done to date if marketing effort drives share-of-wallet, or vice versa. Simultaneity is of utmost concern. Finally, knowing the share-of-category for a customer provides a clearer picture of the firm’s relationship with the customer than does firm sales alone, allowing for better informed CRM decisions. However, knowing competitor shares, rather than just aggregate competitor share, provides an even clearer picture of the competitive environment for each customer. Addressing these limitations is an important contribution of our research.

Pharmaceutical Sales

This study incorporates sales effort in the form of detailing, but does not investigate salespeople. In fact, the analysis focuses on the customers. In the context of ethical drug sales, the customers are the physicians. Although a review of sales research in general would not be appropriate, a summary of the recent pharmaceutical sales literature will be of value in presenting the context for this study.

Using Bayesian methods, Manchanda and Chintagunta (2004) are able to investigate physicians’ response to detailing at the individual physician level. They focus on the total number of prescriptions written in a particular drug category and find that detailing does positively influence the number of prescriptions written, although, as expected, at a decreasing marginal rate. A discussion of the potential benefits of reallocating details is included in the study.

The potential endogeneity inherent in a pharmaceutical sales response model is analyzed by Manchanda, Rossi and Chintagunta (2004). They model the number of prescriptions written in the category as a function of detailing, but then make detailing dependent on the parameters of the response function. They report that accounting for reverse causality results in better model fit. Substantive findings include an apparent overdetailing of high volume physicians. The authors suggest that their results may be due to the effects of latent competitor sales efforts. In this study, as well as others (e.g. Manchanda and Chintagunta 2004), competitor effort is unaccounted for, although it may actually be partially controlled for implicitly, since the individual specific intercept represents unobserved heterogeneity in Bayesian analysis. In this paper, endogeneity resulting from omitting the competitors’ sales effort will be addressed explicitly as discussed in the analysis section.

Missing Data

Customer databases for most firms consist primarily of firm-specific data. In other words, competitor data related to the customers in the database are missing. Imagine a rectangular customer database with customers on the rows and variables relating to those customers on the columns. The missing data literature deals primarily with situations where some of the values in any particular column are missing. If a firm has firm-specific data, but no competitor data, entire columns of data could be considered to be “missing”, not just some of the values in the columns. Little can be done to impute the missing values when this is the case. However, since augmentation of the customer database for some customers via a survey is part of this research, the projection of values for variables collected in the survey of those customers not included in the survey involves methods used to address missing data. Fortunately, assuming the participants in the survey are randomly selected, the mechanism that produced the missing data is the easiest to address. Even so, an understanding of the key issues in missing data analysis is appropriate.

Little and Rubin (2002) discuss the importance of discovering the mechanism that leads to missing data, since the mechanism determines the appropriate methodological response. The authors list three missing data mechanisms, with the key issue being if the actual value of the missing data is the reason it is missing.

Using their notation, consider a complete rectangular data set Y, with each element in the dataset represented as yij, where i is the row and j is the column. Also, consider a matrix M of the same dimensions, where the value for element mij is 1 if the value is observed and 0 if it is missing. Data are called missing completely at random (MCAR) if the conditional distribution of M is dependent only on some unobserved parameters,[pic], but not on the values of the data Y, expressed as

[pic] for all Y,[pic]. (1)

If the observed elements in Y are labeled Yobs and the missing elements are labeled Ymis, data are considered to be missing at random (MAR) if

[pic] for all Ymis,[pic], (2)

indicating that the reason the data are missing is dependent only on the values of the elements in Y that are observed. Finally, missing elements in Y are not missing at random (NMAR) if the distribution of the matrix M is dependent on the actual values in Y that are missing.

The primary source of missing data in this study will be from a survey. Of particular importance is not individual missing values on any one survey, but rather non-response. If the sample of physicians to be included in the survey are randomly selected from the customer database, and if the mechanism behind any non-response is unrelated to the values that would have been entered on the survey if completed, then the missing data will be MCAR. If non-response is due to observed values in the existing database, the missing data mechanism will be MAR. The non-response will be categorized as NMAR if the non-response is dependent on values related to the survey items. MCAR is the simplest missing data mechanism to address, while NCAR is the most difficult.

Database Augmentation

Database augmentation techniques are firmly entrenched in the missing data literature. In fact, augmentation is a special case of imputation, a common technique for handling missing data (Kamakura and Wedel 2003). Typically, a firm will conduct a survey or purchase data for a random sample of their customer database. This data, along with data already existing for customers included in the survey, will be analyzed to discover relationships between the survey data and the internal data. Predictive models based on these relationships will then be developed to estimate the values for the surveyed variables for those customers not included in the survey. The objective is to leverage the survey data in such a way that informs decision making concerning all of the customers in the database.

In a paper particularly relevant to the current research, Du et al. (2007) demonstrate a database augmentation method in a banking context. They use survey data on share-of-wallet for a variety of banking product categories, along with internal data on customer’s income and tenure, to estimate share-of-wallet for customers excluded from the survey. Their method simultaneously imputes whether the customer has an external balance in a category, then if they do, the size of the external balance. Their method does not consider competitor brand shares.

Sub-sampling, whether in the form of surveys or test markets, creates a need for database augmentation. Methods for imputing missing values can be as simple as entering the mean level for the observed values for a variable where the value is unobserved. At the other extreme, sophisticated methods designed to account for large proportions of missing data and a variety of measurement scales for the missing values have been developed (e.g. Kamakura and Wedel 2003).

All of these methods involve imputing values based on models utilizing the information found in not only the survey data but the existing internal data as well. Little and Rubin (2002) give three criteria to guide imputations. First, the imputation should be conditioned on observed variables. Second, when possible, the procedure should be multivariate to preserve correlations between missing variables. Third, imputed values should be drawn from a predictive distribution rather than just imputing means to avoid overstating a central tendency. Additionally, the authors encourage the use of multiple imputation, as opposed to single imputation, to account for imputation uncertainty. Multiple imputation involves drawing a series of complete datasets for analysis, with parameter estimates being the mean from each of the analyses and the standard errors including imputation uncertainty.

3. DATA

Two pharmaceutical datasets each representing a category of ethical drugs will be used in this research. Each row of data will represent a particular physician, with columns consisting of variables from the following categories: physician demographics, firm prescriptions, firm marketing effort, competitor prescriptions, and competitor marketing effort. A graphical representation of the database that will be collected in August of 2007 is presented in Figure 8. Physician demographic variables will include gender, age, and years in practice. Monthly prescription data for each brand in the market, by physician, over approximately four years will be provided. Marketing effort data for the firm will include detailing, sampling and other promotional activities. The dataset is not fully rectangular because the competitor marketing effort variables will be measured via a survey of only a sample of the physicians in the database. A firm who is supporting this dissertation has agreed to fund the survey and to provide all of the necessary variables for each physician in their database.

We will analyze an existing dataset prior to the data collection. This dataset is limited to three periods of prescription data and includes only the physicians that participated in the survey. This preliminary analysis will allow us to address software and estimation issues prior to data collection. But most importantly, conducting the analysis on an existing dataset will assist us in determining the items that will need to be included in the survey.

Figure 8: Graphical Representation of the Databases Used in the Study

|Physician demographics |Firm prescriptions by period |Firm marketing effort |Competitor prescriptions by brand |Competitor marketing effort |

| | |by period |by period |by brand |

| | | | |by period |

| | | | | |

Rows represent physicians. Columns consist of variables in the indicated categories.

4. MODEL

Demand for Products in a Category

Each firm, of course, is interested in maximizing profits. Obviously, this maximization applies across all of the firm’s products, but even with the available data pertaining to a single product in a particular category, a consideration of the firm’s profit function is worthwhile.

A physician’s total category demand for a particular class of drugs, over some defined time period, can be conceptualized as follows. Each physician has a limited, and generally fixed, number of appointment slots available to see patients. This number will be represented as n. Obviously, this number will vary across physicians for a variety of reasons. For example, the time spent with each patient, on average, may depend to some extent on whether or not the physician is employed by a health maintenance organization (HMO). A certain proportion, q, of each physician’s patients will be diagnosed with a condition that could be treated with a drug from the category in question. Again, this proportion would be expected to vary by physician. For instance, a cardiologist might be expected to prescribe a particular heart medication to a higher proportion of patients than would a family practice doctor. Of those patients diagnosed with a particular condition, a physician would treat a certain percentage of them, h, with a drug from the category being considered. This percentage would likely vary across physicians due to several reasons, for example, years in practice.

Therefore, using the indicated notation presented above, the expected number of prescriptions for a particular drug category and physician would be the product of the number of patients seen in a period, the proportion of those with a condition treatable by drugs in the category, and the percentage of those with the condition where drugs in the category are the best treatment option, or n × q × h. Obviously, these parameters could change over time. For example, if a physician is enjoying a growing practice, more patients will be seen and n will increase. Greater specialization over time in conditions treatable by drugs in the category would increase the proportion of patients seen that will be diagnosed with the relevant condition, so q will increase. Finally, positive experience with drugs in the category or evolving best practices could result in a greater percentage of those with the condition being treated with drugs in the category, increasing h. Each firm’s marketing mix could certainly impact the total category demand for a category of drugs, primarily by increasing the percentage of patients diagnosed with the condition being treated with a drug from the category, represented by h. This impact would most likely be seen relatively early in the life cycle of the category. In a mature category, firms’ marketing efforts would be less likely to alter a physician’s total category demand, but rather would influence each brand’s share of prescriptions for the physician.

With this conceptualization of total category demand as a foundation, several aspects of the ethical drug market have led to reasonable simplifications in the profit function in previous research (e.g. Manchanda et al. 2004). First, the costs of producing an ethical drug are primarily sunk. In fact, the marginal costs are so small compared to the sales price that they are typically assumed to be zero. Second, expenditures on the sales force (detailing) dominate other marketing expenditures. In a representative drug category, 80% of total marketing expenditures pertain to detailing (Manchanda and Chintagunta 2004). The response to changes in price, typically a key variable in analyzing demand, is of much less importance in the ethical drug market. Price is only indirectly salient to the patient and far less important to the physician than the appropriateness of a particular drug for each patient. Therefore, in an ethical drug context, detailing is the critical variable. Third, although the cost of a detail can certainly vary from one visit to the next and over physicians, the cost will not be nearly as variable as say, for example, different advertising campaigns. Therefore, the marginal cost of a detail is typically assumed to be constant.

The resulting simplified profit function for the firm is

[pic], (3)

where j = physician, r = revenue from a prescription, S = number of prescriptions (or scripts), c = marginal cost of a detail and D = number of details. We assume the number of prescriptions written is some function of detailing. Ideally, once this functional relationship is specified, first order conditions can be calculated, allowing for the determination of the optimal level of detailing. Additional variables could certainly be added and a more sophisticated cost function could be applied, but regardless, it is evident that within this context, the main consideration is the impact of detailing on prescriptions. We will develop a linear model very loosely of the form

[pic], (4)

where α represents the intercept and δ is the impact of detailing on prescriptions. Estimating the parameter γ allows for a state dependence for prescriptions over time. In the general model, marketing effort, D in this case, and lagged prescriptions, S, will incorporate all brands in the category. Attempting to precisely specify this relationship will be the central modeling task in this research.

General Model

The proposed model for the number of prescriptions written for drug i by physician j in period t begins with a model for brand share, mijt. Kotler (1971) considers the well-known multiplicative competitive interaction (MCI) model to be the fundamental theorem of market share, represented as

[pic] (5)

where Mijt is the marketing effort for drug i directed at physician j in period t and the denominator represents the combined marketing effort for all of the brands (Cooper and Nakanishi 1988). Although statistically equivalent, Cooper and Nakanishi (1988) describe how marketing effort in the MCI model can alternatively be conceptualized as the attraction consumers feel for each particular brand. In this paper, relative marketing effort is of primary concern.

Typically, the MCI model is specified using a multiplicative function of marketing mix elements. Suppressing all but the subscript for brand, i, marketing effort can be expressed as

[pic], (6)

where αi is a parameter for the constant effect of brand i, Zyi is the value of the yth marketing mix variable Zy for brand i, βy is a parameter corresponding to variable Zy, and εi is an error term.

Our objective is to build upon the MCI model in equation (5) to produce a model that is linear in its parameters and that represents the mean number of prescriptions physician j writes for the focal brand in period t. To minimize notational complexity and therefore improve expositional clarity, we will demonstrate this transformation assuming two particular marketing mix variables are relevant in the model. Once the transformation is complete, we will express it in its general form.

Expanding equation (5) produces an initial brand share model,

[pic], (7)

where i = brand, j = physician, t = period, D = detailing, A = promotional activities and αij = the constant effect of brand i with respect to physician j in a category with K brands. The parameters δ and φ represent the effects of detailing and promotional activities, respectively. The parameters δ and φ can vary by brand, physician, or both, addressing heterogeneity in physician response to marketing effort. The specification in equation (7) is referred to as the differential-effects MCI model (DeSarbo et al. 2002). We could further parameterize the model to incorporate cross-competitive effects in what is called the fully extended MCI model. However, DeSarbo et al. (2002) found the fully extended model to provide little improvement over the differential-effects model, particularly since the fully-extended model requires the estimation of almost twice as many parameters. Therefore, we will limit the investigation of the heterogeneity in response to across brands and physicians.

Several steps are required to transform equation (7) into an equation that is linear in its parameters. First, a logarithmic transformation generates

[pic]. (8)

Next, a log-centering operation is required. The first of two steps in this process are to sum equation (8) across all brands, i = (1, …, k), then divide by the number of brands, k, producing

[pic] (9)

where [pic],[pic], and[pic] represent the geometric means of brand share, detailing, and promotional activities, respectively. The second step in the log-centering operation requires subtracting equation (9) from equation (8), resulting in

[pic] (10)

This can also be written as

[pic], (11)

where α* = αij – α1j, ε* = εijt – ε1jt and d = 1, if m = i and 0 otherwise (DeSarbo et al. 2002).

The left hand side of equation (11) is market share in a log-centered form. However, our previously stated objective was to model the mean number of prescriptions physician j writes for the focal brand in period t. In effect, we need to combine the brand share model in equation (11) with a model of total category prescriptions to generate a brand prescriptions model. Models combined in this way are referred to as indirect brand sales models (Leeflang et al. 2000). This approach will prove to be convenient when estimating the model.

Two adjustments to equation (11) need to be made. First, since the left hand side is now a ratio, either brand shares or the actual number of brand prescriptions can be used. Since the objective is to model brand prescriptions, we will use brand prescriptions, Sijt, in place of brand share, mijt, from this point forward, resulting in

[pic]. (12)

Expanding the left hand side, as follows, illuminates the need for the second adjustment

[pic]. (13)

The left hand side of equation (12) is the log ratio of brand prescriptions to the geometric mean of brand level sales for the category. The geometric mean can be thought of as an expression of total category prescriptions. We can isolate the log of brand prescriptions by adding [pic] to the left hand side of equation (13), but that change has to be modeled on the right hand side. Since

[pic], (14)

a reasonable alternative is

[pic]. (15)

Essentially, equation (15) provides a flexible model of total category prescriptions for each physician, allowing for varying trends in brand prescriptions across brands and physicians. Incorporating this adjustment, focusing on brand 1 (the focal brand), and combining error terms, we transform equation (12) into

[pic]. (16)

This baseline model, fully specified, introduces a number of challenging, but addressable, econometric issues that will be discussed in full. It also provides us a convenient platform for testing a variety of nested models that allow investigation into the value of various types of competitor data. Applying a general notation, reorganizing terms and allowing for a variety of marketing mix elements produces

[pic], (17)

where Xy is the yth marketing mix variable.

The objective is to model prescription writing for the focal brand by each physician in each time period. Up until now, the number of prescriptions written has been treated as if it was a continuous variable. Obviously, prescriptions will always be a non-negative integer. Therefore, we will assume that the number of prescriptions written by physician j for the focal drug in period t, pijt, is distributed Poisson

[pic]. (18)

The Poisson assumes the mean and variance of the distribution are equivalent. Often times in empirical work, the data are overdispersed - the variance exceeds the mean. If overdispersion is suggested by the data, the more general negative binomial will be used to alleviate the variance restriction found in the Poisson. Using the common exponential link function, S1jt in equation (17) represents the mean number of prescriptions written.

5. MISSPECIFICATIONS OF THE GENERAL MODEL

We will address our research questions by estimating and comparing various specifications of the general model shown in equation (17). The second and third terms, representing brand prescriptions and marketing effort, respectively, will be manipulated to produce the alternative specifications that will be considered in the analysis. We will consider three levels of data the firm may have concerning prescriptions for the competing brands. First, the firm may only know the prescription volume for their own brand by physician. Second, the firm may know their own prescription volume, as well as the aggregate of competitor prescriptions, by physician. Third, the firm may have data concerning the prescriptions for all brands by physician. For each of the three levels of data the firm has on competitor prescription volume, the firm may or may not have data on the marketing effort of the competitors, by brand and by physician. The resulting six specifications (one of which is the general model) are shown in Table 1.

Since all of the alternatives are essentially the general model with omitted variables, it will be beneficial to expand the general model as presented in equation (17) to easily identify the omitted variables in each alternative. To produce terms where the focal firm variables are distinct from the competitor variables, the relevant expansion of equation (17) can be demonstrated over several steps. The term representing brand share can be expanded as

[pic]. (19)

The lagged prescription terms are now distinct between the focal brand and the competitor brands. Accomplishing a similar result with respect to the marketing effort term is slightly more

Table 1: Model Specifications Based on Availability of Competitor Data

| |Available Competitor Prescription Data |

| | |Firm knows own and aggregate competitor prescriptions |Firm knows prescriptions for each brand |

| |Firm knows only own prescriptions | | |

|Available |Firm does not know|(1) Firm Demand Model |(2) Category Demand Model |(3) Brand Demand Model |

|Competitor |competitor effort |(see Equation 22) |(see Equation 25) |(see Equation 28) |

|Marketing | | | | |

|Effort Data| | | | |

| |Firm knows |(4) Firm Demand w/ Effort Model |(5) Category Demand w/ Effort Model |(6) Brand Demand w/ Effort Model |

| |competitor effort |(see Equation 29) |(see Equation 30) |(see Equation 21) |

involved since the values for each marketing variable for brand 1,[pic], also appear in the geometric mean that makes up the denominator,[pic]. First, equation (19) can be rewritten as

[pic]. (20)

Rearranging terms and expanding produces the general model with the focal brand variables distinct from the competitor variables as follows

[pic][pic] intercept,

[pic] lagged prescriptions for focal brand,

[pic] lagged prescriptions for competitor brands,

[pic] marketing effort for focal brand,

[pic] marketing effort for competitor brands.

[pic] and error term. (21)

Note the parameters for the fourth and fifth terms are restricted to be the same for each variable, Xy. We will modify the general model referencing the expression of the model as shown in equation (21) for each of the alternative specifications in Table 1.

[pic]Firm Demand Model

The firm demand model is the sparsest of the alternatives, with the assumption that the firm has no knowledge of competitor prescription volume or competitor marketing effort.[1] This is equivalent to saying the firm’s database does not include the last two categories of variables as depicted in Figure 8. Dropping the unobserved terms from equation (21) produces

[pic]. (22)

The terms remaining in the firm-focused model are virtually assured of being correlated with the omitted terms, resulting in biased parameters estimates, indicated by the superscript associated with the parameters.[2]

[pic]Category Demand Model

The category demand model assumes no knowledge of competitor effort, but does contend the firm is aware of the firm’s share-of-category-demand. This corresponds to a database like the one in Figure 8, but where the columns indicating prescriptions for each competing brand for each time period have been collapsed into a single column for each time period representing aggregate prescriptions for the competing brands. The specification of this model is not as straight forward as for the firm demand model. Consider the third term from equation (21),

[pic]. (23)

There are two important aspects that need to be recognized. First, the parameter γ cannot vary across the competitor brands since competitor prescriptions is an aggregate measure. Second, the term (with no variation in γ across k) can be written as

[pic], (24)

where the subscript C indicates all of the competing brands in aggregate. If the firm only knows share-of-wallet, not all brand shares, the product of all brand prescriptions cannot be calculated. We will make the necessary assumption, therefore, that all competitor brand shares are equivalent. The category demand model with unobserved variables omitted that incorporates this assumption is

[pic]

[pic]. (25)

At first glance, this model does not appear to be nested within the general model because of the modification of the competitor share term. However, consider an expansion of the third term in equation (21)

[pic]. (26)

Also consider the expansion of the third term in equation (25)

[pic]. (27)

The terms in equation (27) are similar to those in equation (26) with two qualifications. First, the parameters are not allowed to vary across brands, but instead are restricted to be equal. Second, instead of using the actual lagged competitor brand prescriptions, each term includes the mean of those lagged prescriptions. In effect, equation (27) is equation (26) with parameter restrictions and measurement error.

[pic]Brand Demand Model

For the brand share model, it is still assumed the firm has no knowledge of competitor marketing effort, but the firm does knows the brand shares of each competitor. The firm’s database would be missing only the final category of variables indicated in Figure 8. Omitting the term relating to competitor effort from the general model in equation (21) produces

[pic]. (28)

[pic]Firm Demand with Effort Model

In this model, the firm is unaware of competitor prescription volume, but does have knowledge of competitor marketing effort. The firm’s database would correspond to the database depicted in Figure 8, but without the fourth category of variables. The alternative model is

[pic]. (29)

[pic]Category Demand with Effort Model

The category demand with effort model assumes the firm knows competitor prescription volume only in aggregate, but competitor marketing effort by brand. The database would be similar to the one for the category demand model, but with the final category of variables shown in Figure 8 included. The model is

[pic]

[pic]. (30)

Obviously, this model is quite similar to the general model, with the only difference being the firm knows only the firm’s share of category demand rather than each competing firm’s share.

[pic]Brand Demand with Effort Model

This is the general model as shown in equation (21), where both competitor share and marketing effort are known. The firm’s database would be equivalent to the one represented in Figure 8.

6. ANALYSIS OF RESEARCH QUESTIONS

The research questions all pertain to physicians’ demand for the focal firm’s brand in a particular ethical drug category. Essentially, our research questions focus on the extent to which the estimated impact of the firm’s marketing efforts on prescription writing is biased when the competition is ignored. A graphical representation of the research questions appears in Figure 9. The first two questions consider movement along the horizontal and vertical axes, respectively. What is the value of knowing more about prescriptions written for competing brands? What is the value of knowing the competitors’ marketing efforts? The remaining research questions revisit these two primary questions by sequentially considering simultaneity, data augmentation, cross-sectional versus panel data, and monetary value.

Research Question #1: How biased is the estimated impact of the firm’s marketing efforts on prescription writing when competitor prescription volume is aggregated, or even ignored?

Research by Du et al. (2007) demonstrate an effective way to augment a database with survey data concerning the share of each customer’s category demand held by the firm, then use

Figure 9: Graphical Representation of Research Questions

that data to produce estimates of the share-of-category-demand for every customer in the firm’s database. The implication, as discussed earlier in the literature review, is that share-of-wallet is a valuable metric in making CRM decisions. If a survey is done to determine the share-of-wallet held by the firm, any attempt to disguise the name of the firm sponsoring the research would result in share-of-wallet figures for not just the focal firm, but for each of the competitors as well. Of course, projecting brand shares rather than share-of-wallet onto the rest of the customer database would be a greater challenge.

The objective in the Du et al. (2007) paper was to get a better understanding of the firm’s relationship with the customer by uncovering each customer’s share-of-wallet, not just each customer’s demand for the firm’s offerings. The primary objective of this question is to determine whether knowing the brand share for each competitor provides a meaningfully clearer picture of each customer compared with only knowing the share-of-wallet.

Comparisons of the alternative models can be done as follows to address this question. Each of the three models low on the vertical axis in Figure 9, where competitor marketing effort is unknown, can be compared to one another. Likewise, the three models high on the vertical axis, where competitor marketing effort is known, can be compared.

We anticipate that response parameter estimates should become more precise as the understanding of competitor prescription data improves. Obviously, more accurate or complete data should lead to better insight. The real concern is the extent to which the parameter values change. Aggregating brand prescriptions eliminates the opportunity to estimate parameters for each lagged prescription term. Also, variation among competitor brand prescriptions is lost because only the mean is relevant as shown in the third term of equation (25). The category demand models are unable to differentiate between a customer where the focal firm holds a ten percent share and three competitors each hold a 30 percent share versus a customer where the focal firm holds a ten percent share and a single competitor holds the remaining ninety percent. Obviously, the competitive situation for the two customers is significantly different.

Insight into this question can begin by calculating a likelihood ratio for each pair of models, LR ≡ 2[L ([pic]) – L ([pic])], where [pic] is the unrestricted estimator and [pic]is the estimator with constraints imposed. LR is distributed [pic]with Q constraints. Consider a comparison of the brand demand model to the category demand model. To determine the number of parameters that will be estimated for each model, assume the unobserved heterogeneity will be differenced away and observed heterogeneity will be addressed by making the parameters functions of physician characteristics, where c = the number of physician characteristics. Under those assumptions, (K + Y) × (c + 1) parameters will be estimated for the brand demand model, where K is the number of brands, Y is the number of marketing effort variables, and c is the number of physician characteristics. For the category demand model, there will be (Y + 2) × (c + 1) parameters. The number of constraints, therefore, will be the difference between the number of parameters for the brand demand model and the number of parameters for the category demand model, or (K - 2) × (c + 1). Although the likelihood ratio will address issues of model fit, the superiority or inferiority economically will be determined in a later test.

Research Question #2: How biased is the estimated impact of the firm’s marketing efforts on prescription writing when competitor marketing efforts are ignored?

Three pairs of models can be compared to address this question: firm demand vs. firm demand with effort, category demand vs. category demand with effort, and brand demand vs. brand demand with effort. Each of these comparisons involve nested models, so evaluations of relative model fit accounting for the additional variables can be done in addition to comparisons of response parameter estimates.

In the unexpanded general model, equation (17), it is evident that competitor effort is represented in the model by the geometric mean of the marketing effort of each brand,[pic]. This term is the denominator in a term that has the effort of the focal firm in the numerator. Expanding this term, as shown in equation (21), reveals that the same number of parameters will be estimated whether competitor effort is included in the model or not. If included, the parameters for the competitor effort term are restricted to be the same as for the focal firm’s effort. Omitting the competitor effort term is equivalent to setting the parameters for that term equal to zero. Because the number of constraints is unchanged when comparing the model without competitor effort to the model with competitor effort, the likelihood ratio test is not appropriate to choose the superior model.

The comparisons of interest for this research question, however, are differences in the parameter estimates between the three models that omit competitor effort versus their corresponding models with competitor effort included. Although determining whether a meaningful economic difference exists between the estimates, a discussion of the differences in the parameters will also be of value.

Research Question #3: How does ignoring simultaneity bias impact the parameter estimates in the models?

The analysis done for research questions #1 and #2 could potentially suffer if simultaneity bias exists, but is ignored. Implementing instrumental variable methods and assessing the change in parameter estimates will address this question.

Analysis of the first two research questions can be done using techniques discussed above to address potential simultaneity issues or the analysis can be done with the assumption that marketing effort is exogenous. Parameter estimates derived where instrumental variable techniques have been implemented can be compared to estimates resulting from estimation without the instruments to determine if simultaneity is an issue.

Research Question #4: How does the use of augmented competitor marketing effort data for some physicians, rather than measured competitor marketing effort data for all physicians, impact the parameter estimates in the models?

In most cases, not all customers will be included in a survey designed to augment the database with variables useful for modeling. Cost issues, or even non-response, virtually insure that is the case. The paper by Du et al. (2007) focuses on this particular issue, developing a method to project the share-of-wallet for customers not included in the survey using the survey results from those that were in the survey along with some demographic variables. In this dataset, brand shares are available for all of the customers. Competitor marketing effort will be available for only those customers included in the survey. Multiple imputation techniques can be utilized to address this missing data problem.

Projected data will necessarily be less accurate than survey data. The error in the projected data will be a non-linear function of the number of physicians included in the survey. The model can be calibrated on various proportions of the surveyed physicians, with the rest being put in the validation sample. Parameters for the models with effort can be estimated for each proportion used for the calibration to determine the sensitivity of the parameter estimates to the survey proportion.

Research Question #5: How does the use of cross-sectional data rather than panel data impact the parameter estimates in the models?

Although the time element of the data is key in accounting for endogeneity and heterogeneity in the models, the models can be estimated with the lagged variables excluded. Comparisons of parameter estimates can be made.

Research Question #6: How much is competitor data worth?

The carryover effects of marketing effort are inherent in the lagged prescription terms in the models. Estimates of the derivatives related to the firm’s marketing efforts are, therefore, relevant only at the levels of the variables in the models. Therefore, optimizing the allocation of marketing efforts is not an option. However, gauging the value of reallocation of marketing efforts is achievable by examining the impact of incremental changes in the marketing effort variables from their current values. Comparing the value of these reallocations to the estimated costs of the various types of competitor data can provide insight into whether it is worthwhile to collect the competitor data.

Optimal incremental changes in the allocation of marketing effort can be made using the estimates from the brand demand model with effort. Using estimates of the value of a new prescription, the cost of changes in the marketing mix elements, and the cost of data, the profit from a reallocation can be estimated.

Allocation decisions can also be made using the misspecified models. These decisions can then be applied, but with the estimated changes in prescriptions predicted by the general model. The loss in profit can then be compared to the estimated cost of the data excluded in the model being tested, indicating whether acquisition of the data is worthwhile monetarily.

7. ECONOMETRIC CHALLENGES

As with most research where the data being analyzed has not been generated experimentally, issues of endogeneity and response heterogeneity cannot be ignored.

Endogeneity

Endogeneity exists when a variable in the model is correlated with the error term. Three types of endogeneity are typically discussed in the econometric literature: omitted variable, measurement error, and simultaneity (Wooldridge 2002). Additionally, in a dynamic model, a lagged dependent variable is necessarily correlated with the error term. All four sources of endogeneity are likely present in at least some of the alternative models previously presented. First, endogeneity can result from a relevant explanatory variable being omitted from the estimated model. If the omitted variable is correlated with any of the remaining variables in the model, the parameter estimates for any or all of the variables can be biased. In the firm demand model, both competitor brand level prescriptions and competitor effort variables are omitted and most likely correlated with the error term and the remaining explanatory variables.

Second, measurement error can create an endogeneity problem. The explanatory variable measured with error is the sum of the unobserved explanatory variable (the actual value) plus the measurement error. If the unobserved explanatory variable is correlated with the error, then the explanatory variable measured with error must be correlated with the error, producing a situation analogous to the omitted variable problem. In the brand demand model, the log of the product of the competitors’ brand prescriptions is included in the model. In the category demand model, the average of the competitors’ brand prescriptions is raised to a power equivalent to the number of competitor brands, producing an explanatory variable similar to, but not equivalent to, the variable in the brand demand model. There is no reason to suspect the variable in the brand demand model (the unobserved variable in the category demand model) to be correlated with the difference in the variable between the brand demand and the category demand models. Therefore, the variable in the category demand model is likely correlated with the measurement error, producing an endogeneity problem.

Third, endogeneity can arise from an explanatory variable in the model being determined simultaneously with the dependent variable in the model. As mentioned in the literature review, the endogeneity of detailing in a pharmaceutical context has been investigated (Manchanda et al. 2004), as has the heterogeneity of response to marketing efforts (DeSarbo et al. 2002). Specifically, in the marketing of an ethical drug, detailing levels and other marketing mix elements cannot be considered to be exogenous variables in a model for prescription writing. Conversations with the company confirm the statements reported by other researchers (e.g. Manchanda et al. 2004). Pharmaceutical companies group physicians into deciles based on total category prescriptions, with higher levels of detailing being assigned to the higher volume physicians. Detailing levels are then adjusted based on managers’ individual knowledge of the market. Obviously, detailing will be endogenous, a function of total category demand and most likely the response to detailing.

Methods exist that will yield unbiased parameter estimates when there are endogenous explanatory variables as described in the previous section. Instrumental variables are central to these methods. An observed variable that does not appear in the model can be a valid instrument if two criteria are met (Wooldridge 2002). First, the instrument must be uncorrelated with the error term. Second, the instrument must be partially correlated with the endogenous variable once the effects of the exogenous variables in the model on the endogenous variable have been accounted for. Two-staged least squares (2SLS) is an effective method when there are multiple instruments.

Endogeneity is likely to be an issue for each of the six models. The potential sources of endogeneity for each model are presented in Table 2. The first source of endogeneity to consider is the lagged dependent variable which appears in each of the models. If the parameter for the lagged term is in fact zero, the implication would be that there is no state dependence over time for prescriptions. In other words, the effects of the firm’s marketing efforts apply only to the period in which they are undertaken. Making that assumption would be convenient econometrically, but difficult to defend substantively. State dependence in prescriptions is highly likely in this context. First-differencing, coupled with lagged differenced instruments, will produce a consistent estimate of the parameter for the lagged prescription term (Cameron and Trivedi 1998).

Endogeneity due to simultaneity is expected for the firm’s marketing effort variables. Fortunately, panel data provides convenient instruments. Whether or not first-differencing is implemented, lagged marketing effort variables are effective instruments (Wooldridge 2002).

Finally, endogeneity resulting from omitted variables or measurement error can be addressed via first-differencing as long as effective instruments can be found. In the brand demand model and the brand demand with effort model, lagged competitor prescriptions are omitted from the model. An excellent candidate for an effective instrument would be an additional lagged focal brand prescription term. Similarly, omitted competitor effort could be accounted for with additional lagged focal brand marketing effort variables.

Heterogeneity

Heterogeneity of physician response has been demonstrated in a number of studies (e.g. DeSarbo et al. 2002; Manchanda and Chintagunta 2004). There are observed variables that could impact a physician’s response. Unobserved heterogeneity must also be considered.

Table 2: Sources of Endogeneity for Each Model Specification

|Model |Sources of Endogeneity |

|Firm Demand |lagged dependent variable |

| |simultaneity with marketing effort |

| |omitted competitor prescriptions |

| |omitted competitor effort |

|Category Demand |lagged dependent variable |

| |simultaneity with marketing effort |

| |measurement error in competitor prescriptions |

| |omitted competitor effort |

|Brand Demand |lagged dependent variable |

| |simultaneity with marketing effort |

| |omitted competitor effort |

|Firm Demand with Effort |lagged dependent variable |

| |simultaneity with marketing effort |

| |omitted competitor prescriptions |

|Category Demand with Effort |lagged dependent variable |

| |simultaneity with marketing effort |

| |measurement error in competitor prescriptions |

|Brand Demand with Effort |lagged dependent variable |

| |simultaneity with marketing effort |

A primary benefit of analyzing panel data is the ability to use the time dimension to account for unobserved heterogeneity across subjects. First-differencing, an integral part of the solution to the endogeneity problems discussed in the previous section, proves valuable for addressing heterogeneity, too. First-differencing removes the fixed effects that are likely to vary across physicians.

Observed heterogeneity can be handled in several ways. First, latent class methods or mixture models can be used to allow the response parameters to vary across classes of physicians (e.g. DeSarbo et al. 2002). In that case, the subscript j that appears in each of the models would refer not to individual physicians, but rather to classes of physicians. Second, the response parameters in the models could be modeled as functions of observed physician variables such as age, years in practice, medical specialty, gender, and sampling. Since prescriptions for only the focal brand are being modeled, there is no hierarchical aspect to the data. Observed heterogeneity would be accounted for at the physician level. An additional benefit would be the introduction of interactions between marketing effort variables and physician characteristics into the model (Manchanda and Chintagunta 2004).

Data Augmentation

Using the survey data, along with the internal data already existing in the database, a multivariate, multiple imputation method will be used to augment the database for all customers. Imputed values will be drawn from a predictive distribution to produce a series of complete datasets for analysis.

8. CUSTOMER ACQUISITION, DEVELOPMENT AND RETENTION

Research in CRM often relies on the customer lifecycle framework, focusing on the acquisition of new customers, as well the development and retention of existing customers (Kamakura et al. 2005). This research is consistent with that conceptualization. For example, selecting customers for upselling is fundamental in customer development. Bias in relevant response parameters due to missing competitor data could significantly impact the effectiveness of upselling targeting decisions.

The identification of customers at risk of defection, or churn, is a common theme in CRM research (e.g. Neslin et al. 2006). Decision makers require unbiased estimates of the effectiveness of marketing elements used to improve customer retention. Ignoring the competition’s efforts to develop shared customers could be detrimental to decisions related to retention.

Customer lifetime value (CLV) is a common measure in the CRM literature (Berger and Nasr 1998). A key element found in CLV models is the expected monetary value of the purchases a customer is expected to make over time. Obviously, the market structure for each customer in terms of competing brand shares, as well as competitor marketing effort, will greatly determine the confidence a firm will have in the estimates of a customer’s future transactions with the firm. A measure closely related to CLV, consumer lifetime value, considers the value of a customer across all competing firms (Kamakura et al. 2005). Consumer lifetime value directly addresses a customer’s potential. For example, a large customer where the firm holds a small share has more potential than a small customer where the firm has a small share (Du et al. 2007). Distinguishing customers in this way requires the firm to collect competitor data. The incorporation of competitor data similarly impacts estimates of customer equity (Blattberg and Deighton 1996; Blattberg, Thomas, and Getz 2001).

9. CONTRIBUTIONS

CRM research has been built primarily by considering customer databases consisting of transactional data between the firm and its customers. Interactions between the firm’s customers and competing firms have largely been ignored. One competitive measure that has received some research interest, share-of-wallet, is at best a variable with considerable measurement error issues due to aggregation.

Our research answers the call for incorporating competitor data into CRM. When the competition is ignored, estimates of the impact of marketing efforts on firm sales can be biased, leading to poor marketing allocation decisions. Our research investigates the extent to which this is the case.

Contributions of this research will be as follows. First, we will determine how ignoring competitor sales volume or competitor marketing effort biases the estimates of the impact of the firm’s marketing efforts on firm sales. Research that incorporates competitor data into CRM is essential in redirecting CRM research back towards its roots as a market-oriented undertaking (Boulding et al. 2005). Second, we will examine the influence of endogeneity, data augmentation, and panel data on the estimation of these models. These issues have been previously contemplated in this context, but not in a single study nor with particularly suitable data. Finally, we will estimate the financial implications of these biases to directly address practitioner concerns.

10. DISSERTATION SCHEDULE

Activity Approximate Date

Collect second data set Summer 2007

Prepare data for analysis Fall 2007

Data analysis Winter 2007-8

Write up results and prepare for defense Spring 2008

Defend dissertation April 2008

11. REFERENCES

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Berger, Paul D. and Nada I. Nasr (1998), "Customer Lifetime Value: Marketing Models and Applications," Journal of Interactive Marketing, 12 (1), 17-30.

Bhattacharya, C. B., Peter S. Fader, Leonard M. Lodish, and Wayne S. DeSarbo (1996), "The Relationship Between the Marketing and Share of Category Requirements," Marketing Letters, 7 (1), 5-18.

Blattberg, Robert C. and John Deighton (1996), "Manage Marketing by the Customer Equity Test," Harvard Business Review, 74 (4), 136-44.

Blattberg, Robert C., Jacquelyn S. Thomas, and Gary Getz (2001), Customer Equity: Building and Managing Relationships as Valuable Assets. Boston: Harvard Business School Press.

Boulding, W., R. Staelin, M. Ehret, and W. J. Johnston (2005), "A Customer Relationship Management Roadmap: What Is Known, Potential Pitfalls, and Where to Go," Journal of Marketing, 69 (4), 155-66.

Bowman, Douglas and Das Narayandas (2004), "Linking Customer Management Effort to Customer Profitability in Business Markets," Journal of Marketing Research, 41 (4), 433-47.

Cameron, A. Colin and Pravin K. Trivedi (1998), Regression Analysis of Count Data. Cambridge: Cambridge University Press.

Cao, Yong and Thomas S. Gruca (2005), "Reducing Adverse Selection Through Customer Relationship Management," Journal of Marketing, 69 (4), 219-29.

Cooper, Lee G. and Masao Nakanishi (1988), Market-Share Analysis: Evaluating Competitive Marketing Effectiveness. Boston: Kluwer Academic Publishers.

DeSarbo, Wayne S., Alexandru M. Degeratu, Michael J. Ahearne, and M. Kim Saxton (2002), "Disaggregate Market Share Response Models," International Journal of Research in Marketing, 19 (3), 253-66.

Du, Rex Yuxing, Wagner A. Kamakura, and Carl F. Mela (2007), "Size and Share of Customer Wallet," Journal of Marketing, 71 (2), 94-113.

Hanssens, Dominique M., Leonard J. Parsons, and Randall L. Schultz (2001), Market Response Models: Econometric and Time Series Analysis, 2nd ed. Boston: Kluwer Academic Publishers.

Kamakura, Wagner A. and Michel Wedel (2003), "List augmentation with model based multiple imputation: a case study using a mixed-outcome factor model," Statistica Neerlandica, 57 (1), 46-57.

Kamakura, Wagner, Carl F. Mela, Asim Ansari, Anand Bodapati, Pete Fader, Raghuram Iyengar, Prasad Naik, Scott Neslin, Baohong Sun, Peter C. Verhoef, Michel Wedel, and Ron Wilcox (2005), "Choice Models and Customer Relationship Management," Marketing Letters, 16 (3/4), 279-91.

Kotler, Philip (1971), Marketing Decision Making: A Model Building Approach: Holt, Rinehart and Winston.

Leeflang, Peter S. H., Dick R. Wittink, Michel Wedel, and Philippe A. Naert (2000), Building Models for Marketing Decisions. Boston: Kluwer Academic Publishers.

Little, Roderick J. A. and Donald B. Rubin (2002), Statistical Analysis With Missing Data, 2nd ed. Hoboken, New Jersey: John Wiley & Sons, Inc.

Manchanda, Puneet and Pradeep K. Chintagunta (2004), "Responsiveness of Physician Prescription Behavior to Salesforce Effort: An Individual Level Analysis," Marketing Letters, 15 (2-3), 129-45.

Manchanda, Puneet, Peter E. Rossi, and Pradeep K. Chintagunta (2004), "Response Modeling with Nonrandom Marketing-Mix Variables," Journal of Marketing Research, 41 (4), 467-78.

Neslin, Scott A., Sunil Gupta, Wagner Kamakura, Junxiang Lu, and Charlotte H. Mason (2006), "Defection Detection: Measuring and Understanding the Predictive Accuracy of Customer Churn Models," Journal of Marketing Research, 43 (2), 204-11.

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Reinartz, Werner J. and V. Kumar (2003), "The Impact of Customer Relationship Characteristics on Profitable Lifetime Duration," Journal of Marketing, 67 (1), 77-99.

Reinartz, Werner, Jacquelyn S. Thomas, and V. Kumar (2005), "Balancing Acquisition and Retention Resources to Maximize Customer Profitability," Journal of Marketing, 69 (1), 63-79.

Ryals, Lynette (2005), "Making Customer Relationship Management Work: The Measurement and Profitable Management of Customer Relationships," Journal of Marketing, 69 (4), 252-61.

Wooldridge, Jeffrey M. (2002), Econometric Analysis of Cross Section and Panel Data. Cambridge, Massachusetts: The MIT Press.

Zeithaml, Valarie A. (1985), "The New Demographics and Market Fragmentation," Journal of Marketing, 49 (3).

-----------------------

[1] We will assume the firm always knows the number of brands in the market, K, which seems reasonable, particularly in this context.

[2] The superscripts correspond to the model numbers in Table 1.

-----------------------

Customer 2 – all brands same marketing effort

Customer 1 – Brand C greatest marketing effort

B

C

A

B

C

A

Customer 2 – Brand C same share as Brand B

Customer 1 – Brand C greater share than Brand B

B

C

A

B

C

A

Brand Demand

w/ Effort

Eq (21)

Category Demand

w/ Effort

Eq (30)

Firm Demand

w/ Effort

Eq (29)

Brand Demand

Eq (28)

Category Demand

Eq (25)

Firm Demand

Eq (22)

Available Competitor Marketing Effort Data

By Brand

None

None

Aggregated

By Brand

Available Competitor Prescription Data

Customer 2

Customer 1

B

C

A

B

C

A

B

C

A

Customer 2

Customer 1

B

C

A

A

Customer 2

Customer 1

A

“point”

Customer 1 – brand shares

B

C

A

Share for Brand C

Share for Brand B

0%

25%

50%

75%

100%

Share for Brand A

25%

50%

75%

Customer 1 – 25% Brand A, 25% Brand B, 50% Brand C

100%

100%

75%

100%

50%

25%

0%

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