Dynamic and Competitive Effects of Direct Mailings

Transcription

1 Dynami and Competitive Effets of Diret Mailings Merel van Diepen, Bas Donkers and Philip Hans Franses ERIM REPORT SERIES RESEARCH IN MANAGEMENT ERIM Report Series referene number ERS MKT Publiation August 2006 Number of pages 51 Persistent paper URL address orresponding author Address Erasmus Researh Institute of Management (ERIM) RSM Erasmus University / Erasmus Shool of Eonomis Erasmus Universiteit Rotterdam P.O.Box DR Rotterdam, The Netherlands Phone: Fax: info@erim.eur.nl Internet: Bibliographi data and lassifiations of all the ERIM reports are also available on the ERIM website:

2 ERASMUS RESEARCH INSTITUTE OF MANAGEMENT REPORT SERIES RESEARCH IN MANAGEMENT ABSTRACT AND KEYWORDS Abstrat We propose a dynami diret mailing response model with ompetitive effets, where purhase and promotion history are inorporated. We then map the dynami ompetitive interations amongst the firms sending the mailings. We investigate the short- and long-run impat of a diret mailing on the revenues of the firm sending the mailing and on the revenues of its ompetitors. The model aounts for unobserved heterogeneity aross households. We estimate the model in the haritable giving setting, as sending diret mailings represents a large part of haritable fundraising ativity. Households often reeive diret mailings of different harities within a short period of time and ompetition is highly relevant. We onstrut a unique database by merging the databases of three large harity organizations in the Netherlands. This results in household level data on the diret mailings reeived and the donations made by eah household to eah harity. Our results show that haritable diret mailings are short-run omplements, that is, the diret mailings tend to inrease the total pie that is divided among the harities. At the same time, the haritable diret mailings are long-run substitutes. In the long run they fight for a piee of the pie that households have available for haritable giving. Free Keywords Availability Dynamis, Competition, Diret Mailings The ERIM Report Series is distributed through the following platforms: Aademi Repository at Erasmus University (DEAR), DEAR ERIM Series Portal Soial Siene Researh Network (SSRN), SSRN ERIM Series Webpage Researh Papers in Eonomis (REPEC), REPEC ERIM Series Webpage Classifiations The eletroni versions of the papers in the ERIM report Series ontain bibliographi metadata by the following lassifiation systems: Library of Congress Classifiation, (LCC) LCC Webpage Journal of Eonomi Literature, (JEL), JEL Webpage ACM Computing Classifiation System CCS Webpage Inspe Classifiation sheme (ICS), ICS Webpage

3 Dynami and Competitive Effets of Diret Mailings * Merel van Diepen Erasmus Researh Institute of Management & Eonometri Institute Erasmus University Rotterdam Bas Donkers Department of Business Eonomis Erasmus University Rotterdam Philip Hans Franses Eonometri Institute Erasmus University Rotterdam August * We thank the haritable organizations and the foundation SOFN for providing us with the data, Peter Exterkate for his help with data preparation, Rihard Paap and Dennis Fok for all their help and Peter Verhoef and seminar partiipants at Tilburg University for very useful omments. Address for orrespondene: M. van Diepen, Eonometri Institute, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR Rotterdam, The Netherlands, mvandiepen@few.eur.nl

4 Dynami and Competitive Effets of Diret Mailings Abstrat We propose a dynami diret mailing response model with ompetitive effets, where purhase and promotion history are inorporated. We then map the dynami ompetitive interations amongst the firms sending the mailings. We investigate the short- and longrun impat of a diret mailing on the revenues of the firm sending the mailing and on the revenues of its ompetitors. The model aounts for unobserved heterogeneity aross households. We estimate the model in the haritable giving setting, as sending diret mailings represents a large part of haritable fundraising ativity. Households often reeive diret mailings of different harities within a short period of time and ompetition is highly relevant. We onstrut a unique database by merging the databases of three large harity organizations in the Netherlands. This results in household level data on the diret mailings reeived and the donations made by eah household to eah harity. Our results show that haritable diret mailings are short-run omplements, that is, the diret mailings tend to inrease the total pie that is divided among the harities. At the same time, the haritable diret mailings are long-run substitutes. In the long run they fight for a piee of the pie that households have available for haritable giving. Keywords: Dynamis, ompetition, diret mailings 1

5 1 Introdution The use of diret marketing (DM) has inreased steadily over the past deades, with ompanies in the US spending more than 160 billion dollar on DM ativities in From all diret marketing ativities, diret mailings are the most important one, aounting for 31% of total expenditures in DM. Expenditures on DM have even been growing at a faster pae than sales (Diret Marketing Assoiation 2005). This rise in DM ativities an be easily linked to the inreased fous on building ustomer relationships (e.g. Reinartz and Kumar 2003; Rust and Verhoef 2005) and to the development of advaned targeting tools (Ansari and Mela 2003; Bodapati and Gupta 2004; Kim et al. 2005), whih enhane the performane of DM. Most researh desribing response behavior to diret mailing ativities has foused on a stati single-firm ontext, negleting potential ompetitive and long-term effets (e.g. Bult and Wansbeek 1995). However, when multiple ompanies send multiple ommuniations to individuals, there is likely to be interferene and the response to a given message will be affeted by messages reeived previously (Greyser 1973). Only reently, attention has been paid to the dynamis of response behavior at the individual level (e.g. Ansari et al. 2006; Simester et al. 2005) and orresponding improved mailing strategies (e.g. Campbell et al. 2001; Elsner et al. 2004; Gönül and Shi 1998; Gönül and Ter Hofstede 2006; Simester et al. 2006). However, these studies fous on a single ompany, ignoring ompetitive ativity. Thus, so far, the diret marketing literature has foused on, and shown the effets of, messages sent by the foal firm, while interferene is equally likely to result from messages reeived from ompeting firms (Unnava and Sirdeshmukh 1994; Yoo and Mandhahitara 2003), analogous to own and ross prie elastiities in market share models (.f. Kamakura and Russell 1989). The present study addresses the above two issues by analyzing the dynami ompetitive interations among diret mailings at the household level. We fous on diret mailings that eliit a diret response, suh as atalogs, all kinds of promotional offers, and soliitation letters from harities, with the latter being the subjet of our appliation. Our main goals an be summarized as follows: 1) Establish that ompetitive interations exist among diret marketing ommuniations. 2) Illustrate the dynami behavior of these ompetitive interations. 3) Develop a parsimonious model that still aptures the potential rihness of these ompetitive dynamis. Few messages (mailings in our ontext) generally have a positive impat, while tedium or irritation may arise when too many mailings are reeived (Elliot and Spek 1998; Greyser 1973). Hene, in line with Berlyne s two-fator theory (Berlyne 1970) diret mailings might have both positive and negative primary demand effets. 2

6 Negative primary demand effets might arise when individuals get bored or even irritated by the large number of diret mails and onsequently develop defensive strategies against the diret mailings (Diamond and Noble 2001). Note that the term junk mail suggests that at least some people get irritated by diret mailings. At the same time, eah diret mail ould trigger an order from the atalog or a donation to harity that otherwise would not have been made, thereby enlarging total sales. To summarize, it is not immediately lear whether a ompany s own diret mailings have a positive or a negative effet on its own revenues. For a given ompany, one might expet negative effets of ompetitive mailings, ertainly in markets where market expansion effets are limited. When diret mailings enhane total spending, the effet is not known. In our appliation onerning haritable giving, one ould imagine eah letter reating some feeling of guilt of not donating. A letter of one harity might inrease guilt enough for the household to donate to a subsequent soliitation letter of another harity, and hene positive externalities ould exist. Besides the signs of the effets, the dynamis are also not obvious in advane. How does the passage of time affet the influene of past mailings on today s response behavior? An individual will be more aware of reent events than of events in the distant past, as people tend to forget things (Zielske 1959). To model this, we implement a Koyk model where past events reeive less weight (see Ansari et al. (2006) for a reent appliation), so that the effet of an event deays over time. The remainder of this paper is organized as follows. Setion 2 provides an overview of the relevant theory. Setion 3 presents our model and Setion 4 disusses the empirial appliation to haritable organizations. Finally, Setion 5 onludes the paper. 2 Bakground In this setion we desribe the relevant bakground of our study. The number of diret mailings seems unabatedly on the rise. Sending diret mailings ould inrease awareness and liking and provides ustomers a diret purhase opportunity. However, some ompanies are starting to realize the negative effet these high mailing frequenies ould have in the long run. In a reent survey amongst pratitioners in diret marketing, long-term effets of diret mailings and diret mail indued irritation were suggested as two important researh avenues (Verhoef et al. 2003). Also, Campbell et al. (2001) present an example of a ompany that reognized the annibalization that ourred between essentially redundant mailings. The onsequenes of this are even more serious, as target seletion results in the best ustomers reeiving the largest number of mailings. If this results in 3

7 irritation, the ompany is harming the relationship with its best ustomers. Indeed, Simester et al. (2005) find that for the best ustomers, inreasing mailing frequeny results in a loss in revenues. The negative impat of additional mailings is likely the result of irritation and/or budget onstraints, for whih ompetitive interferene may be an important driving fore in addition to the firm s own mailings. In this paper we investigate the role of ompetitive interferene in dynami response behavior to diret mailings. 2.1 Dynami effets The first dimension we desribe is the dynami feature of the diret mailing proess. Although in many marketing siene studies attention has been given to dynamis (think, for example, of the short-/long-term distintion in Mela et al. (1998), Pauwels et al. (2002) and Sloot et al. (2006)), the issue has not reeived muh attention in the diret mailing literature. Traditionally, both aademis and pratitioners have foused on a stati ontext, sidestepping potential long-term effets. An example an be found in target seletion literature and pratie where often a seletion is made for a one-event mail-shot without reognizing the overall effet on individuals (Kestnbaum et al. 1998). However, as people tend to (partially) remember past events and inorporate their memories into an overall attitude whih may influene urrent deisions, omitting dynamis will generally lead to unreliable results and suboptimal hoies. A diret mailing organization has to bear in mind that the deision to mail an individual today does influene the probability of response to future mailings (Campbell et al. 2001; Piersma and Jonker 2004). When we fous on the dynamis, we make a distintion between the promotion history and the purhase history of individuals, as has also been done by Elsner et al. (2004), for example. Promotion history We start with desribing the relevane of the promotion history of an individual and, aordingly, of the timing of mailings by a diret mailing ompany. Campbell et al. (2001) note that, in partiular for the diret mailing ontext, timing next to ontent is an important fator in the saturation effet between two mailings. The more time between two mailings, the smaller is the saturative impat (Campbell et al. 2001). Also, Bult et al. (1997) suggest that the sequening of diret mailings is an important issue. Although a reent stream of researh has aknowledged the importane of the appropriate number and timing of mailings for individuals over a long-term horizon (e.g. Elsner et al. 2004; Gönül and Shi 1998; Gönül and Ter Hofstede 2006; Piersma and Jonker 2004), the exat long-term effet of a ompany s diret mailings on revenues is not immediately lear. 4

8 On the positive side, repeated advertising exposures an lead to familiarity and liking of a ompany and an prevent forgetting over time (Naik and Piersma 2002, among others). Diret mailings an thus serve as a reinforement of the message. Furthermore, sending many mailings ould minimize the probability that an individual does not read the mailing beause it gets lost in the mail or s/he is simply not interested. Also, eah diret mail ould trigger an order from the atalog or a donation to a harity, for example, that would otherwise not have been made, thereby enlarging total revenues. Diret mailings may also have a negative long-run effet. For example, individuals might get bored or even irritated by the large number of diret mails and onsequently develop defensive strategies against diret mailings (Diamond and Noble 2001). Elliott and Spek (1998) show that exessive diret mailing lutter an lead to a negative attitude, suh as irritation, whih redues effetiveness of the mailings (see also Naik and Piersma (2002)). Causes ould inlude that, due to the large stak of diret mailings, regular mail may easily be overlooked (Elliott and Spek 1998) or that individuals do not like being onfronted with an appeal (in the ase of soliiting mails of harities, see Diamond and Noble (2001)). Finally, besides the diretion of the diret mailing effet, also its shape is not straightforward as its effet may not be linear. In this respet, the dynami response phenomena of buildup, wearout and deay from the advertising poliy literature are partiularly relevant. In short, buildup means that eah promotion in the past ontributes to the overall goodwill, or positive attitude towards the promotions. Wearout refers to the diminishing returns to sale of repetitive promotions, meaning that the effetiveness of eah additional exposure is smaller than earlier exposures in ase of ontinuous promotions (Little and Lodish 1969; Naik et al. 1998). Finally, deay represents the degree of forgetting when promotions are absent (Little and Lodish 1969; Naik et al. 1998). These deay effets have been found to be positive but diminishing over time (Bronnenberg 1998). However, almost all of these studies analyze effetiveness of advertising using measures like advertising awareness, brand name reall or brand attitudes. In ontrast, we will fous on revenues as a measure of advertising effetiveness, whih is known to be more reliable than stated preferene data. To summarize, mailing frequeny effets may be non-linear, ould be positive or negative, and most likely deline with the passage of time. Purhase history We now desribe the relevane of the purhase history of an individual in his/her response to diret mailings. From the state-dependene literature we know that past purhase behavior influenes today s purhase behavior (e.g. Seetharaman and 5

9 Chintagunta 1998; Seetharaman et al. 1999). Indeed, it is well known that past behavior is a very good preditor of future behavior (Bult and Wansbeek 1995; Rossi et al. 1996). Many studies, investigating the effets of individuals urrent hoies on their future hoies, have demonstrated the existene of both positive and negative state dependenes. Positive state dependene, or inertia, arises if an individual routinizes his/her purhases. In the ase of diret mailings this ould mean, for example, that the fat that an individual has purhased from a ertain organization in the past has a positive influene on the urrent probability of purhasing from that ompany. Or, the more purhases in the past, the higher is the probability of purhase today, thereby apturing loyalty effets. Negative state dependene, or variety seeking, arises if an individual satiates himself/herself with a brand / ompany, so that a purhase at a ompany in the past has a negative influene on the probability of purhase today. For example, an individual gets tired of ordering from the same diret mailing organization and hene deides to try a different one. Another negative purhase history effet might be due to budget restritions. If an individual has already spent a lot, then s/he may not have muh money left to spend, whih ould redue the urrent amount. This phenomenon an be viewed as annibalization. We an onlude that purhase deisions in the past partially determine an individual s deision proess today, although the sign of the effet is not lear a priori. Furthermore, state dependene is also subjet to deay. Beause of forgetting, a statedependene effet an diminish, so that an individual does not exhibit the same level of state dependene over time (Ansari et al. 2006; Chintagunta 1998; Seetharaman et al. 1999). For example, if an amount was spent long ago it is likely that the individual now has some budget to spend again. Also, the then purhased produt might now be out of fashion or in need of replaement due to usage. Indeed, although not always under this denomination, several studies aknowledge that variables overing more reent time periods (say, last week) may be more relevant preditors than variables overing the more distant past (say, past six months) (see Baesens et al. (2002) and Bukinx and Van den Poel (2005) for example). Finally, as an example of non-linear effets of purhase history, we mention the situations of either a very reent or a very distant last response. In the first situation, an individual might be unwilling to respond again, while in the latter situation the individual might have lost interest. In both ases response behavior might be lower than in the ase of a response in between. In sum, to understand responses to diret mailings, time matters and dynamis should be inluded in a model of response behavior. 6

10 2.2 Competitive effets Although some studies do inorporate dynamis by aknowledging the importane of the total number and timing of mailings over a long-term horizon instead of fousing on a single mailing ontext, there is yet another dimension that is almost always overlooked, whih is ompetitive effets. All researhers would agree that ompetitive effets are highly relevant to inlude in models, but mostly the lak of data has prevented the possibility of extensive researh in this area. A ompany may have information on its own sales, but it generally has no insights into purhases from ompetitors or into the individuals hoie and onsideration sets. This problem has frequently been aknowledged, for example by Allenby et al. (1999), and it has also often been brought up as either a limitation or as a further researh suggestion (Gönül and Shi 1998; Naik et al. 1998). Although muh researh has been devoted to the study of ompetitive interferene on memory and brand evaluations (D Souza and Rao 1995; Keller 1991), little is known about its effets on onsumer behavior in general, and on responses to diret mailings in partiular. Some studies do present little piees of information, whih at the least emphasize the importane of thorough researh on ompetitive interations in the diret mailing field. For example, Dwyer (1997) onludes that people typially divide their purhases aross a number of ompeting organizations. For a omprehensive piture of diret mail response ompetition this is relevant, as many people likely reeive mailings of multiple organizations. Furthermore, it is generally believed that own and ross effets, that is effets of a ompany s own ations vs. its ompetitors, differ and are thus of importane separately. Looking at dynami ompetitive effets, the promotion and purhase history distintion an again be applied. Regarding the ompetitive promotion history, several studies have shown that ompetitive interferene an severely undermine the effetiveness of marketing ations (Unnava and Sirdeshmukh 1994). Therefore, one would generally expet negative ompetitive effets. An explanation an be found in the advertising lutter theory, where high mailing frequenies may lead to irritation and market shrinkage. On the other hand, there may be situations where positive ompetitive externalities exist. Examples are new produts, where ompetitive advertising may inrease awareness thereby enhaning total sales (Prins and Verhoef 2006), new attribute promotion, where ompetitive advertising may help remember old attributes thereby better distinguishing the new ones (Jewell and Unnava 2003) and haritable soliitations, where ompetitive advertising may inrease guilt of not donating thereby inreasing response probabilities (for the guilt motivation for donating, see Andreoni (1990) and Sargeant (1999) for example). 7

11 Regarding the ompetitive purhase history, the same phenomena arise as with the ompany s own purhase history. For example, the budget restrition implies that an individual who has just spent a lot, probably has not muh left to spend now. Finally, also ompetitive effets are not neessarily linear. In sum, to understand one own effetiveness in diret mailing, one needs to know what ompetitors do and what they have done. 2.3 The RFM framework A well-known framework for desribing purhase and promotion history that enables the inorporation of dynami ompetitive effets into a mailing response model is the RFM framework. In marketing it is diffiult to find variables more pervasive than the Reeny, Frequeny and Monetary value variables. Multiple variations have been proposed in eah ategory. Examples are the number of time periods sine the last purhase was made or an indiator for response to the last mailing for Reeny, the number of purhases in the past or the fration of mailings the individual responded to for Frequeny, the total amount spent in the past or the average amount spent per purhase for Monetary value. An important advantage of these variables is that they are often available at a low ost, as many ompanies keep trak of their ustomers purhase histories in databases (Rossi et al. 1996). Also, they have proven to be very effetive behavioral preditors and are often the only type of data available (Donkers et al. 2006). Many studies on a wide range of topis have used this RFM framework, if not in its original form then in a related format. Whereas the original RFM method boiled down to a straightforward (although rather subjetive) ustomer lassifiation, the literature now employs the RFM variables mostly as independent variables in modeling future response probability using regression methods (Colombo and Jiang 1999). Topis of studies exploiting RFM variables inlude optimal target seletion (Colombo and Jiang 1999), mail order repeat purhasing (Baesens et al. 2002) and partial ustomer defetion (Bukinx and Van den Poel 2005). Also, the RFM framework is frequently used by pratitioners in segmentation, target seletion and resoure alloation (Reinartz and Kumar 2000; Verhoef et al. 2003). The fat that firms generally assign the least importane to Frequeny (Reinartz and Kumar 2000) is another indiation that dynamis are indeed undervalued. They often fous on how reent the last purhase was made. We believe that this is a rather stati approah that ignores the development of a ustomer-ompany relationship over time. Sure enough, RFM variables are the best andidates for desribing past events and in this way adding dynamis to a model. We will apply the framework s basi priniples to desribe both an individual s purhase and promotion history. In the next setion, we will turn to our implementation of both dynamis and ompetition in a diret 8

12 mailing response model, where we also address unobserved heterogeneity aross individuals. 3 The model In this setion we present our model of individual response behavior to diret mailings of ompeting ompanies. Based on the well-known RFM framework, we assume that a response deision depends on purhase history and on promotion history. As desribed in the previous setion, purhase history refers to what the individual has done in the past and promotion history refers to what the diret mailing organizations have done in the past (Elsner et al. 2004). The key elements of our model originate from the following assumptions. In a given time period, an individual reeives a number of diret mailings. For eah reeipt, the individual deides whether s/he will respond or not and if so, with what amount. These two variables onstitute our dependent variables. We onsider the prototypial individual who, upon reeiving a diret mailing, instantly makes the response deision (see also Colombo and Jiang (1999)). The deision made is thus a response/nonresponse deision to a partiular mailing, and not a hoie between ompanies. Note that we assume that two mailings do not arrive at the very same time. As always, individuals are likely to vary in their response behavior. We mention loyal and variety-seeking individuals, who would reat quite differently to an impulse. We aommodate for this by inorporating heterogeneity, that is, individual-speifi parameters, thereby better apturing the true but unknown underlying deision proesses. 3.1 Explanatory variables Let τ=1,,τ i indiate the mailing events for individual i. As eah individual reeives a different number of mailings over time, the number of observations per individual varies and hene the data onstitute an unbalaned panel. As desribed above, we relate the response deision at a mailing event τ to both promotion history variables and purhase history variables. More speifially, we expet this deision to depend on mailing ations from all ompanies in the past and all (or most) of the individual s past response behavior. For example, if an individual reeives a mailing from a ompany today, then not only do all mailings from this ompany in the past ount in the deision to respond today, but also do all mailings from the ompetition. Note that it is likely that past mailings from the ompany that sent today s mailing affet today s deision differently than mailings from other ompanies. To differentiate between suh effets, we will make a distintion between own effets and ross effets. Below we will desribe and motivate our explanatory variables in more detail. 9

13 Promotion history: mailings in the past We inlude promotion history variables in our model as we expet that the extent to whih an individual has been approahed with diret mailings in the past influenes the response deision today. Although they are usually used to desribe purhase history, RFM variables also onstitute the basis of our promotion history variables. However, as Monetary value is not appliable for the ompany s mailing deisions, we only take into aount Reeny and Frequeny of mailings. We expet that the response deision today is influened by every mailing in the past, although it is likely that the effet is larger the more reent the mailing, as people tend to forget past events over time. In other words, the effet of a mailing is diminishing over time. Now, let the alendar time of mailing event τ for individual i be t iτ. Then Δt isτ = t iτ - t is denotes the number of time periods elapsed between mailing event s and τ. Hene, Δt isτ onstitutes a measure of the reeny of mailing s at the time mailing τ is reeived. Then, instead of simply ounting the number of diret mailings reeived in the past, whih tends to grow over time and results in non-stationarity, we ombine Frequeny of mailings with Reeny to reate a single explanatory mailing variable. To aount for the effets of forgetting we apply a multivariate finite duration adjustment of the geometri lag, or Koyk, model with unequally spaed observations, similar to Ansari et al. (2006). Using exponential deay dynamis with deay parameter λ m the (disounted) number of mailings is given by: τ 1 s = 1 is mailings = λ mail with { own, other} (1) iτ Δt τ m isτ In (1), we sum over all mailing events before mailing event τ. Furthermore, as we expet different own and ompetitive effets, we distinguish between mailings of the ompany that sends the mailing at event τ and mailings from the ompetition. Thus, dummy variable that indiates that the mailing individual i reeived at mailing event s was sent by the same ompany as the mailing at event τ, while other mail isτ own mail isτ is a indiates that it was sent by a ompeting ompany. To ensure that the effet of a mailing is diminishing over time the deay parameter λ m must be in the interval (0,1). Then, the longer ago individual i reeived mailing s, the smaller will be the ontribution of this mailing to the variable at time τ, whih orresponds to forgetting. To ahieve this, we speify the deay parameter λ m as: λ m exp( ϕm) 1 + exp( ϕ ) = (2) m 10

14 The advantage of this approah is that it nullifies the initial onditions problem that inextriably goes with summing over all events in the past. That is, the longer the time period over whih you alulate the total number of mailings, the larger it will be if every mailing ounts without deay; this variable will explode over time. Through the deay parameter, the effet of mailings long ago will be negligible 1 so that the variable stabilizes if the time period is long enough, hene avoiding non-stationarity and the orresponding estimation problems. We have no expetations onerning the effet of mailings τ, as past researh i implies that it ould go both ways. For example, ompetitive effets will generally be negative, but there ould be some exeptions, suh as new produts (see Prins and Verhoef 2006) and harity organizations (beause of inreased guilt). Furthermore, as the effet of the number of marketing ommuniations need not be linear, we also inlude it quadratially in our model. In this way we allow for negative effets of very high and very low frequenies of mailings, whih both seem plausible. Purhase history: past response behavior We inlude purhase history variables in our model as it is well known that past behavior is the best preditor for future behavior (Bult and Wansbeek 1995; Rossi et al. 1996). Again, RFM variables onstitute the basis of our variables. We distinguish between own and ompetitive past behavior variables as the own and ross effets on response to the urrent mailing most likely differ. Our first purhase history variable is a Frequeny measure of response, namely a disounted version of the well-known response rate. As a response rate reflets the overall tendeny to respond, it is related to the attitude an individual has towards a ompany. For example, if the response rate was high in the past, then it is likely to be high in the future, so that we expet this variable to have a positive influene on the probability of response, apturing an individual s general attitude and possible loyalty effets. Instead of the ommonly used response rate, we apply a weighted average of responses, plaing more weight on reent events. Again, based on the Koyk struture, the weights are an exponential funtion of reeny and the deay rate λ r, to reflet the diminishing effet of past responses over time. Hene, as a Frequeny measure for purhase history we use response iτ τ 1 Δtisτ λr Ris s = 1 = τ 1 Δtisτ λr s = 1 mail mail isτ isτ with { own, other} (3) 11

15 In (3), R is is a dummy variable that indiates if individual i responded to mailing s. Thus, we average over all mailing events before mailing event τ to obtain the weighted past response rate to either the mailing ompany itself ( mail τ =1) or to the ompetition other ( mail τ =1). is Our seond purhase history variable measures the Reeny of responses, while at the same time aounting for their frequeny. We use a disounted version of the number of responses in the past, either to the mailing ompany or to the ompetition, where again we use exponential disounting by reeny to reflet that the effet of a response diminishes over time due to forgetting. Note that it might be important to also inlude responses before the last response, in partiular for ompetitive mailings. It ould well be that an individual responded twie, to different ompetitors, in a very short period and both events still affet today s response behavior. own is response _ reeny iτ = τ 1 s = 1 λ Δtisτ r R is mail isτ with { own, other} (4) To explain why we onsider this a Reeny measure we note the following. Conditional on the individual s general response tendeny, aptured by response τ, this term is small if i the last response was long ago, as the variable diminishes over time through the deay parameter when no new response is added. Furthermore, if the last response was very reent, this term is large. Thus, a high value of the Reeny variable implies a very reent last response, whereas a low value implies a last response long ago. For the deay parameter λr we adopt the same formulation as for λ m, although with its own parameter ϕ r, and similarly for λ a, whih is used to disount the amounts of money spent, see (5) and (6) below. There ould be a non-linear effet of reeny on urrent response behavior. For example, if an individual just responded this may strongly redue the probability to respond again. Furthermore, if an individual has not responded in a very long time, there is a hane s/he has lapsed in the sense that s/he stopped being a ustomer with the ompany. To allow for suh non-linear effets of Reeny, we also inlude it quadratially in the final model below. Finally, we present our Monetary value measures for purhase history. The first variable is the weighted average past amount. Although the effet on today s deision of an amount in the past dereases over time, the amount an individual spends at eah purhase is often of the same order of magnitude. Thus, the level of the present amount is best explained (and predited) by the weighted average amount in the past, where we again use an exponential funtion of reeny and the deay rate as weights. 12

16 Furthermore, as average past spending is related to the attitude towards a ompany this variable will also apture loyalty effets. Now, let A is be the natural logarithm of the amount spent in response to mailing s, if a purhase is made, and zero otherwise. With the remaining variables defined as above, we model the (weighted) average natural logarithm of the amount spent with either the mailing ompany itself or with the ompetition as: amount iτ τ 1 s = 1 = τ 1 s = 1 λ λ Δtisτ a Δtisτ a A R is is mail mail isτ isτ with { own, other} (5) In (5), we average over all mailing events before mailing event τ to whih individual i atually responded (R is =1) to obtain the weighted average past amount 2 for either the own other mailing ompany itself ( mail τ =1) or the ompetition ( mail τ =1). Note that this is formulation an approximate both the unweighted average (for λa 1) and the last amount spent (for λ a 0), whih are two other frequently used Monetary value measures. Our seond Monetary value measure is the total disounted amount in the past, either for the mailing ompany itself or for the ompetition, where eah amount is disounted by its reeny. This variable mimis the effets of budget restritions, in the sense that if an individual has already spent muh (either at the mailing ompany or at the ompetition), so that this variable is large, then s/he may not have muh money left to spend, whih ould redue the urrent amount. Furthermore, onditional on the average amount spent in (5), a low value indiates that the last amount has been spent long ago and it is likely that the individual now has some budget to spend again. Also, if the last amount has been spent long ago, the produt then purhased might now be out of fashion or in need of replaement due to usage. Thus, our final explanatory variable is: is amounts _ reeny iτ = τ 1 s = 1 λ Δtisτ a A is mail isτ with { own, other} (6) The lassifiation of our explanatory variables is summarized in Table Insert Table Diret mailing response model We model the individual response deision at mailing event τ using a Tobit-II speifiation (Amemiya 1985, p.385). Thus, we assume that the individual jointly deides 13

17 whether to respond or not and if so, with what amount. Although modeling both response and amount may seem like a logial step, in the diret mailing literature the fous is mostly on modeling response inidene only (Gönül and Ter Hofstede 2006). In our explanatory variables we used R is and A is for s=1,,τ-1, so that at mailing event τ the explanatory variables ontain only lagged information. Now, let R iτ indiate whether individual i responds at mailing event τ or not. Furthermore, A iτ indiates the natural logarithm of the amount individual i spends at mailing event τ onditional on the deision to respond. Let R * iτ be the latent variable related to R iτ and A * iτ the ensored variable related to A iτ, where ensored means partially observed and partially latent. Note that we take the natural logarithm of the amount to ensure positive amount preditions. Then the Tobit-II model reads as: * 1 if Riτ > 0 R iτ = (7) 0 otherwise if > 0 = 0 otherwise * * Aiτ Riτ Ai τ (8) with R * iτ and A * iτ = = R0i A0i + C C C C + C C C C R1i R3i R4i R6i A3i A4i A6i mailings response amount iτ iτ iτ C C R2i response _ reeny A1i mailings response amount iτ iτ iτ C C R7i A7i mailings iτ + C 2 iτ R5i + amount _ reeny A2i response _ reeny mailings iτ + C amount A5i response _ reeny 2 iτ + _ reeny iτ iτ + ε + ε Riτ response _ reeny Aiτ 2 iτ 2 iτ + + (9) (10) with C = { own, other} and where εriτ and ε Aiτ represent unobserved fators that influene the response deision and amount, respetively. Furthermore, (ε Riτ, ε Aiτ )~N(0,Σ ε ) with the restrition that Σ ε,11 =1 for identifiation of the response equation. Note that through the deay parameters the effets of the explanatory variables hange over time. The subsripts R and A indiate that the parameters are equation-speifi, as opposed to the lower ase subsripts r and a for the deay parameters, that indiate variable-speifiity. 14

18 Thus, as the parameters an be different for the response and amount equation, not all explanatory variables have to be equally relevant for the two dependents. Previous studies have established that deisions on whether or not to donate may be influened differently by the same variables than deisions on how muh to donate (see Smith et al amongst others). For example, it has been found that past amounts have little explanatory power in the response equation, but are highly relevant in the amount equation (Donkers et al. 2006; Piersma and Jonker 2004) 3. Unobserved heterogeneity We speify individual-speifi random effets for model interepts, mailing and past behavior variables, so that individual-speifi inferenes an be made. All random effets may be orrelated both within and aross equations. We use Bayesian methods, where we model unobserved heterogeneity with a multivariate normal distribution. We apply MCMC tehniques to obtain draws from the posterior distributions of the parameters and thus estimate the model. Further sampling details, suh as prior and full onditional distributions, are desribed in the appendix. 4 Dynami and ompetitive effets for harities In this setion we apply our model to donating behavior to harities, where we first desribe our dataset and then present our results. We estimate our model in the haritable giving setting, as diret mailing forms an important part of haritable fundraising ativity. Furthermore, as people often reeive many soliiting mailings of various harities in a short period of time, this is also a setting where ompetition is indeed highly relevant. 4.1 Data For this researh we have a unique dataset at our disposal, onsisting of the databases of three large harity organizations in the Netherlands that are ative in the health setor. In these databases, the harities trak their donators by reording who gave what and when. This means we have revealed preferene data, that is, we have individual reords of atual response behavior to ompeting organizations, whih enable investigation of donating to multiple harities and hene ompetitive interations between different harities. The relevant information that is generally available for eah individual in the database of a partiular harity organization inludes the following: name of the respondent omplete address of the respondent for eah soliiting mailing that was sent: 15

19 date of the mailing if the individual responded: date of response if the individual responded: amount donated Using the name and address data, we onnet the three databases so that we an trak for eah individual when s/he reeived a mailing from one of the three harities and his/her exat response behavior towards these ompeting organizations. We have 3½ years of data at our disposal on donations to three health harities, say harity 1, 2 and 3. The data period is January 2002 June From the millions of individuals in the database we randomly selet 2500 individuals, where we restrit attention to those that are mailed by multiple harities during the data period, to really fous on the ompetition aspet (see Kamakura and Russell 1989 for a similar approah). For the smallest harity, 57% of all individuals in the database are also being mailed by at least one of the other two harities and 23% by both. For the largest harity, the perentages are 23% and 3%. For eah individual in our sample we use as a start-up period one year after the first date eah harity that mails him/her during the data period has sent a mailing. Thus, suppose an individual reeives mailings from harity 1 and 2 in our period, where the first mailing of harity 1 is on January 20 th 2002 and the first mailing of harity 2 on February 1 st Then his/her start-up period is February 1 st January 31 st The individual start-up period enables us to alulate reasonable initial values of the explanatory variables. The remainder of the data is used as the estimation period. Note that we only onsider individuals who are ative in the estimation period, where ative is defined as being mailed at least one. In our sample, 2220 individuals have reeived mailings from two harities during our time span, and 280 of three harities. Furthermore, 2163 individuals reeive mailings from harity 1, 2421 from harity 2 and 695 from harity 3. These numbers are roughly proportional to the atual numbers of donators in the databases of the three harities, and are thus representative for the relative harity magnitudes. See Table 2 for some desriptives of the data. Here averages are taken over the whole sample, explaining the low values for the smallest harity (harity 3) Insert Table For example, we an dedue that at an overall response rate of 0.19, people on average respond to about one out of five mailings, although this varies somewhat aross harities. This may seem high for diret mailings but is atually a reasonable response 16

20 rate for the harity industry 4. Furthermore, our observation period of 3.5 years ontains over mailing events in total. To get a better piture of what the data look like, Figure 1 depits a possible senario for an individual that reeives mailings from all three harities. In the start-up period s/he reeived eight diret mailings, three of whih s/he responded to. In the estimation period s/he donated twie out of the eight mailing events Insert Figure As appears from Figure 1 and from the model desribed in the previous setion, we assign eah mailing event to a single date, while in pratie we may have both a mailing and a response date. We hose to onsider the mailing date as the mailing event date in the model, as we assumed an individual instantly makes the response deision upon reeiving a mailing. Thus, as only the information known at that time an be taken into aount in the response deision, we feel this should also be the only input in the explanatory variables. Furthermore, over 50 perent of the responses to a diret mailing were made within a week of the mailing date. Finally, varying the implementation of the mailing event date did not lead to qualitatively different results. 4.2 Results To investigate the effets of mailing ations and the ompetitive interations between harity 1, 2 and 3, we estimate the model desribed in Setion 3, by applying MCMC tehniques to obtain draws from the posterior distributions of the parameters. Estimation results Using the Gibbs sampling tehnique of Geman and Geman (1984) we estimate our model, where we use iterations as burn-in. After the hain has onverged, we retain every tenth iteration of the next iterations to obtain an approximately random sample from the posterior distribution. Our posterior results are based on the resulting 4000 draws. In Table 3 we present the posterior means of the effets of our variables in both the response and the amount equation, where posterior standard deviations are in parentheses. Below we will disuss the parameter estimates for the various types of variables Insert Table

21 Mailing variables The effet of mailings on response to a future mailing of the same harity is signifiantly negative. Thus, eah extra mailing a harity sends to an individual negatively affets the probability that this individual will respond to future mailings, possibly refleting diret mailing irritation. For own mailings, we do not find evidene for a non-linear relationship of response inidene and mailing frequeny, as the square of mailings is not signifiant. For ompetitive mailings a non-linear relationship with response inidene is found. As the effet of mailings is signifiantly positive and the effet of square of mailings is signifiantly negative, small (disounted) numbers of ompetitive mailings have a positive effet but larger (disounted) numbers have a negative effet, suggesting irritation aused by too many mailings. Thus, it seems that a little ompetition an be reinforing, but too muh may be detrimental. However, as the deay parameter for mailings is small, it may be the ase that for most events in our dataset the past disounted number of mailings is relatively small, so that an extra mailing will have a positive overall effet. To gain more insight, we therefore study whether the marginal effet of an extra mailing, whih arises from the linear and quadrati term, is positive or negative for the atual mailing events in our data, eteris paribus. For around two thirds of the ases we find a negative effet of an extra mailing. Or, in around two thirds of the ases too many ompetitive mailings are reeived. We find similar results for the effets of mailings on the amount donated on subsequent donating oasions. Additionally, we find a non-linear effet of own mailings. The higher the (disounted) number of mailings, the stronger is the negative effet of an extra mailing on future donated amounts. Response variables The variable response reflets an exponentially weighted version of the response rate and has a positive effet on response, both to own and ompetitive mailing events. The own effet aptures loyalty effets towards the harity. That is, if an individual has frequently donated to a ertain harity in the past, this inreases the probability that s/he will donate again. Furthermore, the ompetitive effet indiates a general positive attitude towards haritable donating. That is, if an individual has frequently donated to other ompeting harities in the past, this reflets a positive attitude towards haritable donating and inreases the probability of response to this harity in the future. As all three harities in our data are from the health ategory, the ross effet reflets that individuals who frequently donate to one health harity are also more likely to donate to other health harities and thereby spread their donations over different health auses. 18

22 For the amount equation, only the own effet is signifiant. This positive effet indiates that individuals with high response rates at a harity also tend to donate larger amounts to this harity, again apturing loyalty effets. For reeny of response, we find both a signifiant main effet and a signifiant quadrati effet on response inidene. Hene, the effet of response reeny is nonlinear, in line with our expetations. More speifially, for both own and ompetitive responses, we find that very low and very high reeny values derease the probability of response, while intermediate values have a positive effet. Thus, if an individual just responded it is unlikely s/he will respond again, but if the last response has been very long ago, s/he may have lapsed in that s/he has stopped being a donator to the harity. Regarding the effet of response reeny on amount, we find that reeny dereases the amount donated. Thus, an individual that has reently donated, or has donated frequently in the past, will donate a lower amount to the urrent mailing, although this effet is somewhat weakened by the positive quadrati term. Although we did not antiipate it, this effet orresponds to a budget restrition, in that individuals that have reently or frequently donated do not have budget left to donate a large amount now. Amount variables For the response equation, we find both own and ompetitive effets of the amount variables, although in opposite diretions. The variable own amount, refleting the weighted average past donation, has a positive effet on future response. This finding again suggests a positive attitude towards the harity and possibly loyalty. Thus, the higher the past donations to a ertain harity, the higher the probability this individual will donate again. On the other hand, the variable ompetitive amount has a negative effet on future response, so that the higher the past donations to the ompetition, the lower the probability the individual will donate to this harity, suggesting loyalty towards the ompetition. For the amount equation, we find both positive own and positive ompetitive effets. Partiularly the own-effet is quite substantial, whih one would expet as donation sizes tend to be rather stable over time. The ompetitive effet indiates that the higher the average donation at ompetitors of this harity, the higher the donated amount will be, suggesting a ertain general generosity. Next, we find a negative own effet of amount reeny on response inidene, whih we an interpret as a budget restrition. If an individual has reently donated money to a harity or has already donated a lot, s/he may not have budget left to donate to this harity again. The negative ompetitive effet of amount reeny has a similar interpretation. 19