Interpersonal communications have long been recognized as an influential source of information for consumers.

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1 CELEBRATING 30 YEARS Vol. 30, No. 4, July Augus 2011, pp issn eissn X doi /mksc INFORMS A Dynamic Model of he Effec of Online Communicaions on Firm Sales Garre P. Sonnier, Leigh McAliser Red McCombs School of Business, Universiy of Texas a Ausin, Ausin, Texas {garre.sonnier@mccombs.uexas.edu, leigh.mcaliser@mccombs.uexas.edu} Oliver J. Ruz Yale School of Managemen, Yale Universiy, New Haven, Connecicu 06521, ruz@uw.edu Inerpersonal communicaions have long been recognized as an influenial source of informaion for consumers. Inerne-based media have faciliaed informaion exchange among firms and consumers, as well as observabiliy and measuremen of such exchanges. However, much of he research addressing online communicaion focuses on raings colleced from online forums. In his paper, we look beyond raings o a more comprehensive view of online communicaions. We consider he sales effec of he volume of posiive, negaive, and neural online communicaions capured by Web crawler echnology and classified by auomaed senimen analysis. Our modeling approach capures wo key feaures of our daa, dynamics and endogeneiy. In erms of dynamics, we model daily measures of online communicaions abou a firm and is producs as conribuing o a laen demand-generaing sock variable. To accoun for he endogeneiy, we exend he laen insrumenal variable echnique o accoun for dynamic endogenous regressors. Our resuls demonsrae a significan effec of posiive, negaive, and neural online communicaions on daily sales performance. Failure o accoun for endogeneiy resuls in a severe aenuaion of he esimaed effecs. From a managerial perspecive, we demonsrae he imporance of accouning for communicaion valence as well as he impac of shocks o posiive, negaive, and neural online communicaions. Key words: word of mouh; Bayesian esimaion; endogeneiy; dynamics Hisory: Received: April 2, 2010; acceped: January 17, 2011; Eric Bradlow and hen Preyas Desai served as he edior-in-chief and Michel Wedel served as associae edior for his aricle. Published online in Aricles in Advance June 6, Inroducion Inerpersonal communicaion, or word of mouh, is recognized as an influenial source of informaion for consumers. For example, Ris (2005) repors ha inerpersonal communicaion is he mos influenial informaion source among various ypes of media when making a purchase. As recenly as 10 years ago, mos inerpersonal communicaion ook place in person or over he elephone. Today, billions of people engage in conversaions via Inerne-based social media such as blogs and online social communiies. From he perspecive of consumers, online communicaions are scalable. Raher han one-o-one or one-o-few, online communicaions end o be one-o-many or many-omany, faciliaing informaion exchange and he diffusion of user-generaed conen (Godes e al. 2005). As he populariy of social media increases wih consumers, firms are increasing spending on word-ofmouh markeing. From 2007 o 2008, spending on word-of-mouh markeing rose 14.2% o $1.54 billion and is expeced o reach $3 billion by 2013 (PQ Media 2009). From he perspecive of he firm, online communicaions are observable. Observabiliy faciliaes he measuremen of online communicaions, which enables he esimaion of he impac of online communicaions on sales and oher quaniies of ineres o he firm. As consumers are influenced by inerpersonal communicaion, here is reason o expec ha online communicaions will influence consumer decisions, especially for search goods (Giese e al. 1996). Regarding valence, consumer behavior heory argues ha negaive communicaions may be more diagnosic and hus have greaer impac compared wih posiive communicaions (Herr e al. 1991). However, behavioral research has also idenified siuaions where posiive communicaions may be more diagnosic. For example, Ahluwalia (2002) finds ha posiive informaion is more persuasive in he case of a familiar brand. Alhough heory poins o a poenially sronger effec for posiive and negaive communicaions because of heir diagnosic naure, communicaions scored as neural may help spread awareness and inform consumers abou he insalled 702

2 Markeing Science 30(4), pp , 2011 INFORMS 703 base of he firm s producs. Higher awareness can lead o adopion by innovaors, whereas informaion abou he insalled base can lead o adopion by imiaors (Bass 1969). Much of he research addressing he impac of online communicaions has resriced consideraion o raings. Raings for producs such as books and movies are widely available on sies such as Amazon.com or Yahoo! Movies and are also inherenly quaniaive. Chevalier and Mayzlin (2006) find ha differences in he number of raings (volume) and he average raing (valence) across online book reailers affec relaive sales. Dellarocas e al. (2007) demonsrae ha he volume and valence of online cusomer movie raings are relaed o fuure box office revenues. However, oher sudies have found mixed resuls in erms of he effec of raings volume and valence. Duan e al. (2008) find ha raing valence does no affec movie box office revenues direcly, bu raher indirecly hrough an effec on he volume of raings. Chinaguna e al. (2010) find ha raings valence explains opening-day movie box office revenues, whereas he volume and variance of raings does no. Moe and Trusov (2011) argue ha he informaion conen in online raings may be limied by social dynamics in he raings environmen. They find ha consumers raings are influenced by previously posed raings and ha he resuling sales effec resuling from his social dynamic is small. Some empirical work addresses he effecs of online communicaions more broadly defined han raings daa colleced from a single websie or small se of websies. 1 Dhar and Chang (2009) find ha he overall volume of blog poss abou a music album across he Inerne predics he album s sales rankings. Their daa do no conain he valence of he blog poss. A problem wih obaining he valence informaion in his seing is he sheer magniude of he daa. Godes and Mayzlin (2004) navigae around his problem by resricing heir daa gahering o commens posed in a single online communiy and handcoding senimen for a random sample of 10% of heir daa. They find ha he dispersion of online conversaions regarding new elevision programs across Usene forums predics he program s Nielsen raings, whereas he volume and valence of conversaions do no. Similarly, Liu (2006) resrics his daa gahering o ex reviews posed on he Yahoo! Movies websie. He also hand-codes valance for his sample of ex reviews 1 Ouside he realm of online communicaions, Luo (2007, 2009) uses daa on cusomer complains filed wih he U.S. Deparmen of Transporaion o show ha he number of complains abou an airline is associaed wih lower sock reurns. and finds ha volume, bu no valence, explains box office revenue. 2 A cenral ension in he invesigaion of he effec of online communicaions beyond raings is ha considering a wider swah of online communicaions exacerbaes he problem of coding valence. In response, researchers looking beyond raings have ended o resric heir aenion o a single websie or online forum when valence is of ineres (Godes and Mayzlin 2004, Liu 2006). Conrary o he normaive findings of he consumer behavior lieraure, hese sudies have no found an effec for valence. The burden of collecing online communicaions from a broader se of sources han a single websie or forum and subsequenly hand-coding valance has recenly been eased by wha a recen New York Times aricle refers o as senimen analysis (Wrigh 2009). For example, firms such as Visible Technologies and Scou Labs measure he volume and valence of online communicaions across a variey of social media, including blogs, cha rooms, news sies, YouTube, and Twier. Senimen analysis ools hold he promise of assising companies sruggling o assimilae and undersand he orren of communicaions abou heir producs and services. 3 The inended conribuion of our research is boh subsanive and mehodological. Subsanively, we invesigae he effec of he volume of posiive, negaive, and neural online commens, capured by Web crawler echnology and classified by auomaed senimen analysis, on daily sales performance. Compared wih previous research, our daa provide a more comprehensive view of online communicaions regarding our firm. We are among he firs o sudy he effec of online communicaions wih valence classified by auomaed senimen analysis and he firs o show ha posiive, negaive, and neural commens all affec firm sales performance. Mehodologically, our modeling approach capures wo key feaures of our online communicaions daa, dynamics and endogeneiy. Previous research has shown ha he effec of online communicaions may be dynamic (Godes and Mayzlin 2004, Liu 2006). We 2 In a recen working paper, Tirunillai and Tellis (2010) invesigae he effec of online reviews on sock reurns. Similar o Liu (2006), hey code ex reviews from Amazon, Yahoo!, and Epinions as posiive or negaive. They find an effec for he oal volume of reviews and for negaive reviews, wih he former being sronger. 3 Two recen working papers make use of auomaed senimen analysis daa. Shin e al. (2010) find ha posiive (negaive) online commens are a leading indicaor of fuure price increases (decreases) for low price and follower brands (all brands) of MP3 players. Onishi and Manchanda (2010) invesigae he effec of blogging during new produc inroducion and find a posiive sales effec for he cumulaive volume of blogs and he number of posiive blogs bu no effec for he number of negaive blogs.

3 704 Markeing Science 30(4), pp , 2011 INFORMS view daily measures of online communicaions abou a firm and is producs as conribuing o a laen dynamic demand-generaing sock variable. Similar o goodwill models of adverising (e.g., Nerlove and Arrow 1962, Bass e al. 2007), our model demonsraes a parsimonious means of allowing informaion conained in pas daily online communicaions o affec sales. Whereas goodwill adverising models have considered he poenial endogeneiy of adverising in he sock equaion (Bass e al. 2007), because of a lack of appropriae insrumens, he problem has no been addressed. In he conex of our problem and daa, endogeneiy concerns loom large because of measuremen error, omied variables, and simulaneiy. Furher complicaing maers, our measure of poenially endogenous online communicaions is mulivariae and dynamic. Our mehodological conribuion sems from he need o address his challenge. We do so by exending he laen insrumenal variable (LIV) mehod (Ebbes e al. 2005, Zhang e al. 2009) o accoun for a dynamic mulivariae endogenous regressor. We are among he firs o use he LIV mehod o address endogeneiy and he firs o consider he mehod in he conex of ime-series daa. Our daa are provided by a well-known echnology firm selling a variey of durable goods in an online channel. The firm s producs could be characerized as search goods because produc feaures and characerisics are easily evaluaed prior o purchase (Nelson 1970). The firm parners wih a leading provider of social media-monioring ools o collec daa on he number of imes he firm and is producs are menioned on he Inerne. The commens in which he firm is menioned are classified via a proprieary ex mining algorihm as posiive, negaive, and neural. Raher han raings daa from a single websie such as Yahoo! Movies (Duan e al. 2008) or posings from a single forum such as Usene (Godes and Mayzlin 2004), our daa capure a broader view of he online communicaions abou he firm and is producs on he Inerne. Of ineres o managers and academics is he quesion of wheher or no such daa explain sales performance. We use he online communicaions daa along wih daily sales daa o esimae our model, employing a Bayesian forward-filering, backward-sampling algorihm o esimae he dynamic parameers. Log Bayes facors and sep-ahead forecass srongly suppor our proposed model. Our resuls indicae ha posiive and neural commens increase he dynamic sock, whereas negaive commens decrease i. Furhermore, he magniude of he effecs is larger for posiive and negaive online commens compared wih neural online commens. In erms of dynamics, he duraion of he effec of a shock o online communicaions is esimaed o be slighly longer han one week. We find significan correlaions in he residual erms of he sock and online communicaions equaions, and we demonsrae ha ignoring his endogeneiy leads o severely biased esimaes of he effecs of online communicaions. We demonsrae he managerial relevance of our findings by showing he imporance of commen valence. We conras our model wih ha of an alernaive model ha uses oal commen volume aggregaed across valence. A subsiue for cosly auomaed senimen daa is volume daa available from public sources (e.g., Technorai). We aggregae he online communicaions ino a coun of oal commen volume analogous o he volume daa available from public sources and reesimae our proposed model. We find ha he model ha accouns for valence provides superior fi. Perhaps more imporanly, we find ha he effec of online communicaion on sales is masked when using commen volume aggregaed over valence. We also use he model o demonsrae he magniude of he effec of shocks o posiive, negaive, and neural commens. Our resuls sugges ha firms seeking o iniiae posiive and neural communicaions as par of markeing campaign may be jusified in doing so (Godes and Mayzlin 2009). Our resuls also sugges ha firms should proacively manage siuaions leading o negaive commens, as such commens can resul in a subsanial negaive impac on sales. The remainder of our paper is srucured as follows. In 2, we presen our dynamic model of he effec of online communicaions on sales. In 3, we discuss some perinen feaures of our daa and he esimaion resuls. In 4, we discuss some managerial implicaions of our resuls. In 5, we summarize and conclude. 2. Model Sales response models have a rich hisory in he markeing lieraure. Recenly, researchers have considered sales response models hrough he lens of dynamic linear models (Van Heerde e al. 2004, Bass e al. 2007, Naik e al. 2010). Building on hese models, we rea daily sales observaions as a funcion of a laen, dynamic demand-generaing sock of informaion and exogenous covariaes (Naik e al. 2010, Ruz and Bucklin 2011). The informaion sock, in urn, is affeced by he previous period s sock and online communicaions. Le sales and he informaion sock a ime be denoed by y and S, respecively. Le he K-dimensional vecor x conain he exogenous covariaes. Finally, le posiive, negaive, and neural online communicaions be denoed by c p, c n, and c o, respecively. To moivae he specificaion of our model, consider a model of sales as a funcion of curren and

4 Markeing Science 30(4), pp , 2011 INFORMS 705 pas online communicaions. Such a model could be expressed as L y = x + c + c l l + (1) where L denoes he lag lengh, c = c p c n c o, are parameers o be esimaed, and N 0 2 is an error erm. To esimae Equaion (1), he researcher mus specify L. Wih daily ime-series daa, he number of appropriae lags is poenially large, creaing a proliferaion of parameers. Lagged regressors are also ypically correlaed, leading o mulicollineariy problems in esimaion. Consisen wih his issue, he significance of differen lagged erms is ofen sensiive o L. To allow for a more parsimonious reamen of dynamics, we specify he sales model as l=1 y = x + S + S = S 1 + c + S (2) In Equaion (2), sales is a funcion of exogenous covariaes x and a laen informaion sock, S. The scalar parameer measures he carryover effec in he sock equaion, and he parameer vecor measures he effec of posiive, negaive, and neural online communicaions on he informaion sock S. Assuming S N 0 2, he model can be esimaed as a Bayesian dynamic linear model (DLM) wih he equaions for y and S as he observaion and sae equaions, respecively (Wes and Harrison 1997). The model specificaion in Equaion (2) accouns for dynamics in he effec of online communicaions on sales by allowing pas online communicaions o accumulae in a laen sock of demand-generaing informaion. From our perspecive, his is appropriae as i seems unlikely ha daily online communicaions are direc calls o acion. Given ha our echnical firm sells durable search goods, consumers are likely seeking informaion abou produc feaures and characerisics prior o purchase. Curren and pas online communicaions abou he firm and is producs can be a source of relevan informaion for consumers o use during heir search process. In a similar seing, Naik e al. (2010) argue ha corporae adverising (i.e., adverising for Ford as a brand versus Ford Explorer as a produc) does no direcly generae sales revenue bu raher conribues o a sock of corporae goodwill. Our expecaion is ha posiive online communicaions will replenish he demandgeneraing sock, whereas negaive online communicaions will diminish i. Wih respec o neural online communicaions, we argue ha hey may help spread awareness and produc informaion or inform consumers abou he insalled base of he firm s producs, which may replenish he sock variable (Bass 1969). In erms of esimaion, he full condiional disribuion of he dynamic sae variable S can be sampled via he forward-filering, backward-sampling algorihm. Condiional on he curren draw of S and assuming online communicaions are exogenous, sandard Bayesian regression seps can be used o sample from he full condiional disribuion of he and parameers. However, esimaion of he parameers via sandard regression echniques will resul in biased esimaes if online communicaions are endogenous. We argue ha here are hree reasons o be concerned abou he poenial endogeneiy of online communicaions: measuremen error, omied variables, and coevoluion beween he informaion sock and online communicaions. Measuremen error seems o be a likely source of endogeneiy when using Web crawler echnology o measure online communicaions. For example, if consumers use jargon or abbreviaions (e.g., MS o refer o Microsof) o refer o he company and is producs, he crawler echnology may no capure he communicaions. The crawler echnology may also erroneously classify unrelaed communicaions as relevan. Alhough exclusion erms can be included in he crawler search (e.g., search for Ford, exclude Harrison Ford), measures of online communicaion are unlikely o be error-free. More imporanly, i is very unlikely ha eiher human or auomaed classificaion of he valence of an online communicaion is error-free (Wrigh 2009). I is well known ha measuremen error induces correlaion beween he regression residual and he mismeasured regressor (Greene 2000). In erms of omied variable bias, i is possible ha unobserved firm aciviy affecs goodwill and is also correlaed wih online communicaions. Firms have become more engaged in paricipaing in online communicaions wih cusomers (Godes e al. 2005) and even seeding online communicaions (Godes and Mayzlin 2009). I is likely ha unobserved aciviy, such as adverising or promoion, coincides wih online communicaions, generaing correlaion beween he sock equaion error erm and measures of online communicaion. 4 Finally, i is possible ha he informaion sock and online communicaions are codeermined. We noe ha feedback 4 In mos cases, adverising daa are available on a weekly or monhly level, bu no daily. For example, Taylor Nelson Sofres, he provider of he Leading Naional Adverisers daa, offers weekly adverising daa, bu no daily. This creaes an inheren rade-off for he researcher. The daa could be aggregaed o a level for which markeing mix daa (e.g., adverising) are available. However, daily variaion in online communicaions and sales would be ignored, and he effec of online communicaions on sales may suffer from aggregaion bias. However, if he markeing mix daa are no available a he finer level of emporal aggregaion, omied variable bias becomes a greaer concern.

5 706 Markeing Science 30(4), pp , 2011 INFORMS effecs have been found in previous research considering raings and online word of mouh (Godes and Mayzlin 2004, Duan e al. 2008). Empirical applicaions of adverising goodwill models have considered he possible endogeneiy of variables in he sock equaion, bu hey have no addressed his issue because of a lack of insrumens (Bass e al. 2007). Indeed, wihou appropriae insrumens, here is lile ha can be done. Finding appropriae insrumens is nonrivial. In he case of endogenous prices in demand models for producs wih commodiy inpus, for example, inpu prices may be a suiable insrumen (Kuksov and Villas-Boas 2008, Musalem e al. 2008). For daily online communicaions, his is less applicable. The mos obvious candidae for an insrumen is lagged online communicaions. However, if online communicaions are measured wih error, or if pas online communicaions are correlaed wih he conemporaneous values of he omied variable, lagged values are invalid as an insrumen (Angris and Krueger 2001). 5 Weak or invalid insrumens can resul in parameer esimaes ha are more biased han hose obained by simply ignoring he endogeneiy problem (Sock e al. 2002, Zhang e al. 2009). To address he endogeneiy of online communicaions in he sock equaion, we make use of he LIV echnique (Ebbes e al. 2005). As wih frugal insrumenal variable echniques, which exploi he momens of he disribuion of he endogenous regressor, he LIV approach alleviaes he problem of finding valid insrumens. The LIV approach funcions much like he sandard insrumenal variable approach ha expresses an endogenous regressor as a funcion of some observed insrumen presumed o be correlaed wih he endogenous regressor bu orhogonal o he error erm. In he LIV approach, a laen variable model is used o accoun for dependencies beween he endogenous covariae and he error by inroducing unobserved discree binary variables. These laen variables are used o decompose he endogenous covariae ino a sysemaic par ha is uncorrelaed wih he error and one ha is possibly correlaed wih he error. This allows for unbiased esimaion of he effec of endogenous covariaes, such as online communicaions, in he sock equaion. To elaborae our approach, we begin by expressing he vecor of communicaions a ime as follows: c p c p p c n = c n + n (3) c o c o 5 Noe ha such a problem could also plague he sandard vecor auoregression approach as he impulse response funcion could be biased by he errors in variables. o where c = c p c n c o is he sysemaic componen of he communicaion variables and is independen of S, he goodwill residual, and c = p n o, he random componen of he communicaion variables. Le = S c. We assume follows a mulivariae normal disribuion, MVN 0, where is a full 4 4 marix. The hree off-diagonal elemens in he firs row of are he covariance erms beween he goodwill and online communicaion residuals. Nonzero covariance erms imply he condiional disribuion of S, given c = c p c n c o, depends on c p, c n, and/or c o. Thus, esimaion of he srucural parameer (he effec of online communicaions on he informaion sock) via a sandard Bayesian regression sep will resul in biased esimaes (Rossi e al. 2006). 6 If we observe a se of variables ha are correlaed wih online communicaions bu orhogonal o S, we can use hese observed insrumens in esimaion. Denoe such an insrumen for online communicaions by he vecor z = z p z n z o. We may hen express he sysemaic porion of online communicaions as c p z p p c n = z n n (4) c o z o o where he parameers are o be esimaed. As noed above, such insrumens are difficul o observe in general and especially in our conex of daily mulivariae observaions. To overcome his issue, Ebbes e al. (2005) propose a laen discree binary variable o decompose a single disribued endogenous regressor ino a sysemaic par uncorrelaed wih he error erm and a par poenially correlaed wih he error erm. Zhang e al. (2009) exend his approach o he case of muliple endogenous regressors. Following Zhang e al. (2009), we can express he sysemaic par of our vecor of endogenous online communicaions as a funcion of a laen binary insrumen, v, ha divides he online communicaion measures ino discree caegories and, he caegory parameers: c p c n = c o v p p v n n v o o (5) We call he model described by Equaion (5) he caegorical LIV model. Each laen insrumen v l (for 6 We use he erm srucural o differeniae beween he parameers in Equaion (2) versus he reduced-form represenaion achieved by subsiuing for he endogenous regressors, according o he researcher s specificaion for c.

6 Markeing Science 30(4), pp , 2011 INFORMS 707 l = p n o follows a J -dimensional mulinomial disribuion wih probabiliies 1 l l J, where l j is he probabiliy ha he jh laen insrumen for he lh ype of online communicaions is one. The properies of he LIV esimaor are discussed in Ebbes e al. (2005). As discussed herein, he model is idenified by he likelihood, wih he requiremen ha J 2. For any of he endogenous regressors, wih J = 1 he sysemaic porion is consan, and here is no informaion wih which o esimae he srucural parameer. I follows ha as any of he j l approach 0 or 1, he laen insrumen is weakened in is abiliy o idenify he srucural parameer. Ebbes e al. (2005) apply he caegorical LIV model o he classic problem of esimaing he effec of educaion on earnings. They find ha ordinary leas squares esimaes suffer from an omied variable bias ably conrolled for by he caegorical LIV approach and ha he approach is robus o misspecificaion of he number of caegories. Zhang e al. (2009) apply he caegorical LIV mehod o accoun for endogeneiy in a mediaion analysis of he effec of aenion o feaure adverisemens on sales. The daa ses used in boh hese sudies make use of cross-secional variaion. In conras, our daily sales daa are imeseries daa. A concern wih he caegorical LIV model for our applicaion is ha he behavior of he esimaor in he presence of a dynamic endogenous variable is no well undersood. If he laen caegories fail o capure much of he correlaion wih he endogenous regressor, here will be less informaion o idenify he srucural parameer. We propose an alernaive specificaion of he LIV model o accoun for dynamic endogenous regressors. Specifically, we model he endogenous online communicaions as a funcion of a dynamic sae variable uncorrelaed wih he sock residual S. Le he sysemaic porion of online communicaions be c p p c n = n (6) c o where = p n o is a dynamic sae mached o he observed vecor of online communicaions as in Equaion (3). The sae equaion for is o = 1 + (7) where is a diagonal marix of parameers and he vecor of residual erms is disribued as mulivariae normal wih full covariance marix, MVN 0. We refer o he model described by Equaions (6) and (7) as he dynamic LIV model. The model hierarchy for our dynamic LIV model is y x S 2 y x S 2 2 y x S S y x c S 1 c c S S 1 c S S 1 c S S The model is compleed by proper bu diffuse prior disribuions for he iniial condiions of he wo dynamic sae variables, as well as priors for oher model hyperparameers. Deails are included in he appendix. In he caegorical LIV model, he insrumen is specified via laen caegories and he caegory parameers. In he dynamic LIV model, he laen insrumen is specified via an auoregressive process. As wih a sandard Bayesian DLM, he auoregressive process on allows for separae idenificaion of he error variances and. Analogous o he case of a single caegory in he caegorical LIV model, if he dynamic LIV is modeled using a process wih a consan mean, he variances would no be separaely idenified. To assess he performance of our dynamic LIV model and he caegorical LIV in he presence of a dynamic endogenous regressor, we simulae hree daa ses according o he model described by Equaion (8) wih a single endogenous regressor for ease of exposiion. The daa ses differ in he daageneraing values of he parameer, which governs he carryover dynamics in he laen insrumen. We invesigae values of = 0 5, 0.7, and 0.9. The diagonal elemens in, which represen he variance of he informaion sock S and he variance of he endogenous regressor c, are se o 0.5 and 1.0, respecively. The off-diagonal elemen of, which represens he covariance beween he sock residual S and he residual of he insrumen equaions c, is se o Finally, we se he srucural parameer o 1. 7 The direcion of he bias is deermined by he sign of he correlaion. A negaive correlaion will induce a downward bias in he srucural parameers, whereas a posiive correlaion will induce an upward bias. (8)

7 708 Markeing Science 30(4), pp , 2011 INFORMS Table 1 Coefficien Esimaes for a Dynamic Endogenous Regressor Under Differen Carryover Parameers for he Dynamic Laen Insrumen Specificaion of endogenous regressor Exogenous Endogenous Variable Caegorical LIV Dynamic LIV Esimaes for b Daa-generaing value, a = 0 5 Poserior mean c Poserior sandard error (0.03) (0.18) (0.03) 95% coverage inerval Daa-generaing value, = 0 7 Poserior mean Poserior sandard error (0.04) (0.11) (0.05) 95% coverage inerval Daa-generaing value, = 0 9 Poserior mean Poserior sandard error (0.03) (0.07) (0.04) 95% coverage inerval a The parameer governs he carryover dynamics in he dynamic laen insrumen. b The parameer is he effec of he endogenous regressor on he sock variable. In all hree cases, we generae daa wih = 1 c Bold indicaes he 95% coverage inerval spans he daa-generaing value of = 1. The remaining deails of he simulaion are omied for breviy bu are available from he auhors upon reques. For each of he hree simulaed daa ses, we esimae he exogenous sock model described by Equaion (2), he caegorical LIV model, and he dynamic LIV model. In Table 1, we repor he poserior mean and sandard error of he esimaes from he hree models, as well as he 95% coverage inervals. Given he daa-generaing parameers, we expec o see a downward bias in he esimaes of he srucural parameer ha ignores endogeneiy. For all hree simulaed daa ses, reaing he endogenous regressor as exogenous resuls in biased esimaes of he srucural parameer, wih poserior mean esimaes of ranging from 0.70 o 0.76 across he daa ses. None of he coverage inervals spans he daa-generaing value of = 1. The caegorical LIV esimaor does no seem o be able o capure sufficien exogenous variaion in he dynamic endogenous regressor o remedy he endogeneiy bias, yielding poserior mean esimaes of ranging from 0.69 o 0.74 across he daa ses. As wih he exogenous model, none of he coverage inervals spans he daa-generaing value of = 1. 8 For he 8 For each scenario = , we generaed muliple daa ses and esimaed he exogenous model, caegorical LIV model, and dynamic LIV model. In he ineres of breviy, we do no presen a full simulaion sudy. For he exogenous and dynamic models, he resuls are consisen wih he esimaes repored in dynamic LIV model, he poserior mean esimaes of range from 0.95 o 0.98 across he hree daa ses. In all cases, he 95% coverage inerval spans he daageneraing value of = 1. We now urn our aenion o he performance of he models in our empirical applicaion. 3. Daa and Esimaion Resuls Online communicaion daa for our firm were colleced by a leading provider of social mediamonioring ools via heir proprieary Web crawler echnology. The daa consis of daily couns of online commens for he firm and is producs and services for he period April 1, 2007 o December 7, The valence of each menion is classified by a proprieary algorihm as posiive, negaive, or neural. 9 Table 2 presens some descripive saisics for he daily couns. The neural caegory accouns for he majoriy of observaions. In addiion o he online communicaion daa, our cooperaing firm provided us wih daily sales revenue daa and daa on he dae of new produc launch announcemens (covering he same period as he online communicaions daa). To specify our model of sales performance, we include in he vecor x a dummy variable for weekends and a dummy variable for new produc launch announcemens. We esimae four models. Model M1 is described by Equaion (2) and reas he online communicaions as exogenous. Models M2 M4 rea online communicaions as endogenous. Model M2 uses lagged communicaions as an insrumen, model M3 uses he caegorical LIV approach, and model M4 uses our dynamic LIV approach. Table 3 repors he poserior mean esimaes of he srucural parameers and he parameers on he weekend and new produc dummies, along wih he sandard error of he esimaes (in parenheses) across he four models. The aserisks in he ables denoe parameer esimaes for which he coverage inervals of he esimaes do no span zero. We use he coverage inervals o assess he saisical significance of he parameer esimaes. Table 1. However, on occasion, he coverage inerval for he caegorical LIV model conains he daa-generaing value for he srucural parameer. In hese cases, he poserior mean of he sandard error is relaively high and he coverage inervals relaively wide. This is similar o he case of esimaion wih weak insrumens, which someimes alleviae parameer bias bu a he expense of higher sandard errors. 9 The provider uses supervised machine learning o perform he auomaed senimen analysis. Two broad caegories of daa feaures are used: hose derived from naural language processing and hose derived from social conex. The feaures are derived from iles, bodies, hreads, sies, permalinks, auhors, publicaion daes, queries, cusomers, ec. For example, a simple feaure migh be he exisence of a word such as love in a pos, which would be saisical evidence in favor of a posiive classificaion.

8 Markeing Science 30(4), pp , 2011 INFORMS 709 Table 2 Descripive Saisics: Posiive, Negaive, and Neural Commens Valence of commen Average per day Median Sandard deviaion Posiive Negaive Neural For model M1, which reas online communicaions as exogenous, he 95% coverage inervals on he coefficiens for posiive, negaive, and neural online communicaions all span zero. We find a similar resul for model M2, which uses lagged online communicaions as an insrumen. For model M3, he caegorical LIV model, he 95% coverage inerval on posiive online communicaions does no span zero; he 95% coverage inervals on he negaive and neural coefficiens do. However, he poserior mean esimaes of he probabiliies for he caegorical laen insrumens are 0.98, 0.02, and 0.04 for posiive, negaive, and neural online communicaions, respecively. This is an imporan poin because hese esimaes indicae ha here is lile variaion wih which o idenify he srucural parameers (Ebbes e al. 2005). The resuls for models M2 and M3 sugges ha lagged values as insrumens, as well as he caegorical LIV approach, do lile o alleviae endogeneiy concerns. For model M4, he dynamic LIV model, we find ha posiive and neural commens have a posiive effec on he sock variable, whereas negaive commens have a negaive effec. In all cases, he 95% coverage inervals of he esimaes do no span zero. The poserior mean esimae of he coefficien on posiive Table 3 Parameer Esimaes for Posiive, Negaive, and Neural Commens and Exogenous Covariaes Across Alernaive Model Specificaions Exogenous Specificaion of online communicaions Endogenous M1: M2: M3: M4: Variable Exogenous Lagged IV Caegorical LIV Dynamic LIV Commen valence Posiive Negaive Neural Exogenous covariaes Weekend New produc launch announcemen Noe. Cell enries are poserior mean and poserior sandard error (in parenheses). 95% coverage inerval does no span zero. commens is larger in magniude han ha of negaive commens. This resul is consisen wih behavioral research ha finds posiive informaion is more persuasive in he case of a familiar brand (Ahluwalia 2002). The coefficien for neural commens is posiive, bu i is smaller in magniude han hose for posiive and negaive commens. This is consisen wih he idea ha neural commens spread awareness and/or inform consumers abou he insalled base of he firm s producs, he laer of which can be imporan if adopion is influenced by imiaors (Bass 1969). 10 Under he dynamic srucure of he model, he conemporaneous effec of an increase in he lh caegory of online commens a ime on sales a ime is measured by l. 11 The effec on fuure sales in period k > is given by l k 1. I follows ha he cumulaive effec up o ime k on sales of an increase in he lh ype of online commens a ime is k =1 l 1, a geomeric series. Assuming an infinie horizon, we measure he long-run effec of an increase in he lh caegory of online commens a ime as l / 1. Table 4 repors he conemporaneous and long-run elasiciies of sales wih respec o each caegory of online communicaions. Posiive and negaive commens have elasiciies ha are larger in magniude compared wih neural commens. Among posiive and negaive commens, posiive commens have a slighly larger elasiciy. These resuls demonsrae he imporance of valence in measuring he effec of online communicaions. Figure 1 presens a plo of he duraion of he elasiciies wih respec o a change in online commens of each ype a ime. The majoriy of he effecs have dissipaed wihin a week. The magniude of he long-run elasiciies and he duraion of he elasiciies indicae ha ignoring he dynamic effecs would severely undersae he effec of online communicaions on sales. For all four models, he coefficien on he weekend dummy is negaive, indicaing a sales drop on he weekends. The 95% coverage inervals on he esimaes do no span zero for any of he four models. In conras, he new produc launch announcemens do no appear o have a significan effec on sales. 10 As discussed in Wes and Harrison (1997) and Van Heerde e al. (2004), an advanage of he DLM framework is ha he model may be specified direcly in levels raher han changes, even in he presence of a random walk. However, concerns may linger over he issue of serial correlaion in he observaion equaion errors. Using he Durbin Wason and Bruesch Godfrey ess (Greene 2000), we find no evidence of serial correlaion in he errors. If serial correlaion were presen, i could easily be accommodaed in he DLM by augmening he sae space o allow for auoregressive error erms. See Ruz and Bucklin (2011) for deails. 11 Recall ha l p n o sands for he hree caegories of online communicaions: posiive, negaive, and neural.

9 710 Markeing Science 30(4), pp , 2011 INFORMS Table 4 Conemporaneous and Long-Run Elasiciies of Sales wih Respec o Online Communicaions Valence of commen Conemporaneous Long run Posiive Negaive Neural Noe. Cell enries are poserior mean and poserior sandard error (in parenheses). 95% coverage inerval does no span zero. Table 5 Model Comparison Specificaion of online Log Bayes Model communicaions Insrumens facor a MAE b MSE c M1 Exogenous M2 Endogenous Lagged communicaions M3 Endogenous Caegorical LIV M4 Endogenous Dynamic LIV a Model M4 is he null model. b Mean absolue error of sep-ahead forecas. c Mean squared error of sep-ahead forecas. To compare he models esimaed hus far, we compue log Bayes facors using he sep-ahead predicive densiies (Wes and Harrison 1997, Van Heerde e al. 2004, Bass e al. 2007). We also compue he mean absolue error (MAE) and mean squared error (MSE) of he sep-ahead forecass (Wes and Harrison 1997). We rea model M4, he dynamic LIV model, as he null model. A log Bayes facor beween 1 and 2 indicaes evidence in favor of he null model, whereas a log Bayes facor greaer han 2 indicaes srong evidence in favor of he null model. Table 5 repors he resuls. We find srong evidence for he dynamic LIV model over he alernaive models. Figure 2 presens a plo of weekday sales along wih he sep-ahead forecass and coverage inervals. Figure 3 presens he evoluion of he sock variable S for our dynamic LIV model. The poserior mean esimae of he carryover parameer is 0.58 (wih a sandard error of 0.10). The 95% coverage inerval does no span zero. In Table 6, we repor he poserior mean esimaes of he correlaion beween he sock equaion error Figure 1 Elasiciy Wearou for Online Communicaions erms and he errors from he dynamic LIV equaions. We find negaive correlaions beween he sock error and he LIV error for posiive and neural commens (poserior mean esimaes of 0 80 and 0 46, respecively). We find posiive correlaion (poserior mean esimae of 0.32) beween he sock error and Figure Plo of Weekday Sales Revenues and Sep-Ahead Forecas Sales Sep-ahead forecas 95% coverage inerval Time in days Noes. To aid he graphical presenaion of he daa, he plo excludes weekends because weekend sales are orders of magniude lower han weekday sales. In he model, he drop in sales on weekends is ably capured by he weekend dummy. Elasiciy Days Posiive Negaive Neural Figure 3 Plo of Poserior Mean of a Sock Variable wih a 95% Coverage Inerval % coverage inerval Poserior mean Time in days

10 Markeing Science 30(4), pp , 2011 INFORMS 711 Table 6 Variable pos neg neu Error Correlaions for he Sock and Insrumen Equaions of he Dynamic LIV Model Correlaion esimaes S Noe. Cell enries are poserior mean and poserior sandard error (in parenheses). 95% coverage inerval does no span zero. he LIV error for negaive commens. For all hree correlaions, he 95% coverage inerval does no span zero. These resuls srongly indicae he presence of regressor-error dependencies in he sock equaion. Furhermore, given he esimaed signs of he coefficiens (posiive for posiive and neural commens and negaive for negaive commens) and he correlaions (negaive for posiive and neural commens and posiive for negaive commens), he expecaion is ha ignoring he dependencies in esimaion will bias he coefficien esimaes oward zero. This is consisen wih he esimaion resuls for model M1, which reas online communicaions as exogenous, giving face validiy o our resuls. 4. Managerial Implicaions Our resuls hus far demonsrae ha online communicaions beyond hose capured by produc raings and reviews have an effec on firm sales. We now urn our aenion o wo specific managerial implicaions of our resuls. Firs, we examine he imporance of accouning for he senimen of online communicaions. Second, we examine he revenue impac of shocks o posiive, negaive, and neural online communicaions The Imporance of Accouning for Senimen Several new senimen analysis companies are aemping o ineres clien firms in heir abiliy o help undersand he informaion being exchanged in he online space (Wrigh 2009). However, auomaed senimen analysis daa are osensibly more cosly. Indeed, firms can obain volume daa for free from sies such as Technorai. Furhermore, previous research has found an effec for he simple overall volume of communicaions. We invesigae he imporance of accouning for senimen by esimaing a resriced model, M5, which ses p = n = o =. This ess he null model, M4, agains a resriced model where online communicaions have he same effec across posiive, negaive, and neural commens (i.e., a single coefficien on he oal volume of commens aggregaed over posiive, negaive, and neural). For he sake of compleeness, we also es a second resriced version of he dynamic LIV model, M6, which ses p = n = o = 0. This ess he null model agains he resriced model, where online communicaions have no effec. The log Bayes facor as well as he MAE and MSE of he sep-ahead forecass, repored in Table 7, indicae srong suppor for model M4, which accouns for senimen. Furhermore, he 95% coverage inerval for in model M5, which aggregaes over valence, spans zero. Thus, he effec of online communicaions is masked by ignoring commen valence capured by auomaed senimen analysis. This resul demonsraes he value of auomaed senimen daa. Firms ha currenly rely on free or less cosly oal volume daa may be underesimaing he value of online communicaions Revenue Effecs of Shocks o Posiive, Negaive, and Neural Communicaions Firms are increasingly aemping o iniiae word-ofmouh communicaions among exising and poenial cusomers wih he goal of generaing awareness and spreading posiive informaion (Godes and Mayzlin 2009). Alhough i seems exremely unlikely ha a firm would aemp o rigger negaive commens, i is he case ha small misakes by firms can also Table 7 The Imporance of Accouning for Senimen Specificaion of Resricions on Model online communicaions Insrumens srucural parameers Log Bayes facor a MAE b MSE c M4 Endogenous Dynamic LIV None M5 d Endogenous Dynamic LIV p = n = o = M6 e Endogenous Dynamic LIV p = n = o = a Model M4 is he null model. b Mean absolue error of sep-ahead forecas. c Mean squared error of sep-ahead forecas. d Model M5 aggregaes posiive, negaive, and neural communicaions ino a oal coun. e Model M6 resrics he effec of online communicaions o zero.

11 712 Markeing Science 30(4), pp , 2011 INFORMS quickly become large problems. For example, in 2006, a Comcas repair echnician fell asleep during a service call o a cusomer s home. The cusomer sho a video of he sleeping echnician and posed i o a blog. The video generaed more han 200,000 views and was discussed by he echnology blog Gizmodo and he mainsream news, including MSNBC and he New York Times (Belson 2006). Using our model, we invesigae he effec of a shock o posiive, negaive, and neural online communicaions. Under our dynamic LIV model, a shock o he lh caegory of online commens a ime will carry over o fuure values. To capure his dynamic, we use he forecas disribuions of he observaion and sae variables in our DLM (Wes and Harrison 1997) o generae 14-day forecass of online commens and sales. Leing T represen he erminal period of our daa, he poserior disribuions of he dynamic sae variables in he model become he prior disribuion for he T + 1s period. We firs compue a baseline forecas and subsequenly shock he T + 1s prior, in urn, for each of he l p n o caegories and recompue he forecass. Figure 4 presens he cumulaive revenues over he forecas period for he baseline and he hree scenarios where posiive, negaive, and neural commens receive a 10% shock in he iniial forecas period. For posiive commens, he shock resuls in an 18% increase in cumulaive revenues over he forecas period. For negaive commens, he shock resuls in an 11% decrease in cumulaive revenues. For neural commens, he shock resuls in a 7% increase in cumulaive revenues. The resuls on posiive and neural communicaions complemen he exising lieraure ha shows ha word-of-mouh campaigns can be an effecive ool for he firm (Godes and Mayzlin 2009) while also underscoring he imporance of managing siuaions ha may resul in negaive communicaions. For example, given he expeced revenue decline following a negaive shock o online communicaions, Figure Foureen-Day Cumulaive Revenue Forecass Under Baseline and 10% Shocks 212 Revenue under baseline Revenue under shock Posiive Negaive Neural 191 he firm may wan o increase adverising and promoional spending o offse he decline. On he oher hand, following a posiive shock o online communicaions, he firm may wan o decrease spending o boos profiabiliy. A full reamen of his issue would require spend daa, which we unforunaely do no have. 5. Summary and Conclusions The rise of Inerne-based social media has faciliaed he spread of online communicaions as well as he observabiliy and measuremen of he same. In paricular, raings and reviews permeae he online space for a wide range of caegories. The academic markeing lieraure has begun o explore he role of online raings in explaining firm oucomes. We argue ha alhough ineresing and imporan, raings daa are only a narrow slice of online communicaions abou a firm and is producs. Web crawler echnology has enabled firms o measure he number of menions regarding a firm and is producs or services across a much wider swah of he online space. Such daa are currenly available o firms via public and privae sources. Furhermore, privae firms are invesing in auomaed classificaion of online commens as posiive, negaive, or neural (Wrigh 2009). In his paper, we invesigae wheher and how such informaion affecs sales and develop an esimaion mehodology for uncovering such an effec. Our measures of online communicaions consis of daily couns of commens for a durable goods firm selling via an online channel. The daa are capured by Web crawler echnology. Raher han raings daa from a single websie such as Yahoo! Movies (Liu 2006, Duan e al. 2008) or posings from a single forum such as Usene (Godes and Mayzlin 2004), our daa capure a broader view of he online communicaions abou he firm and is producs across he Inerne. Via a proprieary echnique for conducing auomaed senimen analysis, he commens are classified as posiive, negaive, and neural. Wih hese daa, we model he effec of online communicaions on sales. Our model of he effec of online communicaions conains wo imporan feaures. Firs, we accoun for dynamic effecs of online communicaions by modeling sales as arising from a demandgeneraing dynamic sock variable. Posiive, negaive, and neural online communicaions conribue o he evoluion of he dynamic sock. The model is inspired by goodwill models of adverising. However, such models ypically assume exogeneiy of he adverising variables in he sock equaion, promping he second imporan feaure of our model. We accoun for poenial endogeneiy in he esimaion of he effec of online communicaions on he sock variable by

12 Markeing Science 30(4), pp , 2011 INFORMS 713 exending he laen insrumenal variable esimaor o accoun for dynamic endogenous regressors. We argue ha endogeneiy of online communicaions is a concern for a leas hree reasons. Firs, Web crawler echnology operaes by searching for keywords. For some firms and producs, keywords may no be unique. Alhough searches can be narrowed and refined by exclusion erms, he possibiliy of measuremen error looms. Furhermore, he algorihms ha classify menions as posiive, negaive, and neural are unlikely o be error-free, which also raises he poenial for measuremen error. Second, we do no have daa on daily adverising or promoional aciviies of he firm. In addiion, firms may engage in effors o mediae, moderae, or seed online communicaions (Godes e al. 2005). These unobserved aciviies are likely o be correlaed wih observed measures of online communicaions, causing an omied variables problem. Finally, research on he effec of raings and reviews on sales has demonsraed feedback effecs in sales and raings daa. Similarly, he sock variable and our measures of online communicaion may coevolve. The essenial problem wih an endogenous regressor is correlaion beween he regressor and he error erm. Wih a valid observed insrumenal variable in hand, correcing for endogeneiy bias is sraighforward. However, he search for good insrumens is a classic problem in applied economerics. Wih weak or invalid insrumens, he soluion may aggravae raher han ameliorae he problem. Recen work in markeing has considered a new esimaor o correc for endogeneiy bias based on laen insrumens. The LIV esimaor (Ebbes e al. 2005) divides he endogenous regressor ino sysemaic and random componens. The sysemaic componen is hen modeled as arising from a se of laen caegories wih caegoryspecific means. Mos, if no all, of he exising applicaions of he LIV mehod make use of daa wih cross-secional variaion. The properies of his esimaor are no well explored in he conex of imeseries daa. In simulaed ime-series daa as well as our acual daa, we find he caegorical LIV mehod is unable o correc he endogeneiy bias. To overcome he problem, we exend he LIV mehod by modeling he sysemaic componen of he endogenous regressor as a laen dynamic sae mached o he observed endogenous online communicaions variable and, by consrucion, orhogonal o he sock equaion error erm. Our empirical resuls show ha endogeneiy bias hampers esimaes of he effec of online communicaions on sales. Models ha rea online communicaions as exogenous or use lagged communicaions as an insrumen sugges no effec. In conras, our dynamic LIV model finds a significan impac of online communicaions on sales. Log Bayes facors and sep-ahead forecas performance indicae srong suppor for our proposed dynamic LIV model. We are among he firs o documen he impac of online communicaions measured by Web crawler echnology and scored wih auomaed senimen analysis. To he bes of our knowledge, we are he firs o documen an effec for posiive, negaive, and neural commens in his domain. Our findings underscore he imporance of accouning for dynamics and endogeneiy in he model. We find ha he effec sizes for posiive and negaive commens are larger han ha of neural commens and ha he effec size for posiive commens is larger han ha of negaive. In erms of he duraion of he effecs, we find ha he majoriy of he effecs have dissipaed afer abou a week. Imporan for managers, we find ha aggregaing online commens over valence masks he effec on sales. Thus, alhough obaining he senimen analysis daa is cosly relaive o publicly available daa on he oal volume of commens, he senimen analysis daa improve model fi and lead o a fundamenally differen conclusion regarding he effec of online communicaions. Previous research has noed he increasing propensiy of firms o aemp o iniiae word-of-mouh communicaions among exising and poenial cusomers (Godes and Mayzlin 2009). Our forecasing exercise demonsraes ha firms have good reason o focus on increasing posiive and neural commens, bu i also demonsraes ha evens precipiaing negaive commens can adversely affec revenues. A limiaion of our sudy is ha our daa are for a single firm. However, our goal here is o provide an iniial sep oward undersanding he effec of online communicaions on sales performance. To his end, we develop a mehod for coping wih he challenges of dynamics and endogeneiy inheren in his new daa. Fuure research should srive o replicae his resul across oher firms and indusries. Addiional fuure research opics in his area are pleniful. As noed in 1, firms are increasing spending on word-of-mouh markeing. We do no have daa o address issues such as he relaionship beween adverising and promoional spending and he generaion of online communicaions. Our daa were colleced by our cooperaing firm wih an inenionally broad focus. Fuure research may invesigae a more refined classificaion of online communicaions, such as brand commens, produc commens, or service commens. Such refinemens could lead o imporan sraegic findings in erms of differenial effecs across ypes of online communicaion. Finally, an ineresing issue o consider is he sraegic role of

13 714 Markeing Science 30(4), pp , 2011 INFORMS he firm. Beyond lisening o and measuring online communicaions, firms may ake a more acive role in shaping or seeding online conversaion. Indeed, our resuls sugges ha firms have an incenive o involve hemselves in he process. However, as firms become more engaged in he process, consumers percepions regarding he auheniciy of online communicaions may be harmed, evenually dampening or eliminaing he effec. Fuure research should seek o undersand effecive sraegies for firm involvemen ha preserve he auheniciy of he informaion and is ulimae effec. Acknowledgmen O. J. Ruz s curren affiliaion is he Foser School of Business, Universiy of Washingon, Seale, WA Appendix We deail he sampler used o esimae he dynamic LIV model described in Equaion (8): y x S 2 y x S 2 2 y x S S y x c S 1 c c S S 1 c S S 1 c S S Where convenien, we drop he subscrip for ease of exposiion. 1. Generae y X S 2. [ 1 y X S 2 (b MVN X X [ ] 1 1 [ b = X 1 X X ỹ Generae 2 y X S. ỹ = y S = 10 6 I K = 0 K ] 1 ) ] 2 y X S IG ( a ỹ X ỹ X b + T 2 a = 2 + K b = 1 ) 3. Generae S y x c S 1. We esimae he informaion sock via a dynamic linear model (Wes and Harrison 1997). The observaion equaion of our DLM maches observed sales wih he laen dynamic variable of ineres in our case, he sock variable. The observaion and sae equaions of he DLM are given by y = x + S + S = S 1 + c + S (9) where N 0 2. The laen insrumen equaion for he vecor of online communicaions is c = + c and MVN 0, where is a full 4 4 marix. We pariion such ha = ss sc cs cc, where ss is he scalar variance of S, cc is he 3 3 covariance marix of c, and sc = cs is a 3 1 vecor of covariance erms for S and c. We use he forward-filering and backward-smoohing algorihm (Wes and Harrison 1997) o sample S. The poserior a 1 is S 1 D S 1 N ms 1 CS 1 (10) The prior a ime is S D S 1 N as RS (11) where a S = ms 1 +c + sc 1 cc c and R S = CS 1 + ss sc 1 cc cs. The sep-ahead forecas disribuion is y D S 1 N f S QS (12) where f S = a S + x and QS = RS + 2. Finally, he poserior a ime is S D S N ms CS (13) where m S = as + AS y f S, CS = R S AS QS AS, and AS = R S QS 1. We use backward sampling o obain draws of S for all = 1 T. Firs, we sample S T DT S from is condiional disribuion as described in (13). Second, for each = T 1 T 2 0, we sample from S S +1 D S N g S H S, where gs = m S + B S S +1 a S +1, H S = C S B SRS +1 BS, and B S = CS RS Generae c S S 1. Le =, ỹ = S sc 1 cc c, x = S 1 c, and ss = ss sc 1 cc cs. Then ( [ ] 1 1 ) ỹ X MVN b X X + 1 ss [ ] 1 1 [ ] b = X 1 X + 1 X ỹ + 1 ss ss = 106 I 4 = Generae c S S 1. c S S 1 ( ( ) T IW q + T V + ) =1

14 Markeing Science 30(4), pp , 2011 INFORMS 715 = S c = S 1 + c q = 6 V = I 4 6. Generae 1. To generae, we ransform o he reduced form of he model. To accommodae he ransformaion, we define he following erms. Le p n o S = S S 1 ỹ = S c F = p n o = S + c c L = and = L L The observaion equaion of he reduced form maches he sock variable and online communicaions wih he laen dynamic insrumen. The observaion and sae equaions of his DLM are given by ỹ = F + = 1 + (14) where MVN 0. We use he forward-filering and backward-smoohing algorihm (Wes and Harrison 1997) o sample. The poserior a 1 is The prior a ime is 1 D 1 N m 1 C 1 (15) D 1 N a R (16) where a = m 1 and R = C 1 +. The sep-ahead forecas disribuion is where f = F a and Q = F R F +. Finally, he poserior a ime is ỹ D 1 N f Q (17) D N m C (18) where m = a + A ỹ f, C = R A Q A, and A = R Q 1. We use backward sampling o obain draws of for all = 1 T. Firs, we sample T DT from is condiional disribuion as described in (18). Second, for each = T 1 T 2 0, we sample from +1 D N g H, where g = m + B +1 a +1, H = C B R +1 B, and B = C R Generae 1. Le p = diag ỹ = X = 0 1 n o = I T ỹ X MVN b X 1 X b = X 1 X X 1 ỹ Generae 1. = 106 I 3 = 0 3 and 1 ( ( T IW q + T V )) References =1 q = 5 V = I 3 Ahluwalia, R How prevalen is he negaiviy effec in consumer environmens? J. Consumer Res. 29(2) Angris, J. D., A. B. Krueger Insrumenal variables and he search for idenificaion: From supply and demand o naural experimens. J. Econom. Perspec. 15(4) Bass, F. M A new produc growh for model consumer durables. Managemen Sci. 15(5) Bass, F. M., N. Bruce, S. Majundar, B. P. S. Murhi Wearou effecs of differen adverising hemes: A dynamic Bayesian model of he adverising-sales relaionship. Markeing Sci. 26(2) Belson, K Your call is imporan o us. Please say awake. New York Times (June 26), hp:// 26/echnology/26comcas.hml. Chevalier, J. A., D. Mayzlin The effec of word of mouh on sales: Online book reviews. J. Markeing Res. 43(3) Chinaguna, P. K., S. Gopinah, S. Venkaaraman The effecs of online user reviews on movie box office performance: Accouning for sequenial rollou and aggregaion across local markes. Markeing Sci. 29(5) Dellarocas, C., M. Zhang, N. F. Awad Exploring he value of online produc reviews in forecasing sales: The case of moion picures. J. Ineracive Markeing 21(4) Dhar, V., E. A. Chang Does chaer maer? The impac of user-generaed conen on music sales. J. Ineracive Markeing 23(4) Duan, W., B. Gu, A. B. Whinson The dynamics of online word-of-mouh and produc sales An empirical invesigaion of he movie indusry. J. Reailing 84(2) Ebbes, P., M. Wedel, U. Böckenhol, T. Seerneman Solving and esing for regressor-error (in)dependence when no insrumenal variables are available: Wih new evidence for he effec of educaion on income. Quan. Markeing Econom. 3(4) Giese, J. L., E. R. Spangenberg, A. E. Crowley The effec of produc-specific word-of-mouh communicaion on produc caegory involvemen. Markeing Le. 7(2)

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