Choice Behavior Under Dynamic Quality Changes

Choice Behavior under Dynamic Quality Changes:

State Dependence Versus 'Play-It-By-Ear' in Selecting Ski Resorts

Klaus Moeltner

Jeffrey Englin

Paper Submission for the

Second World Congress of Environmental and Resource Economists

Monterey, CA

June 24-27, 2001

(Long Paper Presentation)

Corresponding Author:

Klaus Moeltner

Assistant Professor

Department of Applied Economics and Statistics

University of Nevada, Reno

MS 204

Reno, Nevada 89557

Phone: (775) 784-4803

Fax: (775) 784-1342

e-mail:

web page:

JEL Codes: C15, C35, D12, Q26

ABSTRACT AND KEY WORDS

The literature on brand loyalty has focused on products that exhibit constant quality over time. In this study we consider ski resorts, for which quality attributes change frequently. This requires a model that includes dynamic quality features and indicators for state dependence, while controlling for individual heterogeneity. We show that purchase history and dynamic choice characteristics have a significant and offsetting effect on repurchase decisions. This suggests a third category of consumer in repeated choice settings next to habit formers and variety seekers: the play-it-by-ear type who, unaffected by purchase history, moves across brands in pursuit of consistent quality.

KEY WORDS: Repeated brand choice; Dynamic quality features; Random parameters;

Simulated choice probabilities.

1

1. introduction

When consumers repeatedly choose over several products, past choices can affect the probability of selecting a given product again at a later occasion. This phenomenon is commonly referred to as ‘state dependence’ (Heckman 1981a). Generally, state dependence can increase a consumer’s propensity to repurchase a specific good (habit formation), or decrease the probability of repurchase (variety seeking). A key element of the research on the effects of state dependence to date has been the stability of characteristics for goods under consideration. This study examines the role of purchase history for products with both fixed and time-variant attributes. Our empirical application is based on a set of ski areas in the Sierra Nevada. The dynamic quality attributes are snow and temperature.

In the marketing literature, state dependence is often labeled as purchase carryover or purchase-event feedback (Allenby and Lenk 1995; Keane 1997). Understanding these forces that guide consumer choice is important to managers when making marketing and pricing decisions. As pointed out in Keane (1997), temporary promotional efforts may affect consumer behavior well into the future if people are susceptible to habit formation. On the other hand, if consumer choice is relative insensitive to past purchases, or if variety seeking is the dominant element of state dependence, the promotional impact on sales may be short-lived.

Interest in the effect of state dependence on choice behavior has also found entry into the recreation literature in recent years. Some examples are McConnell, Strand, and Bockstael (1990), Adamowicz (1994), and Smith (1997). In those studies, the ‘products’ people are choosing from are not food or household items, as commonly investigated in marketing research, but rather recreation sites such as fishing spots (Adamowicz 1994; Swait, Adamovicz, and van Bueren 2000), or beach destinations (McConnell, Strand et al. 1990). In this context, understanding demand effects attributable to state dependence aid public land managers in making policy decisions on site access, pricing, and quality.

Regardless of the application, researchers must take care to disentangle ‘true’ state dependence (Heckman 1981a) from the effect of time-variant exogenous variables and consumer heterogeneity. Specifically, the effect of true state dependence may be inflated if consumer preferences are erroneously assumed to be homogeneous, or dynamic exogenous variables are omitted (Heckman 1981a; Keane 1997; Erdem and Sun 2001). In recent marketing contributions heterogeneity has been explicitly captured in repeated choice models by introducing random coefficients into random utility models (RUMs) (Allenby and Lenk 1995; Erdem 1996; Keane 1997). Allenby and Lenk (1995), Keane (1997), and Erdem and Sun (2001) also include time varying price and marketing variables (display and advertising) to disentangle their effect on purchase decisions from true state dependence.

For the household products generally considered in marketing applications (ketchup, peanut butter, detergents, etc.), price and marketing variables may well be the main candidates among time varying exogenous factors that could lead to erroneous inferences about state dependence if omitted from a multi-choice model. Other product attributes, such as quality features, usually do not change over the research period for a specific brand item. Thus, they can plausibly be held constant over time in a repeated choice specification. However, there are consumer products that are inherently susceptible to quality changes over time, within the same brand label. One such example would be wine, where the same winery and appellation (the ‘brand’ or ‘label’) can sell products of varying quality, depending on vintage. If one were to ignore the dynamics in these attributes when examining consumer loyalty or variety seeking for wine labels over time, the above mentioned problem of ‘spurious state dependence’ (Heckman 1981a) may transpire, even after controlling for heterogeneity and marketing effects. This issue becomes even more important if the goods under consideration are recreation sites. As these sites are not the end product of a highly controlled manufacturing process, they are by nature susceptible to a multitude of quality changes over time. The importance of these changes for repeated site choices will depend on the type of recreational activity, and individual preferences. However, to our knowledge there does not yet exist a multi-site recreation study with focus on state dependence that includes either dynamic quality variables or individual heterogeneity.

This research extends existing marketing and recreation studies by analyzing the separate effects of quality changes and state dependence on consumer choices, while allowing for individual heterogeneity. In addition, we examine if consumers who place a relatively large weight on a specific time and site-varying attribute are less likely to form habits. Conversely, we investigate if what appears to be behavior driven by variety seeking is in fact a manifestation of a ‘play-it-by-ear’ attitude fueled by strong preferences for the changing attribute in question. This requires a product that is purchased relatively frequently, and exhibits both time variant and time invariant features. Ski resorts are well suited for this purpose. Their terrain and level of difficulty remain unchanged over time, while on a given day the quality of a visit to the resort will be heavily affected by day-specific attributes such as snow conditions and weather. To our knowledge, this is the first such application for a multi-choice model with state dependence.

The remainder of this text is structured as follows: In the next section we develop an econometric model of state dependence, dynamic quality effects, and heterogeneity. The empirical part of this study then discusses data, estimation results, and operational implications for ski resort managers. Concluding remarks and a summary of key findings are given in the last section.

1. Model Formulation

Following the majority of brand choice studies, we embed our model in a random utility (RUM) framework. Specifically, we assume that the utility individual i derives from a visit to resort j at time t is given by

(1)

where Aj is a vector of time-invariant resort attributes, Pijt is the price to i for visiting resort j at time t, Qjt is a vector of quality characteristics that change over resorts and time, and Sijt is a vector of variables associated with state dependence. The symbols i, i, i, and i denote individual-specific coefficient vectors, and ijt is an i.i.d. random error term.

Time periods are generally defined as purchase occasions in brand-choice studies (e.g. Allenby and Lenk 1995; Erdem 1996; Keane 1997). This preempts an investigation of inter-purchase time effects on choice decisions. As shown in Papatla and Krishnamurthi (1992), Chintagunta (1998), and Chintagunta and Prasad (1998), the length of time between purchases can affect the nature and intensity of state dependence. To capture such effects in our model, and in synchronicity with the nature of our data (day trips) we choose days as the relevant time unit. It should be noted that for household goods it is often assumed that a given product is being consumed continuously throughout the inter-purchase period (e.g. Papatla and Krishnamurthi 1992). This is different for recreation sites, where actual consumption ends with the visit. In fact, non-consumption at time t becomes a separate choice. This is usually modeled as ‘staying-home’ option or ‘nonparticipation’ in a RUM specification (e.g. Morey, Shaw, and Rowe 1991; Morey, Rowe, and Watson 1993). We follow Adamowicz (1994) by modeling nonparticipation as an additional alternative to actual sites with associated utility

(2)

where the “0” subscript indicates the stay-home option. We reduce all quality indicators to a constant, and set price to zero for this choice. We do, however, retain variables measuring state dependence as described below.

While some studies on repeated choice let state dependence work through attributes of brands purchased in the past (e.g. Trivedi, Bass, and Rao 1994; Erdem 1996), we follow recent contributions in marketing (Keane 1997; Chintagunta and Prasad 1998; Erdem and Sun 2001) and recreation (Adamowicz 1994; Swait, Adamovicz et al. 2000) by defining variables for state dependence based on brands (sites) chosen at previous purchase occasions. The question then arises as to how far back into a consumer’s purchase history the model should reach. At one extreme, one could include only the choice decision made in the preceding period (‘1st order’ process, Erdem and Sun 2001). At the other extreme, one could explicitly model the individual effect of all past choices made by the consumer (Heckman 1981b). Some authors have proposed a middle ground by using a weighted average of past purchases to model choice history (Guadagni and Little 1983), or by including the number of uninterrupted times (‘run’) a given brand was chosen prior to the current time period (Heckman 1981b; Bawa 1990). For our application the number of time periods during the skiing season of interest (151 days) is far too large to allow the separate inclusion of all previous choices. However, we a priori concur with McConnell, Strand et al. (1990) that recent visits ought to weigh more heavily for current site decisions than visits further in the past. We therefore include two indicators for past site choices in the model: the total number of times a given resort was chosen prior to t (Nijt), as in Adamowicz (1994), and the consecutive number of times a given resort was chosen up to t uninterrupted by any visits to other destinations (Rijt). This variable conveys the notion of ‘run’ mentioned above. Since our data do not include many day-to-day runs, we allow for interruption by the stay-home option for this indicator. Our hypothesis is that whatever manifestation of state dependence, if any, drives individual i ought to manifest itself more strongly through Rijt than Nijt. We also specify two analogous indicators for the stay-home option: the number of times during the season prior to t an individual chose not to participate (Hit) (Adamowicz 1994), and the number of consecutive days of non-skiing immediately preceding t (Dit) (Provencher and Bishop 1997; Swait, Adamovicz et al. 2000). Thus, the elements of Sijt, j=0...J, materialize as

,(3)

where dijt , j = 0...J, is a zero / one dummy taking the value of one if resort j was chosen by i at time t, while hij,t is a dummy equal to one if j is the stay-home option, and equal to zero if j is an actual resort. This implies that Rijt and Dit equal zero for j = 0, while Hit only applies to nonparticipation. While somewhat counterfactual, setting Dit, the number of days since the last ski trip, to zero for the stay-home option is necessary to preserve this indicator in a RUM specification. In essence, Dit can be interpreted as the relative effect of prolonged nonparticipation on choice probabilities for resorts versus the probability to stay home in the current period as well.

Theoretically, both nonparticipation indicators could measure a building up of ‘eagerness’, i.e. an increased probability of skiing as they grow large, or ‘rustiness’, i.e. the opposite effect. In essence, ‘eagerness’ is the equivalent to ‘variety seeking’ for actual sites, while ‘rustiness’ corresponds to ‘habit formation’, or ‘inertia’. Adamowicz (1994) for example, finds that eagerness dominates behavior in his ‘Rational Model’ (increased probability of visits as Hitincreases), while Provencher and Bishop (1997) find that as more time elapses since the last visit the probability of participation decreases. Swait, Adamovicz et al. (2000), in turn, report initial rustiness following a preceding visit that turns into eagerness after about ten weeks of nonparticipation. As we will show, the stay-home counter reaching through the entire season (Hit) is a much more robust indicator of state dependence for nonparticipation than the recent ‘run’ of days at home. Specifically, the latter measure masks a skier’s preferences for time-variant attributes if they are omitted from the model. In other words, what appears to be short-term rustiness turns out to be a wait for the right conditions, or a ‘play-it-by-ear’ effect in our terminology. This is one of the key findings in this study.

As mentioned previously, to correctly estimate and interpret indicators for state dependence and the effect of time-variant exogenous factors, we need to control for individual heterogeneity in our model. The rationale behind this requirement is that probabilities associated with repeated choices made by the same person will be correlated due to unobserved individual characteristics and preferences. If ignored, such inherent ‘tastes’ may be incorrectly interpreted as an indication for state dependence. In recent contributions to the brand choice literature, heterogeneous reactions to pricing and marketing variables were found to be a significant factor in the process that drives repeated purchase decisions (Allenby and Lenk 1995; Erdem 1996; Keane 1997; Erdem and Sun 2001). Erdem (1996) and Erdem and Sun (2001) explicitly allow for and find significant heterogeneity in the way past brand choices and attributes affect individuals’ repurchase decisions. In a RUM framework, it is convenient to introduce heterogeneity through random coefficients (Revelt and Train 1998; McFadden and Train 2000). In contrast to Allenby and Lenk (1995), and Keane (1997), who allow for time-varying taste parameters, and following Erdem (1996), and Erdem and Sun (2001), we assume individual preferences remain constant throughout our research period (151 days). Collecting i, i, i, and i into a single coefficient vector i, we stipulate that parameters are distributed multivariate normal with

(4)

Thus, we estimate a vector of parameter means, and the elements of the variance-covariance matrix . In contrast to previous studies, the covariance terms in  are of major interest and importance in this paper. Specifically, we a priori expect a negative sign for covariances between (presumed positive) coefficients associated with dynamic quality attributes and (positive) coefficients for state dependence, if habit formation dominates. Conversely, if a coefficient for state dependence is negative (indicating variety seeking tendencies), its covariance with coefficients for dynamic quality should be positive. In other words, we hypothesize that the stronger the effect of quality seeking for a given individual, the smaller will be the absolute value of the coefficient for state dependence drawn for this individual. The intuition behind this premise is that quality-sensitive skiers, i.e. the play-it-by-ear types, should be less likely to be influenced by past resort choices. As we will show below, our results generally confirm this stipulation. This constitutes the second key finding flowing from this research.

We assume that remaining serial correlation in our model is accounted for by observed time-varying site attributes and indicators for state dependence. This implies that ijt in (1) is a truly random error term uncorrelated with the elements of i. The stipulated density of this error will dictate the specification of choice probabilities. Two frequently used distributions in the choice literature are normal, resulting in a multivariate probit specification (Hausman and Wise 1978; Keane 1997), and type I extreme value. The latter distribution, in combination with the random coefficients in i, yields a random parameter logit, or ‘mixed logit’ model (Revelt and Train 1998; Brownstone and Train 1999). In either case, the estimation of choice probabilities requires solving a high-dimensional integral. As discussed in Layton (2000), the dimension of integration proliferates with choice occasions in the multivariate probit model, and with the number of random parameters in a mixed logit specification. In our application, each individual faces 1359 choice occasions in a model with a limited number of random coefficients. For the sake of computational tractability we therefore choose the mixed logit approach for our application. Thus, the probability of skier i choosing option j at time t, conditional on φi, is given by (McFadden 1974)

,(5)

where Vijt is defined as in (1). The conditional probability of observing an individual’s entire sequence of trip decisions is therefore (Erdem 1996)

,(6)

where dijt is defined as in (3). Relaxing conditionality on coefficients yields

,(7)