رونمایی از رابطه بین زمان بندی معامله، هزینه و رفتار ترک تحصیل مشتریان

The customer lifetime value combines into one construct the transaction timing, spending and dropout processes that characterize the purchase behavior of customers. Recently, the potential relationship between these processes, either at the individual customer level (i.e. intra-customer correlation) or between customers (i.e. inter-customer correlation), has received more attention. In this paper, we propose to jointly unveil the direction and intensity of these correlations using copulas. We investigate the presence of these correlations in four distinct product categories, namely online music albums sales, securities transactions, and utilitarian and hedonic fast-moving consumer good retail sales. For all product categories, we find a substantial amount of inter- and intra-customer correlation. At the inter-customer level, on average frequent buyers tend to spend more per transaction than the other customers. In addition, on average, large buyers have a longer lifetime. At the intra-customer level, we find that the existence and intensity of compensating purchase behaviors vary across product categories and across customers. From a managerial viewpoint, our approach improves the forecasts of the firm’s future cash flows, especially for the product categories and customers where the correlations are the strongest. Moreover, the correlation parameters also provide additional insights to traditional customer valuation analysis on the magnitude, durability and volatility of the cash flows that each customer generates. We conclude by discussing how these insights can be used to improve customer portfolio decisions.

Over the last decade, customer lifetime value (hereafter, CLV) has become a powerful customer valuation metric (Blattberg et al., 2009, Gupta et al., 2004, Gupta et al., 2006, Kumar and Reinartz, 2006, Kumar et al., 2008, Rust et al., 2004 and Venkatesan and Kumar, 2004). Its success among academics and practitioners can be explained by the increasing pressure to make marketing accountable and the need to identify profitable customers and allocate resources accordingly (Gupta et al., 2006, Kumar and Reinartz, 2006 and Venkatesan et al., 2007). In this context, accurate CLV forecasting has become of upmost importance to managers. The CLV metric integrates three key decision processes a customer goes through: (i) the transaction timing process, or when to buy, (ii) the spending process, or how much to spend, 1 and (iii) the dropout process, or when to become permanently inactive ( Fader, Hardie, & Lee, 2005a). Together, these decisions determine the cash flows that firms can expect from each customer over her lifetime. These three purchase decisions have traditionally been assumed independent of each other ( Fader et al., 2005a and Schmittlein and Peterson, 1994). In particular, the model proposed by Fader et al. (2005a) assumes three underlying distributions that are independent: an exponential distribution for the customer’s interpurchase times, a gamma distribution for the spend per transaction and an exponential distribution for the customer’s unobserved lifetime. They assume customer heterogeneity in the various processes using independent mixing distributions. In practice however, various forms of correlation are likely to violate the independence assumption and consequently lead to inaccurate CLV forecasting. One type of correlation occurs at the intra-customer level when the timing at which a customer makes a purchase interrelates with the value of this transaction. For instance, Jen, Chou, and Allenby (2009) find evidence that some customers adjust their purchase quantities upwards when interpurchase times are longer. Another type of correlation occurs at the inter-customer level when the expected number of transactions, transaction value and/or customer lifetime correlate across customers. For instance, customers with a high purchase frequency have been found to generate greater income streams and have longer expected lives than those who purchase infrequently by Blattberg, Getz, and Thomas (2001) and Jacoby and Kyner (1973). 2 In total, three inter-customer correlations – (i) between timing and spending, (ii) between timing and dropout and (iii) between spending and dropout – can arise between customers, as well as one intra-customer correlation for each individual customer. 3 Lately, several methods have been proposed to unveil either the intra-customer correlation between the timing and spending processes (Boatwright et al., 2003, Glady et al., 2009, Jen et al., 2009 and Romero et al., 2013), or the inter-customer correlation between the timing, spending and/or dropout decisions (Abe, 2009a, Abe, 2009b and Borle et al., 2008; we refer to the next section for a complete review). In all instances, research has shown that ignoring any of these correlations substantially biases the model predictions since it fails to account for the covariance between the processes when forecasting the CLV (Park & Fader, 2004). However, to date no single study has been able to capture all correlation types at once. In this paper, we propose a model for estimating CLV that jointly accounts both the intra- and inter-customer correlations between the timing, spending and dropout decisions of customers. Methodologically, we extend the model proposed by Fader et al. (2005a) by replacing the independent distributions for each customer’s interpurchase time and spend per transaction by a joint distribution (intra-customer level) and also specify a joint distribution for the transaction rates, spending rates and dropout rates across customers (inter-customer level). To link these distributions, we use copulas ( Danaher and Hardie, 2005 and Danaher and Smith, 2011). They are able to “couple” different families of distribution and to unmask the true strength of dependence between any two processes, which a classical correlation coefficient (e.g. Pearson) would not be able to identify. We show that accounting for both the intra- and inter-customer correlations improves predictions of customer purchase decisions, above and beyond incorporating none or some of them (intra or inter). Beyond the gains in predictive accuracy, we also discuss how the intra- and inter-customer correlations can guide customer portfolio decisions. Managerially, they contain useful information as to the magnitude, durability and volatility of the cash flows generated by every customer. Finally, we also contribute to the customer valuation literature by developing a typology of the different correlations between the transaction timing, spending and dropout processes. We explain how they translate in terms of purchase behavior and why they are likely to occur. We focus on a number of rationales which underlie customer purchase decisions and create tradeoffs between the various decisions customers make (Chintagunta, 1993 and Gupta, 1988). Finally, we ensure the generalizability of our findings by applying our model to four customer transaction databases, representing different product categories and/or industries. The first one pertains to music albums sales at an online retailer (CDNOW).4 The second includes securities transactions at a major financial institution. The last two data sets concern the retail industry; one contains transactions of a utilitarian fast-moving consumer good (FMCG), the other of a hedonic FMCG. The remainder of the paper is organized as follows. In Section 2, we define the intra- and inter-customer correlations between the timing, spending and dropout processes, review the existing literature, and discuss the behavioral rationales underlying each correlation. In 3 and 4, we explain the copula methodology and show how to incorporate it into the CLV framework by Fader et al. (2005a). We describe our data in Section 5 and apply our methodology in Section 6. 7 and 8 conclude with a number of managerial implications for customer portfolio management and a discussion of promising future research directions.

While the CLV framework developed by Fader et al. (2005a) has been adopted as a powerful customer valuation method, the potential correlation between the timing, the spending and the dropout processes, both at the intra- and inter-customer levels, called for the development of a conceptual and methodological framework to better understand the trade-offs and interplay between the various purchase decisions that customers make. Using copulas to account for correlation, we offer a method to improve the model predictions and generate new insights into the purchase behavior of customers. Despite our efforts, we should mention some limitations. First, while we explore the correlation across a variety of product categories, the set of variables available in each application is limited. We do not have access to marketing-mix variables, neither to competition variables, which would be interesting to consider in a future analysis. For the financial securities data, we do not have stock market fluctuation data, which may admittedly have a sizeable influence on customers’ purchase and selling behavior. For instance, when the stock market is on the upward trend, customers might make more frequent and larger transactions. This omitted variable may drive both the timing and spending processes and may therefore inflate the intra-customer correlation. Addressing this problem is not trivial given that stock market fluctuations are difficult to predict. Second, our method captures the contemporary correlation between the various purchase decisions but overlooks the possibility of lead-lag relationships between the variables. Future research could benefit from adapting our framework to a context where longer lags would be added. Third, the range of copulas could be extended. For instance, pair-copula construction method could have been used (Kumar et al., 2014). Finally, our managerial recommendations based on the magnitude, durability and volatility of the cash flows generated by each customer constitutes a first step towards a different approach to customer portfolio decisions. Nevertheless, it requires an in-depth analysis in which one would optimize customer portfolios incorporating the information available on the correlations. We hope that this research opens up new avenues for a better understanding of the correlations between the timing, spending and dropout decisions of customers.