Leveraging loyalty programs using competitor based targeting

Abstract

Loyalty programs (LPs) are widely used by firms but not well understood. These programs provide discounts and perks to loyal customers and are costly to administer, but produce uncertain changes in spending patterns. We use a large and detailed dataset on customer shopping behavior at one of the largest U.S. retailers before and after joining a loyalty program to evaluate how behavior changes. We combine this with detailed spatial data on customer and store locations, including the locations of competing firms. We find significant changes in behavior associated with joining the LP with a large amount of heterogeneity across customers. We find that location relative to competitors is the factor most strongly associated with increases in spending following joining the LP, suggesting that the LP’s quantity discounts work primarily through business stealing and not through other demand expansion. We next estimate a model of what variables determine how spending will change after joining the LP. We use high-dimensional data on spatial relationships between customers, the focal firm’s stores, and competing stores as well as customers’ historical spending patterns. This model is used to test whether past sales data reflecting customer’s vertical value to the firm or spatial data reflecting customer’s horizontal vulnerability are more important determinants of post-LP spending increases. We show how LASSO regularization estimated on complex spatial relationships are more effective than are models using past sales data or simpler spatial models. Finally, we show how firms can use customer and competitor location data to substantially increase LP performance through spatially driven segmentation.

Appendices

Appendix 1: Distance metrics

In the table below, x denotes the competitor type. In our empirical application this is either the big box generalist (BB), the small box generalists (SB1 or SB2), or the small box specialist (SS).

Table 12 Distance metric descriptions

Appendix 2: Spatial variable contribution

In this supplementary section we provide an additional measure of the contribution of spatial variables to the model fit relative to other types of variables. Specifically, we compare different spatial model performance in targeting as well as highlight that our spatial metrics contribute substantially more towards R² relative to traditional vertical variables.

1.1 Discussion of spatial model segmentation performance

In this section we discuss the relative performance of different types of spatial models at profitably segmenting LP customers. All the results discussed here correspond to Table 9. First we test a simple spatial model that takes the standard approach to spatial data of only considering distances between the focal store and customer and each of the four competitors. We see that the out-of-sample performance is actually worse than a mass marketing approach. In other words, while horizontal data is valuable in principle a simplistic approach to incorporating it that misses the nuances of competitive structure is not necessarily effective.

The second and third models extend the simple model with additional spatial metrics. First we include the count of the number of each of the four competitors within a 10 kilometer (6 miles) radius, approximately the average driving distance. Then, we augment the original spatial model with the apex angle, or the angle formed between the customer, focal store, and a given competitor with the customer at the apex. The results show that also knowing the number of nearby competitors is much more valuable than simply knowing distance between the customer and each store. In addition, knowing the angle between customer and competitors improves substantially over simply knowing distance. In terms of comparing these two data types, they perform roughly similarly as one another.

Next, to provide another comparison, we estimate three spatial models in the spirit of classic gravity models. These models date back to Reilly (1931) who coined the “law of retail gravitation” and are extended to a more flexible model by Huff (1964). These gravity models are designed to predict store choice while we have richer data on spending, but only at the focal store. We attempt to preserve the theoretical insight of these models but adjust the specification to instead predict the probability of a positive change in spend with $p_{k=1} = \frac {w_{1}/d_{1}^{\alpha }}{{\sum }_{k=1}^{5} w_{k}/d_{k}^{\alpha }}$, where d represents the distance between the customer and each store type k (the focal store and the four competitors) and w are the weights or “attractiveness” of each store.

We consider several Huff-style model specifications. In the first, we set the store attractiveness or mass to be the square footage of each competitor type and in the second specification we treat each store attractiveness as a parameter to estimate. In both of these cases, the decay parameter α is estimated using maximum likelihood. In our third specification we allow α_k to differ over store type. For segmentation, we take the models predictions and group the customers based on the percentile of positive spend in the training data.²⁶

We find that the gravity models perform quite well overall at identifying profitable customer groups. They outperform the mass marketing approach and the rule of thumb strategies. They also do better out-of-sample than the models using simple sales data or distance data alone, suggesting that those models are prone to overfitting in a way the more parsimonious gravity models are not. However, performance is similar to the augmented simple spatial models. In the next subsection we show that our preferred specification performs about three times as as well as the Huff-style gravity models, however.

1.2 Contribution to model fit

Table 13 presents the model fit using our two dependent variables of interest, where each row represents a single subset of the available variables. The first column displays the pseudo-R² from a logistic regression and the second column the standard R² from a linear regression. The variables are separated into one of five labels: our proposed spatial metrics, RFM (trip frequency and sales information), basket composition (number of items per basket, distinct items, distinct categories, etc.), the marketing indicator satisfying the exclusion restriction, and finally the selection correction polynomials from the first stage.

The spatial metrics explain considerably more than any of the alternative variable types. The sum of the R² values across the partial models is similar to the fit from the aggregate model in the final row. This suggests that the variable types tend to be relatively orthogonal to each other. In other words, the spatial information appears to be adding a non-trivial amount of unique information to the model that would otherwise be absorbed into the residuals.

A natural rebuttal to this table is that the results are driven simply by the sheer number of spatial variables relative to the other variable types. This is only partially true: recall that all of the spatial metrics are derived solely from the latitude and longitude of the focal store, competition, and the customer. From a managerial perspective it is very easy to recreate the diverse set of spatial metrics once these few location points are obtained. In this sense, it is more the variety among the spatial variables we designed, rather than simply the number of variables, that contributes a substantial amount of information to each model.

Table 13 Pseudo-R² and R² by variable type