Estimating the Impact of Consumer Expectations of Coupons on Purchase Behavior: A Dynamic Structural Model

We examine the basic premise that consumers may anticipate future promotions and adjust their purchase behavior accordingly. We develop a structural model of households who make purchase decisions to minimize their expenditure over a finite period. The model allows for future expectations of promotions to enter the purchase decision. Households with adequate inventory of the product may face a trade-off of buying in the current period with a coupon or defer the purchase until next period, given their expectations of future promotions. Thus, we provide a framework for examining the impact of consumer expectations on choice behavior. The target audiences for our paper are (a) empirical researchers who intend to make structural models part of their applied research agenda; and (b) managers who value and seek to understand the impact of consumers' coupon expectations on current purchase behavior. Our research objective is to provide an empirical framework to examine whether and to what extent consumers anticipate future coupon promotions and adjust purchase behavior. The central premise of our approach is that a rational consumer minimizes the present discounted value of the cost of a purchase where cost in a single period consists of purchase price, inventory holding cost, gains from coupons, and potential stockout cost. We aim to test whether our hypotheses regarding the various elements of the cost structure are supported and that whether consumers take into account future discounted cost when making current purchase decisions. The research methodology we adopt is relatively new in econometrics and known as the estimable stochastic structural dynamic programming method. The methodology amounts to incorporating a maximum likelihood routine embedded in a dynamic programming problem. The dynamic programming problem is solved several times within a maximum likelihood iteration for each value of the state space elements and for each value of the parameters in the parameter set. The state space in our model consists of purchase and nonpurchase alternatives in each time period, coupon availability and no coupon availability in each time period, level of inventory in each time period for each household, and consumption rate of each household. We use scanner panel data on purchases in the disposable diaper product category and promotions. We estimate the inventory holding and stockout costs, brand-specific value of coupons, and consumers' expectations of future coupons. The key insights and lessons learned can be summarized as follows: (1) Our results are consistent with the notion that consumers hold beliefs about future coupons, and that such beliefs affect the purchase decision. We find that the dynamic optimization model performs significantly better than a single-period optimization model and a naive benchmark model. (2) We find a high and significant stockout cost, consistent with the essential nature of the product category. Our estimate of the holding cost yields a reasonable annualized percentage value when converted to the cost of capital. We find that consumer valuation of coupons differ markedly across brands. (3) Our empirical evidence supports the notion that consumers hold beliefs about future coupon availability. We also find that the expectations about future coupons, estimated endogenously, differ depending upon whether or not a coupon was available in the current period. Thus, the proposed model structure yields rich managerial insights and facilitates several “what if” scenarios. A possible limitation of our model, and estimable structural models in general, is the computational cost. While it is possible to conceptually extend the state space to accommodate variations across households and add a richer parameter structure, each addition multiplies the size of the state space and the computation time. For this reason, we have kept the state space as tight as possible and refrained from additions that would otherwise enable us to incorporate heterogeneity in consumer decisions. For example, we assumed that consumers are similar other than reflected by their purchase behavior. We built a category purchase incidence model rather than a brand choice model. We refrained from including unobserved heterogeneity in the parameters. We chose to opt out of modeling autocorrelation and other time-dependent error term patterns in the likelihood function. Thus, we have made an effort to build a structural model that reasonably reflects consumer purchase behavior without requiring expensive computation. Currently, there are developments in econometrics to approximate the computation of the valuation functions without sacrificing much accuracy. When these methods are well developed we expect that structural models will become more commonplace in marketing.