Counter-cyclical price promotion: Capturing seasonal changes in stockpiling and endogenous consumption

Abstract

This paper provides a new and complementary demand-side-oriented explanation for counter-cyclical pricing, which we define as the presence of more frequent price discounts during high-demand seasons than in low-demand seasons in seasonal product categories. Our study focuses on how an increase in marginal utility of consumption in high-demand seasons (resulting in a seasonal upward demand shift) can increase price elasticity in storable and frequently-purchased product categories, where consumers may exhibit forward-looking price expectations and engage in stockpiling and where consumption may be endogenous. We propose that during high-demand periods, a price discount is more likely to increase purchase quantities due to lower satiation of consumption and to increase total consumption which induces category expansion. This leads to higher price elasticity during high-demand periods than during low-demand periods as consumers have forward-looking price expectations and stockpile and/or consumption is endogenous. Thus, we present stockpiling and endogenous consumption as the consumer behavioral mechanisms behind counter-cyclical price elasticity. Unlike most existing studies, our proposed mechanisms capture forward-looking consumers’ dynamic trade-offs created by temporary price reductions and, therefore, shed light on the practice of counter-cyclical price promotion, as opposed to a seasonal change in mean prices. We investigate the roles of stockpiling and endogenous consumption using the framework of a dynamic inventory model with endogenous consumption by allowing consumption utility to be subject to exogenous seasonal fluctuation. Our model indicates that during high-demand periods, demand elasticity increases by 9.63% relative to low-demand periods, offering a motivation for counter-cyclical price promotion. Counterfactual experiments were done to validate the roles of the proposed mechanisms of stockpiling and endogenous consumption, both of which explain counter-cyclical patterns in price elasticity as individually, as well as collectively, when the marginal utility of consumption varies across seasons.

Appendices

Appendices

Appendix A. Lack of a post-promotional dip

In this section, we present additional descriptive evidence suggesting endogenous consumption in the canned-soup category from a store-level data set.²⁶ If a promotion leads to stockpiling without changing the consumption rate, the sales volume for the category decreases in the period immediately following the promotion, producing a post-promotion dip in sales. By contrast, if the consumption rate increases as an outcome of an increase in purchase quantity due to a promotion, the post-promotion dip is less likely to occur. We verify this prediction using the Nielsen Retail Scanner Data that include an extensive number of retailers and a variation in pricing formats. In particular, we compare the category-wide sales volume following a promotion at a retailer with a high-low pricing policy (HILO) against a retailer with an everyday-low-price policy (EDLP). We choose an EDLP with a sales volume comparable to that of HILO during the periods of regular prices and assess the impact of promotions by measuring the difference in sales volume across two formats.

Fig. 7

Weekly sales volume for canned soup by pricing format

In the data set, we find a pair of retail chains that exhibit different pricing formats, representing EDLP and HILO, respectively.²⁷ The two retail chains are comparable in terms of geographic concentration, the number of stores, and the aggregate sales volume during the periods of regular prices at HILO. The left panel of Fig. 7 shows the weekly trend in the sales volume for canned soup aggregated over all stores in each retail chain. The sales volume in HILO tends to fluctuate week to week as a result of promotions, while the sales volume in EDLP is rather stable week to week. An observation related to our interests is that the sales volume in HILO does not decrease below that of EDLP in the weeks following the promotions. Due to the lack of a post-promotion dip in sales volume, the aggregate sales are higher in HILO relative to sales in EDLP, suggesting a category expansion by the promotion. In the right panel of Fig. 7, we compare the store-level sales of a pair of stores from the same zip code with different pricing formats, which reveals a similar pattern. In addition, we check the robustness of this finding from another pair of retail chains with different pricing formats from another regional market. In sum, a price promotion generates an immediate peak in canned-soup sales that is not followed by a post-promotion dip in the subsequent weeks. This pattern is consistent with our prediction for the store-wide sales when a promotion accelerates the consumption rate.

We note that the lack of a post-promotion dip can be caused by reasons other than endogenous consumption. Thus, in the following analyses, we discuss three other possible explanations for the observed pattern.

First, the lower average price at HILO relative to that at EDLP could drive the higher aggregate sales. Table 11 reports the average unit price for major products at the two stores. The prices at EDLP are actually lower even during high season, when there are more frequent price promotions at HILO. Figure 8 shows the weekly price trend for a best-seller UPC across stores, confirming the lower price level at EDLP.

Table 11 Mean price of major brands by pricing format (cents per ounce)

Fig. 8

Weekly price trend for a sample UPC by pricing format

Second, we consider the possibility that the sales peak at HILO is caused mainly by the households that switch stores from EDLP to buy canned soup during price promotions, rather than by the existing customers at HILO. To investigate the store-switching behavior, using the panel data sets, we find 149 households that ever bought canned soup in the EDLP retail chain in the Northeastern market that we use for the main analysis. One fifth of them, or 29 out of 149 households, do not switch stores for a canned-soup purchase, always buying at the same store. Then, the remaining 120 households purchase canned soup at both types of pricing formats. If they strategically switch stores to HILO to benefit from price promotions on canned soup, the purchase price at HILO stores should be lower than that at EDLP stores. Thus, we compare the unit price averaged over shopping trips at each type of pricing format by households. A paired-sample t-test result indicates that there is not a significant difference in the unit price paid at HILO $(M=.098, SD=.026)$ and EDLP $(M=.100, SD=.028)$ stores; $t_{119}=-0.6180$, $p=0.7311$. Households’ store-switches do not seem to be driven mainly by price promotions on canned soup at HILO stores.

Lastly, a particular product assortment in HILO could possibly lead to a favorable outcome for its stores. To compare the product assortments of the two stores, we examine the market shares by brand, can size and UPC. Figure 9 shows that the market shares by brand and can size are very similar across the two stores. Also, the two stores offer similar UPC assortment. Almost all the major UPCs that take up more than 1% of market share at one store are also offered at the other store. There is no major change in UPC assortment across seasons in either store. In sum, we do not find any particular product assortment, in terms of brand, can size or specific UPC, that is exclusively offered at HILO and drives higher sales.

Fig. 9

Market shares across pricing formats

Appendix B. Reduced-form analysis for endogenous consumption

This section reports a reduced-form analysis that suggests endogenous consumption. We estimate an extended version of the price-consideration model proposed by Ching et al. (2009). More specifically, we incorporate the idea of endogenous consumption in their model in a reduced-form way. The price-consideration model is a variation of a logit demand model that allows for the notion that consumers may not know the prices when they are not in need of the category, whereas a typical demand model assumes that consumers are always aware of the prices.²⁸ We choose the framework of the price-consideration model for the following reasons. First, because the price-consideration model captures the impact of inventory on category consideration, it allows us to examine the data pattern consistent with stockpiling behavior. Second, the model requires us to construct a measure of inventory given an assumption regarding consumption behavior, and incorporating alternative assumptions is relatively simple. We take into account the endogenous-consumption behavior in the model by modifying the function for the inventory measure.

We describe the model that we estimate. At each time period t, a household makes decisions in two sequential stages: category consideration and purchase. The probability that a household i considers the category with J brands at time t is specified as:

(14)

where $I_{it}$ is inventory; is an indicator for high-demand periods; and $\gamma _{0i}$ is the intercept. The inventory variable is a function of purchase and consumption as follows:

$$\begin{aligned} I_{i,t+1}=I_{it}+\sum _{j} d_{ijt}q_{j} - R_{it}, \end{aligned}$$

(15)

where $d_{ijt}$ is an indicator equal to 1 if brand j is bought at t; $q_{j}$ is the purchase volume; and $R_{it}$ is the consumption rate of household i at time t. To incorporate the notion of endogenous consumption, we allow the consumption rate to change over time as a function of available inventory. In particular, we adopt a functional form defined in Ailawadi and Neslin (1998), as follows.

$$\begin{aligned} R_{it} = \max \bigg \{ 0; A_{it} \bigg ( \frac{ \bar{C_{i}} }{ \bar{C_{i}} + A_{it}^{{\varvec{f}}} } \bigg ) \bigg \}, \end{aligned}$$

(16)

where $A_{it}$ denotes available inventory, or the sum of beginning inventory and the quantity purchased at time t, and $\bar{C_{i}}$ is the average consumption rate for household i. Flexibility parameter f governs the impact of inventory on the consumption rate. The estimated value for f being smaller than one indicates that the consumption rate is flexible and increases with available inventory. The functional form implies that with f being greater than one, the impact of available inventory on the consumption rate exponentially decreases as the inventory amount increases. At the value of f being equal to one, the consumption rate does not increase above the average consumption rate $\bar{C_{i}}$ despite the increase in the available inventory.

If the household decides to consider the category, then it looks at prices and makes a purchase decision from among available brands. The utility that household i receives from brand j is specified as

$$\begin{aligned} U_{ijt} = \beta _{ij}+\alpha P_{jt} + GL_{ijt}\lambda +\epsilon _{ijt}, \end{aligned}$$

(17)

where $P_{jt}$ is price, and $\beta _{ij}$ is brand fixed effects. The term $GL_{ijt}$ is the brand-loyalty variable that depends on the household’s purchase history for brand j (Guadagni & Little, 1983), and we specify this variable in an exponential smoothing function, $GL_{ijt}=\delta GL_{ij,t-1} +(1-\delta ) d_{ij,t-1}$, where $d_{ij,t-1}$ is an indicator equal to one if brand j is bought at $t-1$. We normalize the utility of no-purchase to zero; that is, $U_{i0t}=\epsilon _{i0t}$. We assume that the error term $\epsilon _{ijt}$ follows an extreme value distribution. Thus, the conditional probability that household i buys brand j at time t given the category consideration is

$$\begin{aligned} P_{it}(j|C) = \frac{ exp( \tilde{U}_{ijt} ) }{ 1+ \sum _{k} exp( \tilde{U}_{ikt} ) }, \end{aligned}$$

(18)

where $\tilde{U}_{ijt}$ is the deterministic component of the utility. Finally, the unconditional probabilities are given by

$$\begin{aligned} P_{it}(j)= {\left\{ \begin{array}{ll} P_{it}(C)P_{it}(j|C), &{} \text {if } j>0 \\ P_{it}(C)P_{it}(0|C)+(1-P_{it}(C)), &{} \text {if } j=0. \end{array}\right. } \end{aligned}$$

We allow $\gamma _{0i}$ and $\beta _{ij}$ to be random coefficients - i.e., $\gamma _{0i}\sim \mathcal {N}(\gamma _{0},\sigma _{\gamma })$ and $\beta _{ij}\sim \mathcal {N}(\beta _{j},\Sigma _{\beta })$. We use simulated maximum likelihood to estimate the model. The set of parameters we estimate is $\{ \gamma _{0}, \gamma _{1}, \gamma _{2}, \beta _{j}, \alpha , \lambda , \delta , \sigma _{\gamma }, \Sigma _{\beta } \}$.

Table 12 Price-consideration-model results

Table 12 reports the estimation results for two models. The full model allows the flexible consumption rate to vary, depending on the available inventory amount, and estimates the flexibility parameter f , whereas the nested model restricts the flexibility parameter to be one ${({\textbf {f}} =1)}$. We first look at the full model with the focus on the category-consideration component. The negative sign for the inventory coefficient $(\gamma _{1}=-10.180)$ indicates that households restock the canned soup when the inventory is low, consistent with households’ inventory behaviors. The flexibility parameter is smaller than one ${({\textbf {f}} =-1.452)}$, suggesting that the consumption rate increases with the available inventory amount, rather than being constant over time. A t-test rejects the null hypothesis that the estimated flexibility parameter is greater than one $(t=-37.657$, $p<0.001)$. The estimated coefficients suggest that the inventory affects the purchase incidence and consumption rate for the canned-soup market. Then, we compare the goodness of fit of two models. The nested model constrains the consumption rate to be the average consumption rate despite the increase in available inventory. A log-likelihood ratio test rejects the nested model in favor of the full model $(LLR=9.333$, $p<0.01)$. In sum, the reduced-model results are consistent with the endogenous-consumption hypothesis.

Appendix C. Estimation procedure

This section provides each step for the estimation of our model. We first estimate the price process separately from the structural parameters for consumer preferences. Then, we estimate the dynamic discrete choice model, where the estimated price process is used to form households’ expectation about future prices. The structural estimation essentially follows the nested fixed-point algorithm (Rust, 1987).

The households’ optimal decision in terms of purchase and consumption is described as a solution to a dynamic programming problem. The consumption decision is nested in the purchase decision; that is, the solution for the consumption-optimization problem is obtained conditional on the optimal brand-quantity decision for each value function. Thus, the alternative-specific value functions for a purchase choice option jq is a max function with respect to consumption amount $c_{it}$ given state variables. We discretize the consumption amount into ten grid points, allowing the maximum weekly consumption of up to ten cans of soup.

Note that the state variables in our dynamic programming problem include continuous variables, ${{\textbf {P}} _{t}}$ and $I_{it}$. It is not possible to solve for value function at every point in a continuous state space. Thus, within the estimation routine, we approximate the household-specific value functions using the interpolation method (Keane and Wolpin 1994). We approximate the value function at a set of discrete grid points using a polynomial function and interpolate the value function at points of state space not in the given grids. We specify the polynomial as a function of price, inventory, and interaction of price and inventory, as below:

$$\begin{aligned} V({\textbf {P}} _{t}, I_{it}) = \sum _{k=0}^{2} A_{0,k,0}^{V} I_{it}^{k} + \sum _{j=1}^{2} \sum _{k=1}^{2} \sum _{l=0}^{2} A_{j,k,l}^{V} I_{it}^{k} P_{j}^{l} , \end{aligned}$$

(19)

where $A_{j,k,l}^{V}$ are parameters to be estimated separately for each season and each type of household. The polynomial for the value function without a store visit $W({\textbf {P}} _{t}, I_{it})$ is similarly defined, resulting in another set of parameters $A_{j,k,l}^{W}$. We fit the polynomial function by least squares based on 500 grid points of price and inventory. The sample grid points for brand-specific prices are randomly drawn from the empirical distribution of the data. The grid points for inventory are set to be the Chebyshev quadrature nodes in the interval (0, 160).

Given the solution to the dynamic programming problem, the estimation algorithm searches for values of parameters that maximize the likelihood of the observed sample. The likelihood of household i’s observed choice is formed by integrating over k latent taste types. In order to construct the likelihood, there is an initial-conditions problem because we do not observe each household’s inventory at the start of the observed data (Heckman, 1981). We hold out n initial histories of store-visit and purchase for each household from the calibration sample and use them to impute the initial inventory by setting the inventory at the first period of observed data to be zero and solving the dynamic programming problems over n periods until the initial point of the calibration sample. Following a routine for the estimation of maximum likelihood estimators, standard errors are calculated using the inverse of the Information Matrix. For empirical application, we use the household samples with more than three purchases during the sample period in order to investigate the effect of inventory. There are 212 such households from the Eau Claire market. In addition, we set $n=10$ (hold-out initial history) and $K=2$ (latent taste types).

Table 13 Model fit

Appendix D. Model fit

Our proposed model accounts for the consumer’s strategic decisions on when, what, and how much to buy under endogenous consumption. To assess the validity of our hypothesis of endogenous consumption, we compare our full model with a baseline model in which consumption amounts are exogenously given. In addition, we also consider two more baseline models that ignore other crucial components of the full model: the seasonal nature of category preference and consumer heterogeneity that creates the seasonal fluctuation in consumer composition. Goodness-of-fit statistics for models are reported in Table 13. The main result is that accounting for endogenous consumption substantially improves fit over accounting for other components. To see this, compare Model 1 with Models 2-4, which show an overall upward shift in model fit. This indicates the importance of recognizing consumption as an endogenous decision variable instead of an exogenously given constant.

Table 14 Sample and predicted distributions - Choice

We discuss how well the model approximates the data with the focus on the full model. Table 14 compares the sample choice frequencies and simulated choice frequencies across the choice options - by brand, by quantity, and by interpurchase time. Our model generates a distribution of choices very close to the data. For example, the purchase probability in the data is 8.9%, and our model generates a probability of 8.1%. The predicted shares by brands and quantity options fit the sample distributions well. The model generates a fairly reasonable distribution of interpurchase time as well.

Table 15 Sample and predicted distributions - Price

Finally, we compare the simulated price distribution based on the estimated price process with the sample price distribution. The first two rows of Table 15 report the probability of price decrease by brands across seasons. The frequency of price decrease generated by our price-process model is very close to the sample distribution in terms of seasonality and brand heterogeneity. The bottom two rows report the average price change conditional on price decrease, showing that our model underestimates the depth of price decrease compared to the sample distribution. Our model, however, captures major stylized features of counter-cyclical pricing - deeper sale during high season and the difference between brands.

Table 16 Purchase patterns: Other seasonal categories

Appendix E. Other seasonal product categories

Although we apply the model to canned-soup data, the proposed explanation for counter-cyclical pricing can be applied to other consumer packaged goods with seasonal demand for which consumption is plausibly flexible. In this section, we examine whether other seasonal products are subject to counter-cyclical pricing, stockpiling and endogenous consumption. In addition to canned soup, we examine multiple seasonal product categories: soft drinks, beer, and ice cream.²⁹ In Table 16, we report the regression results for three different categories, replicating the analysis we have shown for canned soup. In Table 17, we report the sales volume and price by season for each category. In the “Sales volume in ounces” rows, we report the weekly sales volume averaged across all stores separately by season to verify the seasonality in demand. In the “Unit price in cents” rows, we report the average unit prices by season in order to check whther the prices exhibit the counter-cyclical pricing pattern.

We find that soft drinks show similar patterns in households’ purchases. A sale induces the increase in purchase volume and accelerates purchase timing, but delays the subsequent purchase timing, and, finally, increases consumption rates. These patterns indicate that this category is subject to stockpiling and endogenous consumption. The impact of a sale is heightened during the high season even after controlling for exogenous seasonal shifts, in particular for purchase volume and consumption rate. These purchase patterns are consistent with the seasonality in stockpiling, endogenous consumption, and price elasticity. The impacts on the shopping cycle are not clearly consistent with the patterns shown in canned soup. Subsequent to a purchase of a product on sale, consumers delay the next purchase. We also find moderate patterns of counter-cyclical pricing for soft drinks. Soft drinks may be a good sample category to which our model can be extended.

Ice cream also shows a similar pattern in pricing - a drop in high season. However, the consumption rate does not increase during a sale. The counter-cyclical pricing for ice cream does not seem to be associated with endogenous-consumption behavior. For beer, we do not find an increase in consumption rate during a sale. Also, the purchase volume and interpurchase time do not appear consistent with stockpiling behavior. We conjecture that most people might have a natural threshold in beer consumption or that beer might incur high storage or shopping costs so that stockpiling is not convenient. Furthermore, the beer prices do not drop during the periods of high demand, which we define as May through September based on the sales trend of the data. This observation is different from the findings in Meza and Sudhir (2006), who define peaks of demand as the weeks of annual holidays, typically lasting from one to two weeks, and find that prices fall during the demand peaks.

Table 17 Seasonality in demand and prices by category

Appendix F. Fixed-effects for brand-quantity options

Table 18 reports the fixed effects for brand-quantity options, the common parameters for both consumer types.

Table 18 Structural-model-estimation results - Fixed effects for brand-quantity options