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  1. 1. Joint estimates of purchase timing and brand switch tendency: results from a scanner panel data set of frequently purchased products F. F. Gönül, P. T. L. Popkowski Leszczyc, and T. Sugawara Carnegie Mellon University, University of Alberta, and Carnegie Mellon University ABSTRACT. In the marketing literature, purchase timing and brand choice behavior of households have generally been treated independently. The subsumed independence of the two events can be restrictive. In this paper we relax and test the independence assumption. We study purchase behavior in two stages: In the first stage we model the timing of purchases. The second stage focuses on the conditional probability of switching given that a purchase took place. We use longitudinal data on household purchases for two different product categories; diapers and ketchup. The joint formulation exploits the information in the scanner panel data more fully than has been possible before. I. INTRODUCTION Our purpose in this paper is to measure the correlation between purchase timing and brand switch behavior of households. More specifically, we want to study (i) whether households switch brands more often for the products they purchase more frequently or for the products they purchase less frequently. (ii) We want to identify the demographic variables that influence purchase timing; and to identify the marketing variables that influence the brand switching decisions. These research issues are of utmost importance to brand managers of consumer products who are interested in encouraging purchase acceleration and loyalty to their brand. Managers can implement our model in identifying market segments that buy more often but switch less often, the heavy users of a brand or segments with growth potential. Our data is from the scanner panel purchase data collected in two cities by the A.C. Nielsen Company for a period of approximately one year. We aggregate the purchases to weekly units and select two categories. We test our model and find that while for purchases of diapers there is no evidence of a significant correlation between purchase timing and brand switching, for ketchup purchases, there is a significant positive relationship between the timing of purchases and brand switching. II. ECONOMETRIC MODEL The likelihood function for a purchase occasion i that constitutes a switch from the previous purchase that
  2. 2. took place t periods ago is, Li = Pr(j → k,t) = Pr(j → k  t) ⋅ f(t) where j denotes the origin brand, k denotes the destination brand, and t stands for the interpurchase time. Conversely, the likelihood function for a repeat purchase occasion i (a nonswitch event) after t periods is given by, Li = (1-Pr (j → k  t)) • f(t). We assume the switch from j to k is a discrete choice governed by a random utility model. That is, Ujk = _jk + ujk, where ujk is normally distributed ( u jk _ N(0, σ u 2)). 1 We assume brand switching imposess switching costs and hence we assume different utilities for switching and staying with the same brand. A switch occurs if the utility of switching is greater than the utility of not swtching. (We arbitrarily normalize the utility of not switching to zero). We further assume that the interpurchase time (t) is lognormal, and is correlated with the random utility component. Then Li has a closed-form expression given by a bivariate normal. More explicitly, Pr(j → k) = Pr(_jk + ujk > 0), and Pr(j → k  t) = Pr(_jk + ujk > 0  ln(t)) J, where J is the Jacobian of the transformation from t to ln(t). Then, the likelihood for a switch occasion is, Li = Pr(_jk + ujk > 0  ln(t)) J f(t). Since the conditional distribution, g(ujk  ln(t)), is a normal distribution, the likelihood function is the product of two normal distributions and is easy to evaluate. Specifically, σ u (ln(t) - ))] 1 _ φ ( ln(t) - µ t ) Li = [1 - Φ(- _ jk - ρ µt 2 σt ln(t) σ t σt 2 where ln( t) _ N( µ t , σ ), φ ( _ ) 3 stands for the standard normal p . d . f ., Φ (•) 4 denotes the standard t normal c.d.f., and the correlation coefficient, ρ = Corr(ujk, ln(t)), measures the correlation between purchase
  3. 3. timing and the probability of a switch. A positive correlation indicates that when interpurchase time 2 increases the likelihood of a switch increases. We impose the restriction that σ (1 - ρ ) = 1 5 in order to 2 u identify the bivariate normal model. III. ESTIMATION We estimate our model on two data sets, with diaper purchases and ketchup purchases. The diaper data consists of 152 households who regularly bought diapers from among 3 national brands during the course of a year. There are a total of 2675 purchases. The ketchup data consists of 200 households who regularly bought ketchup from among 2 national brands and store brands (combined as one brand, since the purchase data is across stores) over the course of one year. There are a total of 1567 ketchup purchases. The average interpurchase time for disposable diapers is about 2 weeks, and for ketchup about 10 weeks. Our findings are presented in Table 1. --Insert Tabel 1 here-- Diapers Households that have higher incomes are likely to buy diapers more frequently, ceteris paribus, and households that are better educated are likely to buy diapers less frequently, ceteris paribus. Coupons rather than price are the determining factor in influencing brand switches in the diaper market. There is no significant correlation between interpurchase time and the propensity to switch. Ketchup Households that are larger in size are likely to buy ketchup more often, ceteris paribus. The remaining demographic variables have no influence on purchase timing. Price, significantly and negatively influences the probability of a switch. In-store displays do not play a role in encouraging consumers to switch brands. The correlation coefficient is positive and significant. Households that buy less often may "forget" the brand and tend to switch more often than other households.
  4. 4. IV. CONCLUSION Our empirical analysis shows that it is possible to identify the characteristics of households that buy a certain product more often than others. This facilitates target marketing and enables managers to better target advertising and promotional campaigns to different consumer segments. For example, a managerial policy could be to target reminder advertising to heavy users and target price incentives to switchers. We also show that brand switching is caused by different characteristics depending on the product category. For diapers, price is not a significant factor but coupon is. In a category like ketchup, where coupons are negligible, store display does not induce households to switch, while price does. Different from the prior literature, in this work, we measure the correlation between the timing of purchases and brand switches. We find that when the purchase interval gets longer, consumers are more likely to switch. Hence, frequent purchasers are more likely to be brand loyal. For ketchup purchases we observed a significant correlation between interpurchase time and the propensity to switch. Thus, we are led to conclude that if the product is essential and bought regularly like diapers, loyalty may continue. However, if the product is not essential like ketchup, where there are many substitutes, then switching may be more prevalent. These results are consistent with findings in the promotional literature. Price promotions, reflected in the price of ketchup, tend to lead to purchase acceleration, while coupons (mostly used for diaper purchases) generally do not lead to purchase acceleration.
  5. 5. _____________________________________________________________________________________ Table 1 Results of Analysis of Purchase Timing and Brand Switching _____________________________________________________________________________________ DIAPER KETCHUP ______________________________________________________________________________________ Interpurchase Time Constant 0.5941** 1.7766** (0.0704) (0.1179) Education 0.0316** 0.0135 (0.0092) (0.0130) Income -0.0172** 0.0016 (0.0058) (0.0089) Household Size ---- -0.0808** (0.0173) Switch Propensity Constant -0.9121** 0.1074 (0.3360) (0.2579) Price -0.0131 -0.3526** (0.0230) (0.0661) Coupon 0.4387** ---- (0.0584) Display ---- -0.1427 (0.0960) Correlation between 0.0251 0.0871* Interpurchase Time and Switch (0.0278) (0.0440) Propensity ____________________________________________________________________________________ Notes: Standard errors are in parentheses. Significance at 1% is denoted by (**) and at 5% by (*). Household size is not included in the diaper model, since there is not much variation in size among the purchasing households. Coupon is not included in the ketchup model, since coupon activity is negligible in the category. Likewise, display activity is virtually nonexistent in the diaper category. We exclude these variables without loss of significant information. 5