A Dynamic Structural Model of Addiction, Promotions, and Permanent Price Cuts Brett R. Gordon * Graduate School of Business Columbia University 3022 Broadway, Uris 511 New York, NY 10027 Email: brg2114@columbia.edu Tel: 212-854-7864 Fax: 212-854-7647 Baohong Sun Tepper School of Business Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA15213 Email: bsun@andrew.cmu.edu Tel: 412-268-6903 Fax: 412-268-7357 First Draft: December 11, 2008 Current Draft: August 17, 2009 Abstract Addictive goods fundamentally differ from non-addictive goods: consuming more of an addictive good today reinforces the addiction and increases the likelihood of future consumption. Thus, addiction creates an intertemporal link between a consumer’s past and present decisions, altering their incentives to purchase and to hold inventory. Despite the influence of addiction, its impact on consumer purchase strategies and its implications for firms remain unclear. We construct a dynamic structural model with rational addiction and endogenous consumption to investigate how consumers respond differently to temporary versus permanent price promotions for addictive and non-addictive goods. We apply our model to unique consumer panel data on purchases of cigarettes, crackers, and butter. We find that addiction accumulated through past consumption affects decisions for cigarettes but not the two non-addictive categories. Ignoring addiction for cigarettes leads to biased estimates of price sensitivity, inventory holding costs, and stock-out costs. For cigarettes, we find an interesting asymmetry: the temporary consumption elasticity is smaller than the permanent consumption elasticity, but the converse is true for the purchase elasticities. No such asymmetry exists for crackers or butter. We discuss additional implications for retailer and manufacturer pricing strategies. Keywords: rational addiction; dynamic structural model; endogenous consumption; price cut; permanent price cut * Brett Gordon is Assistant Professor of Marketing at the Graduate School of Business at Columbia University. Baohong Sun is Professor of Marketing at the Tepper School of Business at Carnegie Mellon University. We appreciate comments from Ron Goettler, Avi Goldfarb, Wes Hartmann, Ran Kivetz, Oded Netzer, and participants at the 2007 Marketing Science Conference. All remaining errors are our own. 2 1. Introduction Addictive products are fundamentally different from non-addictive products. Consuming more of an addictive good today reinforces addiction and increases the likelihood of future consumption. Thus addiction influences consumers’ decisions by creating a link between past and present consumption utility, which alters their incentives to purchase more and to hold inventory. Consumers must manage their purchase and consumption decisions in order to avoid the negative consequences of excess addiction. Despite the influence of addiction on consumers’ decisions, its impact on retailer and manufacturer pricing strategies remains unclear. To address these issues, we construct a dynamic structural model of addiction with endogenous consumption and future price uncertainty. We use the model to investigate how consumers respond differently to temporary versus permanent price promotions for addictive and non-addictive goods, to understand the empirical implications of ignoring addiction, and to examine the consequences for firm’s promotional policies. Unlike most past work with non- addictive goods that assumes consumption is exogenous or coincides with purchase (Erdem and Keane 1996, Gonul and Srinivasan 1996, Erdem, Imai, and Keane 2003), we explicitly model purchase and consumption as separate decisions. 1 Distinguishing between them is necessary because stockpiling causes short-term consumption and purchases to differ, and addiction is a function of consumption and not purchases. Although we do not observe inventories, we can distinguish between them through joint variation in inter-purchase times and quantities. Endogenizing consumption also allows us to incorporate the key features of addictive products that separate them from non-addictive products. Consumers possess a stock of addiction that depends on their past consumption and that affects their present marginal utility of consumption. Addiction decays over time, and current consumption replenishes it. We use a flexible form for utility and unobserved heterogeneity to permit varying levels of addiction (if any) to exist among consumers. Our specific formulation for addiction is consistent with 1 Two recent exceptions are Hendel and Nevo (2006) and Hartmann and Nair (2008). 3 theoretical (Becker and Murphy 1988), empirical (Tauras and Chaloupka 1999), and experimental work (Donegan et al 1983, Peele 1985) on the relationship between addiction and consumer behavior. Although the economics literature on addiction often uses the terms “addiction” and “habit persistence” interchangeably (Pollack 1970, Iannaccone 1986), the marketing literature usually takes habit persistence to mean the effect of past propensities to choose a specific brand on current choice probabilities (Heckman 1981, Roy, Chintagunta, and Haldar 1996, Seetharaman 2004, Dube, Hitsch, and Rossi, forthcoming). For example, in Roy, Chintagunta, and Haldar (1996), habit persistence makes the last brand-size combination purchased more likely to be purchased again. 2 Addiction, however, differs from this notion of habit persistence in three critical ways. First, the reinforcing effect of addiction implies that past purchase quantities can increase current purchases (Ryder and Heal 1973, Boyer 1978, Becker and Murphy 1988, Orphanides and Zervos 1995), whereas existing marketing models of habit persistence do not explicitly model purchase quantity and make the last brand or size purchased more likely to be purchased again. Second, addiction operates at the category level, whereas past work formulates habit persistence at the brand level. Category-level consumption is the most relevant input to determine addiction as opposed to any brand-level factors (Mulholland 1991). Third, our modeling approach uses specific behavioral processes, such as the reinforcement effect of consuming an addictive good, to motivate the source and nature of choice dynamics. We apply our model to unique consumer panel data on cigarette purchases. Cigarettes are an ideal category for our purposes because there is strong evidence that smoking is addictive (Chaloupka and Warner 2000). For comparison, we apply the model to two non-addictive categories, crackers and butter, using the same consumer sample. We estimate the model with 2 Similarly, the model in Guadagni and Little (1983) implies that the last brand-size purchased is more likely to be purchased in the future. However, this outcome is due to positive state dependence in the form of brand and size loyalty terms. In contrast, Roy, Chintagunta, and Haldar (1996) use serial correlation in the errors terms of the utility-maximizing alternatives across periods to induce the persistence in choices. 4 unobserved heterogeneity and with/without addiction on all three categories, and calculate the elasticity of consumption and purchase with respect to temporary and permanent price changes. Our key results are the following. First, consumers make different purchase and consumption decisions for addictive products and non-addictive products. Addiction accumulated through past consumption not only generates direct utility but it also enhances the marginal benefit of consumption. Consumers with higher addiction are less price sensitive and have higher stock-out costs. Second, we find the dynamic addiction model fits best for cigarettes, whereas the dynamic model without addictions is a better fit for crackers and butter owing to being more parsimonious, consistent with the intuition that such a model should be preferred for categories that are truly not addictive. Third, ignoring addiction for cigarettes leads to biased estimates of inventory holding costs, stock-out costs, and price sensitivity. For a temporary price cut, the model without addiction overestimates consumption and underestimates short-term inventories, producing a downward bias in the price coefficient since consumers anticipate the cost of sustaining the higher consumption after the price reverts. We also find an asymmetry in cigarette elasticities: temporary consumption elasticities are smaller than permanent consumption elasticities due to the smoothing of consumption via addiction, but temporary purchase elasticities are larger than permanent purchase elasticities because addiction creates strong stockpiling incentives to avoid stock-outs. In contrast, for non- addictive goods both consumption and stockpiling inventories are higher for temporary changes than for permanent changes. We decompose the impact of temporary and permanent price changes on purchase patterns, consumption, and displacement. We find that temporary price changes are less effective at inducing switching between product tiers compared to permanent price cuts due to the interaction between addiction and inventory. These results demonstrate the importance of recognizing the dynamics introduced by addiction and stockpiling in the context of addictive products. 5 We contribute to the existing literature in the following ways. From a theoretical perspective, we adapt the rational addiction model of Becker and Murphy (1988) to a dynamic structural model that accounts for inventory dynamics and embeds a continuous consumption choice within a dynamic discrete-choice framework. 3 Two assumptions of the Becker-Murphy model are that consumers are forward-looking and have time-consistent preferences. Numerous papers find strong evidence in support of the forward-looking behavior in the context of cigarettes (Chaloupka 1991, Becker, Grossman, and Murphy 1994, Arcidiacono, Sieg, and Sloan 2005, Wan 2005). Despite some evidence in support of time-inconsistency (O’Donoghue and Rabin 1999), time-consistent preferences are used to empirically model addiction in a variety of settings. 4 The formal identification of time-consistent versus time-inconsistent preferences from data remains unclear. Fang and Wang (2008) show that the discount parameters in time- inconsistent models are only partially identified under certain exclusion restrictions and in the absence of consumer heterogeneity. 5 Relaxing the time-consistency assumption would be a valuable extension especially from a public policy perspective (Gruber and Koszegi 2001). 6 On the empirical side, despite the long tradition in economics of using rational addiction models to study cigarette consumption, most of the work uses large-scale surveys and reduced- form models (Chaloupka 1991, Becker, Grossman, and Murphy 1994, Coppejans et al 2007). This approach restricts the range of possible policy experiments and often relies on aggregate (e.g., state level) price data to conduct inference. Our structural model enables us to perform a number of counterfactual simulations and uses rich, individual-level panel data. We perform a cross-category analysis and demonstrate that consumers respond differently to price cuts for 3 See Dockner and Feichtinger (1993) and Orphanides and Zervos (1995) for two extensions. 4 See Waters and Sloan (1995) for an application to alcohol, Olekalns and Bardsley (1996) for caffeine, and Choo (2000) and Arcidiacono, Sieg, and Sloan (2005) for cigarettes. 5 Rust (1994a, 1994b) show that the discount factor is generically not identified for standard dynamic discrete choice models, and Magnac and Thesmar (2002) generalize these results to dynamic single-agent models. 6 Machado and Sinha (2007) develop an analytical model of time-inconsistent smokers’ participation and cessation decisions, and using a hazard-rate model estimated on survey data, find support for their model. 6 addictive and non-addictive goods. We compare the effects of temporary and permanent price cuts on addictive and non-addictive goods. Our model makes several methodological contributions relative to existing research. In marketing, our work draws on the broad class of dynamic consumer models applied to frequently purchased products (Erdem and Keane (1996), Gonul and Srinivasan (1996), Sun, Neslin, and Srinivasan 2003, Sun 2005). In particular, our model most closely relates to the dynamic stockpiling models of Erdem, Imai, and Keane (2003) and Hendel and Nevo (2006), who examine ketchup and laundry detergent, respectively. Chen, Sun, and Singh (2007), who examine how consumers adjusted their cigarette brand choices following Philip Morris’s permanent price cut in response to the growth of generic brands, do not model the purchase quantity and consumption decisions. To our knowledge, there is no research that examines consumer purchase and consumption decisions in the presence of addiction and inventory dynamics. In addition, we explicitly compute the optimal consumption path as a function of inventory and addiction. Finally, as consumers continue to embrace healthier lifestyles and consider more products containing unhealthy ingredients (e.g. nicotine, caffeine, sugar, and salt) as “products of vice,” we make a first attempt to understand how the unique features of addictive goods affect purchase and consumption decisions and the implications on price and promotion effects. The rest of the paper proceeds as follows. Section 2 presents the model and estimation approach. Section 3 discusses the data, identification, parameter estimates, and model fit. Section 4 compares the resulting consumer policy functions for purchase and consumption and presents the results of the pricing simulations. Section 5 concludes with a discussion of limitations of the present work and avenues for future research. 7 2. Model This section develops a dynamic model of rational addiction where consumers face uncertainty about future prices and store visits. Consumers must optimally balance the impact of current consumption on future addiction and inventory levels. The model does not impose addiction by assumption, and relies on the intertemporal relationship between past consumption and present decisions to identify the addiction process. We explicitly model consumption and purchase as separate decisions, and later show that distinguishing between them is necessary to understand the consumer decision process for addictive goods and has important policy implications. 2.1. Period Utility There are I consumers who make periodic (e.g., weekly) decisions about which product to purchase, how much to purchase, and how much to consume at T equally spaced time periods. There are 0, ,jJ=  product alternatives where choice 0j = represents a no-purchase decision. Let ijt c be consumer i’s consumption of product j in week t and define the dummy variable 1 ijqt d = as a choice of product j and quantity q. Then 1 J it ijt j cc = = ∑ is the category consumption choice, { } , it ijqt jq dd= is the vector of purchase quantity indicators, and , 1 ijqt jq d = ∑ . A consumer’s period (indirect) utility in state { } ,, it it it t s aIP= is the sum of consumption utility, purchase utility, and inventory costs: (1) (, ,;) (, ; ) (,;,) (;) it it it it i c it it i p it t i i it i Ucds uca udP CIh θ α βξ =+− where the stock of addiction 0 it a ≥ summarizes the cumulative effect of past consumption, 0 it I ≥ is the consumer’s inventory, { } 1 , , t t Jt PP P= is a vector of prices, and { } ,,, i i iii h θ αβξ = is the parameter vector. We discuss each component of the utility function in turn. For consumption utility, we require a form that can capture the distinct features of addictive goods: reinforcement, tolerance, and withdrawal (Peele 1985, Chaloupka 1991). 8 Reinforcement implies that greater past consumption raises the marginal utility of present consumption. Tolerance suggests that a given level of consumption yields less satisfaction as cumulative past consumption rises. Finally, withdrawal refers to the negative reaction from a decrease or interruption in consumption due to a stock-out or intentional cessation. 7 A convenient form that can encompass these effects—without imposing them by assumption—is a quadratic utility function. It allows for the necessary complementarity between consumption and addiction and satisfies standard regularity assumptions found in the habit formation literature (Stigler and Becker 1977). Thus the period utility from consumption is (2) 22 0 1234 5 ( , ; ) 1{ 0} c it it i i it i it i it i it i it i it it u c a c c c a a ac αα α α α α α = =++++ + . If consumption is zero, the first coefficient, 0i α , is the cost of a stock-out, or withdrawal. Consumption may be zero when the inventory is exhausted and the consumer is unable to make a purchase (no store visit). The next two coefficients, 1i α and 2i α , represent the instantaneous utility of consumption independent of addiction. For the following two coefficients, 3i α captures the direct utility from addiction and 4i α allows for the tolerance effect. The last term represents the reinforcement effect: if 5 0 i α > , then addiction increases the marginal utility of consumption. Addiction plays an important role because it creates an intertemporal link between past consumption and current decisions. We use this simple law of motion to govern a consumer’s stock of addiction: (3) ,1 (1 ) i t i it it a ac δ + =−+ , where 01 i δ ≤≤ is the constant rate of depreciation of addiction over time. Overall cigarette consumption strengthens addiction regardless of a cigarette’s brand, and addiction directly 7 Although we do not explicitly model the cessation decision, our model partially captures it because implied consumption for a consumer could be zero in a period. Such periods may or may not indicate a decision to quit smoking depending on whether the consumer obtains cigarettes from a source outside our data set or fails to properly record their purchases. Choo (2000) who uses a dynamic model of rational addiction and annual survey data to examine smoking and quitting decisions in response to changes in the smoker’s health. 9 influences consumers’ preferences by changing the marginal utility of consumption. 8 Our formulation of addiction is theoretically (Iannaccone 1986, Becker and Murphy 1988), empirically (Becker, Grossman, and Murphy 1994), and experimentally (Peele 1985, Rose 2004) consistent with prior work on the relationship between addictive goods and consumer behavior. Although the literature contains numerous formulations for habit persistence (Heckman 1981, Erdem 1996, Roy, Chintagunta, and Haldar 1996, Seetharaman 2004), none would produce a pattern consistent with addiction because they do not explicitly model purchase quantity decisions. These approaches make a consumer more likely to repeatedly purchase the same brand-size combination, but not more likely for the consumer to increase their purchase quantity. In addition to consumption, consumers simultaneously choose to purchase from among a discrete set of product-quantity combinations for each product j. Purchase utility is given by: (4) 2 1 23 , ( ,;,) ( ) p it t i i ijqt i jqt ijt i ijt i ijt ij ijqt jq udP d pq q q βξ β β β ξ ε = + + ++ ∑ where ijt q denotes the purchase quantity, jqt p denotes the per-unit price for quantity q, and jqt ijt pq is the total expenditure. The parameter 1i β measures consumer’s price sensitivity. We account for product-level differentiation through the fixed-effects ij ξ and quantity-related differences through the linear and quadratic quantity terms. The squared term on quantity allows for a non-linear relationship between purchase size and utility. The variable ijqt ε is a random, unobserved shock to utility that affects consumer i's decision, distributed i.i.d. extreme value distribution to obtain the usual multinomial logit choice probabilities. Quantities purchased in the current period are available for immediate consumption. Products not consumed are stored at a holding cost of i h , such that (;) it i i it CI h h I= ⋅ . Inventory is not product specific, and evolves according to 8 We could extend the model to allow the evolution of addiction to depend on brand-specific characteristics such as tar and nicotine levels, but we would not expect this to have a significant impact on our results. 10 (5) 1 , it it ijqt ijt it jq I I dq c + =+− ∑ . The inventory state variable is important because it creates another intertemporal link between purchase and consumption: the cost of holding additional inventory must be balanced against the desire to avoid a costly stock-out. In summary, collecting the formulations for the individual components of utility, the indirect utility function is: (6) 22 0 12345 2 1 23 , ( , , ; ) 1{ 0} () it it it it i it i it i it i it i it i it it ijqt i jqt ijt i ijt i ijt ij ijqt i it jq U c d s c c c a a ac d p q q q hI θα α α α α α β β β ξε = =+++ + + + + + ++ − ∑ Next we discuss how consumers form expectations about future prices and store visits, and then formulate the consumer’s dynamic decision problem. 2.2. Price Expectations Stockpiling is common for many consumer-packaged goods, including cigarettes, and consumers make decisions based on their expectations of the future distribution of prices (Erdem and Keane 1996, Gonul and Srinivasan 1996, Sun, Neslin, and Srinivasan 2003). A key component of the model is the random process governing future prices. In order to generate robust predictions, the price process should be realistic and capture several features of real world prices, such as the dependence of current prices on competitors’ prices and own lagged prices. Let jt P be the aggregate price of product j, which we distinguish from jqt p , the price for a particular product-quantity combination. Similar to Erdem, Imai, and Keane (2003), we assume logged aggregate prices follow a first-order Markov process, (7) 1 2 1 3 ,1 1 ln ln ln 1 jt j j jt j j t jt lj PP P J γγ γ η −− ≠ =++ + − ∑ , where 1jt P − is the past price of product j at time t – 1. Price competition enters through the inclusion of the mean log price of competing tiers. The variable jt η is the random shock of [...]... biased parameter estimates, and that the model produces reasonable estimates on the non-addictive categories A series of simulations using temporary and permanent price cuts reveal that short-term purchase and consumption elasticities for cigarettes can markedly differ We also demonstrate that temporary and permanent price changes have an asymmetric effect on purchase and consumption of addictive goods Decomposing... (2000), “Rational Addiction and Rational Cessation: A Dynamic Structural Model of Cigarette Consumption,” Working paper, Yale University Chaloupka, F J (1991), “Rational Addictive Behavior and Cigarette Smoking,” J of Pol Econ., 99(4), 722–742 Chaloupka, F J and K E Warner (2000), “The Economics of Smoking,” in Handbook of Health Economics, Volume 1, Eds: A J Culyer and J P Newhouse Chandon, P and B Wansink... addiction and inventory levels The addiction state variable does not capture any meaningful state dependence for crackers and does not influence consumers’ decisions 4.2 Differential Effectiveness of Temporary and Permanent Price Changes Structural models allow us to conduct a variety of counterfactual simulations (Chintagunta et al 2006) To understand the implications of addiction and stockpiling on manufacturer... provides an informal discussion of the model s identification, and discusses the model fit and parameter estimates Due to space considerations, additional details are in Appendices B and C 3.1 Data The data come from an ACNielsen Wand panel collected from two separate submarkets in a large Midwestern city during the 118 weeks from January 1993 to August 1995 Our data consist of detailed purchase histories... 50% and a sales-weighted price of $1.95 for a 16-ounce box, compared to a 22% share for the private label brand with an average price of $1.10 per 16-ounce box 3.2 Identification We provide an informal discussion of identification and offer some descriptive statistical evidence The panel aspect of our data greatly facilitates the identification of preferences and heterogeneity The identification of. .. cigarette data contain patterns consistent with this notion of addiction, and that these patterns differ from those found in the non-addictive categories More specifically, we estimate a joint model of purchase incidence and purchase quantity along the lines of Gupta (1988) and Bucklin and Gupta (1992) A logit model determines purchase incidence, and conditional on a purchase occasion, a truncated-at-zero... 148–155 Baumann, D J., R B Cialdini, and D T Kendrick (1981) “Altruism as Hedonism: Helping and Self-gratification as Equivalent Responses,” Journal of Personality and Social Psychology 40: 1039–46 Becker, G S., and K V Murphy (1988) A Rational Model of Addiction, J of Pol Econ 96(4), 675–700 Becker, G S., M Grossman, and K V Murphy (1994), “An Empirical Analysis of Cigarette Addiction, American Economic... working paper 33 30 Heckman, J J (1981), “Statistical Models for Discrete Panel Data,” in C Manski and D McFadden, eds., The Structural Analysis of Discrete Data Cambridge: MIT Press 31 Herrnstein, R J., and D Prelec (1997), A Theory of Addiction, in The Matching Law, eds Howard Rachlin and David I Laibson Cambridge, MA: Harvard University Press, 160–87 32 Hendel, I and A Nevo (2006), "Measuring... 41 Narayanan, S., and P Manchanda (2006), “An Empirical Analysis of Individual Level Casino Gambling Behavior.,” Working paper, Stanford University GSB 42 Olekalns, N., P Bardsley (1995), “Rational Addiction to Caffeine: An Analysis of Coffee Consumption,” Journal of Political Economy, 104(5), 1100-1104 43 O’Donoghue, T and M Rabin (1999), “Addiction and Self-Control,” in Addiction: Entries and Exits,... "Decision-making Under Uncertainty," Marketing Science 15: 1–20 Erdem, T., S Imai, and M P Keane (2003), "Consumer Price and Promotion Expectations: Capturing Consumer Brand and Quantity Choice Dynamics under Price Uncertainty," Quantitative Marketing and Economics 1: 5–64 Evans, W N., and M C Farrelly (1998), “The Compensating Behavior of Smokers: Taxes, Tar, and Nicotine,” RAND Journal of Economics . Hendel and Nevo (2006) and Hartmann and Nair (2008). 3 theoretical (Becker and Murphy 1988), empirical (Tauras and Chaloupka 1999), and experimental. dominant brand with a market share of nearly 50% and a sales-weighted price of $1.95 for a 16-ounce box, compared to a 22% share for the private label brand