A Dynamic Structural Model of Addiction, Promotions, and Permanent Price Cuts pot

Gordon*Graduate School of Business Baohong Sun Tepper School of Business Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, PA15213 Email: bsun@andrew.cmu.edu Tel: 412-268-6903 We

A Dynamic Structural Model of Addiction, Promotions, and Permanent Price Cuts

Brett R Gordon*Graduate School of Business

Baohong Sun Tepper School of Business Carnegie Mellon University

5000 Forbes Avenue Pittsburgh, PA15213 Email: bsun@andrew.cmu.edu Tel: 412-268-6903

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

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)

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

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

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

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

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

I ≥ is the consumer’s inventory, P t ={P1t, ,P Jt}is a vector of prices, and θi ={α β ξi, i, ,i h i}

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)

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) u c a c( ,it it;αi)=αi01{c it =0}+αi1c it+αi2c it2+αi3a it +αi4a it2+αi5a c it it

If consumption is zero, the first coefficient, α , is the cost of a stock-out, or withdrawal i0Consumption may be zero when the inventory is exhausted and the consumer is unable to make a purchase (no store visit) The next two coefficients, α and i1 α , represent the instantaneous i2utility of consumption independent of addiction For the following two coefficients, α captures i3the direct utility from addiction and α allows for the tolerance effect The last term represents i4the reinforcement effect: if α > , then addiction increases the marginal utility of consumption i5 0

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) a i t, 1+ = − (1 δi)a it +c it ,

where 0≤ ≤ is the constant rate of depreciation of addiction over time Overall cigarette δi 1consumption 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

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:

jqt ijt

p q is the total expenditure The parameter βi1 measures consumer’s price sensitivity We account for product-level differentiation through the fixed-effects ξij 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 εijqt 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 h , such that ( ; ) i C I h it i = ⋅ Inventory is h I i it

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.

In summary, collecting the formulations for the individual components of utility, the indirect utility function is:

Let P be the aggregate price of product j, which we distinguish from jt p jqt, 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,

where P jt−1 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 ηjt is the random shock of

product j at time t, which follow a multivariate normal distribution, ηjt N(0, Ση) The diagonal elements denote the corresponding variance of ηjt , and the off-diagonal elements denote the

covariance between the prices of different products The correlation across products helps further capture the co-movement of prices of competing tiers

The system above describes the process governing product-level prices We model the price process for product-quantity specific prices as contemporaneous functions of the aggregate product price P jt The price process for a given quantity q in product j is:

We allow the probability of a store visit to depend on whether the consumer visited a store in the previous period We use a binomial distribution to model store visit behavior Let

2.4 Dynamic Decision Problem

Given their current state, period utility function, and expectations about future prices and store visits, consumers simultaneously make their optimal product-quantity,d ijqt* , and consumption,

*

it

c , decisions The value function when a consumer visits a store is V s( )it and the value function without a store visit is W s( )it We assume the discount factor is fixed and known at β =0.995.9Given the period utility function, the Bellman equation during a period with a store visit is:

The operator E denotes the conditional expectation over future prices given the consumer's t

state s During a period without a store visit, the consumer’s value function is: it

one-2.5 Heterogeneity, Initial Conditions, and Estimation

We account for unobserved heterogeneity by assuming that each consumer belongs to one of M

unobserved preference segments (Kamakura and Russell 1989) We denote m

i

φ as the probability

9 The discount factor in dynamic models is generally not identified (Rust 1994a, Rust 1994b), hence we fix its value

to yield a sensible annual discount rate A model with time-inconsistent preferences requires two discount factors to

be specified, significantly increasing the difficulty of proper parameter identification

that consumer i belongs to preference segment m More formally, the probability that a consumer in the sample is of type m is

(12)

' ' 1

δφ

δ

=

=

where δm, for m= 1, ,M, are a set of parameters to be estimated

We estimate the model using maximum likelihood Let D it denote the observed

product-quantity decision at time t, let T i* ⊂ denote the subset of all time periods in which consumer T i

made a store visit, and θ ={θ1, ,θM} denotes the dynamic parameters of interest Given the extreme value distribution of the error term, the probability of observing consumer i∈m making decision d ijqt at time t∈ is T i*

(13) *

1 ,

exp( )

exp( )

m M

ijqt m

To calculate the likelihood, let D be the vector of choices over households in period t t

We must calculate the likelihoodL D s( t| ; )t θ , which contains the unobservable state variables a it

and I Since both of these evolve deterministically, we can calculate their law of motions given it

some initial distribution for a and i1 I Then for a given value of the parameter vector, the log- i1

likelihood function of the sequence of choices over all the households is

Several issues are worth note concerning the solution and estimation of the model First,

we face an initial conditions problem since we do not observe the inventory and addiction levels

at the start of the data We start with initial inventory and addiction levels of zero and solve the dynamic programming problem, and then we simulate the model 50 times for 2T periods This process generates an initial bivariate density over inventory and addiction that we use to simulate the initial states for each consumer Second, all the state variables are continuous, making it is impossible to solve exactly for V ijqt and W ijqt at every point in the state space We discretize the state space using a sufficiently fine grid, use local polynomial interpolation to calculate the expected continuation values on points off the grid, and use Monte Carlo simulation with Halton draws to approximate the integral In evaluating the likelihood, we recalculate the optimal purchase and consumption decisions for each consumer and period to avoid approximation error

in using the estimated policy functions More computational details are in Appendix A

3 Empirical Application

This section describes the data set, 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

The cigarette category contains several hundred distinct products with variants in terms

of strength (regular/light), size (e.g., 100s), and flavor (e.g., menthol) To keep our study manageable, we classify products into three quality tiers based on common industry classifications of premium, generic, and discount value products We aggregate to the tier level instead of the brand level for two reasons First, the taste of cigarettes is more likely to differ across tiers than within a tier due to varying levels of tar and nicotine (Mulholland 1991 and Viscusi 2003) Second, our focus is not on inter-brand competition Although modeling brand-level dynamics, such as loyalty, would no doubt improve the model’s predictive ability, addiction exists independently of brand choice

Figure 1 plots the distribution of purchase quantities of cigarettes in our sample The large spikes at 10, 20, and 30 correspond to purchases of cartons each containing ten packs Based on this distribution, we discretize purchase quantity into five bins of {1-2, 3-4, 5-9, 10-19, 20+} and use each bin’s midpoint in our model Thus, we have 15 tier-size combinations On average, nearly 80 percent of average weekly purchases were for nine packs or less

[Figure 1 about here]

In addition to cigarettes, we consider purchases from the crackers and butter categories Crackers are a particularly good comparison category because, like cigarettes, they are storable and purchased with some frequency (compared to, say, detergent) but are not addictive We include butter for comparison to a less frequently purchased category We avoided perishable products, such as yogurt or milk, because this would introduce a product characteristic not observed in cigarettes and could confound the comparison

Choice models applied to panel data typically define and estimate the utility function at the household level However, members of a household may have different preferences and consumption patterns Defining addiction at the household-level would inevitably understate or overstate the importance of addiction for some household members, introducing a potential bias into our estimation To avoid this issue, we split the household-level observations into individual observations based on the gender and age of the purchaser, recorded with each purchase

To facilitate these cross-category comparisons, we use the same sample of individuals across the three categories We select those individuals who made at least ten cigarette purchases, ten crackers purchases, and four butter purchases Of the 1,351 individuals defined at the household-gender-age level who purchased cigarettes at least once, 584 satisfy all these criteria We have no reason to believe that smokers who purchased sufficient quantities of crackers and butter differ on some unobserved dimension from smokers who did not meet our sample criteria We randomly select 300 individuals for estimation and use 50 for a hold-out sample The individuals in our estimation sample made an average of 42 cigarette purchases across a total of 12,689 purchase observations We construct similar product tiers for crackers and butter based on product prices and brands

[Table 1 about here]

Table 1 provides sample descriptive statistics about the categories and product aggregates For cigarettes, the average purchase quantity per incidence was 13.39, and

consumers' average consumption per week is 4.93 packs The premium tier is the market leader, capturing approximately 51 percent of the total market The average price of cigarettes ranges from $1.63 for the premium tier to $1.12 for the discount tier Crackers and butter both contain three large brands that occupy different price tiers and account for more than 80% of sales For crackers, Nabisco is the 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 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 the purchase utility coefficients is straightforward The price parameter, βi1, is identified through variation in prices over time The quantity parameters, βi2

and βi3, and the fixed effects, ξij, are jointly identified through differences in the purchase probabilities across product tiers and purchase sizes

The arguments behind the identification of the consumption, storage cost, and addiction parameters are more subtle since the corresponding quantities are unobservable However, it is important to note that given a set of initial conditions, the structural model provides a direct mapping from the observed purchase quantity to the current consumption, which in turn determines next period addiction and inventory Thus we identify the consumption parameters,

0

i

α , α , and i1 α , through the joint distribution of inter-purchase times and quantity choices; that i2

is, a large number of cigarettes purchased over a short period of time implies a high rate of consumption For the inventory parameter, h , consider the case of two consumers who face the i

same (stationary) price process over time, purchase the same quantity during this period, but one consumer purchases more frequently than the other This variation leads us to conclude that the

one who purchases more frequently has higher storage costs than the other A similar argument exists to help identify the addiction parameters, α , i3 α , and i4 α Suppose two consumers i5purchase the same quantity of cigarettes at the same frequency, but one consumer makes additional visits to the store without purchasing anything during those visits This variation lets

us conclude this consumer gained less utility due to addiction because she was more able to resist the temptation to purchase cigarettes during the additional store visits

As discussed earlier, the fundamental distinction between addiction and other forms of state dependence is the emphasis on quantities: more consumption in the past implies more consumption in the present We present reduced-form evidence that the 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 Poisson model determines the number of units bought We use the flexible consumption rate function found in Ailawadi and Neslin (1998), and calculate inventory recursively based on the implied weekly consumption c In addition to explanatory variables it

such as inventory and mean consumption, we include a consumption stock variable, defined as

, (1 ) , 1 , 1

s = −δ s − +c − This variable helps capture persistence in consumption over time and loosely proxies for the addiction state variable in our structural model The model specification, parameter estimates, and further details are in Appendix C

The estimates in Table C1 suggest a difference between cigarettes on the one hand and crackers and butter on the other in terms of the importance of the consumption stock In particular, the consumption stock has a positive and significant effect on purchases of cigarettes but it has no effect for crackers and butter This suggests that past consumption quantities have a positive influence on current purchase decisions for cigarettes, which is consistent with addictive behavior Further, the estimates in Table C1 show most of the other variables are of the expected

sign and magnitude: for example, inventory exerts a negative influence on purchases for all categories, but its effect is greatest for cigarettes and smallest for butter

To be clear, we view these results as purely descriptive evidence for purchase behavior consistent with addiction We must use the structural model to specify a causal link between observed purchases and unobserved consumption and addiction Although this result only provides descriptive evidence for some form of consumption dynamics, it helps identify the fundamental correlations in the data that we require to estimate our structural model

3.3 Model Evaluation and Comparison

In order to demonstrate the importance of the key components of our model—forward-looking consumers, endogenous consumption, and addiction—we estimate three models for comparison Model 1 removes forward-looking behavior, endogenous consumption, and addiction from the full model This myopic model is commonly adopted to study consumer brand choice behavior for non-addictive products Model 2 adds forward-looking behavior and endogenous consumption, but still excludes addiction Model 3 is the full model with forward-looking behavior, endogenous consumption, and addiction

[Tables 2A, 2B, and 2C about here]

Table 2A reports the model fit statistics for the estimation and holdout samples for cigarettes The fit statistics show that the full model with two segments fits the data the best Estimating the model with additional segments did not sufficiently improve the performance Table 2B compares the tier transition matrix in the data to the simulated switching probabilities the model generates In general, the simulated transition probabilities do a good job of replicating those found in the data Table 2C compares simulated values of choice probabilities, average purchase quantity, purchase incidence, and the average inter-visit duration with those from the sample The full model fits remarkably well on all these dimensions, indicating the

model is able to replicate several key features of the data

[Table 2D about here]

For consistency, we use two segments to estimate Models 1 – 3 on crackers and butter

The results in Table 2D show that the dynamic model with addiction fits best for the addictive category and that the dynamic model without addiction fits best for the two non-addictive

categories The addiction process fails to provide additional explanatory power for crackers and butter In contrast, the addictive process for cigarettes alters consumers’ decisions and, as we later show, their responses to price changes

3.4 Parameter Estimates

Table 3 reports the parameter estimates for the utility function for Model 2 (without addiction) and Model 3 (with addiction) for each category.10 First, we discuss the results for Model 3 with cigarettes, and then compare them with the estimates for Model 2 to demonstrate the bias from ignoring addiction Finally, we contrast the cigarette estimates to those from crackers and butter All the price process estimates are in Appendix D

[Table 3 about here]

For cigarettes, the addiction depreciation coefficient, δi, is significant for both segments, indicating that past consumption quantities affect current decisions The linear and quadratic coefficients on consumption and addiction are positive and negative, respectively, in both cases and the coefficient on the interaction between consumption and addiction is positive These estimates suggest that addiction plays an important role in explaining consumer purchase and consumption behavior of addictive goods The estimates imply that the consumption utility function is concave, and that past consumption reinforces the marginal utility of present

10 We omit the estimates from Model 1 because the primary comparison is between the dynamic model with and without addiction

consumption Thus, the parameter estimates in the utility function satisfy the conditions required for addiction (Becker and Murphy 1988)

The parameters differ between consumer segments Consumers in segment one receive less instantaneous utility from consumption, have a higher marginal utility for addictive consumption, are less price sensitive, and have higher stock-out costs Addiction plays a larger role for segment one: the mean (standard deviation) of the addiction level for a consumer in segment one is 4.63 (1.65) and in segment two is 2.27 (1.38) For example, if we consider representative consumers from each segment, the interaction term between consumption and addiction accounts for 73% and 21% of consumption utility for segments one and two, respectively In economic terms, a one-unit increase in consumption for both consumers would produce a period surplus increase of $5.90 for segment one versus $1.41 for segment two

The stock-out coefficient implies a cost of roughly $8.90 for segment one and $3.88 for segment two, with the more addicted segment suffering the higher stock-out cost The inventory holding costs of $0.31 and $0.27, roughly the same for each segment, imply that higher inventory reduces the probability of purchasing and increases the rate of consumption

Comparing the results for Model 2 and Model 3, there are several points to note First, including addiction increases the price coefficients for both segments by roughly 30% Ignoring addiction leads the model to underestimate price sensitivity because addiction helps account for some lack of responsiveness in demand to price changes (Keane 1997) Second, the linear consumption parameters decrease in magnitude by about 25%, mostly due to the new interaction term between consumption and addiction Ignoring the effect of past consumption and present consumption, Model 2 places more weight on the instantaneous benefits of consumption and overestimates many of the consumption utility parameters Third, including addiction in the model raises the stock-out cost estimates and lowers the holding cost estimates Without addiction, the model partially rationalizes a given level of consumption with higher inventory holding costs and lower stock-out costs The presence of addiction provides an alternative

mechanism for the model to explain why a consumer might, say, decrease consumption in the presence of inventory A low rate of consumption need not imply low holding costs because the negative effect of consumption on addiction, through α , may outweigh the costs of holding i4additional inventory, h i

Comparing the results above for cigarettes to those obtained using the crackers and butter categories, consumers appear to shop differently for addictive and non-addictive products in a few ways First, and most importantly, consistent with the model fit statistics in Table 2D, the estimates for both categories do not change significantly after adding addiction into the model All the addiction terms are insignificant in Model 3 with the sole exception of the linear addiction term for crackers, which is modestly significant but small in magnitude Although this suggests the addiction process may be picking up some other type of state dependence in crackers in addition to stockpiling, the underlying process does not appear consistent with a model of addiction because the coefficient on the interaction between addiction and consumption

is insignificant These results demonstrate that the model is suitable for both addictive and addictive products because it finds evidence of addiction when appropriate and produces reasonable parameter estimates on categories that lack addiction

non-Second, the inventory holding cost parameters for all three categories are significant, demonstrating the importance of accounting for state dependence in the form of stockpiling for these categories Third, the average estimates for the monetary cost of stock-outs are $0.91 and

$0.32 for crackers and butter, respectively, which are considerably lower than the stock-out estimate for cigarettes Relative to cigarettes, crackers or butter are less likely to induce a store trip, and thus the cost of a trip for cigarettes is less likely to be distributed over multiple products

In addition, the stock-out cost estimates for cigarettes might include a psychological cost component associated more with addictive goods

4 Implications on the Effectiveness of Price and Promotion

In this section we discuss how the consumers’ policy functions for purchase and consumption vary depending on their addiction and inventory levels We also present purchase and consumption elasticity estimates for temporary and permanent price changes, and decompose the results the effects of the price changes into tier switching, consumption, and displacement

4.1 Optimal Purchase and Consumption Decisions

We study the optimal decisions for purchase and consumption as a function of inventory and addiction to understand how consumers’ decisions are driven by the endogenous state variables For cigarettes, both inventory and addiction affect the shape of the policy functions To highlight the impact of the addiction state variable, we compare the decision functions from the cracker category estimated with addiction to those from cigarettes, and show that the addiction state variable plays almost little in influencing cracker purchases and consumption.11

[Figures 2A, 2B, 3A, and 3B about here]

Figure 2A plots the optimal consumption averaged over both segments as a function of inventory and addiction.12 Figures 3A and 3B depict the policy functions for crackers from Model 3 First, we focus on how consumption varies with inventory for a given level of addiction As the utility function (Equation 6) shows, consumers must balance the instantaneous benefits of consumption—including the reinforcement effect—with the consequences of excess addiction At low levels of addiction, the results are similar to those in Ailawaide and Neslin (1998) and Sun (2005) for non-addictive products: optimal consumption increases at a declining rate with inventory due to inventory pressure and consumers strategically smoothing consumption to preserve inventory for the future in the event of no store visit However, when

11 A comparison with the decision functions from butter yields similar conclusions

12 To construct this decision function, we simulate the model over the data set This generates a sequence { ,c a I*it it, it}

of consumption, addiction, and inventory levels for each consumer in each period, representing the empirical

decision function We use local polynomial regression to smooth the decision function to create the 3-D plots

addiction becomes sufficiently high, the reinforcement effect and inventory holding costs increase the level of consumption Optimal consumption is not only significantly higher than when addiction is low, but consumption also increases monotonically with inventory However, the consumption policy function for crackers in Figure 3A does not exhibit any significant

variation in the addiction dimension

Holding inventory constant at a low level, optimal consumption as a function of addiction resembles an inverted-U shape as consumers balance the reinforcing effects of consumption with the costs of a large addictive stock For sufficiently high levels of inventory, holding costs and the reinforcement effect dominate, leading consumption to rise with addiction The interaction

between addiction and inventory alters consumers’ decisions because lower holding costs (h)

make it easier to store goods but also creates more temptation to consume more in the future These results differ from earlier work that documents a monotone relationship between inventory and consumption for non-addictive products (Assunção and Meyer 1993)

Figure 2B plots the optimal purchase quantity for cigarettes against inventory and addiction, and Figure 3B plots the same for crackers At sufficiently low levels of addiction, purchase quantity increases with inventory and an individual consumes all of her purchase plus some of her inventory In contrast to results for non-addictive goods, purchase quantity increases with inventory due to the high cost of stock-outs relative to holding costs for addictive goods For intermediate levels of addiction, purchase quantity exceeds consumption and inventory rises This creates a tension between holding sufficient inventory to avoid a stock out cost and the burden of holding the extra inventory However, at high addiction levels, purchase quantities decrease with inventory despite the fact that consumption increases Thus, a highly addicted consumer draws down her inventory, gradually limiting her future consumption and reducing her addiction In contrast, for crackers the purchase quantity monotonically increases with inventory

For low levels of inventory, purchase quantity always increases with addiction despite the fact that consumption starts to decrease at sufficiently high values of addiction This is due to the