The impact of soda taxes on consumer welfare: implications of storability and taste heterogeneity

Transcription

1 RAND Journal of Economics Vol. 46, No. 2, Summer 2015 pp Te impact of soda taxes on consumer welfare: implications of storability and taste eterogeneity Emily Yucai Wang Te typical analysis on te effectiveness of soda taxes relies on price elasticity estimates from static demand models, wic ignores consumers inventory beaviors and teir persistent tastes. Tis article provides estimates of te relevant price elasticities based on a dynamic demand model tat better addresses potential intertemporal substitution and unobservable persistent eterogeneous tastes. It finds tat static analyses overestimate te long-run own-price elasticity of regular soda by 60.8%, leading to overestimated consumption reduction of sugar-sweetened soft drinks by up to 57.9% in some cases. Results indicate tat soda taxes will raise revenue but are unlikely to substantially impact soda consumption. 1. Introduction Obesity as become an alarming concern among ealt professionals and policy makers alike, wit one in four American adults believed to be obese and estimated medical costs now exceeding $147 billion a year (Finkelstein et al., 2009). Te American Heart Association implicates te overconsumption of added sugars largely from sodas and fruit drinks as a major contributing factor to te ig US obesity rate. Since 2009, te Centers for Disease Control and Prevention as listed reducing te intake of sugar-sweetened beverages as one of its top obesity prevention strategies (Keener et al., 2009). Te public ealt concern as prompted public calls for a tax on sugar-sweetened beverages. Proponents of te tax ope tat consumers, faced wit iger prices for sugar-sweetened beverages, will reduce teir consumption of sugar-sweetened beverages by substituting to nontaxed, low-sugar alternatives. Currently, 34 states apply sales tax to soft drinks (Jeffords, 2010). As of May 2011, 15 states ave discussed imposing specific taxes on sugar-sweetened beverages during teir legislative sessions. In te November 4, 2014 election, University of Massacusetts, Amerst; emilywang@resecon.umass.edu. Tis article is a revised version of te second capter of my PD tesis. I deeply appreciate te guidance and advice provided to me by Andrew Sweeting as well as Arie Beresteanu, James Roberts, and Cris Timmins. I sincerely tank te editor, Aviv Nevo, and two anonymous reviewers for teir constructive comments and suggestions. In addition, tis article as benefitted from fruitful discussions wit Pat Bayer, Federico Bugni, Paul Ellickson, Gautam Gowrisankaran, Jun Isii, Carl Mela, Angela de Oliveira, Cristian Rojas, Steven Tadelis, and Ken Wilbur. I am grateful for te opportunity to work wit te IRI data, provided by Paul Ellickson, Carl Mela, and Andrew Sweeting. Furtermore, I would like to tank Cristop Bauner for te support and elp e provided trougout tis project. Any errors are my own. Copyrigt C 2015, RAND. 409

2 410 / THE RAND JOURNAL OF ECONOMICS Berkeley, California, enacted te first soda tax in te United States, establising a penny-perounce tax on sugary drinks. Tis article estimates te effectiveness of potential soda taxes and sows tat suc policies may not be as effective at curbing consumption as previously predicted. Te taxes are effective, owever, at raising revenue. A large ealt literature debates te effectiveness of soda taxes by predicting te reduction in te consumption of sugar-sweetened beverages induced by suc a tax. Following Andreyeva, Long, and Brownell (2010), most of tese studies use price elasticity estimates from traditional static demand models. Tese static models face two key sortcomings. First, tey ignore te fact tat most beverage products are storable and experience frequent price reductions, suggesting potential for sizable intertemporal substitution. Second, te traditional models ignore te fact tat consumers tend to ave strong preferences over product coices for reasons not entirely observable, suggesting unobservable persistent eterogeneous tastes. Tese two factors imply tat existing studies overpredict price elasticity and exaggerate te consumption response from a given tax. Tis article provides estimates of te relevant price elasticities based on a dynamic demand model tat better addresses potential intertemporal substitution and unobservable persistent eterogeneous tastes. Wen applied to weekly scanner data from 2002 to 2004, te model finds price elasticities to be substantially lower, and te resulting public ealt gains from various proposed taxes significantly smaller tan wat as been claimed in te literature to date. Te cosen dynamic demand model is in te style of Hendel and Nevo (2006b). Houseolds in te model are forward -looking and may coose to stockpile for future consumption. To accommodate te current application, I replace te traditional ouseold-brand-size fixed effects wit ouseold-specific random coefficients. Tis allows consumers taste eterogeneity to be modelled as a function of observable attributes as well as unobservable persistent preferences. Te resulting specification allows for more flexible substitution patterns, wic provides te necessary foundation for analyzing te distributional impact of relevant taxes. I find tis expanded scope of substitution important in my estimation and subsequent welfare analysis. I use te estimated distribution of ouseold preferences to perform policy analysis. Specifically, I study two of te more prominent tax proposals: a 10% sales tax and a penny-per-ounce tax. For eac income bracket, I calculate te effects of te sugar taxes at four pass-troug levels: 25%, 50%, 75%, and 100%. I simulate te posttax soda consumption pattern, calculate te compensating variation, and estimate te consumer welfare loss. Te results sow tat ignoring inventory and unobservable persistent tastes leads to an overestimated long-run price elasticity of regular soda 1 of rougly 60.8%, furter leading to overestimated reduction in sugar-sweetened soft drinks by as muc as 57.9% in some cases. Moreover, I find tat toug te policies generate a small deadweigt loss, tey are regressive in nature and tax-poor ouseolds more tan teir ric counterparts. Tis is because poor ouseolds not only consume more regular soda tan ric ouseolds, but also ave a less elastic demand for regular soda tan ric ouseolds. Te article is organized as follows. Te remainder of te introduction reviews te related literature. Section 2 presents industry details and te data. Sections 3 and 4 present te model and te estimation procedure. Section 5 presents te empirical results. Section 6 provides a discussion on welfare implications of te sugar taxes, and Section 7 concludes te article. Related literature. Various taxes ave been proposed as a means of controlling te consumption of sugar-sweetened soft drinks. Proponents of suc taxes draw on existing ealt literature tat establises a link between soft drinks and ealt problems. For instance, Sculze et al. (2004) provide evidence for a correlation between soda consumption and diabetes. Similarly, Bray, Nielsen, and Popkin (2004) find a correlation between obesity and ig fructose corn syrup, a main ingredient in regular soda. One possible explanation for te correlations is te increase in 1 Te term price elasticity of regular sodas will be used to refer to te aggregate category-level price elasticity trougout te text. Price elasticities for individual products are specified directly (e.g., te price elasticity of regular Coke).

3 WANG / 411 soda consumption. Nielsen and Popkin (2004) sow tat average daily caloric intake from soft drinks increased from 2.8% rougly 50 calories in 1977 to 7.0% rougly 144 calories in Te large increase in soda consumption in conjunction wit evidence sowing tat small dietary canges can effectively combat obesity (Hall and Jordan, 2008) suggests tat soda taxes may elp reduce obesity. Several articles argue tat sugar-sweetened soft drinks are te largest cause for obesity and suggest tat tey sould be taxed to improve public ealt (Jacobson and Brownell, 2000; Nielsen and Popkin, 2004; Mello, Studdert, and Brennan, 2006; Brownell and Frieden, 2009; Brownell et al., 2009; Smit et al., 2010). Te most prominent of tese are Brownell and Frieden (2009) and Smit et al. (2010). Brownell and Frieden (2009) state tat we are experiencing an obesity epidemic and ence sould tax soda eavily, similar to oter sin goods. Te autors cite a study conducted by Yale University s Rudd Center for Food Policy and Obesity suggesting tat every 10% increase in price will lead to a 7.8% decrease in soda consumption. 2 Furtermore, tey state tat te pennyper-ounce excise tax proposed in New York is expected to reduce consumption by 13%. Te autors do not document ow tese estimates are obtained, but te estimates are consistent wit igly elastic demand for soda. Tis contrasts my estimates, wic suggest tat demand for sugar-sweetened soft drinks is inelastic. Following a prompt from te Institute of Medicine and te National Academies of Science, te Economic Researc Service division of te USDA (Smit et al., 2010) examined te ealt effects of taxing sugar-sweetened beverages, reporting tat a 20% soda tax would be expected to reduce overweigt prevalence from te current 66.9% to 62.4%, and obesity from te current 33.4% to 30.4%. Te report draws on te Nielsen Homescan and te National Healt and Nutrition Examination Survey (NHANES). Applying Deaton and Muellbauer s (1980) Almost Ideal Demand System (AIDS) to te Nielsen weekly ouseold purcase panel, te autors find tat te category own-price elasticity of caloric-sweetened beverages is 1.264, suggesting an elastic demand. Te price elasticity estimate is ten applied to individual beverage intake data reported in te NHANES to estimate canges in caloric intake in response to a tax-induced 20% increase in te price of caloric-sweetened beverages. In comparison to tis report, I find a muc lower price elasticity of demand for regular sodas, at Tere as also been a growing body of literature opposing soda taxes. Kaplan (2010) points out tat te medical trials used in Brownell et al. (2009) do not provide enoug evidence for te claim tat sugar taxes will decrease obesity in te population. Hall and Jordan (2008), Katan and Ludwig (2010), and Patel (2012) suggest tat small dietary canges would not cause muc cange in weigt. Te most salient to my researc is Patel (2012). Patel (2012) analyzes te impact of ypotetical soda taxes using a static Berry, Levinson, and Pakes (1995) (BLP) framework applied to a five-year panel of Nielsen Scantrack data from April 2002 to April Te article finds tat te median body mass index (BMI) for an obese individual is and te median expected reduction in BMI for tese individuals is BMI canges of tis magnitude are not likely to result in meaningful reductions in illnesses or medical costs. Altoug Patel (2012) finds little evidence tat soda taxes will be as effective as claimed by teir proponents, tat researc differs significantly from te current one in te models 2 Tis study refers to Andreyeva, Long, and Brownell (2010), wo review 160 studies conducted in te United States since 1970, 14 of wic are relevant for te soft drinks category. Te autors report tat according to tese previous studies, soda drinks are among te products most responsive to price canges wit an average price elasticity estimate of 0.79 (in absolute value). Tey state tat a 10% increase in soft drink prices sould reduce consumption by 8% to 10%. Following tis article, a large sare of te literature in public ealt uses tis estimate to determine te effectiveness of a soda tax. 3 As bot articles use weekly scanner data, te differences in elasticity estimates come predominantly from te models employed. Te AIDS model does not account for intertemporal substitution. Hence, wen applied to weekly data, any differences in quantity canges are interpreted as canges in immediate consumption, wen in fact ouseolds may be stockpiling in anticipation of iger prices in future weeks.

4 412 / THE RAND JOURNAL OF ECONOMICS implemented, leading to significantly different policy implications. Similar to te USDA (Smit et al., 2010) report, Patel (2012) uses weekly market sale volume canges from temporary price reductions. As consumers stockpiling beavior is not modelled or incorporated in te analysis, it similarly overestimates te long-run own-price elasticities. As a result, te article finds demand for soda, regular and diet, to be elastic, wit an own-price elasticity of for regular Coke and for diet Coke. Tese estimates are close to tose previously found in te public ealt literature (generally estimated around 5). Despite tese elastic demand estimates, Patel (2012) finds little cange in consumers BMIs. Tis result is driven by te conversion of calories in soda to consumers BMIs in te steady state. It takes a large decrease in caloric intake to decrease an individual s BMI. Tis is an important but different point tan te one illustrated in tis article. Wen inventories are accounted for explicitly in te model, demand elasticity estimates are muc smaller in absolute value (for instance, 1.20 for regular Coke). Terefore, te resulting decreases in consumers weigt become negligible. Some proponents of soda taxes support tese policies from a revenue-generation point of view. For example, Jacobson and Brownell (2000) acknowledge tat sugar taxes may not improve public ealt but claim tat tey will generate sizable revenues for ealt programs. On te opposite side, Gostin (2007), Byrd (2004), and Powell et al. (2007) argue against tese taxes on te grounds tat tey are regressive and target te poor and minorities. In tis article, I find tat te imposed taxes do not generate large deadweigt losses: A large portion of te population as strong preferences for regular soda and do not switc out of teir preferred drinks posttax. However, I find tat soda taxes are regressive in nature. As poor ouseolds ave eavier consumptions tan teir ricer counterparts, tey are also impacted more by te taxes. On te metodological front, tis article builds on two strands of literature 4 : static demand models wit consumer eterogeneity and dynamic demand models of storable goods. In terms of static demand models, te literature started by Bresnaan (1981) and BLP (1995), and continued by Nevo (2000) models static consumer decisions for differentiated products. Tese articles and tose tat ave followed sow tat it is important to incorporate consumer eterogeneity in demand systems to obtain realistic predictions for differentiated products. Altoug tis article also incorporates consumer eterogeneity into te demand system, it differs from tese articles in two ways. First, ouseolds in te model are forward looking. Second, te model is better suited for disaggregated ouseold panel data, unlike BLP-style models, wic are adapted for aggregated market-level data. Tis article also fits into te recent literature on dynamic demand models of storable goods. Tis literature originates from works bot in industrial organization and marketing and as seen increased applications (Erdem, Imai, and Keane, 2003; Hendel and Nevo, 2006a, 2006b; Hartmann and Nair, 2010; Hendel and Nevo, 2013; Osborne, 2013). Witin te field of industrial organization, Hendel and Nevo ave produced a series of influential articles on storable products. Hendel and Nevo (2006a) find evidence for te presence of stockpiling beavior during periods of price reductions. Using scanner data on laundry detergent as an example, tey find tat as time-sincesale lengtens, total quantities purcased increase. Tis suggests tat ouseolds intertemporally substitute purcases. Te important implications ere is tat static demand estimates of long-run price elasticities may be misestimated for storable goods tat experience frequent sales. Having sown evidence for stockpiling beavior, Hendel and Nevo (2006b) build a dynamic demand framework tat explicitly accounts for inventory. Again using laundry detergent as an example, te autors use tis framework to estimate te magnitude of te misestimation tat can result from using a static demand model in a storable goods market. Teir results suggest tat 4 Tere is also a line of literature on dynamic demand models of durable goods. Examples include Geottler and Gordon (2011), Conlon (2012), and Nair (2007). Some of tese articles, suc as Gowrisankaran and Rysman (2009), incorporate unobservable eterogeneous tastes into dynamic durable goods demand models. However, in most cases, durable goods are purcased once instead of repeatedly. Te decisions tat consumers make in tese models focus on te timing of product replacement instead of stockpiling. Hence, tese models and metods are not appropriate for studying consumption of storable goods.

5 WANG / 413 static demand estimates may (i) overestimate own-price elasticities by 30%, (ii) underestimate cross-price elasticities by up to a factor of five, and (iii) overestimate te substitution to te no-purcase by over 200%. Tese results ave significant ramifications for predicting te effect of soda taxes, suggesting tat using a static demand model to estimate te elasticities of soda a storable good may lead to exaggerated reductions of regular soda consumption. Hendel and Nevo (2013) propose a new dynamic demand model tat accommodates ow consumers respond to temporary price reductions. Te model is simple in its design and implementation but still captures inventory. It provides a quick and appropriate way of computing price elasticities for storable products. As I sow in te robustness ceck section in te Appendix, te long-run own-price elasticities in te model proposed in Hendel and Nevo (2012) are comparable to tose implemented in te article at and, wic provides assurances for te full model and its implementation. However, tis framework does not allow for more complex welfare analyses tat require estimating te distribution of tastes. To understand te impact of te proposed taxes on consumer welfare, we need to estimate te sare of te population wit strong tastes for te products taxed. Tese distributions are difficult to recover from aggregate data. Hence, implementing te ricer model proposed in tis article is necessary for predicting te policy implications of te proposed taxes. 2. Data I use weekly scanner data from 2002 to 2004 provided by Information Resources, Inc. (IRI). Te data comprises two components: a ouseold panel of randomly selected ouseolds 5 and a store panel. For eac ouseold in eac week, I observe weter any soda was purcased; if so, I observe wic products were purcased, were it was purcased, ow muc was bougt, and te total dollar amount paid. From eac store in eac week I observe te price carged, te total quantity sold, and all promotional activities for eac product sold in te store. Sales from tese stores account for over 97% of all purcases of soft drinks observed from te ouseolds in te panel. For eac ouseold, I observe a few basic demograpic variables suc as race, income, and ouseold size. For eac product, I observe te product name, brand, packaging, volume, and weter it is regular or diet. Eac observation from bot panels as unique identifiers for te product, store, and week. Tese identifiers allow me to link te two sets of data and track prices and promotions for all products available to ouseolds on any given sopping trip. Tat is, I observe not only information on te purcase itself but also information regarding eac ouseold s complete coice set. Houseold panel. I separate ouseolds into tree groups by per-capita income: less tan $10K, between $10K and $20K, and more tan $20K per-capita. 6 Table 1 reports some statistics associated wit eac income bracket. Te data reveals several interesting patterns. (i) On average, te ouseold size is decreasing in income. (ii) Te average weekly ouseold soda purcase is sligtly increasing in income. (iii) Te number of trips were ouseolds bougt soda is decreasing in income. Hig-income ouseolds make fewer purcases of soft drinks on average tan lower income ouseolds. Because tey also purcase more units, tis implies tat ric 5 IRI randomly selects a sample of ouseolds in two suburban areas around te Midwest and New England and requests teir participation. Participating ouseolds conform fairly well to local demograpics. Te data does not suggest a selection bias in te panel. 6 Te data is collected predominantly from suburban areas of New England and te Great Lakes region. As a result, tere is little variation in etnicity. Te majority of ouseolds in te sample are Wite. However, tere are substantial income differences. Altoug in an ideal world we would like to observe racial diversity, previous literature indicates tat obesity correlates more significantly wit income tan wit race (Food Researc and Action Center, 2010). In addition, te main point made in tis article is tat previous literature, wic does not account for stockpiling or eterogeneous tastes, overestimates te effect of taxation on soft drink consumption. Tis can be generalized to areas wit oter demograpic compositions.

6 414 / THE RAND JOURNAL OF ECONOMICS TABLE 1 Houseold Demograpics Bracket 1 Bracket 2 Bracket 3 Demograpics Bracket definition (K) <10K [10K 20K) 20K Avg. income (K) Avg. ouseold size Number of observations Soda Purcase Avg. weekly vol. purcased (liters) Avg. weekly dollars spend Avg. annual total number of soda trips Brand Purcase Sares Coke market sare 50.13% 46.69% 54.14% Pepsi market sare 40.13% 40.80% 41.72% Store brand market sare 9.74% 12.51% 4.14% Diet vs. Regular Sares Diet market sare 39.49% 36.32% 51.55% Regular market sare 60.51% 63.68% 48.45% ouseolds tend to buy more soda per sopping trip. Tere are two ways of reconciling tis fact. First, if we assume soda is purcased only for immediate consumption, ten ric ouseolds do not drink soda as frequently as poorer ouseolds do, but tey consume more wen tey do drink it. Te oter explanation is inventory: ric ouseolds purcase more soda in fewer trips because tey stockpile more tan poor ouseolds. Tey are more likely to ave larger ouses and, ence, more storage area at ome. Te second explanation seems more plausible, and I sow in te last part of tis section tat te inventory explanation better fits te data. Table 1 also presents a breakdown of te products tat ouseolds purcased in terms of te sares of cola drinks (Coke, Pepsi, and store brand) as well as sares of diet versus regular drinks. It is clear from te table tat ig-income ouseolds purcase more branded products and poorer ouseolds purcase more regular soda. Te same pattern olds for all brands of soda. Store panel. From te store panel, I observe weekly prices and advertising information for all items sold. 7 For eac store in eac week, tere are over 250 different products offered on average, a combination of all brands, regular/diet types, packaging, volume, and flavors. In estimating te model, prices and promotions of all products become part of te state space. Carrying prices and promotions of all products is computationally infeasible in te dynamic programming problem. Quantities sold of specialty items, suc as IBC Root Beer, are very small. I terefore restrict te set of soda brands to tose wose market sares exceed 1%. In addition, I also include te generic versions of tese branded products were tey are available, even if teir market sares fall below 1%. Consumers substitution beavior between regular and diet sodas is one of te crucial components of policy study ere, so I allow for bot varieties in te analysis. In Table 2, I rank all products included in te analysis according to teir market sare by sales volume in Te soda market is fairly mature and market sares terefore remain stable over time. Sales volumes in 2003 and 2004 are similar to tose in One pattern emerges clearly from Table 2: te market for soda is fairly concentrated. A few large brands namely Coca-Cola, Pepsi, Sprite, and Mtn Dew capture its majority. At te top, regular Coca-Cola (Coke) acieves nearly 20% of te market. By te 10t-ranked product, diet 7 I do not directly observe te price of eac product. Instead, I observe weekly total revenue and total units sold for every Universal Product Code (UPC) (product). I take te average and use it as a proxy for product price. In terms of promotional activities, for eac product in every week, I observe weter it is on display, on feature, and/or as price discounts.

7 WANG / 415 TABLE 2 Market Sare in 2002 By Volume Product Name Market Sare Cumulative Sare 1 Coca-Cola (Regular) 19.39% 19.39% 2 Pepsi Cola (Regular) 18.34% 37.73% 3 Coca-Cola (Diet) 13.47% 51.20% 4 Pepsi Cola (Diet) 10.23% 61.43% 5 Mtn Dew (Regular) 5.83% 67.26% 6 Sprite (Regular) 5.14% 72.40% 7 Dr Pepper (Regular) 4.23% 76.63% 8 7 UP (Regular) 2.58% 79.21% 9 Dr Pepper (Diet) 1.80% 81.01% 10 Mtn Dew (Diet) 1.47% 82.48% 11 Generic Cola (Regular) 1.44% 83.92% 12 Sprite (Diet) 1.27% 85.19% 13 7 UP (Diet) 1.20% 86.39% 14 Generic Cola (Diet) 0.54% 86.93% 15 Generic Lemonlime (Regular) 0.48% 87.41% 16 Generic Lemonlime (Diet) 0.12% 87.53% Oter 12.47% 100% FIGURE 1 WEEKLY COLA DRINKS SOLD (PERCENTAGE OF ANNUAL TOTAL) Mtn Dew, te market sare as decreased to a little over 1%. Tis suggests tat consumers ave strong preferences for top brands, and ence, implies tat capturing ouseolds intrinsic product tastes in te model may be important for studying te impacts of policy canges. Te combined market sare of all products included in te analysis is close to 90%. Seasonality. One concern about soft drinks is tat teir consumption could be influenced by olidays. I observe a very small effect in te data. Figure 1 sows weekly cola product sales by volume as a percentage of annual total observed in stores. Te gray bars indicate te presence of

8 416 / THE RAND JOURNAL OF ECONOMICS FIGURE 2 SALES VOLUME OF REGULAR COKE (WITH AND WITHOUT PRICE REDUCTION) a oliday, were olidays are defined very liberally (Super Bowl Sunday is counted as a oliday). Te figure below presents te panel for 2004; te graps for te oter two years are similar. We see tat tere are increases in te volumes sold around some olidays. Te dominant ones are around July 4t and Tanksgiving. I do not model oliday effects ere and use data from te 2nd to te 26t week of eac year, excluding most major olidays suc as July 4t, Tanksgiving, and Cristmas. Houseolds tat are present in multiple panels are treated as separate observations. Robustness cecks wit eac ouseold counted once turned up no major differences in estimates. Stockpiling beavior. Te main competing model is one in wic consumption is directly influenced by price and no storage occurs. If tis were true, we sould expect to see sales volume increase wen price reductions are available, but decrease and remain largely constant wen tere is no sale. However, tis is not te case. Te following grap sows tat sales volume drops dramatically immediately after eac sale ends, ten slowly grows again. Tis can be explained by stockpiling: ouseolds fill teir inventories during price reductions. Hence, tey do not need to purcase muc soda immediately afterward. As time passes, ouseolds deplete teir inventories and more and more ouseolds ave to restock. As an example, I use te sale of regular Coke from a representative store in Figure 2 sows ow sales volume evolves over te duration of a year and ow it is influenced by price reductions. Eac bar sows te sale volume for one week. Black bars indicate price reductions and gray ones denote weeks witout sales. It is clear tat te demand for regular Coke dramatically increases wen tere is a price reduction. Moreover, we see tat sales volume decreases drastically immediately after a price reduction and picks up again in te following weeks. (Tese occurrences are marked by te orizontal lines beneat te bars.) Tese dips in purcases are consistent wit ouseolds stocking up on soda wen tere are price reductions, reducing te need to buy soda immediately

9 WANG / 417 FIGURE 3 PURCHASE BEHAVIOR OF TWO HOUSEHOLDS (BY INCOME) afterward. However, as teir stocks become low tey make more purcases again. Static models do not account for tis effect but assume tat all purcased units are immediately consumed. Hence, tese models are misspecified. To furter distinguis between static and dynamic beavior, I analyze ow past prices influence current purcase size coices. Using weekly store sales data, te following regression provides additional evidence for te presence of stockpiling beavior. To be more precise, I regress te weekly quantities sold for eac product in eac store on its current week s price, inflation adjusted, and te number of weeks (duration) since it last experienced a sale. Table 3 sows te results from tis simple regression.

10 418 / THE RAND JOURNAL OF ECONOMICS TABLE 3 Regression of Quantity Purcased Coefficient Duration since last sale * (0.1044) Current price of product * (1.3694) Constant term * (5.0503) Notes: * Statistically significant at 99% level. TABLE 4 Transitional Probability of Purcase Prob(brand in per. 2 brand in per.1) Prob(diet in per. 2 diet in per.1) Prob(Coke Coke) 84.81% Prob(regular regular) 63.83% Prob(Pepsi Coke) 15.19% Prob(diet regular) 36.17% Prob(Coke Pepsi) 26.66% Prob(regular diet) 22.04% Prob(Pepsi Pepsi) 73.34% Prob(diet diet) 77.96% If a static model is correct, we sould expect duration to ave no impact. Tat is, purcase decisions depend only on current prices and marginal utilities of consumption. However, if an inventory model is correct, purcase quantities sould be greater as more time passes since te last sale. If ouseolds are stockpiling items not needed for immediate consumption, tey can delay teir purcases wen prices are unfavorable. However, as tey go troug longer periods of ig prices, teir inventories become depleted and take larger purcases to restock. Indeed, as Table 3 sows, te coefficient on duration to last sale is positive and igly statistically significant. Tis indicates tat purcases are correlated wit past prices, justifying a dynamic specification. Altoug stockpiling beavior is present across te entire population, tis beavior differs significantly across income groups. Low-income ouseolds are less able to stockpile compared to teir iger income counterparts. Recall from Table 1, we see tat iger income ouseolds, on average, purcase more per sopping trip tan te lowest income group. Several factors may contribute to tis penomenon. For instance, low-income ouseolds may ave less capacity to stockpile at ome, tey are more likely to experience iger transportation cost (e.g., aving to rely on buses), and may face more budget constraints. Tese factors all limit poor ouseolds ability to take advantage of temporary price reductions. In Figure 3, I plot te sopping beaviors of two representative ouseolds. Te left grap plots te sopping frequency and timing of a middle-income ouseold and te rigt one plots te same for a low-income ouseold. Bot ouseolds purcased around 30 two-liter bottles of Coca-Cola in In bot graps, I indicate te price movements of a 2-liter bottle of Coke by gray lines and I denote te purcases by red dots. We see from te above grap tat ricer ouseolds are more likely to make purcases only wen prices are low, using teir inventory during ig-price periods and waiting for te next sale. Poorer ouseolds, on te oter and, make purcases more frequently, even during nonsale periods. Tis speaks to te differing abilities to stockpile across income groups and implies tat poorer ouseolds are more limited in teir ability to take advantage of temporary price decreases. As tey cannot stockpile as muc wen a sale appens, tey are also more affected by price fluctuations. In te estimation, tis fact will be reflected as iger estimated storage costs. Furtermore, poor ouseolds limited storage ability coupled wit iger persistent preferences negatively affects teir welfare. Houseolds tat are less able to stockpile but are also less willing to switc to ceaper alternatives will end up paying more for teir preferred product. Tis will be furter exaggerated by te proposed taxes. As we will see in te policy simulations, te combination of tese factors implies tat te tax is regressive in practice.

11 WANG / 419 Persistent eterogeneous preferences. Table 4 sows te probability of observing brand and diet purcases conditional on te observed last purcases. I display te transition of brand purcases in te first column and te transition of diet soda purcases in te second column. If ouseolds do not ave intrinsic brand or diet preferences, ten te product coice in te second period sould be independent from tat of te first. Tat is, te probability of buying product x in period t + 1 conditional on buying te same product in period t sould be rougly te same as te probability conditional on buying product y in period t. However, tis is not te case, as seen in Table 4. Te probability of purcasing Coke in period t + 1 conditional on purcasing Coke in period t is 84.81%. Te probability of purcasing Coke in period t + 1 conditional on purcasing Pepsi in period t, owever, is only 26.66%. Te same is true for diet preferences. Te probability of observing a purcase of a regular soda in period t + 1 conditional on purcasing regular in period t is 63.83% and te probability of buying a regular soda in period t + 1 conditional on observing a diet purcase in period t is 22.04%. Tis suggests tat ouseolds ave persistent brand and diet preferences. 3. Model Te model built ere is ouseold specific. Eac ouseold as its own intrinsic tastes for products, its own capacity for storage, and its own willingness to pay for goods. Houseolds derive utilities from product-specific consumptions and from any available advertising or promotions. Tey face prices for te goods and inventory costs for storing unused quantities of purcased goods. Togeter, tese factors influence ow eac ouseold responds to possible soda taxes. Houseolds in te model are forward -looking and maximize teir present value of expected future utilities. As suc, tey use current market information to form expectations over future prices and may coose to build inventories to guard against future price increases. Soft drinks are storable: quantities not currently consumed are stored for future consumption. In eac period, ouseolds make tree decisions: ow muc soda to consume, ow muc soda to purcase, and if tey coose to buy anyting at all wic soda products to buy. Tese decisions are governed by ouseold persistent preferences, available information (current prices, advertising, consumption sock, and inventories) and expectations concerning future prices and consumption socks. Tis model builds on te dynamic demand framework of Hendel and Nevo (2006b). Similar to Hendel and Nevo (2006b), te model flexibly incorporates observable consumer taste eterogeneity. Houseolds differ according to teir observable attributes, for example, income and race. In addition, te model allows for a greater degree of persistent unobservable consumer taste eterogeneity. Houseolds differ in teir tastes for product caracteristics, suc as weter te product is regular or diet as well as teir sensitivities for prices/advertising and teir abilities to stockpile. Tese persistent preferences are modelled as random coefficients and pick up systematic differences in purcase patterns wen observable caracteristics are identical across ouseolds. Model setup. Houseolds maximize te sum of discounted utilities derived from consuming soft drinks and an outside good. Eac ouseold in eac period t obtains a per period utility from consuming soft drinks and an outside good: U ( c t,υ t ) + η m t, were c t is te amount of soda consumed; υ t is a stocastic sock tat canges te marginal utility from consumption; is a vector of ouseold-specific preferences; η is te marginal utility from consuming te outside good; and m t is te consumption of te outside good. Tere are a total of J different products offered in te market, eac is denoted by j. Te total consumption of all soda products in period t by ouseold is c t = j c jt.

12 420 / THE RAND JOURNAL OF ECONOMICS Te utility of consumption, U(c t,υ t ), is a function of ouseold s consumption in period t, c, and a sock to te marginal utility of consumption, t υ t. Recall tat consumption is equal to te total volume of all products consumed in te period. Following Hendel and Nevo (2006b), ouseolds do not obtain product-specific utility at te time of consumption. Instead, utility associated wit eac product is derived at time of purcase. Hence, te types of products available in storage do not affect consumption. Houseolds receive a sock, υ t, in eac period, wic introduces randomness in ouseolds need to consume and allows teir consumption to depend on factors tat are unobserved by te researcer. Te sock influences te utility in te following way. If ouseold draws a ig realization of υ t, ten its marginal utility of consumption would be smaller tan if a low realization ad been drawn. Terefore, a ig realization decreases ouseolds need to consume and ence, makes demand more elastic. In implementation, I follow previous literature in assuming te following functional form for te utility of consumption: U(c t,υ t ) = α log(c t + υ t ), (1) were te consumption level and te stocastic sock enter additively into te utility. Unlike previous literature, te marginal utility of consumption, α, enters into te model as a random coefficient and is ouseold-specific. 8 As ouseolds cannot consume a negative amount of soda, te total consumption, c t, is restricted to be nonnegative. Houseolds ave te ability to build inventories of goods, allowing tem to smoot consumption in times of ig prices. However, tis strategy is costly; te cost of te inventory at time t (i t )isgivenby F ( i ) t+1 = β i + ( 1 t+1 β 2 i 2 t+1), (2) were β and 1 β 2 are ouseold-specific random parameters. Tese parameters represent ouseold s ability to store leftover products. Houseolds ability to take advantage of sales will depend on teir marginal cost of inventory, and tus on parameters β and 1 β. Houseolds 2 inventory costs influence teir abilities to adapt to canges posttax. Houseolds wit lower costs of inventory are able to stock up on larger quantities of soda during sales. Houseolds wit iger costs of inventory will be more affected by te taxes because tey will find it more costly to stock up. Following simple accounting rules, te end-of-period inventory, i t+1, is equal to te beginning-of-period inventory, i, plus te total current purcase, t s t, minus te total consumption, c. Tat is, i = i t t+1 t + s t c t. As ouseolds cannot consume more tan wat is available in teir storage or make negative purcases, te total inventory, i, and purcase, t s t, are restricted to be nonnegative. Te last piece of te flow utility, G ( p jst, a jst,ε ) jst, is associated wit ouseold s purcase of product j at volume s in period t. It is a function of prices, p jst, promotional activities, a jst, product preferences,, and a random sock, ε jst. In application: G ( p jst, a jst,ε jst ) = γ 1 p jst + γ 2 a jst + j 1 jt ( ζ j + ψ j ) s jt + ε jst (3) were j 1 jt = 1. Parameters γ 1 and γ 2 measure ouseold s marginal utility of income and utility from any available promotional activities, respectively. Variable a jst is an indicator tat denotes te presence of any features or displays. j 1 (ζ jt j + ψ j )s jt represents ouseold s intrinsic preferences for product j weiged by total volume purcased. Decomposing a ouseold s product tastes into two sets of mutually exclusive product caracteristics (i.e., j 1 jt = 1): a preference for te brand 8 Tecnically, te marginal utility of consumption is α / ( ) c t + υ t, wic depends on te consumption level and te consumption sock. For simplicity, I call α te marginal utility of consumption.

13 WANG / 421 and a preference for weter te product is diet. Parameter ζ j denotes ouseold s persistent taste for te brand of product j and parameter ψ j denotes ouseold s persistent preference for weter product j is diet. Bot are ouseold-specific and time-invariant random coefficients. As sodas can be generally classified as eiter regular or diet, for identification purposes, ψ j measures ow muc more ouseold prefers regular over diet. If a ouseold prefers regular over diet versions of te same brand, ten ψ j is positive, and ψ j is negative if te ouseold prefers diet instead. Houseolds persistent preferences for te brand, ζ j, and te diet type are especially important wen it comes to studying te impact of te taxes, directly influencing weter te ouseold would switc away from regular soda. Consider a ouseold wit strong preferences for regular Coke. Tis ouseold may not switc away from its favorite product at all. Rater, it would simply pay into te tax revenue. Alternatively, te ouseold could purcase larger quantities of te product during a steep sale. Tese intrinsic tastes elp determine ow many people will alter teir consumption beavior posttax. Te last component, ε tsi, denotes an idiosyncratic sock to ouseold s product coice. Its distribution is discussed below, along wit oter assumptions. Houseold s objective is to maximize its discounted value of expected future utility, V (φ t ), for any state φ t in any period t wit respect to te consumption level c, te purcase volume s, and te product coice j, were te state space φ t consists of current prices and promotions, te beginning-of-period inventory, te sock to utility from consumption, and te sock to utility for eac product. Matematically, ouseold s problem in period t = 1 can be represented by te following infinite orizon maximization problem: V (φ 1 ) (4) = max δ t 1 E [ U ( c {c (φ t ),s (φ t ), j t (φ t )},υ ) t F ( i ) t+1 + G ( p jst, a jst,ε ) ] jst φ 1 t=1 s.t. i t, c t, s t 0,i t+1 = i t + s t c t, were δ is te standard notation for te discount factor. Tis can equivalently be written as te following Bellman equation: V ( φ ) 1 {[ α log(c + υ ) = max {c,s, j} + δe ( β i ( 1 + β ) ) 2 i 2 +γ p 1 js + γ a 2 js+ j 1 jt ( ζ j + ψ j ] ) s j + ε js [ ( (φ V ) )] } φ, 1 c, s, i,, (5) were ouseolds maximize te sum of teir current period flow utilities plus te discounted expected future values wit respect to consumption, product, and volume purcases, conditional on te current state and unobserved persistent preferences. Following Hendel and Nevo (2006b), product differentiation in tis model takes place at te moment of purcase. Altoug ouseolds ave intrinsic preferences for different products, tese preferences and te differences between products affect ouseolds beaviors exclusively at te store but do not give different utilities at te moment of consumption. Because consumptions and inventories are not observed, tis specification avoids putting extra structure on consumption rates of different items in inventory. Furtermore, tis assumption significantly decreases te state space. Instead of carrying te wole vector of inventories for eac brand, only te total quantity in stock is tracked. Differentiation at purcase, represented by j 1 (ζ jt j + ψ j )s jt, captures te expected value of te future differences in utility from consumption. More specifically, te term ζ j + ψ j captures te expected utility from future consumption of one unit of product j at te time of purcase. As Hendel and Nevo (2006a) state, tis assumption is appropriate as long as

14 422 / THE RAND JOURNAL OF ECONOMICS (i) brand utilities are linear and (ii) discounting is low. Condition 1 olds in tis model, as can be seen from equation (4). Condition 2 is likely to be satisfied as well, given tat decisions are made weekly and most purcases are presumably meant to be consumed in te relatively near future. Additionally, to simplify te computational burden associated wit estimating te model, I make te following assumptions, wic are common in te literature: Assumption 1. Consumption socks, υ t, are distributed independently and identically across ouseolds and over time. In principle, serial correlation in υ t increase in computational burden. 9 can be accommodated, but only wit a significant Assumption 2. Prices and advertising activities follow an exogenous first-order Markov process: Pr (p t p 1,...,p t 1, a 1,...,a t 1 ) = Pr (p t p t 1 ) and Pr (a t p 1,...,p t 1, a 1,...,a t 1 ) = Pr (a t a t 1 ). More specifically, prices follow te AR1-process, p t = a 0 + a 1 p t 1 + v, were v is distributed normally wit mean zero and advertising follows te AR1-process Pr(a t = 1) = 1. 1+exp(b 0 +b 1 a t 1 ) Tis assumption is often employed in te empirical literature to reduce te state space in te dynamic programming problem. 10 Assumption 3. Te product coice sock, ε tsi, follows a type I extreme value distribution and is independent and identically distributed across eac ouseold, period, and purcase. Tis assumption is commonly made in te literature and can be relaxed at te cost of significantly increased computational burden. Assumption 3 allows me to calculate te probability of observing any particular brand diet purcase, conditional on volume and unobservable persistent preference, according to te standard logit formula: Pr ( j t s t,φ t, ) = [ exp γ1 p jst + γ2 a jst + ( ) j 1 jt ζ j + ψ j s jt + M ( φt, j, s )] ( ) ζ j + ψ j s jt + M ( φt, j, s )], j,s exp [γ 1 p jst + γ 2 a jst + j 1 jt { ( were M(φ t, j, s ) = max c U c t,υt ) F ( it+1 ) + δe [ V ( φt+1) j t, ct,φ t, ]}. Similar to Hendel and Nevo (2006b), given te preceding model and assumptions, te optimal consumption, conditional on te volume purcased and ouseold s persistent preferences, is not brand specific. Tat is, M ( φ t, j, s ) is independent of brand coice. Tis implies tat Pr ( j t s t,φ, ) exp [ γ 1 t = p jst + γ a 2 jst + ( ) ] j 1 jt ζ j + ψ j s jt j,s exp [ γ 1 p jst + γ 2 a jst + ( ) ]. (7) j 1 jt ζ j + ψ j s jt From tis equation, it is straigtforward to see tat a ouseold s two purcase decisions, product j t and volume s, are treated differently. Conditional on bot te volume, t s t, and ouseold s 9 Under unobserved persistent preferences, ouseolds consumption patterns could be correlated wit teir systematic preferences. It is terefore important tat ouseolds marginal utility of consumption, α, be allowed to differ across ouseolds. Once tis as been controlled for, any remaining source of dependence would be present if ouseolds wit different preferences ave consumption socks wit different variances. However, it is unclear wat would cause suc a correlation, and any suc effects are likely to ave minor influences on te estimation results. 10 Tis assumption implies tat consumers use only te current period prices and promotions to predict future prices and promotions, wic seems to be a reasonable approximation of te formation of consumers price expectations. Te main concern migt be seasonal price fluctuations, wen te probability of advertising increases. Tis concern sould be ameliorated as I use only data from te 2nd to te 26t week of eac year. (6)

15 WANG / 423 persistent preference,, te product coices, j t, are uncorrelated across periods. Tis split in te likeliood simplifies te state space, as it allows me to keep track of only a single inventory variable instead of one inventory per product. However, te same split in estimation as seen in Hendel and Nevo (2006b) is no longer feasible due to te persistent random tastes. As discussed in Aguirregabiria and Nevo (2013), te split of te likeliood in estimation relies on te assumption tat taste parameters are conditionally independent of eterogeneity. Allowing for persistent random components,, violates tis assumption. Te computation of te probability of product purcase j t, conditional on volume s t but unconditional on persistent preferences, requires te integration of te probability of conditional on volume s t, wic is dynamic. As a result, tis split can no longer be used in estimation. Te volume purcase decisions, s t, depend on current consumption as well as past consumption levels, purcase decisions, initial inventories, and persistent preferences. Consumption and volume purcase decisions, in turn, are determined by ouseolds optimal policies and are correlated over time. Hence, te probability of observing any sequence of volume purcased, Pr ( s 1 s T φ, ) t, depends on tat ouseold s optimal policy rule, wic is te solution to te dynamic programming problem. 4. Estimation and Identification Te computational cost to estimating a dynamic demand model suc as specified above is ig. Some of te cost can be attributed to te large state space associated wit te model: not only are all current prices and promotional activities of all products and sizes part of te state space, te current period inventories and consumption socks are also state variables. Tis causes te calculation of te value functions underlying te dynamic model to be very time-consuming. Te computational burden is exacerbated by te introduction of random coefficients. As tese random coefficients need to be integrated out, te value function needs to be calculated many more times compared to a model witout random coefficients. Combined, te computational burden makes te traditional fixed point approac to estimation infeasible. Consequently, I adopt a simulated maximum likeliood approac tat exploits Importance Sampling tecniques to mitigate te computational burden. I furter reduce te computational burden by leveraging te assumption tat ouseold decision processes are mutually independent, allowing me to precalculate coice probabilities in a parallel fasion. Altoug te estimation rougly follows tese metods, it as to deal wit issues specific to tis article. I start te discussion of te estimation by providing an overview of te estimation procedure; a more detailed description of te estimation details can be found in te Appendix. Estimation. Te objective of te estimation is to maximize te likeliood of te observed sequence of actions wit respect to te parameters tat govern te distribution of ouseolds tastes. Embedded in te likeliood are te infinite-orizon utility-maximization problems faced by every ouseold in every period. Several key factors of te model complicate te dynamic programming problem. First, current period inventories are unknown as neiter current consumption nor initial inventories are observed. Te process of estimating current inventories becomes an initial conditions problem tat is solved in te estimation procedure. Second, te distribution of ouseolds unobservable persistent preferences is modelled as random coefficients; ence, te likeliood as to be integrated over te joint distribution of tese parameters. Te necessity of aving to solve ouseolds dynamic programming problems at every guess of te parameters for every guess of te distribution of te random coefficients presents a significant computational burden. Recall from te data section tat only purcases made are observed. Terefore, te likeliood is a function of tese purcasing decisions, d t, wic are decomposed into product purcases, j, t and volume purcases, s t (i.e., d t ={j, t s t }). Assume for now tat te econometrician observes