Complexity, Efficiency, and Fairness in Multiproduct Liquor Pricing∗ Eugenio Miravete† University of Texas & CEPR Jeff Thurk§ University of Notre Dame

Katja Seim‡ University of Pennsylvania

Joel Waldfogel¶ University of Minnesota & NBER

Abstract The Pennsylvania Liquor Control Board (PLCB) controls the purchase and sale of alcoholic beverages across the state and is legally mandated to charge a uniform 30% mark-up on all products. This paper investigates the welfare implications of this uniform markup. We show that consumption patterns vary across the state and these variations are correlated with consumer demographics. Using detailed data on prices, quantities, and demographics across 499 local markets, we estimate a multiproduct discrete choice model of demand. We use the demand estimates and data on wholesale prices to assess the consumer welfare implications of the current uniform mark-up. We find that the current system transfers rents from high income and educated households to minorities by underpricing those liquor varieties that this latter group favors. We further show the returns (to welfare and profits) of more sophisticated pricing strategies are small. Keywords: multi-product pricing, public enterprise, regulation JEL Classification: L10, L21, L32 ∗

We thank Thomas Krantz at the Pennsylvania Liquor Control Board and Mike Ehtesham at the National Alcohol Beverage Control State Association, Inc., for helping us to get access to the data. All errors are our own. † University of Texas at Austin, Department of Economics, Austin, Texas 78712-0301, [email protected]. ‡ Wharton School, University of Pennsylvania, Philadelphia, PA 19104-6372. [email protected]. § University of Notre Dame, Department of Economics, Notre Dame, IN 46556, [email protected]. ¶ Carlson School of Management, University of Minnesota, Minneapolis, MN 55455, [email protected].

1

Introduction

In general, there is a tradeoff between the profits of a firm and the surplus enjoyed by its consumers. Private firms are well-understood to set prices to maximize profits, without regard for the well-being of their consumers. Indeed, managers of private firms have a fiduciary duty to their shareholders to generate profit, while the pursuit of other objects is viewed as malfeasance. Government-run firms might have other objectives, however. The planner might attach importance to both consumer and producer surplus. Given a well specified demand system, we can assess whether the system maximizes profit and, if it does not, how highly it values consumers. That is, we can quantify the marginal rate of substitution (MRS) between producer and consumer surplus implied by the firm’s price level. While there is in general only a single price, or price vector, that maximizes profits, there is generally a family of prices that achieves a sub-maximal level of profit. A firm that attaches some welfare weight to consumers, and therefore forgoes some profits relative to the maximum, must choose among a locus of iso-profit price vectors. Because different types of households consume different products, the firm’s chosen price vector can be used to reveal the differential welfare weights that the planner implicitly attaches to different types of households. These considerations suggest a series of questions that one might ask of a firm’s pricing. First, does the firm maximize profit? Second, what does the firm’s pricing choice indicate about its marginal rate of substitution between profits and consumer surplus? If the firm is profit maximizing, then its pricing is concerned only with profits. On the other hand, if prices fall short of profit maximizing prices, then the firm’s pricing betrays a concern for consumers and allows direct quantification of the planner’s MRS between consumer and producer surplus. Finally, if the firm has multiple products, one can calculate the MRS for each product’s price. What does the pattern of these MRS terms across products reveal about the relative welfare weights for different types of consumers? In general, there should be a negative relationship between producer and consumer surplus, but a pricing scheme can also be Paretodominated, in the sense that price reductions would increase both producer surplus and consumer welfare. Thus, in addition to asking what welfare weights that prices reveal about consumers, we can also ask whether alternative pricing schemes could make either consumers, producers, or both better off.

1

This paper analyzes the pricing decisions of a government-run retailing entity, the Pennsylvania Liquor Control Board (PLCB). The PLCB is the monopolist seller of wine and spirits in the Commonwealth of Pennsylvania and operates over 600 stores throughout the state. The PLCB’s current pricing reflect a uniform markup over marginal costs on all products, and each product’s price is the same at all of the system’s stores. Using detailed 2005 data on prices, quantity sold, and market attributes, we estimate a random coefficients demand system for all spirits products available in each of close to 500 local liquor markets. The resulting demand system, together with information on each product’s wholesale cost, allows us to calculate the quantities, profits, and consumer surplus associated with any markup rule or price vector and, in particular, allows us to ask the questions posed above. We find that the current markup gives rise to prices that are, on average across markets, 8.1% higher than the prices that would maximize profits and satisfy Pennsylvania’s uniform markup rule. That the system is foregoing profits reveals that the planner places weight on the welfare of consumers. In particular, the current markup indicates a willingness to forgo 4.3% in profit, while simultaneously decreasing consumer welfare by 10.03% in the average store market. The fact that the average MRS between PS and CS is positive indicates the availability of Pareto-improving price changes. This tradeoff varies substantially across products, however. Allowing for product-specific prices suggests that current prices for the mean gin, rum, and vodka products are below profit-maximizing levels, but above monopoly prices for tequilas and whiskeys. We similarly find that prices for high-end products are currently too high on average and that a move to product-specific pricing would lower them by 8.8%, while raising prices for low-end products by 8.2%. This repricing would introduce a shift, in particular by high income and highly educated customers, toward higher-quality products, which would increase both profit, by 10.4%, and consumer welfare. Product-specific prices would also serve to limit the quantity expansion associated with a move toward the optimal uniform markup, which may be an implicit policy goal of the agency. The paper proceeds in 8 sections. Section 2 lays out a theoretical framework. The paper then takes an extended detour into demand estimation: Section 3 describes the regulation of Pennsylvania’s liquor retail markets. Section 4 discusses the data used in the study. Section 5 presents the demand model, and Section 6 presents estimation results. In section 7 we make use of the estimated demand model to address the main 2

questions of the study. A brief conclusion follows.

2

Theoretical Framework

Our goal is to infer the welfare weights implied by policy-makers’ pricing decisions. The theory underlying this is well understood (Ross (1984); Ahmad & Stern (1984)). Accordingly, our strategy here is to employ the simplest possible model for illustrative purposes. Consider a firm facing a linear inverse demand curve pi = ai − bi qi . Suppose that fixed and marginal costs are zero. The firm is operated by a planner whose goal is to maximize a weighted sum of producer and consumer surplus. That is W = P S +βCS, where β is the weight that the planner attaches to consumer surplus (CS) relative to producer surplus (P S). The coefficient β ≤ 1. When β = 0, the firm is a usual ai private monopolist setting the profit maximizing price, pM i = 2 . When β = 1, the planner cares about consumers as much as the firm’s surplus and so chooses pM = 0. ai (β−1) In general, the welfare maximizing price is given by pW i = (β−2) . It is easy to verify that β = 0 gives the monopoly solution, while 0 < β < 1 gives pW < pM i i . W M Negative welfare weights are also possible, and β < 0 implies that pi > pi . Of course, the logic works in reverse as well. If we know the structure of demand for product i – here, {ai , bi } – and if we observe the price, we can infer the welfare weight i −ai . If we find negative that the planner attaches to consumers of product i, β = 2p pi −ai implied welfare weights, then Pareto-improving price changes are possible. The term β is the planner’s willingness to trade off CS for P S among consumers of product i, and it has a natural interpretation. By choosing different prices, the planner can generate a range of consumer and producer surplus. Imagine reducing the price from ai . At ai , there are no purchases, and therefore neither P S nor CS. As price falls below ai , both CS and P S rise, until price reaches a2i , which is the monopoly solution. As price continues to fall, CS rises and P S falls. When price falls to 0, a2 P S is zero, and CS equals the entire area under the demand curve (here, 2bii ). The resulting curve is a welfare possibilities frontier. The planner can be conceived to have utility defined over P S and CS and therefore to have indifference curves in this space. When we see a chosen price – and given that we know the structure of demand – we can infer the planner’s MRS under the assumption that the slope of the welfare frontier equals the slope of the planner’s indifference curve at the planner’s choice. 3

Figure (1) illustrates this for p = 100 − q. The full area under the demand curve is 5, 000. Profit is maximized at p = 50, with P S = 2, 500 and CS = 1, 250. The process outlined above gives us a β for each product. What we want is the weight that the planner attaches to each type of household. If different households consume different products, then we can transform a vector of weights with a length equal to the number of products to a vector of household weights, provided that the number of products exceeds the number of households. Define sk|j as the share of product j, j = 1, ..., J, consumed by consumers of type k, P k = 1, ..., K. Thus, K k=1 sk|j = 1. Let C be the J ×K matrix of these shares. We can express each product welfare weight as a weighted sum of household welfare weights, based on the types’ consumption shares: βj = s1|j ω 1 + s2|j ω 2 + ... + sK|j ω K , where the β’s are the product-specific welfare weights derived above, and the superscripted ω’s are the household welfare weights that we seek to determine. We can write the weighted-sum equations in matrix notation as Cω = β. Our task is to determine ω. Provided, again, that J exceeds K, we can obtain ω by least squares as ω = (C 0 C)−1 C 0 β

(1)

This framework encompasses the questions we propose to explore. First, we will ask whether the PLCB is profit-maximizing (whether β = 0). We find that the system is not profit maximizing and therefore that its planner implicitly attaches welfare weights to consumers of its products. We determine these welfare weights and then translate them into welfare weights for different types of households. Finally, we use the framework to identify Pareto-improving prices. Our actual implementation differs from this simple example in that our demand system is both nonlinear and, more important, allows for cross-product effects. Moreover, our demand system allows us calculate CS and P S from a consistent model that also allows calculation of standard errors for functions of the model (such as the welfare weights). We outline how we adapt the framework here to our specific setup in Section 7.3.

4

3

Regulation of Pennsylvania Liquor Markets

As a consequence of Prohibition, Pennsylvania, together with 18 other “control” states, continues to be actively involved in the whole and retail sales of alcoholic beverages in the state. It operates a privatized system for the sale of beer, allowing the controlled entry of private retailers. Through its agency, the Pennsylvania Liquor Control Board, the state acts, however, as a monopolist in the wholesale and retail distribution of wine and spirits. As of 1/2005, the PLCB operates a system of 624 state-run stores spread across the state. The State Legislature exerts regulatory control over several aspects of the daily operations of the stores. Most notably, as per the Pennsylvania Liquor Code (47 P.S. §1-101 et seq.) and the Pennsylvania Code Title 40, the legislature imposes a uniform mark-up rule upon the prices that the PLCB can charge for its products, both across products and across stores. The legislature prescribes applying a 30% markup and an 18% liquor tax to the wholesale price. Accordingly, the retail price p of a given product is calculated as p = (cw × 1.3 + bottle f ee) × 1.18, where the bottle f ee, a handling charge, amounts typically to $1 and the PLCB rounds the resulting retail price to the nearest nine cents. A given product sells at this price in all stores that carry it. An additional 6% Pennsylvania sales tax is then applied to the posted price to generate the final price paid by the consumer. The PLCB has limited ability to depart from this uniform markup rule. It conducts monthly sales (28-day periods beginning on the Monday closest to the end of the month) when it reduces the price of a subset of products by a fixed amount. Within the spirits category, the median share of products on sale at a given point in time is 25.2%, with an inter-quartile range of 22.2% to 26.7%. The median sale discount is $2.00, with discounts ranging from $0.50 to $9.00. In the median pricing period, the sale products account for 22.9% of bottles sold, suggesting that they are less popular products on average. Subject to product availability, the sale price is available in all stores, maintaining the within-product uniformity of prices. The monthly sales are a source of inter-temporal variation in prices that we exploit below in the estimation of our demand model. The PLCB also operates seven outlet stores close to the state’s borders, in an effort to address the “border bleed”of consumers who illegally import lower-priced products into Pennsylvania from neighboring states. While these stores offer wines and spirits

5

at discounted prices, the PLCB remains within the uniform markup policy by selling products in the outlet stores not found in regular stores, for example multi-packs or unusual bottle sizes for a particular product. Pennsylvania’s mark-ups are in line with the mark-ups in other control states that hold state monopolies over the distribution of liquor, ranging from 17.6% in the case of Wyoming to 64.5% in the case of Utah (National Alcohol Beverage Control Association 2004). Using 2005 price information for 250 spirits varieties obtained from the National Association of Beverage Control States, Inc., Table 1 compares the ratio of a reference control state’s retail price to that in Pennsylvania for five types of spirits across six control states. Pennsylvania’s prices are comparable and frequently somewhat lower than those in the other control states. We are unaware of systematic information to compare Pennsylvania’s prices to those in the possibly more similar open states in close proximity to Pennsylvania. Data compiled for the 2008 ACCRA cost of living index shows, however, that a 1.5 liter bottle of Livingston Cellars retails for $7.99 in Pennsylvania, compared to a median price of $6.99 in the 37 sample cities in neighboring states, with prices in all but one city being below Pennsylvania’s.1 A 2008 comparison of the prices of five popular spirits products by the newspaper Tribune Review instead found that only 50% of out-of-state prices were below Pennsylvania’s.2 There is thus only limited evidence that the PLCB’s pricing policies lead to systematically higher prices across the full spectrum of products. Other aspects of the system’s operations are fully left to the control of the PLCB. The agency selects store locations, oversees store operations and manages the warehousing and distribution of alcoholic beverages. It maintains six distribution centers across Pennsylvania, each of which serves those stores closest to the center. The majority of stores are standalone retail stores. In 2005 and 2006, the PLCB opened a small number of outlets within the premises of grocery stores. As of the first week of 2005, 65 stores, or 10.37%, are designated premium-collection stores that are larger in size and carry a wider variety of products than the remaining locations. Assigning consumers to the store closest to them, each store serves an average population of 18,154, with an inter-quartile range of 12,842 to 24,781. The PLCB is further responsible for product selection and negotiates wholesale 1

ACCRA Cost of Living Index, The Council for Community and Economic Research, P.O. Box 100127, Arlington VA 22210 USA. www.coli.org. 2 http://www.pittsburghlive.com/images/video//2008 pdfs/GX-Liquor-bn-09-01.pdf, accessed January 13, 2011.

6

prices directly with its suppliers. A new product’s wholesale price remains fixed for one year after introduction. For established products, the PLCB re-negotiates over cost increases on a quarterly basis, rotating through product categories every reporting period, which are four-week long accounting periods. Proposed wholesale price declines go into effect immediately. Thus each reporting period, the wholesale price of a subset of products is adjusted, translating into changes in the retail price. In contrast to sales periods, reporting periods begin on a Thursday, usually in the middle of the month. Prices can therefore change at two discrete times per month. The PLCB has long held that its size awards it significant monopsony power in negotiating wholesale prices.3 It is difficult to compare the PLCB’s wholesale prices to those in other states and under different regulatory regimes systematically. Table 2 provides two relevant comparisons. Each depicts the average ratio of wholesale prices by liquor type of a reference state relative to Pennsylvania for the products from Table 1. The top panel compares Pennsylvania to five other control states that similarly serve as monopoly distributors of spirits in their state. We use retail prices, together with information on each state’s markup and tax formulas for determining the retail price (see National Alcohol Beverage Control Association (2004)) to back out the price that each state would have paid to the distiller for a particular product. The comparison suggests that Pennsylvania’s wholesale prices are slightly below those paid by the New Hampshire and Vermont liquor regulators, but are above those paid in Michigian, Ohio, and Washington. The bottom panel compares Pennsylvania’s wholesale prices to those paid by retailers for a select set of open and control states.4 The table suggests that markups added by liquor distributors - regardless of whether the distributor is a state’s liquor control board or a private wholeseller - result in higher wholesale prices paid by retailers in these states relative to Pennsylvania’s wholesale price. The absence of double-marginalization in the vertical chain offsets the markups added by the PLCB under its pricing formula to result in prices that are 3

According to then Chairman Jonathan Newman, “We leveraged our power as the largest purchaser of wine and liquor in the country and the largest purchaser of California wine in the world to obtain dramatic discounts on brand-name wine and spirits, and we are passing these savings on to our customers,”PLCB press release, July 15, 2003. http://www.lcbapps.lcb.state.pa.us/webapp/agency/press/press detail.asp?psearch=&offset=342, accessed January 13, 2011. 4 For the three open states in the table, wholesale prices were obtained from trade publications in the cases of Massachusetts and Rhode Island and from the Department of Consumer Protection in the case of Connecticut. See notes to Table 2 for details.

7

comparable to other states (Table 1). The evidence regarding Pennsylvania’s ability to exploit its monopsony power to achieve lower input prices is mixed, however, at least for the particular subset of products and states investigated.

4

Data

We obtained a store-level panel data set from the PLCB under the Pennsylvania Right-to-Know Law. The data contain daily information on quantities sold and gross receipts at the product and store level during 2005. In addition, we received information on the wholesale cost of each product that is constant across stores and varies over time according to the reporting periods described above. We geocode the stores’ street addresses to assign them to a geographic location, which we link to data on population and demographic characteristics for nearby consumers based on information from the 2000 Census. Because stores open and close during the year, the characteristics of stores’ ambient consumers change over time. We focus our analysis on sales of 750 ml bottles of products in the spirits category. The advantages of spirits relative to wines are twofold. First, spirits make up a smaller, better-defined group of products than wines, limiting the size of the consumer’s choice set to a manageable number of products. Second, the products themselves are more standardized, recur over a long time horizon, and can be described by several, easily measurable product characteristics, including the type of spirit, the alcohol content, whether or not a fruit or other flavor is added, and whether or not the product is imported. We use each product’s name to identify whether the product is a wine, a spirit, or another product, such as glass wares, gift sets, etc. Within spirits, we consider five types, gin, rum, tequila, vodka, and whiskey. For products within these five categories, the sales-weighted average alcohol content is 80.9%; 55.8% of product sales are for imported products; and 16.3% of products contain flavor add-ins. Table 3 summarizes these product characteristics further by type of spirit for the 250 products that are sold in at least one pricing period in 2005. Within spirits, vodkas and whiskeys have significantly larger market shares (32.8% and 33.7%, respectively), than rum at 17.9% and gin and tequila that account for 8.5% and 7.2% of sales, respectively. The differences in product variety within each category mirror the differences in market shares, with only approximately one third as many gin and tequila varieties as vodka and whiskey varieties. Flavored products are 8

primarily rums and vodkas. Lastly, while 100% of tequilas are imported, imported products make up roughly 40% of gins, rums, and whiskeys, and 50% of vodkas. Within spirits, the 750 ml bottle is the most popular size of product in terms of unit sales and product variety, accounting for 38% of bottles sold and 51% of available spirits products, closely followed by the 1750 ml bottle with a share of 32% of unit sales and 22% of available spirit products.5 We aggregate our data across days to the level of the pricing period, which we define to be a set of days during which the products’ prices remain constant because they share both the same reporting period and the same sales period. The average length of a pricing period is 14.3 days. This periodicity accounts for the strong seasonality inherent in liquor sales, which are disguised in more aggregate definitions. Averaging across 12,026 store weeks in 2005, stores sell an average of 5,785 750mlbottles per reporting period, 29.9% of which are spirits. While overall sales increase by 50.3% during the end-of-year holiday month, the sales of spirits increase only by 27.1%. As a result, the share of spirits sold declines to 83.2% of its mean share over the year. Another compelling reason to aggregate the data to a roughly bi-weekly level lies in the fact that we need to rely on the observation of a sale to deduce the availability of a product and a more aggregate sale period limits instances where a particular product is on store shelves, but does not record any sales over the time period. While stores differ in the product composition of purchases, these differences reflect heterogeneity in consumer preferences more than differences in the availability of products across stores. Absent store-level inventory information, we treat a product as being available in a store if it sold at least once during a given pricing period. Of the 100 best selling products statewide in 2005, the median store carried 98.0%, while a store at the fifth percentile carried 72.0% of the products. Similarly, of the 1000 best selling products statewide in 2005, the median store carried 82.03%, while a store at the fifth percentile carried 44.2% of the products. The product availability at premium stores is somewhat better than the average, with the median premium store carrying all of the top 100 products and 95.1% of the top 1000 products. The fact 5 Second-degree price discrimination along the dimension of product size is common in frequently purchased retail markets and is the subject of, for example, McManus (2007). To keep the analysis tractable, we abstract from this dimension of the consumer’s choice problem and focus on horizontal differentiation between products and its effect on optimal mark-ups across products and third-degree price discrimination.

9

that most stores carry most products, together with the absence of price differences across stores, supports our assumption below that differences in product availability do not drive customers’ store choices to a significant degree and that consumers visit the store closest to them. In assigning consumers to stores, we calculate for each of Pennsylvania’s 1,775 zip codes the straight-line distance to each store and assign consumers to the closest open store for each pricing period. In the 123 instances where the PLCB operates more than one store within a zip code at some point during 2005, we aggregate sales across stores to the zip-code level.6,7 We consider the resulting 499 zip-code zones as separate markets. Figure 2 shows these zones. We then derive consumer demographics for the store’s zone by calculating population-weighted average demographics across the zip codes that share a particular store. The assumption that consumers frequent the closest store allows us to abstract from the consumer’s store choice problem in estimating demand, focusing instead on the consumer’s choice between different liquor products available at the chosen store. In making this assumption, we follow previous studies using scanner data (e.g., Chintagunta, Dub´e & Singh (2003)). Our empirical analysis below investigates whether the rigid pricing formula used by the PLCB benefits different types of households differentially and whether the PLCB could improve profitability with a more nuanced pricing strategy. Here, we provide descriptive evidence to suggest that there is heterogeneity in demographic characteristics across market zones and that these demographics correlate with category-level market shares. Such heterogeneity in demand is necessary for price discrimination – either at the level of the product or at the level of the geographic market – to yield profit increases for the firm and for consumer surplus to be unevenly distributed across consumer groups. Table 4 summarizes the demographic attributes of our zip-code markets. The table illustrates the substantial variation across Pennsylvania in median household income and in the share of minority households, here defined to be black or Hispanic households. The table also suggests large differences in market size, reflecting the uneven distribution of population across the state. Figure 3 depicts plots of the 6 Note that these instances include both store relocations, where a store moved from one location in a zip code to another during 2005, but the data contain separate records for the store in the two locations, and instances where the PLCB operates two stores simultaneously within a zip. 7 We drop wholesale stores, administrative locations, and stores without valid address information, or a total of 15 stores.

10

average 2005 category share of each type of liquor against the demographic attributes summarized in Table 4. The figures suggest that the consumption of vodka increases and that of rum declines in the share of older heads of household in a zip code zone; that the zone’s consumption of rum increases strongly in the share of hispanic households in the area, while vodka declines; and that more educated and richer households tend to purchase more vodka at the expense of whiskey and rum. The patterns in Table 4 and Figure 3 are suggestive of the degree of demand heterogeneity necessary for price discrimination across products and markets to yield profit increases. The theory literature has illustrated, however, that the welfare effects of price discrimination, and thus the implicit gains afforded to different types of households from its absence, are ambiguous and depend critically on the elasticities of demand of the products studied (Varian (1985), Schmalensee (1981), Tirole (1989)). We therefore turn to a formal model of demand that we estimate to assess the quantities of interest in the context of our application.

5

Demand Model

Our empirical strategy evaluates different models of supply conduct, comparing the PLCB’s current pricing policies to those of a benevolent social planner and a profitmaximizing monopolist and assessing the distributional effects of price changes. This requires a model of consumer demand to consistently estimate own and cross-price elasticities under alternative sets of prices. We follow the recent literature (see e.g. Berry (1994), Berry, Levinsohn & Pakes (1995), Nevo (2001)) in employing a discretechoice model of demand, which facilitates the estimation of own and cross-price elasticities for a large-dimensional set of similar products.

5.1

Consumer Choice Problem

We specify a consumer’s choice between a set of J differentiated spirits products. We observe t = 1, ..., T markets, here a pricing period-zip code zone combination, with i = 1, ..., It consumers. We assume that on a given shopping trip in a particular pricing period and zone, each of Mt consumers select one of the J spirits or opts to purchase a 750 ml bottle of wine, our outside option denoted by j = 0.8 The 8

Mt thus equals the total number of 750 ml bottles sold in store market t.

11

consumer’s conditional indirect utility from purchasing one bottle of product j is

uijt = xjt βi∗ + αi∗ pjt + ξjt + ijt = Vijt + ijt , i = 1, . . . , Ijt ;

j = 1, . . . , Jt ;

(2)

t = 1, . . . , T ,

where: xjt : N dimensional (row) vector of observable characteristics pjt : price of product j ξj : unobserved characteristic of product j ij : mean-zero stochastic component, ij ∼ Type 1 extreme value. The observable characteristics include the product attributes summarized in Table 3, as well as aggregate shifters of the demand for spirits, such as seasonal variation in demand. The vector ξ captures the effect of unobserved pricing-period level, zonespecific product attributes, including the placement of the product within the store or on the shelf and promotional efforts, such as product tastings, that vary across zones and pricing periods. We assume that both consumers and the PLCB observe all product characteristics. We model the distribution of consumer preferences over characteristics and prices as multivariate normal with a mean that shifts with consumer attributes. We define: αi∗ βi∗

! =

α β

! + ΠDi + Σνi ,

νi ∼ N (0, IN +1 ).

(3)

The population of consumers in the store is characterized by a vector of demographic characteristics, d of which are observed in the data, Di , and some of which are not, summarized in variable νi . Π is a (N + 1) × d matrix of coefficients that measure the effect of attributes D on the consumer valuation of product characteristics. Σ measures the covariance in unobserved preferences across characteristics. Allowing for the resulting random coefficients generates correlations in utilities for the various alternatives and, thus, relaxes the restrictive substitution patterns generated by the Independence of Irrelevant Alternatives (IIA) property of the logit model. As noted above, we allow for the option of consuming outside of the liquor category. The inclusion of this outside option is important for the counterfactual pricing analyses below in allowing the total consumption of spirits to vary with overall changes in 12

price levels across products. We normalize the mean utility of the no-purchase option to zero. We follow the literature in decomposing the deterministic portion of the consumer’s indirect utility Vijt into a common part shared across consumers, δjt , and an idiosyncratic component, µijt . These mean utilities of choosing product j and the idiosyncratic deviations around them are given by: δjt = xjt β + αpjt + ξjt

(4)

µijt = [ xjt pjt ] (ΠDi + Σνi ) In estimation, we take advantage of the additive specification of normally-distributed deviations from mean utility and extreme-value random shocks to integrate over the distribution of i analytically. The probability that consumer i purchases product j is then given by: sijt =

exp(δjt + µijt ) P exp(δkt + µikt ) 1+

(5)

k=1,...,J

Deriving product j’s aggregate market share requires integrating over the empirical distributions of consumer attributes Di and νi . We denote them by PD∗ (D) and dPν∗ (ν), respectively. Collapsing the parameter coefficients into the vector θ, the model thus predicts a market share of product j in market t of: Z Z sjt = ν

sijt dPD∗ (D)dPν∗ (ν)

(6)

D

Similarly, the aggregate demand for product j is given by sjt Mt . In the absence of individual-level information on the demographic attributes of consumers, we follow Berry et al. (1995), henceforth BLP, and Nevo (2001) in using the aggregate distribution of demographic attributes for each of our local zip-code markets from the Census. We exploit information on three demographic attributes: household income, educational attainment, and whether the head of household is black or Hispanic, respectively. We use simulation techniques to integrate numerically over the observed distributions of household attributes, assuming – in the absence of more detailed Census information – independence across attributes. The Census reports only discretized information on household income, providing the percentage of the

13

population falling into each of several income categories. To facilitate the process of integrating over the distributions of income, we fit continuous distributions to these market-specific discretized empirical distributions, assuming that household income follows a generalized Beta distribution of the second kind. The Appendix provides details of this process and summarizes the estimated empirical distributions. We draw simulated individuals from the fitted distributions for each market area. We generate the individuals’ minority status by comparing a random draw from a uniform distribution to the percentage of blacks and Hispanics in the market, counting somebody as a member of the respective group if the simulated draw is lower than the observed percentage of the group in the market. We similarly generate the individuals’ educational attainment by comparing a uniform random draw to the share of the population with at least a bachelor’s degree. The predicted market share of product j averages over the probabilistic decisions of these simulated individuals. The discrete choice assumption that individuals only purchase one 750 ml bottle per pricing period is dictated by the aggregate, store-level nature of our data and is commonly used in similar demand studies for grocery store products (see, e.g., Nevo (2001)). It abstracts from consumers purchasing varying quantities of a particular product as a form of stockpiling or assortments consisting of multiple products. Using the same data set as in this paper, Seim & Waldfogel (2010) present suggestive evidence that the aggregate demand for alcoholic beverages does not respond to price declines more strongly than average for stores that serve a dispersed population with higher distances and travel costs to the store and thus a higher incentive to buy larger quantities or assortments. If such consumer behavior were important, assuming single-unit purchases could understate the own and cross-price elasticities of demand, in the case of assortment decisions (Hendel 1999), but overstate own-price elasticities in the case of stockpiling (Hendel & Nevo 2006).

5.2

Estimation

We estimate the parameters of the model using the data described in Section 4. As in unregulated industries, there is some potential for price endogeneity. While the prices employed by the PLCB result from the strict markup formula described above, the agency has some ability to tailor prices to time-varying demand conditions. First, the PLCB chooses the subset of products to put on sale in a given month. Similarly, it

14

negotiates directly with distillers over the wholesale price of its products. If the PLCB chose price reductions or adjusted its bargaining behavior based on information about unobserved consumer tastes for the products under consideration, but our estimation did not account for such correlations, the estimate of the price coefficient α would be biased. We thus follow the algorithm laid out by BLP in employing a generalized method of moments estimator by interacting the structural demand side error with instrumental variables that control for the possible endogeneity of prices. In contrast to their work, we focus exclusively on estimating the demand side without specifying a functional form for the supply side. Since our data contain direct information on the firm’s marginal cost per bottle, its wholesale price, we do not need to rely on conduct assumptions governing the PLCB’s behavior to back out its marginal cost. We define the demand error term to be the value of the unobserved product characteristic, ξj . We compute the unobserved characteristic as a function of the data and the values of the coefficient parameters under consideration by solving for the mean-utility levels δ.t (x·t , p·t , S·t ; θ) that set the predicted market shares of each product sjt in Equation 6 equal to the market share observed in the data, Sjt . The mean utility level δ.t is a solution to the implicit system of equations: s·t (x·t , p·t , δ·t ; θ) = S·t ,

(7)

which we solve numerically for every parameter evaluation and every market t. We then project the resulting estimate of δ.t onto prices and characteristics to result in our estimate of ξ.t : ξ(θ)jt = δjt (x·t , p·t , S·t ; θ) − xjt β − αpjt .

(8)

We interact this estimate of ξ with a set of instruments Z. We employ 21 BLP-style instruments. For each market t, we include a constant, the product’s characteristics (its alcohol content, its type of liquor, an indicator of whether flavoring were added, and an indicator of whether the product is imported) and their interactions, as well as the sum of these characteristics for products of the same type of spirit available in market t, and the sum of these characteristics for products of different types of spirits.9 9

The fact that the PLCB charges the same price across geographic markets precludes the use of

15

As in BLP, our identifying assumption is that product characteristics are fixed prior to the firm’s wholesale negotiations, pricing, and sales. BLP further employ the characteristics of competing products since their characteristics enter the markup and thus the optimal price charged for product j. Our concern over price endogeneity does not arise from the PLCB’s choice of optimal markups. Instead, the characteristics of competing products are valid instruments if the PLCB chooses the timing of sales and the magnitude of a product’s price reduction as a function of the prices and characteristics of other products, divided into a more closely competing and a less similar group. At the same time, the availability of close substitutes for a particular product could also be a source of bargaining power that the PLCB might employ in negotiating over wholesale prices. The bargaining process also suggests other possible instruments, including the number of other products that distiller j sells through the PLCB and their characteristics, both within product j’s liquor type and overall. This might be of particular relevance to the spirits category where distillers range from large, multi-product and multi-category firms such as Pernot Ricard to more specialized smaller distillers. Future work will investigate the use of such instruments as an alternative to the current set of Z. The GMM estimator exploits that at the true value of parameters θ? , the instruments Z are orthogonal to the errors ξ(θ? ): E [Z 0 ξ(θ? )] = 0 .

(9)

θˆ = argmin ξ(θ)0 ZW Z 0 ξ(θ) ,

(10)

Our GMM estimates solve:

θ

where W is a weighting matrix and where we loop through every market to define the objective function. We use W = [Z 0 Z]−1 to derive initial parameter estimate. Based on these estimates, we substitute the optimal weighting matrix W = [Z 0 ξ 0 ξZ]−1 .

5.3

Identification

Identification of individual preferences results from observing consumer behavior over time and across markets. We do not rely on additional supply restrictions on prices Hausman-style instruments (Hausman 1996) of prices for the same product in different cities.

16

to aid identification of the demand system. Each product’s own-price elasticity is identified by variation in prices of each product over time and by variation in the choice set, both across time and across stores. Of the spirits products in the PLCB’s inventory during 2005, 74.7% experience at least one price change during the year. The fact that the PLCB does not change the prices of all spirits or of all products within a particular spirit type at the same time introduces variation in relative prices over time, which aids in the identification of cross-price elasticities. The preferences for product characteristics and for spirit types are identified by variation in product characteristics that correlate with differences in market shares of spirits by attribute, spirit type, and by the overall size of the category over time. The individual heterogeneity in such preferences is identified by cross-market heterogeneity in the distribution of demographics.

6

Estimation Results

We present preliminary estimates of the demand model outlined above in Table 5. This base specification lets demand vary with the observed characteristics proof (alcohol content), flavored (indicator of flavor add-ins), and imported (indicator of the product’s import status). We further include indicator variables of the product’s type of spirit (tequila, rum, vodka, and gin), treating whiskey as the base category. Columns (1) and (2) contain ordinary least squares and two-stage least squares (2SLS) models obtained by regressing ln(sjt ) − ln(s0t ) on product characteristics. In both models, the price coefficients are negative, but as expected, the IV price coefficient is significantly larger in magnitude, suggesting that prices are correlated with unobserved product-market attributes. The 2SLS specification implies an own-price elasticity of −4.84 for the average product in the sample. Column (4) in Table 5 contains the results of the full model. Here, we allow for independently distributed, normal random coefficients for each of the characteristics proof, flavored, and imported. We capture the base preference for spirits relative to the outside option of consuming wine with a normally distributed constant, allowing it to vary over time through the inclusion of a holiday indicator that is equal to one for the pricing periods from Nov. 16, 2005 through Dec. 31, 2005. Lastly, we allow the consumer’s price sensitivity to vary with the consumer’s income, 17

specifying αi∗ = α + πα1 incomei + πα2 income2i . The estimated parameters are generally statistically significant at conventional levels. We estimate positive valuations for alcohol content and negative valuations for flavored spirits, with, however, substantial taste heterogeneity in preferences for flavored. The overall market share of spirits amounts to only 29.6% resulting in a negative base preference to spirits relative to wine. The demand shifts further to the outside option during the holidays when other types of alcoholic beverages such as wine or champagne gain in popularity. Demand declines, as expected, in a product’s price, but less so for higher-income households, suggesting that high-income households are less price sensitive than their low-income counterparts. To assess the magnitude of the price coefficient, we calculate own-price elasticities for each product, averaging over the elasticities of individual consumers as in Nevo (2001). Table 6 contains summary statistics, aggregating elasticities to the level of the spirit type. Across spirit types, the average elasticity amounts to −4.87. Since these elasticities are at the product-level, they are significantly more elastic than the aggregate elasticities for alcoholic beverages or for spirits summarized in the review article by Chaloupka, Grossman & Saffer (2002), who report a typical price elasticity for distilled spirits of −1.5 across studies using aggregate state-level data. The elasticities we estimate are instead more in line with the typical elasticities for other frequently purchased consumer goods in mature categories. Across spirit types, demand is least elastic for rum products, while it is most elastic for tequilas. We further divide products into two categories, cheapand expensiveproducts, by comparing a product’s price to the median price of all products in its category at a given point in time. Using this categorization, the demand for cheapproducts is significantly less elastic, with a sales-weighted average elasticity of −3.5, than the demand for expensiveproducts (elasticity of −6.1). These systematic differences between elasticities point to scope for profit gains from tailoring prices to the product, or at least the product category. We investigate the optimality of the uniform markup policy in light of the estimated price demand system in a set of policy analyses.

18

7

Analyses of PLCB Pricing Policies

We use the estimated demand system in several policy experiments. First, we assess whether the PLCB’s current pricing policies maximize the agency’s welfare and how the chosen prices compare to alternative pricing policies that the PLCB could implement to optimize its current system, under a number of possible objectives for the agency. These analyses rely on predicting consumer, profit, and welfare responses to prices that are potentially different from observed prices, highlighting the importance of a flexibly estimated demand system. Our results suggest that the PLCB does not maximize profit. We therefore turn to a second analysis and study what the PLCB’s prices tell us about how the state trades off variable profit versus consumer welfare. We then consider departure from uniform markup policies.

7.1

Empirical Approach

We use our estimated demand to investigate the optimality of the PLCB’s pricing formula and to relax some of its rigidities. In these analyses, we solve a profitmaximizing multiproduct monopolist’s pricing problem. Consider the optimal prices in market t. For each product j, the firm’s first-order condition associated with profit maximization in market t is given by: sjt (p) +

X

(prt − cw rt )

r∈Jt

∂srt (p) = 0. ∂pj

(11)

We express the set of J first order conditions in matrix notation as s(p) − Ω(p − mc) = 0 . where an element of the assortment matrix Ω is defined as:  ∂sj (p,x,ξ;θ) , if {j, r} ⊂ Jt ,   ∂pr [Ωjr ] =   0 otherwise

(12)

(13)

For a given vector of wholesale prices cw , we find the fixed point to the system of equations defined in Equation (12) numerically.10 Depending on the exercise, we 10

In future work, we will consider the possible ramifications of changing prices and thus aggregate

19

constrain optimal prices so that markups, defined by (p? −cw )/cw , are constant across products or across geographic markets. We evaluate the effect of optimizing the current pricing rule or phasing out some of its features by computing changes in variable profit and in consumer surplus. For the random-coefficients demand system without income effects, consumer surplus given a set of prices equals (see Small & Rosen (1981)): CS(p) = −

X t=1,...,T

7.2

Z Mt

1 ln αi

"

# X

exp (Vijt ) dPD∗ (Dt )dPν∗ (ν)

(14)

j=1,...J

Optimal Uniform Prices

We begin with a derivation of the PLCB’s optimal markup, continuing to assume that it remains constant across products and markets, before relaxing the assumption of uniform markups across products and last across markets. We use these benchmarks to inform how close the system comes to profit maximization. Tables 7 and 8 summarize the product-level price changes that result from reoptimizing the PLCB’s pricing rule to choose a percent markup that maximizes the system’s variable profit. Our results suggest that the current 30% markup results in prices that are higher than the profit maximizing ones. Instead, a 17.7% should be chosen if the PLCB’s goal were profit maximization. A move to this lower markup would result - since we continue using the PLCB’s pricing formula including bottle fees and liquor taxes - in an 8.1% drop in average sales-weighted prices. The table indicates a limited amount of heterogeneity in price changes across products that are introduced by the nonlinearity that the bottle fee adds to the pricing rule and departures from the 30% rule due to sales. It results, for example, in percent price declines that are higher for expensive products (8.6%) than cheap products (7.8%). On a dollar basis, a move to the lower markup percentage reduce markups, calculated as the difference between the final retail price and wholesale price, by 18.7% from $6, on average, to $4.88 per bottle. Note that a small share of products experience price increases; these products were heavily discounted in a sale under benchmark prices. In aggregate, such a reduction in markups has two effects. Bottles sold, and consumer welfare, increases. The increase in sales more than outweighs the effects purchase volumes on the PLCB’s ability to negotiate with distillers, which would affect wholesale prices.

20

of the price decline, and variable profits increase on net. Table 9 suggests that in particular the first effect is sizable. In aggregate, for 2005, consumption in terms of bottles of spirits sold increases by 26.9%, from 9M bottles to 11.4M bottles. This translates into an increase in profit of 4.3% or $2.33M. This result is in line with one of the possible justifications for government involvement in liquor sales; high prices are chosen to keep consumption down. We are able to quantify the monetary costs of imposing such restraints; our results here suggest that the amount of profit foregone from doing so is relatively small. We also use our uniform pricing counterfactuals to construct the welfare frontier of alternative uniform markups discussed in section 2 above. Table 10 lists profit and consumer surplus under a range of alternative uniform markups. Figure 4 then plots total profit against consumer surplus under uniform markups ranging from 10 to 40%. In the framework of section 2, the chosen 30% markup employed by the PLCB is consistent with a negative weight on consumer surplus; it is optimal if the PLCB placed a weight of β = −0.315 on consumer welfare. Pareto improvements are thus possible, and in moving to a lower markup, both consumers and the firm benefit. Table 9 also shows the aggregate implications of consumers’ re-optimizing their purchase decisions were markups to fall to 17.7%. The table suggests that at the category-level, profit and consumption of in particular tequila products increases. This arises from the fact that tequilas are relatively expensive, with the average salesweighted bottle costing $20.5, compared to $15.2 for the average product, and that at these prices, demand is significantly more elastic than for other products. Our results similarly indicate that uniformly decreasing prices induces consumers to shift purchases toward more expensive products. Profit from selling expensive products increases by 12.4%, while profit of cheap products actually declines by 5.9%.

7.3

Other Pricing Strategies

Our analysis so far suggests that within the confines of the PLCB’s simple markup formula, the state does not employ the profit-maximizing markup. In light of the large increases in consumption that would result from doing so, we now consider alternative pricing policies that the agency might employ. We consider the implications for consumers and producers from (a) optimizing mark-ups at the level of the product, under the restriction of uniform product-level prices across markets, and from (b)

21

further relaxing the restriction of no spatial price discrimination. Policy (a) continues to satisfy one of the state’s primary motivations for uniform pricing, an equity concern: no consumer should have to pay a higher markup because of where he resides in the state. When allowing for uniform, but product-specific markups, our results suggest that the sales-weighted average price paid by Pennsylvania consumers increases by 1.1%. This statistic masks significant heterogeneity both across and within spirits categories. Figure 5 shows the distribution of price changes by spirit category, where an observation is a product. The figure suggests that across product categories, both price increases and price decreases are common, reflecting heterogeneous consumer valuations for these products. Across categories, the prices of 45.1% of products increase, ranging from 24.2% of tequila products to 54.0% of rums. In aggregate, table 7 suggests that prices for tequilas and whiskeys decline, on average, while those of gins, rums, and vodkas increase. These average effects reflect the lower mean ownprice elasticities of tequila and, to a lesser extent, whiskey products relative to the other product categories exhibited in Table 6. To translate these price changes to the parameters of the PLCB’s pricing rule, Table 8 backs out the percent markups consistent with chosen prices and the observed wholesale cost. At the product category level, optimized average markups range from 14.2% for tequilas to comparable to 33.7% for rums, with an average of 24.2%. These markup percentages are thus typically below the PLCB’s current markup, but above the optimal uniform markup of 17.7%. Average optimal product prices for cheap and expensive products suggest that this discrepancy can be explained by price adjustments along the quality dimension, more so than by adjustments across horizontal product categories. When allowing markups to differ by product, the optimal markup for inexpensive products increases to 38.3% resulting in average price increases of 8.2%, while the markup and prices for expensive products decline to 15.0% and by 8.8%, respectively. Similar to - and more pronounced than - the effect of lowering the optimal uniform markup, this adjustment shifts consumption to higher-end, more profitable, products at the expense of lower-end products. When differential markups by product are ruled out, the optimal uniform markup lies inbetween the average markups for the two categories, but closer to the one for expensive products. In aggregate, the profit implications of introducing product-specific prices are 22

more significant than those of moving to the optimal uniform markup. Across the system, profits increase by 10.4%. A large share of these profit increases comes from the sale of expensiveproducts ˙ whose profits increase by 27.7%, more than offsetting profit declines from the sale of cheapproducts. ˙ Notably, though, because the use of product-specific prices does not translate into the same across-the-board decline in prices, consumption increases, but does so less significantly than under the optimal uniform markup (16.1%). This increase in consumption, and the associated consumer welfare gains, reflect that consumers are able to buy higher quality (expensive)˙ products at lower prices, which induces them to shift from purchasing either the now more expensive low-end products or choosing the outside option of buying wine. The last experiment we summarize in Table 7 is one where we relax the constraint that prices are identical across markets. Our results suggest that the additional flexibility of spatial price-discrimination has only effects on aggregate price changes; for the average product, prices increase by 1.9% instead of 1.1% under uniform productspecific pricing. As expected, the variation in prices across products is larger, however; the standard deviation of the percent price change increases from 12.9% to 14.5%. Translated into profit, total profit increases by 11.6%, only an additional 1.2 percentage points above the level under optimal product-specific prices. These results mirror similar results found for quantity-discounting. There, researcher found that empirically, a relatively small number of price points stipulating different purchase quantities are necessary to generate profit levels close to the maximum amount of profit realized under a fully flexible price function. Here, in the context of third-degree price discrimination, we similarly find that most of the maximum profit achievable (here under zone- and product-specific prices) is generated by introducing product-specific prices only. This is reassuring, in particular since we continue to assume that consumers frequent the store closest to them, even as prices at different stores are allowed to vary. The magnitudes of the profit increases that moving to spatial price discrimination generates for the PLCB are somewhat smaller, but similar in magnitude to the ones reported in Chintagunta et al. (2003), who consider the profit implications of relaxing a zone-pricing policy employed by a large supermarket chain that employed uniform prices at all stores within predetermined geographic zones.

23

7.4

Distributional Consequences of Alternative Pricing Strategies

The analyses so far summarize primarily price changes and the resulting profit implications at the level of the product and in aggregate. To speak to which consumer types are most affected by these changes, we first consider heterogeneity in the experience of local markets under the alternative counterfactual prices. For each market and pricing period and for the system as a whole, we compute the average price paid, weighing a product’s price by the product’s sales in the market. We similarly compute the market-level response in profit induced by the price change. Last, we compute the per-capita compensating variation of the change in prices and the percent change in consumer surplus. The sales-weighted price, profit, and consumer surplus changes, as well compensating variation are summarized in Table 11. Not surprisingly, the weighted-average price paid in a market declines from $14.95 to $14.32 in moving to the optimal uniform markup. Consumer surplus, normalized by expenditures at benchmark prices, increases by 10.02%. Prices paid increase, however, under product-specific and zone-specific prices, by 12.34 and 13.35%, respectively. This reflects the re-optimizing of product purchases as consumers are faced with a menu of product prices that discounts high-end products relative to before, but renders low-end products more expensive. Consumers ultimately end up spending more per-capita on liquor, but also purchase a better product, on average, and are, as a result better off. Consumer surplus under product-specific prices increases by 6.45%, translating into a compensating variation of −6.07. Consumer surplus changes are smaller, but continue to be positive for the average store market, in moving to zone-specific prices. Both producers and consumers thus benefit on average not only by moving to the optimal uniform price, but also by moving to product-specific and zone-specific prices. Given that the optimal uniform price leaves relative prices across products largely unchanged, there is limited variation in the experience of local markets when optimizing along this dimension. There is more significant heterogeneity in the experience of local markets, however, in moving to product-, and in particular, zone-specific pricing. The fact that heterogeneity increases in moving to product-specific prices suggests that there are spatial correlations in local preferences for products whose prices change differentially. Figures 6 and 7 display maps of the change in profit

24

and compensating variation by zip code. We omit similar maps for the move to the optimal uniform markup, given the limited spatial heterogeneity, and for the move to zone specific prices, which are similar to the product-specific maps, for brevity. The maps suggest that compensating variation from moving to product-specific prices is most negative - and consumers benefit most - in the Eastern portion of the state, including suburban Philadelphia and the larger Wilkes Barre and Allentown metro areas at the borders to New York and New Jersey. Similarly, consumers in some of the Pittsburgh suburbs benefit proportionally more. In contrast, benefits are more negligible in downtown Philadelphia and Pittsburgh, and the more rural central portions of the state. On the profit side, Figure 6 suggests less clear-cut spatial patterns in the location of the largest profit increases. Largely, however, the areas that experience large consumer surplus gains are also there areas where large profit gains are realized. To move beyond spatial location to investigate which types of households benefit most from product-specific pricing, we now turn to a second stage analysis that relates the store market-level estimates of various quantities of interest to observable demographic characteristics of the markets. Table 12 first presents product-level weighted least squares regressions, using as weights each product’s sales in a zip-code market zone. Columns (1) and (2) investigate how the change in a product’s price varies with the market’s demographic attributes. Sales-weighted, the price changes associated with the introduction of product-specific prices, are lower for products that are sold in primarily high-income and highly educated areas. The regression results for zone-specific prices are similar, with the exception that we also see larger price increases for products that are sold in primarily minority areas, with the exception of rums for which minority households have more elastic demand, meriting lower prices. In turning to profit increases in columns (3) and (4), we similarly find that sales-weighted, the products that generate the largest profit increases are those that are sold predominantly in high-income, highly educated areas. Given that under both product-specific and zone-specific pricing, it is primarily the prices of higherend products that decline and experience sales and profit increases, these regression models suggest that such products are primarily purchased by households with higher income. We conclude with a set of market-level regressions of these same variables aggregated across products to the store market, on market attributes. For brevity, we 25

again focus on the effects of introducing product-specific prices. In addition to the demographics included in the product-level regressions, we include other market level characteristics that may proxy for different considerations that go into the PLCB’s pricing decisions. These include population density to capture a divergence between urban and rural markets, general attitudes for liquor consumption and political lobbying, which we approximate by the number of churches per capita and the share of registered democrats among registered voters in a store market. We attempt to capture the possible negative externalities from alcohol consumption by including the number of crimes reported by the municipality to Pennsylvania’s uniform crime reporting system that are alcohol related, such as drunk driving, drunkenness and vandalism. This variable suffers from some shortcomings, in particular, simultaneity and the extent of aggregation. To minimize simultaneity concerns, we rely on data from 2002 and 2003. We only observe, however, municipality-wide data; some of the municipalities are not reporting to the system, and other municipalities, such as Pittsburgh and Philadelphia, are very large. As with the product-level regressions, the results in Table 13 suggest that store markets with larger shares of high-income and highly educated households benefit more from product-specific prices and generate higher profit for the seller since they disproportionately spend more on (higher quality) spirits after the adjustment of prices. We also find that the consumer surplus gains, both in terms of percent changes and compensating variation, are less pronounced in more rural areas with lower population densities. There is no statistically significant difference in profit gains across urban and rural areas, however. No clear, consistent patterns emerge for the remaining statistics that proxy for attitudes and effects of alcohol consumption. We leave the study of several additional counterfactual pricing policies to future work. These include finding the welfare-maximizing set of prices that generates the same variable profit as the current prices and, importantly, finding product-specific prices that hold consumption fixed at the current prices. This would take seriously the explanation that the public enterprise may be targeting a fixed, low consumption level and choose prices accordingly. The wedge that optimal product-specific prices drive between the markups on low and high-end products to realize significant profit gains suggests that a similar, albeit less pronounced markup difference between the two product types may yield some profit gains by shifting consumption toward higherend products, even when overall consumption does not change. 26

8

Conclusion

Pennsylvania, together with a number of other states that continue to actively oversee the retail or wholesale of alcoholic beverages, is currently considering the privatization of its state-run retail operations. Limited systematic evidence exists, however, to evaluate the performance of a public enterprise such as the PLCB. We use data on consumer responses to its uniform markup policies to study the welfare implications of one aspect of this public retail monopoly, its pricing policy. We find that in the average market, the uniform markup that is applied both across products and across geographic markets within the state results in above monopoly pricing levels, amounting to a loss of 4.3% of profit for the system and of $10.03 in per-capita consumer welfare for a consumer in the average market. These results point to the availability of pareto-improving price adjustments, rendering both consumers and the firm better off. We find significant heterogeneity in departures from optimal pricing across product categories and quality levels, reflecting heterogeneity in consumer preferences for the differentiated products we study. This highlights the constraints on the realization of welfare objectives that the simple pricing rule imposes. In particular our results suggest that both profit and consumer welfare gains could be realized by lowering the prices of high-end products, for which consumers have an elastic demand at current prices, while raising the prices of lower-end, more inelastically supplied, products. Such adjustments would benefit primarily the purchasers of higher-end products, namely richer and highly educated consumers.

27

Appendix Empirical distribution of income In estimation, we integrate over the distribution of household income numerically. The Census data, our source of demographic information, contains only categorical measures of annual household income, placing households into one of 16 income brackets. We facilitate the numerical integration in estimation by constructing fitted distributions of income that match the observed, discretized Census distributions. We follow McDonald (1984) in assuming that household income in a given zipcode zone is distributed according to a generalized Beta distribution of the second kind with parameters (a, b, p, q) and probability density function: f (x) =

axa−p−1 
a p+q , bap B(p, q) 1 + xb

where: B(p, q) =

x ≥ 0,

(A–1)

Γ(p)Γ(q) Γ(p + q)

(A–2)

is the beta function, and the gamma function Γ is given by: Z∞ Γ(y) =

z y−1 exp(−z)dz .

(A–3)

0

We use maximum likelihood to estimate a separate set of distribution parameters for each zip code zone, weighing the predicted probability of household income falling into each of the 16 income categories by the frequency with which the category is observed in the Census data for the respective zip code zone. Table A-1 presents summary statistics on the parameter estimates across zip code zones. Table A-1: Descriptive Statistics for Parameter Estimates Income (Generalized Beta) Statistic

a

Mean Std. Dev. Min. Max.

2.1 5.6 0.1 123.9

p

q

3.0 42.1 0.0 929.2

6,346.4 14,022.6 0.7 228,663.0

28

b 59,410.6 305,136.9 34.9 5,997,629.5

References Ahmad, E. & Stern, N. H. (1984). The theory of reform and indian indirect taxes, Journal of Public Economics 25(3): 259–298. Berry, S., Levinsohn, J. & Pakes, A. (1995). Automobile prices in market equilibrium, Econometrica 63(4): 841–890. Berry, S. T. (1994). Estimating discrete-choice models of product differentiation, The RAND Journal of Economics 25(2): 242–262. Chaloupka, F. J., Grossman, M. & Saffer, H. (2002). The effects of price on alcohol consumption and alcohol–related problems., Alcohol Research & Health 26(1): 22. Chintagunta, P., Dub´e, J.-P. & Singh, V. (2003). Balancing profitability and customer welfare in a supermarket chain, Quantitative Marketing & Economics 1(1): 111 – 147. Hausman, J. (1996). Valuation of new goods under perfect and imperfect competition, in T. Bresnahan & R. Gordon (eds), The Economics of New Goods, Studies in Income and Wealth, Vol. 58, National Bureau of Economic Research, Chicago, IL. Hendel, I. (1999). Estimating multiple-discrete choice models: An application to computerization returns, The Review of Economic Studies 66(2): 423–446. Hendel, I. & Nevo, A. (2006). Measuring the implications of sales and consumer inventory behavior, Econometrica 74(6): 1637–1673. McDonald, J. B. (1984). Some generalized functions for the size distribution of income, Econometrica 52(3): 647–665. McManus, B. (2007). Nonlinear pricing in an oligopoly market: The case of specialty coffee, The RAND Journal of Economics 38(2): 512–532. National Alcohol Beverage Control Association (2004). NABCA Survey Book, Alexandria, VA.

29

Nevo, A. (2001). Measuring market power in the ready-to-eat cereal industry, Econometrica 69(2): 307–342. Ross, T. W. (1984). Uncovering regulators’ social welfare weights, The RAND Journal of Economics 15(1): 152–155. Schmalensee, R. (1981). Output and welfare implications of monopolistic third-degree price discrimination, The American Economic Review 71(1): 242–247. Seim, K. & Waldfogel, J. (2010). Public monopoly and economic efficiency: Evidence from the Pennsylvania Liquor Control Board’s entry decisions, NBER Working Paper w16258. Small, K. A. & Rosen, H. S. (1981). Applied welfare economics with discrete choice models, Econometrica 49(1): 105–130. Tirole, J. (1989). The Theory of Industrial Organization, Section 3.2.2, The MIT Press, Cambridge, MA. Varian, H. R. (1985). Price discrimination and social welfare, The American Economic Review 75(4): 870–875.

30

Tables and Figures

Table 1: Retail Price Comparison of Spirits, by Type of Spirit Average ratio of retail price in state to retail price in PA ME

MI

NC

OH

VT

VA

gin rum tequila vodka whiskey

1.00 1.02 1.05 1.13 1.05

0.97 1.02 1.10 1.09 1.04

0.91 0.96 1.05 1.03 0.99

0.96 1.03 1.05 1.01 1.01

0.95 0.98 1.09 1.05 0.98

1.05 1.10 1.12 1.22 1.10

all products

1.06

1.05

1.00

1.01

1.01

1.13

Source: Authors’ calculations using price data for Pennsylvania spirits products with nonzero sales during 2005 obtained from the National Alcohol Beverage Control Association, Inc.’s December 2005 shelf-price reports for the states of Maine, Michigan, North Carolina, Ohio, Vermont, and Virginia.

31

Table 2: Wholesale Price Comparison of Spirits, by Type of Spirit Average ratio of wholesale price in state to wholesale price in PA (a) Price paid to Distiller NH Control

VT Control

MI Control

OH Control

WA Control

gin rum tequila vodka whiskey

1.15 1.06 1.10 1.03 1.07

1.01 0.99 1.17 1.19 1.03

0.87 0.89 0.92 0.94 0.92

0.86 0.98 0.90 0.88 0.88

0.79 0.84 0.87 0.84 0.88

all products

1.06

1.08

0.92

0.89

0.85

(b) Wholesale price paid by Retailer CT Open

MA Open

MI Control

OH Control

RI Open

gin rum tequila vodka whiskey

1.29 1.32 1.03 0.99 1.13

1.34 1.28 1.14 1.29

1.40 1.43 1.47 1.51 1.47

1.47 1.55 1.48 1.49 1.49

1.25 1.33 1.26 1.27 1.32

all products

1.12

1.24

1.47

1.49

1.28

Source: Authors’ calculations using price data for Pennsylvania spirits products with nonzero sales during 2005 obtained from the National Alcohol Beverage Control Association, Inc.’s Q1-Q4 2005 retail-price reports. The data for New Hampshire and Vermont was obtained from the states’ respective regulators; the table shows a price comparison as of 8/2010. For the open states, wholesale price data were obtained from the Connecticut Department of Consumer Protection, which requires wholesellers to submit price schedules periodically (http://www.biznet.ct.gov/DCPOpenAccess/LiquorControl/ItemList.aspx, accessed August 5, 2010), and from the August 2010 issues of the Massachusetts Beverage Business Journal Magazine and the Rhode Island Beverage Journal Magazine.

32

Table 3: Product Characteristics by Alcohol Type Share Alcohol Type

# Products Market Share? Proof Flavored Imported

gin rum tequila vodka whiskey all products ?

21 47 30 76 76

8.5 17.9 7.1 32.8 33.7

84.3 77.5 79.7 80.9 82.3

0.0 31.6 3.1 47.0 0.0

43.8 43.9 100.0 51.3 40.1

250

20.0

80.9

16.3

55.8

With respect to total spirit sales.

Table 4: Demographics Across ZIP Code-Store Zones Share Population Mean Std. Dev Min. Max.

25,217 16,369 1,205 106,195

Income ≥ $50,000 36.9 12.9 0.0? 73.9

†

Minority† 10.6 17.1 0.5 99.1

Age ≥ 45 years 39.7 5.3 19.2 59.2

Educ ≥ college 22.0 13.9 4.2 76.7

Minority households are defined to have either a black or a hispanic head of household. ? The Wine & Spirits Store in Erie, PA serves a population of 2,943, with no household reporting income greater than $50,000 and a median household income of $9,928.

33

Table 5: Demand Model Estimates Full Model

price

OLS

OLS

-0.0363 (0.0074)

-0.1801 (0.0107)

IV

β

-0.3058 -0.1600 0.0016 (0.0673) (0.0230) (0.0303)

price× income

0.0200 (0.0162)

price× income2

-0.0141 (0.0128) -0.8091 (0.4250)

σ

constant

-6.2352 (0.4229)

-3.8976 -3.5304 0.1649 (0.8212) (0.0543) (0.0167)

proof

0.7979 (0.0048)

2.4845 2.3330 0.0923 (0.0078) (0.0197) (0.0671)

flavored

-0.6743 (0.1382)

-0.7630 -2.3296 2.1809 (0.2591) (0.0479) (0.0325)

imported

-0.0505 (0.1316)

1.8618 1.0619 1.2420 (0.4419) (0.0522) (0.0121)

tequila

-0.3588 (0.2777)

0.2849 -0.0376 (0.7001) (0.0082)

rum

0.1668 (0.1791)

-0.8671 -0.6513 (0.4419) (0.0012) 0.0009 (0.0067)

rum× minority vodka

0.3151 (0.1713)

-0.1519 0.0259 (0.3518) (0.1225)

vodka×% educ ≥ college

0.0100 (0.0463)

gin

-0.1823 (0.1798)

holiday

-0.4909 (0.1860)

Product Fixed Effects Mean Own-Price Elasticity % Inelastic Demands βprice ± 2seprice

-0.8400 -0.8003 (0.4155) (0.0758) -0.4699 (0.0163)

-0.4061 -5.7793 (0.0320) (0.0122)

No Yes No -0.5722 -2.8401 -4.8335 0.9383 0.0017 0.0001 (0.78,0.99) (0.03,2E-3) (4E-3,1E-4)

No -4.8700 2E-6

Standard errors (in parentheses) computed numerically for full model. 12,026 pricing period, store zones. 1,275,742 observations. 34

Table 6: Estimated Product-Level Price Elasticities by Alcohol Type Average?

Median

25th %

75th %

Std. Dev.

gin rum tequila vodka whiskey

-4.4 -3.9 -6.1 -4.6 -4.9

-3.5 -3.9 -5.7 -4.4 -4.6

-6.2 -4.3 -6.4 -5.8 -6.1

-3.0 -3.4 -5.1 -3.5 -3.3

1.9 0.8 1.9 1.6 1.9

cheap expensive

-3.5 -6.1

-3.6 -5.9

-4.1 -6.8

-2.8 -5.3

0.9 1.3

all products

-4.6

-4.3

-5.8

-3.4

1.7

?

weighted by sales. cheap products denote products with a benchmark price below the unweighted median price in the product category. expensive products are all remaining products.

35

Table 7: Product-level Price and Price-Cost Markup Changes by Alcohol Type Price ($)

(a) Sales-weighted % Change in Prices Optimal Uniform Product-Specific Avg SD %>0 Avg SD %>0

Avg

Zone SD %>0

gin rum tequila vodka whiskey

14.5 12.4 20.5 15.1 16.3

-8.8 -9.0 -8.4 -7.5 -8.1

4.0 5.0 4.3 6.1 5.0

5.2 5.9 7.9 11.2 7.0

2.9 4.7 -6.0 2.0 -1.5

14.5 11.6 7.5 12.6 13.3

53.2 54.0 24.2 45.5 42.7

3.6 5.8 -5.4 3.0 -1.1

15.7 13.8 8.7 14.6 14.1

48.9 57.4 26.7 50.7 41.5

cheap expensive

11.1 20.9

-7.8 -8.6

6.3 3.5

10.8 4.8

8.2 -8.8

12.0 5.3

77.2 7.8

9.1 -8.1

14.1 7.1

74.7 14.5

all products

15.2

-8.1

5.3

8.1

1.1

12.9

45.1

1.9

14.5

46.9

(b) Sales-weighted % Change in Price-Cost Markups Mark Optimal Uniform Product-Specific up ($) Avg SD %>0 Avg SD %>0 Avg

Zone SD %>0

gin rum tequila vodka whiskey

5.8 5.1 7.8 5.9 6.4

-20.6 -20.2 -20.5 -16.7 -19.2

9.9 21.1 22.0 23.4 14.0

5.2 5.9 7.9 11.2 7.0

5.0 12.4 -15.0 5.6 -4.6

32.5 36.3 29.4 38.7 33.8

53.2 54.0 24.2 45.5 42.7

6.6 15.1 -13.4 8.1 -3.5

35.3 42.1 32.9 43.8 35.7

48.9 57.4 26.7 50.7 41.5

cheap expensive

4.6 8.0

-16.4 -21.7

24.3 9.0

10.8 4.8

20.8 -22.7

37.1 13.9

77.2 7.8

23.0 -20.9

42.4 18.6

74.7 14.5

all products

6.0

-18.7

19.6

8.1

2.6

36.6

45.1

4.7

40.7

46.9

Average percent changes calculated using sales under the benchmark prices as weights. Price-cost markups calculated as difference between retail and wholesale prices. Column (2) shows weighted average prices and markups under the benchmark prices. cheap products denote products with a benchmark price below the unweighted median price in the product category. expensive products are all remaining products.

36

Table 8: Product-level Sales-Weighted Average Markup Percentage by Alcohol Type

Alcohol Type gin rum tequila vodka whiskey

Benchmark Avg Std 30.8 6.3 31.1 6.9 29.6 5.7 29.0 8.5 29.6 7.2

Optimal Uniform Avg Std 17.7 0.0 17.7 0.0 17.7 0.0 17.7 0.0 17.7 0.0

Product Specific Avg Std 27.7 19.7 33.7 13.2 14.2 10.7 26.3 16.4 19.9 14.9

Zone Avg Std 28.0 21.5 33.9 16.1 14.3 11.8 26.3 18.4 19.9 16.0

cheap expensive

29.8 29.7

9.0 5.0

17.7 17.7

0.0 0.0

38.3 15.0

16.6 6.8

38.4 15.1

19.2 8.7

all products

29.8

7.6

17.7

0.0

24.2

16.3

24.3

17.9

The table depicts markup percentages derived from alternative prices using Pennsylvania’s pricing rule as markup = (p/1.18 − bottle f ee)/cw .

Table 9: Total Profits and Sales by Alcohol Type (%∆) Alcohol Type gin rum tequila vodka whiskey

Profit ($) 4.2 9.0 3.6 19.4 17.9

% Change in Profit Uniform Product Zone 5.1 7.3 8.9 -3.5 -9.9 -7.5 12.9 44.3 44.6 1.6 4.0 5.0 9.3 21.4 22.4

Quantity 0.7 1.8 0.5 3.3 2.8

% Change in Bottles Uniform Product 28.5 10.2 22.6 -14.4 38.5 73.7 22.6 6.6 32.3 38.5

Sold Zone 12.0 -12.4 74.6 7.6 39.8

cheap expensive

24.0 30.1

-5.9 12.4

-11.3 27.7

-9.6 28.6

5.3 3.8

15.5 42.8

-21.7 68.7

-20.3 70.0

all products

54.2

4.3

10.4

11.6

9.0

26.9

16.1

17.5

Profit and quantity refer to category-level profit and bottles sold under benchmark prices, expressed in millions.

37

Table 10: System-Wide Variable Profit, Consumer Surplus, Total Welfare, and Consumption, Alternative Pricing Strategies ($M) Variable Profit 30% uniform markup 54.17 Alternative uniform markup values 15% 56.42 20% 56.45 25% 55.68 35% 52.63 40% 50.76 Profit-maximizing uniform markup 17.69% 56.50 Product-specific prices 59.80 Zone prices 60.47

Consumer Surplus 42.33

Total Welfare 96.50

Bottles Sold 9.04

59.28 53.25 47.03 37.41 33.70

115.70 109.71 102.71 90.05 84.46

12.00 10.99 9.90 8.14 7.43

56.18 52.17 51.62

112.69 111.97 112.08

11.47 10.49 10.62

Annual variable profit, consumer surplus, and bottles sold reported in millions.

38

Avg Price Paid 15.16

14.56 17.17 17.13

Table 11: Zone-level Prices, Profit, and Consumer Surplus, Alternative Pricing Strategies Mean Status Quo under Benchmark Prices Average Price Paid ($) 14.95 Profit ($K) 111.23 Quantity (K) 18.56 Consumer Surplus ($K) 86.91

Median

25th %

75th %

SD

14.83 79.09 13.57 63

14.04 43.09 7.49 34.39

15.76 155.84 26.41 122.99

1.36 96.55 15.7 74.91

% Change in Price Paid Optimal uniform markup Product-specific prices Zone prices

-4.2 12.34 13.35

-4.29 12.12 13.4

-4.76 10.52 10.06

-3.75 13.86 16.43

0.93 2.93 5.48

% Change in Profit Optimal uniform markup Product-specific prices Zone prices

2.93 9.97 11.2

1.99 8.6 9.3

-0.5 6.97 8.05

5.27 11.14 11.73

5.79 8.38 10.64

% Change in Consumer Surplus Optimal uniform markup 10.02 Product-specific prices 6.45 Zone prices 5.15

10.02 6.2 4.17

9.83 4.83 1.06

10.19 7.89 8.3

0.31 2.81 7.47

Compensating Variation ($ per capita) Optimal uniform markup -10.03 Product-specific prices -6.07 Zone prices -3.83

-10.18 -6.11 -4.13

-11.32 -7.25 -7.47

-8.89 -4.96 -1.19

2.22 1.78 5.07

n = 481 zip-code markets. “Average Price Paid” denotes the weighted average price paid by the representative consumer in the zip-code zone, weighing each product’s price by units sold. The change in consumer surplus is calculated as the difference in consumer surplus normalized by the predicted annual expenditure under benchmark prices.

39

Table 12: OLS: Second-Stage Product-Level Regressions ∆ Prices (%)

minority age % high income % educ ≥ college gin rum tequila vodka rum×minority vodka×% high income holiday constant R2

∆ Profits (%)

ProductSpecific

Zone

Optimal Uniform

ProductSpecific

Zone

1.232 (1.920) 4.426** (1.409) -9.572*** (2.827) -5.333*** (0.985) 4.053 (4.482) 7.336* (3.384) -4.465 (2.695) 2.365 (4.278) -7.795** (2.423) 3.160 (4.679) -3.244*** (0.601) 2.758 (3.094)

5.577** (1.942) -2.066 (1.409) -28.144*** (3.329) -12.568*** (1.083) 3.470 (4.168) 6.999* (3.334) -3.872 (2.675) 4.321 (4.910) -6.775* (2.647) 0.452 (5.925) -3.170*** (0.591) 14.341*** (3.403)

-3.894** (1.267) -1.867 (1.254) 21.625*** (1.942) 10.662*** (0.921) -2.726 (4.342) -8.653** (2.983) 2.624 (3.689) -3.464 (2.751) 5.434*** (1.510) -6.856 (3.604) 2.925*** (0.859) -7.370** (2.550)

-1.117 (2.199) -4.595 (2.375) 12.338** (4.516) 4.329* (2.081) -9.123 (6.830) -23.517*** (5.280) 9.345 (12.179) -5.666 (4.349) 11.722*** (2.480) -15.995* (7.057) 1.423 (1.100) 5.273 (4.135)

0.912 (2.183) -4.758 (2.487) 12.661** (4.218) 7.382*** (2.030) -8.483 (6.613) -22.341*** (5.325) 8.754 (11.929) -6.653 (4.329) 10.925*** (2.504) -14.249* (6.503) 1.224 (1.108) 5.441 (4.159)

0.080

0.198

0.107

0.071

0.065

* p < 0.05, ** p < 0.01, *** p < 0.001. The estimated regression models are weighted OLS specifications using sales under benchmark prices as weights. Robust standard errors clustered by product in parentheses.

40

41 0.124 487

3.331 (5.020)

-1.313 (3.392) 2.622 (9.326) 8.409+ (4.501) 14.990* (5.941) 0.012 (0.051) -3.059* (1.459) 5.827 (3.538)

CV ($) (1) (2)

∆ Q (%) (1) (2)

∆ Price (%) (1) (2)

0.109 372

0.443 487

0.408 372

0.255 487

0.240 372

0.291 487

0.256 372

0.443 487

0.408 372

1.511 -1.686+ -1.143 2.297* 2.128* -5.459 -1.802 -1.686+ -1.143 (3.234) (0.892) (0.935) (0.678) (0.720) (4.794) (4.854) (0.892) (0.935) 13.001 1.633 4.347+ 3.980* 3.533+ 5.605 20.801+ 1.633 4.347+ (7.988) (2.337) (2.263) (1.666) (1.870) (12.771) (11.803) (2.337) (2.263) 13.146* 7.535* 7.781* -6.549* -6.635* 26.221* 30.337* 7.535* 7.781* (2.386) (0.915) (0.806) (0.891) (0.945) (5.203) (3.117) (0.915) (0.806) 10.199* 7.310* 6.838* 1.023 1.724* 31.340* 26.771* 7.310* 6.838* (2.308) (0.985) (0.735) (0.811) (0.747) (6.669) (3.241) (0.985) (0.735) -0.017 0.057* 0.059* -0.052* -0.051* 0.192* 0.181* 0.057* 0.059* (0.049) (0.021) (0.023) (0.017) (0.018) (0.076) (0.081) (0.021) (0.023) -2.858* -0.810 -1.016 -1.264* -1.269+ -5.858* -6.558* -0.810 -1.016 (1.371) (0.596) (0.643) (0.602) (0.665) (2.279) (2.273) (0.596) (0.643) 7.527+ 0.084 0.414 2.230* 2.373+ 4.628 6.475 0.084 0.414 (4.174) (1.245) (1.452) (1.094) (1.223) (5.509) (6.567) (1.245) (1.452) -2.881 0.373 0.850 1.383 0.373 (2.130) (0.940) (1.606) (3.997) (0.940) -1.917 1.785 0.707 -5.197* -5.123* -1.780 -8.564 1.785 0.707 (4.188) (1.207) (1.179) (0.855) (0.938) (6.745) (6.169) (1.207) (1.179)

∆ CS (%) (1) (2)

+ p < 0.10, * p < 0.05. share democrat denotes the share of registered voters that register as democrats. alcohol-related crimes refers to the per-capita number of reported incidences of domestic violence, drunk driving, drunkenness, vandalism over 2002-2003.

R2 N

constant

alcohol-related crimes

churches per capita

share democrat

population density

% educ ≥ college

% high income

age

minority

∆ Profit (%) (1) (2)

Table 13: OLS: Second-Stage Zone-Level Regressions Effects of Moving to Product-Specific Prices

Figure 1: Welfare Frontier Linear demand: p = 100 − q 3,000

2,500

PS

2,000

1,500

1,000

500

0 0

1,000

2,000

3,000

4,000

5,000

6,000

CS

 

Figure 2: Pennsylvania zip code zones  

42

Figure 3: Spirit category market shares by demographic attributes INCOME 55 50 45 40

Market Share

35 30 25 20 15 10 5 0 0

10

20

30

40

50

60

70

60

70

% Households making more than 50K Gin

Rum

Tequila

Vodka

Whiskey

EDUCATION 55 50 45 40

Market Share

35 30 25 20 15 10 5 0 0

10

20

30

40

50

% College Graduates Gin

Rum

Tequila

Vodka

Whiskey

AGE 55 50 45 40

Market Share

35 30 25 20 15 10 5 0 10

20

30

40

50

% Households older than 45 Gin

Rum

Tequila

Vodka

Whiskey

HISPANICS 55 50 45 40

Market Share

35 30 25 20 15 10 5 0 0

10

20

30

% Hispanic Households Gin

Rum

Tequila

43

Vodka

Whiskey

50

Figure 4: Welfare Frontier, Alternative Uniform Markups Estimated Multi-Product Demand System

Figure 5: Distribution of Changes in Product Prices (%) Product-specific prices vs Benchmark

44

Figure 6: Change in Annual Profit by Zip-Code (%) Product-specific Prices

Figure 7: Compensating Variation per Capita by Zip-Code Product-specific Prices

45