Market Power and the Laffer Curve

Transcription

1 Market Power and the Laffer Curve Eugenio J. Miravete Katja Seim Jeff Thurk September 1, 2017 Abstract We characterize the trade-off between consumption tax rates and tax revenue the Laffer curve while allowing for re-optimization by both consumers and firms with market power. Using detailed data from Pennsylvania, a state that monopolizes retail sales of alcoholic beverages, we estimate a discrete choice demand model allowing for flexible substitution patterns between products and across demographic groups while not imposing conduct among upstream distillers. We find that current policy overprices spirits and that firms respond to reductions in the state s ad valorem tax rate by increasing wholesale prices. The upstream response thus limits the state s revenue gain from lower tax rates to only 14% of the incremental tax revenue predicted under the common assumption of perfect competition. The burden of such naïve policy falls disproportionately on older, poorer, uneducated, and minority consumers. Upstream collusion exacerbates these effects. Keywords: Laffer Curve, Market Power, Public Monopoly Pricing, Tax Incidence. JEL Codes: L12, L21, L32 This paper supersedes an earlier version titled Complexity, Efficiency, and Fairness of Multi-Product Monopoly Pricing. We thank the editor, Liran Einav, and three referees for their guidance and thorough reading of our manuscript. We also thank Thomas Krantz at the Pennsylvania Liquor Control Board as well as Jerome Janicki and Mike Ehtesham at the National Alcohol Beverage Control Association for helping us to get access to the data. We are also grateful for comments and suggestions received at several seminar and conference presentations, and in particular to Jeff Campbell, Kenneth Hendricks, and Joel Waldfogel. We are solely responsible for any remaining errors. The University of Texas at Austin, Department of Economics, 2225 Speedway Stop 3100, Austin, Texas ; Centre for Competition Policy/UEA; and CEPR, London, UK. Phone: Fax: E mail: miravete@eco.utexas.edu; Wharton School, University of Pennsylvania, Philadelphia, PA ; CEPR and NBER. E mail: kseim@wharton.upenn.edu; University of Notre Dame, Department of Economics, Notre Dame, IN E mail: jthurk@nd.edu; jthurk/

2 1 Introduction Economic research rarely achieves the overnight policy influence of the Laffer curve the famous inverted U-shape function that relates tax rates and government revenues first scribbled on a napkin (Wanniski, 1978). The concept proved to be a cornerstone of Reaganomics, inspired the 1981 Kemp-Roth tax cuts, and continues to be at the foundation of every discussion of tax reform. And yet, there exists little quantitative evidence of its underlying economic mechanisms so the Laffer curve remains more of an ethereal concept rather than an empirically well-understood fundamental. Our objective is to empirically characterize the determinants of the Laffer curve in the taxation of consumer goods an area which accounts for 17.4% government revenues in the United States and 32.7% of revenues in the average developed country. 1 The industrial organization literature has demonstrated that in many consumer goods categories, ranging from cereals to icecream, soft drinks, and the alcoholic beverages we study, firms possess significant market power in pricing, stemming in part from the differentiated nature of the products they offer and the market segmentation these product offerings facilitate. We therefore build upon earlier work that uses detailed data to study the Laffer curve via reduced-form estimation under the assumption of perfect competition among firms (e.g., Auerbach, 1985; Chetty, 2009) to allow firms to respond strategically in their choice of pre-tax prices to changes in tax policy. Foreshadowing our results, allowing for the possibility that both consumers and imperfectly competitive firms respond to changes in tax policy has significant impact on optimal taxation and the characterization of the Laffer curve. We first use a simple model of monopoly taxation to explore the equilibrium interactions between firms and consumers in response to changes in the tax rate. We show that raising excise tax rates beyond a critical level indeed decreases government revenues under very general demand conditions and that the shape and location of the Laffer curve depends not only on the tax rate and consumer demand elasticity but also on the firm s strategic response. Moreover, we show that the tax rate and the firm price response are strategic substitutes so the latter mutes the change in retail price induced by a change in the tax rate. The effectiveness of tax policy therefore depend on the government s ability to anticipate the strategic pre-tax price response of the firm to tax changes. More generally, incorporating the equilibrium response of the firm is vital to making correct policy recommendations and failing to do so would result in the firm s price response unraveling, at least partially, the government s objective. We evaluate these predictions empirically within the context of alcohol taxation. The production, distribution, and sale of alcoholic beverages is the second largest beverage industry in the United States (behind soft drinks) and an important source of government tax revenues. Using detailed price and quantity data for across all retail liquor stores in Pennsylvania, we estimate the response elasticities of both upstream firms and consumers to the state s choice of ad 1 1

3 valorem tax rate in the market for distilled spirits a product category which generated substantial tax revenue for the state s general fund and represents the industry s fastest growing segment. Several remarkable features of the data enable us to estimate key parameters of the model rather than impose them ex ante, thereby increasing the reliability of both our demand estimates and the Laffer curves they generate. First, in Pennsylvania the state monopolizes both the wholesale and retail distribution of alcoholic beverages and applies a simple pricing rule that translates wholesale prices into retail prices via a single uniform ad-valorem tax. Thus, upstream distillers effectively choose retail prices taking into account this tax. Second, as a product s retail price is common across the state at any point in time, differences in consumer preferences materialize in differences in product purchases. This enables us to let consumer tastes vary systematically across products and demographics leading to more flexible substitution patterns and better estimates of both consumer demand and upstream market power. It also enables us to evaluate the effects of tax policy on different consumer groups. Third, the fact that we observe both wholesale and retail prices enables us to estimate consumer demand without placing any restrictions on upstream conduct and market power ex ante. Our estimation therefore allows for the possibility that firms are price-takers and cannot react strategically to changes in policy. We lever these features to estimate product-level demand for 312 products produced by 37 firms across a variety of consumer types. The combination of robust demand estimates with data on wholesale prices in a model of oligopoly pricing reveals that upstream firms in the industry enjoy considerable market power, earning 35 cents in income for every dollar of revenue. To illustrate the implications of not accounting for the strategic responses of these firms to changes in tax policy, we compare market equilibria when the state can either perfectly anticipate the distillers response to changes in its taxation policy a Stackelberg equilibrium or, alternatively, assume that firms do not respond at all to policy changes, our so-called naïve equilibrium. To complete this counterfactual analysis we also evaluate how the optimal response of upstream firms to tax policy varies with upstream firm market conduct, ranging from single-product pricing to full collusion, and how such a wholesale pricing response translates into changes in the shape and position of the Laffer curve. We show that market power among firms has a significant effect on the shape of the Laffer curve. The estimated Laffer curve for a naïve policymaker is steeper than for the policymaker who correctly anticipates pre-tax price responses. This is particularly true as conduct among upstream becomes more collusive. Not accounting for the strategic response of upstream firms, therefore, leads to poor policy recommendations. For instance, a naïve regulator would have concluded that the state could increase tax revenues 7.75% (or $28.74 million) by reducing the ad valorem tax from 53.4% to 30.68%. This reduction in the ad valorem tax would have increased profits for all upstream firms, but we show that they could do even better by increasing their wholesale prices by 3.79%, or 34 cents, on average. Thus, the estimated model indicates that upstream prices and the tax rate are strategic substitutes a prediction of the simple theoretical model. 2

4 While this change in upstream price may appear small, the fact that upstream distillers price on the elastic region of demand leads to a large change in quantity demanded by consumers. Ultimately, the firm response enables upstream firms to convert 87% of the incremental tax revenue into firm profits, or equivalently the response limits the PLCB to attain only 13.8% of the forecasted incremental revenues ($3.73 million). It is important to note that this substantial undoing of the state s revenue objective requires no coordination among firms. Were distillers to collude in setting wholesale prices, choosing the naïve optimal tax rate leads to a net decrease in tax revenues of 14.18% of current revenue. Alternatively, a regulator attempting to maximize tax revenue and endowed with perfectforesight would have predicted the upstream response and instead would only decrease the tax rate to 39.31%, or 42.07% in the event of collusion among upstream firms. While the state does increase tax revenue roughly two percent, profits among upstream distillers increase 30.8% as does their share of integrated industry profits (from 29.5% to 34.9%). Finally, we show that the political ramifications of naïve policy of assuming perfect competition among firms are significant. Not only would such policy be largely ineffective at increasing tax revenues, but the burden of the tax falls disproportionately on older, poorer, uneducated and minority consumers. This highlights that the ability of policymakers to account for the responses of firms and consumers to policies is of significance both from an equity and an efficiency standpoint. It underscores the importance of recent efforts by, for example, the Congressional Budget Office to consider Dynamic Scoring of new proposed legislation by accounting for the response of firms, workers, and consumers to changes in government policy, a direct albeit delayed response to the Lucas Critique. The major handicap then resides in correctly predicting how agents will react to changes in fiscal policy across different industries Related Literature The current paper contributes to several strands of literature, including the characterization of the Laffer curve, optimal taxation, the analysis of pass-through in non-competitive markets, and the analysis of alcohol pricing regulation. Theoretical analysis of the Laffer curve has fallen mostly within the reign of macroeconomics, which has focused on the possibility of the Laffer curve arising as a result of a general equilibrium effect induced by taxation on the supply of labor and capital. 3 Early empirical attempts such as Stuart (1981) or Fullerton (1982) build upon static two-sector general equilibrium models where households allocate their time between taxed labor and non-taxed leisure. Pecorino (2011) adds a dynamic component as hours worked entail human capital accumulation. Trabandt and Uhlig (2011) allow for household preference heterogeneity within a neoclassical growth model to generate 2 See the presentation by Wendy Edelberg, the CBO s Assistant Director for Macroeconomic Analysis, to the Federal Reserve Bank of Chicago at 3 See Ireland (1994), Novales and Ruiz (2002), or Schmitt-Grohé and Uribe (1997) to name a few. 3

5 labor and capital Laffer curves for the U.S. and fourteen European countries assuming calibrated country-specific Frisch elasticities of labor supply and intertemporal elasticities of substitution. Relative to this literature we focus on excise taxation with particular attention to the responses of not only consumers but also suppliers with market power. Consequently within this literature, our analysis is more related to optimal capital rather than labor taxation. Our results then indicate that modifications of the capital tax rate could be largely undone by providers of capital if they have market power a likely scenario. The advantage of our approach is that we have detailed industry data that allows us not to impose any restrictions on the model such as a predetermined objective of the state. As our model generates robust estimates of consumer demand and upstream market power, this approach increases the reliability of our conclusions. We show that the existence, shape, and location of the Laffer curve in our context depends not only on the interaction of the tax rate and consumers downstream product demand responses (via demand elasticities) but also on upstream market power and firms strategic pre-tax price setting. This is a commonly overlooked aspect of the analysis of taxation since the empirical public finance literature deals primarily with perfectly competitive scenarios despite the well-documented market power of firms in the studied industries. 4 Our data enables us to evaluate this assumption by drawing a distinction between the mechanical effects of and behavioral responses to taxation (Saez, 2001, 3.2). Specifically, we allow the policymaker to be well aware of downward sloping retail demands but potentially naïve regarding the upstream firms reaction to taxes/pricing regulations. A comparison of the Laffer curve with this naïve policy design to the one generated by a policymaker who chooses the tax rate in anticipation of the optimal firm responses (Stackelberg equilibrium) allows us to evaluate the implications of this assumption. Our results indicate that assuming perfect competition among firms, i.e., assuming upstream firms cannot respond to changes in policy, has substantial equilibrium effects on firms, consumers, and overall tax revenue across a variety of assumptions regarding upstream conduct. 5,6 Finally, we are not the first to address the implications of policy in the regulation of alcoholic beverages. Seim and Waldfogel (2013) evaluate the potential welfare effects of free entry in Pennsylvania. Aguirregabiria, Ershov and Suzuki (2016) study the case of partial entry in the wine segment where state-run stores sell side by side with private, yet price regulated, retailers. Illanes and Moshary (2015) take advantage of the privatization of the alcohol distribution system in Washington state to evaluate the effect of potential retail entry on pricing and product offering. In a related paper (Miravete, Seim and Thurk, 2017), we show that current policy is largely consistent 4 For instance, Chetty, Looney and Kroft (2009) and Evans, Ringel and Stech (1999) both assume competitive supply in the beer and cigarette industries, respectively. 5 Weyl and Fabinger (2013) show the impact of imperfect competition on tax pass-through under a variety of model environments but do not address asymmetric firms with horizontally-differentiated products. Consequently, our results provide an empirical extension. 6 There are other papers that address the market conduct in the alcoholic beverage industry. Conlon and Rao (2015) document how the post and hold regulation in some states help wholesalers set collusive prices. Miller and Weinberg (2015) use mergers in the brewing industry to identify collusive behavior. 4

6 with tax-revenue maximization (versus managing ethanol consumption) and compare the current uniform policy to a subsidy-free taxation policy with optimal product-specific ad valorem taxes. We find that the one-size-fits-all policy employed by the state generates significant redistribution within upstream firms and downstream consumers. Griffith, O Connell and Smith (2017) evaluate the use of product-specific corrective taxes to minimize health externalities related to ethanol consumption under the assumption that all firms, including suppliers and retailers, do not respond. In this paper, we abstract from modeling the motivation behind the state s tax code to more clearly illustrate the key determinants of the tax rate/revenue trade-off and to characterize the shape and location of the Laffer curve empirically while accounting for re-optimization by both firms and consumers. 1.2 Organization of the Paper The paper is organized as follows. In Section 2 we provide a simple model of taxation under imperfect competition to illustrate the key mechanisms underlying our results. In Section 3 we present the data, discuss the details of the Pennsylvania pricing rule, address the interaction with the upstream distillers, and document heterogeneous consumption patterns across demographic groups. In Section 4 we present an equilibrium discrete choice model of demand for horizontally differentiated spirits. The model allows preferences to be correlated across products of similar characteristics and incorporates the features of the current pricing regulations while allowing for (but not imposing) imperfect competition in the upstream distillery market. In Section 5 we discuss the estimation procedure and how the unique features of our data help identify the rich substitution patterns across products in our econometric specification. We pay particular attention to dealing with the potential endogeneity of prices using retail price information from other control states and variation in input costs. We also show how we use the estimated model to infer upstream market power among distillers. In Section 6 we show that this market power has significant implications for the shape and location of the Laffer curve while also documenting the variation in Laffer curves across consumer types. We conclude and discuss avenues for future research in Section 7. We include additional data sources, descriptive statistics, robustness of demand estimates, and other results in the Appendices. 2 A Simple Model of the Laffer Curve Under Market Power In this section we present a simple model of monopoly excise taxation to provide an economic framework for the interpretation of our empirical analysis in an oligopolistic environment. Our goal is to illustrate how a regulator s tax rate choice affects its tax revenue when allowing for optimal price responses by taxed firms to changes in policy. We show that tax revenue is not monotonic in the tax rate and that certain tax rates fall into what Arthur Laffer called the Prohibitive Range, when an increase in the tax rate leads to a reduction in tax revenue. To this end, we investigate how the optimal pre-tax price responds to a change in the tax rate, and show that whenever demands are less convex than in the isoelastic case, the pre-tax price and the tax rate are strategic substitutes. 5

7 Consider the case of a single product sold by a monopoly supplier and produced at a constant marginal cost. Focusing on the single-product monopoly case allows us to avoid accounting for cross-product substitution as the excise tax and tax-inclusive prices change; instead we simply consider the marginal consumer s decision to switch between the inside and outside good. Our empirical analysis in the context of multi-product oligopoly upstream suppliers agrees, nevertheless, with all predictions of the model. The monopolist chooses the pre-tax price p w (wholesale price in our empirical context) for a given tax rate τ 0, which impacts the tax-inclusive price the consumer pays, p r (retail price), p r = (1 + τ)p w. (1) In setting its optimal pre-tax price, the monopolist chooses p w to maximize profits Π(p w ) = (p w c)d(p r ), given the retail demand D(p r ), constant marginal cost c, and the chosen tax rate τ, which requires: or equivalently, in terms of the Lerner index, D(p r ) + (p w c)d (p r )(1 + τ) = 0, (2) p w c p w = D(p r ) D (p r )(1 + τ) 1 + τ p r = 1 ε(p r ). (3) This inverse-elasticity pricing rule relates the pre-tax (wholesale) markup of the monopolist to the inverse of the demand elasticity evaluated at the tax-inclusive (retail) price. The monopolist thus sets the pre-tax price p w so that the tax-inclusive price falls in the elastic region of demand. This result is behind the optimal pricing response of the taxed firm to changes in the tax rate shown below. We argue that under general conditions, for any demand that is less convex than an isoelastic demand function, a tax rate increase induces the non-competitive taxed firm to reduce its pre-tax price in order to keep the tax-inclusive market price in a region of demand that is not too elastic. Thus, tax rates and non-competitive firm prices move in opposite directions, i.e., they are strategic substitutes. To characterize the monopolist s optimal price response to a change in tax policy we make use of the retail price definition in equation (1) and totally differentiate the first order condition in equation (2) with respect to p w and τ to obtain: dp w dτ = τ (2pw c)d (p r ) + p r (p w c)d (p r ) 2D (p r ) + (p w c)(1 + τ)d (p r. (4) ) For convenience we define η(τ) as the elasticity of the monopolist s optimal pre-tax price to a change in the tax rate τ. optimal response elasticity as η(τ) dpw dτ We make use of the inverse-elasticity rule (3) to express the firm s τ p w = τ ( ) p w pw ε(p r ) D (p r ) pw p r ε(p r ) D (p r ) 2D (p r ) pr ε(p r ) D (p r ) τ p w. (5) 6

8 Further simplification using the retail price definition (1) yields: η(τ) = τ 1 + τ where κ(p r ) is the curvature of demand given by ( ) 1 1 ε(p r ) κ(p r ) 2 κ(p r, (6) ) κ(p r ) = D (p r )D(p r ) [D (p r )] 2. (7) The curvature of demand κ(p r ) is the key element that determines the sign of η(τ). We are interested in characterizing demand conditions under which the pre-tax price response elasticity η(τ) is negative, given that the firm prices in the elastic region of demand, ε(p r ) < 1. We explore first the case of linear and concave demand followed by somewhat convex demand functions. It is straightforward to show that η(τ) < 0 in equation (6) under profit-maximizing pricing with ε(p r ) < 1 whenever demand is linear or concave as D (p r ) 0 ensures that κ(p r ) 0. Linear demand is commonly used for algebraic convenience but concave demand is frequently assumed in theoretical models, see Tirole (1989, 1.1). There is however a larger set of demand systems that entails the strategic substitutability of p w and τ. For instance, equation (6) indicates that η(τ) is always negative when κ(p r ) [0, 1) and the monopolist prices on the elastic region of demand. The curvature condition of κ(p r ) < 1 describes the class of log-concave demand functions, including both concave and somewhat convex demand functions. 7 Log-concavity characterizes the vast majority of demand specifications commonly used in economic analysis, including discrete choice models of demand based on Type I extreme value distributed errors so widely used in empirical work, including ours, e.g., Fabinger and Weyl (2016, Appendix 3). Even for demand systems with higher curvature, with κ(p r ) [1, 2), it is possible for η(τ) to be negative, depending on the relative magnitudes of ( 1 1 ε(p )) and κ(p r ). 8 Isoelastic demand, a r popular choice in the macro literature (e.g., Dixit-Stiglitz CES preferences), amounts ( to a limiting ) case as it is straightforward to show that for these demand functions κ(p r ) = 1 1 ε(p r ) and thus, η(τ) = 0 according to equation (6). Thus, firms in these models do not alter their pricing decisions in response to changes in tax policy by assumption. But whenever demand is less convex than this popular limiting case, we characterize a large and empirically relevant class of demand specifications where the optimal response of the monopolist to an increase in the tax rate always is to reduce the pre-tax price, i.e., η(τ) < 0 so that the pre-tax prices and tax rates are strategic substitutes. 7 If κ(p r ) < 1, it follows from the definition of curvature that D (p r )D(p r ) [D (p r )] 2 < 0, which is the condition for demand to be log-concave. 8 We restrict attention to demand systems with κ < 2 since κ(p r ) [0, 2) ensures that the revenue function R(p r ) = p r D(p r ) is concave in p r, or equivalently, that the marginal revenue function is decreasing, a common demand restriction in models of imperfect competition. 7

9 We can now explore how total tax revenue collected by the government varies as a function of the tax rate τ when we account for the firm s optimal price response. revenue function is given by The government tax T (τ) = (p r p w )D(p r ) = τp w D ( (1 + τ)p w), (8) where p r and p w are implicit functions of τ, p r (τ) and p w (τ), through the definition of the taxinclusive price (1) and the pre-tax price response elasticity (6). The effect of a change in the tax rate on government tax revenue is dt (τ) dτ ( ) = p w D(p r ) + τp w D (p r )p w + dpw τd(p r ) + τp w D (p r )(1 + τ) dτ ) ( ) = p (D(p w r ) + τp w D (p r ) + η(τ)p w D(p r ) + ε(p r )D(p r ) [( = p w D(p r ) 1 + τ ) ( )] 1 + τ ε(pr ) + η(τ) 1 + ε(p r ). (9) Note that the sign of dt (τ)/dτ is ambiguous and depends on the relative magnitudes of the tax rate, demand elasticity, and the pre-tax price response elasticity. The prohibitive range of the Laffer curve arises for a given tax rate τ when the equilibrium price elasticity of demand ε(p r ) and the equilibrium pre-tax price response elasticity η(τ) are such that: dt (τ) dτ < τ 1 + τ ε(pr ) + η(τ) ( 1 + ε(p r ) ) < 0. (10) When are tax, demand, and upstream conduct conditions such that equation (10) is satisfied? We consider first the case of a naïve policymaker who mistakenly believes that akin to the case of perfect competition the monopolist will not modify its pre-tax (wholesale) price in response to an increase in the ad valorem tax rate τ. When η(τ) = 0, condition (10) will not hold for sufficiently low τ. However, this condition eventually holds as τ increases by reducing the total value of sales receipts as higher tax rates push the price p r into a more elastic region of demand for all demand systems other than the isoelastic limiting case. The macro literature relies on a similar incentive mechanism to generate a Laffer curve: higher income taxation reduces workers labor supply to eventually reduce the labor tax base and income tax revenues. See Trabandt and Uhlig (2011, Proposition 2). Rewriting equation (9) when η(τ) = 0 shows that all we require to be on the prohibitive region of the Laffer curve under a naïve policymaker is that consumer demand is sufficiently elastic at the tax-inclusive equilibrium price, ε(p r (τ)) < ε (τ) = 1 + τ, (11) τ 8

10 For instance, for a tax rate of 50% (similar to the 53.4% tax charged by the PLCB) to be in the prohibitive region of the Laffer curve of a naïve policymaker, the demand elasticity ε(p r ) at the corresponding equilibrium tax-inclusive price needs to be lower than ε (0.5) = 3 (a value that many of our demand estimates exceed). The higher the tax rate and thus final retail prices, the less elastic demand needs to be to reach the prohibitive range of the Laffer curve. Thus, tax revenue will fall if a naïve policymaker increased taxes from a starting tax rate of 70% and the good s demand elasticity at the equilibrium price is at least ε(p r ) < ε (0.7) = Conversely, for many, more moderate, taxation schemes, such as sales taxes, which in the U.S. across states reach only 9.45% in 2015, demand for the affected products is unlikely to be sufficiently elastic for the observed tax rates to be near or beyond the peak of the Laffer curve. 9 To complete the analysis we compare the features of the Laffer curve for a naïve policymaker described above with that of a policymaker with perfect foresight, capable of anticipating how the monopolist re-optimizes its pricing decision after a change of the tax rate. Substituting (6) for η(τ) in condition (10), the prohibitive range of the Laffer curve arises when 2 κ(p r ) + 2τ τ + ε(p r ) + 1 ε(p r ) < 0. (12) For this inequality to hold over the elastic range of demand, ε < 1, it suffices that ε(p r ) < ε (τ, κ) = 2 κ(pr ) + τ τ. (13) How does the implicit relationship between the tax rate and the elasticity of demand that entails a tax rate beyond tax revenue maximizing levels compare to the above, when η(τ) = 0? A general comparison is dependent on the chosen demand system, which dictates a choice of κ(p r ) and ε(p r ). However, when demand is log-concave and κ(p r ) [0, 1), as in our empirical setting, we can show that for any given tax rate τ: ε (τ, κ) = 2 κ(pr ) + τ τ < 1 + τ τ = ε (τ). (14) When allowing for a strategic response by the monopolist to chosen tax rates, demand at taxinclusive retail prices thus needs to be more elastic than under the naïve scenario for any particular tax rate to push tax revenues down the slippery slope of the Laffer curve. For example, for the above tax rate of 50% to be in the prohibitive region for a policymaker with perfect foresight, demand at the resulting tax-inclusive prices needs to be more elastic than 5 or 4 for κ(τ) equal to 0 or 0.5, respectively. This compares to the above critical value for the elasticity of 3 when η(τ) = 0. For a given tax rate, the difference between the elasticity cutoff values for the perfect foresight and naïve cases converges to zero as demand becomes more convex, reflecting that ε (τ, κ) ε (τ) as κ(p r ) 1, and is highest when demand is linear and κ(p r ) = 0. 9 See A rate of τ = 10% falls beyond the peak of the Laffer curve if the demand elasticity at tax inclusive prices would need to be smaller than 11. 9

11 The flip side of this result is that a policymaker with perfect foresight may need to set a higher tax rate to maximize tax revenues when compensating for the reduction in pre-tax price by the monopolist, η(τ) < 0, than the naïve policymaker would have chosen. Expressing equation (14) in terms of the optimal tax rate that maximizes tax revenue given the demand responsiveness at the tax-inclusive prices, we have that τ (ε, κ) = 2 κ(pr ) 1 + ε(p r ) > ε(p r ) = τ (ε(p r )) (15) Note that τ (ε) is not necessarily equal to τ (ε), the tax revenue maximizing tax rate for the naïve policymaker, since the demand elasticities are evaluated at different tax-inclusive retail prices, p r = (1 + τ )p w in the case of the sophisticated policymaker and p r = (1 + τ )p w for the naïve case. Locally, with small changes in the tax-inclusive retail price, however, and supported by the empirical evidence we present below, the difference between τ (ε) and τ (ε) is sufficiently small that τ (ε, κ) > τ (ε(p r )). Moving from the naïve scenario, η(τ) = 0, to one where the policymaker has perfect foresight, η(τ) < 0, not only tends to shift the Laffer curve to the right, but also makes it flatter. This is evident when inspecting the last term in equation (9), η(τ) ( 1+ε(p r ) ) > 0, which equals zero in the naïve scenario. This is the case because of the strategic substitutability of the tax rate and wholesale prices, η(τ) < 0, under perfect foresight and the monopolist s optimal pre-tax pricing on the elastic region of demand, 1 + ε(p r ) < 0. Thus, the stronger the firm response, the flatter the slope of the Laffer curve becomes. In summary, the theoretical model suggests that the downward sloping part of the Laffer curve arises if demand is sufficiently elastic relative to the tax rate and the elasticity of the pricing response of the taxed firm to changes in the tax policy. Even for the monopoly case, empirical analysis is needed to determine the elasticity of demand under alternative tax-inclusive prices and characterize the effective tax revenue function. Similarly, accounting for the firm s price response to excise taxation, which implies a possible shift and flattening of the Laffer curve relationship between tax rates and revenue, requires estimates of firm market power via η(τ) and the slope of consumer demand via ε(p r ). Our analysis of PLCB pricing of spirits allows us to empirically assess the necessary equilibrium responses of upstream firms and consumers. This analysis could be extended to various homogeneous good oligopoly models along the lines of the framework for analyzing tax incidence put forward by Weyl and Fabinger (2013). In our context, however, the PLCB deals with horizontally-differentiated products for which theoretical results do not exist, e.g., Fabinger and Weyl (2016, Appendix E). The main difficulty in evaluating the effect of a tax rate increase in this context is that it not only induces substitution to the outside option but also to other products that are taxed and therefore also generate tax revenues. consequence, addressing our research objective requires evaluating the determinants of the Laffer curve empirically, accounting for the fact that the overall change in tax revenue after a change in the tax rate reflects unequally induced changes in product sales due to heterogeneity in product costs In 10

12 and characteristics. Further, firms and consumers can respond differently to a tax rate change based on differences in market power and heterogeneous preferences, respectively. We account for these effects empirically in characterizing the Laffer curve across not just one, but all spirits products, both in aggregate and for different consumer types. In doing so, we are particularly interested in comparing the tax revenue expected by a naïve regulator who mistakenly neglects the ability of firms to re-optimize after a tax change, η(τ) = 0, to that realized by a policymaker who correctly anticipates firm responses to its actions, η(τ) < 0. 3 PLCB Pricing and Sales Data In this section we describe our data and institutional details that inform our theoretical modeling and econometric specification. We first describe the data we obtained from the state of Pennsylvania and other sources on the sales, prices, and characteristics of all products sold through the state-run network of stores. We then summarize Pennsylvania s current pricing regulations of alcoholic beverages. We document how upstream firms pricing is constrained by rules regarding the frequency and duration of temporary wholesale price adjustments. The fact that distillers need to decide far in advance when to put their products on sale temporarily significantly reduces the endogeneity concerns common in the estimation of models of demand for differentiated products. Next, we explore the nature of competition in the upstream distiller market that mitigates the effectiveness of any tax/pricing policy adopted by the PLCB. Finally, we document the heterogeneity of consumer preferences for different types of spirits, a key source of identification in our empirical strategy. 3.1 Data: Quantities Sold, Prices, and Characteristics of Spirits We obtained store-level panel data from the Pennsylvania Liquor Control Board (PLCB) under the Pennsylvania Right-to-Know Law. The data contain daily information on quantities sold and gross receipts at the UPC and store level for all spirits and wines carried by the PLCB from 2002 to We chose this sample because there were no mergers or acquisitions of relevance in the upstream distiller industry segment resulting in a stable competitive environment. As a result, pricing follows the normal pattern contemplated in the PLCB s rules. In addition, we received information on the wholesale price of each product. These wholesale prices are constant across stores, but vary over time according to well defined pricing periods. As of January of 2003, the PLCB operated a system of 593 state-run retail stores spread across the state. 10 We combine sales of stores in the same zip code and drop several wholesale and outlet stores, resulting in a total of 456 local markets. We then match combined store purchases with consumer demographics by linking store locations with data on local population and demographic characteristics using the 2000 Census. The PLCB opened and closed several stores over the time 10 See Seim and Waldfogel (2013, 2) for a detailed account of the welfare losses induced by the very limited entry allowed in the wine and spirit segment of the Pennsylvania market. Pennsylvania also has a private system for the sale of beer, allowing the controlled entry of private retailers. 11

13 period of our sample. We take these entry/exit decisions as exogenous shifts in the demographic composition of the potential pool of customers of each store. This feature of the data helps in identifying the demographic interactions in our estimated model. 11 Each store carries a multitude of wine and spirit products. We focus on the spirits category as it represents a majority of PLCB off-premise sales, 60.8% of store revenue. These products further constitute a well-defined and mature product category that can be described by few, 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. 12 We further focus on sales of popular 375 ml, 750 ml, and 1.75 L bottles of products in the spirits category, representing 80.9% of total spirit category sales by volume and 91.6% by revenue. The resulting sample exhibits a long right tail common to consumer goods, where many products are available to consumers but are rarely purchased. We therefore restrict the sample to only include the most popular products in each bottle size, spirit type pairing. Consequently, a 750 ml bottle of E&J Brandy (average retail price of $9.95) is in our final sample while a 750 ml bottle Remy Martin Louis XIII Cognac (average retail price of $1,078) is not. 13 Our final sample consists of 3,377,659 observations of market and time-period level purchases of 312 products that span brandy, cordials, gin, rum, vodka, and whiskey for three bottle sizes. The final sample represents 56.8% and 63.2% of the total off-premise bottle sales and revenue from spirits, respectively. Table I reports the average characteristics of products in our sample. The average proof is 75.33; 37.40% of products are imported; and 16.3% of products contain flavor add-ins. 14 Table I summarizes these product characteristics further by type of spirit. Vodkas and whiskeys have significantly larger market shares (31.88% and 24.41%, respectively) than rum (16.18%), cordials (13.38%), brandy (7.24%), or gin (6.91%). The differences in product variety within each category mirror the differences in market shares, with only approximately one half as many brandy and gin varieties as vodkas while 28.9% of the products are whiskeys. Flavored products are primarily cordials and brandies and to a lesser extent vodkas and rums. We also see variation in domestic 11 Appendix A describes how we assign Census block groups to their closest store and how we deal with store openings and closings, and provides detail on the construction of the demographic variables. We also document that the large majority of spirits are sold at every store; this alleviates concerns about assortment differences between stores leading to potential competition for consumers between stores. 12 This contrasts favorably with wines whose quality determinants are mostly unobserved, with a large number of products with limited life cycles. This leads to tiny, highly volatile market shares of wines with frequent entry and exit of products of different vintages. For example, within the popular 750 ml bottle category, the top-100 selling wines (out of 4,675) constitute 45% of total 750 ml wine revenue. 13 We define popular products as the highest selling products that together account for 80% of total off-premise spirit sales of a bottle size, spirit type pair. By this definition, a 375 ml bottle of Captain Morgan could theoretically be excluded from the sample, if it sales rank among 375 ml bottles is too low, while the 750 ml and 1.75 L versions are included. In practice this did not occur. We also drop the Tequila segment as it accounts for few products. Together, these two restrictions allow us to drop a total of 1,240 products from our sample. 14 In 16th century England, if a pellet of gunpowder soaked in a spirit could still burn determined whether the spirit was proof and thus taxed at a higher rate. Only if the alcohol by volume in rum exceeds 57.15% will gunpowder ignite. To simplify, since 1848 in the U.S., a 100 proof corresponds to a spirit with 50% alcohol by volume content. See Jensen (2004). 12

14 Table I: Product Characteristics by Spirit Type Products Price Share % Flavored % Imported Proof By Spirit Type: brandy cordials gin rum vodka whiskey By Price and Size: expensive cheap ml ml L all products Notes: Price is the simple average price between 2002 and 2004 and across products in each category. Share is based on number of bottles sold. Cheap ( Expensive ) products are those products whose mean price is below (above) the mean price of other spirits in the same spirit type and bottle size. versus imported varieties across spirit types: 58.89% of whiskeys and 51.61% of cordials in our sample are imported, but imported products comprise less than half of the products of the other spirit types. We complement these product characteristics obtained from the PLCB with data on spirit product quality from Proof66.com, a spirits ratings aggregator. The product score is largely informative within, but not across, spirit types and is therefore not reported in Table I. We denote spirits as expensive when their simple averaged price exceeds the mean price of other spirits of the same type and bottle size. Table I shows that expensive spirits are purchased nearly as often as cheaper varieties, but are less likely to be flavored or domestically produced and have higher proof. The 750 ml bottle is the most popular size of product in terms of unit sales and product variety, accounting for 50.20% of bottles sold and 54.9% of available spirits products, closely followed by the 1.75 L bottle with a share of 34.61% of bottles sold and 30.1% of available spirit products. The smallest bottles we consider, those in the 375 ml format, account for 15.1% of bottles sold and 15.4% of spirit varieties. Some of this variation is driven by the product set as upstream firms manufacture brands in particular bottle sizes. For instance, our final sample is composed of 198 brands (e.g., Captain Morgan) but 88 of these brands were available only in the 750 ml bottle size while 1 and 31 brands were offered only in the 375 ml and 1.75 L size, respectively. The remaining 78 brands were offered in several bottle sizes (e.g., Diageo sold Captain Morgan in 375 ml, 750 ml, and 1.75 L sizes) This pattern is reflected in the raw data as well where 958 of the potential 1, 192 brands were offered only in one bottle size, usually the 750 ml format. Table B.I in Appendix B provides additional descriptive statistics on the distribution of spirit prices by type and size of bottle. 13

15 3.2 The Mechanics of the Pricing Regulation The PLCB acts as a monopolist in the retail distribution of wine and spirits where the Pennsylvania State Legislature exerts regulatory oversight over several aspects of the daily operations of the stores. Most notably, as per the Pennsylvania Liquor Code (47 P.S et seq.) and the Pennsylvania Code Title 40, the legislature imposes a uniform markup rule upon the retail prices the PLCB charges both across products and across stores. Prices of spirits are thus identical across the state at a point in time and follow a common pricing/taxation rule known to all consumers and upstream manufacturers. This rule has been modified only infrequently over the years. From 1937 until 1980, the retail price for all products was based on a 55% markup over wholesale cost for all gins and whiskeys and 60% markup for other spirits. In 1980, the markup was reduced to 25% for all products and a per-unit handling fee, the Logistics, Transportation, and Merchandise Factor (LTMF ), of $0.81 was introduced and later increased to $0.85 in The agency instituted the current 30% markup in 1993 when it also modified the unit fee to vary by bottle size to better reflect transportation costs from the PLCB s centralized warehouses to the retail stores. The LTMF unit fee for the 375 ml, 750 ml, and 1.75 L bottles in our sample amounts to $1.05, $1.20, and $1.55, respectively. For the average product, the LTMF fee accounts for 26.7% of the final retail markup. In addition, consumers also have to pay an 18% sales tax, the Johnstown Flood Tax, on all liquor purchases. 16 Accordingly, the retail price p r of a given product with wholesale price, p w, is calculated as: 17 p r = [p w LTMF ] (16) Of primary concern for this paper is the uniform markup, an ad valorem tax, applied to all products, amounting to ( ), or 53.4%. The PLCB has limited ability to depart from this uniform percent markup rule. It operates seven outlet stores close to the state s borders, in an effort to address any border bleed of consumers who illegally import lower-priced products into Pennsylvania from neighboring states. While these stores offer wines and spirits 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. Controlling for these stores has little qualitative or quantitative effects on our results. Related robustness checks are reported in Appendix C.1. The PLCB purchase bottles of spirits directly from upstream distillers at wholesale prices p w. Because of the legislated pricing formula, retail price p r is driven by the wholesale pricing decisions p w of the PLCB s suppliers and any change in the wholesale price results in a change to the retail price passed on to consumers. A new product s wholesale price remains fixed for 16 The original 10% tax was instituted in 1936 to provide $41 million for the rebuilding of the flood-ravaged town of Johnstown. Despite reaching the funding goal after the initial six years, the tax was never repealed, but instead rose twice to 15% in 1963 and to 18% in An additional 6% sales tax is then applied to the posted price to generate the final price paid by the consumer. 14

16 one year after its introduction. For mature products, distillers can modify the wholesale price they charge the PLCB at set intervals called pricing periods which last four or five weeks and typically coincide with the month of year. We can therefore aggregate daily data on prices and quantity sold to the level of these pricing intervals without concern of introducing aggregation bias into our demand estimates a useful aspect of our data. The PLCB places some limitations on how often distillers can change the wholesale price for mature products. Temporary wholesale price changes, typically price reductions or sales, amount to 84.8% of price changes in our sample. Distillers can temporarily adjust their wholesale prices up to four times a year, or once per quarter, but need to submit such proposed price changes to the PLCB at least five months before the start of the promotion. A product can thus go on sale for one month, but not for two in a row. Upstream firms can also permanently change the wholesale price of a product, i.e., a change in the reference price for temporary price changes. A permanent price change takes place at the beginning of four-week long reporting periods which, for accounting purposes, occur at a slightly different periodicity than the pricing periods. These price changes are instituted at the beginning of the quarter s first full reporting period, with some discretion on the part of the PLCB as to the choice of actual reporting period. There is a time lag, however: distillers have to submit the request for a permanent price increase by the start of the previous quarter. Permanent wholesale price decreases may be submitted at any time and take effect at the beginning of the next period. We discuss the periodicity of the price series further in Appendix A. The pricing periods we use in our analysis below follow the periodicity of sales, resulting in 34 periods from 2002 to Note that the delay between the request and effectiveness of either permanent or temporary price adjustments limits the ability of the distillers to respond to temporary demand shocks an issue we revisit when discussing price endogeneity concerns in Section 5. Table II: Percent of Products Placed on Sale Over the Year Spring Summer Fall Winter Holiday Year Times By Spirit Type: brandy cordials gin rum vodka whiskey By Price and Size: expensive cheap ml ml L all products Notes: Cheap ( Expensive ) products are those products whose mean price is below (above) the mean price of other spirits in the same spirit type and bottle size. We define the Holiday season as the two pricing periods that encompass Thanksgiving through the end of the year. Statistics reflect the percent of products with a temporary price reduction during the corresponding season except for Times, which denotes the average number of times that spirits in each category are on sale during a year. 15