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Essays in competition and price determination in diverse markets Jing, Yan 2013

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 ESSAYS IN COMPETITION AND PRICE DETERMINATION IN DIVERSE MARKETS  by   Jing Yan   A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF  THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate and Postdoctoral Studies  (Business Administration)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  November 2013  ? Jing Yan, 2013ii  Abstract This thesis studies competition and price determination in three distinctly different markets. Chapter 2 carries out an empirical analysis of the effect of a non-uniform pricing strategy on box office revenues in the theatrical movie market. Using a rich and unique dataset of the Hong Kong market, a nested Principles of Differentiation (nested PD) demand model is estimated and the estimation results are used to simulate theaters' profits under the differential and uniform pricing strategies. The main finding is that differential pricing dominates the uniform pricing (demand effect) but gains from the differential pricing policy are limited due to intensified competition (competition effect).   Chapter 3 examines the relationship between prices and market structure in geographically isolated gasoline markets that are exposed to large demand shocks. The temporal variation in market size provides instrumental variables to overcome the classical endogeneity bias in the standard price-concentration regression. There is evidence of local market power in the studied markets. Additionally, the high margins that characterize concentrated markets dissipate quickly with the increase of the number of gas stations. The results also suggest that the regression analysis that does not account for the endogeneity between entry and prices will significantly underestimate the effect of market concentration on prices.  Chapter 4 studies a public sector problem in which a government faces the choice of using public-private partnerships (PPP) or more traditional public procurement approaches to procure public services. Specifically, a basic trade-off associated with PPPs is modeled: while PPPs marshal the power of competitive markets, they involve long-term contracts that may prove relatively inflexible. It is shown that the optimal choice between PPPs and public procurement depends on factors including the likelihood that changes will be necessary, the productivity of non-contractible effort exerted by private sector partners, the costs of switching, the difference between first-best and second-best projects, and the bargaining power of governments vis-?-vis private parties. It also shows that the optimal choice may depend on whether the government?s objective is to maximize ?value for money? (i.e., deliver the right project at the lowest cost to taxpayers) or to maximize total social surplus.     iii  Preface Chapter 2 is based on joint work with Professor Jason Ho at Simon Fraser University and Professor Charles Weinberg at the University of British Columbia. I collected price data, wrote the estimation algorithms, analyzed the data and drafted the manuscript (with the exceptions of introduction and literature review). Professor Jason Ho and Professor Charles Weinberg participated in data analysis and provided intellectual contributions. Professor Jason Ho also provided financial support for part of the data. Chapter 3 is based on joint work with Professor Mariano Tappata at the University of British Columbia. Professor Tappata and I jointly developed the research design, collected data, wrote the estimation algorithms and drafted the manuscript.  Chapter 4 is based on joint work with Professor Thomas Ross at the University of British Columbia. Professor Ross and I jointly developed the theoretical model which I then solved.  Professor Ross and I then each drafted sections of the manuscript.              iv  Table of Contents Abstract ................................................................................................................................... ii Preface ...................................................................................................................................... iii Table of Contents ...................................................................................................................... iv List of Tables ............................................................................................................................ vi List of Figures.......................................................................................................................... vii Acknowledgements ................................................................................................................. viii Dedication ................................................................................................................................ ix Chapter 1 Introduction .............................................................................................................. 1 Chapter 2 An Empirical Study of Uniform and Differential Pricing in the Theatrical Movie Market ...................................................................................................................................... 5 2.1 Introduction .................................................................................................................................. 5 2.2 Related Literature ......................................................................................................................... 8 2.3 Demand Model ........................................................................................................................... 12 2.4 Data Description ......................................................................................................................... 19 2.5 Demand Model Estimation and Results ..................................................................................... 23 2.5.1 Estimation Strategy.............................................................................................................. 23 2.5.2 Estimation Results ............................................................................................................... 25 2.6 Counterfactual Simulations ........................................................................................................ 31 2.7 Conclusions ................................................................................................................................ 38 Chapter 3 Competition in Retail Gasoline Markets ................................................................. 40 3.1 Introduction ................................................................................................................................ 40 3.2 Related Literature ....................................................................................................................... 41 3.3 Empirical Specification .............................................................................................................. 45 3.4 Data Description ......................................................................................................................... 48 3.5 Results ........................................................................................................................................ 53 3.6 Conclusions ................................................................................................................................ 60 Chapter 4 Efficiency vs. Flexibility in Public-Private Partnerships ......................................... 61 4.1 Introduction ................................................................................................................................ 61 4.2 Some Background on PPPs and Related Literature.................................................................... 62 4.3 General Model ............................................................................................................................ 67 4.4 Comparing PPPs and Traditional Public Procurement ............................................................... 75 4.5 Extensions .................................................................................................................................. 78 4.5.1 A Total Social Surplus (TSS) Objective .............................................................................. 78 4.5.2 Toll Revenue PPPs ............................................................................................................... 83 v  4.5.3 Renegotiation Costs ............................................................................................................. 87 4.6 Conclusions ................................................................................................................................ 88 Chapter 5 Conclusions ............................................................................................................. 90 References ............................................................................................................................... 92 Appendices ............................................................................................................................ 102 Appendix A .................................................................................................................................... 102 Appendix B .................................................................................................................................... 103 Appendix C .................................................................................................................................... 104 Appendix D .................................................................................................................................... 108 Appendix E ..................................................................................................................................... 111 Appendix F ..................................................................................................................................... 115                  vi  List of Tables Table 2.1 Movie Prices in Hong Kong ................................................................................................. 21 Table 2.2 Summary Statistics for the Selected Sample (June 7, 2012-August 30, 2012) .................... 22 Table 2.3 Instrumental Variables for Conditional Market Shares ........................................................ 25 Table 2.4 Parameter Estimates for Different Demand Specifications .................................................. 27 Table 2.5 Price Elasticities for Theater C2 ........................................................................................... 30 Table 2.6 Counterfactual Results of the 4-Theater Market (Competition) ........................................... 34 Table 2.7 Counterfactual Results of the 4-Theater Market (Monopolist) ............................................ 36 Table 2.8 Counterfactual Results of the 4-Theater Market (Restricted Differential Pricing) .............. 38  Table 3.1 Summary Statistics ...............................................................................................................52 Table 3.2 Non-linear Effects of Competition .......................................................................................54 Table 3.3 OLS and IV Regressions ......................................................................................................55 Table 3.4 Demand and Cost Shocks and Market Structure...................................................................59                    vii  List of Figures Figure 2.1 Two-level Nested Logit Models .......................................................................................... 14 Figure 2.2 The PD Model ..................................................................................................................... 14 Figure 2.3 The Nested PD Model ......................................................................................................... 15 Figure 2.4 Three-level Nested Logit Models ....................................................................................... 19  Figure 3.1 Park Visits and Seasonality.................................................................................................50 Figure 3.2 Distribution of Gas Stations by Market Definition ............................................................51 Figure 3.3 Price Reductions After Adding One Gas Station ...............................................................56  Figure 4.1 The Efficiency-Flexibility Trade-Off..................................................................................78                 viii  Acknowledgements  I would like to express my enduring gratitude towards my supervisor Professor Thomas Ross. Professor Ross has enlarged my vision of economics and business and supported me throughout my journey in the PhD program intellectually and financially.   I would also like to thank my committee members, Professor Charles Weinberg and Professor Mariano Tappata, who have inspired me to continue my research in this field. I appreciate discussions with my co-author Professor Jason Ho and the faculty in my department, especially Professor James Brander and Professor Ralph Winter, who gave me helpful and inspiring advice on my research.  I am grateful to Professor Barbara Spencer for expertly serving as my PhD program advisor, especially for her excellent advice on college teaching. I also wish to thank my department secretary Helen Ho and PhD program Administrator Elaine Cho as their dedicated administrative work has made my life easier in the PhD program.  Special thanks are owed to my parents, who have supported me throughout my years of education, both mentally and financially.             ix    Dedication                           To my parents  Liu Xiaozhen and Yan Yi            1  Chapter 1  Introduction Assessing the causes and effects of competition is one of the central research topics in the field of industrial organization (IO). There is a vast literature on various topics related to market competition. Understanding the nature of competition is not only of great academic interest but also has critical policy implications. This line of research indeed shapes the thinking of regulators who oversee market structure and competition policies and hence affects the policy-making process. This thesis studies competition and price determination in three different settings.  Chapter 2 explores the impact of competition on price in markets of heterogeneous goods. In particular, this chapter investigates the uniform pricing puzzle in the movie industry. The uniform pricing puzzle refers to the phenomenon that in North America and most other markets, all non-3D movies shown at the same time within a movie theater have the same ticket price.1 This uniform pricing strategy is an economic puzzle for at least two reasons: (1) movies are highly differentiated products, which implies the possibility of a profitable differential pricing strategy which involves different prices across movie titles based on different demands and (2) the "wholesale price" at which theaters rent movies from studios varies considerably by the appeal of movies, suggesting cost-based reasons for price differentials. Industry executives and academic researchers have questioned the wisdom of this pricing practice. Therefore, understanding and solving the uniform pricing puzzle is of both practical importance and academic interest. In this chapter, I carry out an empirical analysis of differential and uniform pricing strategies in an imperfectly competitive theatrical movie market. Specifically, I assemble a rich and unique dataset of the Hong Kong market where theaters engage in differential pricing based on movie titles. Using this dataset, I first estimate a nested Principles of Differentiation (Nested PD) demand model, and then use the estimation results to simulate profits that theaters would have earned under the two pricing strategies.                                                          1 Typically, within a movie theater, prices are higher for 3D than for non-3D movies. Prices for all 3D movies are identical, however. 2  I find that there are two opposing effects existing when theaters all adapt the differential pricing policy. The first (demand) effect is the increased profits due to the additional surplus differential prices can extract from consumers, e.g., charging lower prices to attract moviegoers who would otherwise not watch a low appeal movie and charging higher prices for high appeal movies with less elastic demand. The second (competition) effect is the lower profits due to intensified competition among theaters which have a larger set of price points or ?weapons?. I find that differential pricing dominates uniform pricing (demand effect) but gains from the differential pricing policy are dampened by intense competition (competition effect). This study sheds light on the literature on uniform pricing for differentiated products. In particular, I examine this subject from the perspective of price competition, especially in a market featuring single-unit consumption products like movies. In terms of methodology, I extend the Principles of Differentiation (PD) model introduced by Bresnahan et al. (1997) to the nested PD model, which allows more flexible substitution between the outside option and the alternatives in the "inside" product category.  In the third chapter, I examine market structure and how it affects price competition in a particular market of homogenous goods. Specifically, I look at the retail gasoline markets. Few industries attract as much attention from consumers, antitrust authorities and academia as does gasoline retailing. In the last two decades, higher oil prices and the increased merger activities have coincided with a rise in accusations of price gauging by the laymen, government investigations and regulatory proposals from legislators and consumer groups. On the academic side, the availability of high frequency station-level data has spawned a vast literature ranging from the existence of Edgeworth Cycles and "Rockets and Feathers" price adjustments to the effect of vertical contracts on retail prices and collusion. However, possibly influenced by the well-known endogeneity problem in price-concentration studies, little is known about the effect of market structure on prices in this industry. This chapter tries to fill this gap by investigating pricing by gasoline stations in geographically isolated markets. These markets range from monopolies to oligopolies and share the special feature of being located near the entrance to national parks in the U.S. and therefore exposed to temporal and large demand shocks which lead to temporal variation in market size. This setting provides valid instrumental variables to address the endogeneity bias in the standard price-concentration regression. Specifically, the instrumental variables are the past visits, 3  which are a proxy for the expected long-term market size and therefore affect entry and exit decisions. On the other hand, gasoline prices at a given time are influenced by the contemporaneous market size which is not correlated with the average market size in this context. The results suggest that local market power exists in these markets during the period of study. I also find that ordinary least square (OLS) estimation significantly underestimates the effect of market concentration on prices. Chapter 4 looks at the increased productive efficiency and the associated inflexibility costs of introducing competition and private provision into the supply of certain public services. One innovation involving expanded use of the private sector in the delivery of public services is the public-private partnership (PPP): "a cooperative venture between the public and private sectors, built on the expertise of each partner, that best meets clearly defined public needs through the appropriate allocation of resources, risks and rewards.? 2  It is shown in the literature that the private involvement in the provision of public goods and services (e.g., roads, hospitals, schools, prisons, etc) introduces competition that improves productive efficiency. But these efficiency gains come at costs, one of which is inflexible PPP contracts. Given the very long lives of PPP projects, it is impossible to anticipate every potential contingency and therefore PPP contracts may need to be renegotiated at some point after the contract has been signed. However, in this case, any changes will have to be renegotiated via bilateral bargaining which will almost certainly raise the cost to government. PPPs' higher productive efficiencies and inflexibility suggest a trade-off faced by governments when choosing between a PPP and more traditional public procurement to secure public services. In this chapter, I model this basic trade-off. I show that the optimal choice between a PPP and traditional public procurement depends on a number of factors including the likelihood that changes will be necessary, the productivity of non-contractible effort exerted by private sector partners, the costs of switching, the difference between first best and second-best projects and the bargaining power of governments vis-?-vis private parties. In addition, the optimal choice may depend on whether the government?s objective is to maximize ?value for money? (i.e., get the right project delivered for the lowest cost to taxpayers) or to maximize total social surplus. I also demonstrate that the relative advantages of PPPs will depend on                                                         2 Canadian Council for Public Private Partnerships: 4  the nature of the PPP contract considered ? that is whether the private partner is compensated based on simply having completed the project or based on the actual usage of the facilities.     While the potential costs of lost flexibility in lengthy PPP contracts have been recognized by industry practitioners and academic researchers, there has been very little formal modeling of the problem. The majority of papers in the literature on PPPs focus on the optimality of ?bundling? of the various tasks such that one private partner tackles multiple tasks. To my knowledge, this is the first economic study that formally models the inflexibility issue of PPP contracts. The conditions under which PPPs are more beneficial offer some guidance on a government's choice of procurement approach. For instance, if demand for the project is stable and easy to forecast as, perhaps, in the transport and water sectors, PPPs are more likely to be suitable. And PPPs may be less likely to be superior for health care and IT services, where the flexibility problem stands out as demand evolves quickly over time.                       5  Chapter 2  An Empirical Study of Uniform and Differential Pricing in the Theatrical Movie Market  2.1 Introduction No two movies are created equal. Yet, despite the apparent variability in appeal and quality, a movie theater in North America or most other markets charges the same ticket price for all non-3D movies it shows (during the same time period) and another price for all 3D movies. Such uniform pricing for differentiated product has been puzzling many industry executives, analysts, and even the general public (e.g., McKenzie 2008). Commenting on the increasing disparity in the production budgets across different movies, Stephen Spielberg recently predicted a change to the uniform pricing practices, ?you are going to have to pay $25 to see the next ?Ironman?. And you?re probably only going to have to pay $7 to see ?Lincoln?? (Kim 2013). However, similar predictions were made by many Hollywood insiders and observers over the years (e.g., Battaglio 1998) and uniform pricing continues to be the dominant practice in the theatrical movie market. Such a pricing puzzle has been attracting attention not only from industry executives but also from marketing academics and economists. Reviewing the movie literature, Eliashberg at el. (2006) have identified the uniform price puzzle as an important knowledge gap. In fact, the uniform pricing policy in the theatrical market is probably the most commonly used example by academics to illustrate the more general puzzle of uniform pricing for differentiated products (e.g., Heidhues and K?szegi 2008; Chen and Cui 2013). While a variety of rationales have been proposed to explain the puzzle (e.g., Orbach and Einav 2007), there is no empirical work directly addressing this puzzle. Such lack of empirical work is potentially due to the dominant practice of uniform ticket prices, which provide no observed price variation across different movie titles within a theater. Specifically, while most theatrical markets have separate prices for non-3D and 3D movies, there is typically no price variation across movies showing at a theater at the same time. A notable exception is the Hong Kong market, where ticket prices vary across theaters as well as within theaters. Building a dataset 6  consisting of ticket prices and daily ticket sales in the Hong Kong market, I am thus able to estimate a demand model, which can characterize how movies would substitute for one another within and across a theater if they are differentially priced. My empirical study, through the use of counterfactual analysis, allows me to shed light on the uniform pricing practice long puzzling both practitioners and academics. The various rationales advanced in by the literature on the pricing puzzle can be categorized into three major types, namely (1) consumer-related factors, e.g., consumers? preference for uniform prices (e.g., Heidhues and K?szegi 2008; Chen and Cui 2013), (2) channel-related factors, e.g., the influence from the upstream channel members, movie distributors, who have a profit function not fully aligned with the theaters? (e.g., Orbach and Einav 2007), and (3) internal factors, e.g., the costs of implementing differential pricing (e.g., McMillan 2007; Eckert and West 2013). Such cost arguments are also in line with the price-stickiness literature in macroeconomics like Rotemberg (1982) and Blinder (1991). A critical factor, infrequently considered in the literature, is the competition among movie theaters. Abstracting away from such issues as consumers? preference for uniform prices, channel coordination and implementation costs, I examine the extent to which competition among asymmetrical theaters reduces the incremental gains of differential pricing over uniform pricing. In this context, I expect the differential ticket pricing would create two opposing effects. The first (demand) effect is the increased profits due to the additional surplus the differential ticket prices can extract from consumers, e.g., charging lower prices to attract moviegoers who would otherwise not go to a low appeal movie and charging higher prices for high appeal movies that people value relatively highly. The second (competition) effect is the lower profits due to the competition intensified by each theater now having a larger set of price points or ?weapons?. It is unclear a priori to what extent one effect dominates the other. Capitalizing on my unique dataset, I attempt to investigate empirically how the two forces balance each other in the Hong Kong theatrical market.  Our empirical approach consists of two steps, namely (1) estimation of a structural demand model with the theatrical market data from Hong Kong, and (2) counterfactual simulations to compare the outcomes of differential and uniform ticket pricing games played by competing theaters. To generate useful insights from the counterfactual simulation, it is important to adopt a tractable but rich structural demand model on which the simulation is based on. I 7  thus modify the Principles of Differentiation (PD) model introduced by Bresnahan et al. (1997) to a more general model called Nested PD model.   As discussed in more detail below, the nested PD model has two important features. First, as is found in the PD model, it does not a priori assume how consumers perceive similarities among alternatives and thus does not preclude one substitution structure or another. Instead, the nested PD model is essentially a mixture of some commonly competing substitution structures, which allow the possibility that two alternatives are perceived to be similar on some occasions but not so similar in the others. In this context, such flexibility allows data to exhibit a spectrum of possibilities between two extremes, namely all moviegoers care more about where they see a movie than what to watch versus all moviegoers care more about what than where. At the extreme of ?more where than what?, moviegoers perceive different movies at a theater as closer substitutes than movies at different theaters, meaning that the cannibalization within a theater would be stronger than switching between theaters. At the other extreme, movie consumers are primarily driven by specific movie titles and thus consider different theaters as close substitutes, implying that switching between theaters is common and can be easily triggered by a price cut at one theater. In contrast to such nested logit models as in Draganska and Jain (2006), the nested PD model does not preclude one extreme or the other but let the data lead us to a point on the spectrum. The second feature of my nested PD model is to allow more flexible substitution between the outside option and the alternatives in the product category. This is an important extension from the original PD model, which has a rather strong restriction on the substitution with the outside option and potentially leads to overestimating the market expansion (contraction) effect as a consequence of price decrease (increase) inside the product category. I believe my extension provides a better characterization of how different pricing policies extract surplus from consumers who originally prefer the outside option, and thus leads to a richer representation of how the two effects of surplus extraction and intensifying competition balance each other, as discussed earlier. I compare the nested PD model to the PD model and the nested logit model, and find that my proposed model achieves a better model fit than the other models examined. In terms of the effect of price on demand, I find, using the nested PD model, that consumers are sensitive to the price of movies and that there is greater sensitivity to 2D than 3D movie prices. Moreover, 8  my results show that substitution occurs both among movies in a theater and across theaters but the effect of across theater substitution is greater than the effect of within theater substitution. Finally, I find evidence of market expansion effect, i.e., if price competition leads to lower overall prices, market expansion might take place.  Using the estimated nested PD model, I then run several counterfactual simulations to test the profit impact of uniform versus differential pricing strategies under different game structures. In a monopoly case in which only one movie theater strategically manages its prices, I find unambiguous results favoring differential pricing as predicted by theory. In the case where the movie theaters play a Bertrand pricing game, a full differential pricing (movie specific pricing), as compared to uniform pricing, leads to a very small improvement in profits (about 1%) and total admissions (about 2%). However, when theaters employ a restricted differential pricing policy, then the improvement of profits and admissions as compared to uniform pricing goes up to 18% and 20%, respectively. 3  This restricted differential pricing policy appears to soften the competition among firms and thus leads to higher profits. These results suggest the presence of both demand effect and competition effect in the Hong Kong market. The demand effect is stronger than the competition effect but the competition effect is large enough to reduce the incremental gains of differential pricing over uniform pricing.  The remainder of the chapter is organized as follows. In the next section, I will review the related literature. The model specification is then discussed, followed by a description of the dataset. In section 2.5 and 2.6, I discuss first the model estimation details and results, and then the counterfactual simulations. Section 2.7 concludes.   2.2 Related Literature Probably due to the economic and cultural significance of the movie industry as well as the abundance of publicly available field data on various marketing mix variables, there have been an increasing number of studies situated in the movie market (Eliashberg et al. 2006). A                                                         3 Here restrictions mean (1) the same price for the same movie with multiple language versions; (2) the price difference between the 2D and 3D versions of the same movie differs by the same amount for all movies with both versions. See detailed discussion in Section 2.6. 9  number of these studies examined the competition aspect in the theatrical movie markets implicitly or explicitly. A common approach in these studies is to characterize the demand for movies as a choice model depending on strategic decision variables like media spending, distribution intensity, product design as well as other market factors like seasonality, critics? reviews and word-of-mouth (e.g., Ainslie et al. 2005; Einav 2007; Moul 2007). There are also studies using some measures of competition intensity as the control or focal variables in explaining movies? box office performances (e.g., Elberse and Eliashberg 2003; Basuroy et al. 2006; Ho et al. 2009; Chintagunta et al. 2010; Calantone et al. 2010). However, the strategic behaviors of the competing movie distributors or theaters are typically abstracted away in these studies, except those like Krider and Weinberg (1998) and Einav (2010), which explicitly model the strategic choice of movie release dates by distributors; or Moul (2008) and Raut et al. (2008), which examine the contracts set by distributors to the movie theaters. The least studied strategic behaviors are probably the ones among competing movie theaters, the downstream channel members in the market in general and their choices of ticket prices in particular. Chisholm and Norman (2006), Davis (2006a) and Chisholm et al. (2010) are the few studies examining how movie theaters strategically compete in screening time, market entry and movie assortment, using reduced form models. For pricing competition, Chisholm and Norman (2012) find from their reduced form model that ticket prices do not have a statistically significant effect on theaters? admission in the Boston and South Florida markets. In addition to some potential endogeneity issue of the price measure, this could be due to the low observed ?across theater? price variation in their two markets, which are of large size in the overall North American market. In fact, prices seem to be a non-strategic variable for movie theaters in the large North American local markets. Davis (2005) uses reduced form models to study the relation between ticket prices and competition structure variables like the number of nearby competing theaters and finds the relation is relatively weak in the largest 101 local markets. Applying a structural choice model to daily box office data at the theater and movie level for 36 local markets, which exclude the largest ones in the U.S., Davis (2006b) finds that the theaters in his sample have low cross-price elasticities. Using a similar structural model to Davis? (2006b), de Roos and McKenzie (2011) also find the cross-price elasticities across rival theaters in the greater Sydney area to be low. Using data from a major Asian theatrical market and a more recent time period, my study should shed light on 10  whether the limited role of ticket prices in theater competition is generalizable beyond the North American and Australian markets and the past market situation where differentially pricing movies is not a common practice. Specifically, as my data allow me to observe not only across-theater but also within-theater price variation ? ticket prices of different movies may be different, I believe such price flexibility within theaters could lead to intense competition among rival theaters.4  Our study also builds on and extends the broader literature on uniform pricing for differentiated products. Probably due to the lack of observed price variation by definition, there are only a few empirical studies of uniform pricing, which is in stark contrast to the abundance of empirical studies of price discrimination (e.g., Borenstein 1991; Leslie 2004), which is essentially the flip side to uniform pricing. Despite the differences in methodological approach and in product categories the studies are situated in, the empirical studies of uniform pricing mostly focus on estimating how much improvement a non-uniform pricing policy can add beyond a uniform pricing policy, and understanding why uniform pricing is the dominant practice in their focal product categories. For example, based on the survey data of individual respondents? willingness to pay for a variety of songs, Shiller and Waldfogel (2011) compare an online music retailer?s revenues if an optimal uniform pricing policy is adopted as opposed to a variety of non-uniform ones, and find the optimal uniform pricing policy would generate at least 15% less revenues than the non-uniform alternatives. Focusing on a different music market, namely pop music concerts in the U.S., Courty and Pagliero (2012) use a reduced form model to estimate the effect of a pricing policy, which charges different prices for different types of seats in a concert and find such a pricing policy generated 5% additional revenues over a uniform pricing policy. Note that these studies on comparing uniform and non-uniform pricing policies typically assume the retailer to be a monopolist or abstract away from any specific market structure. In particular,  the competition softening effect of uniform pricing is not examined in these comparisons. On the other hand, some empirical studies of uniform pricing focus on the factors conducive to a uniform pricing policy over the non-uniform ones. For example, using a reduced form                                                         4 de Roos and McKenzie (2011) observe some within-theater price variation in the form of Tuesday discount. The within-theater price variation I observe in my data include not only the Tuesday discount but also different prices across different movie titles in a given day. 11  model to explain the minimal price variation across and within brands in the Canadian beer category, Eckert and West (2013) find their data are more in line with the menu cost explanation for uniform pricing. Focusing on grocery stores in the urban Chicago area which charged different prices for different flavors within each soft drink brand, McMillan (2007) develops a structural demand model and conducts counterfactual simulations to estimate the profit differences between uniform and non-uniform pricing. McMillan also argues that the menu cost may prohibit any attempt for non-uniform pricing. Aside from the menu cost argument, empirical studies like Draganska and Jain (2006) explore other factors favorable to uniform pricing. Focusing on the consumer-side (demand-side) arguments, they show that the high substitutability across different flavors within each yogurt line would reduce the effect of non-uniform prices across different flavors. However, the optimal non-uniform pricing in their counterfactual simulation was obtained by assuming a retailer acts as a monopoly. As discussed earlier, I argue that the competition softening effect of uniform pricing would be a key driver by itself.  Although I will compare the outcomes of non-uniform and uniform pricing policies, the current study abstracts away from how the rival theaters enter into a non-uniform pricing game as opposed to a uniform pricing game, or vice versa. Busse?s (2000) study of rival cellular telephone service providers? identical prices across multiple markets provides some evidence supporting a collusion explanation for competitors selecting a uniform pricing game. If, as I suggest, uniform pricing leads to a softening of competition, then that would be consistent with the possibility, at least, of implicit competition. Several theoretical models in the uniform pricing literature provide helpful insights to my empirical study of uniform pricing in the theatrical movie market. The notion that uniform pricing is a way to soften competition is not new in this theoretical literature stream; the improved profitability of uniform over non-uniform pricing policies has been shown in analytical models in a variety of contexts, e.g., couponing (Shaffer and Zhang 1995; 2002) and offering customized for brand switchers (Chen 1997; Villas-Boas 1999; Taylor 2003). Some of these models also explore factors beyond the competition softening effect of uniform pricing. For example, Chen and Cui (2013) assume that consumers have fairness concern in terms of paying a higher price than other consumers.  However, there is a general agreement on the role of uniform pricing in softening competition. 12  Note that the above mentioned theoretical studies of uniform pricing tend to capture product differentiation in a linear (Hotelling) city setting where the role of the outside option tends to be rather limited. Specifically, all consumers along the market line are assumed to buy in the product category with certainty, implying that low equilibrium prices would nearly be equivalent to low equilibrium profits. One may wonder whether the need to soften competition is inflated due to the stylized setups. Holmes (1989) and Corts (1998), nevertheless, do reach the similar competition softening conclusion using some general demand functions. Both Holmes and Corts derive their results in a duopoly setting, but their models differ in whether the two rival firms are symmetrical. Specifically, a key assumption used in Holmes? derivation is the cross-price elasticities of the two firms are identical. Under this setup, Holmes provides some examples in which price discrimination would decrease profits. On the other hand, Corts sets up the duopoly as asymmetrical, and shows that under a condition named best response asymmetry, the weaker retailer would provoke ?all-out competition? by setting the prices of its products aggressively low. As my empirical study is situated in a market with a number of competing theaters, it would be difficult to directly test for such conditions as best response asymmetry in Corts (1998). However, I do predict that uniform pricing within theaters would soften competition across theaters, suggesting competition would dampen the effect of the differential pricing on profit improvement, which would be otherwise higher under a monopoly situation.    2.3 Demand Model As discussed earlier, my demand model needs to capture three types of substitution, namely (a) substitution across movies, (b) substitution across theaters, and (c) substitution to the outside option in a non-restrictive manner. A key challenge to characterize (a) and (b) flexibly is that each choice alternative facing moviegoers is a combination of a movie and a theater, and it is difficult to determine a priori whether a moviegoer, who initially prefers, say viewing The Dark Knight Rises at theater 1, would be more likely to be enticed by a $1 price drop of the same movie from another theater 2 or the price decrease of the same magnitude for The Dictator at the same theater 1. If I do not want to distinguish the two cases or to essentially restrict the consumer to be equally affected by both cases, I can simply 13  represent the demand by a standard multinomial logit model, which assumes the random component of each choice alternative to be identically and independently distributed and therefore exhibits the restrictive property, Independence of Irrelevant Alternatives (IIA) (Refer to Ben-Akiva and Lerman (1985) for a detailed discussion of the IIA property). On the other hand, if I am willing to a priori impose the restriction that the consumer would be more affected by the price drop of the same movie from a different theater (i.e. movies are the primary dimension of differentiation), I can use a nested logit model with different theaters screening the same movie clustered into one nest (movie-primary NL model in Figure 2.1a). On the contrary, if I a priori impose the restriction that the consumer would be more affected by the price change of a different movie at the same theater (i.e., theaters are the primary dimension of differentiation and hereby have some local monopoly powers), I can use a nested logit model with different movies screened at the same theater forming a nest (theater-primary NL model in Figure 2.1b). However, as stated earlier, my goal is to adopt a flexible demand model, allowing the data to reveal any of the above structures, as opposed to a priori imposing a structure. I thus develop my choice model on the basis of the Principles of Differentiation (PD) model introduced by Bresnahan et al. (1997). PD models (Figure 2.2) can be considered to be a mixture of several alternative nesting structures. In my context, a PD model is a mixture of the two nesting structures discussed above, differentiation by movies vs. differentiation by theaters. In other words, if I consider the two nesting structures as the two extremes of a spectrum, the PD model would be between the two extremes with its position on the spectrum dependent on the data.          14               Figure 2.1a  A Two-level Movie-Primary Nested Logit Model          Figure 2.1b  A Two-level Theater-Primary Nested Logit Model Figure 2.1 Two-level Nested Logit Models            Figure 2.2 The PD Model   Movie B at Theater 2 Movie B at Theater 1 Movie A at Theater 2         Outside Option Theater Movie A at Theater 1 Movie Outside option     Theater 2  Movie B at Theater 1 Movie A at Theater 1 Movie B at Theater 2 Movie A at Theater 2 Theater 1 Movie B Movie A at Theater 2 Outside option Movie A at Theater 1 Movie B at Theater 2 Movie B at Theater 1 Movie  A     15  As competition usually drives prices down, to assess the profits of each competitor at equilibrium, I need to adequately capture not only how the lower prices would affect the consumers who switch among competing sellers yet basically remain in the market anyway but also how the lower prices may encourage consumers who otherwise would not purchase in the product category, i.e., the market expansion effect. This effect is primarily determined by how I characterize the substitution with the outside option. While the PD model allows a flexible structure to capture substitution (a) and (b), the substitution with the outside option remains to be relatively restrictive. Specifically, the outside option is assumed to be equivalent to a movie under the nesting structure by movies (Figure 2.1a) and to be equivalent to a theater under the nesting structure by theaters (Figure 2.1b). The implication of such an assumption is that the outside option would have a rather restrictive substitution pattern (i.e. IIA) with movies or theaters, respectively. I thus extend the PD model to the nested PD model by allowing the outside option to be at an extra nesting level in comparison to a cluster of movie-theater alternatives (Figure 2.3). This additional nesting level not only allows a separate parameter to capture the substitution with the outside option but also represents a more intuitive assumption: any choice alternatives involving viewing a movie at a theater would be more similar to one another, in comparison to the outside option.              Figure 2.3 The Nested PD Model      watching movies in theaters  Outside Option  Movie    Movie A at Theater 1 Movie A at Theater 2 Movie B at Theater 1 Movie B at Theater 2 Theater       16  Now I discuss the detailed specification of the nested PD model. The nested PD model is motivated by the generalized extreme value (GEV) model introduced by McFadden (1978). In my setting, each consumer   chooses among the available movie-theater combinations (  ) on a given day ( ), with the option of not watching any movie at a theater on that day. Assume that potential moviegoers watch at most one movie at a theater each day. Consumer  's utility of watching movie   at theater   on day   takes the following form:                    (2.1) where      is the mean value of consumer utility of watching movie   at theater   on day   and       measures the difference of consumer  's value for "product"    (movie-theater combination) on day   from the average valuation     . Specifically,       is a mean zero individual and product specific stochastic term and each consumer receives a random draw from its cumulative distribution  . The draws are independent across consumers but may be correlated across products that share similar product characteristics.  As for the mean utility     , throughout, I will assume that it is given by:                                                (2.2)      is the evening ticket price at theater   of movie j on day d. To capture the differential effect of pricing 3D movies, I create one dummy variable     to represent a 3D movie and then multiply that variable by the price charged.     is the movie fixed effect, which can be considered as the mean utility of movie j. I do not  use movie specific variables for two reasons. First, movie fixed effects would provide a better control of omitted variables. Secondly, movie specific variables like star power are potentially correlated with prices, which are of utmost importance in the present study.     is the "age" of movie   on day  , defined as the number of weeks since the release of movie  . To capture the observed decay pattern in box office revenues of most movies, I estimate movie specific decay effects.5     is the theater fixed effect that includes all theater specific characteristics that affect consumers' choices of theater  , such as the theater location, the chain the theater belongs to, the capacity and the quality of sound system and stadium seating.                                                          5 See Moul (2007). 17      is the day-of-week fixed effect (    = MON, TUE, ?, SUN). This variable is included because demand for movies varies on different days of a week. For instance, consumers have more leisure time over the weekend and are more likely go to movie theaters.6       represents all unobserved (by researchers) product characteristics. Given equal conditions, consumers prefer a product with high     .  The demand system is completed with a specification of the outside option (not watching a movie at a theater). Consumer  ?s utility from the outside option on day   is:                       (2.3) where     = MON, TUE, ?, SUN    is time-invariant constant and     is the day-of-week effect.      is the random utility specific to consumer   and the outside option on day  . Throughout, I normalize the mean utility of the outside option to be zero. To estimate the above model, I need to parameterize  . Based on Proposition 1 in Appendix A, different specifications of the function      in the Cumulative Distribution Function lead to different correlation patterns of       and hence different substitution patterns across products.7 The function      of the nested PD model takes the following form:                                                                    (2.4) where    is the set of theaters screening movie   on day   and    is the set of movies screened at theater   on day  ;       ,       ,      ;                     ,                    ,        . The parameter  ,    and    are nesting parameters that capture the degree of substitutability among options in the same group relative to the substitution among options in other groups. In my specification, the smaller the nesting parameter is, the larger substitution is among                                                         6 See Davis (2005). 7 Cumulative Distribution Function                                      18  options within group. For instance, suppose the price of movie   screened at theater   increases, consumers would consider switching to other options. If      , that is, consumers care more about what movie to watch, then they are more likely to choose movie   screened at another theater than other movies (whether screened at the same theater or not).8 To be consistent with the random utility maximization, nesting parameters must lie in the unit interval. As nesting parameters go to one, there is zero correlation between within-group options. By contrast, as nesting parameters approach zero, all options in the same group tend to be perfect substitutes. Both the nested logit model and the PD models belong to the GEV model family. The      function of a nested PD model is the weighted sum of      functions of two three-level nested logit models (Figure 2.4a and 2.4b) with    and    being the weights on movie and theater dimensions respectively. 9 In other words, the three-level nested logit model is a special case of the nested PD model. If   =1(  = 0), the nested PD model becomes a movie-primary NL model and a theater-primary NL model if    =1(  = 0). As mentioned above, the nested PD model is a PD model with one extra nesting structure on the top. This is reflected in the function      of the PD model:                                                              (2.5) The nesting parameter   in equation (2.4) captures the substitution of the "inside" options (viewing a movie at a theater) compared with the outside option and hence measures the market expansion (contraction) effect. When    , the model becomes a PD model which restrictively equalizes the effects of any change on the inside and outside options.10 As   becomes smaller, correlation between inside options becomes stronger and thus less substitution from the outside option and smaller market expansion (contraction) effect. When                                                         8 Assuming consumers still remain in the market, i.e., they do not choose the outside option. 9 In the movie-primary NL model, the function      takes the following form:                                       , where    is the set of theaters screening movie   on day  .  In the theater-primary NL model, the function      takes the following form:                                       , where    is the set of movies screened in theater t on day  . 10 Strictly speaking, equal effects only happen when the outside option and inside options have the same probability to begin with. 19    reaches another extreme, i.e. the case where    , there is perfect substitution among the inside options, meaning that any change in an inside choice alternative would ONLY affect other inside choice alternatives. In other words, there will be no substitution from the outside option and hence no market expansion (contraction).            Figure 2.4a  A Three-level Movie-Primary Nested Logit Model            Figure 2.4b  A Three-level Theater-Primary Nested Logit Model Figure 2.4 Three-level Nested Logit Models  2.4 Data Description In this section, I describe the data used for estimation. To empirically compare differential and uniform pricing strategies, I need to find a market in which I can observe price variation Theater Theater 2 Theater1 Movie B at Theater 1   Outside option Movie A at Theater 1 Movie B at Theater 2 Movie A at Theater 2       Movie B Movie A at Theater 2   Outside option Movie A at Theater 1 Movie B at Theater 2 Movie B at Theater 1 Movie A Movie        20  of movie titles within theaters. As mentioned earlier, Hong Kong is a market where I can observe how consumers react to the within-theater price variation. I combine data from multiple sources, both public and private, to generate a unique theatrical movie database for Hong Kong. I collect data on daily admission (the number of tickets sold in one day) and ticket price at theater-movie title level. I also have information on the characteristics of theaters such as the location, the chain brand name, the number of screens and seats for each screen. In addition, I collect movie title specific characteristics like genre, MPAA rating, movie critic ratings, running time, etc.     There is sufficient variation in my price data from three major sources. First, prices differ across theaters. Some theaters have better facilities or locate in a more desirable area and hence charge a higher price. Secondly, theaters charge different prices at different show times. All theaters reduce ticket prices on Tuesday ("Super Tuesday") for all movies, a practice that occurs in some North American cities as well. Also, some Hong Kong theaters charge higher prices on the weekend. Besides adjusting prices based on the day of a week, theaters set prices at different time slots on a single day as well. Most theaters charge a lower price in the morning.12 Since no hourly admission data are available and given the fact that evening admission accounts for the majority of daily admission, I use the evening ticket price to measure price.13 As stated in Section 2.1, a unique feature of my data is that there is within-theater price variation across movie titles. Table 2.1 shows the ticket prices for six theaters in Hong Kong. As in North America, 3D movies have higher prices than non-3D movies within every theater. More importantly for my study, in the same movie category (3D or non-3D), some movies charge higher prices than the others. Most of these higher priced movies are blockbusters with high production costs and long running times. It is worth pointing out that a movie's price in a given theater does not vary over time during its screen life. That is, once a price is set in the first week of a movie?s run, the price remains the same for as long as the movie runs in that theater.                                                          12 For example, the prices of morning shows at theaters of the Broadway chain are HK$28 less than the evening prices on average. "Morning" is defined as the period before 11:35a.m for all Broadway theaters except PALACE ifc (on or before 11:00a.m). 13 If defining the beginning of an evening to be 5pm, Ho (2005) shows that around 70% of the total admission comes from the evening showings using data from a multiplex movie theater in the Netherlands.  21  Table 2.1 Movie Prices in Hong Kong           AMC Festival Walk Broadway Tues Wan GH Mongkok MCL The Grand Cinema UA Cityplaza UA Langham The Dark Knight Rises  (non 3D) 90 85 90 85 70 90 The Dictator (non 3D) 70 65 70 75 55 70 3D The Amazing Spider-Man  115 100 115 125 100 115 3D Men in Black 3  100 90 100 115 75 95 Note: Prices are evening prices in HK dollars (HK$1   U.S.$0.13) on a non-Tuesday weekday.  To facilitate later estimation, I apply the following sampling criteria: (1) special preview showings are excluded; (2) each movie version (e.g., English and dubbed Cantonese) has to be shown for more than six days; and (3) each movie version has to be screened at more than one theater. Throughout my analysis period, new movie showings begin on Fridays and end on Thursdays. My data window is from June 7 (Friday), 2012 to August 30 (Thursday), 2012. The main reason for choosing this time period is that summer is a peak season for movies. During the summer, there are more blockbusters released and movie attendance is much higher than during most time of the year (except the Christmas and holiday season). The resultant sample contains 88 movie titles and 35 first-run theaters from 5 major theater chains (AMC, Broadway, Golden Harvest, MCL and UA) in Hong Kong and consists of 23140 observations, each of which is a movie-theater-day combination. 14  The selected sample accounts for about 90% of the population of the original dataset on the Hong Kong market from June 1 to August 31, 2012.                                                           14 Due to the agreement with the company that provides the data on theater admissions, I will not release the names of the theaters in estimation and simulations. Instead, a theater is identified with "Letter"+"Number", where ''Letter" stands for the chain the theater belongs to (A, B, C, D and E) and "Number" stands for the id of the theater in this chain. Theater Movie 22  Table 2.2 Summary Statistics for the Selected Sample (June 7, 2012-August 30, 2012) Variable Mean Std. Dev. Minimum Maximum Price 76 17.90 40 135 Market Share 0.00013 0.00019 3.10e-07 0.00264 Number of Showings 4 3.48 1 37 Number of Observations: 23140 Unit of Observation: per title per theater per day      By Movies     Total Daily Admission 2952 6477 8 83193 Total Number of Theaters 12 10.45 2 35 Average Number of Showings 3 2.23 1 21           By Theaters     Total Daily Admission 1854 1168.11 30 7691 Total Number of Movies 8 3.21 2 23 Average Number of Showings 4 1.47 1 13           Note:  Price is the evening price (HK$). Number of Showings measures how many times a movie is screened in a theater on a single day. market share of movie j at theater t on day d =                                              In the second panel: Total Daily Admission is the total number of tickets of a particular movie sold in one day. Total Number of Theaters is the total number of theaters screening a particular movie in one day. Average Number of Showings is the average number of showings of a particular movie across theaters screening it in one day. In the third panel: Total Daily admission is the total number of tickets a particular theater sells in one day. Total Number of Movies is the total number of movies screened at a particular theater in one day. Average Number of Showings is the average number of showings in a particular theater across movies screened in it in one day.   Table 2.2 provides summary statistics of major variables of interest for the selected sample. In the first panel, for all three variables (price, market share and the number of daily showings), the unit of observation is a movie-theater-day combination. As is shown, there is large variation in the price data. The average market share is very small because admission of a particular movie in a particular theater is small relative to the market size (the number of all potential moviegoers). On average, a theater shows one movie 4 times a day. The second and 23  the third panels provide summary statistics based on the movie and theater group, respectively. The average daily admission of a movie is 2952. On average, each movie is screened at 12 (of 35) theaters in one day and the average daily number of showings of a particular movie (across theaters screening this movie) is 3. There is considerable variation in these variables. A movie's daily admission can be as high as 83193. A movie can be screened in all theaters in the market and shown 21 times a day at the maximum. At the minimum only 8 people watch a movie. It is possible that on a single day a movie is shown only once and that a movie is screened in only 2 theaters. The third panel shows that on average a theater screens 8 movies every day. Variation in daily admissions across theaters is very large as well. This reflects the fact that theaters are differentiated in terms of their locations, the set of screening movies, the facilities, etc. The mean value of the average daily number of showings (across all movies screened in the theater) is 4. Theaters' decisions on the number of showings depend on many factors such as the appeal of movies, contracts with distributors and the capacity of the theater.   2.5 Demand Model Estimation and Results In this section, I present and analyze the estimation results. I first describe the estimation strategy of the nested PD model. And then I report results of the nested PD model and compare to the PD model and the three-level nested logit models.  2.5.1 Estimation Strategy As shown in the literature of discrete choice models, there exists a unique one-to-one mapping from observed market shares to the mean utility.15 One nice property of the nested PD model is that it has a closed form solution for market share:                                                                                    (2.6) where                                                                                                              15 For example, see Berry(1994), BLP (1995) and Nevo (2000). 24  Another appealing feature of the nested PD model is that I can avoid the contraction mapping procedure of inverting the systems of equations of market shares to get the mean utility. Based on Razzolini (2009), I derive the following regression equation from (2.6):                                                                                              (2.7) where                                     ;          is the market share of the movie-theater combination jt on day   conditional on movie j is chosen on day  ,         is the market share of the movie-theater combination jt on day   conditional on theater t is chosen on day   and        is the market share of the movie-theater combination jt on day   conditional on the inside option being chosen (i.e. viewing a movie at a theater).16 There are several sources of endogeneity in this regression equation. The first endogenous variable is price. The error term      contains unobserved movie and theater characteristics to researchers but known by theaters and taken into account when they set prices. In addition, since the error term      appears in market shares,        ,         and        are endogenous by construction. I use a standard nonlinear instrumental variable method to estimate regression equation (2.7). Specifically, I use generalized method of moments (GMM). The GMM estimator is constructed as below:                          where N is the sample size, Z is the set of instrumental variables and   is the standard weighting matrix. To implement the nonlinear GMM estimation, I need a set of valid instrument variables. Following the literature, I use the observed product characteristics of the competing products as instrumental variables.17 In particular, price has two instrumental variables: the average running time and the average budget of competing movies screened in the same theater on the same day. The justification of the first instrumental variable is that blockbusters typically                                                         16 To be specific, the conditional shares are computed in the following way:                        ,                      ,                          , where      is demand for movie   screened at theater   on day  . 17 See BLP(1995) and Nevo (2000). 25  have longer running times and charge higher prices.18 The movie production budget, as a measure of production cost, could be a potential instrumental variable for price. However, the final set of instrumental variables also keeps all exogenous variables, including movie fixed effects. Given that the budget and movie fixed effects are highly correlated, the weighting matrix   will become singular. Therefore, I do not consider the movie budget as a valid instrumental variable. Rather, I use the average budget of competing movies in the same theater on the same day, which vary by movie title, theater and time (day). The instrumental variables for each conditional market share are summarized in Table 2.3. The instrumental variables used in the nested PD model pass the over identification test (Woodridge 2002) at 10% significant level (J-statistic     ), implying that the sets of instrumental variables are not correlated with the error structures in the regression equation. In addition, the first stage regression of endogenous variables on the instrumental variables suggest that the coefficients of these instrumental variables are both statistically significant and economically meaningful. Table 2.3 Instrumental Variables for Conditional Market Shares  Conditional Market Share  Definition  Instrumental Variables         market share of the option jt on day   conditional on movie j is chosen                 the characteristics (the number of showings of movie j) of theater t's competing theaters  screening movie   on day            market share of the option jt on day   conditional on theater t is chosen                 the characteristics (critic ratings, the number of showings) of movie j's competing movies screened in theater   on day           market share of the option jt on day   conditional on an inside option is chosen (watching a movie in a theater)                      the characteristics (critic ratings, the number of showings) of option jt's  all competing movies and all competing theaters on day     2.5.2 Estimation Results For comparison, in addition to the nested PD model, I estimate three competing models: the                                                         18 Ainslie et al.(2005) include the running reel time of a movie to distinguish between blockbusters and art-house films as blockbusters typically have longer running times. 26  PD model and two three-level nested logit models.19 For the nested logit model, I consider two nesting structures: (1) the movie-primary NL model: all theaters that screen a specific movie form a group; (2) the theater-primary NL model: all movies screened at the same theater are grouped together. Table 2.4 presents results of the four models: the nested PD model, the PD model, the movie-primary NL model and the theater-primary NL model. I only report the key parameters of interest, which are nesting parameters   ,    and   ), two price coefficients (  and    ) and day-of-week effects.20  I believe that the nested PD model is the most appropriate model for my study for two reasons. First of all, the nested PD model outperforms the other three models in terms of the better model fit (its BIC is smallest among the four models) and plausibility of the parameter estimates.21 Secondly, as mentioned above, in theory it is difficult to justify a priori within this context which of the two nesting structure is the right one. Compared with the nested logit models, the nested PD model incorporates both dimensions of "differentiation" (movie and theater) into the model and lets data reveal the relative importance of these dimensions. Compared with the PD model, the nested PD model allows an additional parameter to capture the degree of substitution between the inside alternative choice (viewing a movie at a theater) in comparison to the outside option. In this sense, the nested PD model is a more flexible model that imposes fewer restrictions and produces a more reasonable substitution pattern.  In the nested PD model, both    (0.71) and    (0.80) are between zero and one. The fact that    is larger than    implies that consumers perceive the different theaters screening a particular movie to be more similar than movies screened within one theater. In other words, the movie dimension is a more important determinant of the consumer's utility than the theater dimension. This conclusion is supported by the result that the range of estimated movie fixed effects is larger than that of the estimated theater fixed effects. Here the range is defined as the difference between the highest and lowest estimate for the movie (theater) fixed effects. The range for the movie fixed effects is 5.343 whereas the range for the theater                                                         19 Please refer to Appendix B for estimation details of the PD model and the three-level nested logit models. 20 See Appendix C for the full report of theater and movie fixed effects for the nested PD model. 21 I use a GMM version BIC (Andrews 1999): GMM-BIC=J-(r-k)*log(N) where r is the number of moments; N is sample size; k is the number of parameters (r>k); J is Hansen's J-statistics used in the over identification test. The model with the smallest GMM BIC is preferred.  27  fixed effects is 1.583. The significance and magnitude (0.6) of   indicate existence of market expansion or contraction effect. This means that a drop in the price of a movie or a theater not only makes consumers switch to this movie or theater but also attracts more consumers who would otherwise choose the outside option (market expansion effect). Therefore it is important to model the first nesting level of the nesting structure where consumers decide whether to watch a movie at a theater. Table 2.4 Parameter Estimates for Different Demand Specifications Parameters Nested PD PD  Movie-Primary NL  Theater-Primary NL    0.71* 0.63* 0.64*   (0.005) (0.009) (0.016)     0.80* 0.61*  0.66*  (0.017) (0.005)  (0.023)   0.60*  0.36* 0.55*  (0.009)  (0.014) (0.025) Price   -0.06* -0.04   -0.04* -0.05*  (0.013) (0.020) (0.008) (0.008) Price (3D vs. non-3D)     0.02* 0.01   -0.02* -0.02*  (0.005) (0.008) (0.007) (0.006) Tuesday -0.53* -0.29 -0.03 -0.05  (0.179) (0.278) (0.168) (0.128) Wednesday -0.03* 1.48E-04 0.004 -0.01  (0.008) (0.012) (0.129) (0.095) Thursday 0.22* 0.28* 0.24 0.21*  (0.008) (0.012) (0.127) (0.093) Friday 0.35* 0.38* 0.38* 0.39*  (0.008) (0.012) (0.128) (0.095) Saturday 0.82* 0.83* 0.82* 0.85*  (0.011) (0.016) (0.128) (0.095) Sunday 0.77* 0.79* 0.76* 0.79*  (0.011) (0.016) (0.127) (0.094)  Number of Observations  23140 23140            23140    23140 GMM-BIC  -16.28 -13.77           -12.97   -12.92  Note:  Statistical significance of 5% is indicated by *. The standard errors are GMM standard errors with weighting  matrix            (Z is the set of instrumental variables).  28  Both estimated price parameters in the nested PD model have face validity. In particular, the single price coefficient   is negative and significant as expected.     is positive and significant, suggesting that demand for 3D movies is not as price sensitive as that for non-3D movies. All the day-of-week effects are reasonable and significant. Note that the base case is Monday. Since consumers are more likely to go to movie theaters over the weekend than on weekdays, both Sunday and Saturday effects are not only positive but also larger than the effects of other weekdays. Only Tuesday and Wednesday effects are negative and the Tuesday effect is smallest, suggesting that demand for movies is lowest on Tuesday.  Both nesting parameters for movies and theaters of the nested PD model are larger than their counterparts in the other 3 models, suggesting the smallest substitution effect within the same option group in the nested PD model. Note that    in the movie-primary NL model is smaller than    in the theater-primary NL model. This supports the result obtained in the nested PD model that the movie dimension has a greater impact on consumer preferences than the theater dimension. The nested PD model also has the largest   compared with the PD model and the nested logit models, suggesting the strongest market expansion (contraction) effect. The single price coefficient is very similar across the four models in terms of magnitude. In the PD model, however, the price coefficient is marginally significant (p-value = 0.055) at the 5% significance level. The results for the price coefficient of the 3D movies are not so consistent. In the PD model, this price coefficient is positive but not significant while in the two nested logit models it is significant and negative, which is not very plausible. As for the day of week effects, both Tuesday and Wednesday coefficients are insignificant except in the nested PD model, suggesting that there is no significant difference in demand for movies between Tuesday/Wednesday and Monday. The other day of week effects do not differ much in terms of both magnitude and sign across all models except that the Thursday effect is insignificant in the movie-primary NL model.  To have a good picture of the substitution pattern among the movie-theater options, in Table 2.5a, I present price elasticities based on the nested PD model for theater C2, one of the top 5 theaters based on admission.22 The first six rows give the own and cross price elasticities of movies screened at C2. The rest are the cross price elasticities between movies at C2 and                                                         22 I also calculated the elasticity estimates for other top four theaters and find a similar pattern. 29  movies at the other 4 theaters. For instance, for 3D Ice Ages (Cantonese) (m4 in Table 2.5a), its own price elasticity is -6.707, the cross price elasticity with respect to 3D the Amazing Spider-Man (m6 in Table 2.5a) screened at C2 is 0.050, the cross price elasticity with respect to 3D Ice Ages (Cantonese) screened at A1 is 0.263, and the cross price elasticity with respect to 3D the Amazing Spider-Man screened at A1 is 0.019. Evident from this table, own price elasticities are very high, ranging from -9.564 to -6.707. On  average, the mean cross-price elasticities between a movie with respect to other movies screened at C2 is lower than the mean cross-price elasticities between the same movie screened at other theaters (see Table 2.5b). Take The Dark Knight Rises (m7 in Table 2.5a) for example. Its cross price elasticity with respect to all other movies screened at C2 is about       (                                 ) on average. And its cross price elasticities with respect to The Dark Knight Rises screened at all the other 4 theaters are higher (A1: 0.617; D6: 0.632; E2: 0.743; E5: 1.024; and the average cross elasticity across these four theaters is 0.754). This is consistent with the earlier observation that different theaters screening a specific movie to be closer substitutes than different movies within a given theater.                  30     Table 2.5 Price Elasticities for Theater C2 Table 2.5a Own and Cross Price Elasticities   With respect to: Percentage change in:   C2    m2 m3 m4 m6 m7 m9 C2  m2 -6.782 0.164 0.204 0.188 0.219 0.181  m3 0.801 -7.117 0.986 0.884 1.086 0.840  m4 0.152 0.140 -6.707 0.166 0.200 0.159  m6 0.042 0.039 0.050 -7.841 0.054 0.043  m7 0.901 0.822 1.109 0.995 -9.564 0.945  m9 0.175 0.164 0.204 0.188 0.219 -8.159 A1 m4 0.078 0.078 0.263 0.078 0.078 0.078  m5 0.078 0.078 0.078 0.078 0.078 0.078  m6 0.019 0.019 0.019 0.313 0.019 0.019  m7 0.354 0.354 0.354 0.354 0.617 0.354 D6 m1 0.079 0.079 0.079 0.079 0.079 0.079  m4 0.066 0.066 0.195 0.066 0.066 0.066  m5 0.066 0.066 0.066 0.066 0.066 0.066  m6 0.019 0.019 0.019 0.301 0.019 0.019  m7 0.363 0.363 0.363 0.363 0.632 0.363  m8 0.079 0.079 0.079 0.079 0.079 0.079  m9 0.079 0.079 0.079 0.079 0.079 0.476  m11 0.079 0.079 0.079 0.079 0.079 0.079  m12 0.079 0.079 0.079 0.079 0.079 0.079 E2  m4 0.065 0.065 0.253 0.065 0.065 0.065  m6 0.011 0.011 0.011 0.174 0.011 0.011  m7 0.416 0.416 0.416 0.416 0.743 0.416  m9 0.019 0.019 0.019 0.019 0.019 0.271  m10 0.019 0.019 0.019 0.019 0.019 0.019 E5 m4 0.148 0.148 0.595 0.148 0.148 0.148  m6 0.032 0.032 0.032 0.546 0.032 0.032  m7 0.564 0.564 0.564 0.564 1.024 0.564  m9 0.062 0.062 0.062 0.062 0.062 0.730   m10 0.062 0.062 0.062 0.062 0.062 0.062 Note: Each entry in this table represents the percentage change in the share of movie i in theater C2 with respect to a percentage change in the price of each movie-theater pair.  Calculation is based on one Saturday (July 21, 2012). m1: Abraham Lincoln Vampire Hunter; m2: 2D Ice Ages (Cantonese); m4: 3D Ice Ages (Cantonese); m5: 3D Ice Ages (English); m3: 2D the Amazing Spider-Man; m6: 3D the Amazing Spider-Man; m7: The Dark Knight Rises; m8: Elles; m9: Painted Skin: the Resurrection; m10: Silenced; m11: The Four; m12: W.E.  31   Table 2.5b Comparison of Average Within and Across Theater Price Elasticities      m4 m6 m7 m9 Average Average within-Theater Cross Price Elasticity 0.510 0.484 0.356 0.434 0.446 Average across Theater Cross Price Elasticity  (with respect to the same movie)   0.326 0.333 0.754 0.492 0.476 Note:  m2 and m3 are only screened in C2 so they are omitted in this table.   2.6 Counterfactual Simulations In this section, I conduct counterfactual experiments using the estimation results of the nested PD model. In the main analysis, I consider two pricing games. The first one is a differential pricing game where each theater is maximizing its profits by choosing an optimal price for each of the movies that it screens. The second one is a uniform pricing game. In this case, following the current practice in the industry, I allow price to differ between 3D and non-3D movies. In other words, each theater is maximizing its profits by choosing one optimal price for all non-3D movies and one optimal price for all 3D movies. I compare the expected profits under each scenario and evaluate the two pricing strategies. I also conduct two supplementary analyses to further examine my supposition that intense competition decreases the benefits of differential pricing. In the first case, I assume that only one movie theater strategically sets price, essentially considering the case of a "monopoly" situation. In the second case, I limit the degree of price competition by restricting theaters to charge the same price for both English and dubbed Cantonese versions of the same movie and allowing a 3D movie to be priced at a uniform level above the price of its 2D version in all theaters. Main Counterfactual Analysis In order to perform the counterfactual exercises, I need to make some assumptions on the game structure. I assume that every day movie theaters compete in prices to sell differentiated products (movies) to consumers. For simplicity, I assume that the marginal costs of theaters are zero. This assumption relies on the fact that the marginal cost of serving one additional consumer is very small. Typically a theater's profits have two components. The first one comes from box office tickets sales. Movie theaters only take a fraction of the gross box office revenues based on the sharing rule specified in the contracts with distributors. Most contracts are "sliding scale" deals, meaning that distributor's 32  share of box office revenues decreases as the weeks go by. 23 For example, it can be as high as eighty percent in the first week and drops to sixty percent by the third week, and as low as thirty percent at the end of a movie's run. If the two parties anticipate that revenues might peak in later weeks, the contract usually includes a "best weeks" clause to ensure that the distributor gets the most revenues in the high demand weeks. If a week?s box office revenue is unusually high, the 90/10 provision will take effect, i.e., ninety percent of the movie?s box office revenues in that week go to the distributor, net of a flat payment to the theater ("house nut"). In general, the distributor chooses the rule that maximizes its share of the box office revenues for the given week. The terms on sharing rules of contracts typically vary by movie and by theater. For simplicity, I assume that each party's percentage share remains fixed throughout the run and is the same across all movies and all theaters and in particular I let theaters keep thirty percent of box office revenues on average.24  The second part is concession sales from selling soft drinks, popcorn, candies and other food, which are all kept by theaters. Since I do not have data on concession sales, I need to make the following two assumptions. First, I assume that an exogenous fraction of moviegoers buy food in the theater. In other words, the prices of food at concession stands are independent of demand for movies. I also assume that concession sales only depend on the number of tickets sold and not the price of the tickets. Similar assumptions are made in most movie scheduling models (Swami et al. 1999 and Eliashberg et al. 2009). I approximate the average concession profit contribution to be HK$13 based on the news report of Hong Kong Times and financial statements of a major theatrical chain Cineplex Odeon. Given these assumptions, each theater solves the following maximization problem in a differential pricing game:                                                                 (2.8)                        ,         ,                                                                  23 Unfortunately I do not have detailed information on contracts between distributors and theaters in Hong Kong. Given the high percentage of Hollywood movies in my data (63.24%), I assume that Hong Kong theaters and distributors follow the practice in North America. Here Hollywood movies are defined as movies screened in more than 600 theaters in North America in the opening week. 24 Raut et al. (2008) argue that a flat rate contract structure represents an attractive alternative to the current practice for distributors. 33  where P is a price vector that contains prices of all movies in all theaters on day  .                                                ,    is the number of movies screened in theater t on a given day and T is the total number of theaters.    is a vector of estimated demand parameters;   is the market size (i.e., all potential moviegoers);          is the fraction of box office revenues kept by theaters and   is the concession per person profit contribution. In the uniform pricing game, theater   maximizes its profit    subject to the constraint that prices of movies in the same category (3D or non-3D) are the same, that is,                             ,         I solve for a nonlinear equation system with the unknowns being prices and the equations being a set of first order conditions from the maximization problem (2.8). Due to the complexity of the equation system and limitation in computer power, I perform the counterfactual exercises only on Saturdays because Saturday sales are the highest compared with other days in a week.25 To have a better idea of how competition affects theaters' pricing decisions, I focus on a four-theater market. Specifically, I take the leading five theaters based on daily admission and run five simulations. In each of these simulations, one combination of four theaters compete with each other in prices. The results reported in Table 2.6 are the average results of each individual simulation.26 For both the uniform (Table 2.6a) and differential pricing (Table 2.6b) games, I report the average price, daily admissions and profits of each theater. In the case of the uniform pricing game, I also report the un-weighted 2D and 3D prices. For a given theater, the average price is the weighted average across all movie titles and days (12 Saturdays), with the weights being each movie's daily admission in this theater (                                        ). The reported admissions and profits are aggregated across movie titles                                                         25 In my sample, total admissions on all Saturdays are the highest compared with those of other days of a week. In my sample (June 7, 2012-August 30, 2012), there are 12 Saturdays in total. 26 The idea is similar to bootstrapping. 34  and days (                                          27  As evident in the first column of Table 2.6b, there is substantial price variation across movie titles in the differential pricing game. The average standard deviation across theaters is about $29. This shows that theaters are able to extract more consumer surplus by raising prices of high appeal movies and reducing prices of low appeal movies. Compared with the uniform prices, the differential prices are slightly lower in general. At each theater, the uniform prices are between the minimum and maximum differential prices, as expected. As for admissions and profits, an important observation from Table 2.6c is that when theaters compete in prices, not every theater is better off by charging differential prices. In this particular scenario, the two theaters in theater chain E earn lower profits when every theater switches from uniform pricing to differential pricing. The whole market still prefers differential pricing to uniform pricing (the demand effect dominates) but the difference between the profits of these two pricing strategies is very small (about 1.4% change). One possible explanation is that theaters are becoming so competitive in the differential pricing game that potential gains from additional surplus extraction under differential pricing are offset to a large extent (the competition effect). In other words, uniform prices soften competition, which would otherwise be intense under the differential pricing strategy.    Table 2.6 Counterfactual Results of the 4-Theater Market (Competition) Table 2.6a  Uniform Pricing Strategy  Theater Average Price  2D Uniform Price  3D Uniform Price Admission Profit (HK$) A1 72 68 129 871493 29987250 C2 79 74 137 599565 21852750 D6 87 80 145 392490 15219750 E2 56 54 114 1021593 30526500 E5 83 76 138 523380 19598250 Total      3408520 117184500 Note:  Average Price is the average weighted (by admission) price paid by all people who attend the theater.  2D Uniform Price and 3D Uniform Price are un-weighted prices.                                                         27 Note that theaters do not necessarily show the same set of movies at a given time. As the product assortment issue is not the focus of this study, in my simulation, I take the movie programming choices as given. 35    Table 2.6b  Differential Pricing Strategy  Theater Average Price 2D  Min 2D Max 3D Min 3D Max Std. Dev. Admission Profit (HK$) A1 71 59 88 121 140 28.40 915370 31191000 C2 78 64 88 128 170 29.95 633228 22802500 D6 86 72 101 137 164 29.84 399305 15402750 E2 56 49 58 106 119 28.72 1010870 30169750 E5 82 70 90 133 150 29.85 516413 19273250 Total            3475185 118839250 Note: Average Price is the average weighted (by admission) price paid by all people who attend the theater.    Table 2.6c  Comparison of the Uniform and the Differential Pricing Strategy  Theater Uniform Admission Uniform Profit (HK$) Differential Admission Differential Profit (HK$) Admission Ratio Profit Ratio A1 871493 29987250 915370 31191000 1.050 1.040 C2 599565 21852750 633228 22802500 1.056 1.043 D6 392490 15219750 399305 15402750 1.017 1.012 E2 1021593 30526500 1010870 30169750 0.990 0.988 E5 523380 19598250 516413 19273250 0.987 0.983 Total 3408520 117184500 3475185 118839250 1.020 1.014  Supplementary Counterfactual Analyses. To get a better idea of how competition affects theaters' pricing decisions, I do the following two additional counterfactual exercises. I first consider a scenario where only one theater strategically chooses prices to maximize its profit taking all other theaters' prices as given.28 This single player will set its price as if it were a monopolist.29 The idea is to compare the differential and uniform pricing strategies in the absence of competition. Specifically, I take four theaters that have the highest admissions and each theater takes turn to be the "monopolist". As a result, I perform this counterfactual simulation four times. The results of each simulation are presented in Table 2.7. As in the case where all theaters compete, uniform prices are still higher than the differential prices on                                                         28 In the simulation, I use the actual prices. 29 To be precise, it is a monopolist on the residual demand curve. 36  average. There is less price variation in the differential prices (Table 2.7b) as compared to the competitive case. As shown in Table 2.7c, the main difference is that now every theater is better off by charging differential prices. Given that this is the monopoly case, this is the expected result and demonstrates that the demand effect exists. Increases in profits from differential pricing due to the absence of competition are also consistent with the view that the competition effect is substantial.   Table 2.7 Counterfactual Results of the 4-Theater Market (Monopolist) Table 2.7a  Uniform Pricing Strategy  Theater Average Price  2D Uniform Price  3D Uniform Price Admission Profit (HK$) A1 61 58 94 1722800 53671000 C2 67 65 101 1338900 44308000 D6 73 70 107 973440 34051000 E5 70 67 102 1193700 40664000          Note:  Average Price is the average weighted (by admission) price paid by all people who attend the theater.  2D Uniform Price and 3D Uniform Price are un-weighted prices.    Table 2.7b  Differential Pricing Strategy  Theater Average Price Min Max Std. Dev. Admission Profit (HK$) A1 60 50 97 17.12 1775600 54972000 C2 66 54 131 18.78 1390200 45635000 D6 73 62 128 18.52 983230 34283000 E5 70 60 114 18.29 1207700 40945000        Note:  Average Price is the average weighted (by admission) price paid by all people who attend the theater.        37   Table 2.7c  Comparison of the Uniform and Differential Pricing Strategy  Theater Uniform Admission Uniform Profit (HK$) Differential Admission  Differential Profit (HK$) Admission Ratio Profit Ratio A1 1722800 53671000 1775600 54972000 1.031 1.024 C2 1338900 44308000 1390200 45635000 1.038 1.030 D6 973440 34051000 983230 34283000 1.010 1.007 E5 1193700 40664000 1207700 40945000 1.012 1.007                The second counterfactual exercise I perform is to simulate a restricted differential pricing game. Full price differentiation under which each movie has its own price may overly intensify price competition. Now I soften competition by imposing two restrictions on theaters' pricing decisions: (1) the difference between the price of a 3D movie (e.g., 3D Marvel's The Avengers) and its 2D counterpart (e.g., 2D Marvel's The Avengers) is a constant across all movies in a given theater; (2) different language versions of the same movie (e.g., the English (original) and dubbed Cantonese versions of Brave) charge the same price. 30 While not all movies in my sample have both English and Cantonese versions, in the main analysis I allow for different prices as they target at different consumer segments.31 Under the second restriction, Brave English and Brave Cantonese share the same price. The results of this simulation are reported in Table 2.8. Compared with the unrestricted differential pricing game, there is less price variation within theaters and a majority of theaters' admissions and profits are much higher. Compared with uniform pricing, the aggregate profit increases by 18% when all theaters engage in the restricted differential pricing policy while there is only a 1.4% increase when theaters adapt the unrestricted differential pricing policy. The result that the whole market achieves a superior performance level under the restricted differential pricing is again in line with the notion that competition is dampening the demand effect and hereby reduces profits.                                                            30 Based on the average difference of actual ticket prices between 2D and 3D movies in the Hong Kong market, I make it HK$30. 31 For instance, children and the elderly who cannot speak English will choose the dubbed version only. 38  Table 2.8 Counterfactual Results of the 4-Theater Market (Restricted Differential Pricing) Table 2.8a  Restricted Differential Pricing Strategy  Theater Average Price Min Max Std. Dev. Admission Profit (HK$) A1 71 44 129 21.91 1143655 39157250 C2 76 41 170 27.23 842518 29739250 D6 85 56 186 31.90 559665 21247000 E2 54 36 119 27.13 1302600 38067750 E5 79 72 162 32.84 414293 15135000 Total        4262730 143346250 Note:  Average Price is the average weighted (by admission) price paid by all people who attend the theater.     Table 2.8b Comparison of the Uniform and Restricted Differential Pricing Strategy  Theater Uniform Admission Uniform Profit (HK$) Differential Admission  Differential Profit (HK$) Admission Ratio Profit Ratio A1 871493 29987250 1143655 39157250 1.312 1.306 C2 599565 21852750 842518 29739250 1.405 1.361 D6 392490 15219750 559665 21247000 1.426 1.396 E2 1021593 30526500 1302600 38067750 1.275 1.247 E5 523380 19598250 414293 15135000 0.792 0.772 Total 3408520 117184500 4262730 143346250 1.251 1.223  As a robustness check, I perform similar analyses on all the Hong Kong movie theaters in my sample to compare the results for differential and uniform pricing and find results similar to those reported above.  The results are presented in Appendix D.    2.7 Conclusions In this chapter, I empirically compare the profitability of two pricing strategies for competing movie theaters, namely the uniform pricing and differential pricing schemes. My research contributes to the literature on uniform pricing for differentiated products, a practice not unique to the movie industry. In particular, I study how competition, a factor rarely considered in the literature, dampens the incremental gains of differential pricing over uniform pricing. In terms of methodology, I extend the PD model introduced by Bresnahan et 39  al. (1997) to the nested PD model, which allows more flexible substitution between the outside option and the alternatives in the "inside" product category. I first estimate the nested PD demand model using data from the Hong Kong movie market, which is one of the few markets where one can observe some degree of price variation across movie titles within theaters. For comparison, I also estimate several competing models, namely the PD model and the three level nested logit model nested by movie or by theater. I find that the nested PD model is the most appropriate model in the context of this study. Using the estimation results, I then conduct counterfactual experiments to compare profits simulated under the uniform and differential pricing strategies. I find that differential pricing dominates the uniform pricing (demand effect) but gains from the differential pricing policy are limited by the presence of competition (competition effect).                      40  Chapter 3  Competition in Retail Gasoline Markets  3.1 Introduction It is important for firms to understand market structure and its impact on prices. Knowledge of market structure is also crucial in firms' entry decisions. Policy makers ? particularly those charged with administering competition laws ? are interested in assessing the extent of intra-industry competition as well. In this chapter, I investigate retail gasoline prices and market structure in isolated markets that are located near the entrance to national parks in the U.S..  This study falls in a strand of the literature that uses reduced-form estimations of the relationship between price (or markup) levels and covariates that include station attributes and market characteristics. Most studies in this literature treat the number of gas stations in the market as an exogenous regressor in a pricing or markup equation. Therefore, the effect of market structure from these estimations is likely biased due to correlation between the number of firms in the market and unobservable factors affecting prices.32 In other words, the equilibrium number of firms is endogenous and is likely to be a function of unobserved demand and cost shifters (Bresnahan 1989). To estimate the true effect of competition on prices, one approach is to use instrumental variables. However, valid instrument variables for the number of firms are not readily available since it is difficult to find one that affects firms' entry-exit decisions but is exogenous in the price equation. My data include weekly prices for gas stations in 45 isolated markets located near the entrance to national parks in the U.S. and spans more than three years. Due to the highly temporal visits to the national parks, a distinctive feature of these markets is that their sizes vary significantly over time and are only partially explained by the local permanent population. The number of visitors to a national park on a given month can change from 10 to even 100 times the local population. In this setting, I can use past visits as a valid                                                         32 It must be emphasized that the main goal of some of these papers is not to find causality but to relate the theoretical literature with the empirical correlations between market structure and price levels or price dispersion.  41  instrumental variable. Past visits are a proxy for the expected long-term market size and therefore affect entry and exit decisions. Moreover, gasoline prices on any given week are influenced by the contemporaneous market size which, in this environment, is not correlated to the average market size. The IV estimates suggest that ignoring the endogeneity bias leads to underestimation of the effect of competition on prices by around 55 and 70 percent depending on the specification used. The size and location of the markets I study allow me to circumvent market boundary issues that arise in larger metropolitan areas. I measure competition by the count of gas stations in each town. I find that entry by an additional gas station leads to a large and negative price reduction in markets with few incumbents and this effect diminishes drastically in markets with more gas stations.33 Like Sen (2005) and Hastings (2004), I also find that a station brand and its competitors' brand affiliation play an important role in explaining price levels. Finally, I exploit the large cost and demand shocks in my data to study the price pass-through conditioning on market structure. I find evidence of local market power in the studied markets. Gas stations in markets with few competitors face less elastic demands and therefore react to a demand shock by increasing prices more than gas stations in less concentrated markets do. Similarly, the proportion of a cost shock passed to prices increases with the number of gas stations in the market. The rest of the chapter is organized as follows. Section 3.2 provides a brief review of the related literature. Section 3.3 discusses the empirical specification and the theoretical predictions. The data, the instrumental variables and markets are described in Section 3.4. Section 3.5 presents the results and concluding remarks are offered in Section 3.6.  3.2 Related Literature For a long time, and perhaps driven by media stories of price gouging, retail gasoline markets have attracted attention from governments and academia. As a result, there is a large literature developed on various topics in this market. Studies that look at the dynamic pattern of retail gasoline prices have found evidence of asymmetric responses to cost shocks (Bettendorf et al. 2003; Verlinda 2008; Lewis 2011) and the presence of Edgeworth Cycles                                                         33 When the number of firms is more than eleven, additional one firm reduces price less than 1 cent per gallon. 42  (Noel 2007a,b; Wang 2009). Price dispersion of retail gasoline prices has also been linked to spatial differentiation (Houde 2012) and consumer search (Chandra and Tappata 2011). In general, there is evidence overwhelmingly pointing to the presence of market power at the gas station level in the retail gasoline markets. Many of the above mentioned price patterns are consistent with models of tacit collusion or imperfect competition. Marvel (1978) estimates the determinants of the level of retail gasoline prices in 22 U.S. cities from 1964 to 1971. He finds that collusive pricing was practiced in at least some portions of the retail gasoline market in the period studied. Shepard (1991) rejects the competing hypothesis of peak-load pricing as an explanation of the observed price discrimination practices in retail gasoline markets. Using panel data on sales volume and gasoline prices in 43 U.S. cities over 72 months, Borenstein and Shepard (1996) find that the observed price patterns in retail gasoline markets consistent with predictions of implicit collusion models among firms. Borenstein et al. (1997) show that asymmetry responses to shocks reflects short run market power among retail gasoline sellers. Eckert and West (2005) investigate the underlying market structure that generates price uniformity observed in the gasoline market in Vancouver, BC. They conclude that tacit collusion at the brand level and imperfectly competitive non-collusive competition in a spatial market are two alternative explanations for observed price uniformity. One typical approach in the literature to explore determinants of gasoline prices is to include market structure variables (station density or concentration measure like Herfindahl-Hirschman Index, HHI) and other factors like costs and gas station characteristics in a reduced form price/markup equation. The results from the existing literature have been mixed. Ning and Haining (2003) explain spatial variation in prices in the retail gasoline market in Sheffield, England. The analysis draws on both supply-side and demand-side factors. They find a statistically significant positive relationship between a gas station?s price and prices of its competitors in the same local market. Using a dataset on the retail gasoline market of Lexington, Kentucky from May to August 2001, Cooper and Jones (2007) examine the pricing behavior of gasoline retailers located on commuter routes. Each route rather than the entire city is treated as a separate market. This study uses location and the number of competitors to measure market concentration. The main finding is that (1) increased station density on a commuter route decreases prices; (2) the count of competitors between a station 43  and the central business district has a larger impact on prices than the density of competitors further from the central business district. On the contrary, Hosken et al. (2008) find that local station density does not affect prices, drawing on a three year panel of prices from a sample of gasoline stations located in suburban Washington DC.  While the above mentioned papers use station level data, some other studies rely on city/state level data to explore the relationship between market structure and prices at the macro level. Using a monthly panel data for 48 U.S. states from 1989 to 1997, Chouinard and Perloff (2007) determine the relative importance of factors that impact gasoline prices such as crude oil prices, tax, environmental regulation, market power and so on. Two measures of market power are used: (1) an dummy variable equal to zero prior to an merger and one thereafter; and (2) the number of stations per square mile. The results suggest that the major variation in national gasoline prices is due to a rise in the price of crude oil over the sample period. Sen (2003) investigates whether higher retail gasoline prices in Canada are the result of international crude oil price fluctuations or local market power exercised by large vertically-integrated firms, based on a city level monthly panel dataset of major Canada gasoline markets. It is shown that wholesale prices play a larger role in price determination than city level market structures. Using the same dataset in Sen (2003), Sen (2005) finds that increasing market shares of smaller or independent gasoline retailers are associated with lower retail prices.    As mentioned above, one issue in this line of research is that market structure is endogenous. That is, the error terms contains unobserved cost and demand factors that are correlated with both prices and market structure variables, leading to inconsistent estimation. This problem is well documented in the empirical price-concentration literature. Evans et al. (1993) formally address the endogeneity issue in a study of the airline industry. They find that the impact of concentration on prices is severely biased using OLS estimation method without correcting for endogeneity. One solution they suggest is a combination of fixed effects and instrumental variables based on panel data. An obvious limitation of this approach is data availability. Another remedy for this problem is a two-stage method. The idea is similar to adding a selection equation proposed by Heckman (1979). In this context, the first stage selection equation is the entry threshold equation in Bresnahan and Reiss (1991). The second stage price equation includes a correction term based on the first stage estimates (similar to the 44  inverse Mills ratio) so that the market structure variable is not correlated with the new error term. This method has been adapted in a several studies (Mazzeo 2002a; Manuszak and Moul 2008; Singh and Zhu 2008). Reiss and Spiller (1989) employ a unique structural approach taking the effect of market structure on both outcomes (price and entry) simultaneously. There are two limitations of this approach: (1) it is based on assumptions about the nature of price competition, a common problem with all structural models; (2) it is difficult to solve for all the equilibrium prices and quantities in a game with more than 2 firms.  The classical way of addressing endogeneity, the instrumental variable approach, has limited success mainly because it is usually difficult to obtain a valid instrumental variable that affects market structure but not prices. There are numerous studies of relationship between market structure and prices on a wide range of industries.34 To name a few, Cotterill?s (1986) on grocery, Borenstein (1989) and Borenstein and Rose (1994) on airline, Calem and Carlino (1991) on banking, Emmons and Prager (1997) on cable television, Claycombe (2000) on household furniture and clothes, Asplund and Sandin (1999) on driving lessons, Ville Aalto-Set  l   (2002) on food retailing, Newmark (1998) and Azzam and Rosenbaum (2001) on cement. To my knowledge, the only two papers that use the instrumental variable approach are Borenstein (1989) and Borenstein and Rose (1994). Both use the characteristics of competitors as instrumental variables for endogenous market structure variables. The identification assumption is that the concentration of the flights on a route not performed by the observed airline is exogenous to the price of the observed carrier.  Similarly, in the gasoline literature, very few studies use the instrumental variable approach to fix the problem. Barron et al. (2004a) review different models for equilibrium price dispersion and then empirically estimate the relationships between seller density and the level and dispersion of gasoline prices in the retail gasoline industry. In the price equation (the dependent variable is retail margin), they include the number of stations within a 1.5-mile radius around station. The paper recognizes the limitations of this empirical analysis by pointing out "both price and the number of sellers in a market are endogenous variables....the                                                         34 Weiss (1989) summarizes more than 100 empirical studies that regressed price on some measure of market concentration controlling for variables related to market level costs in markets of a homogeneous product. Also see survey by Newmark (2004). 45  observed relationship between a change in market density and the expected price cannot accurately capture sellers? pricing responses to an increase in the number of sellers in the market alone." Instead of directly resolving the endogeneity problem, they argue that their specification can reveal whether the correlation between seller density and expected price is as predicted by the particular model in question, which is enough for the research purpose of their study. To my knowledge, the only paper in the gasoline literature that attempts to endogenize market structure by using an instrumental variable is Clemenz and Gugler (2006). Using district level data on Austrian retail gasoline market, this study first tests empirically two hypotheses of spatial competition model: (1) with free entry, retail firm density tends to be higher when the population density is higher; (2) with spatial competition, equilibrium prices tend to be lower when the firm density is higher. And then they infer the nature of market structure (price competition or collusion) based on the empirical evidence. The results show a negative association between prices and stations density. Based on the first hypothesis and the argument that population density is exogenous to prices, they use the population density as the instrumental variable for market structure variable (the number of gasoline station per square km in the district) in the markup equation.   Based on the nature of the data, I propose instrumental variables to resolve the endogeneity problem based on the number of visitors in previous time periods. I argue that the proposed instrumental variables are valid for the following reasons. First of all, entry and hence the number of the gas stations in the market is determined by the foretasted average market size which is the combination of the average number of visitors and population. And at the meantime, average visits do not affect prices in a given month. More detailed discussion on the instrumental variables will be provided below.  3.3 Empirical Specification The goal in this chapter is to identify the effect of competition on market prices. The empirical specification is straightforward since, unlike other industries, gasoline retailing resembles standard "textbook" markets of homogenous goods. The product under study is 46  well defined and firms use simple pricing policies. 35 The prices observed in the data are the uniform transacted prices paid by customers. 36  The product is fairly homogeneous and differentiation, if any, is easily captured by brand identity, fuel type, or station location. 37 In addition, the production technology is very rigid and similar across stations. Moreover, capacity constraints appear to be irrelevant in gasoline retailing.38 Consistent with the industry description provided above, the baseline specification has the following form:                                                (3.1) where      is the price charged by station i at time t in city/market m. Wholesale cost shocks are assumed to be symmetric and are captured by   .39 The variable       measures one vertical differentiation attribute, the fuel type. Besides, following the literature (e.g., Hastings 2004), I create a "brand" dummy variable that classifies stations into high and low value brand stations to capture perceived quality differences by consumers.40 The vector     has market level demographic variables including income, population and the number of visitors to market m's closest national park. Last,    includes different competition metrics (more on this below). I also include other covariates related to market structure that can potentially affect prices (e.g., station i's distance to the park entrance, its distance to the closest competitor and the closest competitor's brand). There are two issues associated with the estimation of the coefficient for   . First, as mentioned earlier, OLS estimation of equation (3.1) can generate biased estimators due to the endogeneity of the number of firms. The term      might contain market-specific unobservable factors that affect cost or consumers' willingness to pay and therefore the number of active firms in the market. For example, if the unobservable factors are associated with positive demand shifters, the OLS estimates would predict a weaker or even positive                                                         35 Gas stations are truly brick and mortar stores and therefore I do not need to worry about the possibility of an online substitute product when defining market boundaries. 36 Promotions, discounts and third degree price discrimination strategies are very rare in this industry. 37 Hosken et al. (2008) show that other stations' attributes are not statistically significant if station brands are included. 38 This assumption is common in metropolitan areas but it could potentially be too strong in isolated markets like the ones used in this study. 39 The assumption of constant marginal cost is common in the gasoline literature. 40  High quality brands are defined to be the following 9 major brands: 76, BP, CHEVRON, CONOCO, EXXON, MOBIL,  PHILLIPS 66,  SHELL and TEXACO. 47  relationship between prices and firms. Those estimates would be capturing the fact that, other things equal, markets that support higher prices also attract more firms. The bias could go the other way if the unobservable factors are associated with lower costs. In such a case, the effect of competition on prices would be overestimated: prices are lower when there are more firms but also there are more firms in markets where costs are lower. I address the endogeneity problem using instrumental variables that affect firms' entry-exit decisions and hence the number of firms but are exogenous in the price equation. Specifically, the instrumental variables I use are based on the average number of visitors to the closest national park to the market between 2002 to 2005. Past average visits are a proxy for the expected long-run market size and therefore affect the profit equation that underlines entry and exit decisions by firms in a given market. Meanwhile, the large volatility in visitors makes the average market size to be uncorrelated (after controlling for other covariates) with everyday pricing decisions by firms.41  The second issue relates to the fact that, in theory, the relationship between prices and the number of firms needs not to be linear. Assuming no cartel behavior, we expect prices to be lower in markets that, other things equal, have more firms. However, we are agnostic about the speed at which this process occurs or the number of firms required to reach a competitive outcome. A Cournot model with linear demand and constant marginal cost predicts a convex relationship between market prices and the number of firms. On the other hand, a Bertrand model with homogeneous products only requires two firms to achieve the competitive outcome. The latter extreme result is tempered once we allow for product differentiation, and the price-competition relationship approaches the Cournot nonlinear prediction. For example, a logit model generates free-entry equilibrium prices that are a linear function of the marginal cost, consumers' preference for diversity and the ratio between entry cost and the number of firms (Anderson and De Palma 1992). On the other hand, consumer search models predict non-monotonic relationships between prices and the number of firms. In these models, posted prices can even increase in more competitive markets (Janssen and Moraga-Gonz  lez 2004). As shown in Section 3.5, examination of the data supports a nonlinear relationship between prices and the number of firms.                                                         41 It is important to note that the proposed instrumental variables would not be valid in contexts where the market size is stable. 48  The extent of local market power is related to the elasticity of the demand faced by each firm in the market. At one extreme of the competition spectrum, monopolists serve the entire market demand. At the other extreme, firms in perfectly competitive markets cannot sell at prices different than the market price. The demand elasticity faced by oligopolistic firms lies somewhere between these two extreme cases and depends on the strength of product differentiation. At the same time, product differentiation is a function of consumer preferences and the number of firms populating the product space. In other words, the way market demand translates into firm demands when departing from the monopoly outcome depends on competition conduct and consumer preferences. A way to assess the effect of additional firms on the demand elasticity perceived by firms is to estimate the impact of cost and demand shocks on market prices. Again, the monopoly and perfectly competitive market structures provide me with the benchmarks to compare my estimates. The post-shock new equilibrium price is determined from the marginal cost and marginal revenue equality in the monopoly case, and from market demand and short-run supply in the competitive case. Therefore, competitive markets are associated with larger cost pass-through and smaller price increases after a demand shock than monopolies.42 My data allow me to study the effect that cost and demand shocks have on prices under different market configurations. In that sense, I can see the extent to which we depart from the monopoly-like result as markets become more dense.  3.4 Data Description I combine data from four different sources. The first dataset contains information on gasoline prices and stations. The data were originally collected by Oil Price Information Service (OPIS) from credit card and fleet card transactions.43 One advantage of using OPIS data is the extensive coverage of stations.44 The data cover daily pricing by 267 stations in 45                                                         42In a perfectly competitive market, if firms face constant marginal cost, all the adjustment to demand shock is done through quantities while monopolists adjust both prices and quantities. In between the two cases, i.e., in markets with various degree of market power, demand shocks result in a price change and the size of this change is larger the more market power firms have. 43 OPIS data were made public trough the AAA website. 44 Note that it is possible that some of the stations in the population are not in the data. OPIS coverage of stations has improved significantly over time. Chandra and Tappata (2011) use similar data for the states of CA, 49  isolated markets from January 2006 to May 2009. I collect information on the price charged, fuel type (regular, midgrade, premium and diesel), date, station brand and station address. The dataset includes all types of service stations: independently owned, jobber owned or company owned.  The markets I study are in towns located near the entrances to a U.S. national park (see Table A.4 and Table A.5 in Appendix E). The demand for gasoline in these markets is therefore determined by the stable local population and park visitors. More importantly, the seasonality of visits causes the market size to vary significantly from summer to winter. I obtained data on monthly recreational visits to the parks from the U.S. National Park Service. National parks commonly comprise a large extension of land and are sometimes associated with many towns through their various entrances. When this is the case, I allocate park visits amongst the associated towns using available information by count location (see Table A.5 in Appendix E).45 Data availability on gas station prices and the fact that some parks are not accessible by car led to the final sample containing 31 parks (21 national parks and 10 national historical parks) associated with 45 towns. The average population of these towns is 5634 inhabitants. 11 towns have just one gasoline station and only 5 towns have more than 10 stations. Table A.4 in the Appendix E displays the list of parks and summary statistics of the monthly visits during the period analyzed. The table shows significant time and cross-section dispersion in park visits. The cross-section dispersion is mainly explained by the popularity of a park and its distance to major urban centers. On the other hand, time dispersion is mainly driven by seasonality in tourism. Figure 3.1 shows representative patterns present in the data. For illustration purposes, I scaled visits by creating an index that captures the deviation from the park mean in a given calendar year (visitors index=monthly visits*100/ average annual visits). For example, visits to Yellowstone National Park are highly seasonal and can easily triple the average annual visits in the summer months; and visits to Colonial National Historic Park are less volatile although still show seasonality.                                                                                                                                                                            FL, NJ and TX and find that the number of stations covered by OPIS is more than 90% of the population of stations reported by the Census Bureau in those states. 45 Park visits are obtained from vehicle counts in different count locations across the park. The conversion and aggregation process is described for each park in I split visits to a park using town and vehicle count locations only when the park is associated with more than one town.  50    Figure 3.1 Park Visits and Seasonality I calculated the driving distance between all pairs of stations in each town and the driving distance from each station to the park's closest entrance.46 I consider market size to match the town boundaries. This is a natural definition given the small size of the towns in the database. Alternatively, and consistent with the literature and industry practice in larger metropolitan areas, I define local markets around each station including all stations within two driving miles of it. The latter definitions imply that there are as many "markets" as stations in the sample, and many of them overlap. Figure 3.2 shows the distribution of stations per town and the average number of stations under the two-mile market definition.                                                           46 I used Google's driving directions application to record driving distances. Given the nature of these markets, using Euclidean distances can easily lead to underestimated distances. 51                                          a) Town                                                       b) Two-mile Boundary Markets Figure 3.2 Distribution of Gas Stations by Market Definition The third dataset includes a proxy for the wholesale cost of gasoline. Stations acquire gasoline at different prices depending on their degree of vertical integration. For example, open dealers and independents pay the branded and unbranded "rack" prices at the terminal.47 Company operated stations are fully integrated while Leasee Dealers obtain the gasoline directly from the refinery at the "Dealer Tank Wagon" (DTW) price, which is private and includes delivery to the station.48 I do not observe these wholesale prices. Instead, I use weekday spot prices from the Energy Information Administration (EIA). These are prices transacted further upstream in the vertical chain and behave very similar to the DTW and rack prices. Based on EIA surveys of stations, the correlation between the rack and spot price is above 99% (Chandra and Tappata 2011).49 Note that my goal is to use the spot price as a wholesale cost or markup shifter and not to estimate with precision the markup level. I complement the data with income and population controls from the 2010 U.S. Census. Income is measured at the county level and population is based on population of the census tracts surrounding a gas station.                                                          47 Open dealer stations are gas stations who sign a contract with a branded refiner to sell its brand of gasoline. Independents are gas stations that can sell any type of gasoline. Independents arbitrage by always buying the cheapest rack price. This is usually the unbranded price although there are cases of inverted rack prices. 48 If a gas station is company operated (company-op), the refiner owns the station and manages the station directly. In the case of lessee dealer, the refiner owns the gas station and leases it to a lessee (a residual claimant) who is responsible for managing the station. 49 The EIA collects DTW and rack prices through monthly surveys and these data are available its website. 52  Table 3.1 Summary Statistics   Mean Median Std. Dev. Min Max  Observation Prices (cents/gallon)       Regular 281.5 284.3 67.2 132.3 555.9 18100 Midgrade 288.7 291.9 66.5 141.9 509.9 6450 Premium 298.3 299.9 65.9 145.9 523.9 5684 Diesel 316.3 294.9 74.4 184.9 599.9 9688        Markups (cents/gallon)       Regular 82.3 77.6 28.7 2.1 324.3 18100 Diesel 116.2 108.8 43.3 18.7 433.7 9688        Market Characteristics       Visitors 89504 30097 124683 0 691787 39922 Visits_Dev 5386 -302 72459 -208653 471543 39922 Population 5634 5403 3582 28 14102 39922 Income 43746 42395 14801 22264 78234 39922 N (town) 13 12 9 1 25 39922 N (2mi) 5 5 3 1 13 39922 Dist2rival (mi) 0.73 0.29 1.45 0 19 38766 Dist2park (mi) 4.97 3.88 3.89 0.03 31 38766 Note: Visitor: monthly visits. Visits_Dev: deviation from the average monthly visits on a given calendar year Dist2rival: the distance to the closest competitor. Distance2park: the distance to the closest park The summary statistics for variables of interest are presented in Table 3.1. Each observation corresponds to a station-week pair. The price per gallon shows significant variation even after subtracting the wholesale cost proxy.50 I display the absolute value of monthly visits (Visitors) as well as the deviation from the average monthly visits on a given calendar year (Visits_Dev). As mentioned before, visitors to a given park can increase market size by various orders of magnitude in a given month of the calendar year. On average, if defined to be the whole town, a market has 13 gasoline stations and this number drops to 5 if I consider the two-mile driving distance ring around each station.51 The median gas station is located just below 4 miles from the park entrance. This metrics drops to 1.22 miles if I only consider the gas stations that are closest to the entrance in each town. Last, Table A.6 in Appendix E                                                         50 Since the spot price is the same for different octane grades of unleaded gasoline, I only display the "markup" for regular unleaded. 51  As expected, the two-mile ring markets have a lower number of firms per square mile than those in metropolitan areas covered by Chandra and Tappata (2011) using the same data source and time period. 53  displays the distribution of station brands in the sample. The classification identifies 55% of the stations as being branded, accounting for about 62% of the sample.  3.5 Results I first investigate the functional form of the relationship between market prices and market structure, one of the two issues in estimation of equation (3.1) discussed in Section 3.3. In the literature, it is typical to assume gasoline price to be a linear function of the number of gas stations. Table 3.2 displays the exploratory results using town ( ) and two-mile ring market (    ) definitions as well as alternative metrics for   .52 Specifically, besides the linear form, I use polynomial, log and the inverse of the number of gas stations. Across all specifications, I observe a negative and significant impact of gas station density on prices. For instance, the point estimates in columns 1 and 5 indicate that adding one gas station reduces market prices by about 1 cent per gallon (cpg) if the town market definition is used and about 1.7cpg if the gas station entered somewhere within a two-mile driving distance. Based on the discussion of oligopoly models in Section 3.3, the preferred competition metric is the inverse of the number of firms. But the specification using the log of the number of firms has the best fit measures compared with the other specifications (highest adjusted R2 and smallest mean absolute error). I therefore report results under these two specifications in the analysis that follows.   I present the main results of this chapter in Table 3.3. Columns 1-4 show the results from the OLS and two stage least square (2SLS) regressions using the full sample. The results in columns 2 and 4 indicate that ignoring the market structure endogeneity leads to underestimation of the effect of competition on prices.53 The instrumental variables used in Table 3.3 are the average annual visits to each park from 2002 to 2005 (in levels and squared term). I cannot reject the null hypothesis of the price equation being identified (Kleibergen-Paap rk LM statistic equal to 18.309 in column 2 and 22.661 in column 4). Instrumental variables are valid (Hansen J-statistic equal to 0.580 in column 2 and 1.143 in column 4) and pass the weak instrumental variable test (Kleibergen-Paap rk Wald F statistic equal to 18.722                                                         52 I present the OLS result in Table 3.2 because I want to compare more directly with most papers in the literature that use the linear form and OLS estimation. 53 The endogenous test shows that the market structure variables cannot be treated as exogenous (Test statistics  equal to 21.795 in column 2 and 19.066 in column 4). 54  in column 2 and 34.784 in column 4), which is also supported by the results of the first stage regression of the market structural variables on the instrumental variables.54  Table 3.2 Non-linear Effects of Competition Dependent Variable: Price (cpg)              (1) (2) (3) (4) (5) (6) (7) (8) N -1.02* -2.61*        (0.148) (0.830)       N2  0.06*         (0.028)       1/N   42.46*         (12.157)      ln(1+N)    -11.98*         (1.862)     N2mi     -1.67* -2.65        (0.452) (1.615)   N22mi      0.08         (0.121)   1/N2mi       19.79*         (6.294)  ln(1+N2mi)        -10.17*         (2.759) Constant 83.99* 87.86* 61.45* 98.10* 78.11* 80.12* 62.47* 86.45*  (6.674) (6.949) (5.996) (7.976) (7.340) (8.325) (6.381) (8.623)          Adj. R-squared 0.842 0.844 0.841 0.844 0.834 0.834 0.834 0.834 Mean Absolute Error       21.120      21.074 21.321 21.039 21.897 21.903 21.983 21.890 Observations (station-week pair) 39922 39922 39922 39922 39922 39922 39922 39922 Note: All regressions are OLS regressions.  Covariates included and not reported: Spot, Fuel-type, Visits, Income, Population and Bdum.  Standard errors clustered by station and time, reported in parenthesis.   Statistical significance of 5% is indicated by *. N = the number of gas stations in town. N2mi = the number of gas stations in a two-mile ring market.                                                           54 The coefficient of the instrumental variable in the regression is 3.18 and significant at 5%. 55  Table 3.3 OLS and IV Regressions Dependent Variable: Price (cpg)         (1) OLS (2) 2SLS (3) OLS (4) 2SLS (5) 2SLSa (6) 2SLSa Spot 1.01* 1.01* 1.01* 1.01* 1.01* 1.01*  (0.022) (0.022) (0.022) (0.022) (0.022) (0.022) Midgrade 7.12* 9.29* 6.34* 6.55* 8.59* 6.97*  (1.251) (1.751) (1.293) (1.601) (1.545) (1.538) Premium 16.155* 17.60* 15.85* 16.25* 17.25* 16.24*  (1.200) (1.425) (1.257) (1.489) (1.533) (1.497) Diesel 8.90* 8.31* 9.33* 9.54* 9.41* 8.84*  (2.444) (2.657) (2.429) (2.511) (2.583) (2.508) Visits 0.58* 0.63* 0.58* 0.61* 0.57* 0.56*  (0.097) (0.091) (0.096) (0.091) (0.090) (0.093) Bdum 8.24* 9.43* 8.89* 10.32* 12.04* 11.28*  (2.381) (3.695) (2.273) (2.778) (2.895) (2.618) Population  -9.38* -1.29 -5.68 3.07 2.57 6.30  (3.128) (4.003) (3.014) (4.079) (4.137) (3.925) Income 2.68* 0.97 1.97* 0.20 0.75 -0.20  (0.979) (0.943) (0.870) ( 0.820) (0.755) (0.775) 1/N 42.46* 139.67*   171.32*   (12.157) (23.496)   (26.367)  ln(1+N)   -11.98* -26.45*  -27.23*    (1.862) (3.428)  (3.356) Rbdum     6.22* 7.45*      (3.135) (2.842) Dist2park (mi)    1.34* 1.38*      (0.364) (0.354) Dist2rival (mi)    -1.90 -1.52      (1.301) (1.119) Constant 61.45* 48.37* 98.10* 135.48* 34.45* 126.92*  (5.996) (7.564) (7.976) (10.624) (8.010)  (10.723) Adj. R-squared 0.841 0.773 0.844 0.821 0.819 0.837 Observations (station-week pair) 39922 39922 39922 39922 38766 38766 Note: Standard errors clustered by station and time, reported in parenthesis. Statistical significance of 5% is indicated by *. I use the entire town to define a market.  Spot: weekday spot price. Omitted Fuel-type is Regular.  Bdum is equal to1 if  the gas station sells high-quality brand and 0 otherwise. RBdum is equal to1 if the closest competitor is affiliated with a high-quality brand station and 0 otherwise. Dist2rival: distance to the closest competitor. Distance2park: distance to the closest park. a: Oligopolistic markets only. 56  Figure 3.3a shows the predicted price reductions when a gas station is added to the market using the point estimates from Table 3.3. New entry reduces market prices more in markets with fewer stations but the predictions are not symmetric across specifications. For example, according to the results in column 2 (       ) moving from a monopoly to a duopoly would reduce prices by 70cpg. Column 4 (            ) results suggest that this reduction would be only 11cpg. The predictions are much more similar for markets that move from six to seven gas stations (3.3cpg and 3.5cpg reductions) and diverge in markets with more gas stations although these differences are very small (less than 1cpg). Overall, the message from these numbers is that, similar to the result in Bresnahan and Reiss (1991), the competition conduct changes quickly as the number of incumbents increases. Figure 3.3b shows how the magnitude of the OLS estimation bias changes with market structure. The nonlinear relationship between market structure and prices implies a larger bias in absolute values for the OLS estimates in markets with few gas stations. Note however that the relative bias is constant. The point estimates from Table 3.3 reveal a relative bias for the OLS estimator of     percent if          is used and    percent if     is used instead.                                         a)                                                                   b)                       Figure 3.3 Price Reductions after Adding One Gas Station    57  The estimators on the other covariates except Population and Income are very similar once endogeneity is corrected. Midgrade and premium gasoline increase the price of a gallon by around 9  (7) and 17 (16) cents in column 2 (4) respectively. Markets with a larger population and lower income tend to have lower prices although these effects are not significantly different from zero. The variable      indicates that prices at stations regarded as high-quality are around 9cpg (10cpg) higher than those at stations perceived as lower quality in column 2 (4). Interestingly, shocks to the spot price have a one to one relationship with prices. Note, however, that to relate cost pass-through to the elasticity of firm's demand, one needs to take into account that gasoline prices include the federal, state and local taxes. Denote specific taxes T and ad-valorem tax rate t. The price of a gallon of gasoline can then be represented by                , where   and   describe the wholesale and other marketing costs respectively; and   measures cost pass-through. Departure from perfect competition would imply    . An upper-bound tax rate for the towns in my sample is approximately 25.5% and that gives me a lower-bound for   of around 0.8.55 That is, at least 80% of a cost shock is passed to the before-tax retail price. The effect of demand shocks are reflected by the coefficient of the variable Visits. A 10000 increase in park visits leads to more than half a cent price increase.56 This is consistent, together with the cost pass-through result, with the idea that gasoline stations face downward-sloping demands and hence enjoy some market power.  I add covariates associated with local competition in specifications 5 and 6 in Table 3.3. These results are valid for markets with two or more gas stations. The point estimate for       indicates that prices are higher by about 6.22cpg in column 5 and 7.45cpg in column 6 if the closest competitor is affiliated with a high-quality brand station. This is consistent with results from the literature supporting vertical product differentiation. Hastings (2004)                                                         55 Gasoline is taxed at the federal, state and local government levels. The federal tax is 18.4cpg for gasoline and 24.4cpg for diesel. State and local taxes include specific and ad-valorem taxes (excise tax, environmental fees, storage tank taxes, general sales tax, and other fees or taxes). These taxes vary at the county level and the American Petroleum Institute reports the average implied tax "rate" for each state ( I use the January 2010 values reported for the states in the sample. This is an upper bound since many local taxes are not ad-valorem. 0.8 is significantly different from the coefficient of spot price (1.01) in column 2 and 4. 56 To put this number in perspective, note that one standard deviation for Visits is more than 70000. 58  shows that stations charge 5cpg less when facing competition from an independent than from a branded competitor.57 The result that distance to the park entrance is associated with higher prices is consistent with the idea that people would more likely want to fill up their gas tanks before heading out to more distant park locations, resulting in a demand that may be more inelastic. On the other hand, the distance to the closest competitor does not seem to affect prices.58 The negative and insignificant coefficient, together with the estimated effect of the distance to park entrance, suggests that station's location might not be a relevant dimension for differentiation within a small market.59 I now explore in more detail the link between the results in Table 3.3 and local market power. As discussed in Section 3.3, I am interested in measuring the extent to which local market power decreases as departing from monopoly market structure. I therefore look at the cost and demand shocks separately for different market configurations. Table 3.4 adds to equation (3.1) various interactions between the spot price and monthly visitors with dummy variables indicating whether the market is a monopoly or an oligopoly with a few gas stations (between two and six gas stations). The omitted market category includes markets with more than six gas stations. All the estimated coefficients are significant at the 5% level. The results are similar across specifications although the monopoly point estimates are larger when        . All coefficients have the signs and magnitudes expected in markets where local market power decreases as the number of firms increases. Markets with more gas stations pass a much higher proportion of cost shocks to prices. Using the estimates from column 1 and the approximated upper-bound tax rate of 25.5%, I find a lower-bound for cost pass-through of 18, 72 and 88 percent for monopolies, oligopolies with less than six gas stations and markets with more than six gas stations, respectively.60                                                                57 Similarly, Sen (2005) finds lower prices in markets with higher proportion of independent retailers. 58 Hosken et al. (2008) also find no significant effect of distance to competitors on prices. 59 The median value for distance to closest competitor is 0.29 mile and the third quartile is 0.69 mile, still less than one mile. 60 The predicted lower-bound for cost pass-through using results from column 2 are: 69, 73 and 88 percent respectively. 59  Table 3.4 Demand and Cost Shocks and Market Structure  Dependent Variable: Price (cpg)     (1) 2SLS (2) 2SLS Spot 1.10* 1.07*  (0.029) (0.026) Visits 0.33* 0.36*  (0.099) (0.099) Bdum 9.01* 8.66*  (2.915) (2.395)     * Spot -0.88* -0.24*  (0.161) (0.083)           Spot -0.20* -0.18*  (0.038) (0.032)     * Visits 6.14* 2.27*  (1.472) (0.638)           Visits 0.69* 0.74*  (0.178) (0.138) 1/N 243.82*   (35.218)  ln(1+N)  -38.42*   (4.849) Constant 33.44* 169.73*  (8.774) (13.475)    Adj. R-squared 0.796 0.835 Observations (station-week pair) 39922 39922 Note: Coefficients for Fuel-type, Income and Population not reported. Standard errors clustered by station and time, reported in parenthesis. Statistical significance of 5% is indicated by *.   Similarly, the coefficients for Visits and its interaction terms with market structure variables reveal that demand shocks increase prices by more in less competitive markets. From column 1 (2), a monopolist reacts to a 10000 increase in park visits by raising prices by 6.47cpg (2.63cpg) while oligopolies with less than six gas stations increase prices by only 1.02cpg (1.10cpg). Last, more competitive markets with more than six gas stations increase prices by only 0.33cpg (0.36cpg). Note that the strong and robust result for demand shocks might also 60  be associated with changes in the composition of buyers, not just a proportional outward shift of the demand curve. It is reasonable to assume that park visitors are less informed about gas station locations and prices and therefore have higher reservation prices than permanent residents. If this is the case, the increase in park visits means a larger and less elastic firm-level demand. To sum up, Table 3.4 provides further support for the result that local market power drops abruptly as the number of gas stations in the market rises.   3.6 Conclusions In this chapter, I revisit an enduring question in industrial organization: what is the effect of competition on market prices? I answer it by studying isolated retail gasoline markets that face significant demand shocks allowing me to use valid instrumental variables for the competition metrics in a reduced form price-concentration type of estimation. I show that ignoring endogeneity in the standard price-competition regression leads to significant underestimation of the effect of competition on market prices. Prices and margins tend to drop quickly as the number of firms increases. The way price reacts to cost and demand shocks is inconsistent with the predictions of models of perfectly competitive markets, suggesting existence of market power in the studied markets. The study of market power in the gasoline industry is of special relevance to policy makers and antitrust authorities that need to regulate and predict the effect of horizontal mergers. Unfortunately, our understanding of the effect of station concentration on market prices is far from complete. Regardless of the methodology used, the results from the existing literature have been mixed. The results of this chapter have immediate policy implications. In the studied retail gasoline market, the competition authority should have a thorough competitive analysis of mergers among the gasoline retailers. Such a merger may well harm competition by creating joint dominance or facilitating tacitly collusion in the retail gasoline market.       61  Chapter 4  Efficiency vs. Flexibility in Public-Private Partnerships  4.1 Introduction Continuing a movement that had earlier involved the privatization of many state-owned firms, the deregulation of major industries and the more widespread use of contracting-out, 61 in the early 1990s a number of governments began to experiment with another innovation involving expanded use of the private sector in the delivery of public services: public-private partnerships (PPP). 62 A large and diverse set of definitions of PPPs exist today, but one that conveys the main idea simply defines a PPP as ?a cooperative venture between the public and private sectors, built on the expertise of each partner, that best meets clearly defined public needs through the appropriate allocation of resources, risks and rewards.?  The increased private involvement in the provision of public sector infrastructure and related services has become a global phenomenon. Yescombe (2007) describes major PPP programs and projects in several countries in Europe, North America, Asia, Australia and Africa. Even middle and lower income countries have come to use various forms of the PPP model for the provision of public services.63 Data from the Infrastructure Journal suggest that major PPP projects with a combined value of US$394 Billion have been undertaken world-wide since 2005.64  In both higher and lower income countries, common industries for this kind of private participation include those related to power, transportation, water and telecommunications. Various kinds of social infrastructure such as hospitals, prisons and schools are common as well.                                                          61 On privatization and deregulation generally see, for example, Viscusi et al. (2005). With respect to privatization in particular, see, e.g., the work by Jones et al. (1990) and a survey of empirical work by Netter and Megginson (2001). For an introduction to the literature on contracting out, see Domberger and Rimmer (1994), Domberger and Jensen (1997) and Hodge (2000). 62 An early version of PPPs was the Private Finance Initiative (PFI) pioneered in the U.K. from the early 1990s.  63 The World Bank and the Public-Private Infrastructure Advisory Facility (a multi-donor technical assistance facility financed by a number of national and multi-national development agencies)  have jointly created the Private Participation in Infrastructure Database (at ) which contains data on more than 4,600 infrastructure projects in 137 low and middle-income countries.   64 Infrastructure Journal Project Database, accessed July 25, 2011. (   62  In a typical PPP, the private (generally for-profit) partner will assume responsibility for some parts of the delivery of a public service, for example, the design, construction and maintenance of a new hospital. Responsibility for the remaining parts, for example, the provision of medical services in that hospital, will stay with the public sector partner. Very long-term, and frequently complex, agreements govern the relationship between the private and public partners.   Advocates of the PPP model argue that such arrangements, by giving a larger set of tasks to the private sector and subjecting their provision to competitive bidding, will unleash the superior power of competitive, for-profit enterprises to minimize costs and to find innovative approaches to addressing social needs. Critics of the PPP model have pointed to a number of potential problems with this model of public sector procurement. One of these ? my focus here ? is the loss of flexibility that comes with the long-lived contractual obligations governments must respect when changing circumstances may require significant changes in the way the public service is provided.   This suggests a trade-off faced by governments choosing whether to proceed with a project as a PPP or by traditional public procurement: while PPPs might have the potential to generate substantial productive efficiencies, they may limit a government?s ability to react to changing demands for the public service. This trade-off is the subject of this chapter. My model allows me to illustrate the trade-off very simply and to explore various factors that will influence that trade-off.  I can show that the optimal choice of procurement mode will depend on the exact nature of the government?s objective function. In this regard I study two commonly proffered objectives: (i) minimizing the cost to taxpayers (or users) of the service and (ii) maximizing total social surplus. I also demonstrate that the relative advantages of the PPP mode will depend on the nature of the PPP contract considered ? that is whether the private partner is compensated based on simply having completed the project or based on the actual usage of the facilities.    4.2 Some Background on PPPs and Related Literature In a PPP, the private and public partners must come to an agreement as to what elements of service delivery each will contribute, how costs will be covered and how the private partner(s) 63  is to be compensated for its contributions. Most of the larger and higher profile partnerships involve the building of new public infrastructure, and the delivery of services using that infrastructure. Essentially, a PPP involves contracting out at a scale and complexity well beyond what is normal for governments. That said, most governments have had experience with contracting out to some extent, so we might ask what really distinguishes modern PPPs from contracting out. De Bettignies and Ross (2004 and 2011) suggest that three key differences distinguish modern PPPs from standard contracting out: (i) compared to standard contracting out, PPP contracts assign a larger number of tasks on a single project to the private sector. For instance, in the famous ?FDBOOM? model, the private sector partner(s) finances, designs, builds, owns, operates and maintains the facility; (ii) PPPs typically bundle multiple tasks in one large contractual agreement between the government and a single contractor, typically a special-purpose corporation created by consortium members to develop and operate the project. In contrast, standard contracting out would allocate one task (or part of a task) per contract, and the various contractors would be independent of each other; and (iii) PPPs often involve the privatization of the finance function and some operations function ? tasks that were historically the exclusive preserve of the public sector.  As suggested, the alleged benefits of PPPs derive from their potential to apply the forces of competition and higher-powered incentives to generate higher levels of efficiency and innovation. While the experiences of governments with PPP are varied, the evidence seems to suggest that the PPP model can be successful in the right circumstances.65 However, critics of PPPs point out that these efficiencies, if they exist, come at some cost. First, given the long lives of many PPP agreements (which can last 50 years or longer) the bidding and contracting process is very complicated and expensive, and the long projects require on-going monitoring of the private partner by the public, all suggesting the potential for significantly higher transactions costs with this form of procurement.66 Second, some have argued that some key elements of service quality may be very difficult to enforce by contract                                                         65 There has not been enough work done to properly evaluate the success of PPP projects ex post, in part because these are generally very long-lived ? and on-going ? agreements;  and a full accounting cannot really be done until the agreements have expired. The UK was an early adopter of the model and some work by the National Audit Office there suggests some success with the private finance initiative (PFI) version of the PPP model ? there are many NAO reports at Australia has also been a leader in the use of the PPP model, and there is evidence of success there as well, e.g., see Infrastructure Partnerships Australia (2009). 66 On this see, e.g., Boardman and Vining (2004) and Daniels and Trebilcock (1996).   64  if measurable, verifiable metrics are elusive.67 Third, many have argued that upon entering into long-term partnership arrangements governed necessarily by complicated and detailed contracts, governments lose control of key aspects of service delivery that they may wish to adjust in the future. To make changes requires negotiation and not only will the renegotiation process involve a new set of transactions costs, it will also involve bargaining without competition on the selling side. This chapter is about this third challenge and how the government might trade off flexibility for efficiency.    While there have been a large number of case studies, consulting reports and government agency reports on PPPs, there has been relatively less work done by economists, particularly economic theorists.68 Some early research considered the question of whether or not PPPs can dominate public procurement methods if quality is not completely verifiable and contractible.69 A larger number of papers have focused on the optimality of ?bundling? of the various tasks so that one private partner tackles multiple tasks (e.g., building and operating) rather than having each task performed by a single independent private partner.70 While, to some researchers, it is the bundling of tasks that defines a PPP, my focus is on the ?privatization? aspect of PPPs ? that they involve the outsourcing of tasks that might otherwise have been performed by public sector agencies and their employees.71   I investigate a different type of contractual incompleteness arising as a result of uncertainty regarding future demands for the public goods or services. Given the very long lives of some of these contracts, it is impossible to anticipate and optimally prepare for every potential contingency. PPP contracts may therefore need to be revisited and renegotiated ? a potentially costly process. In this sense, I say PPP agreements lack flexibility. The flexibility question strikes us as particularly important in dynamic industries such as healthcare, where the kind of hospital services appropriate today may not closely resemble the services we will                                                         67 This was a concern, for example, of Hart et al. (1997) and Hart (2003) with respect to prison projects. 68 For a recent review of theoretical work by economists on PPPs see de Bettignies and Ross (2011).  69 See, for example, Hart et al. (1997).  70 For example, see Benz et al. (2002), Hart (2003), Bennett and Iossa (2006), and Iossa and Martimort (2008). 71 Not surprisingly, it is this aspect of PPPs that have led to their being strongly opposed by public sector unions.  For example: ?The labour movement is opposed to privatization, including public-private partnerships, because it undermines both the values and ethos of the public sector, and the goal of enhancing the public good.? Canadian Labour Congress, 2011, Document No. 8, 24th Constitutional Convention.  Or see ?The case against PFI? from the website of the largest public service union in the UK (UNISON): .  65  be demanding in twenty or fifty years, given advances in medical knowledge and technologies. 72  On the other hand, flexibility may be less important for other kinds of projects, such as roads and bridges.73   A great deal of experience suggests that flexibility challenges are very real in PPP delivery. A review of changes made in PPP type projects in the United Kingdom by the National Audit Office (2008) concluded that changes undertaken in UK projects in 2006 involved extra payments to contractors of approximately ?180 million. While much of this spending provided additional value to taxpayers and users, the NAO noted that ?several components of the cost of changes were problematic? (p.5).74 The report cites some examples where changes were not smoothly and cost-efficiently managed, including the Blackburn Hospital Project.75 While many writers have mentioned the potential costs to the public sector of lost flexibility in lengthy PPP contracts, there has been very little formal modeling to my knowledge. Two papers consider flexibility questions that are different from the one examined here. In ?Case 3? of Iossa and Martimort (2008), the authors are principally focused on the efficiencies of bundling two tasks: building and operating a new facility. They consider a government choosing between sequentially contracting separately with first a builder then an operator (non-PPP approach) versus contracting to one firm (consortium) that will perform both tasks.                                                         72 In the UK, PPP (or PFI) are not recommended for the provision of information technology services, in part because of the high probabilities and costs of changes. See Yescombe (2007, p. 27). From H.M. Treasury (2006, p.32): ?...the PFI procurement structure is unlikely to deliver value for money....where authorities require a significant degree of short-term flexibility due to fast-changing service requirements. It is for this reason and from the evidence of past projects that PFI is not used by the Government for information technology projects...? 73 Making the point that the surrendering of decision-making authority to the private sector in PPPs makes it more difficult for the public sector to adapt to changing demands for public services, see, e.g., OECD (2008, pp 65-69), Yescombe (2007, section 2.12) and PricewaterhouseCoopers (2005, Chapter 2). In recent proceedings about Private Finance Initiatives, the UK Commons Treasury Committee has heard arguments from Members of Parliament about ?the ?inflexible? nature of PFI contracts, arguing it is locking the public sector into long-term contracts that do not allow changes in terms, if and when it becomes clear that the terms of the contract are inappropriate.?  (Partnerships Bulletin, June 14, 2011 at  74 From page 8 of the NAO report: ?Under PFI, almost any requested change , even as small as a new electrical socket, has to be processed through the SPV as it manages the asset during the contractual period and bears the risk of failing to meet service obligations. Often lacking the option of going to a different supplier, even for major changes, there is a risk that the public sector will have reduced leverage in negotiation and that the SPV or FM provider may not be incentivised to keep down the cost of changes or to process them quickly.? This report goes on to list the kinds of changes that come up frequently in long-term PPP contracts.   75 A particularly famous example of inflexibility played out in the British press over attempt by famous chef Jamie Oliver to get government funded schools in Britain to offer better, healthier food to students. Some of these schools were operated as PPPs and, given that the original contracts did not contemplate the provision of healthier and more expensive meals, those contracts had to be renegotiated in what turned out to be a somewhat challenging process. ?Private deals block Jamie?s school dinners?, by Felicity Lawrence and Katharine Quarmby, The Guardian, Monday April 25, 2005.   66  Information from the building stage might allow a better contract to be drawn with the operator in a non-PPP approach.  However, in separating the two tasks, some externalities between them may not be internalized with an associated loss of efficiency.   Athias and Saussier (2010) take the PPP form as the given choice, and ask how much flexibility to introduce into the long-term contract between the public sector and the operator in order to allow adaptation in pricing. Long term contracts that are too flexible risk opportunistic renegotiations trigged by the private sector, while contracts that are too rigid may not allow for efficient adaptation to changing circumstances.76   The paper that is most closely related to the questions addressed here is, in fact, not about public-sector procurement. Bajari and Tadelis (2001), hereafter BT, study private sector procurement, emphasizing an example from the construction industry. As here, they emphasize the trade-off between contracts that provide maximum flexibility to incorporate changes and those that provide the strongest incentives for cost minimization. While there are many parallels between the analysis of BT and that provided here, there are several important points of differentiation. First, my focus on the special problems associated with public-sector procurement provide for a number of new insights. For example: (i) I consider the role played by the actual objective pursued by the public sector ? does it simply seek the lowest quality-adjusted costs (as a private buyer would) or does it care about social welfare more broadly defined; and (ii) I study the two most standard types of actual PPP contracts ? those that pay the supplier a fixed sum and those in which the supplier is paid via tolls paid by users ? to compare them on the extent to which each supports the attainment of the public objectives. Second, my modeling approach is different in a number of ways. For example, I use a less ?reduced form? model that, while less general in some respects, provides for a larger set of specific and intuitive comparative statics results on the importance of key parameters. Third, the source of the inefficiencies that can arise in PPP or fixed-price contracts differs in my models. Fourth, I model the re-negotiation process differently.77   In what follows, Section 4.3 lays out the general model while Section 4.4 studies the two                                                         76 These authors go on to examine the amount of pricing flexibility actually incorporated in a multinational set of 71 toll road projects. 77 I will highlight the differences between this chapter and the analysis of BT at various points below.  67  special cases, PPPs and public provision, that form the core of my analysis. Section 4.5 extends the basic model in three directions. The last section concludes and suggests some directions for future research.   4.3 General Model I begin by taking a fairly general approach to the problem of a government, ?G? (as principal), procuring certain public services (the ?project?) from a firm, ?F? (the agent). Special cases of this model will correspond to provision via public-private partnerships (denoted PPP) and more traditionally by public agencies (PUB).78 The services that G wishes to procure could involve the construction of an important piece of infrastructure plus its operation for many years.    Basic Setup The (net present value of the) gross social benefit of the project is given by      which is not verifiable or contractible. The government can contract with F to deliver these services. There are in general many identical firms willing to compete to provide these services.  The firm?s cost to deliver the project depends, in part, on the non-contractible level of effort or innovation, e, chosen by the firm, and the productivity of that effort: 79         where K is the observable innate cost of the project (including cost of materials, labor, etc) and     captures the marginal productivity of the firm?s effort. I assume that   is private information of the firm, hence that it is not known by the government, ex ante. The disutility costs of this effort for the firm is     . For simplicity, I assume that these costs can be represented by a quadratic disutility function:          The non-verifiability of effort will generate familiar moral hazard problems.                                                         78 In BT?s private sector procurement model, they consider fixed price contracts which have properties similar to my PPP contract, and cost-plus contracts which have incentive properties similar to my PUB arrangements.   79 It is possible that effort is observable. Here I only assume that effort is not contractible, i.e. that its value cannot be demonstrated for a court or any contract enforcement mechanism. 68  Firms wishing to secure the contract to deliver this project will bid competitively. The firm winning the project will be paid a lump sum   by the government and then be responsible for project costs. The firm?s profits are taxed by the government at the rate        . I will explore the consequences of different rates of taxation but assume the level is set by forces outside the model. A firm winning the contract to deliver the project will have after-tax profits given by:                       The original specification of the project comes from government and the government can be right or wrong about this specification. If the government specifies the project correctly, the social benefits will be      as described. However, there is a chance ? with probability   ? that the government will have incorrectly specified the project, or that circumstances will change such that a different design is appropriate. I will refer to this as an unexpected change in the nature or level of demand for the services.80 To suggest a specific example, the project might involve construction of a bridge over a river, and it might become apparent at some point into the project that one lane should be devoted to bicycles (and maybe pedestrians) and not cars.81      While the change in demand is public information, I assume that because demand could have changed in so many different ways, contracts cannot practically be made contingent on changes in demand. Adapting to the new design will restore the    benefits. However if the project is not changed, a lower social benefit    will be realized, where         .    There are many reasons why projects may need to be re-designed or adjusted. In some cases, demand may have been badly estimated or technological changes may alter the way services should be delivered (common in health care, for example). While I will model this adjustment, if it is needed, as occurring before any services have been delivered, this is a modeling device meant only to capture the need for change sometime during the long life of                                                         80 In fact, the most interesting cases involve changes in the nature of demand ? i.e. the kinds of services to be provided. Uncertainty about simply the level of demand for a project can often be dealt with in carefully-drafted contracts.   81 I am deliberately suggesting an example in which the design change will not obviously greatly change the scope or cost of the project as this fits other assumptions in my model. It would be trivial to extend the model to cases in which the design change significantly expands the scope and cost of the project ? and there are many examples of these kinds of changes ? but the additional implications derived would be quite obvious given the results I present here.   69  the project.     If demand changes, efficiency dictates that the project adapt (e.g., the bike lane be added). Since this change represents a change in the contract between G and F, it must be negotiated. I model the negotiations using the familiar Nash bargaining model: the parties will bargain over the surplus created by efficiently adapting to the demand changes.82 I assume that there are real economic costs associated with switching to a new project design (this could include the renegotiation costs) and each of the two parties will bear this cost by paying an amount    .83 After the contracts are settled and, if necessary, any design changes negotiated, the firm picks its level of effort, costs are incurred, contracts honored and payoffs received.    Timing  Reviewing the timing of the game then, we have: 1. Government announces it has a project for which it wishes to receive bids. 2. Firms bid for the project, and it is awarded to the firm offering to provide it at the lowest fixed fee,   . 3. Nature may move to change demand ? if no change, proceed to 5. 4. If demand changes,    is renegotiated (to   ) via Nash bargaining and the design is changed, both parties incur switching costs  . 5. F chooses level of effort,  . 6. Benefits are realized and the government honors its contract.     The objective of the firm in this model is straightforward. It will make decisions to maximize its profits subject to honoring its contracts. The government?s objectives are more interesting. In much of the literature on public-private partnerships, it is argued ? and often just assumed ? that a PPP will dominate the public procurement method in a particular case if the PPP form provides ?value for money? (VFM) relative to traditional methods of procurement. Value for money in this context is typically taken to mean that services of the quality desired are provided at a lower cost to the ultimate payers ? taxpayers or (in the case of tolled                                                         82 In contrast, BT use a ?take-it-or-leave-it? renegotiation model.  83 If this is solely a renegotiation cost, it may seem likely that s would be smaller (or even zero) when the changes can simply be ordered by the government under a traditional public procurement process. I will consider this possibility below.   70  services) end users. This will be my starting point here: I will look for conditions under which a PPP can provide services at a lower cost to the government. Value for money as an objective can be contrasted with the objective of maximizing total social surplus (TSS) that is often applied in cost-benefit analysis. The key differences arise due to transfers that will not matter under a TSS standard but that will affect VFM. For example, firm profits will hurt VFM by pushing up the price the government pays for the project, but as simple transfers from taxpayers to firms will not affect TSS. A later section of this chapter will consider how the choice between PPP and traditional methods (PUB) can depend on the government?s objective function.    Solving the Model After solving this model for the more general case, I will focus on two specific special cases that will allow me to highlight the differences between public-private partnership and traditional public procurement. Traditional public procurement, PUB, will correspond to the case in which     (so that all profits revert to the government) and all bargaining power remains with the government (as it can order its employees to take actions without the need for renegotiation required with an outside contractor). I will contrast this with something more ?private?, here by considering as my PPP example, the case in which     and the bargaining weights are more equal. I solve the model backwards, beginning with the firm?s choice of effort. Firm's Optimal Effort     : Given  , F chooses a level of   to maximize its profit. This gives us the incentive compatibility constraint:                                subject to      The optimal level of effort is then given by:                                 (4.1) Clearly, higher rates of taxation discourage effort. At the extreme, when    ,     = 0.  To be clear, under my assumptions             is the profit-maximizing choice of effort for either the original or a revised design, as the costs of delivering to either design are described by the same cost function and the effort decision is made after any required renegotiations. 71  Renegotiation (if needed): As indicated, with probability   there is a shift in demand that requires that changes be made to project design to preserve the maximum social benefits (  ). In such a case, if switching costs are not too large ? which is assumed for now 84 ? G and F will renegotiate and sign a new contract with payment    going from G to F. Under Nash bargaining, G's threat point is:                  . If renegotiation fails, G gets only    of social benefit from the project but still pays    to F as provided in the initial contract. It also collects taxes on F?s profits to reduce its net cost of the project. Correspondingly, F still receives    and its optimal cost reducing effort remains the same. Thus F's threat point will be given by:                         . I allow for the possibility that the government and the firm have unequal bargaining power, represented by differing bargaining weights in the Nash Product. It may be, for example, that governments will have larger weights given their powers to enact and revise laws and regulations and even to rewrite contacts while shielding themselves from damage actions. In other cases, however, sophisticated and highly motivated private partners may be able to retain higher quality advisory services to assist in their renegotiations, in the process capturing a larger share of the surplus generated.85 To explore the implications of unequal bargaining power, suppose G has a bargaining weight    , and F has the weight    , where      . The Nash Product (NP) will then be:                                                                                                                 Maximizing this with respect to    yields:                                              Initial Payment     : Assuming perfectly competitive bidding and absent any uncertainty about which design is optimal, I would expect potential private partners to bid down to the                                                         84 This requires that the total benefits of making the change (     ) exceed the costs of making the change (2 ). 85 A common concern raised about PPPs, particularly when the public partner is an under-resourced government department of a developing country, is that the private partners will have more legal and technical ?firepower? at the table than will the government.   72  level of costs (which would be perfectly known to the firm and revealed through bidding), leaving the firm with zero profits. When I introduce uncertainty in the efficient design and the opportunity for renegotiation in the absence of competition, however, the picture is more complicated. Renegotiation under Nash bargaining, if needed, will necessarily involve moving to the new, superior design and to a readjustment upward of the fixed fee (to    ) to share the gains of the renegotiation with the private partner. If the original contract was going to provide zero profits to the private partner (because it had been competitively bid), the renegotiated contract will necessarily generate positive profits. Clearly, the potential for this renegotiation ? and the new profits it will provide the private partners ? could affect the original bidding. In a world in which private, risk neutral, bidders could commit to honoring their promises to complete projects regardless of the subsequent profitability of those projects ? perhaps by posting bonds ? these prospective profits in renegotiation would translate into lower prices bid in the initial round. The result would be that ex ante expected profits of bidders would still be zero ? and if the design did not need to be changed, the private partner would in fact suffer losses ex post. However, it is not clear that such commitment ? particularly on large projects ? is possible. Private partners will often be able to walk away from projects once the profits going-forward have turned negative, or to at least make credible threats to walk away if subsidies are not forthcoming. This behavior is facilitated by the ?special purpose vehicle? (SPV) structure that is adopted for many large PPP projects in which the SPV can simply declare bankruptcy and shut without there being any remaining claims on the SPV?s joint-venture parents.   Therefore, I invoke a limited-liability constraint, familiar in the contracting literature, and assume here that the government will not accept as a winning bid any offer that would not allow the private partner to at least break even absent any renegotiations.86 Governments, in their scrutiny of bids, will need to be persuaded that the contract can be honored absent any renegotiations. Therefore, if I assume that private firm has limited liability and no wealth it                                                         86 This is not to deny that there can be a problem of firms adopting strategies in which they win the contract with an apparently attractive bid, only to threaten later that the deal must be renegotiated or they will not continue. However, sophisticated governments will be alert to this possibility, and will want to scrutinize bids carefully to assure themselves that they are feasible. Also, in a world in which most of these private sector PPP players wish to continue to win future bids with the same or other governments, such gaming could be damaging to their reputations as trustworthy partners.   73  can commit ? that is, it cannot be pushed to negative profits in any state (or it would exit) ? F will again bid up to the point where it will break even without renegotiation. The limited liability/wealth approach to the agency problem has been applied by many others as an alternative to introducing risk aversion on the part of one or both players.87  I can then write the limited liability constraint as: 88                              And the winning bid is given by: 89                       Given that           , I can see that                      (4.3) This result suggests that the winning bid will be lower when tax rates are lower, because of the higher levels of effort that follow lower taxes.   Value for Money (VFM): Given the costs of the contract to the government with and without renegotiation, I can easily determine the expected value for money. If there were no change in demand, the value for money would be simply given by the difference between the benefits of the project and the government?s costs to procure it (   minus any tax collected on profits):                            =                If the project does change, the new contract price,    , will be given by, substituting (4.3) into (4.2):                                                                                                            87 The classic reference is Sappington (1983). See also the text by Laffont and Martimort (2002). It can be shown, as well, that the key trade-off between efficiency and flexibility remains even if firms are permitted to bid down to zero ex ante expected profits (and can commit to their bids) as long as there are costs associated with renegotiation.   88 If the limited liability constraint is satisfied it is very easy to see that a participation or individual rationality constraint (requiring firms to earn non-negative profits in expectation ex ante) will never be binding. For this reason I do not include participation constraints here. 89 This does require that the winning bidder can credibly convince the government that its bid will allow it to break even in the absence of any renegotiations.  74  And the VFM after renegotiation will then be given by:                                                            Combining the VFM results with and without a change in project design, we see that the ex ante expected VFM is then                                                                                                                        (4.5) A set of intuitive results regarding the determinants of VFM of a project follow directly. Result 4.1: The value for money of a project will be greater: the lower is the cost of the project (K); the greater is the gross benefit of first and second-best projects (   and   ); the greater is the cost reducing effect of effort (  ; the smaller is the probability     the project design will need to change; the smaller is the switching cost ( ); and the lower the tax rate ( ). Assuming that the net benefit of renegotiation (         ) is always positive ? that is, renegotiation is efficient and therefore always occurs when there are changes in demand ? VFM is higher when the government is in a stronger bargaining position (i.e. when ? is greater). Proof: the results are demonstrated by the following simple comparative statics, assuming                              ;                           ;                      ;                      ;                                ;                     ;                   ;                            . Q.E.D. Most of these results are easily understood and relate to the simple point that the greater the 75  benefits and/or the lower are the costs of the project, the greater will be its VFM. The least obvious results here are those related to the tax rate, the bargaining weights and the likelihood of the need for renegotiation. By discouraging effort, higher tax rates actually hurt the achievement of VFM, even though the taxes received reduce government expenditures. By limiting the ability of the private partner to drive up prices in renegotiation, a greater government bargaining weight increases expected VFM. Finally, the more likely it is that the project will need to be modified, the less attractive it becomes ex ante from a VFM perspective, even though the final gross benefits and costs of production will be in the same in any case.  4.4 Comparing PPPs and Traditional Public Procurement I turn now to the key results of this chapter: considering two special cases of the model above will allow me to compare the relative costs and efficiency of a PPP and more traditional methods of public procurement (PUB). By taxing back all the profits (t approaching 1) and granting the government full power in renegotiation (   ), I essentially transform the firm into an arm of the government and create the traditional public procurement scenario, PUB.90 By contrast when taxes are lower and bargaining weights more balanced, we have more private interests and control in the project.91 To fix ideas here, I take the case in which     and 0 ? ? ? 1 to represent the PPP model. Recall that for a given level of  , lower taxes raise VFM, so indeed in a PPP scenario in which the government is ceding some control rights (i.e.    ), the government will maximize VFM by setting the tax rate to zero.92            Setting    , I can solve for the chosen level of effort, from (4.1), the original contract price, from (4.3), and the renegotiated price, from (4.4):                                                         90 If I allow t to exactly equal 1, I lose uniqueness to my solutions ? since the government taxes back every dollar of profit, it does not care what price it pays. Therefore when I speak of t = 1 here, I more precisely mean  t = 1-  , where   can be an arbitrarily small but positive quantity.   91 An alternative modeling technique could simply involve assuming that under PUB, the government does not need to renegotiate changes and can just order them. This approach, taken in an earlier version of this study, produces essentially identical results. 92 To be clear, I do not see ? as a choice variable except to the extent that a government can choose to procure using traditional public methods, thereby effectively setting ? to one. Any form of private provision will involve, for the purposes of my model, a bargaining weight that is exogenous to the government.   76          ,               ,                                    This will provide an expected VFM in the PPP case given by:                                                         Then, by setting     and    , I can construct the PUB alternative.  This will yield:                           As a result of the lack of profit incentives for F, no effort or innovation will be forthcoming. The fact that it holds all the bargaining power, however, does mean that G will have to pay no more than the costs actually incurred by F.  The expected VFM under PUB will be given by:                                                       Our second set of results highlights the intuitive trade-offs between efficiency and flexibility in the choice of procurement mode. Result 4.2: Under the objective of maximizing VFM, a PPP procurement will dominate public procurement (PUB) when:                                                          (4.8) Therefore, procurement using a PPP is more likely to dominate procurement under PUB: the greater is the cost reducing effect of effort (  ; the smaller is the probability the project design will need to change      the greater is the switching cost ( ); and, the smaller is the difference between the social values of the best project and the other project        . Assuming that the net benefit of renegotiation (        ) is always positive,  the VFM of a PPP is relatively higher when the government is in a stronger bargaining position (     77  Proof:  Follows directly from simple comparative statics as above.93  Q.E.D. The basic trade-off between the efficiency of private providers and the flexibility of public providers comes through very clearly here. When flexibility does not matter because demand is extremely unlikely to change (   ),                    , implying that PPP procurement must dominate PUB because of its efficiency benefits. On the other hand, when the need to provide extra incentive for efficiency is less important, perhaps because there is little potential for innovation in the project (       procurement via PUB will dominate, that is,                    .   Other intuitive results follow from (4.8) quite simply. When the difference between the ?right? project and the ?wrong? one         is large, it is more important for G to renegotiate ? improving the terms that F can extract and reducing the VFM benefits of the PPP. Greater bargaining power on the part of the government expands the range of parameter values under which PPP procurement is preferred under the VFM standard as greater bargaining power on the part of the government limits the ability of the private partner to raise the government?s costs in renegotiation. Finally, higher levels of switching costs ( ), other things equal, tend to favor the PPP mode. Under PUB, the public provider bears the full switching costs of both partners. However, under the PPP structure ? and given Nash bargaining in renegotiation ? the private partners will end up sharing the loss of surplus associated with higher switching costs.  Less than 100% of this cost is then passed on to the public sector.   I can illustrate the efficiency-flexibility trade-off with a simple graph based on values of ? (capturing the importance of effort for efficiency) and ? (capturing the need for flexibility) that lead the PPP and PUB procurement modes to deliver identical levels of VFM (i.e. that set condition (4.8) equal to zero). These levels will be given by                        , which is illustrated in Figure 4.1, where the area under the curve (shaded) is the range within                                                         93 The basic comparative statics are: (assuming           )                              ,                                               ,                                    ,                                             ,                                        .  78  which PUB dominates PPP while the area above represents values such that the PPP mode dominates. Other aspects of Result 4.2 can be illustrated with this graph. For instance, increases in       or decreases in   rotate the curve upward (around the origin), which expands the area in which PUB dominates.         Figure 4.1 The Efficiency-Flexibility Trade-Off The interpretation of Result 4.2 is therefore quite straightforward. Under a PPP contract, F has incentives to exert cost-reducing effort because it captures the gains of its efforts. Those incentives are absent under PUB. The disadvantages of the PPP, however, derive from the incompleteness of the contract. For the government, this involves new costs ? the extra surplus that must be transferred to the private partner under Nash bargaining, which lowers the government?s VFM. Therefore, PPPs will be more attractive when there is little chance for a need to redesign the project ? road or bridge projects may come to mind as examples. On the other hand, when it is more likely that the kind of services needed in the future could be very different from those anticipated ex ante ? as might be the case for sophisticated health care projects, for example ? the flexibility of public procurement contracts may make them superior.    4.5 Extensions 4.5.1 A Total Social Surplus (TSS) Objective In the baseline case, the government pursues a value for money objective, a measure widely                                      79  used in the PPP literature and by PPP practitioners. However, this is not the most commonly assumed objective for governments in normative policy work by economists. More typically, for example in standard cost-benefit analysis, government objectives would be modeled as the maximization of some measure of social welfare or total social surplus. This is a different measure than value for money to be sure ? principally differing as a result of transfers from one party to another. Two examples of transfers that make these objectives different are particularly relevant. First, it has been argued ? for example, by public sector labor unions ? that PPPs facilitate the substitution of poorly paid private sector labor for more highly paid (and unionized) public sector labor. To the extent that this happens, these transfers do improve value for money, but do not represent increases in total social surplus. Second, surpluses moved from taxpayers to private firms in the form of profits will hurt the achievement of value for money but will not necessarily affect total social surplus. In this section, I explore the implications of using a total social surplus (TSS) criterion for selecting between PPP and PUB. Under a TSS objective, the government does not care about the distribution of surpluses, only about the total surplus generated.   To do this however, I need to add a new element to the model. Paying higher prices to private sector partners will not be seen as a cost to a government that maximizes TSS (since inflated prices are merely a transfer) unless raising the required tax revenues generates deadweight losses to the economy. Therefore, without some shadow price of public funds that incorporates this cost of raising revenue, there will not be a unique solution to the question of what price the government will pay for the services provided. I thus add a deadweight cost of government financing (from tax revenues), ? > 0, which represents the additional cost to the economy when a government extracts $1 to pay for the project. Hence, if the government pays the firm , the cost to the government is       .   To be clear, I could have introduced this cost of financing parameter into the VFM analysis above, but it would have made no difference. That analysis identified which procurement mode would provide the lowest cost to government; adding this additional cost would not have changed any of those comparisons, though it would lower the overall desirability of doing the project at all.  To facilitate comparison with VFM analysis, I continue to focus on the two special cases: (i) 80  PUB with    ,    , and (ii) PPP with      ,    . As in the case of VFM, under the PUB contract, G pays         to cover the (non-effort) cost and F exerts no cost reducing effort, that is I have again,       . Changes will be made, if necessary, and G will only have to cover F?s actual costs of the change ( ). The expected total social surplus under PUB, including the cost of government financing, is now                                                                                                                       Under the PPP contract, G initially pays a lump sum       and F again chooses an optimal level of effort,         to maximize its profit:                             . The limited liability constraint still holds so I have              .  If changes in demand necessitate changes in project design, G and F will again enter into Nash bargaining. As I now assume that there is a deadweight cost of financing the project, the  benefit of the original project is now          . Since the government?s current objective is to maximize the total social surplus of the project, G has a threat point that depends on the TSS without renegotiation: the benefit of the ?wrong? project minus the cost of providing it, i.e.,                                      . F has the same objective function as before, so its threat point remains:              . The Nash product in this case is                                                                                             Solving yields the new payment,      :                                          The expected TSS under a PPP contract is then                                                            81                                                                    This leads to my third set of results. Result 4.3:  Under the standard of maximizing TSS, a PPP procurement will dominate public procurement (PUB) when:                                                                      (4.9) As before, a PPP approach is more likely to dominate PUB, the greater is the cost reducing effect of effort    , the smaller is the probability the project design will need to change    , the larger is the switching cost    , and, the smaller is the difference between the social values of the best project and the other project        . When the deadweight loss from taxation     is close to 0 (and, as a result, the renegotiated payment       becomes very large) the conditions for PPP to dominate under a TSS standard are the same as those under a VFM standard. The effect of increases in the deadweight loss of government finance makes the PPP more attractive. Assuming that the net benefit of renegotiation               is always positive, so renegotiation always occurs when there are changes in demand, the TSS of a PPP is higher when the government is in a stronger bargaining position. Proof:  Follows from straightforward comparative statics. 94  Q.E.D. While these results parallel those from Result 4.2, there is one new parameter here (  ). Increases in the marginal deadweight loss of government funding (  ) favor the PPP alternative. This is because increases in the deadweight loss of government funding will favor the procurement mode that involves the lowest cost to government. The PPP mode                                                         94 The basic comparative statics are very similar to those in the VFM case, with the inclusion of the deadweight loss parameter: assuming           ?                                       ,                                                    ,                                         ,                                             ,                                          ,                                               . 82  lowers the cost of production because of the higher levels of effort, and it also shares the switching costs with the private partner whose financing does not create deadweight loss. The intuition with respect to changes in the other parameters is the same as provided with respect to Result 4.2. Comparing TSS and VFM Results Would a government pursuing a VFM objective adopt the PPP mode when the PUB approach would yield greater total surplus under the TSS objective? To compare conditions under which either mode is preferred under VFM vs. TSS standards, I need to make the models more directly comparable by adding cost of government financing to my VFM calculations. The expected VFM of PPP in the presence of financing cost is: 95                                                              (4.10) The expected VFM of PUB is the same as the expected TSS of PUB:                              So the difference between VFM of the two types of contracts is then:                                                                     Comparing the TSS and VFM results provides my fourth set of results which demonstrate that the different objectives can indeed lead to different choices.  Result 4.4: When the public and private partners can have different bargaining weights, the following cases become possible: (i) When the government has the greater bargaining weight (i.e. ? > ?) it is possible for a PPP to maximize VFM while PUB maximizes TSS; (ii) When the government has the lesser bargaining weight (i.e. ?< ?) it is possible for a PPP to maximize TSS while PUB maximizes VFM;      (iii) When the government and firm have equal bargaining weight (i.e. ? = ?), comparisons under     are the same as those under TSS.    Proof:  To see this, I write                      in terms of                     .                                                            95 See the Appendix F for a detailed derivation. 83                                                                                                                              Q.E.D. The last term on the right-hand side of this expression will be positive when      and negative when     . As a result, when the government has the lesser bargaining weight (i.e.      ), it is possible for a PPP to maximize TSS (                        while PUB maximizes VFM                        . And when the government has the greater bargaining weight (i.e.      ), it is possible that a PPP contract is the optimal choice in terms of VFM while PUB is the optimal choice in terms of TSS.96 When the government and firm have equal bargaining weight (i.e.       ), if delivery of a project using a PPP dominates its delivery using public procurement under a VFM objective, it also dominates under a TSS objective (and vice versa). In other words, in this case, whether the objective involves maximizing VFM or total social surplus does not alter the optimal choice of procurement method.  4.5.2 Toll Revenue PPPs In the PPP model I have used to this point, the private partner is paid a set sum to deliver the project. This could have been in the form of a lump sum or a stream of ?availability payments? (i.e. payments dependant only on the facility operating but not on the actual demand for that facility or the extent of its usage). In many PPP arrangements, however, private parties are paid according to the use of the services. Road projects funded by tolls are a common example in which users rather than the government pay the private partners. In other cases private partners are paid according to demand or use of the facilities, but are paid by the government.97                                                           96 An example: When                ,      ,      ,     ,    ,              .                             and                           . Therefore PUB dominates under a VFM standard but a PPP dominates under a TSS standard.  When      ,       ,       ,              ,             ,      ,                     0 5    and                            .  In this case, a PPP dominates under a VFM standard while PUB dominates under a TSS standard.   97 Shadow tolls (where use is measured but the tolls are paid by the government) on road and bridge projects would be an example.   84  In cases in which the private partner is paid based on the project?s success in terms of meeting demand, we can imagine that this player will be much more willing ? even eager ? to amend the project if demand changes make design changes optimal. Similarly, users (or the government if it pays) are not as disadvantaged by a failure to adapt to change since they will not have to pay as much. Put another way, the players? threat points are different in such a situation.   To see the implications of this alternative design, consider a PPP model in which the government and firm share the benefits generated by the project. In this case, the firm?s threat point deteriorates if the project must change and renegotiated terms will improve for the government. I will continue to assume that     in the PPP model with tolls. Suppose that, under the PPP contract, the fraction of the benefit that F gets (via usage fees) is   . The government?s VFM objective here then will be to secure the best project by surrendering the smallest fraction of the benefits to the private partner.  Given   , F chooses an optimal level of effort to maximize its profit. Once again F's incentive compatibility constraint is:                           and the optimal effort level is again        . 98 Potential private partners will bid according to what level of    they are willing to accept, with the contract going to the lowest bidder. I maintain the assumption that the winning firm, F, will have bid to the point where it will break even (its limited liability constraint) absent renegotiation. This implies                                         SO                          If changes in demand materialize, G and F renegotiate and sign a new contract. G's threat point is           . If we think of       as G?s payment to F, then G actually ?pays? less now as            . In this sense, I say that G has a stronger bargaining position than it                                                         98 The optimal effort is the same here in part because effort does not affect demand in this model. It would be interesting to explore the implications of having effort influence demand as well as costs. 85  would in an availability case. If the firm does not agree to change the contract, its payoff is             , which is negative as     . Consistent with my earlier assumption, I assume that F can walk away. So in this case  F's threat point still generates zero profits (in this case through exit). Assume that the target of G is to maximize VFM. The Nash Product is then                                                The new toll rate,    , will then be given by:                                                       Therefore, the expected VFM of the toll contract is                                                                                                                                                                          I can now ask whether a toll contract or an availability contract generates greater VFM for the government. Recall that expected VFM of the availability contract, for clarity here now labeled               , is given by (4.6). This leads to my fifth set of results. Result 4.5: When the objective of the government is to maximize VFM, the toll contract dominates the availability contract. Proof:  The difference between the VFM of the two contracts is                                                                                                                                                                                       Q.E.D. Thus, the toll contract dominates the availability contract in terms of VFM. Additionally, I see that the advantage of the toll contract over the availability contract is greater: the more 86  likely it is that the project will need to change (higher   ; the greater the cost of the project (bigger  ); the smaller the cost reducing effect of effort ( ); and the greater the percentage difference between the "right" and "wrong" project (larger           ). This is because under the toll contract, the government essentially pays less if renegotiation fails and hence the government is in a stronger bargaining position. Finally, as   gets larger, renegotiation is less costly to G with the result that the VFM advantages of the toll contract are greater when G has less bargaining power (i.e. when   is small).   Not surprisingly then, the use of tolling expands the conditions under which the PPP approach can dominate public procurement methods. The condition for a toll-based PPP to dominate the PUB alternative is given in Result 4.6.  Result 4.6: Under the standard of maximizing VFM, a PPP procurement based on toll payments will dominate public procurement when:                                                                              (4.12) Proof: Recall that the expected VFM under the PUB contract is E(                . Then the difference between VFM of the two types of contracts is                                                                                                                                                                                                      Since             , we have                                                                                                                                                                    Q.E.D. Derivatives of this expression reveal comparative statics results similar to those from Result 4.2.99                                                         99 For example: the PPP toll contract is more likely to dominate PUB, the greater is the cost reducing effect of effort (? , the smaller is the probability the project design will need to change    , the larger is the switching cost (s), and, for a given b0, the greater is the value of the other project (i.e., b1). There is a slightly different condition necessary to guarantee this effect of ?. I must assume that the benefits of the doing the right project 87  While in general we might expect a toll-based PPP project to help G secure value for money by both weakening the private partner?s threat-point (because it will lose money without renegotiating) and by strengthening the government?s threat-point (because it will not have to pay as much without renegotiation), only the second effect is operative here. In both cases (tolls and availability payments) the private partner?s alternative to a renegotiated contract is zero profits, in the toll case because it exits to avoid losses, in the availability case because its payments will just cover its costs. As a result, the advantages of the toll version derive here from the strengthening of G?s bargaining position.100    4.5.3 Renegotiation Costs In the base model presented in Section 4.4, a change in the project requires ? under PPP or PUB modes ? that both G and F need to expend resources as switching costs. I indicated that some of these switching costs could be the costs of negotiating a new agreement, but in such an interpretation we might expect that these costs would be lower under the PUB mode since G can more directly order changes. I can model the implications of these kinds of negotiation costs very easily by comparing the VFM generated under the PPP mode with these negotiation costs with the VFM generated under the PUB mode in which these costs are set to zero. To avoid confusion, I will denote these renegotiation costs borne under PPPs with the parameter m (rather than s) and assume that there are no renegotiation costs for either party under PUB.  The expected VFMPPP will then be simply (4.6) again, with m replacing s. The expected VFMPUB will be given by (4.7) with s set to zero.  I can then set out a very intuitive result. Result 4.7: The presence of renegotiation costs under a PPP that do not arise under the PUB mode will lower the expected VFM of a PPP approach to the project relative to the PUB approach.   Proof:  The PPP mode will dominate the PUB mode for project delivery under a VFM standard if:                                                    Q.E.D.                                                                                                                                                                            are big enough:                  . If this condition were not satisfied, the government could not benefit from renegotiation. 100 This said, it would not be difficult to expand the model, for example, by introducing an exit cost for the private partner, which would lead it to have an inferior threat point in the PPP with tolls.   88  It is clear that higher renegotiation costs favor the PUB mode which avoids those costs as long as there is some positive probability of change (?>0) and the government has some bargaining power under a PPP (?>0).     4.6 Conclusions Public-private partnerships are being used to deliver public services in many sectors, such as transportation, water, health care, education and prisons. In this chapter, I have examined an important trade-off associated with the choice between PPP and more traditional public procurement methods (PUB). While the PPP model provides the private contractor with greater incentives for cost reducing effort and innovation, it locks the government into a long-term contract that may be costly to renegotiate if changing circumstances make a project redesign optimal. I show that the PPP model will be superior when possible efficiencies are large, the probability there will be a need to change the project is small, the gains to project redesign are small, the government?s bargaining power in renegotiation is greater and when renegotiation costs are low. This result holds no matter whether government's objective is to maximize value of money (VFM) or total social surplus (TSS), though the different objectives can imply different choices between the PPP and PUB approaches. My analysis has also demonstrated that PPP contracts based on usage sensitive payments (e.g., tolls) can generate higher VFM for the government.  To my knowledge, this chapter is the first to offer a formal model that focuses on this trade-off, though the idea that efficiency comes at a price of flexibility is very intuitive and appears in other contexts (e.g., in the choice of flexible vs. inflexible production technologies). The results may shed some light on why PPPs have become popular in some sectors such as roads and water ? where it could be argued that the need for large changes to designs is likely to be relatively smaller ? while they remain less common (and more controversial) in areas that might seem more dynamic, such as health care and information technology.   I suggest a few directions in which future work could advance our understanding of these trade-offs. First, the basic model here could be generalized in a number of ways, for example incorporating differential switching costs to change project designs, by allowing contracts to 89  be contingent on observed signals of unobservable variables, or by considering alternative functional forms to test the robustness of my results. Second, as efficient risk shifting is a big part of successful PPP projects, I could consider the implications for my model of leaving risk averse private firms subject to some risk that they cannot control. Finally, I could consider some of the strategies that public and private sector partners employ to deal with the deficiencies of the PPP and PUB models presented above. For example, in PPP projects the parties may anticipate the need to renegotiate in the future and may then put into place mechanisms (e.g., third-party arbitration) to limit the ability of the private partner to take advantage of its strong position to extract much higher payments. PUB modes can also be improved by creating incentives for innovation and effort on the part of public sector providers. Indeed, a great deal of effort has been put into making governments more efficient providers of services generally, through, for example, giving managers more authority for the way their units operate but making them also more accountable for the quantity and quality of the services provided.101                                                                          101  Some of these would be viewed as aspects of the ?New Public Management? approach to public administration.  See, e.g., Osborne and Gaebler (1992).  90  Chapter 5  Conclusions This thesis studies competition and prices determination in three different settings: markets of heterogeneous goods (movies), markets of homogenous goods (gasoline) and the provision of public services. In Chapter 2, I study the uniform pricing puzzle in the movie industry by carrying out an empirical analysis of the uniform and differential pricing strategies in a non-North American urban market. Using a unique dataset of the Hong Kong market where there is price variation within theaters, I first estimate a nested Principles of Differentiation (nested PD) demand model and then simulate profits that theaters would have earned under the differential and uniform pricing strategies. I find that differential pricing generates higher profits overall but the difference between profits under the two pricing strategies is very small. I argue that this is because, although differential prices can extract more consumer surplus (demand effect), intensifying competition reduces the gains from the differential pricing policy (competition effect). My research contributes to the literature on uniform pricing for differentiated products. In particular, I suggest competition, a factor rarely considered in the literature as a possible reason for the prevalence of uniform pricing. In terms of methodology, I extend the PD model of Bresnahan et al. (1997) by including an additional nesting structure to capture substitution between the outside option and the alternatives in the inside product category.  Chapter 3 investigates the relationship between market structure and prices in retail gasoline markets. In the price-concentration literature, it is generally difficult to find a valid instrumental variable that is correlated with market structure and exogenous to price. Based on the features of the isolated markets studied in this chapter that face significant demand shocks, I propose novel instrumental variables to address the well-known endogeneity problem. Specifically, the instrumental variables are based on the past visits, which affect entry and exit decisions as a proxy for the expected long-term market size, and meanwhile do not influence directly gasoline prices on any given week. The results suggest that market power exists in the studied market and reject the idea of the perfectly competitive outcome. I also find that ignoring market structure endogeneity in the studied gasoline markets leads to underestimations of the effect of market concentration on prices between 55 and 70 percent. 91  In Chapter 4, I examine the role of competition and private sector participation in the provision of public services. In particular, I study public-private partnerships (PPP), a new form of a cooperative venture between the public and private sectors that strives to marshal the power of competitive markets to address public needs. However, due to the very long lives of PPP contracts and uncertainty regarding future demands for the public goods or services, PPP agreements lack flexibility in the sense it is costly to renegotiate after PPP contracts are signed. PPPs' productive efficiency gains and inflexibility suggest a trade-off faced by governments in the choice between PPPs and traditional public procurement. I propose a model to illustrate this trade-off in a simple way and to investigate factors that will influence that trade-off. The main result is that PPPs perform better when possible efficiencies are large, the probability there will be change in the project is small, the gains to project redesign are small, the government?s bargaining power in renegotiation is greater and when renegotiation costs are low. This result holds regardless of the government's objective (maximization of value of money or total social surplus). 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If            is a nonnegative, homogeneous of degree one function satisfying the following restrictions: the limit of      as any argument goes to   must be equal to   ; mixed partials of      must alternate in sign, and first partials must be nonnegative,  then                                           (A.1) is the cumulative distribution function of a multivariate extreme value distribution, and                                             (A.2) is the corresponding equation determining the market share of product  , where    is the partial derivative of   with respect to    .                   103  Appendix B: Estimation of PD Model and Three-Level Nested Logit Models  Like the nested PD model, the PD model also has a closed form solution for market share and the regression is derived from the market share function:                                                                                     (A.3) where                                                                I follow Razzolini (2009) and estimate the following regression equation:                                                                    (A.4)  I follow Berry (1994) and Richard (2007) to estimate the following regression equations for the three-level nested logit models: for movie-primary NL model, the regression equation is                                                                  (A.5)  for theater- primary NL model, the regression equation is                                                                   (A.6)              104  Appendix C: Theater Fixed Effects and Movie Fixed Effects of the Nested PD Model  Theater          Estimate          Standard Error A2 0.66 0.174 B1 -0.67 0.174 B2 -0.53 0.129 B3 -0.28 0.085 B4 -0.74 0.178 B5 -0.34 0.097 B6 0.13 0.030 B7 -0.64 0.191 B8 -0.54 0.130 B9 0.00 0.029 B10 0.63 0.175 B11 -0.13 0.045 B12 -0.35 0.098 B13 -0.80 0.188 C1 -0.48 0.106 C2 0.15 0.014 C3 -0.54 0.120 C4 -0.49 0.115 C5 -0.40 0.155 D1 0.19 0.076 D2 -0.75 0.180 D3 -0.71 0.149 D4 -0.57 0.121 D5 -0.36 0.089 D6 0.27 0.094 E1 -0.93 0.216 E2 -0.67 0.191 E3 -0.24 0.100 E4 0.09 0.383 E5 0.24 0.042 E6 -0.89 0.215 E7 -0.48 0.152 E8 -0.74 0.208 E9 0.02 0.116          Note: A1 is the base case.   105   Movie Estimate Standard Error 2D BRAVE(Cantonese) 0.90 0.150 2D BRAVE(English) -0.10 0.297 2D ICE AGES(Cantonese) 1.61 0.168 2D ICE AGES(English) 0.40 0.160 2D MADAGASCAR(Cantonese) 1.76 0.157 2D PIRATES(Cantonese) -0.02 0.152 2D PIRATES(English) -0.14 0.166 2D PROMETHEUS 1.15 0.166 2D THE AMAZING SPIDER-MAN 2.25 0.217 2D THE AVENGERS -0.19 0.248 3D ABRAHAM LINCOLN VAMPIRE HUNTER 1.23 0.284 3D BRAVE(Cantonese) 0.67 0.281 3D BRAVE(English) 0.76 0.298 3D DR. SEUSS' THE LORAX -0.44 0.468 3D ICE AGES(Cantonese) 1.35 0.286 3D ICE AGES(English) 0.64 0.289 3D MADAGASCAR(Cantonese) 1.30 0.282 3D MADAGASCAR(English) 0.70 0.287 3D MEN IN BLACK 3 1.01 0.293 3D PARANORMAN 0.62 0.281 3D PIRANHA 1.42 0.311 3D PIRATES(Cantonese) 0.50 0.302 3D PIRATES(English) -0.94 0.297 3D PROMETHEUS 0.98 0.288 3D SADAKO 0.65 0.284 3D SAMMY(Cantonese) 0.31 0.276 3D SAMMY(English) 0.02 0.314 3D STEP UP REVOLUTION 1.28 0.283 3D STREETDANCE 2 -0.07 0.302 3D THE AMAZING SPIDER-MAN 2.08 0.335 3D THE AVENGERS 0.73 0.482 ACT OF VALOR 0.16 0.495 ALBERT NOBBS 1.05 0.297 AMERICAN REUNION 0.91 0.321 BEING FLYNN 0.64 0.162 BELOVED 0.81 0.226 BEST EXOTIC MARIGOLD HOTEL, THE 0.52 0.264 BOURNE LEGACY 1.99 0.169 CHICKEN WITH PLUMS 0.79 0.157 COMME UN CHEF 0.92 0.163 106  Movie Estimate Standard Error DARK KNIGHT RISES, THE 3.62 0.315 DARK SHADOWS 0.14 0.631 DELHI BELLY 0.67 1.024 DICTATOR, THE 1.48 0.177 DIN TAO: LEADER OF THE PARADE 0.50 0.195 DIVA 1.53 0.168 DORAEMON THE MOVIE 2012 1.43 0.171 DOUBLE TROUBLE -0.75 0.159 ELLES 0.51 0.170 FIRST TIME 0.65 0.161 GONE 0.40 0.707 GOOD DOCTOR, THE -0.33 0.159 HOTARU THE MOVIE: IT'S ONLY A LITTLE LIGHT IN MY LIFE 1.34 0.161 I WISH 0.10 0.392 LACUNA -1.73 0.756 LAN KWAI FONG 2 1.99 0.173 LATE AUTUMN 1.25 0.150 MOTORWAY 1.75 0.189 NAKED SOLDIER -0.14 0.149 PAINTED SKIN: THE RESURRECTION 2.09 0.187 PERFECT SENSE -0.52 0.313 POST CARD 0.58 0.216 RAID: REDEMPTION, THE 1.20 0.169 RAVEN, THE 1.48 0.180 REC 3 -0.61 0.162 RED LIGHTS 1.70 0.183 ROCK OF AGES 1.19 0.176 SALMON FISHING IN THE YEMEN 0.70 0.160 SHADOWS OF LOVE 0.32 0.260 SHONEN JUMP HEROES FILM -0.05 0.147 SILENCED 0.81 0.153 SILENT WAR, THE 1.52 0.170 SNOW WHITE AND THE HUNTSMAN 1.25 0.180 THE BOUNTY 1.21 0.176 THE CASES -0.44 0.151 THE FOUR 1.65 0.206 THE PORK OF MUSIC 1.19 0.158 THE WINGS OF THE KIRIN 0.57 0.171 TO ROME WITH LOVE 1.46 0.177 TOTAL RECALL 2.07 0.186 VOW, THE -0.79 0.224 107  Movie Estimate Standard Error VULGARIA 2.20 0.170 W.E. 0.90 0.159 WHAT TO EXPECT WHEN YOU'RE EXPECTING 1.01 0.164 WHEN PIGS HAVE WINGS 0.92 0.243 WOLF CHILDREN 0.87 0.236 WU DANG 1.14 0.180            Note: 2D ABRAHAM LINCOLN VAMPIRE HUNTER is the base case.                           108  Appendix D: Counterfactual Results in the All-Theater Market  Table A.1  Counterfactual Results of the Uniform Pricing Strategy (All Theaters)  Theater Average Price  2D Uniform Price  3D Uniform Price Admission Profit (HK$) A1 76 53 113 706980 20871000 A2 87 58 122 930630 29334000 B1 57 53 122 139240 4045900 B2 87 54 115 174460 5240700 B3 76 52 114 371070 10903000 B4 73 54 114 129080 3816200 B5 75 52 114 331400 9732000 B6 82 53 114 556030 16478000 B7 79 54 117 116760 3481500 B8 73 53 115 239350 7027700 B9 74 52 114 658800 19355000 B10 81 59 121 889950 28241000 B11 81 52 113 503000 14857000 B12 78 53 113 308830 9124500 B13 77 54 114 108610 3234800 C1 76 53 113 262340 7728000 C2 76 54 114 877010 26120000 C3 75 53 114 225020 6641100 C4 76 53 114 224880 6664300 C5 77 53 115 237380 7047500 D1 84 53 116 643400 19235000 D2 79 54 114 139810 4177900 D3 74 53 114 169020 5006000 D4 79 53 113 211550 6275300 D5 79 53 113 339950 10028000 D6 75 55 115 943540 28610000 E1 91 56 118 60952 1868800 E2 78 53 114 172180 5113300 E3 78 53 115 290690 8626900 E4 73 53 114 388130 11371000 E5 76 54 115 889000 26652000 E6 76 54 115 115460 3436500 E7 86 54 115 156940 4699700 E8 82 54 116 124270 3730600 E9 76 53 114 616950 18243000 Total       13252662 397017200 109   Table A.2   Counterfactual Results of the Differential Pricing Strategy (All Theaters)  Theater Average Price Admission Profit (HK$) A1 74 703530 20759000 A2 86 928360 29266000 B1 53 144700 4181100 B2 84 174880 5254700 B3 73 369110 10836000 B4 71 127590 3769000 B5 72 329170 9657100 B6 81 555170 16459000 B7 76 116780 3483600 B8 70 236500 6938900 B9 72 650090 19107000 B10 82 951470 29886000 B11 78 497960 14721000 B12 76 307690 9095800 B13 76 107820 3211400 C1 73 261150 7688300 C2 74 878550 26136000 C3 72 224340 6615500 C4 74 225770 6685000 C5 75 237110 7047500 D1 82 644030 19269000 D2 77 140270 4186400 D3 72 168850 4992700 D4 76 211570 6270200 D5 76 338930 9990800 D6 74 942500 28546000 E1 88 61425 1883800 E2 76 171080 5079800 E3 76 288830 8577600 E4 71 387290 11350000 E5 75 881190 26418000 E6 74 114710 3411200 E7 84 159250 4760600 E8 80 124410 3734700 E9 74 617030 18246000 Total   13279105 397514700     110   Table A.3  Counterfactual Results of the Restricted Differential Pricing Strategy (All Theaters)  Theater Average Price Admission Profit (HK$) A1 60 1151800 30948000 A2 86 818450 25429000 B1 52 162680 4586500 B2 72 393250 10111000 B3 63 666420 17903000 B4 61 163320 4684500 B5 60 573720 15536000 B6 81 493170 14491000 B7 75 101410 3002400 B8 59 405000 10966000 B9 61 1084300 29709000 B10 82 833060 25796000 B11 69 835070 22797000 B12 67 399080 11447000 B13 65 155320 4397900 C1 64 325930 9346700 C2 63 1201100 33659000 C3 120 286890 8217100 C4 62 298190 8566800 C5 70 282530 8195000 D1 82 571920 16893000 D2 68 180500 5205000 D3 66 201820 5819200 D4 69 258060 7434500 D5 69 408200 11720000 D6 72 1264900 36065000 E1 88 54696 1658500 E2 68 215500 6221800 E3 76 251260 7372900 E4 71 334870 9726800 E5 75 753390 22317000 E6 66 143890 4157900 E7 84 142560 4218600 E8 74 158380 4588300 E9 66 713120 20660000 Total   16283756 463847400    111  Appendix E: Tables for Section 3.4     Table A.4 Park Visits (January 2006-May 2009)   Visitors per Month Park Mean Max Min Std. Dev. CV Abraham Lincoln Birthplace NHP 16544 37586 4087 9297 0.56 Badlands NP 65869 217962 7008 73762 1.12 Black Canyon of the Gunnison NP 14048 33598 2070 10283 0.73 Capitol Reef NP 45386 92630 5075 30992 0.68 Colonial NHP 275045 391445 130641 94040 0.34 Cumberland Gap NHP 75183 135909 40281 24519 0.33 Cuyahoga Valley NP 209907 427995 95854 90125 0.43 Everglades NP 81173 241397 27457 33373 0.41 Glacier NP 147963 621046 8017 194498 1.31 Great Basin NP 6039 15267 925 4736 0.78 Haleakala NP 106902 148140 66799 17726 0.17 Joshua Tree NP 112627 260407 46833 43288 0.38 Kenai Fjords NP 20266 89462 0 31120 1.54 Mammoth Cave NP 83001 256832 14034 57909 0.7 Marsh-Billings-Rockefeller NHP 2425 7996 227 2275 0.94 Mount Rainier NP 84567 267285 663 88629 1.05 Natchez NHP 39686 77958 17836 16669 0.42 Nez Perce NHP 15541 42201 2524 9871 0.64 Olympic NP 98424 310024 34294 71000 0.72 Pecos NHP 2731 4920 492 1321 0.48 Redwood NP 31959 82714 10852 18948 0.59 Rocky Mountain NP 217383 653885 50974 204247 0.94 Saratoga NHP 7830 15330 1049 4764 0.61 Sequoia NP 76401 176568 25630 47757 0.63 Sitka NHP 22835 68065 5050 20249 0.89 Theodore Roosevelt NP 36703 108614 351 38060 1.04 Voyageurs NP 17257 49304 210 18289 1.06 Women's Rights NHP 1530 4939 183 1159 0.76 Yellowstone NP 230800 822773 12382 277826 1.2 Yosemite NP 271548 550172 78795 161230 0.59 Zion NP 214961 368739 56137 110222 0.51 Total 84920 822773 0 121862 1.44 Note: CV is coefficient of variation (Std. Dev./Mean)  112  Table A.5  Parks and Nearby Towns  Park/Town Mean Visitors per Month  Population Abraham Lincoln Birthplace NHP   Hodgenville (KY) 16544 3212 Badlands NP   Interior (SD) 31775 95 Wall (SD) 34093 770 Black Canyon of the Gunnison NP   Crawford (CO) 14048 431 Capitol Reef NP   Torrey (UT) 45386 181 Colonial NHP   Yorktown (VA) 275045 65459 Cumberland Gap NHP   Cumberland Gap (TN) 37220 494 Middlesboro (KY) 37963 10321 Cuyahoga Valley NP   Independence (OH) 209907 7113 Everglades NP   Everglades City (FL) 81173 402 Glacier NP   Babb (MT) 43408 195 Columbia Falls (MT) 49867 4685 West Glacier (MT) 54689 367 Great Basin NP   Baker (NV) 6039 68 Haleakala NP   Hana (HI) 106902 1235 Joshua Tree NP   Joshua Tree (CA) 76594 7414 Twentynine Palms (CA) 36033 25123 Kenai Fjords NP   Seward (AK) 20266 2698 Mammoth Cave NP   Brownsville (KY) 41501 836 Park City (KY) 41501 537 Marsh-Billings-Rockefeller NHP   Woodstock (VT) 2425 3048 Mount Rainier NP   Ashford (WA) 51983 217 Packwood (WA) 32584 1330 113  Park/Town Mean Visitors per Month Population Natchez NHP   Natchez Me (MS) 19843 15774 Natchez Wj (MS) 19843 15774 Nez Perce NHP   Grangeville (ID) 15541 3146 Olympic NP   Port Angeles (WA) 51493 19068 Sekiu (WA) 46930 27 Pecos NHP   Pecos (NM) 2731 1392 Redwood NP   Klamath (CA) 31959 779 Rocky Mountain NP   Estes Park (CO) 163756 5876 Grand Lake (CO) 53627 469 Saratoga NHP   Stillwater (NY) 7830 1740 Sequoia NP   Three Rivers (CA) 76401 2182 Sitka NHP   Sitka (AK) 22835 8192 Theodore Roosevelt NP   Medora (ND) 32940 111 Watford City (ND) 3763 1759 Voyageurs NP   Kabetogama (MN) 17257 70 Women's Rights NHP   Seneca Falls (NY) 1530 6669 Yellowstone NP   Cooke City (MT) 8823 140 Gardiner (MT) 27920 851 West Yellowstone (MT) 194056 1272 Yosemite NP   El Portal (CA) 271548 474 Zion NP   Orderville (UT) 51324 580 Springdale (UT) 163636 531     114  Table A.6  Brand Distribution  Brand Bdum Price (cpg) N 76 1 295.80 8 ARCO 0 257.90 2 BP 1 262.10 21 CENEX 0 278.13 6 CHEVRON 1 296.71 21 CIRCLE K 0 290.25 5 CITGO 0 256.49 23 CONOCO 1 303.93 14 CROWN 0 244.12 4 CUMBERLAND 0 259.37 1 DIAMOND SHAMROCK 0 299.62 2 EXXON 1 297.79 18 FINA 0 293.70 1 GULF 0 339.01 2 KROGER 0 259.74 1 KUM \& GO 0 283.66 1 KWIK FILL 0 272.01 3 MAPCO 0 256.27 1 MARATHON ASHLAND 0 241.94 3 MOBIL 1 281.81 14 MURPHY USA 0 258.14 2 OPTIMA 0 252.93 2 PHILLIPS 66 1 285.27 8 PILOT 0 283.78 2 RACETRAC 0 253.04 2 ROYAL FARMS 0 255.80 1 SAFEWAY 0 297.58 1 SHELL 1 286.63 28 SINCLAIR 0 310.69 16 STEWARTS 0 287.43 1 SUNOCO 0 277.40 4 TESORO 0 286.51 2 TEXACO 1 291.37 11 UNBRANDED 0 291.12 23 UNKNOWN 0 282.15 4 WAWA 0 256.30 1    115  Appendix F: Derivation of VFM in the General Case Taking into Consideration the Government?s Cost of Raising Revenue   The Nash product is                                                                             The optimal solution is                                       So the VFM of PPP after renegotiation is                                                        Without any changes in demand, the contract remains the same with VFM is                 The expected VFM under the PPP contract is then                                                                                                                                This is expression (4.10) in the main text.        


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