Franchising and Local Knowledge: An Empirical Investigation in the Pizza Delivery Industry.∗ Elan Fuld November 10, 2011

Abstract A vast amount of economic activity in the U.S. and elsewhere is organized using franchising. Franchising is particularly ubiquitous in retail chains in fields ranging from tax preparation to car repair to pizza delivery. If local owners know more than remote owners about the ever-changing demand conditions in their area, this could be an important driver of the extensive use of franchising in geographically dispersed retail chains. However, the empirical literature has been unable to find evidence that franchisees do in fact know more about local demand, much less test whether such knowledge is a determinant of franchising. This paper examines whether franchised outlets in a U.S. pizza delivery chain know more about local demand fluctuations than company-owned outlets do, as revealed by their pricing behavior.

We find

that franchisees are better informed about local demand. While franchisee pricing is responsive to fluctuations in local demand, company owned stores exhibit no such responsiveness.

∗

I am grateful to my advisors for their many helpful comments and support. I am also thankful for helpful discussions with Lanier Benkard, Phil Haile, Ted Rosenbaum, and for helpful feedback from the participants at the Yale Industrial Organization workshops. I’d also like to thank Stacey Maples for providing outstanding GIS support, and Andrew Sherman for providing great assistance with using Yale’s computing clusters.

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1

Introduction

A vast amount of economic activity in the U.S., and elsewhere, is organized using franchising. In 2001 there were over 750,000 franchised businesses in the U.S. accounting for 7.4 % of private-sector employment.1 A majority of chains that franchise do not franchise all their units but retain a minority as company-owned.2 There is a large literature examining why chains should franchise at all, and what determines whether they franchise and which units they choose to franchise. The empirical literature tends to focus on two explanations of why firms would cede ownership of some of their brand’s outlets in return for royalty fees: moral hazard and risk-sharing. The empirical findings on moral hazard generally match the predictions of the theory; the greater (proxies for) the importance of franchisee effort, the more franchised outlets are observed, and the greater (proxies for) the importance of franchisor effort, the more company-owned outlets are observed. (See LaFontaine and Slade 2007 JEL for a review of the relevant studies.) However, the empirical findings on risk-sharing are the opposite of what the theory would predict: Higher measured riskiness is positively related to franchising. One possible explanation is that franchisees have greater knowledge of the fluctuations in local demand and other outlet specific factors. Franchisees’ superior knowledge would be most valuable where such fluctuations are most important, that is in locations where measured variability (i.e. risk) is greatest. However, the empirical literature has been unable to find evidence that the importance of local knowledge is a determinant of franchising. Even the more fundamental hypothesis of whether franchised outlets are indeed better informed about fluctuations in local demand has not been tested. In this paper, we examine whether franchised pizza delivery stores in a major US chain have greater knowledge of local demand fluctuations than company-owned ones do, as revealed by their pricing behavior. We find that franchised outlets are better informed than company-owned ones about current local demand. The analysis is carried out in two stages. In the first stage, we estimate a spatial logit model of demand that has a census tract-week specific structural error. Since the structural error varies at the tract-week level, the model allows for taste shocks that are both highly localized and that vary at a high frequency. In the second stage, the demand estimates are used to examine whether franchisees’ pricing is more responsive to the shifts in local demand that they face. In the first stage, our spatial logit model of demand makes use of our unusually rich spatial data (precise transaction-by-transaction consumer locations) to overcome two principle 1

Figures come from [22] see Blair and Lafontaine [9] Chapter 4. Blair and Lafontaine also note that franchisors have told them that they try and maintain a target mix of company-owned and franchised stores. 2

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difficulties that would otherwise plague our demand model. The first is that we lack price, quantity, and revenue information for rival stores, but the fine-grained consumer location data allows us to overcome this. The reason for this is that consumers dislike paying more and they dislike waiting longer (and wait time is increasing in distance.) Each store has one price per period but delivers to consumers whose distance from the store and from its rivals varies. The variation in distance from the store is not collinear with the distance from its rivals.3 This allows us to back out the mean utility from a rival without knowing their price because the higher the mean utility consumers get from a rival’s product, the more our store’s share will vary with the distance to that rival.4 The second difficulty our spatial data helps us overcome is the identification of a model with a parameter for every tract-week combination. Even without a single other parameter this would greatly exceed the degrees of freedom available.5 Only by having spatial data that varies at a finer spatial granularity than the taste shocks is identifying such a model even possible. In the second stage, we perform several tests for whether franchised and company-owned stores reveal knowledge of the shift that their residual demand curve has undergone due to the local demand shocks and whether one of these groups reveals more knowledge than the other. These tests are based on the rank correlation between a store’s week-to-week change in price and the week-to-week (parallel) shift in its demand curve. The use of rank correlations is based upon the insight that although the optimal adjustment in price is related to the demand shift in a non-linear way whose precise form is unknown, we do know that this relationship is a monotonically increasing one for any upward sloping supply curve. So, regardless of the specific supply function, a fully informed firm will increase(decrease) prices more in response to a bigger outward(inward) demand shift than in response to a smaller outward(inward) demand shift. Hence, when the rank order of a firm’s price shifts and demand shifts disagree this indicates a lack of information about the demand shock. We perform three types of tests based upon the rank correlations. The first test takes the rank correlation of price and demand shift for all franchised stores and for all companyowned stores and tests whether they’re each significantly different than zero. A significant positive correlation would indicate some knowledge of the current locally generated demand shift. A significant negative correlation would be indicative of a misspecified model because 3

Also, the distance from various consumers to one rival is not collinear with the distances from those consumers to a 2nd rival. The distances from the set of consumers to two stores could be collinear is if those two stores were in precisely the same location. (e.g. there’s a building with a Dominos on the first floor and a Papa John’s on the second floor.) This does not occur in the data. 4 In the extreme case, imagine a rival that makes an aptly named and truthfully advertised “Old Anchovies and Arsenic Pizza” The mean utility from their pizza is −∞, and a consumer’s distance from them, holding distance from our store constant, is independent of the demand our store experiences. 5 The data includes 74 of our chain’s outlets, 60 rival outlets, and over 1,900 tracts.

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it would indicate that the stores have some knowledge of the current demand shift and they use that knowledge in a self-destructive manner.6 By pooling together the franchised and company-owned stores into two groups, this first test could potentially produce positive correlation in the group even if each of the constituent stores had negative correlation, a problem known as Simpson’s Paradox.7 Therefore, our next two tests are constructed to be immune to Simpson’s paradox. Our second test computes the rank correlation of price and demand shift for each individual store and then tests whether the proportion of stores whose correlation is positive is significantly different from half.8 Analogous to the first test, a proportion significantly higher than half is indicative of some local knowledge, whereas a proportion significantly lower than half is indicative of misspecification. The third test computes correlations for each store, and then, for each possible combination of a single franchised and company-owned store looks at which correlation is greater. It then tests whether the proportion of combinations where the franchised store’s correlation is greater is significantly greater than half.9 In this test a significantly positive result would indicate franchisees have greater local knowledge, while a significantly negative one would indicate that company-owned stores know more. We perform each of the three types of tests for each of the 4 demand models we fit, for price changes and demand shifts being specified as level changes and as percentage changes, and for each of two different rank correlation measures: Spearman’s ρ and Kendall’s τ . We also run versions of each of the tests that correlate the shift in prices to the component of the demand shift that’s due to the local taste shocks, as well as ones that correlate the shift in prices to the component of the demand shift that’s due to the change in utility from rival stores. Any observed differences between the pricing behavior of franchised and company-owned stores can not be a priori attributed to differences in knowledge of local demand shocks, as there are alternative explanations. We explore several alternative explanations, including: frictions that cause lumpy price adjustment, (e.g. menu costs.) frictions that cause partial adjustment, (e.g. quadratic adjustment costs.) agglomeration bias, (i.e. Simpson’s paradox.) 6

Allowing for the possibility of a result that would falsify our model serves as an additional robustness check on our model. The fact that we observe no significant negative correlations in any of our tests increases our confidence in our results in the Popperian sense because the results have survived that many more attempts to falsify them. 7 a.k.a agglomeration bias. The name Simpson’s Paradox was coined by Blyth [10] although the concept predates both Blyth and Simpson. 8 Technically, it’s the proportion of stores that have positive correlation out of the stores that have nonzero correlation. If we had a large sample for each store this distinction would be irrelevant. However, we have 9 first differenced observations for each store and zero rank correlations between sets of 9 observations will sometimes happen. 9 This is out of those pairs where the two stores are not tied. Just as zeros are discarded in the second test, ties are discarded in the third test.

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serially correlated shocks, and combinations thereof. Each of these alternative explanations is addressed in turn and is either ruled out by the data or is insufficient to explain the results. For both Spearman’s ρ and Kendall’s τ , and across various specifications and tests, franchisee price shifts have a significantly positive rank correlation with demand shifts while the correlation for company-owned stores is not significantly different from zero. This suggests that franchisees are able to make use of some knowledge of the current local demand shocks but that company-owned stores are not. Additionally, we find that the prices of franchised stores are positively related to the part of the shift in their residual demand curve that is due to the changes in local taste shocks, but not the part due to changes in the utility from rivals; company-owned stores again have no significant correlation to either of these. In none of the tests do we find any significantly negative correlations that would have pointed to a possible misspecification. Taken together these results suggest that franchisees do possess information about the current shocks to the residual demand curve they face and that this is wholly or primarily the result of knowledge of the local taste shocks, rather than of shifts in consumer utility from rival products. Conversely, there is no evidence that company-owned stores are able to utilize any knowledge of current shocks to local demand. The remainder of this paper is as follows: Section 2 provides a brief description of the pizza delivery industry, franchising, and the literature on franchising. Section 3 provides a brief description of the data. Section 4 describes the empirical strategy and results. Section 5 concludes.

2

Industry Description and Literature Review

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In the pizza delivery industry, consumers order pizza and other food from their home either by telephone or internet.11 This paper focuses on pizza delivery by large chains, though many small local firms do exist. When ordering pizza delivery from a chain, consumers are generally not aware of whether they’re ordering from a company-owned or franchised outlet. Besides the brand they’re ordering from consumers observe the address of the store they’re ordering from12 and they observe the price they’re paying. Clearly both these things vary outlet to outlet,which is hardly unique to pizza delivery. What is unique to pizza delivery is these are arguably the only attributes the consumer observes that vary between stores in 10

This section draws from Blair and Lafontaine (2005) [9] and from conversations with employees of the pizza delivery chain we got our data from. 11 They could also walk in to the store to place a delivery order, but this is not very common; it seems to defeat much of the purpose of having food delivered to you. 12 It’s displayed online and in most places one would look up the phone number, and once on the phone the consumer could simply ask.

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a chain. All the product attributes of, for example, Domino’s Pizza are seen as belonging to Dominos and not to a particular outlet. The consumer doesn’t observe the aesthetic, sanitary, and other physical attributes of the store, because the consumer never sees the store.13 Within a chain, some outlets are owned by the franchisor (i.e. the company that owns the brand) and some are owned by franchisees who pay a royalties (i.e. a percentage of sales.) and fixed fees to the franchisor but keep all remaining profits, and absorb all remaining losses. Although franchisees do not have discretion over the product mix they offer, they do have discretion over the prices they charge. It is a per se anti-trust violation for franchisors to impose minimum resale prices on their franchisees, and from 1968-1998 it was a per se violation for them to impose maximum resale prices as well.14 Despite the present legality of imposing maximum prices on franchisees this does not yet seem to be common practice.15 Additionally price controls would be difficult to enforce in a pizza delivery chain, given the great variety of specials, discounts, and coupons that can be used to circumvent them. In pizza delivery each store delivers to consumers in a range of locations, but does not charge different prices based on the location of the consumer, despite knowing the location of the consumer.16 This feature, combined with data on consumer locations for each transaction, is very helpful for demand estimation. One might wonder why firms franchise at all. Franchising is more than just a way for chains to gain capital to expand because mature franchised chains maintain a relatively stable fraction of franchised stores.17 Empirical literature indicates that franchisees are able to extract at least some of the rents generated by the outlet, (See Kaufmann and Lafontaine (1994) and Michael and Moore (1995)) so franchisors clearly incur a cost by franchising, indicating that the presence of an offsetting advantage.18 Moral hazard is one of the commonly advanced reasons for and determinants of franchising. If moral hazard is a determinant of franchising we would expect to find that outlets are more likely to be franchised where shopkeeper effort is more important, and indeed the empirical findings 13

This feature is very helpful for our analysis, as it allows us to avoid modeling or otherwise accounting for unobservable product differences between stores in our chain. 14 Maximum resale price maintenance was made per se illegal in the 1968 supreme court case Albrecht v. Herald Company. The 1998 supreme court decision State Oil Company v. Khan changed this, making the anti-trust status of maximum resale price maintenance subject to a rule of reason. 15 Pizza commercials advertising things such as two pizzas for the price of one on Tuesdays, have tiny print at the bottom stating that this is valid at only at participating franchisees. 16 This is based on conversations with people who work in this industry who stated that this never happens in major chains, and is even rare among small local firms. 17 See Lafontaine and Shaw (2005) 18 When the franchise fees include a percentage of revenue royalty (they typically do) then there is also a dead-weight loss incurred by franchising. For a royalty rate ρ the franchisee faces first order condition (1 − ρ) ∗ marginal revenue = marginal cost. The presence of the royalty in the first order condition leads to higher, prices, lower quantities, and a dead-weight loss.

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generally support this conclusion. The importance of effort is measured in a variety of ways. For example, Woodruff (2002) finds that Mexican shoe manufacturers are less likely to be vertically integrated when they make shoes with more frequent changes in fashion, which is their measure of the importance of effort.19 Another commonly advanced explanation for franchising is risk-sharing, however it is contradicted by the empirical evidence indicating that franchising is associated with riskier locations, even though one would expect that the franchisor’s more diversified portfolio of stores (and better access to capital) would lead it to take riskier locations. Bhattacharyya and Lafontaine (1995)20 propose alternative explanations for these findings that make more sense, in light of the empirical evidence, than risk-sharing does. Another potential determinant of franchising might be local knowledge, which would presumably be more available to local owners. Kalnins and Mayer (2004) perform a study that hints at the presence of local knowledge. They look at the failure rates of franchised chains of pizza shops in Texas. They look at whether local experience by multi-unit owners reduces failure rates, whether multi-unit franchisees or company-owned stores. They find that more local franchisor experience reduces failure rates for both types of stores, but not franchisor’s non-local experience. Similarly, they found that multi-unit franchisee failure rates were decreasing with local experience but not with experience from other areas. This study is suggestive of local knowledge, but the relationship between local experience and failure rates have too many confounding influences for it to be considered evidence of such knowledge. In general, it will be difficult to determine the presence of local knowledge using the locations and ownership structure of stores because of the endogenous location of stores, endogenous ownership structure, heterogeneous abilities of franchisees, and the dynamic nature of location and ownership decisions. Data on consumer locations is enormously helpful not only because each store has numerous dispersed consumers, but also because consumer location is not endogenous with respect to most industries.21

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Data

The dataset used in this paper covers the 10 week period from June 29th to September 6th 2009, and covers delivery orders on geographic Long Island and Roosevelt Island that occur between 4PM and 8PM.22 Focusing on the 4-8PM period accomplishes 2 things: It provides 19

The literature on the determinants of franchising, including the importance of effort as a determinant of franchising, is thoroughly summarized in Lafontaine and Slade (2007) 20 See [8] 21 If one was modeling the demand for public transportation then consumer locations might be endogenous, but not so much for pizza stores. (Real estate listings don’t say “convenient to the subway and Papa John’s”.) 22 Our dataset is a subset of a much larger dataset. The proprietary data sources all cover over a year, and all except for the exclusive delivery territories cover the entire continental U.S. The full dataset was simply

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a good sense of the market size: the number of household-days. Assuming that everyone consumes one meal in that time. It also circumvents the problem of unknown rival hours: Any store that isn’t open from 4-8PM isn’t open at all. This paper utilizes a number of different datasets, several are proprietary datasets from a major U.S. pizza delivery chain, and several are public datasets from the U.S. Census Bureau. There are 4 proprietary datasets used in this paper. The first one provides the exclusive delivery territories for the stores of ”our chain” (i.e. the one the data came from.) The second provides ownership structure information, including which outlets are franchised along with a franchisee identifier (so we can see which are owned by the same franchisee) and some franchisee characteristics. The third proprietary dataset contains the locations of rival outlets of major brands. For rival firms, we observe brand, location, whether they are franchised, whether they deliver, and entry and exit (on a semi-annual basis.)23 we also observe other characteristics such as whether they have a drive-through window, whether they are open 24-hours, etc. The data on firm locations is only reliably complete for large chains, so the analysis throughout focuses on the three largest U.S. pizza delivery chains: Papa John’s, Domino’s, and Pizza Hut. The fourth is the transaction data.The transaction level data includes: price paid, items ordered, whether a coupon was used, time, date, the location of the consumer,24 and the location of the store. The transaction data contains a price paid for each order, but it is neither practical nor desirable to use these order by order observations of price times quantity for either stage of our analysis.Instead we compute a single average weekly price for each store. The details of the construction of this price index can be found in the appendix. The variation in the pricing and the changes in pricing are central to our analysis. In our data, both franchised and company-owned stores do exhibit non-negligible week to week price changes, although to big to estimate a spatial model of demand on it. The geographic area we use was chosen because it could be treated as a closed system. Geographic Long Island is comprised of the boroughs of Brooklyn, Queens as well as Nassau and Suffolk county (the 2 counties that people call “Long Island.”) Long Island is large enough to provide rich data, but is not impacted by stores or consumers outside the chosen area because it’s an island. Roosevelt Island is a small island that lies between Manhattan and Queens. There are no pizza stores on Roosevelt Island, though it is served by one of our chain’s outlets in Queens and it is not served by any pizza delivery stores outside the geographic area we study. (This was verified by calling the Manhattan pizza shops near Roosevelt Island posing as a customer, and unsuccessfully trying to convince them to deliver there.) 23 For the 10 week period we study their locations at ”mid-year 2009” are the relevant ones. 24 The location of consumer is missing for % 5-10 of observations, which are discarded. Discussions with people at the pizza firm, led us to believe that the process that determines missingness is fairly innocuous. Sometimes address is entered with a type-o or as a locally known name that is not known to GIS. We correct for this selection in a simple way allowing the proportion of orders correctly geocoded varies by store and week, but is otherwise missing at random.

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franchisees do exhibit greater week to week variation in price. The histogram of week to week price changes both as levels and as percentage changes, are shown below for franchised and company-owned stores.

(a) Histogram of change in price for (b) Histogram of change in log price Franchised (top) and company-owned for Franchised (top) and company(bottom) outlets owned (bottom) outlets

Figure 1: These histograms show the relative frequencies of price changes in levels and in logs, for franchised and company owned stores.

There are 4 public datasets used in this analysis. Demographic data comes from the redistricting file of the 2010 census and from the 2005-2009 5-year American Community Survey (ACS.) The census provides a few key figures at the 2010 census block level: number of people and households, how many are Hispanic (or not), and how many are of various races. All other demographic data comes from the ACS and is measured at the 2000 Census tract level.25 we use the 2009 TIGER file provided by the Census Bureau to get the 2000 census blocks and tracts. The 2000 census geography is used throughout. Because the 2010 redistricting file is on 2010 blocks we also use the census bureau’s 2010 census block relationship file which lists which 2000 blocks correspond to which 2010 blocks. For most blocks (about 90%) there is a one-to-one correspondence. For blocks that aren’t one-to-one we approximate the population in the 2000 block as of the 2010 census in the following way: we assume each 2010 block’s population (and number of households) is uniformly distributed over it’s land area, this is used to impute the population in the 2000 block.26 Consumer location data, though geocoded at the address level, is discretized to the census block level, since that is the smallest area for which population is known. Store locations are not discretized, but are geocoded with the greatest accuracy possible.27 25

The ACS contains a number of demographic variables at the block group level. However, many more variables are available at the slightly higher census tract level, and all variables have less sampling error at the tract level. 26 For example, if a 2000 block consisted of 60% of a 2010 block with 100 people and 50% of another 2010 block with 10 people, it’s population would be imputed as 65. 27 For many stores the dataset provided address level matching, and for many others ZIP+4 level matching,

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4 4.1 4.1.1

Empirical Strategy and Results Demand Demand Model

In this model households decide each day what to get for dinner. They can either get food from one of the big 3 pizza delivery chains28 , or they can eat something else. Each chain’s food is treated as a single-product, and each outlet is treated as having a single delivery price in each time period. This product is the basket of food offered by that chain. (e.g. Pizza Hut food) For our chain’s outlets, we use the transaction data to construct an index of average weekly price for each store. The methodology used to construct the price index is detailed in Appendix A. Consumers get disutility from paying more and waiting longer. The disutility from price is allowed to vary with the median income of the tract. The disutility from waiting is captured by a county-specific disutility from (Euclidean) distance to the store. The further the store is the longer the expected wait, but how long it takes to travel a mile is allowed to vary by county: It’s different in Brooklyn than it is in the Hamptons. There is a tract-week specific utility for the category of pizza delivery ξC(b(i)),t , where b(i) denotes the block containing consumer i and C(b(i)) denotes the tract containing that block. There is also the usual consumer-alternative-time specific I.I.D Type I extreme value error i,j,t that is characteristic of logit models of demand. This yields: Ui,j,t = −(α0 + αy ∗ log (yC(b(i)) ))pj,t − γC db(i),j + ξC(b(i)),t + i,j,t a level that is almost as good since a business will frequently have it’s own ZIP+4 code, or possibly share it with an adjacent structure. When the dataset provided a less accurate match, or no match at all the store was manually geocoded using Google maps, and other internet mapping services. Whenever there was any doubt as to the location we used Google street view to get visual confirmation and/or called to get directions. This was necessary when the address was imprecise (e.g. Route 66 Randomville,KS) 28 They can only order from a chain if they’re within range of it. For our chain’s outlets we observe the delivery territories, so we know precisely which consumers are in range of each of our outlets. For the other chains’ outlets we say that a consumer is within range of an outlet if: 1) It is the closest outlet of that brand AND 2) It’s distance to the consumer is less than the lesser of furthest delivery observed in that county and 5 miles.

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Where db(i),j is the distance from store j to the centroid of consumer i’s block,29 γC is the disutility from distance for county C 30 , yC(b(i)) is the median household income of tract C(b(i)) as measured in the American Community Survey, (ACS) and pj,t and is the price of store j in week t. Because The dataset does not include rival prices, quantities or revenues, for rival chains, the price term in the utility function is replaced by a store-time fixed effect. ρj,t Ui,j,t = ρj,t − γC db(i),j + ξC(b(i)),t + i,j,t

The utility from the outside option is normalized to zero. Since the tract-time specific utility for the pizza delivery category can be alternatively thought of as a tract-time specific utility for the outside option, (i.e. by subtracting ξj,t from the utility from each alternative.) this is not actually an additional restriction. Note that this model contains two potential sources of time-varying local demand. The first is the tract-time specific utility for pizza delivery ξC(b(i)),t , the second is the time-varying mean utility from rivals ρj,t , which shifts the residual demand for pizza from our chain’s outlets for consumers in the areas that the rival in question delivers to. Our analysis will look at the variation in local demand from that arises jointly from theses two components, as well as the variation that arises from each component separately in order to determine whether the results are being generated by one or both of these components.31 4.1.2

Demand Estimation

The empirical strategy for turning the above model of consumer utility into a working model of demand requires a careful consideration of the strengths and weaknesses of the data at hand. The data on outlets of our chain is incredibly detailed containing ownership structure, location, entry and exit, transaction data, and consumer locations. The consumer location data is something fairly unique about this dataset, and is the major strength of the dataset, and will be the major source of identifying variation. Although we discretize the locations to the census block, this still leaves a tremendous amount of variation. While we observe a great deal about the outlets and customers of our firms, we observe little about rival firms. We 29

I actually use the census bureau’s “internal point” for each census block. This point is not necessarily a centroid per se For example it is required to lie within the block (sometimes a binding restriction for non-convex blocks) and required to be on land. These properties seem more desirable than being precisely at the centroid of a geographic area as small as a census block, and thus this was chosen as the representative point rather than the true centroid. 30 I use the county that the store is located in, rather than doing some ad hoc interpolation for the few orders where the consumer is in a different county than the store is. 31 As we’ll see later, it turns out that it’s ξj,t that franchisees know more about not ρj,t

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observe a list of locations of pizza firms as of mid-year 200932 whether they deliver, whether they’re franchised, their brand, and their location but we do not observe price or quantity data for rivals. Between our rich location data for our consumers, and the location being the only continuously varying attribute of rival firms that is observed, it is apparent that the spatial information is going to be key for our identification strategy. In a traditional BLP setup 33 the expected purchase probabilities are aggregated up to fairly large “markets” and then taken as market shares. Because these markets each contain a large number of consumers the predicted shares must be very close to the observed shares if the model is an appropriate one, therefore in that framework the observed and predicted market shares are constrained to be equal, and then the distance to the GMM moment conditions is minimized conditional on these equalities holding. However, in the setting of this paper, where spatial variation is the crux of the identification strategy, aggregating purchase probabilities up to an area that is large enough to be considered anything resembling a market would destroy the spatial variation that constitutes most of the demand information contained in our data.34 Because spatial variation is so important in this setting the purchase probabilities are aggregated to the smallest level possible, the block-week level.35 Aggregating to such a small level makes it wildly inappropriate to match the predicted and observed purchase probabilities.36 At such a low level of aggregation the observed purchase probabilities still contain a good deal of sampling error, and consequently are sometimes zero. The only way to get a predicted share of zero is for utility to be −∞, when clearly sampling error is what is causing the lack of observed purchases.37 Therefore, rather than matching the purchase probabilities and minimizing the distance to the moment conditions, we minimize the “distance” between the observed and predicted shares, conditional on matching the moment conditions. The distance metric chosen is the negative log-likelihood. This means that instead of performing Generalized Method of Moments (GMM) estimation, we perform constrained maximum likelihood estimation. (MLE) What is the likelihood of observing xb,j,t purchases on block b for outlet j at time t? Strictly speaking, it is given by the 32

Recall, our demand estimation covers the 10 week period 6/29/09-9/6/09 See [4] 34 Not only would this destroy any hope of identifying our demand model, but any model that aggregates up to a larger area wouldn’t be suitable for examining local variation in demand in any case. 35 Since the census block is the smallest level of geography for which population counts are available, it is not possible to aggregate to a smaller geographic area since there would be no way of knowing the number of potential customers in that area. 36 They are not referred to as “market shares” because to call a census block-week a “market” is an abuse of the term. 37 The alternative would be to suppose that whenever there are no purchases observed for a given block week it is due to the people holding the view that “hell is delivered pizza.” 33

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binomial. However, since there are small purchase probabilities38 and a large number of draws.39 We use the Poisson approximation to the binomial. So the number of orders observed in a block week is distributed as a Poisson with λb,j,t = sˆb,j,t ∗ Mb ∗ gj,t where sˆb,j,t is the predicted purchase probability, Mb is the number of dinners on that block week (7 times number of households.) and gj,t is the percentage of delivery orders that store j correctly geocoded during week t.40 Because the improperly geocoded orders did in fact occur, We deflate λ accordingly, so that it is the rate at which properly geocoded orders arrive, but more importantly, so that predicted share does not reflect fluctuations in geocoding. If there was no endogeneity problem, that is one could safely assume that the ξ’s were mean independent of the prices, then the demand model would be a straightforward MLE estimator, implemented by minimizing the negative log Poisson likelihood. But of course, there is a clear endogeneity problem here: outlets that deliver to areas with high overall levels of pizza demand will charge higher prices. Even if stores aren’t able to quite keep up with the latest shocks in local demand41 they would still incorporate them into their pricing eventually. Therefore, instruments are required. A valid instrument for ξC(b(i)),t must be a variable that is orthogonal to ξC(b(i)),t but correlated to price. One such variable is the percentage of all orders (by all stores) in that week that use a coupon.42 Which is clearly not related to the demand level of a single tract. Other instruments can be formed by taking the population-weighted average of the characteristics of all tracts in a store’s delivery area except for the tract being instrumented for.43 The characteristics chosen are those already in the model, income and distance. Further instruments are constructed by interacting coupon rate with the characteristics of the other tracts. The instruments ZC(b),j,t enter into the demand estimation by enforcing them as constraints on the existing MLE structure. The estimation of the vector of demand parameters θd then takes the form44 : min θd

subject to

XXX b

j

XXX C(b)

j

sˆb,j,t (θd )Mb gj,t − xb,j,t log (ˆ sb,j,t (θd ))

t

Mb ξC(b),t ZC(b),j,t = 0 for each instrument

t

38

Because the purchase probability is the proportion of dinners consumed that are pizza delivery ordered from our chain; this is going to be a lot closer to zero than it is to 1. 39 The number of potential orders is 7 times the number of households in a block, the mean value is 327, the median is 161. 40 This proportion is typically over 90%. The minimum observed is 73% but that is an outlier. 41 Which is what this paper tests. 42 Most coupons are not issued by the individual store. 43 Instruments of this sort are used in George and Waldfogel [31] and in Gentzkow and Shapiro [30] 44 The negative log Poisson likelihood is simplified, and all terms that don’t depend on parameters are removed as they don’t effect the minimization.

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I estimate The above model with different sets of instruments, including a specification with no instruments. The results are found in table 1. Note that since there is no explicit intercept term in the demand model, and since ξ is not constrained to be mean zero, this corresponds to the intercept.45 We now move on to a discussion of the argument for identification of this (1) price 0.0739 price*log(income) 0.0040 distance: Kings County 0.2893 distance: Nassau County 0.2139 distance: Queens County 0.6311 distance: Suffolk County 0.2241 ξ¯ (i.e. intercept) -4.9756 IV: % coupon No IV: log(income) No IV: log(income)*coupon No IV: distance No IV: distance*coupon No

(2) 0.0742 0.0039 0.2905 0.2140 0.6318 0.2242 -4.9876 Yes Yes Yes No No

(3) 0.0730 0.0037 0.2907 0.2144 0.6319 0.2367 -4.9722 Yes Yes Yes Yes No

(4) 0.0718 0.0040 0.2906 0.2139 0.6317 0.2220 -5.0141 Yes Yes Yes Yes Yes

Table 1: Above are the price and distance coefficients from the demand model, with various sets of instruments. Also included is the population weighted mean of ξ, which corresponds to the intercept

model from the data. 4.1.3

Demand Identification

Recall the utility specification for consuming pizza from our chain . . . Ui,j,t = −(α0 + αy ∗ log (yC(b(i)) ))pj,t − γC db(i),j + ξC(b(i)),t + i,j,t

. . . and for consuming pizza from a rival chain: Ui,j,t = ρj,t − γC db(i),j + ξC(b(i)),t + i,j,t

In the above equations distance is the only thing that varies within a census tract. Everything else varies at the tract- time level, or tract-store-time level. Therefore, a specification that 45

Also, note that as long as the instruments are mean zero, which they are because we construct them that way, then the orthogonality conditions are valid, since Cov(X, Y ) = E[XY ] as long as at E[X] ∗ E[Y ] = 0, which only requires one of them to be mean zero.

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contains only the distance term, a tract-store-time fixed-effect, and  is a generalization of both of these models. So Let’s begin by considering that generalization: Ui,j,t = δC(b(i)),j,t − γdb(i),j + i,j,t

Where δ is used to denote the part of mean utility that comes from things other than distance. Thus distance and δ are the only two components of mean utility. In a given block, we allow the closest outlet of each rival brand to compete in the block. There are three major delivery brands in this area: Pizza Hut, Dominos and Papa Johns. Hence, for each tract in question there are at most 3 δ’s to estimate, plus there are 4 γ’s that must be estimated. Let Db(i) be the set of firms that deliver to block b(i). The predicted market share of our firm in a given census block is given by: sbb(i),j,t =

1+

P

eδC(b(i)),j,t −γdb(i),j δC(b(i)),k,t −γdb(i),k k∈Db(i) e

So for each block-time we observe: an empirical share for our firm46 and the distance from the block to each of the 3 firms delivering there 47 And with those we need to recover the mean utility of the census tract for each of the 3 brands delivering there. We are solving for γC too, but those are just 4 parameters for the whole dataset of nearly 2,000 tracts is the same unknown across tracts. So if all consumers were at their tract centroid this would be 3N equations in 3N + 4 unknowns, where N is the number of tracts, which is clearly indeterminate. Recall, the imprecision of the shares on the block level discussed above. Fortunately, there are a number of points for each tract, one for each block in fact. There are an average of 26.62 blocks per tract. Each of these blocks has the same vector of δ’s and the same γ but different vectors of distances. This means we have more equations than unknowns and that these equations are actually linear in the exponentiated mean utilities. To see this, take the share equation and rename eδC(b(i)),j,t = ∆C(b(i)),j,t and edb(i),j = Db(i),j then multiply both sides by the denominator and subtract the numerator from both sides and get. 

 sbb(i),j,t 1 +

X

−γ  −γ ∆C(b(i)),k,t ∗ Db(i),k − ∆C(b(i)),j,t ∗ Db(i),j = 0

k∈Db(i) 46

Number of orders, which combined with a specification for market size gives us a share. Not all blocks will have a firm from both of the 2 rival brands delivering there, but the case with 2 rival brands is the “hardest” so we focus on that. 47

15

So by having multiple blocks within a tract we are varying the D’s and share’s while holding the δ’s and γ constant. Since there are more blocks in a tract than unknowns in the equation are degrees of freedom to spare, which means that matching the shares is actually an impossibility, even without any zero shares. However, we can find the values of the unknowns δ andγ that minimize the distance between the predicted and observed shares. Since the parameters enter linearly into a logit, the likelihood should be unimodal, and the model with the δ’s is identified. In order for this to work though we must rule out collinearity of distances. If the distances from one of these stores to the set of blocks is collinear (or nearly so) with the distances from another store to the set of blocks, we will not be able to separately identify those 2 firms respective δ’s. There are 2 ways that this can occur. The first is if most or all of the block centroids in a tract lie on or very near the line connecting the 2 stores. This one seems implausible. The second way is if the two stores lie extremely close to each other so that distances between other points and the two of them will be nearly co-linear. Fortunately, this does not occur in the data, the closest two rival stores are to each other is .29 miles.48

4.2

Testing for Local Knowledge

This section presents the results of the tests for “local knowledge.” The demand model specified above has two components that are time varying, and both are local. The first is the time varying tract level demand for pizza delivery ξC,t , and the second is the time-varying mean utility from each rival outlet ρj,t . The dataset does not include rival prices, and so it is necessary to allow the mean utility from a rival store to vary over time. Greater knowledge of ξC,t and ρj,t are both forms of local knowledge. They can be roughly thought of as “knowing your customers” and “knowing your competitors.” In this section we will first examine whether franchisees have greater overall “local knowledge,” and then examine whether this is due to better knowledge of ξC,t , of ρj,t , or of both. As will be shown below, there is fairly compelling evidence that franchisees have better local knowledge than company-owned stores do, and that this is due to better knowledge of ξC,t . To test for informational differences between franchisees and company-owned stores,we must ensure that our results are indeed caused by differences in local knowledge and not one or more of a number of alternative explanations: frictions that cause lumpy price adjustment, (e.g. menu costs.) frictions that cause partial adjustment, (e.g. quadratic adjustment costs.) agglomeration bias, and serially correlated shocks. Menu costs, and other lumpy adjustment models, can be ruled out by looking back at 48 there is one instance where a rival store is only 214 feet from one of ours (.04 miles) However, that is still a block away, so the distances won’t be quite collinear, and that kind of close proximity is not the norm.

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the histograms of price changes in figure 1, if menu costs were a factor we would expect to see a large number of near-zero price changes, and a number of large price changes with a “donut hole” in the middle, since menu costs would make comparatively modest price changes not worthwhile. Neither franchised or company-owned stores exhibit such a “donut hole,” regardless of whether we measure the price changes in dollar or in percentage terms. Since the price data are inconsistent with a menu cost explanation, we conclude that menu costs are not present here and we need not concern ourselves further with them. Serially correlated demand shocks can also be ruled out as a substantial influence on pricing. If serial correlation of demand shocks was a substantial factor affecting prices, then the a store’s price one week would predict it’s price next week. Observing such persistence in pricing is far from sufficient to demonstrate the presence of serially correlated demand shocks, but the absence of such persistence would suggest that if such serial correlation is present that it is not sizable enough to be a significant factor in pricing. As shown below in Table 2, once we include store fixed effects to account for the fact that different stores have different average prices, there is no statistically significant persistence in outlets’ pricing. This holds true for both franchised and company owned stores, it holds whether we look at prices in levels or in logs, and whether we also include week dummies to account for any week specific component of price. Note that this lack of persistence also makes it highly unlikely that partial adjustment frictions are present in the data, as substantial partial adjustment behavior would induce persistence as well. The tests we present below, would not be robust to a setting where both serially correlated shocks and partial adjustment frictions are present, though it would be robust to either one of them alone. However, the lack of price persistence we observe allows us to effectively rule out the case where substantial partial adjustment frictions and serially correlated shocks are both present, and also makes it much less likely that either one of them is a sizeable factor here. Nevertheless, in the discussion below we allow for the presence of one of these factors as well as for the presence of agglomeration bias to demonstrate how our tests could be used in a setting where either substantial serial correlation or substantial adjustment costs are present. The tests used below all involve some form of examining the relationship between price and demand shifts for one or more outlets. Therefore, we now discuss how price and demand shifts are defined for these tests. A price shift can either be described as the change in the level of the price: pt − pt−1 or the percentage change in price (pt − pt−1 )/pt−1 .49 Defining demand shifts is a bit more subtle. The predicted share of a single block at time t can be expressed: ˆ pj,t ), and the total predicted demand for a store at time t is simply the ˆ C(b),t , ρˆt , θ, sˆb,t (xi 49

Note that for these tests the percentage change in price will always yield identical results to log pt − log pt−1 by construction.

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Table 2: Price dynamics: This table shows the price dynamics, or lack thereof, present in the data. The regressions all have store fixed effects and we include the fraction of the variance that is explained by the fixed-effects.

pricet−1 : franchised
log pricet−1 : franchised fraction variance due to fixed-effects pricet−1 : company-owned
log pricet−1 : company-owned fraction variance due to fixed-effects Store fixed-effects week dummies

price 0.0597 (1.09)

.6734 -0.0018 (-0.03)

.5557 Yes No

price log(price) 0.0407 (0.73) 0.0599 (1.09) .7032 0.0836 (1.35)

.5398 Yes Yes

log(price)

0.0406 (0.73)

.6672

.6976

-0.0056 (-0.09)

0.0805 (1.30)

.5570 Yes No

.5413 Yes Yes

t-statistics in parentheses * denotes .05 significance, ** .01 significance and *** .001 significance

population weighted sum of the block shares. Where the 3 arguments represent the local estimated value of ξ the relevant estimated value(s) of ρ the non-local model parameters, and the firm’s price at time t, respectively. Clearly, any measure of the demand shift must hold the price constant, otherwise it confounding the demand shift with an endogenous movement along the demand curve. Thus, the baseline definition of a shift in demand curve for a store is: X ˆ pj,t−1 ) − sˆb,t−1 (ξˆC(b),t−1 , ρˆt−1 , θ, ˆ pj,t−1 ) Mb ∗ (ˆ sb,t (ξˆC(b),t , ρˆt , θ, b

where Mb is the “market size”50 of each block. The demand shift is defined as the change in demand that would be predicted if price was left unchanged at pt−1 .51 An analogous percentage shift in demand can be defined by dividing each term in the above equation by ˆ pj,t−1 . Using the above definitions of a demand shift would test for sˆb,t−1 (ξˆC(b),t−1 , ρˆt−1 , θ, general local knowledge, whether generated by superior knowledge of ξC,t , the vector of ρt or both. It is straightforward to modify this to test for local knowledge of only ξC,t , simply by setting ρ to ρt−1 in both sˆt and sˆt−1 , just as we do with price, this would give a measure of 50

7 times the number of households As a robustness check, we also ran all tests assuming that the price was pt , rather than pt−1 , for both periods. This did not qualitatively change any of the results. 51

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the demand shift generated by ξ alone, and if price changes are positively related to it, that would indicate knowledge of ξ.Of course, a measure of the demand shift generated by ρ alone can be analogously defined by setting the ξ’s to their t − 1 values in both expressions, and allowing the ρ’s to change from t − 1 to t. Each test below is run with each of these 3 types of demand shifts, and for both level price changes vs. level demand shifts, and percentage price changes vs. percentage demand shifts. Before presenting the results comparing rank correlations of stores’ price and demand shifts, it is important to discuss what can and can’t be inferred from such tests. Let’s start by considering a firm with 5 periods of data, and therefore 4 first differences. Suppose that the firm experiences two inward demand shifts, one “large” and “small,” and two outward demand shifts, one “large” and “small.” If this firm is fully informed about the demand shifts then several things can be said about it’s price adjustment behavior. If it’s starting from the previously optimal price, it will adjust prices up when demand shifts up and down when demand shifts down, it will raise(lower) it’s prices more in response to the “large” outward(inward) demand shift than for the “small” one, and this is all true regardless of whether it experience partial adjustment frictions. This means that a firm starting from the previous period’s optimal price and having full knowledge of the shock will have price changes whose rank order matches the rank order of the demand shifts. Therefore, we could test for greater rank correlation between a franchisee’s price changes and demand shifts as opposed to that for company-owned outlets. A higher rank-correlation would imply a firm that is acting more like it is fully informed if firms started from the previous period’s optimal price. The problem is, if firms experience adjustment costs then they would not fully adjust for the previous shock and would not start from the previous period’s optimal price, even if they were fully informed. Nevertheless, rank correlation tests can produce inferences that are indeed robust to partial adjustment frictions. Consider two fully informed firms, one of whom has lower adjustment costs (i.e. adjusts a larger fraction of the way to the optimal price.) could have a rank higher correlation. Therefore, results about which of 2 informed firms is more informed than the other are not robust to all manner of informational frictions; the firms are equally well informed yet have different true rank correlations. This implies that conclusions about the magnitude of rank correlations are not robust to informational frictions. However, there is still a relevant class of results that are robust to this: Those about whether a firm is informed about the current local demand shift at all. If a firm’s price change and demand shift have a significantly positive rank correlation that indicates at least some knowledge of that shift, regardless of whether partial adjust frictions are present, while such frictions can attenuate the price shifts of a fully informed firm, they can’t induce an uninformed

19

firm to act informed.52 Therefore, results presented below can be divided into 3 categories that are robust to partial adjustment and other non-informational frictions. A statistically significant positive relationship between price change and the demand shift indicates some knowledge of the current local demand shift. A relationship that is neither significantly positive or negative would indicate no evidence that the firm has knowledge of the local demand shift.53 Finally, if the data show a statistically significant negative relationship between price change and demand shift this would imply some de facto knowledge of the demand shift that is being used self-destructively.54 The absurdity of such a scenario is a strength of these tests rather than a weakness, as it adds an extra element of falsifiability to the test; significantly negative rank correlations would indicate that a potential problem with the tests. All the tests performed indicated either a significant positive relationship or a no significant relationship. There were no significant negative relationships observed. In the first set of tests we pool together all franchised outlets and all company-owned outlets, and examine the rank correlations of each group’s price shifts with its demand shifts. The results are shown in Table 3 (for Spearman correlation) and table 4 (for Kendall correlation.) The results in the two tables are broadly consistent with each other. Company-owned stores price shifts exhibit no significant correlation with their demand shifts. Franchised stores price shifts are positively correlated with their overall demand shifts, and these results are consistently significant at the 0.1% level. The franchised stores price changes also exhibit a consistent positive relationship with the shift in demand due to ξ this is significant at the .05 level or greater (for each table) for 7 out of the 8 specifications tested. The exception (for both Spearman and Kendall) is for the level price change vs. level demand shift on model (4),55 but it is not a very worrisome exception as in both cases it narrowly misses being significant at the .05 level .56 and thus is broadly consistent with the other results. In no specification do either franchised or company-owned stores respective price 52 One might say that positive rank correlation with the current shock could occur if one only knew the previous shock, and the shocks are serially correlated. Although table 2 indicates that serial correlation is not a problem here, even if it were it would not refute the argument above. If the shocks are serially correlated, then knowledge of today’s shock through knowledge of yesterday’s shock is a payoff-relevant form of knowledge about today’s shock. An analogous situation would be someone who didn’t know the weather report for today, but knew that it rained yesterday, and that rainy days are serially correlated. Such a person is surely more informed than someone who just arrived in town and neither saw the weather report nor knew whether it had rained yesterday. 53 Not the same, as evidence that they have no knowledge. Failure to reject the null is not evidence for the null, but rather a lack of evidence against it. 54 Returning to the rain analogy, this would be like the man saying “I know that if it rained yesterday, it’s more likely to rain today, but I’ll only bring an umbrella if it didn’t rain yesterday” 55 This is the model that has the most orthogonality conditions, it corresponds to the 4th demand model in table 1. 56 with p-values of .0535 and .06 respectively

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changes have anything remotely resembling a significant relationship with the part of the demand shift due to ρ. This does not necessarily mean that they have no knowledge of ρ. It is possible that these tests lack the power to pick up such a relationship. For example, if the impact of changes in ρ on residual demand for our outlets is very small relative to the impact of changes in ξ then knowledge of ρ would be difficult to pick up, because it’s such an unimportant part of the pricing decision. Table 3: Spearman Pooled

(1) price change vs. demand shift: -0.0700 company-owned (.2422) price change vs. demand shift: .2315*** franchised ( < .0001) price change vs. demand shift from ξ: -0.0487 company-owned (.4162) price change vs. demand shift from ξ: 0.1463** franchised (.0092) price change vs. demand shift from ρ: 0.0038 company-owned (.9491) price change vs. demand shift from ρ: -0.0101 franchised (.8573) % price change vs. % demand shift: -0.0526 company-owned (.3799) % price change vs. % demand shift: .2319*** franchised ( < .0001) % price change vs. % demand shift from ξ: -0.0680 company-owned (.2557) % price change vs. % demand shift from ξ: .1572** franchised (.0051) % price change vs. % demand shift from ρ: 0.0272 company-owned (.6496) % price change vs. % demand shift from ρ: -0.0155 franchised (.7832)

(2) -0.0678 (.2569) .2331*** ( < .0001) -0.0502 (.4013) 0.1474** (.0086) 0.0082 (.8916) -0.0085 (.8798) -0.0504 (.3997) .2329*** ( < .0001) -0.0693 (.2469) .1577** (.0049) 0.0290 (.6278) -0.0139 (.8052)

(3) -0.0720 (.2290) .2258*** (.0001) -0.0516 (.3884) 0.1315* (.0192) 0.0064 (.9155) 0.0011 (.9851) -0.0532 (.3737) .2256*** (.0001) -0.0709 (.2359) .1448** (.0099) 0.0278 (.6426) -0.0002 (.9973)

(4) -0.0764 (.2017) .2215*** (.0001) -0.0534 (.3723) 0.1085 (.0536) 0.0053 (.9298) 0.0126 (.8230) -0.0574 (.3373) .2215*** (.0001) -0.0742 (.2147) .1211* (.0312) 0.0267 (.6557) 0.0091 (.8716)

p-values in parentheses * denotes .05 significance, ** .01 significance and *** .001 significance

As alluded to earlier , the above results for pooled Spearman and Kendall correlations, are robust to neither Simpson’s paradox nor to heterogeneous adjustment costs. Finding that franchised stores, when pooled together as a group, have price shifts that are positively related to demand shifts does not necessarily imply that this is true of all or even any of the constituent stores. For example it could be generated by a set of franchised stores that 21

Table 4: Kendall Pooled

price change vs. demand shift: company-owned price change vs. demand shift: franchised price change vs. demand shift from ξ: company-owned price change vs. demand shift from ξ: franchised price change vs. demand shift from ρ: company-owned price change vs. demand shift from ρ: franchised % price change vs. % demand shift: company-owned % price change vs. % demand shift: franchised % price change vs. % demand shift from company-owned % price change vs. % demand shift from franchised % price change vs. % demand shift from company-owned % price change vs. % demand shift from franchised

ξ: ξ: ρ: ρ:

(1) -0.0472 (.2382) 0.1529*** (<.0001) -0.0311 (.4372) 0.0945* (.0121) 0.0002 (.9965) -0.0042 (.9126) -0.0354 (.3769) .1547*** (<.0001) -0.0447 (.2639) .1037** (.0059) 0.0147 (.7130) -0.0089 (.8134)

(2) -0.0458 (.2526) 0.1539*** (<.0001) -0.0315 (.4313) 0.0952* (.0115) 0.0039 (.9236) -0.0032 (.9328) -0.0338 (.3986) .1555*** (<.0001) -0.0452 (.2590) .1039** (.0058) 0.0169 (.6737) -0.0078 (.8357)

(3) -0.0488 (.2233) 0.1493*** (.0001) -0.0322 (.4209) 0.0878* (.0198) 0.0025 (.9509) 0.0027 (.9429) -0.0359 (.3694) .1499*** (.0001) -0.0460 (.2510) .0958* (.0109) 0.0159 (.6914) -0.0001 (.9987)

(4) -0.0516 (.1975) 0.1458*** (.0001) -0.0339 (.3979) 0.0708 (.0600) 0.0017 (.9671) 0.0107 (.7766) -0.0389 (.3314) .1478*** (.0001) -0.0482 (.2282) .0797* (.0342) 0.0149 (.7102) 0.0068 (.8565)

p-values in parentheses * denotes .05 significance, ** .01 significance and *** .001 significance

each have a slightly negative correlation, but each store’s mean price shift was strongly positively correlated with it’s mean demand shift. In that case, the pooled results could show a positive correlation. This is what’s known as Simpson’s paradox. As a robustness check against both these possibilities, we perform store by store tests. Each store has only 10 time periods of data, and therefore 9 first differences, so testing the significance of each store’s rank correlation would be highly unreliable. If franchised stores had some knowledge of the local shock, then each store’s true rank correlation (of price and demand shifts) would be positive, regardless of whether adjustment costs are present. Thus, we’d expect to see more franchised stores with positive correlations than negative ones, even though we’d see some negative ones due to the small samples. Using this insight, we test the null that the proportion of stores with positive rank correlations is greater than .5. Due to the small 22

samples, some stores may have rank correlations of exactly 0, and so the zeros are discarded and we use the proportion of non-zero correlations that are positive for the test.57 The results of these tests is provided below in table 5 (for Spearman correlation) and table 6 (for Kendall correlation.) These results are robust to both partial adjustment frictions and to Simpson’s paradox, and they are consistent with the earlier results in tables 3 and 4. Franchised stores price and demand shifts are positively correlated significantly more than often than by chance. This holds for both measures of correlation, and for shifts measured as both levels and as percentages, and holds for across different demand specifications. The same holds for the part of the demand shift due to ξ, though the results are significant by a smaller margin. For the part of the demand shift due to ρ the proportion of franchisee positive correlations is not significantly different from the null of .5. For company-owned stores, the proportion of positive correlations is not significantly different from the null under any of the specifications. As discussed above, if we are concerned about robustness to partial adjustment behavior in this market, we can’t make inferences about whether some firms have better knowledge of local demand, just about whether firms have some knowledge of local demand. There is no particularly strong reason to believe that in this industry a larger price change incurs costs that a smaller one does not. So it seems worthwhile to examine whether there is evidence that franchised stores have greater local knowledge than company owned ones. If there was 1 store of each type, with a large amount of data, a simple test would be to test whether the difference in their correlations was zero. As before, since each store has a small amount of data we make this comparison for each possible combination of a franchised and a company-owned store and test whether the proportion (of the differences) that are positive is greater than the proportion that are negative. Also as before, observations where the difference is zero are discarded. Standard errors based upon independent binary data will be much too small because the data are dependent by construction.58 Therefore, a simple bootstrap procedure is employed to get the standard errors.59 These results are shown in 57

In the tables, the proportion of stores that are dropped due to having zero correlation is given in brackets. 58 This is because if, for example, one franchised store had a very high correlation it would make it’s correlation much more likely to be higher than that of each company-owned store, not just one of them. 59 This procedure takes two collections of random numbers, and for all possible pairings sees for what proportion one group is higher. This is repeated 1 million times and the sample standard deviation of those results is taken as the standard error. This procedure has a slight flaw, in that it does not have discarded ties, and thus has too large a sample size. This leads to underestimating the standard errors. The underestimation should be roughly proportional to the reciprocal of the square root of the proportion that are not tied. The significant results have lower proportions of ties, and are not borderline significant, so this is not generating the results we see. The results with the largest proportion of ties are those that are not significant anyway and larger standard errors will only shrink their t-stats further.

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Table 5: Spearman sign test, by store (1) 0.3824 [.0286] (-1.3517) 0.8718*** [0] (4.5838) 0.4118 [.0286] (-1.0137) 0.7179* [0] (2.6871) 0.5429 [0] (0.4998) 0.5714 [.1026] (0.8330) 0.3429 [0] (-1.8326) 0.8947*** [.0256] (4.8022) 0.3824 [.0286] (-1.3517) 0.6667* [0] (2.0548) 0.5714 [0] (0.8330) 0.5588 [.1282] (0.6758)

(2) 0.3824 [.0286] (-1.3517) 0.8718*** [0] (4.5838) 0.4118 [.0286] (-1.0137) 0.7179* [0] (2.6871) 0.5429 [0] (0.4998) 0.5714 [.1026] (0.8330) 0.3429 [0] (-1.8326) 0.8947*** [.0256] (4.8022) 0.3824 [.0286] (-1.3517) 0.6667* [0] (2.0548) 0.5429 [0] (0.4998) 0.5455 [.1538] (0.5143)

price change vs. demand shift: company-owned price change vs. demand shift: franchised price change vs. demand shift from ξ: company-owned price change vs. demand shift from ξ: franchised price change vs. demand shift from ρ: company-owned price change vs. demand shift from ρ: franchised % price change vs. % demand shift: company-owned % price change vs. % demand shift: franchised % price change vs. % demand shift from ξ: company-owned % price change vs. % demand shift from ξ: franchised % price change vs. % demand shift from ρ: company-owned % price change vs. % demand shift from ρ: franchised t-statistics in parentheses proportion of correlations that were exactly 0 (and were discarded) are in brackets * denotes .05 significance, ** .01 significance and *** .001 significance

(3) 0.3824 [.0286] (-1.3517) 0.8462*** [0] (4.2677) 0.4118 [.0286] (-1.0137) 0.6842* [.0256] (2.2410) 0.5143 [0] (0.1666) 0.5714 [.1026] (0.8330) 0.3429 [0] (-1.8326) 0.8947*** [.0256] (4.8022) 0.3824 [.0286] (-1.3517) 0.6667* [0] (2.0548) 0.5429 [0] (0.4998) 0.5758 [.1538] (0.8571)

(4) 0.3824 [.0286] (-1.3517) 0.8462*** [0] (4.2677) 0.4118 [.0286] (-1.0137) 0.7368** [.0256] (2.8813) 0.5143 [0] (0.1666) 0.6286 [.1026] (1.4994) 0.3429 [0] (-1.8326) 0.8421*** [.0256] (4.1619) 0.3824 [.0286] (-1.3517) 0.6923* [0] (2.3709) 0.5429 [0] (0.4998) 0.6061 [.1538] (1.1999)

table 7 (for Spearman) and table 8 (for Kendall.) The sign and pattern of the results are perfectly consistent with the earlier results. Franchisees price shifts are more correlated with their demand shifts than those of company owned stores are, and these results hold both for the overall demand shifts and for the portion of those shifts due to ξ, but not for the portion of these shifts due to ρ. The results above all point towards a single set of conclusions. There is substantial evidence that franchisees have some knowledge of the current overall demand shock, there is also substantial evidence that franchisees have some knowledge of the current demand shift generated by ξ but there is no evidence that they have knowledge of the current shift in demand generated by ρ. There is no evidence that company-owned stores have any knowledge of the current demand shift; throughout company-owned store price shifts exhibit no significant relationship, either positive or negative, with the current demand shock, and there is evidence that franchised stores have greater knowledge than they do about the overall demand shift, and the portion of that shift due to ξ. Thus, there is evidence that franchisees 24

Table 6: Kendall sign test, by store (1) (2) price change vs. demand shift: 0.4412 [.0286] 0.4412 [.0286] company-owned (-0.6758) (-0.6758) price change vs. demand shift: 0.8378*** [.0513] 0.8378*** [.0513] franchised (4.0541) (4.0541) price change vs. demand shift from ξ: 0.3939 [.0571] 0.3939 [.0571] company-owned (-1.1999) (-1.1999) price change vs. demand shift from ξ: 0.7297** [.0513] 0.7297** [.0513] franchised (2.7568) (2.7568) price change vs. demand shift from ρ: 0.5667 [.1429] 0.5625 [.0857] company-owned (0.7180) (0.6960) price change vs. demand shift from ρ: 0.5882 [.1282] 0.5882 [.1282] franchised (1.0137) (1.0137) % price change vs. % demand shift: 0.3824 [.0286] 0.3824 [.0286] company-owned (-1.3517) (-1.3517) % price change vs. % demand shift: 0.8649*** [.0513] 0.8649*** [.0513] franchised (4.3784) (4.3784) % price change vs. % demand shift from ξ: 0.3636 [.0571] 0.3636 [.0571] company-owned (-1.5428) (-1.5428) % price change vs. % demand shift from ξ: 0.7222* [.0769] 0.7222* [.0769] franchised (2.6294) (2.6294) % price change vs. % demand shift from ρ: 0.5938 [.0857] 0.5625 [.0857] company-owned (1.0440) (0.6960) % price change vs. % demand shift from ρ: 0.5556 [.0769] 0.5556 [.0769] franchised (0.6573) (0.6573) t-statistics in parentheses proportion of correlations that were exactly 0 (and were discarded) are in brackets * denotes .05 significance, ** .01 significance and *** .001 significance

(3) 0.4412 [.0286] (-0.6758) 0.8158*** [.0256] (3.8417) 0.3939 [.0571] (-1.1999) 0.7222* [.0769] (2.6294) 0.5484 [.1143] (0.5301) 0.5714 [.1026] (0.8330) 0.3824 [.0286] (-1.3517) 0.8684*** [.0256] (4.4820) 0.3636 [.0571] (-1.5428) 0.7143* [.1026] (2.4990) 0.5625 [.0857] (0.6960) 0.5556 [.0769] (0.6573)

(4) 0.4412 [.0286] (-0.6758) 0.8158*** [.0256] (3.8417) 0.3824 [.0286] (-1.3517) 0.7353* [.1282] (2.7033) 0.5484 [.1143] (0.5301) 0.6286 [.1026] (1.4994) 0.3824 [.0286] (-1.3517) 0.8378*** [.0513] (4.0541) 0.3636 [.0571] (-1.5428) 0.7222* [.0769] (2.6294) 0.5625 [.0857] (0.6960) 0.6111 [.0769] (1.3147)

Table 7: Clustered Spearman Comparisons

price change vs. demand shift: price change vs. demand shift from ξ: price change vs. demand shift from ρ: % price change vs. % demand shift: % price change vs. % demand shift from % price change vs. % demand shift from

(1) 0.7674*** [0.0081] (3.9563) 0.7052** [0.0110] (3.0363) 0.4844 [0.0593] (-0.2305) 0.7751*** [0.0132] (4.0702) 0.7066** [0.0088] ξ: (3.0569) 0.4708 [0.0601] ρ: (-0.4325)

(2) 0.7674*** [0.0081] (3.9563) 0.6990** [0.0117] (2.9453) 0.4794 [0.0571] (-0.3047) 0.7756*** [0.0139] (4.0788) 0.7039** [0.0103] (3.0176) 0.4766 [0.0608] (-0.3463)

t-statistics in parentheses proportion of comparisons that were (discarded) ties are in brackets * denotes .05 significance, ** .01 significance and *** .001 significance

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(3) 0.7642*** [0.0088] (3.9100) 0.6935** [0.0081] (2.8634) 0.5031 [0.0579] (0.0460) 0.7752*** [0.0125] (4.0727) 0.6960**[0.0095] (2.9005) 0.4984 [0.0593] (-0.0230)

(4) 0.7565*** [0.0073] (3.7950) 0.6817** [0.0103] (2.6890) 0.5148 [0.0579] (0.2186) 0.7634*** [0.0125] (3.8971) 0.6899**[0.0103] (2.8095) 0.4980 [0.0615] (-0.0289)

Table 8: Clustered Kendall Comparisons

price change vs. demand shift: price change vs.: demand shift from ξ price change vs. demand shift from ρ: % price change vs. % demand shift: % price change vs. % demand shift from % price change vs. % demand shift from

(1) 0.7504*** [.0256] (3.7050) 0.6995** [0.0344] (2.9528) 0.4843 [0.0879] (-0.2318) 0.7643*** [0.0366] (3.9105) 0.7079** [0.0220] ξ: (3.0760) 0.4784 [0.0857] ρ: (-0.3201)

(2) 0.7504*** [.0256] (3.7050) 0.6953** [0.0359] (2.8899) 0.4860 [0.0850] (-0.2073) 0.7643*** [0.0366] (3.9105) 0.7039** [0.0227] (3.0173) 0.4856 [0.0842] (-0.2131)

(3) 0.7513*** [.0278] (3.7190) 0.6919** [0.0322] (2.8397) 0.4960 [0.0799] (-0.0589) 0.7652*** [0.0388] (3.9250) 0.7009** [0.0227] (2.9729) 0.5000 [0.0799] (0)

(4) 0.7427*** [.0264] (3.5909) 0.6783** [0.0322] (2.6381) 0.5195 [0.0791] (0.2884) 0.7555*** [0.0352] (3.7809) 0.6938** [0.0190] (2.8678) 0.5056 [0.0813] (0.0826)

t-statistics in parentheses proportion of comparisons that were (discarded) ties are in brackets * denotes .05 significance, ** .01 significance and *** .001 significance

have local knowledge, there is no evidence that company owned stores do, and there is some evidence additional evidence that franchisees have greater local knowledge than companyowned stores do. Furthermore, the tests indicate that this local knowledge comes from an awareness of shifts in local demand rather than from knowing about their local competitors.

5

Conclusion

This paper examines whether franchised outlets of a major U.S. pizza chain have greater knowledge of local demand shocks than company-owned ones do. We find that franchised outlets do have some knowledge of local demand shocks, while there is no evidence that company-owned stores do. Our results further suggest that franchisee local knowledge is wholly or primarily due to knowledge of local taste shocks rather than knowledge of changes in the mean utility from rival products. While previous researchers have surmised that local knowledge may be one of the reasons for and determinants of franchising, this is the first paper to offer substantive evidence that franchisees have local knowledge that companyowned stores do not, a prerequisite for local knowledge being a reason for franchising. This indicates that examining whether local knowledge is in fact a determinant of franchising is an interesting avenue for future research.

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A

Details of Price Index Construction

The price index is constructed using the transaction data. Each item gets a weight equal to it’s average quantity per order, so that the index can be thought of as the average weekly price of an order of average size. The transaction data contains the price paid for each order, whether a coupon was used, the time, day of week, and a list of the items in the order and their quantities. For beverages there is no information on the quantity ordered, just a dummy indicating whether beverage(s) where ordered as part of the order, so in addition to adding a fixed amount to the order, we assume that beverages add a fixed percentage as well. This essentially amounts to assuming that thirst is proportional to hunger. Coupons are assumed to change price by a fixed percentage, and day of week is also permitted to change average price by a fixed percentage.60 The basic pricing model is of the form: Revenuei,j,t =

1day,i 1D,i γ day,t γD,t

1

C,i ∗ γC,t ∗ αj,t

K X

! βk,t qi,k,t

∗ zi,j,t

k=1 1

day where Revenuei,j,t is the amount the customer paid for the order in question. γ day,t is a vector of day of 6 week effects61 each is “turned on” only on that day of the week. 1D,i 1C,i γD,t is a multiplicative effect that’s turned on if the order contains a drink. γC,t is a multiplicative effect that’s turned on if a coupon is used for the order. αj,t is a store-week specific multiplicative effect, that allows stores prices to vary conditional on day of the week and coupon usage. The zi,j,t is an i.i.d multiplicative error term, distributed lognormal with µ = 0. The qi,k,t ’s in the summation are the quantity of each of the K menu items in the order. The βk,t ’s are the “baseline prices” for each of the K menu items at time t, where baseline means the average price of that item on a Monday (the baseline day) when no drink is ordered, when no coupon is used, for a store with α = 1. To estimate this price model we log both sides, yielding62 :

log (Revenuei,j,t ) = log

K X

! βk,t qi,k,t

+ 1day,i ∗ γ day,t + 1D,i ∗ γD,t + 1C,i ∗ γC,t + αj,t + i,j,t

k=1 60

This makes sense, and is also the reason why the period we choose is a week. Average prices systematically vary by day of the week. They are highest on weekends, and lowest on Tuesdays and Wednesdays. Note that this does not mean that the posted “menu price” is varying with day of week, but the average price paid. Variation can come through variation in coupons and specials. This is irrelevant for our purposes, the only difference between changing the base price and changing the discount is how the store chose to frame it’s price. 61 Monday is the baseline. Each day of week effect is that day’s price relative to Monday. 62 since α and the γ’s were arbitrary positive numbers before, their logs are now arbitrary real numbers, which we continue calling by the same names for convenience.

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Note that  N (0, σ 2 ). We estimate the above regression separately for each week.63 Because of the summation inside the log this is a non-linear regression. Note that most of the parameters are the α’s in order to speed the estimation we use an iterative procedure: 1. set our current guess of the α’s to zero. 2. run nonlinear least squares on the non-α parameters, make those our current guess of those parameters. 3. Add the mean residual of each store to that store’s our current guess of that store’s α. Make this our new guess of alpha. 4. Find the sum of squares. 5. Repeat steps 2 through 4 until the sum of squares calculated in step (4) has changed by less than the tolerance. Once the routine has converged and we have our parameter estimates, we can compute the prices for each store week. The only things that are not different for each week here are quantities of each item in the “basket” we’re computing the price of. They are precomputed as the average quantity per order of each item over the whole sample. We then find the average amount the customer would pay for each order if we replace all qi,k,t ’s with the basket for each store week. This is what we use for our price.

63

A fact which was implied by the ubiquitous t subscripts

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B

The Geography of the Long Island Pizza Delivery Market.

(a) Our Chain’s Franchised Outlets

(b) Our Chain’s Company-Owned Outlets

(c) Rival delivery Outlets

Figure 2: These maps shows the geographic layout of pizza delivery stores and (potential consumers.) Each black dot represents a single store, and the locations of our chain’s franchisees, our chain’s company-owned stores, and of rival stores are displayed side by side. The gray lines represent census tract boundaries, and will be denser in more densely populated areas.

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