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Essays on urban structure and dynamics Cosman, Jacob Neal 2015

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ESSAYS ON URBAN STRUCTURE AND DYNAMICSbyJACOB NEAL COSMANA THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Economics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)July 2015© Jacob Neal Cosman, 2015AbstractThis thesis consists of three essays on urban structure and dynamics. These essays use em-pirical tools from empirical industrial organization and applied microeconomics to examinehow cities grow and change.Access to high-quality local services constitutes an important amenity in residents’ val-uation of cities. In “Industry dynamics and the value of variety in nightlife: evidence fromChicago”, I examine consumer preferences for variety in nightlife to understand these pref-erences and their impact on nightlife industry dynamics. I develop a structural dynamicmodel for venue entry and exit in the nightlife industry and estimate the model using apanel of liquor license data from Chicago. I find strong preferences for variety. My resultssuggest that in equilibrium a new entrant can increase profits for incumbent venues in somecases due to increased demand. However, potential entrants face high barriers to entry.In “Land value gradients and the level and growth of housing prices”, coauthor TomDavidoff and I ask whether urban land rent gradients affect the level and growth of housingrents and prices. We use residential rents and the location of Starbucks stores to proxyfor land prices, and calculate a gradient measure that allows for multiple peaks of landrent within a metropolitan area. Our measures of land rent gradients are significantlyassociated with high and rising prices, and explain some of the cross-sectional variationin prices. However, our measure does not explain the abnormally high rent and prices inPacific and Northeastern coastal “Superstar Cities.”Bartik shocks are widely used as an instrument for local labour demand. A potentialconcern with this instrument is potential endogeneity in the presence of correlation betweencity-level industrial composition and the outcome variable of interest. In “A control functionapproach to the correlated components of Bartik shocks”, I formalize this endogeneityconcern and introduce a control function correction that, given additional assumptions,addresses the potential endogeneity. I demonstrate the application of this novel approachby estimating a housing supply function.iiPreface“Industry dynamics and the value of variety in nightlife: evidence from Chicago” is basedon my job market paper. In the preparation of this chapter I identified the economicquestion, collected the data, developed the theoretical model, estimated the parametersof the model, and interpreted the economic significance of the results. This chapter hasbenefited from insightful comments and criticism from my committee members as well asseminar participants.“Land value gradients and the level and growth of housing prices” is a collaborativeproject with Dr. Tom Davidoff of my supervisory committee. For this chapter, I collectedthe data, developed the novel estimator for the gradient, and performed most of the empir-ical estimation. Dr. Davidoff identified the primary research question, situated our resultsin the context of the urban economics literature, and performed a share of the empiricalestimation.For “A control function approach to the correlated components of Bartik shocks”, Iidentified the economic question, developed the theoretical model in close consultation withmy committee members, estimated the parameters of the model, and interpreted the eco-nomic significance of the results. This chapter was developed under the supervision of mycommittee and has benefited from their comments.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Industry dynamics and the value of variety in nightlife: evidence fromChicago . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2.1 Static model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2.2 Dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.3 Estimation strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.4 Identification of colocation benefits . . . . . . . . . . . . . . . . . . . 242.3 Data and industry details . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.1 Nightlife venues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.3.2 Neighbourhoods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.3.3 Regulatory environment . . . . . . . . . . . . . . . . . . . . . . . . . 33iv2.3.4 Neighbourhood attributes . . . . . . . . . . . . . . . . . . . . . . . . 352.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.4.1 Parameter estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.4.2 Goodness of fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442.4.3 Counterfactual scenarios . . . . . . . . . . . . . . . . . . . . . . . . . 472.5 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.5.1 Cluster neighbourhoods . . . . . . . . . . . . . . . . . . . . . . . . . 532.5.2 Separate entry and exit rates . . . . . . . . . . . . . . . . . . . . . . 552.5.3 Profit from Starbucks . . . . . . . . . . . . . . . . . . . . . . . . . . 572.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 Land value gradients and the level and growth of housing prices . . . . 613.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.2 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643.3 Data sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.3.1 Location-specific value . . . . . . . . . . . . . . . . . . . . . . . . . . 653.3.2 Price data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.3.3 Additional controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.4 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754 A control function approach to the correlated components of Bartikshocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.2 Theoretical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.3 Empirical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106vAppendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107A Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107B Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111C Venue category verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 112D Maximum likelihood estimation results . . . . . . . . . . . . . . . . . . . . . 114viList of Tables2.1 Summary statistics for the venues in the sample. Standard deviation forduration in parentheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2 Likelihood ratio tests for Cox proportional hazard survival models of venueentry and exit. The first column adds controls for the number of venues ofeach type in the same neighbourhood. The second column adds controls forthe number of venues of each type in neighbouring neighbourhoods (weightedby the length of shared border between neighbourhoods). ∗, ∗∗, and ∗ ∗ ∗denote statistical significance at the 10%, 5%, and 1% levels. . . . . . . . . 322.3 Summary statistics for the 77 neighbourhoods in the sample. The last tworows are regulatory variables which are not included in the principal compo-nent analysis but rather included directly. . . . . . . . . . . . . . . . . . . . 362.4 Factor loadings for principal component analysis together with the cumula-tive share of variance explained by the principal components. . . . . . . . . 372.5 Maximum likelihood estimation results for the CES parameters η and ρ`.Standard errors in parentheses. . . . . . . . . . . . . . . . . . . . . . . . . . 372.6 Maximum likelihood estimation results for the move arrival rate parametersα` and λ`. All values are measured in 10−3 days−1. Standard errors inparentheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402.7 Maximum likelihood estimation results for the logarithm of deterministiccomponent of the sunk cost of entry and the exit payoff. The “baseline”entry cost reflects the entry cost in the absence of local regulation. Standarderrors in parentheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422.8 Estimated sunk cost of entry. 95% confidence intervals in parentheses. . . . 44vii2.9 Proportion of observations where a new entry would increase the profit of in-cumbent venues. The column variable is the type of the entrant while the rowvariable is the type whose change in profit is shown. All values are expressedin percentage of observations. 95% confidence intervals in parentheses. . . . 492.10 Maximum likelihood estimation results for the CES parameters η and ρ` withclustered neighbourhoods of varying sizes. Table 2.5 shows the correspondingbaseline elasticity values. Standard errors in parentheses. . . . . . . . . . . 552.11 Maximum likelihood estimation results for the CES parameters η and ρ`under estimation matching only the entry rate and only the exit rate. Table2.5 shows the corresponding baseline elasticity values. Standard errors inparentheses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572.12 Maximum likelihood estimation results for the parameters A, B, and C fromthe profit function specification in Equation 2.19. For legibility, all valuesare scaled up by a factor of 103. Standard errors in parentheses. . . . . . . 583.1 Annualized U.S. Census (nominal) median rent growth (1980-2009/2011) and(log real) Freddie Mac Home Price Index growth (1980-2014): Coastal vs.other metropolitan areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.2 Summary statistics for the Craigslist rent location data. Throughout, theunit of observation is the MSA. . . . . . . . . . . . . . . . . . . . . . . . . . 663.3 Summary statistics for the Zillow price data and the rent-price ratio from theZillow price and Craigslist rent data. Throughout, the unit of observation isthe MSA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693.4 Summary statistics for additional control variables. . . . . . . . . . . . . . . 713.5 Correlations between supply inelasticity factors. Throughout, the unit ofobservation is the metropolitan area. . . . . . . . . . . . . . . . . . . . . . . 723.6 Regression results for the current rent without the Coastal indicator. ∗∗∗, ∗∗,and ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively. 733.7 Regression results for current rent with the Coastal indicator. ∗∗∗, ∗∗, and ∗denote statistical significance at the 1%, 5%, and 10% levels, respectively. . 74viii3.8 Regression results for the price-rent ratio without the Coastal indicator. ∗∗∗,∗∗, and ∗ denote statistical significance at the 1%, 5%, and 10% levels, re-spectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.9 Regression results for the price-rent ratio with the Coastal indicator. ∗∗∗, ∗∗,and ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively. 763.10 Regression results for the long-term price growth without the Coastal indi-cator. ∗∗∗, ∗∗, and ∗ denote statistical significance at the 1%, 5%, and 10%levels, respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.11 Regression results for the long-term price growth with the Coastal indicator.∗∗∗, ∗∗, and ∗ denote statistical significance at the 1%, 5%, and 10% levels,respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.1 Regression results for the housing supply curve at the MSA level. For legi-bility, the control function coefficient and its standard errors are scaled by afactor of 103. Standard errors in parentheses. ∗, ∗∗, and ∗∗∗ denote statisticalsignificance at 10%, 5%, and 1%. . . . . . . . . . . . . . . . . . . . . . . . . 89C1 Results of a multinomial logit regression of the licensing categories on themost frequently-assigned Yelp categories. The regression sample is the setof venues which matched with Yelp businesses. The omitted licensing cate-gory is the “Amusement only” category. ∗, ∗∗, and ∗ ∗ ∗ denote statisticalsignificance at the 10%, 5%, and 1% levels. . . . . . . . . . . . . . . . . . . 113D1 Maximum likelihood estimation results for all parameters. If the variablename includes “Log”, I estimate the logarithm of the corresponding modelparameter. Standard errors in parentheses. . . . . . . . . . . . . . . . . . . 118ixList of Figures2.1 Profit by sector in a two-sector example. . . . . . . . . . . . . . . . . . . . . 152.2 Consumer in a two-sector example. Figure 2.1 shows the corresponding venueprofit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Geographical distribution of venues within Chicago. . . . . . . . . . . . . . 282.4 Distribution of venues’ durations within the sample. . . . . . . . . . . . . . 292.5 Comparison of variation in nearest-neighbour differences within and betweenneighbourhoods. The abbreviation “N.s.d” refers to the normalized standarddeviation — that is, the standard deviation divided by the mean. The ab-breviation “n.n” refers to the nearest neighbour. Each label k denotes thenormalized standard deviation for the distance to the kth nearest neighbour.This figure only includes venues in the sample at the end of the sample period.However, results are similar at other points in the sample period. . . . . . . 312.6 Neighbourhood attributes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382.7 First-stage results for venue entry and exit rates as a function of state. Unitsare days−1 throughout. Error bars in grey represent one standard deviation. 392.8 Observed and predicted wait times between state transitions (i.e., venue entryor exit). Each point represents a single (n, d, r) state. . . . . . . . . . . . . . 462.9 Changes to consumer welfare from one additional venue of each type. Allchanges expressed as a percentage of the baseline welfare. . . . . . . . . . . 482.10 Changes to entry probability from lower entry cost. All changes expressed asthe change in the rate of new entrants choosing to enter the market per year. 51x2.11 Changes to entry probability from laissez-faire local regulation. All changesexpressed as the change in the rate of new entrants choosing to enter themarket per year. Results for venues in the “Amusement only” category arenot shown as venues without liquor licenses do not face local liquor regulationand the indirect effect from other venues’ higher entry rate is very small. . . 522.12 Map of clustered neighbourhoods generated using clustering radius d = 500m. 543.1 Spatial distribution of Starbucks locations in four sample cities. . . . . . . . 673.2 Spatial distribution of one-bedroom apartments in four sample cities, to-gether with monthly rent. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.3 Comparison of rent gradient and Starbucks density gradient for metropolitanareas in the sample. Metropolitan areas with a population greater than threemillion are labelled by their principal cities. . . . . . . . . . . . . . . . . . . 72xiAcknowledgementsI am deeply indebted to my committee members Dr. Tom Davidoff, Dr. Nancy Gallini, andDr. Paul Schrimpf for their consistent and invaluable advice and support throughout thethesis process. Their thoughtful and comprehensive guidance has not only been integral tothe completion of this thesis but also to the development of my empirical and theoreticalskills and my research agenda as an economist. As well, I owe particular thanks to Dr.Nathan Schiff (who previously served on my thesis committee before leaving the institu-tion) as well as Dr. David Green and Dr. Sanghoon Lee for providing insightful criticismand commentary that was instrumental in developing my research agenda. I also thankAndrew Ryce of Resident Advisor magazine for sharing his perspective on the nightlife in-dustry. Finally, I am grateful to the faculty and staff of the Vancouver School of Economicsfor providing the supportive and collegial environment that has made this doctoral thesispossible.I am grateful for the NSERC Postgraduate Scholarship which funded the first threeyears of my doctoral program.Special thanks is also due to my parents, who have offered me support and encourage-ment throughout the completion of this thesis.xii1 IntroductionCities have become the dominant environment for human life. As of 2014, 54% of worldpopulation and 82% of the Canadian population live in cities (United Nations, Departmentof Economic and Social Affairs, Population Division, 2014). The economic benefits of manypeople living and working near enough to exchange specialized goods and services wereidentified early in the classical economic literature1 and modern researchers have found thatthe interactions of firms and residents within cities are play an important role in providing ahigh standard of living for their residents (Fujita and Thisse, 2002; Rosenthal and Strange,2004; Glaeser and Gottlieb, 2009). Accordingly, understanding the processes which drivethe development and evolution of cities is essential to social scientists and policymakersseeking to improve their residents’ well-being.The body of this thesis comprises three studies in urban economics which address thestructure and dynamics of cities. In these studies, I build on innovative techniques fromempirical microeconometrics and industrial organization. I use data sets that describeinteractions and dynamics within cities to address questions of how cities grow and change.These studies are linked by their use of empirical evidence to describe the interactionsbetween firms and resident within cities and understand the role of these interactions incities’ structures and dynamics. The first investigates firm dynamics among different typesof nightlife venues, the second introduces a new measure of firms’ and residents’ willingnessto substitute across locations within a city, and the third develops a new empirical techniquefor understanding how changes to local labour demand impact housing prices and othercity-level outcomes.“Industry dynamics and the value of variety in nightlife: evidence from Chicago” studiesthe dynamics of the nightlife industry. In particular, this paper focuses on consumerspreferences for variety both within and between types of nightlife venue and the role of these1In particular, Ibn Khaldun (1377) and Smith (1776) note the increased scope for specialized labourwithin cities while Marshall (1890) identifies productivity gains between firms sharing common suppliersand workers learning skills from each other.1preferences in venues’ decisions to enter and exit the market. This paper contributes to theliterature that attempts to understand firms’ locational decisions by developing models thatrelate firms’ behaviour to firms’ underlying costs and constraints and consumers’ underlyingpreferences (Davis, 2006; Jia, 2008; Dunne et al., 2013). It is the first paper in this literatureto examine the interactions between closely related industries by considering consumerspreferences across different types of nightlife venues.I develop and estimate a structural model of nightlife venues’ entry and exit decisions.This model predicts venues’ entry and exit decisions as a function of the number of nearbyvenues of similar and different types, the stringency of neighbourhood-level nightlife reg-ulation, and the underlying structural parameters of consumers’ behaviour and venues’costs. The model is forward-looking — that is, venues make their entry and exit decisionsin response to each others’ predicted entry and exit decisions. I estimate this model us-ing a continuous-time methodology introduced in Arcidiacono et al. (2012) that allows forcomputationally tractable estimation of a model with multiple interacting venue types.My results suggest that consumers have very strong preferences for variety betweennightlife venues. In fact, these preferences are sufficiently strong that in many observationsmy model predicts a counterfactual new venue would increase profits for nearby incumbentsas the added enjoyment of nightlife would lead to more residents going out and consumingnightlife. The results indicate that these spillovers are present both within and betweendifferent types of nightlife venue. As well, I find that nightlife venues face very high barriersto entry. These barriers can partially be attributed to local regulation but also largelyreflect the high nonregulatory costs of opening a new venue. In additional to their relevanceto the literature on firms’ locational preferences, these results provide some indication ofhow consumer amenities develop within cities; research has shown that these amenitiesare important in determining residents’ migration decisions (Rappaport, 2008; Lee, 2010;Albouy et al., 2013). As well, because this study focuses on the nightlife industry, theresults provide an empirical contribution to the policy discussion of how cities can choselocal policies that promote or restrict nightlife in different neighbourhoods according toresidents’ preferences (Heath, 1997; Campo and Ryan, 2008; Darchen, 2013a).“Land value gradients and the level and growth of housing prices” develops a new mea-2sures of residents’ and firms’ willingness to substitute between neighbourhoods within acity. This paper contributes to an active strain of literature that attempts to use differ-ences in cities’ housing demand growth or housing supply constraints to explain cross-citydifferences in housing price growth (Mian and Sufi, 2009; Huang and Tang, 2012; Davidoff,2013a). Of particular interest to the economic literature is the consistently faster pricegrowth in a few coastal cities, which are closely related to the “Superstar Cities” describedin Gyourko, Mayer and Sinai (2013). Davidoff (2015) finds that the existing measures ofcross-city differences cannot explain these cities’ housing markets’ disparate performancecompared to other cities.Coauthor Tom Davidoff and I introduce and calculate a measure of this willingness tosubstitute between neighbourhoods. The measure is based on the spatial rate of changeof land value within a city. Cities with steeper changes in land value are associated witha lower willingness to substitute within the city. We show that these measures correlateclosely with other measures of supply elasticity within cities (including the measures intro-duced by Gyourko, Saiz and Summers (2008) and Saiz (2010)). Moreover, our measure playsa significant role in explaining cross-city differences in housing rents as well as short-termand long-term price growth. However, even when taken together, our new measure andthe prevalent measures of demand growth and supply constraints cannot explain why thecoastal cities’ housing markets consistently outperform the rest of the country. These re-sults contribute useful information to the understanding of cross-city differences in housingmarkets.“A control function approach to the correlated components of Bartik shocks” introducesa new technique that builds on research tools widely used in the urban economics literature.Bartik (1991) and Blanchard and Katz (1992) introduced the “Bartik shock” instrumentvariable, which is intended to provide a source of variation to labour demand that is drivenby macroeconomic trends and therefore uncorrelated with the particular conditions of agiven city. This purpose of this instrumental variable is to provide a source of variationto city-level outcomes such as housing prices (Saiz, 2010; Paciorek, 2013) and migration(Partridge et al., 2012; Guerrieri, Hartley and Hurst, 2013) decisions that allow researchersto identify the causal impact of shifts in labour demand on these outcomes. As discussed in3Baum-Snow and Ferreira (2014), the Bartik shock instrument is widely used in the economicliterature.In this study, I discuss concerns regarding the Bartik shock’s correlation with the in-dustrial composition of the local workforce. I show that the use of the Bartik shock as aninstrumental variable implicitly assumes that the city’s industrial composition has no rela-tionship with the outcome variable of interest except through its impact on labour demand.In many situations, this assumption is possibly unwarranted; local industrial compositioncan interact with amenities, local regulation, population change, and other conditions inmany complicated ways. I develop a theoretical framework that accounts for this potentialcorrelation and propose an adjusted estimation technique that can potentially account forthis correlation. This adjustment is novel to the economic literature. Its use may accountfor correlation between a city’s industrial composition and other processes within the citythat are important in understanding how cities adjust to changing labour demand.These studies incorporate the close relationships within the spatially concentrated eco-nomic activity that defines cities and provide empirical results that contribute to our under-standing of how cities grow and change. Taken together, they demonstrate the importanceof understanding the interactions and processes within cities to studying and improving thelives of their residents.42 Industry dynamics and the value of vari-ety in nightlife: evidence from Chicago2.1 IntroductionConsumer access to city-specific non-tradeable goods and services plays an integral rolein the growth and development of cities. Glaeser, Kolko and Saiz (2001) suggest thatthe welfare gain from these consumption amenities in cities is an increasingly importantfactor in overall urban growth and an active literature has indicated the importance ofconsumption amenities to urban migration decisions (Rappaport, 2008; Lee, 2010; Albouyet al., 2013). The value of amenities to urban quality of life is also recognized outside of theurban economics literature. For example, Bloomberg Businessweek includes restaurants,bars, libraries, museums, professional sports teams, and park space in its annual ranking of“America’s 50 Best Cities” and Livability.com explicitly includes entertainment and culturalamenities in its “Top 100 Places to Live” rankings.In this study, I focus on bars, clubs, pool halls, arcades, bowling alleys, and other pri-vate businesses which exist primarily to facilitate social interactions in an informal setting.(Throughout, I use the terms “nightlife venues” and “nightlife industry” to describe thesebusinesses.) I estimate a structural model of the nightlife industry with panel data on venueentry and exit to investigate consumer preference for access to variety in nightlife venues.The structural model allows me to assess the impact of consumers’ preference for varietyon venue profit as well as venue entry and exit.Nightlife has been recognized in the sociology literature (Farrer, 2008; Chew, 2009;Grazian, 2009) and in the urban policy literature (Heath, 1997; Campo and Ryan, 2008;Darchen, 2013a) as a particularly important amenity in shaping residents’ views of cities.Peters and Lakomski (2010) directly connect vibrant nightlife to attracting “a creative classof talented professionals” and Dewan (2005) describes a “hipness battle” between US cities,5including an effort in Lansing, Michigan under the “Cool Cities Initiative” to make the citymore attractive to young professionals by providing shuttle buses between bars1. Manycities have enacted policies to encourage the development of nightlife, including severallarge centres in Britain (Heath, 1997), smaller cities in Indiana (Faulk, 2006), and rapidlygrowing cities such Guangzhou in China (Zeng, 2009).Vibrant nightlife is closely associated with access to a variety of nightlife venues. Currid(2007) notes that a dense concentration of nightlife venues is more appealing to consumersthan spatially isolated venues. As one lounge manager stated of a dense nightlife districtin Philadelphia, “It gives you variety. You don’t want to go to the same place” (Harris,2003). Picone, Ridley and Zandbergen (2009) attribute this to a consumer preference for“bar-hopping” (that is, a preference for visiting many venues in one night). However, someconsumers may instead prefer access to different venues on each night; in the context ofnightclub design, Kaiser, Ekblad and Broling (2007) discuss the difficulty of simultaneouslyaddressing the preferences of bar-hopping patrons and patrons who spend the entire nightat a single venue. In both cases, understanding consumer preferences for variety in nightlifeis essential to understanding the development and valuation of nightlife amenities.An emerging economic literature studies consumer valuation of consumption amenitiesand particularly consumer preference for access to variety. These papers generally followthe framework for consumer preference for variety established by Feenstra (1994). Amongothers, Broda and Weinstein (2006) infer consumer preferences for variety in goods fromtrade data, Li (2012) and Handbury and Weinstein (2011) study gains from variety usingevidence from grocery purchases, and Broda and Weinstein (2010) use barcode data tostudy turnover in product variety. The study most closely related to the present work isCouture (2014), which estimates consumer gains from access to variety of restaurants.This study contributes to the literature by quantifying consumer preferences for varietyin nightlife and modelling how these preferences impact nightlife industry dynamics and thelevel of nightlife services provided. I construct and estimate a dynamic structural model1As Zimmerman (2008) notes, policy makers often provide a rationale for encouraging nightlife in termsof the “creative class” concept advanced in Florida (2002) and Florida (2005), which asserts that a city willbenefit from the influx of highly educated professionals if those professionals find the city a pleasant andenjoyable place to live.6of nightlife venue entry and exit using license data from Chicago. The model accounts forthe “vibrancy” of nightlife districts. That is, in situations where consumers attain higherutility by choosing to go out, more consumers choose to go out and profit can potentially behigher — not only for a new entrant, but also for incumbent venues. As the model predictsentry and exit rates as a function of structural parameters, I can estimate the structuralparameters using only data on entry and exit; this strategy is necessary in the presentcontext, where more-detailed information is generally unavailable.Structural estimation allows for the measurement of consumer preferences for variety aswell as the evaluation of counterfactual scenarios which take into account the dynamic re-sponses of venues to each others’ entry and exit decisions. I develop a structural model whichclosely matches the conditions in the Chicago nightlife market. In particular, the model ofindividual venues as decision-making agents corresponds to the reality that nightlife venuesin Chicago are generally atomistic firms rather than centrally-owned chains with coordi-nated decisions. Moreover, the model includes endogenous price variation across venues inresponse ton consumers’ demand. The estimation strategy allows for direct control of localdemographic and regulatory conditions, which assists in distinguishing venue aggregationfrom zoning restrictions and other local conditions; as Datta and Sudhir (2013) note, ac-counting for local regulation is essential for accurate measurements of the benefits of firmcolocation.This study also contributes to the broader urban economics literature which attemptsto explain the observed colocation of economic activity and similar firms in particular. Asdiscussed by Rosenthal and Strange (2004), Puga (2010), and many others, positive agglom-eration effects for firms play a significant role in explaining the structure and concentrationof economic activity in cities. More specifically, several theoretical studies including discussaspects of consumers’ preferences and decision process which could rationalize colocationin industries which offer widely differentiated products. Wolinsky (1983) studies the role ofconsumers’ imperfect information, while Fischer and Harrington (1996) and Konishi (2005)raise the related possibility of taste uncertainty. In these studies, the consumers’ behaviourcan lead to higher profit for colocating firms than for spatially distant firms.The structural model I develop and estimate in this study attempts to explain observed7patterns of venue location through the benefit consumers receive from access to many nearbyvenues. This complements previous reduced-form studies of observed firm colocation includ-ing Picone, Ridley and Zandbergen (2009), Freedman and Kosova´ (2012), and Krider andPutler (2013) and structural studies including Davis (2006), Jia (2008), and Dunne et al.(2013).Data availability on the operations of nightlife venues is generally limited2. Accord-ingly, this study builds upon a literature in industrial organization which uses entry andexit information to estimate the profit function, including Bresnahan and Reiss (1991),Pesendorfer and Schmidt-Dengler (2003), Aguirregabiria and Mira (2007), Ryan (2012),Collard-Wexler (2013), Dunne et al. (2013), and Nishida (2015). This appears to be one ofthe first studies to adopt the continuous-time dynamic discrete choice framework proposedby Arcidiacono et al. (2012)3. This framework allows for the computationally-tractable es-timation of a full-featured structural model with a large state space. In particular, it allowsfor the consideration of spillovers both within and between types of nightlife venues.The results of the estimation suggest that consumers have very strong preferences foraccess to variety in nightlife venues. Consumers gain substantial utility from access tonearby venues of different types. In particular, their preference for access to variety ishighest among venues without music, dancing, or other amenities (i.e. bars) and somewhatlower for nightclubs, performance venues, and other venue types. Overall, these preferencesfor variety are somewhat stronger than the consumer preferences for variety in restaurantsdiscussed in Couture (2014) and comparable to the most variety-specific goods in Brodaand Weinstein (2006) and Broda and Weinstein (2010). These results are robust to sub-stantial changes in specification. In the median neighbourhood, one new venue without2Sales data is available in some cases. Abbring and Campbell (2005) use monthly liquor sales historyfrom a sample of Texas bars to study the survival of new firms. However, this sales data is not linked withother attributes of the venue such as the type of services it provides and therefore it is less helpful for thepresent study. Note that self-reported consumer expenditure on nightlife is prone to under-reporting andtherefore unreliable; Bee, Meyer and Sullivan (2012) describe alcohol spending in the Consumer ExpenditureSurvey’s diary survey as “especially badly reported” compared to other expenditure categories.3In addition to the methodology, several other studies including Pesendorfer and Schmidt-Dengler (2003),Bajari, Benkard and Levin (2007), and Aguirregabiria and Mira (2007) and Pakes, Ostrovsky and Berry(2007) have described estimation strategies for inferring the structural profit function from a small set ofobserved actions. I adapt the framework suggested in Arcidiacono et al. (2012) because the continuous-time framework allows for full use of available data in a rich state space while preserving computationaltractability.8music, dancing, or other amenities raises consumer welfare for nightlife consumers to a levelequivalent to a 13.5% increase in nightlife expenditure.Moreover, I find that consumer preference for variety is strong enough that in manyobservations a (counterfactual) new entrant would increase the profit for incumbent com-petitors. That is, the estimated parameter values predict sufficiently strong preference forvariety that the additional demand from a new venue largely compensates the effect of ad-ditional competition on profits in many cases. This effect holds for incumbents of the sametype as the entrant as well as for incumbents of different types.However, consumers’ welfare in terms of access to nightlife variety is limited by thehigh barriers to entry faced by nightlife entrepreneurs. These high barriers can partiallybe attributed to very local license restrictions (which vary widely across the city) althoughother barriers (including city-wide regulatory cost as well as non-regulatory costs) are muchmore significant. The estimated barriers to entry correspond closely with estimates in theindustry literature.The remainder of the paper is organized as follows. First, I outline a structural modelfor venue profits and venues’ entry and exit decisions in a framework that lends itself tomaximum likelihood estimation and counterfactual evaluation. Then, I estimate this modelusing business license data from Chicago. Finally, I discuss the results of this estimationin the context of consumer preferences for variety and conduct counterfactual exercises toinvestigate the role of these preferences in determining nightlife industry dynamics.2.2 ModelTo parametrize consumer preferences over nightlife amenities and the relationship betweenconsumer preferences and venue entry and exit decisions, I describe a structural model forthe nightlife industry. I build this model in stages. First, I outline a static model for venueprofit and derive theoretical results that show venue profits may increase with the numberof nearby venues due to consumer preferences for more variety in nightlife. Then, I embedthis model of venue profit in a dynamic model that describes nightlife venue entry and exitby forward-looking discounted-profit maximizing venues. This dynamic model lends itself9to the estimation strategy described by Arcidiacono et al. (2012).Before proceeding, it will be helpful to explicitly discuss the modelling choices for con-sumers’ preferences and venues’ decision-making processes. I provide details on parametriza-tion and estimation in further detail below.I model consumer preferences using a constant substitution of elasticity (CES) utilityfunction. This provides a tractable parameterization of consumer preferences in terms ofvariety. As well, the CES functional form makes the results broadly comparable with otherestimates of consumer gains from access to variety, including Broda and Weinstein (2006),Broda and Weinstein (2010), and Couture (2014). However, as the model in this paperallows for the possibility that consumers do not go out and consume nightlife, it is notentirely identical to these other models. This adjustment seems reasonable in the contextof nightlife, where consumers frequently choose not to consume based on the quality of theoutside options. In comparison, it seems highly unlikely that consumers would choose notto consume, e.g., groceries regardless of any outside options.As is common in the literature, this model abstracts from the individual-level micro-foundations of this preference for variety. However, several explanations are possible andmutually compatible. If venues have idiosyncratically high-quality and low-quality nights,then risk-averse customers may gain higher utility from going out in a neighbourhood withmany venues as this would minimize their search costs in finding a high-quality venue. Thisis compatible with both the imperfect-information model developed by Wolinsky (1983) andthe taste-uncertainty model investigated by Fischer and Harrington (1996) and developedby Konishi (2005). Nightlife patrons seeking to meet new people may prefer situations withmany nearby venues to maximize their prospects. All of these scenarios would lead to theempirically-observed preference for neighbourhoods with many venues4.I model venues’ entry and exit decisions in a continuous-time environment. In this en-vironment, potential entrants decide whether to enter the market and incumbent venuesdecide whether to exit. Agents are not able to update these decisions continuously. Instead,they receive opportunities at stochastic intervals via a Poisson process which delivers oppor-4As shown by Anderson, De Palma and Thisse (1992) and noted in Couture (2014), the CES utilitymodel yields equivalent choices to a model with logit shocks to consumer-choice pairs.10tunities at a constant rate. At each opportunity, a potential entrant may decide whether toenter and a potential incumbent may decide whether to exit. Transitions to the policy anddemographic environment are governed by a Poisson process as well. While it requires someadditional notation, the continuous-time approach offers several advantages over standarddiscrete-time approaches:ˆ Allowing for continuous time (as opposed to aggregating daily liquor license obser-vations to a larger time scale) allows for use of all available information in the dataset.ˆ In continuous time, simultaneous moves by two agents arise with zero probability.Accordingly, agents decisions’ need not be integrated over all possible moves by otheragents (and all possible exogenous transitions to the environment). This drasticallyreduces the computational burden required for maximum likelihood estimation andallows for tractable estimation of a richer model.ˆ Discrete time periods imply that all agents all have their sole opportunity to makedecisions at the same time, once per period. For example, discrete monthly periodswould imply that venues decide whether to exit and enter the market simultaneouslyat the beginning of every month. Stochastic decision times likely represent a closerapproximation to reality and relax the assumption that all decisions occur simultane-ously.2.2.1 Static modelThe environment for the static model of the nightlife industry consists of venues and con-sumers. Specifically, the environment includes n` venues of each type ` ∈ 1, 2, . . . , L. Eachtype of venue provides a different kind of nightlife service to consumers. For example, barsare one type while nightclubs are another. These venues serve a market represented by acontinuum of consumers of measure N¯ . Each consumer has a budget w for nightlife ser-vices. Venues of a given type are symmetric — i.e., they face the same profit maximizationproblem. Consumers’ utility includes preference for variety within and across venue types.11The consumer decides whether to go out and consume nightlife services based on the real-ization of a reservation utility shock. Venues set their prices to maximize profit optimallyin response to each others’ prices and consumer preferences.Consumer preferencesConsumer preferences in the model consist of a nested CES utility for consumption acrossnightlife venues with a reservation shock. The inner nest accounts for preferences betweenvenues of the same type while the outer nest accounts for preference for variety acrossdifferent types of venue. The reservation shock represents the possibility that consumerschoose not to go out and consume any nightlife services. Because of the reservation shock,the number of patrons for nightlife services varies with the number and types of venues5.As mentioned previously, I use a constant elasticity of substitution (CES) framework todescribe consumer preferences. Specifically, I assume that consumer utility has the followingfunctional form:U(q) = max∑`(∑iqρ`−1ρ``i) ρ`ρ`−1η−1ηηη−1, V ∗(2.1)The first case on the right-hand side of Equation 2.1 represents a situation where theconsumer chooses to go out and consume nightlife services, while the second case represents asituation where the consumer chooses the reservation utility of not going out. The parameterρ` is the constant elasticity of substitution between venues of type ` while the parameterη is the constant elasticity of substitution across venues of different types. By assumption,ρ` > η > 2 for all types ` — that is, consumers are more willing to substitute betweenvenues of the same type than across different types6.In the case where the consumer chooses to go out, the consumer chooses the level of5This study focuses on consumers’ preference for access to a variety of venues. That is, the utility functiondescribed in this model addresses the preferences of nightlife consumers. As discussed in further detail below,nightlife externalities such as noise and crime may also enter residents’ utility functions. These additionalpreferences regarding negative externalities are beyond the scope of this model of the nightlife industry.However, they are relevant to policymakers considering the general equilibrium effects of nightlife industrypolicy.6The assumption η > 2 is particular to the present model with the added reservation shock. It is requiredto ensure a consistent and unique solution as shown in Proposition 1. In the more general model withoutthe reservation utility shock, η > 1 is sufficient.12consumption qD`i for venue i of type ` subject to the budget constraint∑i∑` p`iq`i ≤ w.For notational convenience, introduce the usual CES price indices P` =(∑i p1−ρ``i) 11−ρ` andP =(∑` P1−η`) 11−ηThen, solving the consumer’s problem for a given vector of prices p ={p11, p11, . . . , p1n1 , . . . , p`i, . . . , pL1, pL2, . . . , pLnL} gives the following demand for nightlifeservices from venue i of type `:qD`i = p−1`i(p`iP`)−ρ(P`P)−ηw (2.2)Substituting this demand into Equation 2.1 yields the following expression for the indi-rect utility V (p):V (p) = wP η−1∑`P−η` (2.3)The reservation shock V ∗ in Equation 2.1 is a uniformly distributed random variableon [0, 1]. (Setting the maximum value of the shock to unity normalizes the prices in themodel.) Each of the N¯ measure-zero consumers experiences a separate realization of theshock. Therefore, the total measure of consumers opting to go out and consume nightlifeservices is N = N¯ min {V (p), 1}. That is, N increases with the value of going out up to thepoint where all consumers choose to go out, at which point N = N¯ . This feature representsthe “vibrancy” aspect of qualitative discussions of nightlife amenities. In equilibrium, aneighbourhood with a wider variety of venues (and therefore higher utility to going out)will induce more consumers to choose to go out and consume nightlife.It is worth noting that this model does not allow consumers to choose between neigh-bourhoods. Instead, they choose only whether to go out. Allowing consumers to choose togo out from a range of neighbourhoods would likely lead to larger estimated spillover effectsas consumers choose to go out in higher-utility neighbourhoods; therefore, the estimates inthis paper potentially underestimate the true spillover magnitude. However, these changeswould likely be relatively small, as any change in venues’ strategies would reflect their abil-ity to unilaterally change the utility of the neighbourhood relative to other neighbourhoods,which is likely limited. In more practical terms, a model that allowed consumers to chooseone of several dozen neighbourhoods would quickly become computationally intractable.13Profit maximizationEach venue sets the price of its services to maximize profit. Venues face the demand qD`i(as given by Equation 2.2) from measure N = N¯ min {V (p), 1} consumers. A venue of type` faces a constant marginal cost of production c` as well as a fixed cost of production κ`.This gives the following profit maximization problem:pi`i = maxp`i{(p`i − c`)(p`iP`)−ρ(P`P)−ηP−1N¯ min {V (p), 1}w − κ`}(2.4)Each venue sets its price as a best response to the other venues’ prices. Therefore, theequilibrium concept is a Bertrand-Nash equilibrium. Taking the first-order condition andrewriting in terms of s`i =q`i∑i′ q`i′= p1−ρ``i Pρ`−1` (the share of demand for venues of type `going to venue i) and S` =∑i q`i∑`′∑i q`′i= P 1−η` Pη−1 (the share of total demand going to allvenues of type `) yields the following optimization condition:p`i =1 + 1ρ`−(ρ`−[1+Sηη−1`∑`′(Sηη−1`′)−1]η)s`i−2(η−1)S`s`i−1 c` if V (p) < 1(1 + 1ρ`−(ρ`−η)s`i−(η−1)S`s`i−1)c` if V (p) ≥ 1(2.5)By assumption, venues in a given sector ` are symmetric. Therefore, they must set thesame prices in equilibrium, which means the share of total demand to venue i of type ` iss`i = 1n` . This yields the following optimal pricing strategy.p`i =1 + n`n`((ρ`−1)−(ρ`−[1+Sηη−1`∑`′(Sηη−1`′)−1]η)−2(η−1)S` c` if V (p) < 1(1 + n`n`(ρ`−1)−(ρ`−η)−(η−1)S`)c` if V (p) ≥ 1(2.6)Considering Equation 2.6 over all sectors ` gives a system of L equations for the pricesover all sectors ` ∈ 1, 2, . . . , L. This is not a closed-form solution, as the industry sharesS1, S2, . . . , SL appear on the denominator on the right-hand side and these are a functionof the prices. In general, no closed form solution exists for the equilibrium prices. However,14(a) Profit in sector 1 (b) Profit in sector 2Figure 2.1: Profit by sector in a two-sector example.the following theorem justifies the use of numerical methods to solve Equation 2.6 forequilibrium prices.Proposition 1. There exists a unique equilibrium set of prices p∗ which solves Equation2.6.Proof. See Appendix A.Figure 2.1 shows the equilibrium profits for a single venue in a two-sector example as afunction of the number of venues in each sector. In these examples, profit is non-monotonicin the number of competitor venues. In general, the model allows for venue profit to increasein the number of venues.This result also has an intuitive explanation. A greater variety of nightlife options meansmore consumers’ utilities exceed their reservation shocks and therefore more consumerschoose to consume at the venues. If an additional venue causes enough consumers to optto go out and consume nightlife that this positive effect on revenue dominates the negativeeffect of additional competition, then profit for an incumbent venue will rise when a newvenue enters the market. That is, the consumer preference for variety represents a positivedemand-side agglomeration effect from the venues’ point of view. The strength of this effectdepends on the CES parameters ρ` and η — lower elasticity of substitution corresponds tostronger preferences for variety and therefore higher profits for venues which are locatednear other venues. (Conversely, in the case where the elasticity of substitution is ∞, the15venues are indistinguishable from the consumers’ point of view and the venue’s problemreduces to the standard Bertrand oligopoly.)However, note that profit will not increase indefinitely with the number of venues.Regardless of parameter values the consumer utility of going out will always reach V (p) = 1for sufficiently many venues:Proposition 2. There exists some n¯ ∈ N such that, when n` ≥ n¯ for ` ∈ 1, 2, . . . , L, theequilibrium prices give V (p) ≥ 1.Proof. See Appendix B.Once V (p) = 1, with higher n` the equilibrium prices eventually converge to the standardCES pricing strategy p`i =ρ`ρ`−1c` and (as in the standard CES case) profit declines withadditional venues. Accordingly, while the agglomerative benefits in this model may providehigher profits to venues located near other venues, the benefit does not grow until venuedensity and profits become infinite. Once the neighbourhood is maximally vibrant andeveryone who would go out is already going out, the profit can no longer increase with thenumber of venues in the neighbourhood.Figure 2.2 shows the corresponding consumer welfare as a function of the number ofvenues in each sector. Note that this includes not only the consumers who choose to goout, but also the consumers whose reservation utility exceeds the utility of going out. Asshown, consumer utility is highest in situations with many venues.2.2.2 Dynamic modelThe static model presented above describes venue profits as a function of neighbourhoodattributes and the number of competitors. I connect this profit function to venue entry andexit data with a dynamic model of entry and exit decisions. In this model, agents observeeach others’ actions and the state of the environment and make entry and exit decisionsas a best response to their beliefs about each others’ actions. In equilibrium, these beliefsabout each others’ actions are consistent and based upon current observable state variables;therefore, the solution concept is a Markov-Nash equilibrium.16Figure 2.2: Consumer in a two-sector example. Figure 2.1 shows the corresponding venueprofit.The agents in the dynamic model are the operators of individual venues — specifically,entrepreneurs who could start a new venue and incumbents with existing venues. As dis-cussed previously, agents receive opportunities to move in continuous time according to therealization of a Poisson process. Upon receiving an opportunity, potential market entrantsmake the decision whether to enter or stay out of the market and incumbent venues makethe decision whether to continue or leave the market. Once an incumbent leaves the market,they have left the market forever. A potential entrant must pay a sunk cost to enter whilean exiting incumbent receives an exit payoff.The sunk cost of entry and the exit payoff consist of a deterministic component and astochastic component. I discuss this in further detail below. The deterministic component ofeach agent’s shock is mutual common knowledge, while the stochastic component is privateknowledge for the agent and realized only once the agent receives a move opportunity.These shocks capture the economic reality that entrepreneurs may face barriers to entry17and owners may receive gains from the sale of capital goods upon exiting the market. Aswell, they give rise to a nondegenerate probability distribution for entry and exit uponreceiving a move opportunity. This allows for the use of observed entry and exit rates toidentify profit functions, which is a key aspect of the estimation procedure outlined below.Agents are assigned to discrete neighbourhoods indexed by m. That is, each entranthas a specific neighbourhood in which it may choose to enter and each incumbent mayeither continue to operate in its neighbourhood or exit the market. Each neighbourhoodhas nm = (nm1, nm2, . . . , nmL) incumbent venues of each type ` ∈ 1, 2, . . . , L as well as ν`entrants of type `. (As the number of potential entrants is unobservable, I treat this as aparameter to be estimated.) As well, each neighbourhood has some persistent demographicattributes dm which affect the profit and some persistent regulatory stringency rm whichaffects the size of the sunk cost of entry7. Potential entrants receive opportunities to enterthe market according to a Poisson process with rate parameter α while incumbent venuesreceive opportunities to exit the market according to a Poisson process with rate parameterλ. I assume that agents discount the future at constant rate δ.It is worth discussing the assumption that potential entrants have a single neighbourhoodin which they can choose to enter. One may interpret an opportunity for an entrepreneur toenter as a particular piece of commercial real estate becoming available as a potential futurevenue. Insofar as a commercial real estate vacancy of a suitable size and configuration is anecessary precursor to opening a new nightlife venue (and building a nightlife venue on anightlife venue on an empty lot is likely infeasible in the context of Chicago) this is likely aplausible interpretation. A richer model could allow potential entrants to choose a neigh-bourhood for entry. However, the much larger state space relevant to each agent’s decisions(i.e., the state of each market) would yield a computationally intractable model. This re-striction may also be justified if we assume that entrants have some particular knowledgeof local conditions within the neighbourhood.Each agent forms its value function based on its consistent belief of other agents’ entriesand exits as well as its expectations of its own move opportunities. An incumbent venuereceives the flow profit pi` as specified by Equation 2.4. Let ι` be a vector with 1 as element7Suzuki (2013) shows that local land use regulations may represent a significant barrier to entry for newfirms.18` and 0 as all other elements — i.e., n + ι` is the vector of incumbent venues after a newvenue of type ` enters. The value function for an incumbent venue of type ` (as a functionof the number of venues nm, the demographic attributes dm, and the regulatory conditionsrm) is as follows:V c` (nm, dm, rm) =[δ +∑`′(ν`′α`′ + n`′λ`′)]−1×[pi (nm, dm) +∑`′( (n`′ − I(`, `′))λ`′σx`′(nm, dm, rm)Vc` (nm + ι`′ , dm, rm) + ν`′α`′σe`′(nm, dm, rm)Vc` (nm − ι`′ , dm, rm))+λ`E [max {Vc` (nm, dm, rm), ψx` + εx}]](2.7)In Equation 2.7, the second line accounts for entries and exits by other agents while thethird line accounts for the incumbent’s decision to remain or exit conditional on receivinga move opportunity. Recall that in the continuous-time environment it is unnecessary toaccount for the possibility of multiple simultaneous transitions as this is a measure-zeroevent.The value function for a potential entrant of type ` which has not yet chosen to enterthe market is similar, although the potential entrant receives no flow of profit:V e` (nm, dm, rm) =[δ +∑`′(ν`′α`′ + n`′λ`′)]−1×[0+∑`′(n`′λ`′σx`′(nm, dm, rm)Ve` (nm + ι`′ , dm, rm) +(ν`′ − I(`, `′))α`′σe`′(nm, dm, rm)Ve` (nm − ι`′ , dm, rm))+α`E [max {Ve` (nm, dm, rm), Vc` (nm + ι`, dm, rm)− ψe(rm) + εe}]](2.8)These value functions lead directly to the conditional choice probabilities for venue entryand exit decisions. Conditional on receiving an entry opportunity, a potential entrant willchoose to enter (and become an incumbent venue) only if the value of being an incumbentexceeds the value of remaining an entrant less the entry sunk cost. Similarly, conditional onreceiving an exit opportunity, an incumbent will exit only if the exit payoff exceeds the valueof continuing as an entrant. The entry cost ψe(r) + εe and the exit payoff ψx + εx consistof deterministic components ψe(r)8 and ψx plus independent and identically distributedstochastic components εe and εx. As noted previously, the fixed components of these shocks8To reflect the possibility that local land-use regulation impacts the sunk cost of entry, I allow ψe to varywith regulatory stringency r.19are mutual common knowledge, while the realizations of the stochastic components areprivate information for each agent upon receiving a move opportunity. For tractability, Iassume Type-I extreme value forms for the stochastic components.Therefore, conditional on receiving move opportunities, the conditional choice probabil-ities of entry σe` and exit σx` are as follows:σe` (n, d, r) = 1− exp (− exp (− (Ve` (n, d, r)− Vc(n, d, r) + ψe(r)))) (2.9a)σx` (n, d, r) = 1− exp (− exp (− (Ve` (n, d, r)− ψx))) (2.9b)Recall that α` and λ` denote the arrival rate for entry and exit opportunities for entrantsand incumbents of type `. Therefore, the entry rate for potential entrants he`(n, d, r) andthe exit rate for current incumbents hx` (n, d, r) are as follows:he`(n, d, r) = α`σe` (n, d, r) (2.10a)hx` (n, d, r) = λ`σx` (n, d, r) (2.10b)Equation 2.10 states that the observed entry and exit rates are equal to the rates at whichagents receive move opportunities multiplied by the conditional choice probabilities of takingthose opportunities. Venue entry and exit rates are observable in the data. In the estimationstrategy below, I outline a scheme for connecting the observed entry and exit rates to theflow profit. Differences in venue entry and exit rates between states correspond to differencesin the flow profit and the barriers to entry. I use these differences to identify the structuralparameters of the model.2.2.3 Estimation strategyI estimate this model using a maximum likelihood strategy following Arcidiacono et al.(2012). The observable outcome of interest in this strategy is the state transition — that is,the entry or exit of a venue. The estimation procedure identifies the values for the structuralparameters which maximize the joint likelihood of the wait time between transitions and20the type of transition.The estimation procedure comprises several stages, as follows:1. Obtain nonparametric estimates h˘e` and h˘x` for the observed venue entry and exit rates.2. Use the estimates h˘e` and h˘x` to write the conditional choice probabilities of entry andexit σˆe` (nmt, dm, rm|θ) and σˆx` (nmt, dm, rm|θ) in terms of the structural parameters.3. Find the value of the structural parameters θˆ which maximizes the likelihood functionof the observed transitions.Because the conditional choice probabilities σˆe` (nmt, dm, rm|θ) and σˆx` (nmt, dm, rm|θ) repre-sent best responses to the estimated entry and exit rates h˘e` and h˘x` by construction, thesecond step enforces that the estimated result represents a Markov-Nash equilibrium.I estimate a single parameter η for the constant elasticity of substitution between sectorsand a single parameter w for the consumer’s nightlife budget. For each venue type `, Iestimate a separate value for the within-sector constant elasticity of substitution ρ`, themarginal cost of production c`, the move arrival rates α` and λ`, the number of potentialentrants ν` and the exit payoff ψx` . I estimate the market size N¯ the fixed cost of operationκ` as a function of local demographic and built environment conditions and the sunk costof entry ψe` as a function of local regulatory conditions.At this point, it will be helpful to introduce some additional notation. For a givenneighbourhood m, let t = 1, 2, . . . , Tm index the observed transitions (i.e., entries or exits).Let τmt be the wait time before transition t, let nmt = (nmt1, nmt2, . . . , nmtL) denote thevector of venues of each type ` before transition t, and let emt` and xmt` be indicatorvariables for whether the transition t in neighbourhood m was an entry of type ` or an exitof type `. As a slight abuse of notation, let Tm+ 1 denote the period from the last observedtransition to the end of the sample9. Then, the log-likelihood of the observed transitions{τmt, nmt, emt`, xmt`} can be written as a function of these entry and exit rates he` and hx`9In this last period, the state after the next transition is clearly unobservable. However, the duration ofthe wait before a transition is itself informative, and therefore included in the likelihood function.21as follows:LLH ({τmt, nmt, emt`, xmt`} | he` , hx` ) =∑m[Tm+1∑t=1(−τmt)∑`(nmt`hx` (nmt, dm, rm) + ν`he`(nmt, dm, rm))+Tm∑t=1∑`(xmt`nmt` log hx` (nmt, dm, rm) + emt`ν` log he`(nmt, dm, rm))](2.11)Equation 2.11 gives the joint likelihood of the observed wait time between transitions andthe observed type of each transition. Specifically, the first sum expresses the likelihood of theobserved wait time between transitions and the second sum expresses the likelihood of theobserved type of each transition (conditional on observing a transition). Below, I maximizethis joint likelihood to obtain the structural parameters. Taking first-order conditions yieldsclosed-form expressions for the nonparametric entry and exit rates:he`(n, d, r) =[∑mTm+1∑t=1Imt {(n, d, r) = (nmt, dmt, rmt)} τmt]−1 [∑mTm∑t=1Imt {(n, d, r) = (nmt, dmt, rmt)} emt`](2.12a)hx` (n, d, r) =[∑mTm+1∑t=1Imt {(n, d, r) = (nmt, dmt, rmt)} τmt]−1 [∑mTm∑t=1Imt {(n, d, r) = (nmt, dmt, rmt)}xmt`](2.12b)In Equation 2.12, I denotes the indicator function. The entry and exit rates in Equation2.12 can be estimated directly from the data. Denote the results of this estimation by h˘e`and h˘x` .Next, I use these first-stage estimates h˘e` and h˘x` to write the value functions in terms ofstructural parameters10. Arcidiacono et al. (2012) shows that the agents’ value functionscan be written in terms of he` and hx` , the move arrival rate parameters α and λ, and theentry sunk cost and exit payoff ψe` and ψx` :V e` (n, d, r | he` , hx` , α, λ, ψe` , ψx` ) =ψx` − ψe(r) + log1− λ−1` hx` (n, d, r)λ−1` hx` (n, d, r)+ log1− α−1` he`(n, d, r)α−1` he`(n, d, r)(2.13a)10It would be possible to address this stage using numerical value function iteration on Equations 2.7 and2.8. However, the strategy outlined here is much faster and yields exact results.22V c` (n, d, r | he` , hx` , α, λ, ψe` , ψx` ) = ψx` + log1− λ−1` hx` (n, d, r)λ−1` hx` (n, d, r)(2.13b)Recall that α−1` he` is the probability of entry conditional on receiving a move opportunitywhile λ−1` hx` is the probability of exit conditional on receiving a move opportunity. Thevalue of an agents’ decision conditional on receiving a move opportunity can be written interms of the same objects11:E [max {V e` (n, d, r), Vc` (n+ ι`, d, r)− ψe(r) + εe} | he` , hx` , α, λ, ψe` , ψx` ] =− log(1− α−1` he`(n, d, r)) + γ (2.14a)E [max {V c` (n, d, r), ψx` + εx} | he` , hx` , α, λ, ψe` , ψx` ] = − log(1− λ−1` hx` (n, d, r)) + γ (2.14b)Substituting the first-stage estimation results h˘e` and h˘x` into Equations 2.13 and 2.14 givesconsistent estimates for the value functions. Substituting these estimates into the right-hand sides of Equation 2.7 and 2.8 yields expressions for the value functions in termsof the structural parameters (including the structural parameters of the profit function).Substituting these structural expressions for the profit function into Equation 2.9 gives thechoice probabilities for venue entry and exit (conditional on receiving a move opportunity)as a function of the structural parameters. Denote these structural conditional choiceprobability estimates as σˆe` (nmt, dm, rm|θ) and σˆx` (nmt, dm, rm|θ) where θ is the vector ofparameters including the move opportunity rates α and λ, the number of potential entrantsν, and all parameters of the profit function. This yields the following expression for thelog-likelihood of the observed transitions in terms of the structural parameters:LLH ({τmt, nmt, emt`, xmt`} | θ) =∑m[Tm+1∑t=1(−τmt)∑`(nmt`λ`σˆx` (nmt, dm, rm|θ) + ν`α`σˆe` (nmt, dm, rm|θ))+Tm∑t=1∑`(xmt`nmt` log λ`σˆx` (nmt, dm, rm|θ) + emt`ν` logα`σˆe` (nmt, dm, rm|θ))](2.15)11In Equation 2.14 γ ≈ 0.5772156649 is the Euler constant. This constant arises from the integration overthe stochastic components of the entry cost and exit payoff. It is specific to the assumed Type-I extremevalue functional form of these shocks.23I solve numerically for the parameter vector θˆ which maximizes the structural log-likelihoodas specified by Equation 2.15. This estimate θˆ forms the basis of the empirical results ofthis study.It remains to discuss the parameterization of N¯ , κ`, and ψe` . I use log-linear specificationsin demographic conditions d to estimate N¯ and κ`:N¯(d) = exp(θN¯o + θN¯dd) (2.16a)κ`(d) = exp(θκ` + θκdd) (2.16b)For the sunk cost of entry ψe` , I use a log-linear specification in regulatory conditions r:ψe` (r) = exp(θψo + θψrr) (2.17)For the sake of tractability, I discretize all persistent state variables (the neighbourhoodattributes dm and the regulatory stringency rm into five evenly spaced bins. When esti-mating the transition rates in Equation 2.12, I smooth across bins using a multidimensionalGuassian kernel with optimal bandwidth. I set the future discount parameter δ at 0.9 peryear12. I calculate the standard errors from the score function of the likelihood.2.2.4 Identification of colocation benefitsThe model outlined above ascribes differences in venue entry and exit rates as a function ofother venues in the neighbourhood (holding constant regulation, demographic attributes,and the build environment) to consumer preferences for variety. This may initially seem tobe a strong assumption as in general firms in the same industry may benefit from colocationfor reasons other than consumer preferences. However, consumer preferences for variety arelikely to be particularly strong in the context of the nightlife industry. Moreover, I arguethat other sources of agglomerative benefits are unlikely to be as important here as in other12The assumption of a constant discount rate follows the convention in the literature. Other studieswhich assume a constant discount rate of 0.9, 0.925, or 0.95 to estimate a dynamic structural model includeAguirregabiria and Mira (2007), Bajari, Benkard and Levin (2007), Ryan (2012), Collard-Wexler (2013),Dunne et al. (2013). As Magnac and Thesmar (2002) note, the discount factor is generally not well-identifiedin dynamic discrete choice models.24industries.One immediate alternative hypothesis is that venues may gain some production costadvantage to colocation. However, as noted by Samadi (2012), the average nightlife venue’scosts are unlikely to vary significantly within a city. Specifically, the average venue’s spend-ing on wages, alcohol purchases, and utilities constitutes 70.0% of its total spending. (Theremainder is accounted for by depreciation and other expenses.) While alcohol purchases(which account for 45.6% of spending) may seem to offer possible cost advantages if distrib-utors offer discounts to nearby venues, this does not appear to be the case. Wirtz BeverageIllinois (one of the largest distributors in Chicago) makes deliveries within the city limitsbased on a flat minimum order Wirtz Beverage Illinois (n.d.).An alternative explanation for colocation studied by Toivanen and Waterson (2005),Yang (2013), and Shen and Xiao (2014) is that firms learn about the profitability of agiven location by observing each others’ success. However, these studies generally considerlearning effects for firms seeking to open in new cities. Learning seems as though it wouldbe less of a concern in the current context. Most venues are owned by a firm that owns noother venues; insofar as the owners of these firms are likely to be located in Chicago, theirknowledge of local conditions is likely strong13. The cost of acquiring information is likelyrelatively low in Chicago, which is a very large and prominent city with well-documenteddistinct neighbourhoods. Moreover, as shown in Figure 2.3, the spatial distribution of venuescovers the densely populated areas of the city. Accordingly, the ability to learn about verylocal conditions from other venues’ experiences appears to be fairly well-distributed acrossthe city.Holmes (2011), Arcidiacono et al. (2012), Igami and Yang (2014), and others havediscussed the role of stragetic siting by retail chains as a possible explanation for observedfirm location patterns. However, this would not seem to be relevant in the current context.As discussed in further detail below, concentration in the nightlife industry in Chicago isvery low. The overwhelming majority of venue licenses are held by firms which hold noother venue licenses.13Chinco and Mayer (2014) provide evidence for strong informational advantage of local investors in thehousing market.25As Datta and Sudhir (2013) note, failing to account for local heterogeneity and zoningleads to misspecification errors. These may overstate the importance of agglomerativeeffects. However, in this paper, I account for neighbourhood heterogeneity and regulatoryconditions directly.In the context of nightlife specifically, consumer demand may be higher in neighbour-hoods with more foot traffic or higher-quality commercial districts. These unobservableneighbourhood attributes could lead to colocation of venues, which the model would misat-tribute to consumer preference for variety. I address this possibility directly as a robustnesscheck using the locations of Starbucks coffee shops as a proxy for these unobservable neigh-bourhood attributes. I find no evidence of a systematic relationship between Starbuckslocations and nightlife venue profitability.Accordingly, it seems reasonable to attribute the effect of the number of competitorson firm profitability to consumers’ preference for variety. Not only is consumer preferencefor variety likely to be particularly relevant in the nightlife industry (where consumersprefer the ability to visit several venues with low travel cost) but also the other potentialagglomerative effects on firm profitability seem less significant.2.3 Data and industry detailsTo estimate the structural model outlined above, I use data from Chicago. To explain howthe data set corresponds with the model outlined above, I discuss the specific conditions ofthe Chicago nightlife industry in some detail.2.3.1 Nightlife venuesFor information on nightlife venues, I use business license data from the City of Chicago DataPortal, which provides information on the new, renewed, and expired business licenses fromJanuary 2006 through July 2014. Representative examples of nightlife venues in my sampleinclude “Ted’s Firewater Saloon”, “Los Globos Ballroom”, and “Zero Degrees KaraokeBar”. I assume that a new liquor license represents a new entrant while an expired liquorlicense represents an incumbent exiting the market. This data set contains information26on liquor licenses (both for establishments which primarily serve alcoholic beverages andestablishments with “incidental” consumption of alcohol) as well as an indication of whetherthe licensee’s operations including music or dance and an indication of whether the licenseeis a “Public Place of Amusement” . (Public Places of Amusement include theatres, concerthalls, bowling alleys, pool halls, karaoke bars, and arcades as well as nightclubs and similarfacilities (Chicago City Council, 1990a).)In this study I examine consumer’s preference for variety among similar venues as wellas their preference across different types of venues. I use characteristics of venues’ businesslicenses to assign them to separate sectors. Business license attributes delineate the followingfour categories of nightlife venues:ˆ Venues which have Public Place of Amusement licenses with either no liquor licensesor licenses only for “incidental” consumption (“Amusement only”)ˆ Venues with alcohol licenses which do have Public Place of Amusement licenses andwhich do not have music/dance licenses (“Drinks only”)ˆ Venues with alcohol licenses and Public Place of Amusement licenses but not musicand dance licenses (“Drinks and amusement”)ˆ Venues with alcohol licenses and music/dance licenses and possibly also Public Placeof Amusement licenses (“Drinks and music”)I compare these venue categories to venue categories listed on Yelp and find that thebusiness license categories are strongly predictive of the Yelp categories. (Appendix Ccontains details of this comparison.) While the data set includes restaurants and mobilefood vendors, I do not include these categories in the estimation. Restaurants may notcontribute as strongly to nightlife amenities and they are frequently owned by chains whichmay optimize according to a very different strategy than the one described above. I amunable to sensibly assign mobile food vendors to a particular neighbourhood due to theirmobile nature.Figure 2.3 shows the geographical distribution for venues across Chicago. As shown,all venue types are widely distributed across the city. Table 2.1 shows summary statistics27Figure 2.3: Geographical distribution of venues within Chicago.for the venues in the sample. Relatively few venues are present for the entire sample. Forexample, of the 794 “Drinks only” venues, only 22 survive the sample while 408 enter andthen exit during the sample period. This is consistent with the high exit rates for newvenues documented by Abbring and Campbell (2005) and provides sufficient variation inentry and exit rates to estimate the model outlined above.Figure 2.4 shows the distribution of durations in the sample for each type. As shown,venues of the “Drinks and music” type tend to have the longest durations within the sample,to the extent that they almost strictly first-order stochastically dominate all other venuetypes’ duration. Conversely, the sample durations for the “Amusement only” are almostfirst-order stochastically dominated by all other venue types. However, each venue type hassignificant variation in sample duration.28Amusement Drinks Drinks Drinksonly only and music and amusementEnters in sample 50 252 29 14Exits in sample 21 112 5 22Enters, exits in sample 54 408 56 42Entire sample 13 22 2 9Total count 138 794 92 87Duration (days) 2032 2413 2646 2515(1079) (940) (789) (864)Table 2.1: Summary statistics for the venues in the sample. Standard deviation for durationin parentheses.Figure 2.4: Distribution of venues’ durations within the sample.It is worth emphasizing that the licensing data set suggests the industry has a very lowlevel of concentration. With fewer than a dozen exceptions (e.g. multiple Four Seasonshotels with their own bars) the license for each venue is held by a different firm. Matchingfirm names for licenses in the data set gives a Herfindahl index of 0.00694. This is consistentwith the description of Samadi (2012), who describes the market share concentration as“low” and notes that the nightlife industry “in general, consists of small businesses, with29few major operators and many being family owned and operated”14. Therefore, it seemsreasonable to treat the individual venue as the decision-making unit.2.3.2 NeighbourhoodsTo discretize the city into separate nightlife markets, I use the community area boundariesdeveloped by the University of Chicago’s Local Community Research Committee in the1920s to provide a more salient alternative to census tracts (Seligman, 2004). Inevitably,any partition scheme for discretizing a city into neighbourhoods is somewhat artificial.However, these neighbourhood boundaries appear to provide a reasonable approximationto actual geographical segmentation of the market for nightlife venues. Not only are theseboundaries used for city planning and public service (e.g., the Chicago NeighbourhoodStabilization housing market program organizes its activities by neighbourhood), but theyare also frequently used in real estate listings as well as media reports comparing Chicagoneighbourhoods and therefore likely reflect popular usage (Rodkin, 2010; Taylor, 2013;Moser, 2013). Accordingly, in terms of spatial units which consumers and venues mightuse, community areas seem like a reasonable choice. Many authors in various public policyliteratures have also adopted the community area as a unit of analysis (Wilson and Daly,1997; Shah, Whitman and Silva, 2006; Illinois Assisted Housing Action Research Project,2010).These neighbourhood boundaries imply that in this model consumers gain no varietyfrom venues outside a given neighbourhood, no matter how close they are to the boundaries.This would appear to be a strong assumption on the model. However, practically speaking,the neighbourhood boundaries appear to capture areas in which the local density of venues isrelatively uniform. Figure 2.5 compares the normalized standard deviation of distance to thekth nearest neighbour venue for k from 1 to 10. As shown, the normalized standard deviationis much lower within neighbourhood than between neighbourhood, particularly when k ≥ 3.14It appears that this low concentration is broadly representative of other large cities. While none offer apanel of similar length to the Chicago data, the business license data set for currently-operating businesses inthe category “Drinking places (alcoholic beverages)” from San Francisco Data suggests a Herfindahl index of0.0146 while the 2012 business license data set from data.seattle.gov for business in the category “Drinkingplaces (alcoholic beverages)” suggests a Herfindahl index of 0.0108. These values are higher than the verylow concentration in Chicago, but still reflect an industry composed of many small firms.30Figure 2.5: Comparison of variation in nearest-neighbour differences within and betweenneighbourhoods. The abbreviation “N.s.d” refers to the normalized standard deviation —that is, the standard deviation divided by the mean. The abbreviation “n.n” refers to thenearest neighbour. Each label k denotes the normalized standard deviation for the distanceto the kth nearest neighbour. This figure only includes venues in the sample at the end ofthe sample period. However, results are similar at other points in the sample period.Therefore, despite the possibility of nearby venues in other neighbourhoods, it appears thatconsumer access to variety is relatively constant across all venues in a given neighbourhoodcompared to the difference in consumer access to variety across neighbourhoods.Moreover, reduced-form regression results suggest that within-neighbourhood neigh-bouring venues have less meaningful effects on entry and exit rates. For each of the fourvenue types, I estimate three Cox proportional-hazards regression models for the entry andexit rates with the following controls:1. The first four principal components of neighbourhood attributes and the share of theneighbourhood covered by dry areas and moratoria (as discussed below and as shownin Figure 2.6)2. All the controls from the previous regression as well as the number of venues of each31Likelihood ratio betweenModels 1 & 2 Models 2 & 3EntryAmusement only 19.50∗∗∗ 1.64Drinks only 43.79∗∗∗ 15.64∗∗∗Drinks and amusement 20.98∗∗∗ 1.55Drinks and music 24.76∗∗∗ 6.80∗ExitAmusement only 21.78∗∗∗ 0.81Drinks only 69.62∗∗∗ 15.05∗∗∗Drinks and amusement 9.11∗ 6.21Drinks and music 22.21∗∗∗ 1.36Table 2.2: Likelihood ratio tests for Cox proportional hazard survival models of venueentry and exit. The first column adds controls for the number of venues of each type in thesame neighbourhood. The second column adds controls for the number of venues of eachtype in neighbouring neighbourhoods (weighted by the length of shared border betweenneighbourhoods). ∗, ∗∗, and ∗ ∗ ∗ denote statistical significance at the 10%, 5%, and 1%levels.type in the same neighbourhood3. All the controls from the previous regression as well as the number of venues of eachtype in neighbouring neighbourhoods (weighted by the length of the shared boundary)The third model nests the second model, which in turn nests the first model. Accordingly, itis possible to compare models using the likelihood ratio. Table 2.2 shows the likelihood ratiocomparisons. As shown, the likelihood ratio is highly statistically significant in all caseswhen controls for venues in the same neighbourhood are added. However, the likelihoodratio between models with and without controls for venues in neighbouring neighbourhoodsare always much smaller and (with the exception of “Drinks only” venues) not statisticallysignificant. This indicates that the community area boundaries provide a practical strategyfor market delineation that in most cases captures the variation with substantial impact onvenues’ entry and exit decisions.Below, I explore alternate definitions of neighbourhood boundaries as a robustness check.I find that results for consumer preference for variety are not sensitive to the specific bound-aries between neighbourhoods.322.3.3 Regulatory environmentVenues in Chicago face citywide regulatory barriers to entry as well as very local within-cityregulation. Citywide regulatory barriers include a licensing fee of at least $4,400 (with addi-tional fees for patios and later hours of operation) and applications for new licenses must in-clude extensive documentation as well as liquor liability insurance and criminal backgroundchecks for investors, corporate officers, and managers (Chicago Department of Business Af-fairs and Consumer Protection, n.d.). These represent significant sunk investment costs,particularly since liquor license applications are sometimes rejected (Kindelsperger, 2011;Maidenberg, 2013; Morgan, 2013) and therefore investors may be reluctant to contribute toopening a new venue. Moreover, the regulatory process may introduce unpredictable andpotentially costly delays to the process.At the local level, Chicago has a distinct system of liquor license regulation which fea-tures two forms of restriction on liquor licensing: bans and moratoria (Chicago Departmentof Business Affairs and Consumer Protection, n.d.). Bans prohibit outright the issuanceof liquor licenses; all incumbent venues must exit when a new ban is enacted. Moratoriaplace restrictions on the locations of new primary liquor licenses — most importantly, amoratorium sets a minimum distance from existing primary liquor licenses.Bans are instituted by popular vote in precinct-level referenda which take place along-side other elections (Illinois General Assembly, 1934). The legislation to empower votersto enact outright bans on liquor licenses was enacted in 1934 immediately after the end ofProhibition, when many state legislatures were granting local control over liquor purchaseand consumption (Strumpf and Oberholzer-Gee, 2000). In the modern context, these refer-enda are unique to Chicago among large American cities. The precincts are the lowest levelof political division in Chicago and therefore these referenda are very local. In the fortyreferenda since 2000, the total ballot count has averaged 241, and none has returned morethan 490 ballots. The ban can be repealed, but it seems this rarely occurs. Only one of theforty referenda since 2000 considered a potential repeal, and this referendum was defeated.It appears that venues regard the referendum process as beyond their ability to influence.Incumbent venues affected by dry precinct bans tend to accept a referendum once it is33announced (Cawthon, 1998; Mitchell, Moore and Yousef, 2011; Byrne, 2012). Potentialentrants are often deterred very early in the entry process by potential referenda regardless ofsupport from local politicians and institutions (Lambert, 2008; Mitchum, 2008; Lam, 2008).These media reports suggest that venue owners regard attempts to influence proceedings asineffective.Liquor license moratoria are established by decisions of city council (Chicago City Coun-cil, 1990b). Moratoria also impact liquor license at a very local scale; some moratoria applyonly to one side of a particular street. Within a moratorium zone, new liquor licenses areprohibited within 400 feet of existing licenses. Existing licenses may only be transferredto immediate family members, business partners, or inheritors. If a previously-licensed siteloses its license, any attempt to open a new venue on the same premises faces steep regu-latory hurdles, including the written consent of the majority of registered voters within a500-foot radius. Accordingly, the license moratorium drastically increases the cost of marketentry.The City of Chicago Data Portal provides information on the locations of dry precinctsand local moratoria. The local shares of dry precincts and local moratoria change onlyslightly over the sample period (predominantly in a few already heavily-regulated neigh-bourhoods with few venues). Accordingly, I use the average level of regulatory stringencyover the sample period. While time-varying regulatory stringency would be possible in thisempirical framework, including variation in regulation substantially would increase the sizeof the state space while providing minimal additional information about venues’ decisions.In addition to the moratoria and dry precincts, municipal noise regulations prohibitliquor licenses within 100 feet of schools, libraries, churches, and certain categories of busi-nesses (Chicago City Council, 1990c). The City of Chicago Data Portal provides informationon the locations of schools and libraries, as well as the list of institutions given exemptionsfrom water charges. I infer the locations of churches and similar religious edifices fromthe names of institutions granted exemptions15. As these restrictions are virtually indis-tinguishable from the dry precincts, I include these with dry precincts as a single form of15In particular, I assume that any institution granted an exemption with “church”, “temple”, “masjid”,“synagogue”, “mosque”, “tabernacle”, or a similar term in its name is a religious edifice near which newliquor licenses are prohibited.34regulation.Figures 2.6a and 2.6b show the proportion of each neighbourhood covered by liquor li-cense moratoria and dry areas. Most neighbourhoods are less than 5% covered by moratoria,while several are over 50% covered by dry precincts.In this study, I construct a model which captures the effects of these regulations onnightlife venues. Precinct-level bans and license moratoria reduce the available real estatefor nightlife venues and therefore make it more difficult to find a venue site. In the model,this raises the cost of entry for potential entrants. Moreover, the presence of positiveeffects of venue colocation on profit complicates the dynamic response of industry to anygiven policy change; if more stringent policy causes some venues to exit the market, nearbyvenues benefit from the reduced competition but also may lose customers due to reduceddensity of nearby venues.2.3.4 Neighbourhood attributesLocal demographic and infrastructure characteristics may impact venue profitability. Toaccount for this, I obtain tract-level data from the 2010 US Census as well as demographicdata from the 1% sample of the American Community Survey (ACS) through the IPUMSdatabase(Ruggles et al., 2010). The ACS data contains geographic specification to thelevel of the Public Use Microdata Area (PUMA), which is a Census designation for ageographical region of approximately 100,000 residents. I match the tract-level and PUMA-level data to the community areas using GIS software. Table 2.3 shows summary statisticsfor neighbourhood attributes.Ideally, the estimation would condition on all these variables. However, this would sub-stantially increase the dimensionality of the state space and create a challenge for the numer-ical algorithms used for likelihood maximization. Moreover, many of these neighbourhoodattributes are closely correlated. I address this by considering four principal componentsof the data. Table 2.4 shows the loading factors for the four principal components. Thesefour components collectively explain 93% of the variance between neighbourhoods. Theremaining components account for a much smaller share of the variance. The first principalcomponent primarily corresponds to dense areas near the central business district while the35Mean Std. dev. Min MaxTransit stations 1.62 2.68 0 18Pop. dens. (km2) 770.04 525.41 125.94 2808.52Age 20–34 (%) 24.51 5.70 17.80 47.50Nonfamily (%) 10.03 2.90 4.89 18.97HH with children (%) 12.52 1.74 6.02 17.11Renters (%) 44.68 12.38 19.87 79.25African-American (%) 26.93 27.61 2.27 98.10Latino/Hispanic (%) 33.39 22.77 1.54 85.54HH income ($1000) 62.77 20.18 35.41 117.42HH income ≤ 25k (%) 29.69 9.62 13.18 47.07HH income ≥ 100k (%) 19.49 9.29 6.86 39.76Poverty (%) 23.48 9.34 7.16 42.09Detached housing (%) 38.05 23.45 4.23 86.12> 50 unit housing (%) 9.04 15.15 0.47 61.30Pre-1990 housing (%) 90.76 8.34 60.15 97.06Dry area (%) 12.39 18.48 0.02 73.45Moratorium area (%) 1.15 1.48 0.00 9.06Table 2.3: Summary statistics for the 77 neighbourhoods in the sample. The last two rowsare regulatory variables which are not included in the principal component analysis butrather included directly.second principal component primarily corresponds to poorer and less dense areas furtherfrom the city centre. The neighbourhood attributes are summarized graphically in Figure2.6.2.4 Results and discussionIn the discussion of the empirical results, I focus on consumer preferences for variety andthe parameters determining venues’ entry and exit decisions. Appendix D shows the fullset of estimated parameter values including the impacts of demographic attributes on theparameters of the profit function. Figure 2.7 shows the first-stage nonparametric entry andexit rates h˘e` and h˘x` on which the structural estimates are based. As shown, all venuetypes have a wide range of entry and exit rates across states. I calculate the standarderrors for the results in Figure 2.7 using the Nadaraya-Watson asymptotic variance for thenonparametric entry and exit rates. As shown, the entry and exit rate estimates appear tobe quite precise.36Principal component 1 2 3 4Age 20–34 (%)Nonfamily (%)HH with children (%)Renters (%)African-American (%) -0.459 -0.654Latino/Hispanic (%) 0.409 0.316Income ≤ 25k (%) 0.229 -0.107Income ≥ 100k (%) -0.181 0.17Poverty (%) 0.213Detached housing (%) -0.197 -0.235 0.126> 50 unit housing (%) 0.12 0.228Pre-1990 housing (%) -0.124HH income ($1000) 0.112 -0.647 0.567Transit stations 0.961Pop. dens. (km2) -0.988Cum. share of variance 0.444 0.763 0.863 0.932Table 2.4: Factor loadings for principal component analysis together with the cumulativeshare of variance explained by the principal components.Elasticity Symbol EstimateBetween sectors η 2.04(0.002)Amusement only ρ1 4.90(0.013)Drinks only ρ2 2.15(0.001)Drinks and amusement ρ3 3.56(0.224)Drinks and music ρ4 7.96(0.290)Table 2.5: Maximum likelihood estimation results for the CES parameters η and ρ`. Stan-dard errors in parentheses.2.4.1 Parameter estimatesTable 2.5 shows the estimated CES parameters for consumer preference across venues. Asshown, the elasticity of substitution between sectors η is very low, which indicates a strongpreference for variety between sectors. The elasticity of substitution within sectors varieswidely. Consumers have a particularly strong preference for variety among “Drinks only”venues (e.g., bars without live music and taverns) and a less-strong preference for varietyamong “Drinks and music” venues (e.g., bars with live music and performance venues).37(a) Share of area dry (%) (b) Share of area moratorium (%)(c) First principal component (d) Second principal component(e) Third principal component (f) Fourth principal componentFigure 2.6: Neighbourhood attributes.Insofar as I estimate these results based on a CES utility function, they are broadlycomparable with other results in the international trade and urban literatures that examineconsumer preference for variety16. The estimate for the constant elasticities of substitution16However, as noted previously, the consumers’ reservation shock is novel to this model and therefore the38Figure 2.7: First-stage results for venue entry and exit rates as a function of state. Unitsare days−1 throughout. Error bars in grey represent one standard deviation.between “Drinks and music” venues is close to the elasticity of substitution in the rangeof 8.4–8.8 for restaurants reported by Couture (2014). Meanwhile, the elasticity of sub-stitution between “Drinks only” venues is very low — the value of 2.15 is below the firstpercentile of goods reported in Broda and Weinstein (2010) and comparable to the elasticityof substitution between varieties for highly variety-specific goods such as coffee, automotiveparts, and footwear in Broda and Weinstein (2006). The elasticities of substitution for theother two venue types are more comparable to the 5th to 25th percentile of elasticities forconsumer goods reported in Broda and Weinstein (2010).These results suggest a strong preference for variety in nightlife compared to other con-sumption goods and services, particularly among bars, taverns, and similar venues withoutmusic, dancing, or other amusement. (Below, I quantify this preference by assessing themarginal impact of a new venue on consumer welfare.) This strong preference for varietymay indicate a consumer preference for the ability to “bar-hop” between many venues ofinterpretation of these elasticities is not precisely identical to others in the literature.39Move arrival rate Symbol EstimateEntryAmusement only α1 4.00(0.01)Drinks only α2 905(98)Drinks and amusement α3 718(86)Drinks and music α4 14.8(24.3)ExitAmusement only λ1 5.09(1.07× 10−7)Drinks only λ2 9.03(4.51× 10−3)Drinks and amusement λ3 2.31(0.01)Drinks and music λ4 2.10(3.62× 10−5)Table 2.6: Maximum likelihood estimation results for the move arrival rate parameters α`and λ`. All values are measured in 10−3 days−1. Standard errors in parentheses.this type. As well, this may reflect an ability by venues without music and and dancelicenses or Public Place of Amusement licenses to differentiate themselves in some otherunobservable attributes (e.g. de´cor or types of beverages offered).Table 2.6 shows the arrival rates for agents to enter and exit the market. Entry oppor-tunities arise most frequently for the “Drinks only” sector, followed closely by the “Drinksand amusement sector”. The other sectors experience fewer opportunities to enter the mar-ket. Meanwhile, incumbent venues face opportunities to exit the market at a low frequency(on the order of once per year) across all sectors. This may reflect the timescale of leases,supplier agreements, or other contractual obligations, or it may reflect a low rate of arrivalfor preferable outside opportunities for nightlife venue operators.In the dynamic model, the sunk cost of entry and the payoff of exit consist of a deter-ministic component plus a stochastic component. Table 2.7 shows the estimated values forthe logarithm of the deterministic component of the sunk cost and the exit payoff. Thesevalues are denominated in model units. I convert to dollar values below. As shown, thebarriers to entry are quite high compared to the payoff from exit.In Table 2.7, I also report the effect of dry precincts and moratoria on the barriers40to entry. As I estimate the deterministic component of the barrier to entry as a log-linear function of the prevalence of regulation, these should be interpreted as elasticities.Specifically, a 1% increase in dry precincts in a neighbourhood raises the barrier to entry by0.47% while a 1% increase in moratoria in a neighbourhood raises the barrier to entry by0.11%. As shown in Figure 2.6a, some neighbourhoods are over 60% dry precincts; thereforethe estimation results suggest that this poses a substantial deterrent to entry.The estimated parameter values imply a payoff from exit much lower than the sunkcost of entry. This may partially be explained by the non-transferability of liquor licenses.Licensing regulation allows for a nightlife venue to be sold, but it does not allow for a newoperator to use the license for a location that previously hosted a nightlife venue but exitedthe market (Chicago City Council, 1990b). Accordingly, a nightlife venue operator cannotrecoup the significant costs associated with the licensing process upon exiting the market.An exiting nightlife venue operator is also unlikely to be able to recover the cost of thestructural renovations which were necessary to open a new nightlife venue. As discussedbelow, the costs of building improvements can be substantial.These estimated parameters are all in terms of model units, which are determined bythe normalization condition on the reservation utility shock max {V ∗} ≡ 1. To understandthese parameter values in terms of policy implications, it is useful to express these termsin dollar values. According to Samadi (2012), the average revenue for a nightlife venuein the United States is $345,121 annually. I assume that this value is representative forvenues which only serve drinks, which is the most-numerous venue category in the sampleand which seems likely to be most representative of the national average. As well, I assumethat 3.6% of revenue is profit as suggested in Samadi (2012) is a representative value for mysample. This suggests a profit of $12,424 annually17. Given the discount factor of 0.9 peryear, this indicates that (in a hypothetical steady-state environment) the net present valueof an incumbent venue is on the order of $124,240. The median continuation value acrossall states for “Drinks only” venues is 1.24. Therefore, one model unit is approximately$99,810.17Specifically, Samadi (2012) notes that profit margins can be as high as 59.7% of revenue, but 3.6% is theaverage. This broad dispersion suggests that any dollar values should be interpreted as generally indicativerather than as precise estimates.41ParameterEntry costAmusement only baseline 2.11(0.003)Drinks only baseline 2.17(0.008)Drinks and amusement baseline 2.11(0.02)Drinks and music baseline 1.81(0.25)Role of dry precincts 0.470(0.003)Role of moratoria 0.106(0.03)Exit payoffAmusement only -4.01(0.82)Drinks only -4.06(0.06)Drinks and amusement -2.76(0.32)Drinks and music -3.23(0.07)Table 2.7: Maximum likelihood estimation results for the logarithm of deterministic com-ponent of the sunk cost of entry and the exit payoff. The “baseline” entry cost reflects theentry cost in the absence of local regulation. Standard errors in parentheses.As a strategy for verifying the conversion factor from model units to dollars, I considerthe cost of purchasing an operating venue. This cost should be comparable to the netpresent value of an incumbent venue. I use data from BusinessBroker.Net (n.d.) to obtainthe price for purchasing an incumbent nightlife venue. While this data includes only theasking price rather than the purchase price, it provides some indication of the net presentvalue of a nightlife venue. This data source contains relatively few Chicago-specific venues;as of writing, only one nightlife venue is listed in Cook County for an asking price of$150,000. Therefore, I consider all businesses listed in the “Food & Beverage: Bars, Clubs,Nightspots” category which include the term “bar”, “pub”, “club”, “tavern”, or “lounge”in the description but exclude “restaurant”. The median price in this sample is $250,000with an interquartile range of [$150,000,$250,000]. Insofar as these are asking prices ratherthan price received by the seller and this illiquid market is likely prone to negotiation thesevalues may overstate the market value somewhat. Together with the single observation of42a $150,000 asking price in Chicago, this lends some plausibility to the net present valueconversion factor of $124,240.This conversion factor allows me to assign dollar values for the sunk cost of entry andthe payoff from exit. I use the parameter estimates from Table 2.7 to find the deterministiccomponent and then add the median value of the stochastic component18 then convert frommodel units to dollars using the factor suggested by the results in Samadi (2012). Table2.8 shows the resulting estimates. In general, the parameter estimates suggest barriers toentry on the order of several hundred thousand dollars. These are high barriers to entrywhich represent several years’ profit in most cases. Accordingly, potential entrants likelyonly choose to enter when they receive a particularly favourable value for the stochasticcomponent of the sunk cost of entry19. These results suggest that barriers to entry maysignificantly reduce the variety offered to the consumer.Table 2.7 includes confidence intervals for each of these estimates. I calculate confidenceintervals using a Monte Carlo process. I re-draw one thousand parameter vectors from annormal distribution with the estimated parameters as its mean and the estimated variancematrix as its variance. Then, I re-calculate the median entry costs and exit payoffs undereach of these re-drawn parameter vectors. I use the resulting distribution of median entrycosts and exit payoffs to form confidence intervals.As noted previously, the payoff upon exit is substantially lower than the sunk cost ofentry. However, the parameter estimates suggest a deterministic component of the exitpayoff that is small compared to the stochastic component. Therefore, depending on therealization of the stochastic components, venues facing an opportunity to exit face a rangeof possible realizations of the exit payoff shock.Abbring and Campbell (2005) find that the value of a nightlife venue in its first year of18Given the extreme-value functional form of the shocks, the median value of the stochastic component is− log log 2.19However, while these values appear high, they are comparable in magnitude to costs discussed in thenon-academic business literature. Ingram (n.d.) suggests initial improvements to the building when openinga nightclub cost $18,000 to $65,000, sound equipment can cost $50,000 to $300,000, and the lease for thefacilities will generally exceed $10 per square foot. As well, Ingram (n.d.) notes that the total cost ofacquiring a liquor license can range as high as $1 million depending on the jurisdiction. As noted previously,venues in Chicago face an extensive regulatory process which includes licensing and application fees as wellas extensive documentation requirements. Fullbright (n.d.) gives a “low-end estimate” of the cost to starta nightclub of $239,250 and a “high-end estimate” of $837,100. Samadi (2012) suggests the cost of openinga venue ranges from $100,000 to $200,000 to $1 million or more, depending on venue size.43Value (thousands of dollars)Entry costAmusement only baseline 862[839, 886]Drinks only baseline 943[871, 1023]Drinks and amusement baseline 892[797, 995]Drinks and music baseline 670[83, 7588]Exit payoffAmusement only 38.4[36.6, 3383.7]Drinks only 38.3[37.5, 39.8]Drinks and amusement 42.9[36.8, 201.4]Drinks and music 40.5[38.5, 44.3]Table 2.8: Estimated sunk cost of entry. 95% confidence intervals in parentheses.operation lies mostly in its potential to exit the market; their structural estimates indicatethat the payoff from exit is 124% the continuation value of a firm in its first year of operation.Conversely, my estimates suggest that for a “Drinks only” venue that has just entered themarket that has just entered the market, the payoff from exit is 35.5% of the continuationvalue. While still substantial, this result is much lower than the Abbring and Campbell(2005) estimate. The discrepancy may arise from differences in the attribution of fixedcosts. While my model includes an initial sunk cost immediately upon entry and a constantfixed cost thereafter, Abbring and Campbell (2005) account for the cost of entry by allowingfixed cost to vary over time and therefore their model yields a lower continuation value earlyin the firm’s operation as the cost of entry is effectively being subtracted from the flow ofprofit.2.4.2 Goodness of fitIn interpreting these results, it is worth examining how well the model’s predictions matchobserved data. As a check on the model’s goodness of fit, I use the estimated parametervalues to solve for the equilibrium via value function iteration then compare the wait timesbetween transitions (i.e., venue entry or exit) as predicted by the model to the wait times44between transitions as actually observed. Recall that the parameters are set by maximizingthe joint likelihood of the wait time between transitions and the type of transition — i.e.,whether it is an entry or and exit and which type of venue is entering or exiting. Thegoodness-of-fit measure described here only accounts for the former. Insofar as the arrivalof each venue’s move in a given state is equivalent to the arrival time of a Poisson process,this measure reflects the total intensity of the collection of Poisson processes in a givenstate.This measure indicates reasonably close fit; the correlation between observed and pre-dicted wait times is 0.322. Averaging over observations with the same number of incumbentsof each type nm (but different demographics dm and regulation rm) gives a correlation of0.479. Both of these values are highly statistically significant. Figure 2.8 plots the observedand predicted wait times between state transitions. The observed and predicted values areclearly positively correlated. The model has some tendency to overestimate the frequencyof state transitions; most of the time, this occurs because the model predicts more rapidexit of venues than actually observed.It is worth discussing which aspects of the model might influence its ability to closelyfit the data. The dynamic model of venue entry and exit involves several restrictions whichare necessary for computational tractability or identification but which necessarily reducethe flexibility. As mentioned previously, I assume that venues discount the future at theconstant rate δ = 0.9. While this follows the standard approach in the literature, it maybe a poor approximation to reality if a venue’s discount rate is driven by its cost of capitaland that discount rate is substantially lower than 10%20. In this context, the model couldoverpredict exit if an incumbent is more “patient” and chooses to continue operating in low-profit situations if other venues’ entry and exit decisions are likely to lead to higher profitsin the future. Also, the assumption that the move arrival rates α` and λ` are constant isnecessary for the identification of venues’ entry and exit probabilities, but this may fail toaccount for cycles in local real estate markets or changes in landlords’ attitudes towardsnightlife venues which may impact venues’ entry or exit decisions. The assumption that20However, it is likely that nightlife venue operators face high borrowing costs. Ortiz-Molina and Penas(2008) present evidence that the average small-business line of credit has an interest rate on the order of8%.45Figure 2.8: Observed and predicted wait times between state transitions (i.e., venue entryor exit). Each point represents a single (n, d, r) state.the stochastic components of the entry cost and exit payoff are distributed according toan extreme value random variable may be a poor reflection to reality and may lead toan unrealistic incidence of “tail events” where entrants receive a very low entry cost orincumbents receive a very high exit payoff compared to reality.The static model also includes several abstractions which allow for a closer focus oncompetition and consumer preferences for access to variety. Agents receive no labour incomeor non-pecuniary utility from operating a nightlife venue, although in the real world thismay prevent venues with very low profit from taking exit opportunities. Also, there is nochannel for entrepreneurs to learn additional information about market conditions or theirown competence after entering the market; the decision to remain in the market is drivenwholly by profit (as predicted by local demographics and presence of competition) and thearrival of exit opportunities.462.4.3 Counterfactual scenariosThe estimation results above allow for the evaluation of counterfactual scenarios in boththe static and dynamic context. I use it to evaluate the impact on consumer welfare andprofits of the marginal venue entry in each neighbourhood as well as the dynamic impactsof changes to barriers to entry.Static counterfactualsFigure 2.9 shows the median changes in consumer welfare across all observations underscenarios where each neighbourhood gains a single venue of a given type `. These resultsaccount for changes to consumers who choose to go out as well as those who choose to con-sume their reservation utility. Recall that the reservation utility V ∗ is uniformly distributedon the unit interval and that consumers will only consume their reservation utility if it isgreater than the utility V of going out. Therefore, the expected overall consumer welfareW as a function of the utility of going out V is as follows:W (V ) =12 +12V2 V < 1V V ≥ 1(2.18)As shown in Figure 2.9, the South Side of Chicago is particularly underserved at currentlevels and welfare would increase substantially with additional venues of any type. Utilitygains are particularly strong for “Amusement only” venues in the South Side and for “Drinksonly” venues throughout the city. The median welfare gain from a new “Drinks only” venueis on the order of 13.5% while the median welfare gain for the other types is below 3%.To interpret these welfare gains, it is helpful to express the welfare changes in termsof the magnitude of venue price reduction that would give consumers the same increase toutility. Since both prices and consumer budget w are normalized by the entry cost, this isequivalent to the increase in w that would give the same increase in utility. As shown inEquation 2.3, the utility V (p) for consumers who choose to go out and consume nightlifeservices is proportional to w. (As shown in Equation 2.6, venue prices are independent47(a) Amusement only (b) Drinks only(c) Drinks and amusement (d) Drinks and musicFigure 2.9: Changes to consumer welfare from one additional venue of each type. Allchanges expressed as a percentage of the baseline welfare.of w.) Therefore, the compensating variation in w (i.e., the change in w that would giveconsumers the same welfare gain as a new venue) is identical to the proportional change inwelfare shown in Figure 2.9.It is worth emphasizing that this analysis of consumer welfare omits any potential neg-ative externalities associated with nightlife venues. Dense concentrations of bars and clubsare also associated with negative spatial externalities, including noise, crime, and litter(Danner, 2003; Currid, 2007; Campo and Ryan, 2008; Darchen, 2013a) and nearby residentsand other businesses demand regulation to reduce the number of venues. These negativeexternalities are beyond the scope of the model and therefore not included in the consumerwelfare results presented above. Accordingly, these results should not be interpreted as the48Amusement only Drinks only Drinks and amusement Drinks and musicAmusement only 36.3 13.2 6.7 14.1[0.0,36.3] [0.0,13.6] [6.4,19.1] [0.0,14.1]Drinks only 13.3 13.2 17.8 8.4[12.7,13.6] [0,14.5] [9.5,18.5 ] [0.0,8.6]Drinks and amusement 0.0 1.1 32.2 12.4[0.0,0.3] [0.0,1.2] [0.0,86.8] [0.0,12.4]Drinks and music 0.0 1.1 13.3 25.3[0.0,0.0] [0.0,1.1] [0.0,13.3] [0.0,26.3]Table 2.9: Proportion of observations where a new entry would increase the profit of incum-bent venues. The column variable is the type of the entrant while the row variable is thetype whose change in profit is shown. All values are expressed in percentage of observations.95% confidence intervals in parentheses.equilibrium welfare change for Chicago residents as a result of nightlife activity, but ratherthe utility of potential nightlife consumers.Table 2.9 summarizes the share of observations in which one (counterfactual) entrantof type `′ would increase profits for incumbents of type ` in the same neighbourhood. Asshown, in a significant (albeit imprecisely estimated) share of observations, an additionalvenue would lead to enough additional demand to increase incumbent profit. Venues of the“Amusement only” and “Drinks and amusement” types have a high incidence of spillover tovenues within the same type, while venues of the “Drinks only” type have a high incidenceof spillover to venues of different types.The presence of positive profit spillovers from new entrants may partially rationalizebusiness improvement districts (BIDs). Business improvement districts exist to promotebusinesses in a specific neighbourhood. The are typically founded by the decision of a collec-tion of nearby businesses to levy mandatory tax-like fees on all businesses in the district anduse these fees to fund joint improvements and promotion(Briffault, 1999). Businesses havevoted to create such districts specifically to promote entertainment and nightlife (Darchen,2013b). This study’s results suggest that under some circumstances subsidizing nearby busi-nesses can be increase profits. However, the formation of a business improvement districtis not necessarily a Pareto improvement for its members. Brooks and Strange (2011) showthat some firms oppose the formation of business improvement districts and many proposeddistricts fail to gain the necessary approval. When approved, property value benefits accrue49primarily to large anchor firms. The heterogeneous profit spillovers implied above are con-sistent with these results; new entrants would only improve profits for incumbents in somesituations and the benefit varies widely with the type of incumbent and entrant venues.As with the consumer welfare results, these results for nightlife profit do not necessarilyrepresent the full equilibrium impact of the nightlife industry on the profits for all firmsin the local economy. Insofar as nightlife venues occupy scarce retail real estate, theyreduce the supply of storefronts available to other industries. Therefore, the opening of anew nightlife venue may disrupt similar benefits of colocation for other retail and serviceindustries. In many parts of Chicago, available retail real estate is relatively constrainedand it is reasonable to suppose that nightlife venues displace other economic activity. Forexample, in the River North and West Loop real estate submarkets, the vacancy rate in2012 was 3.5%, while in the East Loop the vacancy rate was 2.2% (Bujwit, 2013). Withoutknowing which businesses are being displaced by nightlife venues and how those businessesbenefit from access to variety, the impact of this externality on commercial real estate isunclear.Dynamic counterfactualsNext, I use the model to evaluate dynamic counterfactual scenarios. Throughout, I assumethe stochastic form of the sunk cost shock and the exit payoff shock remain unchanged.Under each counterfactual, I re-solve the model using value function iteration under thecounterfactual. Note that these counterfactual predictions also represent a Markov-Nashequilibrium; in the counterfactuals, agents have consistent beliefs regarding each others’actions as a function of the current state.First, consider a dynamic counterfactual where the deterministic component of the sunkcost of entry is exogenously lowered by 25% for all potential entrants in all neighbourhood.This change is approximately one standard deviation of the within-sample variation in entrycost. Figure 2.10 shows the net difference in annual venue entry rate — that is, the numberof additional entries per year minus the number of additional exits per year under thecounterfactual. As shown, the effects of lower barriers to entry are substantial. In someneighbourhoods, this would increase the rate of entry (relative to the final period of the50(a) Amusement only (b) Drinks only(c) Drinks and amusement (d) Drinks and musicFigure 2.10: Changes to entry probability from lower entry cost. All changes expressed asthe change in the rate of new entrants choosing to enter the market per year.model) by five “Drinks only” venues per year and over 0.7 “Amusement only” and “Drinksand amusement” venues per year. The effects are largest on the South Side (which has alower density of venues venues) and smallest in Central Chicago (which has a higher densityof venues). This result suggests that policy changes to lower the entry costs could potentiallylead to a drastic increase in the number of venues in neighbourhoods with relatively fewvenues. These results are dominated by increased entry; changes to the exit rates aresmaller.Next, consider a laissez-faire counterfactual where all local regulation (i.e., dry precinctsand moratoria) are removed. Under this counterfactual, venues still face barriers to entry(due to startup costs and citywide regulation) but the cost is substantially lower. As shown51(a) Drinks only(b) Drinks and amusement (c) Drinks and musicFigure 2.11: Changes to entry probability from laissez-faire local regulation. All changesexpressed as the change in the rate of new entrants choosing to enter the market per year.Results for venues in the “Amusement only” category are not shown as venues withoutliquor licenses do not face local liquor regulation and the indirect effect from other venues’higher entry rate is very small.in Figures 2.6a and 2.6b, the impact of this counterfactual is largest in a few particularlyheavily-regulated neighbourhoods. Figure 2.11 shows the change in entry rate under thisscenario. As shown, the effect under the laissez-faire counterfactual is generally smallerthan the effect under the counterfactual with across-the-board entry barrier reduction. Tosome extent, this may be because the heavily-regulated neighbourhoods tend to be the less-profitable neighbourhoods. At any rate, this counterfactual provides evidence that the highbarriers to entry are not primarily driven by local liquor license restrictions (as opposed tomunicipal regulation or non-regulatory startup costs).522.5 RobustnessTo ensure that the model above is well-specified (and, in particular, to ensure that theeffects attributed to η and ρ` actually represent the effects on venue profit from consumerpreferences for variety) I re-estimate the model under different specifications.2.5.1 Cluster neighbourhoodsThe results presented above use the community area boundaries developed by the Uni-versity of Chicago’s Local Community Research Committee to define neighbourhoods. Asdiscussed previously, these do not seem to be an unreasonable unit for discretization. Com-munity areas have a reasonable size for nightlife consumers to travel within them, they areroughly convex, and in many cases they correspond with residents’ contemporary definitionof neighbourhoods.To ensure that these neighbourhoods correspond reasonably with nightlife consumers’actual choice sets, I re-estimate the model using a definition of neighbourhoods based on theclustering algorithm introduced in Rozenfeld et al. (2011). I fix a spatial distance d, and usethe algorithm to define a neighbourhood as the maximal spatial region in which no venue isat a distance greater than d from any other venue. To ensure time-invariant neighbourhoodboundaries, I include all sites at which a venue is ever observed in the sample. Let V denotethe set of all venues in the sample - then, the algorithm proceeds as follows:ˆ Choose a venue vo that is not yet assigned to a neighbourhood. Draw a circle of radiusd around venue vo. Assign the set of venues {v′ ∈ V | |v′ − vo| ≤ d} (that is the set ofvenues in the circle of radius d around the venue vo) to the same neighbourhood asvo.ˆ For each newly-assigned venue v′ from Step 1, draw a new circle of radius d and assignall not-yet-assigned venues to the same neighbourhood.ˆ Repeat Step 2 until the newly-drawn circles of radius d no longer incorporate any newvenues. The union of all circles from Steps 1 and 2 define a neighbourhood.53Figure 2.12: Map of clustered neighbourhoods generated using clustering radius d = 500m.ˆ Repeat Steps 1 through 3 starting with a new unassigned venue to define new neigh-bourhoods until no unassigned venues remain.At the end of this process, every venue is assigned to a neighbourhood. The resulting clusterneighbourhoods are independent of the starting point; each radius d defines a unique set ofneighbourhoods. Within each of these neighbourhoods, no venue is at any distance greaterthan d from at least one other venue. Moreover, any venue within distance d of a givenvenue is in the same neighbourhood.For suitable values of d, this defines a neighbourhood as including the maximal set ofvenues that consumers could access in a single night. I consider d = 250m, d = 500m, andd = 750m to give neighbourhoods of a comparable size to the community areas describedabove. Figure 2.12 shows the resulting cluster neighbourhoods for the case d = 500m. Ire-estimate the model using these new neighbourhoods.Table 2.10 shows the elasticity estimates under varying cluster sizes. As shown, the54Elasticity Symbol d = 250m d = 500m d = 750mBetween sectors η 2.02 2.07 2.04(0.001) (0.002) (0.001)Amusement only ρ1 5.68 6.72 4.32(0.008) (0.02) (0.009)Drinks only ρ2 2.05 2.07 2.08(0.0004) (0.0005) (0.0004)Drinks and amusement ρ3 3.82 5.73 5.44(0.04) (0.28) (0.65)Drinks and music ρ4 5.88 8.35 6.52(0.08) (0.33) (0.17)Table 2.10: Maximum likelihood estimation results for the CES parameters η and ρ` withclustered neighbourhoods of varying sizes. Table 2.5 shows the corresponding baselineelasticity values. Standard errors in parentheses.elasticity results under cluster neighbourhoods are very similar to the results generatedusing the community areas in Table 2.5. In particular, the elasticity between sectors ηis again slightly greater than 2 and the within-sector elasticities have similar values andranking orders. This provides supporting evidence that the results presented above are notan artifact of the community area neighbourhood boundaries.The estimation results suggest that consumer preference for variety is stronger withsmaller clusters in the “Drinks and amusement” and “Drinks and music” categories. Insofaras consumers are more averse to travelling long distance between venues on a single nightout, this may indicate that consumer preference in these categories arises from bar-hoppingin the course of a single night. However, the other two sectors do not display a similarpattern.2.5.2 Separate entry and exit ratesIn the model presented above, entrants’ actions are estimated partially based on the actionof the pool of entrants and incumbents’ actions are estimated partially based on the actionof the pool of incumbents. Accordingly, there is an aspect to the estimation that resemblesreflection; for example, in a neighbourhood of many successful incumbents with a lowexit rate, I observe successful venues and attribute their success to positive agglomeration55effects21. This may cause concern that the parameter σ is not actually capturing the benefitsof other nearby venues but some other factor in venues’ decisions —- for example, “animalspirits” among entrants that cause them to enter irrationally based on the rate of eachothers’ entry. Therefore, as an additional check, I address this by estimating the structuralparameter from the entry and exit decision separately.Specifically, I estimate the potential entrants’ entry decisions using the structural valuefunctions as a response to the nonparametric forms of the exit rates and with a separatelikelihood maximization estimate the incumbents’ exit decisions using the structural valuefunctions as a response to the nonparametric forms of the entry rates. That is, I estimatethe parameter vector θ from Equation 2.15 using first-stage nonparametric estimates hˆx(s)from Equation 2.12 for exit rates but structural predictions (which depend on the parametervector) for entry rates. Then, I repeat this process with first-stage nonparametric estimateshˆe(s) for the entry rates and structural productions for the exit rates. While these esti-mations provide the second-stage likelihood estimation with fewer observations, it ensuresthat the structural parameters are estimated from one group of agents’ actions in responseto another group’s actions.Table 2.11 shows the elasticity results under these restricted estimation schemes. Asshow, estimating the structural parameters by matching only the exit rate gives very similarresults to the baseline estimates in Table 2.5. However, matching using only the entry ratesgives a very poor model fit and disparate values for the elasticity parameters.It is worth noting that fitting the model using only the exit rates yields a modestimprovement to fit of wait times between transitions as compared to the results presentedin Figure 2.8. The correlation between observed and predicted wait times averaged overall demographic and regulatory states is 0.507, compared to 0.479 in the baseline results.Perhaps unsurprisingly, this improvement appears to arise from a closer match betweenobserved and predicted entry rates. Relative to the full model, fitting only the exit ratesgives less prediction of rapid exit of incumbent venues.21Note that due to the structural nature of this model this is not reflection in the strictest sense of theterm. However, as a check on the model’s ability to identify the profit function, it is useful to check whetherthis issue influences the results.56Elasticity Symbol From entry rate From exit rateBetween sectors η 6.72 2.03(1.3× 10−9) (0.002)Amusement only ρ1 45.81 4.79(4.4× 10−8) (0.02)Drinks only ρ2 8.25 2.25(9.6× 10−9) (0.002)Drinks and amusement ρ3 6.71 3.30(1.3× 10−9) (0.20)Drinks and music ρ4 9.93 7.31(8.5× 10−10) (0.36)Table 2.11: Maximum likelihood estimation results for the CES parameters η and ρ` un-der estimation matching only the entry rate and only the exit rate. Table 2.5 shows thecorresponding baseline elasticity values. Standard errors in parentheses.2.5.3 Profit from StarbucksWhile the estimation results presented above control for observable characteristics includingdemographics, transit access, and the nature of the built environment, they may still bebiased by unobservable heterogeneity. For example, if some other attribute uncorrelatedwith these observable characteristics positively impacts venue profits and more venues enterin neighbourhoods with this attribute, then the estimation will erroneously attribute thisincreased entry rate to consumer preference for variety. One particularly salient source ofpotential unobservable heterogeneity is whether the neighbourhood is a pleasant area forconsumers – for example, due to ease of pedestrian movement, appealing-looking buildings,a positive reputation, or other attributes. Researchers in the urban planning literature referto these aspects of a commercial neighbourhood’s aesthetic quality and ease of access asthe “streetscape”22.To investigate the possibility that the estimation results above reflect streetscape qualityrather than the presence of many nightlife venues, I re-estimate the model using the venues’response to the local density of Starbucks rather than the local density of other venues.Insofar as Starbucks locations tend to cluster near areas with high consumer foot traffic,Starbucks outlets seem like a reasonable proxy for unobservable streetscape attributes. The22 Campo and Ryan (2008) describe the importance of the streetscape for nightlife venues. Darchen (2013b)and Zimmerman (2008) discuss policymakers’ attempts to promote nightlife by upgrades and renovations tothe streetscape.57Amusement only Drinks only Drinks and amusement Drinks and musicA −0.09 3.37 0.42 1.42(0.18) (1.10) (0.95) (0.62)B −8.70 6.04 10.25 −4.72(0.34) (0.74) (3.32) (0.81)C 6.17 0.89 −9.18 2.65(0.03) (0.03) (0.32) (0.05)Table 2.12: Maximum likelihood estimation results for the parameters A, B, and C fromthe profit function specification in Equation 2.19. For legibility, all values are scaled up bya factor of 103. Standard errors in parentheses.same data set that contains the liquor licenses also contains Starbucks locations, includingspatial coordinates and entry and exit dates.Specifically, I re-estimate the model using a profit function of the following form:pim`i = A` +B`ζm + C`ζ2m +Ddm (2.19)In Equation 2.19, ζm is the number of Starbucks locations in neighbourhood m, dm is thevector of demographic attributes in neighbourhood m, and A`, B`, C`, and D are parametersto be estimated. Under this model, venues form their forward-looking expectations basedon entry and exit of Starbucks locations, which I estimate nonparameterically. I allow thesunk cost of entry to vary with neighbourhood-level regulation as above. If the profit isconstant with respect to the number of Starbucks, this provides supporting evidence thatρ` and η are actually measuring consumer preference for variety of venues rather than someother local condition.Table 2.12 shows the resulting parameter values for the relationship between Starbucksdensity and profit. As shown, the estimations results indicate no systematic role for Star-bucks in the profit function. Conditional on neighbourhood attributes, the signs of thecoefficients are neither systematically positive nor negative. These results do not supportthe hypothesis that the preference for variety implied by the results in Table 2.5 is actuallydriven by unobservable local-level attributes of local commercial districts.582.6 ConclusionEconomic literature and urban policymakers have recognized that consumer amenities arean important determinant of migration and quality of life. While consumers appear tovalue nightlife as a particularly important amenity, it has received less attention in theeconomic literature, possibly due to a scarcity of detailed data. In this paper, I estimatea dynamic structural model which identifies the profit function and consumer preferencesfor variety from observed venue entry and exit decisions. I use the estimation results toexamine counterfactual scenarios of industry dynamics.The results of the estimation suggest that consumers place a high value on variety innightlife venues. In particular, consumers have less of a strong preference for access tovariety in venues with music and dance (i.e., nightclubs) while they are very sensitive tovariety in venues which serve drinks but do not offer additional amenities (i.e., bars). Thepreference for variety in the latter category is comparable to the preference for varietyin highly-variety specific goods in the international trade literature. The CES parametervalues for venues with musical performances are comparable to the results in the literaturefor preference for variety across restaurants.The results also indicate that nightlife venues face very high barriers to entry. Thislimits the available variety of venues and lowers consumer welfare. Initially this would seemto suggest that the optimal policy response would include lower barriers to entry. However,as this study does not account for the negative impacts of nightlife venues, the optimalresponse is less straightforward. In terms of policy applications, this study does estimatethe value to nightlife consumers as well as the impact of new venues on incumbents. Inparticular, if the new entrant is a nightclub then existing venues experience a relativelysmall decline in their own profits as the draw of additional customers largely compensatesfor the increased competition.These results appear to be fairly robust. Changes to specification do not appear to affectthe estimates of consumer preference for variety. As well, as discussed above, the structure ofthe Chicago nightlife industry and additional estimation results rule out plausible alternateexplanations for the observed results.59This study also indicates directions for further research in understanding the valuationand development of consumption amenities in cities. In particular, a similar model ofconsumer preference for high-variety amenities could be used to investigate other urbanconsumption amenities with limited data — for example, musical performances or othercultural events. With a more detailed data set, one could infer additional details of consumerpreference for variety, particularly in terms of consumers preferences across differing incomelevels or demographic groups. More broadly, a structural model of this form could be usedto provide micro-level foundations for models of network formation where participants canpotentially gain from increased connectivity, such as Atalay et al. (2011) or Fershtman andGandal (2011).The theoretical and empirical results in this study could be extended by allowing greaterflexibility in venue location choices. In the current model, entrants can only choose to entera specific neighbourhood rather than a specific location within the neighbourhood. Thiscould theoretically be relaxed to allow potential entrants to choose a neighbourhood oreven to allow potential entrants to choose any location. As mentioned previously, greaterflexibility would massively increase the dimensionality of the state space and this estimationwould require a much larger data set. However, this extension would allow for a morecomprehensive understanding of the agglomerative forces arising from consumer preferencesfor variety in the nightlife industry.603 Land value gradients and the level andgrowth of housing prices3.1 IntroductionHousing rents and prices have grown significantly more rapidly in Coastal California, andthe Northeastern “Acela Corridor” than elsewhere in the U.S. in recent decades.1 Table 3.1presents summary statistics for rent and price growth in and away from these “Coastal”markets. The 25th percentile of coastal rent and price growth exceeds the 75th percentileamong other markets.Economists have put forward several explanations for why prices and rents have grownfaster in coastal markets. Physical and regulatory supply constraints are a popular expla-nation (Green, Malpezzi and Mayo (2005), Saiz (2010), Glaeser, Gyourko and Saks (2005),and many others). Moretti (2013), Diamond (2013a), and others have also observed thatproductivity and amenity appear to have grown more on the coasts than elsewhere.This paper considers an additional explanation for price growth on the coasts that ismotivated by fundamental results in urban economics and real options theory, but hasreceived relatively little empirical attention. We ask if cities where land values are moreconcentrated have higher levels and growth of housing rents and prices than elsewhere. Asa matter of casual observation, New York, Boston, and D.C. are more strongly monocentricthan is typical of “flyover” states. On the California Coast, while cities tend to be poly-centric, proximity to and views of the ocean appear to command high premiums. Having a“there there” thus seems to be associated with high and rising real estate prices2.In the standard Thunen-Alonso-Muth-Mills-Wheaton model of a monocentric city, loca-1One might think of these coastal markets as the Gyourko, Mayer and Sinai (2013) list of “SuperstarCities” purged of noise.2Ironically, Gertrude Stein’s remark about no “there there” was about Oakland, part of the San FranciscoBay Area, where location matters much more than most U.S. markets.61Quantile Annualized Price Growth Annualized Rental GrowthNon-Coastal Coastal Non-coastal CoastalMin -2.1 .1 .1 .925th -.9 .8 .8 1.450th -.6 1.2 1 1.475th -.1 1.6 1.3 1.5Max 2.1 2.5 1.8 1.7Table 3.1: Annualized U.S. Census (nominal) median rent growth (1980-2009/2011) and(log real) Freddie Mac Home Price Index growth (1980-2014): Coastal vs. other metropoli-tan areastions within a metropolitan area vary by the time or money cost of commuting to a centralpoint. Locations are described by their distance from the center, and commuting costsare monotonically increasing with distance. If the gradient of the cost function were zeroeverywhere, there would be no urban land rents, and the cost of a given home on a given lotsize would be the same everywhere inside the metropolitan area, and would grow only withconstruction or land opportunity costs. If the cost gradient is positive, then as the urbanboundary increases, the value of land within the boundary grows. We thus know that froma starting point of homogeneity, introducing heterogeneity of land values across locationsincreases the sensitivity of price growth to growing demand.Whether the result that a steeper land rent gradient increases the sensitivity of landprices to demand growth extends past a constant zero gradient is a non-trivial theoreticalquestion. Draft work by Joe Williams suggests the answer is yes, because for a given levelof demand and expected demand growth, land value growth options are greater in citieswith steep gradients, so less land is developed for a given increase in demand. This resultmay depend, though, on the elasticity of lot size with respect to land price.We ask empirically whether cities where land quality is more strongly differentiated haveenjoyed increasing rents over time by measuring current median rents, historical rent andprice appreciation, and forward-looking appreciation as measured by ratios of rent to price.A technical innovation in this paper is the introduction of a generalized urban landrent gradient that allows for non-monocentricity. Wheaton (2004) presents and summarizesevidence that the monocentric city model of commuting is a poor approximation for most62cities. Greater Los Angeles and San Francisco stand out as metropolitan areas where themonocentric city model might not describe the land market well.Standard measures, summarized in McMillen (2003), estimate decay from a single cen-ter. To allow for polycentricity, rather than measuring a decay from a single central point,we introduce a measure which takes into account conditions over the entire metropolitanarea. Specifically, to measure the extent to which some locations are better than other, weestimate land value gradients averaged across all locations in the metropolitan area. Landvalues are difficult to observe in most metropolitan areas, so we proxy for land rents in twoways. First, we use a proxy for very high land value: Starbucks locations. Casual obser-vation reveals that Starbucks tends to locate in high-traffic neighborhoods. Unlike someretailers, Starbucks has a small footprint, so there is reason to think that their willingnessto pay per square foot of land would fall off more steeply with declining location qualitythan larger retailers, such as Walmart. Walmart and other “big box” stores are rarely foundin prime urban locations. A second proxy for land values comes from apartment rents.An additional contribution of this paper is to ask whether any of the standard expla-nations for high housing prices on the coasts have value in explaining home prices insideor away from the coasts. There is reason to suspect not. Several studies, including Mianand Sufi (2009) and Huang and Tang (2012) that the volatility of home prices in the 2000shousing cycle is unconditionally highly correlated with supply constraints. However, David-off (2013a), recognizing that supply-constrained cities typically feature attractive environ-ments (such as mountains and oceans, the primitive of the standard Saiz (2010) measureof constraints) and productive workers, finds that within states, or conditional on histori-cal measures of demand growth, supply constraints are not associated with price volatility.Davidoff (2015) shows that a coastal indicator swamps many demand measures in explain-ing historical price growth. An important question is whether urban economists (ourselvesincluded) have explained why the coasts have witnessed more price growth and volatility,or instead have unsuccessfully sought to deduce the drivers of price growth from the per-formance of set of markets that differ from other U.S. markets in ways that are hard tocharacterize.633.2 Theoretical modelWe define a city-level measure of the spatial rate of change of local land value. To discussthis measure, it will be helpful to define some notation. For a given city in the data, weobserve a collection of pairs (xi, yi) for i ∈ 1, 2, . . . , N where xi is a spatial position andyi is a corresponding rent observation. The density of observations corresponds to therealization of some underlying probably distribution f(x) for rent observations at locationi. The value of yi corresponds to the realization of some valuation function yi = r (xi) + εiwhere r (x) = E [y | x] is the expected rent conditional on location. Our measure focuses onthe rate of change in this expected rent function r.Specifically, we estimate the average magnitude of the density-weighted gradient of rent.The gradient of r is defined by the vector ∂r∂x . Its magnitude corresponds to the rate ofincrease in r along the direction of steepest ascent; a larger magnitude for the vector ∂r∂xcorresponds to a situation where rents change more rapidly with position.Powell, Stock and Stoker (1989) and Powell and Stoker (1996) describe estimators for thethe average density-weighted gradient E[f(x) ∂r∂x]. The argument to the expectation hereis the rate of change in r with respect to position, weighted by the density of observations.This vector-valued expectation describes the average rate of change of rent (with respect tomarginal changes in position northward and eastward) across the entire city. This measureis unsuitable for our purposes as averaging the vector of spatial derivatives over the extentof a city can give an average vector for which the magnitude is difficult to interpret. Forexample, a constant-density city where rents decrease smoothly and symmetrically withdistance from the city centre would have an average density-weighted gradient of zero, aseach observation would be precisely cancelled out in the average by an observation on theopposite side of downtown.Instead, we consider the magnitude of the average density-weighted gradient of rent,defined as g¯ = E[f(x)∣∣ ∂r∂x∣∣]. This scalar-valued measure describes the average absoluterate of change in rents with respect to position. To estimate g¯, we form an estimate fˆ(x)of the density of observations f(x) using a kernel density estimator and an estimate∣̂∣ ∂r∂x∣∣ ofthe gradient magnitude∣∣ ∂r∂x∣∣ from a local cubic regression of rent as a function of position.64Then, we take the sample analogue of g¯ to obtain an estimate gˆ:gˆ =1NN∑i=1fˆ(xi)̂∣∣∣∣∂r(xi)∂x∣∣∣∣ (3.1)As fˆ(x) consistently estimates f(x) and̂∣∣∣∂r(xi)∂x∣∣∣ consistently estimates∣∣ ∂r∂x∣∣, Equation3.1 yields a consistent estimate of g¯.The kernel density estimate of f(x) requires a bandwidth parameter to determine thespatial scale of smoothing. While the optimal bandwidth for g¯ is not well studied, Powelland Stoker (1996) provide a algorithm for estimating the optimal bandwidth for E[f(x) ∂r∂x].We use this procedure to estimate a bandwidth for each city in our sample. While thebandwidth described by Powell and Stoker (1996) minimizes the mean squared error forthe vector f(x) ∂r∂x over the extent of the city, this is likely a close approximation to thebandwidth which minimizes the mean squared error of its magnitude f(x)∣∣ ∂r∂x∣∣.We estimate g¯ for one-bedroom apartment rent and for the local density of Starbucksoutlets. For the rent gradient, we can use observed rents directly as yi. For the Starbucksgradient, we use the method suggested in Ruppert (1997) to form a consistent binnedestimate of the density of Starbucks locations (with bins over the extent of the metropolitanstatistical area) and use this estimate as yi.3.3 Data sourcesTo calculate the gradient measure g¯ as described above, we collect data on local rent condi-tions at a fine level of spatial disaggregation. To test the role of these gradient measures inthe price response to a demand shock, we collect data on price movements, demand shocks,and additional controls related to supply elasticity and housing markets.3.3.1 Location-specific valueFor precise estimates of the gradient measure described above, we require data on locationalvalues at a spatially fine level within metropolitan areas. We use two measures: the locationof Starbucks coffee shops and the rent for one-bedroom apartments listed on Craigslist.65Mean Std dev N1 bedroomRent ($) 744 372 227Square footage 712 129 1982 bedroomRent ($) 945 616 244Square footage 1024 177 2173 bedroomRent ($) 1145 556 259Square footage 1528 747 2404 bedroomRent ($) 1634 695 182Square footage 2045 487 167Table 3.2: Summary statistics for the Craigslist rent location data. Throughout, the unitof observation is the MSA.We obtain a list of Starbucks locations in the United States from the Starbucks website.Starbucks locations have a steep bid-rent curve and tend to cluster disproportionately inaffluent areas with high levels of commercial activity(Meltzer and Schuetz, 2012; Davidoff,2013b). These attributes make Starbucks a feasible proxy for the presence of higher-rentretail districts.Figure 3.1 shows the distribution of Starbucks locations in four representative urbanareas. As shown, Starbucks locations are very heavily clustered downtown within NewYork City and San Francisco and highly dispersed around Los Angeles and Phoenix. Weuse the location of Starbucks to calculate a gradient measure as discussed above. Thegradient scores, in parentheses, are consistent with visual inspection.We gather rent data at a fine level of spatial disaggregation by scraping Craigslist rentalapartment listings3. In addition to the asking rent, the number of bedrooms, and the squarefootage, these listings indicate the spatial coordinates of the housing for rent to a highdegree of geographical precision. Table 3.2 shows summary statistics for the Craigslist rentdata. Throughout, the unit of observation is the median value for a metropolitan statisticalarea. (We aggregate rent data to the MSA level to match the price data described below.)Information on square footage is somewhat less complete than information on rent; 30% ofads include a rent but not a square footage.To calculate a locationality measure from the rent data, we use only the rent for one-bedroom units. Insofar as one-bedroom units are likely to be comparable in structural3Specifically, we scraped Craigslist listings corresponding to metropolitan areas in March 2014.66(a) San Francisco (7.02) (b) Phoenix (0.11)(c) Los Angeles (0.99)(d) New York (4.43)Figure 3.1: Spatial distribution of Starbucks locations in four sample cities.attributes, one-bedroom rent reflects the varying value of underlying land. Therefore, therent of a one-bedroom apartment is a reasonable measure of the spatial variation in thevalue of locations within a city.Figure 3.2 shows the spatial distribution of one-bedroom rental units across four sample67(a) San Francisco (b) Chicago(c) Los Angeles (d) New YorkFigure 3.2: Spatial distribution of one-bedroom apartments in four sample cities, togetherwith monthly rent.markets, together with prices. As shown, the Craigslist rental data provides spatially densecoverage of residential areas.3.3.2 Price dataAs we cannot directly observe the present market price of the housing units in the sample, weuse housing price information from Zillow. Zillow is a proprietary service which compileshousing data for the United States. Previous economic studies including Hubbard and68Mean Std dev N1 bedroomPrice ($1000) 136 95 158Price-rent ratio 140 86 1222 bedroomPrice ($1000) 141 94 236Price-rent ratio 141 41 1743 bedroomPrice ($1000) 186 113 256Price-rent ratio 159 75 1864 bedroomPrice ($1000) 261 140 251Price-rent ratio 181 127 145Table 3.3: Summary statistics for the Zillow price data and the rent-price ratio from theZillow price and Craigslist rent data. Throughout, the unit of observation is the MSA.Mayer (2009), Mian and Sufi (2011), and Huang and Tang (2012) have used Zillow. Theauthors of of these studies note its close correlation with other housing price indices. Thisdata set includes a housing price for each zipcode for 1, 2, 3, and 4-bedroom apartments.To match the Craigslist rent data discussed above, we use the Zillow values for March2014. Table 3.3 shows summary statistics for the Zillow rent data. Throughout, the unit ofobservation is the metropolitan statistical area.We use the ratio of housing prices to housing rent as a measure of the price response to ademand shock, or alternatively the market expectation of future price growth conditional ondemand. A model of housing as an investment asset provides a rationale for this measure.Let P be the current price of a house, R be the rent, and P ′ be the expected future priceof the house. Then, the return i on owning the house is given by i = RP +P ′P — that is,the return is equal to the dividend plus the capital appreciation. If the equilibrium rate ofreturn i is constant across cities (e.g., if it is equal to the economywide rate of return oninvestment assets) then differences in the price-rent ratio PR reflect differences in the priceappreciation P′P . Studies have used the price-rent ratio for housing to assess how far theprice of housing has diverged from “fundamental” levels and to indicate the presence ofhousing market bubbles (Davis, Lehnert and Martin, 2008; Campbell et al., 2009; Duca,Muellbauer and Murphy, 2011). In a retrospective review of the drastic house-price cycleof the 2000s, Gerardi, Foote and Willen (2010) point to the divergent price-rent ratio asevidence for a potential housing price bubble.As the Zillow data set includes historical prices, it is possible to directly compare ob-69served price-rent ratios to changes in housing prices. At each unit size, the median price-rent ratio at the zipcode level in our data set and the year-over-year change in zipcode-levelhousing prices are positively correlated to a high degree of statistical significance.3.3.3 Additional controlsIn addition to the gradient measures described above, we control for existing measuresof supply elasticity from the literature, growth in housing demand, and property taxes.Specifically, we control for supply elasticity measures from Saiz (2010), which measures theshare of land near the centre of the metro area available for building housing and fromGyourko, Saiz and Summers (2008), which measures the regulatory stringency applied tothe construction of new housing.To construct a measure of growth in housing demand, we follow Bartik (1991) andBlanchard and Katz (1992) to define Bartik shocks, which interact the variation cities inindustrial composition with the variation between industries in performance at the nationallevel. Specifically, we calculate the Bartik shock for metro area m between years t1 and t2as follows:Bm =∑ind(N ind−m,t2 −Nind−m,t1) N indm,t1∑ind′ Nind′m,t1(3.2)In Equation 3.2 the superscript ind indexes industries and N indmt is number of workers inindustry ind in MSA m at time t. The notation −m denotes the wage for all metro areasother than metro area m. As defined in Equation 3.2, the Bartik shock is positive in metroareas with improving labour market outcomes and negative in metro areas with worseninglabour market outcomes.We calculate values for the Bartik shocks using data from 1980 and 2010 Census data.We divide industries at the two-digit level. Following Guerrieri, Hartley and Hurst (2013)and others, we restrict the labour force sample to full-time workers (at least 48 weeks ofwork in the past year with at least thirty hours of work in the typical week) aged between25 and 55.Unfortunately, no data set contains property tax rates for all municipalities. However,Minnesota Taxpayers Association (2011) reports property tax levels in all fifty states and70Mean Std dev NBartik shock 0.617 0.178 117Unusable land (%) 25.1 20.8 82WRLURI 0.115 0.691 82Population (million) 1.74 2.49 117Starbucks count 135 157 73Property tax (%) 1.76 0.86 111Coastal status 0.154 0.362 117Graduate degree (%) 5.12 1.98 116Democratic lean -0.338 0.323 116Table 3.4: Summary statistics for additional control variables.the District of Columbia as well as separate rates for New York City and Chicago (whichdiffer substantially from property tax levels in other parts of their respective states). Weuse the rates reported for urban apartment property taxes in this report.Table 3.4 shows summary statistics for these additional variables. Throughout, the unitof observation is the metropolitan area.3.4 Empirical resultsFigure 3.3 compares the Starbucks and rent gradient measures. As shown, among largemetropolitan areas, Chicago, Boston, San Francisco, and New York have high particularlyhigh gradients. These two gradient measures measures are highly correlated with each other;as well, they are highly correlated with the measures of supply inelasticity from the liter-ature. Table 3.5 shows the correlations between these measures. These high correlationsare unsurprising; all of these measures capture the high-amenity, high-regulation, predom-inantly high-income “superstar” cities highlighted in Gyourko, Mayer and Sinai (2013).To investigate the relationship of these measures with the response of housing prices toa demand shock, we regress the rent, the price-rent ratio, and the long-term housing pricegrowth on the gradient measures, the Bartik shock, and other measures of supply elasticity.Each observation is a MSA-bedroom count pair. We use this factor to weight regressionsthat include the Starbucks gradient or rent gradient. We control for heterogeneity within71Figure 3.3: Comparison of rent gradient and Starbucks density gradient for metropolitanareas in the sample. Metropolitan areas with a population greater than three million arelabelled by their principal cities.Rent Unusable WRLURI Coastal Democratic Gradgradient land lean degreesStarbucks gradient 0.190 0.145 0.207 0.247 0.426 0.395Rent gradient 0.297 0.155 0.274 -0.115 0.052Unusable land 0.37 0.38 0.38 0.42WRLURI 0.43 0.48 0.56Coastal 0.47 0.49Democratic lean 0.71Table 3.5: Correlations between supply inelasticity factors. Throughout, the unit of obser-vation is the metropolitan area.each bedroom count by including a separate control for square footage for each bedroomcount and control for heterogeneity in the user cost of housing by controlling for propertytaxes. Throughout, we control for potential scale effects by controlling for the population ofthe MSA and the number of Starbucks locations. All extensive variables are in logarithmswhile index variables are untransformed.72Intercept −9.100∗ −7.862∗ −4.731 −4.739(4.910) (4.610) (4.904) (4.802)Bartik shock 0.084 0.130 0.075 0.111(0.168) (0.180) (0.167) (0.178)WRLURI 0.220∗∗∗ 0.204∗∗∗ 0.215∗∗∗ 0.208∗∗∗(0.064) (0.069) (0.069) (0.072)Unusable land 0.094∗∗ 0.078∗ 0.067∗ 0.065(0.039) (0.040) (0.040) (0.041)Starbucks gradient 0.064∗∗∗ 0.053∗∗(0.021) (0.021)Rent gradient 0.101∗∗ 0.062(0.047) (0.048)Observations 243 243 236 236Adjusted R2 0.626 0.642 0.635 0.644Table 3.6: Regression results for the current rent without the Coastal indicator. ∗∗∗, ∗∗,and ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively.Table 3.6 shows results for regressions of median housing rent on the Bartik shock,unusable land, and regulatory stringency. The supply elasticity and gradient proxies allhave significantly positive relationships with rent unconditionally. The supply and gradientproxies, not surprisingly, reduce each others’ magnitude in combination. As shown in Table3.7, when the Coastal indicator is included, its coefficient is highly statistically significant.Again, the Coastal indicator has substantial explanatory power even conditional on all othercontrols.Table 3.8 show regression results for the price-rent ratio on the Bartik shock, the WR-LURI and the share of unbuildable land, and the Starbucks and rent gradients. As shown,the covariates that measure supply constraints have a positive relationship with the price-rent ratio. Given that the price-rent ratio measures the expected price increase, it seemsreasonable that a measure of a positive demand shock and measures of supply inelasticitywould show this positive relationship. However, only the Starbucks gradient is consistentlyhighly statistically significant. In particular, the coefficient on the Starbucks gradient isconsistent across regressions, including a specification which includes both the Starbucks73Intercept −11.615∗∗∗ −10.483∗∗ −6.275 −6.263(4.413) (4.259) (3.910) (3.897)Bartik shock 0.053 0.087 0.037 0.039(0.147) (0.158) (0.136) (0.141)WRLURI 0.119 0.121 0.083 0.084(0.077) (0.081) (0.096) (0.098)Unusable land 0.076∗∗ 0.068∗ 0.030 0.031(0.038) (0.038) (0.036) (0.036)Starbucks gradient 0.043∗∗ 0.002(0.019) (0.027)Rent gradient 0.153∗∗∗ 0.151∗∗(0.051) (0.059)Coastal 0.318∗∗∗ 0.279∗∗∗ 0.401∗∗∗ 0.398∗∗∗(0.070) (0.073) (0.084) (0.099)Observations 243 243 236 236Adjusted R2 0.661 0.667 0.687 0.686Table 3.7: Regression results for current rent with the Coastal indicator. ∗∗∗, ∗∗, and ∗denote statistical significance at the 1%, 5%, and 10% levels, respectively.gradient and the rent gradient. However, as shown in Table 3.9, conditional on the Coastalindicator, neither the Starbucks gradient nor the supply constraint measures are not signif-icant.Table 3.10 presents regressions similar to those in Tables 3.8 and 3.6, with the dependentvariable reflecting realized past price and rent growth, rather than the current level ofrent or implied market rent growth expectations. In Table 3.10, the dependent variableis real Federal Housing Finance Agency Home Price Index growth between October, 1980and October, 2014, at the metropolitan level. The supply constraints and the Starbucksgradient are statistically significant predictors here. Table 3.11 incorporates the Coastalindicator. As above, the Coastal indicator is highly statistically significant and the statisticalsignificance of other coefficients is generally reduced.74Intercept 5.764 6.733 5.816 5.741(5.556) (5.548) (5.655) (5.532)Bartik shock 0.036 0.063 0.037 0.065(0.145) (0.158) (0.147) (0.154)WRLURI 0.069 0.061 0.068 0.063(0.051) (0.051) (0.052) (0.051)Unusable land 0.040 0.032 0.040 0.039(0.033) (0.032) (0.034) (0.034)Starbucks gradient 0.034∗∗ 0.040∗∗(0.015) (0.016)Rent gradient 0.000 −0.029(0.032) (0.038)Observations 218 218 214 214Adjusted R2 0.437 0.451 0.434 0.450Table 3.8: Regression results for the price-rent ratio without the Coastal indicator. ∗∗∗, ∗∗,and ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively.3.5 ConclusionConsistent with intuition and an elementary monocentric city model, land rents are onaverage greater in markets where location matters. Some of the relationship between hous-ing costs and conventional measures of supply elasticity appear to be attributable to landrent gradients, but it is difficult to draw conclusions about causality given high correla-tions among multiple measures of constraints on growth and demand factors such as Bartikshocks, average education, and environmental amenity. Notably, across specifications, anumber of attributes shared by coastal metropolitan areas fail to explain away the highprices in those markets.75Intercept 1.098 1.215 3.052 2.946(3.425) (3.560) (3.529) (3.481)Bartik shock −0.013 −0.010 −0.013 −0.025(0.104) (0.108) (0.107) (0.106)WRLURI −0.050 −0.050 −0.062 −0.067(0.043) (0.043) (0.044) (0.048)Unusable land 0.029 0.029 0.015 0.014(0.024) (0.025) (0.027) (0.027)Starbucks gradient 0.003 −0.014(0.016) (0.021)Rent gradient 0.052∗∗ 0.064∗(0.025) (0.036)Coastal 0.376∗∗∗ 0.374∗∗∗ 0.402∗∗∗ 0.421∗∗∗(0.046) (0.052) (0.048) (0.064)Observations 218 218 214 214Adjusted R2 0.604 0.602 0.612 0.612Table 3.9: Regression results for the price-rent ratio with the Coastal indicator. ∗∗∗, ∗∗, and∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively.76Intercept 5.213 7.457 7.127 5.288(5.161) (5.086) (8.532) (8.088)Bartik shock −0.055 −0.002 −0.064 0.012(0.236) (0.235) (0.230) (0.228)WRLURI 0.350∗∗∗ 0.326∗∗∗ 0.348∗∗∗ 0.329∗∗∗(0.083) (0.074) (0.084) (0.074)Unusable land 0.135∗∗∗ 0.115∗∗ 0.127∗∗ 0.124∗∗(0.048) (0.045) (0.056) (0.052)Starbucks gradient 0.077∗∗ 0.085∗∗∗(0.035) (0.032)Rent gradient 0.030 −0.034(0.085) (0.086)Observations 60 60 59 59Adjusted R2 0.587 0.616 0.568 0.599Table 3.10: Regression results for the long-term price growth without the Coastal indicator.∗∗∗, ∗∗, and ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively.77Intercept −6.544∗∗ −5.693 −0.776 −0.722(3.088) (3.820) (5.262) (5.151)Bartik shock −0.035 −0.024 −0.064 −0.072(0.166) (0.174) (0.154) (0.163)WRLURI 0.117∗ 0.118∗ 0.099 0.096(0.068) (0.067) (0.072) (0.075)Unusable land 0.097∗∗∗ 0.093∗∗ 0.067∗ 0.067(0.035) (0.036) (0.041) (0.041)Starbucks gradient 0.017 −0.010(0.026) (0.031)Rent gradient 0.097∗ 0.105∗(0.058) (0.061)Coastal 0.686∗∗∗ 0.665∗∗∗ 0.715∗∗∗ 0.729∗∗∗(0.070) (0.085) (0.070) (0.096)Observations 60 60 59 59Adjusted R2 0.807 0.805 0.812 0.809Table 3.11: Regression results for the long-term price growth with the Coastal indicator.∗∗∗, ∗∗, and ∗ denote statistical significance at the 1%, 5%, and 10% levels, respectively.784 A control function approach to the cor-related components of Bartik shocks4.1 IntroductionA Bartik shock is an instrument for local aggregate demand. It is intended as a sourceof exogenous variation in situations where aggregate demand may be simultaneously de-termined with the outcome variable of interest. For example, Paciorek (2013) uses Bartikshocks as an instrument for demand in a study of cross-sectional differences in housingprice dynamics, Partridge et al. (2012) uses Bartik shocks as an instrument in a study ofwithin-US migration, and Luttmer (2005) uses Bartik shocks as an instrument in a studyof neighbours’ economic performance and subjective well-being. Bartik (1991) and Blan-chard and Katz (1992) initially popularized this instrumentation strategy. As documentedin Baum-Snow and Ferreira (2014), Bartik shocks are now widely used in urban economics.Bartik shocks are typically useful when regressing some city-level outcome variable ofinterest on demand growth. For example, consider estimating a housing supply curve byregressing price growth Pi on employment growth Yi:Pi = α+ βYi + ei (4.1)Estimating this equation via OLS will not necessarily yield consistent estimates, as in generalemployment growth Yi is not exogenous to price growth — that is, E [Yi, ei] 6= 0. Asdiscussed in detail below, this endogeneity could arise through local demand shocks fromcity-specific amenities, scarcity of land for housing and other economic activity, or localgovernment decisions on land use regulations or infrastructure. To address this potentialendogeneity, it would be helpful to find an instrument Bi that predicts labour demand Yi(i.e., E [Bi, Yi] 6= 0) but which is excluded from the second-stage regression (i.e., E [Bi, ei] =790).The Bartik shock is designed to provide such an instrument. It is defined by interactingnational-level industry trends with local industrial composition. Specifically, if yij is thegrowth in employment in city i in industry j, κij is the share of the population of city i inindustry j, and I is the number of cities, then the Bartik shock Bi for city i is defined asfollows:Bi =∑jκij1I − 1∑i′ 6=iyi′j (4.2)Insofar as employment growth in city i in industry j is correlated with employment growthin city i′ 6= i in industry j, Bi will be correlated with aggregate employment growth in cityi. The utility of the Bartik shock as an instrument arises from the insight that employmentin all cities in all industries is affected by national industry-level trends, but the trend for agiven industry has more impact in a city where the industry employs a greater share of thepopulation. For example, the Bartik shock calculation for Cleveland would place a higherweight on the nationwide performance of manufacturing in the rest of the country and alower weight on the nationwide performance of tourism than the Bartik shock calculationfor Las Vegas.To be an effective instrument, the Bartik shock must have strong predictive power andit must be exogenous to the outcome variable of interest. Studies including Duranton andTurner (2011), Luttmer (2005), and Aizer (2010) have tested the predictive power of theBartik shock instrument — that is, the ability of the Bartik shock to predict changes inemployment. They report that the instrument has strong first-stage predictive power.The exogeneity of the Bartik shock is more complicated to interpret. In situations wherethe outcome variable of interest is likely unrelated to the composition of the local labourforce (as in. e.g., Aizer (2010)), then it is probably reasonable to treat the Bartik shock as anexogenous shift in local labour demand. However, if the outcome variable of interest is likelycorrelated with the city’s industrial composition, then Bartik shocks are less unambiguouslyexogenous, as high-Bartik shock and low-Bartik shock cities may be systematically differentin ways that impact the outcome variable. For example, this correlation with industrialcomposition could arise via productivity spillovers between industries (as discussed in, e.g.,80Moretti (2004) and Beaudry, Green and Sand (2012)) or amenities correlated with industrialcomposition (as discussed in, e.g., Rappaport (2008) and Diamond (2013b)). Davidoff (2015)finds that the Bartik shock for a given city is highly correlated with city-level attributesincluding scarcity of buildable land, stringency of land use regulation, and the initial shareof immigrants in the population.Researchers using instrumentation strategies based on Bartik shocks are aware of thispotential complication. In their discussion of using the Bartik shock as an instrument,Baum-Snow and Ferreira (2014) express the concern as follows:[I]t may be the case that manufacturing intensive cities have declined not onlybecause the demand for skill has declined more in these locations, but also be-cause they have deteriorated more in relative amenity values with the increasingblight and decay generated by obsolete manufacturing facilities.As discussed in further detail below, many papers that use the Bartik shock as a source ofidentifying variation assume its exogeneity in situations where this assumption seems verystrong. However, some studies do explicitly test whether relevant sources of endogeneity arepossible. Beaudry, Green and Sand (2012) and Beaudry, Green and Sand (2014) address thepossibility that workers migrate away from cities where a high-paying industry is leavingregardless of the industry in which they are currently working as the workers perceive theprobability of acquiring a high-paying job to be decreasing. They test for this scenario usinga Heckman selection-type procedure based on Dahl (2002) and for their application theyfind no significant effect.In this study, I introduce a novel control function approach to accounting for this addi-tional potential endogeneity. This approach isolates the city-specific component of labourmarket performance and then uses it to account for the correlation of potentially endoge-nous residual terms with industrial composition. It may be used separately or together withthe Bartik shock instrument.The derivation of the control function approach requires an additional identifying as-sumption on the correlations between error terms. Due to the additional assumption, theapproach introduced here represents a potential improvement over the Bartik shock instru-81ment primarily in situations where the potentially endogenous components of the residualare correlated with the city-specific component of employment growth. For example, if theresidual term is potentially endogenous due to productivity spillovers from dominant indus-tries, and productivity spillovers are strongly correlated with the city-specific componentof employment growth, then the assumption required to motivate the control function islikely justifiable. As with any identifying assumption, it cannot be tested. Therefore, anyempirical application of the control function approach should likely be accompanied by atheoretical argument that rationalizes this identifying assumption.To demonstrate the application of this new technique, I estimate a housing supplyfunction with and without the Bartik shock as an instrument and with and without thecontrol function adjustment. For this particular empirical application, the control functionadjustment has a modest but statistically significant impact on coefficient estimates. Idiscuss the relative performance of the Bartik instrument and control function estimatorsin the context of the two techniques’ underlying identifying assumptions.The remainder of this study is organized as follows. In the next section, I discuss howeffects arising from industrial composition can interfere with the exogeneity assumptionsrequired for the Bartik shock instrument and propose a control function approach to addressthis issue. Then, I estimate this model using United States labour force and housing marketdata to examine the impact of the control function adjustment in an empirical context.4.2 Theoretical modelIn this section, I discuss the potential endogeneity of the Bartik shock instrument. I describethe theoretical model that underlies the instrument, identify the potential endogeneity, anddiscuss how this endogeneity relates to common uses of Bartik shock instruments in theliterature. Then, I introduce a control function approach that may mitigate this endogeneityin some situations.Before proceeding, it will be useful to define some notation. Consider a populationof workers in cities i ∈ 1, 2, . . . , I and industries j ∈ 1, 2, . . . , J . I consider a situationwith fixed J and asymptotically large I — for example, J is the set of one-digit industrial82classifications and I is the set of all metropolitan areas in the United States. Let Yi denoteemployment growth in city i and let yij denote employment growth in city i in industryj. (Throughout, I consider employment growth over a single time period — for example, asingle decadal Census.) Let κij be the share of the population in city i employed in industryj at the beginning of the time period. Then, Yi and yij are related by Yi =∑j κijyij . Fornotational convenience, define κi to be the vector composed of κij for j ∈ 1, 2, . . . , J .For city i and industry j, the employment growth yij may be decomposed without lossof generality as the sum of a city-specific term ui, an industry-specific term vj , and anuncorrelated residual term εij :yij = ui + vj + εij (4.3)The use of Bartik shocks as an instrument is motivated by the supposition that the in-dustry trends for broadly-defined industries j are determined by exogenous macro-levelcircumstances. Accordingly, I consider a framework where the vj terms in Equation 4.3are predetermined while the city-specific ui terms, the idiosyncratic city-industry εij termsand the industrial composition κi terms are jointly drawn from some unknown distributionG (u, , κ) independently for each city i ∈ I. Also without loss of generality, assume thedata is suitably de-meaned such that E [ui] = E [εij ] = 0.The Bartik shock is intended to control for the endogeneity caused by correlation be-tween the city-specific component of employment growth ui and the outcome variable ofinterest. For example, consider estimating a housing supply curve by regressing house pricegrowth Pi on employment growth Yi in the following specification:Pi = α+ βYi + ei (4.4)In Equation 4.4, the residual term ei includes amenities, land scarcity, infrastructure, andother attributes of city i that other than employment growth Yi affect the price of housing.In general, these attributes will not be uncorrelated with Yi, and therefore the regressor Yiis endogenous. Formally, decomposing E [Yiei] using the decomposition from Equation 4.383yields the following potential sources of endogeneity:E [Yiei] = E [uiei] +∑jvjE [κijei] +∑jE [κijεijei] (4.5)The correlation between city-specific employment growth component ui and residual pricecomponent ei is of immediate concern as a source of potential endogeneity bias. The Bartikshock instrument corrects the bias caused by this first term on the right-hand side of Equa-tion 4.5. To see this, note that the Bartik shock as defined in Equation 4.2 can be rewrittenas 1I−1∑−i 6=i u−i+∑j κijvj +1I−1∑−i 6=i∑j κijε−ij for city i. For I →∞ and independentdistribution of ui, κi, and i across cities, this reduces to Bi =∑j κijvj . Substituting thisform for Bi and using the independence of observations across cities yields the followingcorresponding condition to Equation 4.5 for the Bartik shock:E [Biei] =∑jvjE [κijei] (4.6)The implicit identifying assumption in using the Bartik shock as an instrument is thatE [Biei] = 0. Equation 4.6 shows that this is equivalent to assuming that κij and ei areuncorrelated. In other words, the Bartik shock instrumentation strategy assumes that,conditional on employment growth Yi, industrial composition κi is uncorrelated with theoutcome variable of interest.In many cases encountered in the literature, this assumption may be strong. For ex-ample, studies including Guerrieri, Hartley and Hurst (2013) and Partridge et al. (2012)have used Bartik shock instruments to study migration responses to labour demand shocks,but the response to national labour demand shocks is likely very different in cities wherea single large industry dominates. Compared to a more diversified city, a decline in thedominant industry would limit a worker’s ability to adjust by finding a new job in the samecity, and the worker may be more likely to perceive a risk of other employment prospectsdeclining in the future. Duranton and Turner (2011) use the Bartik shock to instrument fordemand for vehicle distance travelled, although the demand for shipping and commutinglikely varies widely in cities with different industrial composition. As discussed in Davidoff84(2015), the use of Bartik shock instruments to estimate housing supply functions in Saiz(2010) implicitly assumes that industrial composition is uncorrelated with land scarcity,amenities, regulation, or other city attributes that would also affect prices. Similarly, in theLuttmer (2005) study of subjective well-being, the Bartik shock instrument implicitly re-quires industrial composition to be uncorrelated with local amenities or taste for regulation,as these local conditions likely enter into residents’ utility functions.The assumption that∑j vjE [κijei] = 0 is untestable. However, it is possible to usethe available information in the model to focus the correlation issue more narrowly. Defineγ = Cov(ui,ei)Var(u) , so that ei = γui+ωi where ωi by definition is the component of ei orthogonalto ui. Then, impose the following identifying assumption on the uncorrelated componentωi:Assumption 1.∑j vjE [κijωi] = 0Assumption 1 requires that the correlation with industrial composition in ei must bereflected in the city-specific component of industrial performance ui. That is, it statesthat projecting ei onto ui removes the component of ei which is correlated with industrialcomposition. As with any identifying assumption, Assumption 1 cannot be directly testedin the data. To see this, note that the “true” values of ei and therefore ωi are not observable.The projection of ei onto ui accounts for some sources of potential endogeneity, but isby no means universally applicable. Assumption 1 is likely defensible in situations wherethe primary exogeneity concern of the Bartik shock arises from the decline of a single largesector impacting workers’ decisions more than industry-weighted labour market performancewould suggest. For many of the confounding local conditions in the Bartik shock framework(e.g., productivity spillovers, amenities, and taste for regulation), whether these conditionscan be projected out onto the city-specific component ui of the employment growth is anempirical question.Note that Assumption 1 is not a radical departure from the standard Bartik shockidentifying assumption. As discussed previously, to justify the use of the Bartik shock as aninstrumental variable, it is implicitly necessary to assume E [Biei] = 0. Given the result ofEquation 4.6, this is equivalent to assuming∑j vjE [κijei] = 0. Therefore, Assumption 1 in85some sense generalizes the standard Bartik assumption by placing restrictions only on theωi component of ei which is orthogonal to ui (and therefore not accessible from observablelabour market outcomes) rather than on the entire ei term. In the special case γ = 0, theapproach based on Assumption 1 reduces to the standard Bartik instrument approach.Assumption 1 yields potentially useful moment conditions in terms of Yi. ExpandingE [Yiωi] analogously to Equation 4.5 yields the following expression:E [Yiωi] = E [uiωi] +∑jvjE [κijωi] +∑jE [κijεijωi] (4.7)Then, applying Assumption 1 and the fact that E [uiωi] = 0 by definition yields thefollowing moment condition for Yi:E [Yiωi] =∑jE [κijεijωi] (4.8)Similarly, expanding E [Yiωi] and applying Assumption 1 yields the following momentcondition for Bi:E [Biωi] = 0 (4.9)The moment conditions specified by Equations 4.8 and 4.9 suggest a control functionapproach to estimating the parameters of Equation 4.4 under Assumption 1. To implementthis, form estimates uˆi of ui (as discussed in detail below) then estimate the followingequation:Pi = α+ βYi + γuˆi + ωi (4.10)The optimal approach to estimating Equation 4.10 depends on whether the remaining biasterm in Equation 4.8 is of concern. If this term (which involves the correlation betweenindustrial composition, the industry-city residual of labour market performance, and the ωiresidual component) is negligible, then Equation 4.10 can be estimated via OLS. However,the moment condition specified by Equation 4.9 suggests that Equation 4.10 will also be con-sistently estimated using the Bartik shock as an instrument. Accordingly, the novel controlfunction approach in this paper is complementary to the canonical Bartik instrumentation86strategy in terms of its ability to account for endogeneity.It is worth emphasizing that this control function approach adds information to theregression compared to solely using the Bartik shock. To see this, compare a “first-stage” regression that decomposes Yi onto Bi (plus an orthogonal error) with one thatdecomposes Yi onto Bi plus uˆi (plus an orthogonal error). These two decompositionsare not equivalent; in general, uˆi neither orthogonal nor collinear with Bi. (Specifically,Cov (uˆi, Bi) = 1J∑j vjCov (ui, κij) +1J∑j∑j′ vjCov(εij′ , κij).) Accordingly, the use ofthe uˆi control function is not equivalent to regressing employment growth on the Bartikshock and then using the residual of this regression to form a control function.Intuitively, the control function approach adds “flexibility” by allowing ui to enter boththrough Yi and through the residual. As made explicit by Assumption 1, if the residual eican be projected on to ui, then the control function approach addresses the endogeneityin the moment condition given by Equation 4.6 and replaces it with the moment conditiongiven by Equation 4.9. Therefore, this yields an unbiased estimate for β.It remains to obtain an estimate uˆi for ui. Unfortunately, it is only possible to ui toO( 1J ). To see this, define the estimator vˆj;i for each i as vˆj;i =1I−1∑−i 6=i y−ij (since I isasymptotically large, this estimator is consistent). Then, define uˆi as follows:uˆi =1J∑j(yij − vˆj;i) (4.11)Equation 4.11 uses the definition of ui as the city-level component of industrial performanceto obtain an estimate. However, the bias in this estimate is ui − uˆi =∑j εij . Given thatE [εij ] = 0, this term would decrease to zero as J →∞. Since J is finite, the bias term fora given city i is in general nonzero. Rather, it will decrease in magnitude as J increasesat a rate proportional to 1J . This issue is comparable to the bias that arises from toomany regressors in a classical linear regression model; effectively, the number of parametersuˆi is increasing proportionally to the sample size. However, for sufficiently disaggregatedindustries J , this represents an arbitrarily close estimate. Moreover, correlation from εij isgenerally a secondary concern compared with correlation from ui terms.874.3 Empirical resultsTo demonstrate the use of the control function approach introduced above, I estimate thehousing supply function specified by Equation 4.4. In using the control function approach,I assume that Assumption 1 holds. For this assumption to be valid, all factors in residualterm ei (which contains all aspects of housing prices uncorrelated with Yi) would have toeither lie parallel to ui or be uncorrelated with industrial composition. This is an identifyingassumption which cannot be directly tested. However, this demonstration represents a situ-ation where a researcher could conceivably be concerned with the Bartik shock’s correlationwith industrial composition and where assuming that the undesirably correlation could beprojected out along ui is a potentially reasonably assumption.I consider four specifications:1. OLS estimation without accounting for ui terms. The moment conditions for thisspecification are equivalent to assuming the right-hand side of Equation 4.5 is zero.2. IV estimation using the Bartik shock to instrument for city-level employment growth(the classic Bartik approach). As discussed previously, this requires the assumptionthat right-hand side of Equation 4.6 is zero.3. OLS estimation using a control function approach to account for ui. This is equivalentto Assumption 1 combined with the assumption that the right-hand side of Equation4.8 is zero.4. IV estimation using the Bartik shock with a control function approach to account forui. This is equivalent to Assumption 1.I estimate this model using 2000 and 2010 Census and FHFA House Price Index data. Toensure consistency and comparability, I use consistent Public Use Microdata Area bound-aries mapped to consistent boundaries and consistent 1990 industry classifications. I focuson the broadest category of industrial sectors, such as “manufacturing” and “retail trade”(J = 13) and delineate cities using the metropolitan statistical area and metropolitandivisions in the FHFA data (I = 398). Following the literature, I only include civilian88OLS IV OLS IVNo control No control Control ControlConstant 0.3602∗∗∗ 0.3589∗∗∗ 0.3595∗∗∗ 0.3578∗∗∗(0.0096) (0.0085) (0.0096) (0.0087)Employment growth 0.3896∗∗∗ 1.3968∗∗∗ 0.3940∗∗∗ 1.3704∗∗∗(0.1094) (0.1760) (0.1092) (0.1712)Control function (×10−3) 0.0515∗∗ 0.0738(0.0223) (0.0479)Table 4.1: Regression results for the housing supply curve at the MSA level. For legibility,the control function coefficient and its standard errors are scaled by a factor of 103. Standarderrors in parentheses. ∗, ∗∗, and ∗∗∗ denote statistical significance at 10%, 5%, and 1%.workers between the ages of 25 and 55 who work at least 35 hours per week. I only con-sider metropolitan statistical areas or metropolitan divisions with at least 25,000 workersin these categories in 2000. I calculate vˆj with cities weighted by population. This followsthe literature and gives stable estimates.Table 4.1 shows the results of these estimations. As shown, the OLS regressions predictmuch smaller price responses to employment than the IV regressions. The estimates forγ are small but positive, which indicates that a local labour market that outperforms itsindustry-weighted average predicted performance is likely to have a positive house pricepremium. The coefficient γ is statitically significant at p < 0.05 in the OLS case, but notin the IV case.The addition of the control function modestly increases the estimated magnitude of theprice response in both the OLS and IV regressions. However, the impact of the controlfunction adjustment is much smaller than the impact of the Bartik shock adjustment. Thesmall impact of the control function is likely driven by the relatively small estimate for γ,which indicates that, if Assumption 1 is valid, the correlation between ui and the first-stageerror ei is not particularly strong in this context. Accordingly, projecting ei along ui doesnot remove much of the variation in ei.If the magnitude of γ were higher and Assumption 1 holds then the difference betweenthe IV estimates with and without the control function would be much larger. UnderAssumption 1 the bias in the IV estimate without the control function (relative to thevalue with the control function) is given by γ∑j vjE[uiκij ]Cov(Yi,Bi). Estimating∑j vjE[uiκij ]Cov(Yi,Bi)from the89data gives a value of -53.8, which is substantial on the scale of the estimated parameters.Therefore, conditional on Assumption 1 holding, the small difference between the Bartikshock IV estimates with and without the control function does not indicate that correlationbetween the residual term ei and the industrial composition κi should not be of concern asa source of endogeneity bias. Rather, it indicates that the control function approach cannotaccount for a substantial share of ei because γ is relatively low in magnitude.The large difference between the instrumented and uninstrumented regressions com-pared with the smaller difference between controlled and uncontrolled regressions has twopossible explanations. The first possibility is that the similar differentials between OLS andIV estimates with and without the control function suggests that the rightmost term inEquation 4.5 and the right-hand side term of Equation 4.8 are responsible for most of theendogeneity bias. That is, the Bartik shock improves estimates not by addressing substan-tial endogeneity not only from E [uiei] terms but also from E [κijεijei] or E [κijεijωi] terms.Note that this scenario is possible regardless of whether Assumption 1 holds as Assumption1 does not affect the εij terms. However, under this scenario, if Assumption 1 did hold,this would mean that∑j vjE [κijωi] = 0 but∑j E [κijεijωi] 6= 0 — that is, the correlationbetween the κij industrial share terms and the ωi terms would need to be acting throughthe εij terms. These could potentially be the case if, for example, city-specific idiosyncraticgrowth in high-tech industries or decline in manufacturing only affects housing prices if theindustry is already particularly large in that city. In this situation, the estimation usingboth the Bartik shock instrument and the control function yields unbiased estimates.The other possibility is that the estimates for uˆi are particularly noisy — that is, if thebias from the εij terms is substantial. In this case, uˆi would be less effective at projectingout the component of ei parallel to ui, and therefore the additional information from addingthe uˆi (to either the instrumented or uninstrumented regression) would be limited. Thissituation is consistent with the very low estimates for the coefficient γ. Moreover, thispossibility seems feasible from the data, as the outliers in the set of calculated values foruˆi are very disperse. Note that it is not possible to recover the “true” values for ui andtherefore not possible to assess whether the uˆi values closely represent the underlying ui.Increasing J to 34 by subdividing the manufacturing and the transportation, commu-90nication, and public utilities sectors does not substantially reduce the incidence of the veryextreme outlying estimated values for uˆi. This may be because finer industries can havelarger idiosyncratic city-industry shock terms εij .4.4 ConclusionBartik shocks are widely used as an instrument for local aggregate demand. They are highlypredictive, but other researchers in the literature have expressed concerns that effects arisingfrom differences in industrial composition may influence the instrument’s predictive powerand complicate its interpretation as exogenous. This study introduces a control functionapproach to estimation. The control function approach requires an additional identifyingassumption. As with any identifying assumption, the validity of Assumption 1 cannotbe tested but must be argued as plausibly valid for a given empirical application. In somesituations, the control function described here may offer a more plausible source of variationthan the Bartik shock. Moreover, the control function estimation outlined in this study maybe used in conjunction with the Bartik shock instrument.I demonstrate the use of this control function approach in estimating a housing supplycurve. My results suggest that in the context of this particular application the controlfunction has minimal impact. The small impact of the control function relative to theBartik instrument may suggest that endogeneity is driven by idiosyncratic city-industryspecific shocks. Alternately, it may suggest that the estimation strategy outlined above toestimate uˆi does not provide a close estimate to ui given the finite value of J .915 ConclusionThis thesis consists of three empirical studies in economics. In the first, I estimate a modelof nightlife industry dynamics to uncover profit spillovers between closely related industries.In the second, my coauthor and I introduce a new measure of urban structure and show thatit has substantial impact on housing price dynamics. In the third, I introduce a potentialimprovement to an econometric technique that is widely used in urban economics. Takentogether, this work constitutes a significant contribution to the body of economic knowledge.Each of the three studies in this thesis offer a novel contribution to the economic lit-erature. “Industry dynamics and the value of variety in nightlife: evidence from Chicago”estimates a structural dynamic model of nightlife venue entry and exit and finds evidenceof positive profit spillovers both within and between types of venue. “Land value gradientsand the level and growth of housing prices” introduces a new measure of willingness to sub-stitute between neighbourhoods and shows that this new measure has a close relationshipwith cross-city differences in housing prices. “A control function approach to the correlatedcomponents of Bartik shocks” introduces a new estimation technique that in some situationsmay improve upon the existing widely-used Bartik shock methodology.It is also worth discussing the limitations of these papers. In particular, due to theshort timeframe of the available data relative to the scale of neighbourhood change “In-dustry dynamics and the value of variety in nightlife: evidence from Chicago” relies on astructural framework in which firms are forward-looking regarding each others’ behaviourbut consumers cannot choose to relocate. While it performs well compared to other mea-sures in the literature, the new gradient measure introduced in “Land value gradients andthe level and growth of housing prices” cannot explain away the higher housing price levelsand growth in coastal cities. The estimation of the control function described in “A controlfunction approach to the correlated components of Bartik shocks” may not yield a suffi-ciently close approximation to the “true” underlying control function in realistic data sets.Each of these issues suggest directions for continued investigation.92In addition to the relevance of the empirical results and novel methods to the academicliterature, several elements of this thesis are also useful in the context of urban policy andplanning. As discussed previously, nightlife is an active focus of policy concern in a broadrange of cities. “Industry dynamics and the value of variety in nightlife: evidence fromChicago” directly tests the impacts of local zoning policies and other policies which posebarriers to entry for nightlife venues. As well, “Land value gradients and the level andgrowth of housing prices” provides useful results for policymakers seeking to understandcross-sectional differences housing market dynamics and their implications for housing af-fordability and macroprudential housing cycle regulation.Each of these studies indicates future directions of research. In particular, I plan toexpand on the model developed in “Industry dynamics and the value of variety in nightlife”using richer data sets to understand how firms in other retail industries (such as the restau-rant industry) differentiate themselves in location and characteristics. This research couldsubstantially contribute to the understanding of how people interact with the cities theyinhabit and how firms respond to that behaviour. 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In n` = 0 forsome type, then no well-defined equilibrium price exists. However, upon removing the type` with n` = 0 from consideration, the proof does hold for the remaining types.For clarity, I focus on the case where N < N¯ — that is, where V (p) < 1 and thereforesome consumers are opting not to go out and instead to consume their reservation utility.The proof for the case where N ≥ N¯ follows the same rationale but with less complexity.First, I prove the uniqueness of the vector of prices. Equation 2.6 gives prices p`i as afunction of the market shares S`:p`i =1 +n`n` (ρ` − 1)−(ρ` −[1 + Sηη−1`∑`′(Sηη−1`′)−1]η)− 2 (η − 1)S`c` (1)Note that Equation 2.2 suggests that the share of consumption to sector ` S` can be writtenin terms of the price index P` as follows:S` =P 1−η`∑`′ P1−η`′(2)For symmetric venues, P` = n11−ρ` p`i. Substituting p`i gives the following fixed-point107equation for S`:S` =n1−η1−ρ``1 + n`n`(ρ`−1)−(ρ`−[1+Sηη−1`∑`′(Sηη−1`′)−1]η)−2(η−1)S`1−ηc1−η`∑`′ n1−η1−ρ`′`′1 +n`′n`′ (ρ`′−1)−(ρ`′−[1+Sηη−1`′∑`′′(Sηη−1`′′)−1]η)−2(η−1)S`′1−ηc1−η`′(3)This defines a system of L equations for the shares S` which map the hypercube [0, 1]Linto itself1. As this is a continuous mapping of a closed set into itself, Brouwer’s fixed pointtheorem applies. Therefore, an equilibrium S` must exist.Next, note that this equilibrium must be unique. To see this, note that the left-handside of Equation 3 is strictly increasing and continuous in S` while the right-hand side isstrictly decreasing and continuous. Therefore, they must intersect at most once. BecauseBrouwer’s fixed point theorem guarantees that they intersect at least once, it must be thatthey intersect exactly once. Therefore, there exists a unique equilibrium set of shares S`.Substituting into 2.2 gives a corresponding unique equilibrium set of prices.This completes the proof. While the exposition has focused on the case where V (p) < 1,a directly analogous proof holds for V (p) ≥ 1. In this case, the expression for the fixed-pointequation for S` (the equivalent of Equation 3) is as follows:S` =n1−η1−ρ``(1 + n`n`(ρ`−1)−(ρ`−η)−(η−1)S`)1−ηc1−η`∑`′ n1−η1−ρ`′`′(1 + n`′n`′ (ρ`′−1)−(ρ`′−η)−(η−1)S`′)1−ηc1−η`′(4)It remains to show that either the case V (p) < 1 or the case V (p) ≥ 1 yields consistentresults. That is, it remains to show that either when venues follow the pricing strategyspecified by the first option in Equation 2.6 the value to consumers of going out is less than1 or when venues follow the pricing strategy specified by the second option in Equation 2.6the value to consumers of going out is greater than 1. That is, let pnon be the vector of1Strictly speaking, Equation 3 defines a mapping on the set [0, 1]L \ 0 as the term Sηη−1`∑`′(Sηη−1`′)−1is not defined when all shares S` are identically zero. However, this singularity is removable; setting thisterm to one when all shares are zero yields a continuous function.108venue prices given by the first-order condition for the case V (p) < 1 and pmax be the vectorof venue prices given by the first-order condition for the case V (p) ≥ 1. Then, it remainsto show that in all situations either V (pnon) < 1 or V (pmax) ≥ 1.I prove this by showing pmax ≤ pnon. Then, according to Equation 2.3, V (pnon) ≤V (pmax). From here, the desired consistency result follows immediately. To show this,rearrange Equation 2.6 as follows:(pnon`ic`− 1)−1=(pmax`ic`− 1)−1+ ηSηη−1`(∑`′Sηη−1`′)−1− (η − 1)S` (5)From here, it is sufficient to show ηSηη−1`(∑`′ Sηη−1`′)−1− (η − 1)S` ≥ 0 for all possible S`.Note that this is guaranteed to hold for S` = 0 and for S` = 1. It remains to show that itholds for the interior critical point. Taking the first-order condition and rearranging yieldsa minimum when ηSηη−1` =∑`′ Sηη−1`′ . However, at this value of S`, the necessary conditionholds whenever S−1` > η − 1, which is satisfied whenever η > 2. Therefore, pmax ≤ pnon.This completes the proof.It is worth discussing the intuition for the requirement η > 2. In the case η ≤ 2,consumers are very sensitive to variety between venues. In this case, depending on parametervalues, it is possible that an individual venue in the V (p) < 1 case may lower prices belowpmax to entice more consumers to come out. In this case, there is no guarantee that eitherpricing strategy will be consistent with the consumers’ indirect utility. However, empiricallyit does appear that η > 2.Note that in some cases multiple equilibria are possible — that is, it is possible fora neighbourhood to be in a state such that setting a price vector pnon according to theV (p) < 1 case gives V (pnon) < 1 but also setting a price vector pmax according to theV (p) ≥ 1 case gives V (p) ≥ 1. When this occurs, I assume that the venues set pricesaccording to pnon. Not only would any unilateral deviation to pmax result in lower profits,but also as a practical consideration using the pnon case whenever it is consistent leads tofewer “jumps” in profit as a function of parameters and therefore more tractable estimation.Numerical simulation suggests that when multiple equilibria arise they are both very close109to V = 1 with similar prices to each other.110B Proof of Proposition 2This appendix provides a proof of Proposition 2, which states that with sufficiently manyvenues the equilibrium prices give V (p) ≥ 1 — that is, with sufficiently many venues,nightlife is sufficiently vibrant that all consumers choose to go out. To prove this result, Ishow that with sufficiently many venues the optimal price vector pnon based on the optimalpricing strategy for the case V (p) < 1 yields V (pnon) > 1. Since Proposition 1 showsthat V (pnon) < V (pmax) (i.e., the optimal pricing strategy when V (p) < 1 always gives alower utility than the optimal pricing strategy when V (p) ≥ 1), the desired result followsimmediately.First, rewrite the indirect utility from Equation 2.3 entirely in terms of the venues’ pricesp`i:V (p) = w∑`nηρ`−1` p−η`i(∑`nη−1ρ`−1` p1−η`i)−1(6)From here, it remains to show that for all ` ∈ 1, 2, . . . , L, nηρ`−1` p−η`i grows faster in n` thannη−1ρ`−1` p1−η`i when p = pnon. This will provide the necessary result, since it indicates that thevalue of going out under the V (p) < 1 pricing strategy increases indefinitely with n`.Note that in Equation 2.6 the price for the case V (p) < 1 (expressed in big-O nota-tion in n`) is O(1). Specifically, as n` increases, the optimal price for the case V (p) < 1approaches the constant markup price p`i =ρ`+1ρ`c`. Accordingly, nηρ`−1` p−η`i is O(nηρ`−1`)while nη−1ρ`−1` p1−η`i is O(nη−1ρ`−1`). As ηρ`−1 >η−1ρ`−1, the numerator term grows faster with n`than the denominator term. Therefore, the overall indirect utility under the V (p) < 1 pricesmust eventually exceed 1 for sufficiently large n`. This completes the proof.111C Venue category verificationTo ensure that these venue types inferred from the liquor licensing data set correspond toreal-world qualitative categories of venues, I match the venues to Yelp listings. I search foreach venue by latitude and longitude using the Yelp API and then match business names inthe licensing data to business names on Yelp using pattern matching. The pattern matchingalgorithm does not require an exact match. For example, I match the venue “Checker BoardLounge” from the business license data with the Yelp listing “Checkerboard Lounge” andthe venue “Six Penny B P” from the business license data with the Yelp listing “Six PennyBit”. Yelp assigns categories to businesses, such as “Buffets” or “Sports Bars” or “Massage”.An individual business may be assigned multiple categories. The Yelp API does not returnall businesses which have already closed and I am unable to match businesses which operateunder substantially different names than their names in the license data. Accordingly, I canidentify only 19% of the businesses on Yelp.I use a multinomial logit regression to examine how closely the Yelp categories and liquorlicensing categories coincide. I regress the liquor licensing categories on indicator variablesfor whether Yelp assigned the venues to the six most commonly-assigned Yelp categoriesin the sample: “Dance Clubs”, “Pubs”, “Lounges”, “Music Venues”, “Sports Bars”, and“Bars”. Table C1 shows the results of this regression. As shown, the Yelp categories aregenerally significant predictors of the liquor licensing categories. In particular, many ofthe coefficients are large in magnitude and significantly different from zero, venues whichYelp assigns to the “Dance Club” category are much less likely to be in the “Drinks only”license category, and venues which Yelp identifies as “Pubs” are much less likely to be in the“Drinks and amusement” license category. Therefore, the comparison with Yelp suggeststhat the categories based on business licenses constitute a reasonable division of the venuesinto categories that would be relevant to consumers.112Drinks only Drinks and amusement Drinks and musicIntercept 0.993∗∗ −1.474∗∗ −0.998∗(0.404) (0.665) (0.601)Dance Clubs −0.273 2.485∗∗ 2.096∗(1.207) (1.226) (1.223)Pubs 16.864∗∗∗ 0.742∗∗∗ 16.997∗∗∗(0.357) (0.000) (0.357)Lounges 2.297∗∗ 2.947∗∗ 2.222∗(1.086) (1.217) (1.220)Music Venues −0.053 1.742 0.570(1.185) (1.262) (1.355)Sports Bars 17.685∗∗∗ 17.387∗∗∗ 17.256∗∗∗(0.444) (0.644) (0.612)Bars 18.471∗∗∗ 18.375∗∗∗ 17.678∗∗∗(0.361) (0.477) (0.485)Log Likelihood -141.689 -141.689 -141.689Deviance 283.379 283.379 283.379Num. obs. 812 812 812Table C1: Results of a multinomial logit regression of the licensing categories on themost frequently-assigned Yelp categories. The regression sample is the set of venues whichmatched with Yelp businesses. The omitted licensing category is the “Amusement only”category. ∗, ∗∗, and ∗ ∗ ∗ denote statistical significance at the 10%, 5%, and 1% levels.113D Maximum likelihood estimation resultsTable D1 shows the full set of parameter results from the maximum likelihood estimation,including not only the parameter values discussed above but also the parameters relatingneighbourhood attributes to the profit function. Equations 2.16 and 2.17 define how theestimated parameters relate to the model quantities.114Parameter Symbol EstimateElasticity between sectors η 2.04(1.62× 10−3)Elasticity within sector Amusement only ρ1 4.90(1.31× 10−2)Elasticity within sector Drinks only ρ2 2.15(8.6× 10−4)Elasticity within sector Drinks and amusement ρ3 3.56(2.24× 10−1)Elasticity within sector Drinks and music ρ4 7.96(2.9× 10−1)Marginal cost Amusement only c1 0.127(4.17× 10−3)Marginal cost Drinks only c2 1.45(4.19× 10−3)Marginal cost Drinks and amusement c3 3.85(2.69× 10−2)Marginal cost Drinks and music c4 2.54(6.62× 10−3)Entry arrival rate Amusement only α1 4.00× 10−3(1.29× 10−5)Entry arrival rate Drinks only α2 9.05× 10−1(9.76× 10−2)Entry arrival rate Drinks and amusement α3 7.18× 10−1(8.59× 10−2)Entry arrival rate Drinks and music α4 1.48× 10−2(2.43× 10−2)115Parameter Symbol EstimateExit arrival rate Amusement only λ1 5.08× 10−3(1.07× 10−10)Exit arrival rate Drinks only λ2 9.03× 10−3(4.51× 10−6)Exit arrival rate Drinks and amusement λ3 2.31× 10−3(1.39× 10−5)Exit arrival rate Drinks and music λ4 2.10× 10−3(3.62× 10−8)Log baseline entry cost Amusement only θψe`1 2.11(2.97× 10−3)Log baseline entry cost Drinks only θψe`2 2.17(8.33× 10−3)Log baseline entry cost Drinks and amusement θψe`3 2.11(1.13× 10−2)Log baseline entry cost Drinks and music θψe`4 1.81(2.52× 10−1)Log exit payoff Amusement only ψx1 -4.01(8.22× 10−1)Log exit payoff Drinks only ψx2 -4.06(6.25× 10−2)Log exit payoff Drinks and amusement ψx3 -2.76(3.24× 10−1)Log exit payoff Drinks and music ψx4 -3.23(7.07× 10−2)116Parameter Symbol EstimateLog entry cost Dry precincts θψer1 0.470(3.36× 10−3)Log entry cost Moratoria θψer2 0.106(2.67× 10−2)Log baseline fixed cost Amusement only θκ`1 -4.17(1.73× 100)Log baseline fixed cost Drinks only θκ`2 -14.1(4.44× 102)Log baseline fixed cost Drinks and amusement θκ`3 -2.39(3.59× 10−1)Log baseline fixed cost Drinks and music θκ`4 -14.1(2.89× 103)Log entrants Amusement only ν1 0.0471(1.44× 10−3)Log entrants Drinks only ν2 0.0109(7.77× 10−4)Log entrants Drinks and amusement ν3 0.0185(5.92× 10−3)Log entrants Drinks and music ν4 0.215(1.98× 10−2)Log budget w 2.12× 10−3(4.04× 10−3)117Parameter Symbol EstimateFixed cost parameter Principal component 1 θκd1 3.65× 10−5(8.21× 10−3)Fixed cost parameter Principal component 2 θκd2 9.36× 10−3(5.45× 10−2)Fixed cost parameter Principal component 3 θκd3 −1.44× 10−4(8.41× 10−2)Fixed cost parameter Principal component 4 θκd4 1.12× 10−4(2.92× 10−2)Market size Constant θN¯o 4.52(5.31× 10−3)Market size Principal component 1 θN¯1 1.60× 10−3(3.21× 10−4)Market size Principal component 2 θN¯2 −2.48× 10−4(3.91× 10−4)Market size Principal component 3 θN¯3 1.76× 10−3(4.76× 10−4)Market size Principal component 4 θN¯4 -2.25× 10−5(3.7× 10−4)Table D1: Maximum likelihood estimation results for all parameters. If the variable nameincludes “Log”, I estimate the logarithm of the corresponding model parameter. Standarderrors in parentheses.118


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