Spatial Equilibrium and Search Frictions - an Application to the New York City Taxi Market∗

Ida Johnsson‡

March 18, 2018

Abstract

This paper uses a dynamic spatial equilibrium model to analyze the effect of matching frictions and pricing policy on the spatial allocation of taxicabs and the aggregate number of taxi-passenger meetings. A spatial equilibrium model, in which meetings are frictionless but aggregate matching frictions can arise endogenously for certain parameter values, is calibrated using data on more than 45 million taxi rides in New York. It is shown how the set of equilibria changes for different pricing rules and different levels of aggregate market tightness, defined as the ratio of total supply to total demand. Finally, a novel data-driven algorithm for inferring unobserved demand from the data is proposed, and is applied to analyze how the relationship between demand and supply in a market with frictions compares to the frictionless equilibrium outcome.

Keywords: spatial equilibrium, matching, industry dynamics, taxicabs JEL codes:

∗I would like to thank Professor Hashem Pesaran and Professor Hyungsik Roger Moon for their guidance and support. ‡Department of Economics, University of Southern California. Email: [email protected] 1 Introduction

The distribution of taxicabs in big cities tends to be imbalanced, in some areas passengers have a hard time finding a taxi, in others taxis can’t easily find a passenger. In the taxi market, trades occur bi- laterally between agents, and the equilibrium outcome depends on the nature of the meeting process. For example, the matching mechanism between yellow cabs in New York and passengers, who have to hail the cab from the street, is different than for ride-hailing services such as Uber or Lyft that match passengers and cabs using an algorithm.

As prices are typically fixed, the key equilibrium variables in the taxi market are meeting proba- bilities and aggregate market tightness (AMT), defined as the ratio of total supply to total demand. In this paper I first consider the spatial equilibrium model proposed by Lagos (2000), in which the taxi-passenger matching process is frictionless. Frictions in the model can arise endogenously if taxis choose to locate in such a way that there is excess supply in some locations and excess demand in others. Frictions depend on aggregate market tightness and location heterogeneity. I calibrate the model using data on over 45 million taxi rides and show that an equilibrium with frictionless matching yields excess supply of cabs in all locations, and that aggregate matches are thus determined by total demand. I then extend the model of Lagos (2000) to analyze how varying the pricing policy impacts the ratio of supply to demand in each location, as well as the aggregate number of matches. I consider both the current two-part tariff as well as a demand-dependent pricing policy.

Finally, I consider a taxi-passenger matching process that involves local frictions in the sense that the number of rides originating from a neighborhood with x empty taxis looking for passengers and y customers in looking for a taxi might be smaller than min{x, y}. This type of matching process is considered by for example Frechette et al. (2015) and Buchholz (2016). Similar to Frechette et al. (2015), Buchholz (2016) and Afian et al. (2015), I propose a method of inferring unobserved taxi demand in the presence of local matching frictions. My method is based on defining a local measure of taxi availability, which can be approximated using data on taxi rides. I than compute time-specific local market tightness (tLMT), defined as the ratio of supply to demand in a specific location during a certain time interval, and compare the empirical outcomes with the results implied by the equilibrium of the frictionless matching model.

1.1 Related Literature

Lagos (2000) proposes a spatial equilibrium model in which taxi drivers choose their location depending on demand and policy parameters. Matching is assumed to be frictionless, and it is shown that frictions arise endogenously in equilibria that correspond to certain parameter values. Lagos (2000) shows

2 that an aggregate matching function exists, and characterizes it’s properties with respect to distances between locations, the size of agent populations, as well as policy parameters. He shows that the spatial equilibrium depends on the demand transition matrix, the full set of bilateral distances, demand and policy parameters that determine fare rate and the number of medallions. Lagos (2003) uses the model of Lagos (2000) to quantify the impact of increasing taxi fares and the medallion cap on the medallion prices and the process that rules meetings between passengers and taxicabs in New York. I also use the model of Lagos (2000). The differences between my work and that of Lagos (2003) are as follows. Lagos (2003) assumes that all medallions are active throughout the day and uses data on 22,604 trips in 1988 to calibrate the model, characterize all equilibria, and quantify the meeting process generated by Manhattan’s market for taxicab rides. I use data from January-March 2013, which includes comprehensive information on all taxi rides during that period - around 45 million trips. Instead of assuming that all medallions are active throughout the day, I consider two different time periods - day and night - and calculate the number of active medallions from my data. Further, Lagos (2003) simplifies the map of Manhattan by dividing it into seven locations, whereas I consider forty different neighborhoods, both in and outside of Manhattan. Similar to Lagos (2003), I calibrate the frictionless spatial equilibrium model and characterize the no-frictions frontier. Further, I extend the model to include demand-driven pricing rules and calculate the equilibrium allocations for selected pricing rules.

Another strand of literature considers equilibrium models of the NYC Taxi market in the presence of matching frictions. Frechette et al. (2015) propose a dynamic general equilibrium model of the NYC Taxi market, and back out unobserved demand through a matching simulation. They assume that taxi search times and passenger wait times (the latter unobserved) are an unknown function of the unobserved number of waiting passengers, searching taxis and other exogenous time-varying variables. They simulate the matching process of waiting passengers and searching taxis on a grid that represents a simplified version of Manhattan to back out the unknown function and the unobserved inputs. The authors do not consider location-specific heterogeneity. Buchholz (2016) models the driver’s choice problem using a state dependent value function. He assumes that demand for rides in each location comes from a location-specific Poisson distribution, and estimates the parameters of these distributions as well as the supply of taxis from the equilibrium of the model. My work is similar to Buchholz (2016) in the sense that I also consider location-specific supply and demand. However, rather than assuming a model for the equilibrium behavior of taxis and passengers and backing out unobserved supply and demand from the model equilibrium, I take advantage of the fact the we observe passenger pick-up and drop-off locations. I define a measure of taxi availability in each neighborhood and time period, and estimate taxi and passenger arrival rates directly from the data. This approach is similar to the one taken by Afian et al. (2015).

3 The rest of the paper is structured as follows. Section 2 describes the data. In Section 3 I present the benchmark model with frictionless matching, and analyze how the no-frictions frontier changes for different pricing policies. In Section 4 I introduce the matching process with local frictions and show estimates of local market tightness for different matching efficiency parameters. Section 5 concludes.

I what follows I use lowercase letters to denote scalars, lowercase bold letters for vectors and uppercase bold letters for matrices.

2 Data

I use a data set obtained by Mr. Chris Whong through a Freedom of Information Law (FOIL) request submitted to the Taxi and Limousine Commission (TLC)1. The data contains information on more than 173 million yellow cab trips in 2013. Each record contains complete information about a taxi ride. I use the following variables (a speciﬁcation of all variables available in the data can be found in Appendix A).

• Medallion - a unique identiﬁer of the taxi cab.

• Pickup and drop-oﬀ time and geographical coordinates

Note that data on all yellow cab rides from 2009 till the present date, as well as green cab rides from mid-2013 onward and Uber rides for selected months of 2014 and 2015 is freely available in Google Big Query. However, that data does not contain information on the taxi or driver identiﬁers, which is crucial for inferring unmet demand.

Green cabs were introduced in the summer of 2013. Hence, I restrict my analysis of the yellow cab market to the period before the summer of 2013. Specifically, I consider data from January-March, which contains information on approximately 45 million taxi rides. I restrict my analysis to this period due to the computational costs of geofencing the data. Using the geographical coordinates of the pickup and drop-off locations for each trip, I map the trip start and end points to a neighborhood. I use the neighborhood definitions of the NYC Neighborhood Tabulation Areas (NTAs)2, which are shown in Fig- ure A7 in Appendix A. Mapping pickup and dropoff coordinates to NTAs for January-March 2013 took approximately 72 hours running on an Amazon Web Services (AWS) memory-optimized PostgreSQL instance of type db.r3.8xlarge with 32 vCPUs and 244GiB Memory.

1Mr. Whong made the data set available on his website http://chriswhong.com/open-data/foil_nyc_taxi 2See https://www1.nyc.gov/site/planning/data-maps/open-data/dwn-nynta.page

4 I consider 15-minute time intervals during the time period January-March 2013. Plots of pickups and drop-offs, aggregated into 15-minute time intervals, during a randomly chosen week in March for selected neighborhoods are shown below in Figure 1. As we can see, the data follows a pattern where pickups/drop-offs are generally higher during the period 6am-11pm, although the pattern varies by neighborhood. For example, pickups and Midtown-Midtown South are lower on weekends, whereas the opposite is true for Chinatown. This suggests that the taxi-passenger meeting dynamics vary according to the time of the day. I consider 40 neighborhoods for which the average number of pickups in a time interval during the time period considered is at least 5. These neighborhoods are listed in Table 1. Further, I divide my data into two time periods: (a) - from 6:00am to 11:00pm, and (b) from 11:00pm to 6:00am. Hence, the first observation in (a) each day is the number of pickups between 6:00am and 6:15am, and the last observation is the number of pickups between 10:45pm and 11:00pm, and so on. There are 6,210 intervals in (a) and 2,430 intervals in (b).

Remark 1 (Time Intervals). The choice of time intervals (a) and (b) is tentative, in continued work I plan to explore the sensitivity of the results with respect to the choice of time intervals.

Let yit and zit denote the pickups and drop-oﬀs in neighborhood i in time period t, respectively.

Summary statistics for yit and zit for all time periods, as well as for a and b separately, are presented in

Table 1. Note that out of the total of 345,600 observations, yit = 0 in 2.4% of the cases and zit = 0 in 0.6% of the cases. As we can see there is substantial location heterogeneity.

5 Figure 1: Pickups and drop-oﬀs for selected neighborhoods during a selected week in March

6 Table 1: Summary statistics for pickups yit and drop-oﬀs zit

mean std min median max interval a + b a b a + b a b a + b a b a + b a b a + b a b

Pickups yit Astoria 12.1 10.4 17 8 6 11 0 0 0 10 9 13 86 48 86 Battery Park City-Lower Manhattan 120.6 151.3 42 69 52 40 0 4 0 135 156 26 334 334 215 Brooklyn Heights-Cobble Hill 9.4 11.1 5 7 6 6 0 0 0 8 10 3 41 38 41 Carroll Gardens-Columbia Street-Red Hook 11.6 13.2 8 9 9 9 0 0 0 9 11 4 58 56 58 Central Harlem North-Polo Grounds 4.8 5.2 4 4 4 4 0 0 0 4 4 3 47 36 47 Central Harlem South 15.3 17.5 10 9 8 9 0 1 0 14 16 7 71 64 71 Central Park 62.5 82.7 11 46 38 12 0 1 0 61 85 7 203 203 170 Chinatown 92.0 71.4 145 89 45 138 0 8 0 59 54 88 520 295 520 Clinton 213.6 239.4 148 96 74 114 0 26 0 214 232 102 513 483 513 DUMBO-Vinegar Hill-Downtown Brooklyn-Boerum Hill 20.4 21.6 17 13 11 17 0 0 0 18 20 10 84 73 84 East Harlem North 17.2 20.2 10 10 9 7 0 3 0 16 18 8 91 91 59 East Harlem South 37.2 46.0 15 20 15 11 0 4 0 39 45 11 145 145 85 East Village 172.1 158.1 208 133 93 196 0 17 0 128 130 120 742 638 742 East Williamsburg 6.4 2.8 15 11 4 16 0 0 0 2 1 10 96 55 96 Fort Greene 6.2 5.8 7 6 5 8 0 0 0 4 4 4 58 58 49 Gramercy 138.2 158.6 86 76 60 86 0 14 0 137 150 47 377 377 353 Greenpoint 5.8 3.6 12 9 4 13 0 0 0 3 2 6 56 38 56 Hamilton Heights 4.9 5.4 4 4 4 4 0 0 0 4 5 3 42 42 40 Hudson Yards-Chelsea-Flatiron-Union Square 481.9 558.6 286 242 198 233 0 28 0 527 569 192 1081 1081 929 Hunters Point-Sunnyside-West Maspeth 18.6 20.1 15 9 8 10 0 3 0 17 19 12 101 101 79 JFK Airport 74.8 89.7 37 46 39 42 0 0 0 76 90 16 216 216 188 La Guardia Airport 95.3 122.7 25 74 64 50 0 0 0 102 129 2 328 315 328 Lenox Hill-Roosevelt Island 206.6 260.9 68 118 87 61 0 15 0 233 262 46 563 563 396 Lincoln Square 196.3 247.1 66 112 78 75 0 9 0 228 252 34 546 546 440 Lower East Side 28.6 26.7 34 23 14 37 0 3 0 23 24 17 188 105 188 Manhattanville 4.7 5.3 3 3 3 3 0 0 0 4 5 2 62 62 24 Midtown-Midtown South 848.2 1028.6 387 440 342 308 0 52 0 938 1065 274 1982 1982 1437 Morningside Heights 51.5 62.8 23 29 24 18 0 2 0 53 62 17 244 244 129 Murray Hill-Kips Bay 234.1 281.6 113 125 93 113 0 18 0 254 286 64 531 531 483 North Side-South Side 33.8 20.2 68 45 24 64 0 0 0 15 9 45 267 149 267 Park Slope-Gowanus 11.6 9.4 17 14 10 21 0 0 0 6 6 8 143 101 143 Queensbridge-Ravenswood-Long Island City 7.6 8.3 6 4 4 4 0 0 0 7 8 5 37 37 30 SoHo-TriBeCa-Civic Center-Little Italy 262.1 292.9 184 143 119 167 0 13 0 267 284 112 667 596 667 Stuyvesant Town-Cooper Village 18.1 21.5 9 12 11 10 0 1 0 16 19 6 64 64 63 Turtle Bay-East Midtown 348.2 429.2 141 200 162 126 0 21 0 369 422 91 894 894 619 Upper East Side-Carnegie Hill 354.6 467.8 65 239 179 70 0 18 0 396 493 37 1108 1108 510 Upper West Side 237.9 300.5 78 132 89 76 0 17 0 275 306 51 677 677 574 Washington Heights South 5.0 5.7 3 4 3 4 0 0 0 5 5 2 48 32 48 West Village 364.9 382.4 320 208 167 282 0 16 0 335 353 202 1063 997 1063 Yorkville 144.8 179.5 56 80 59 54 0 18 0 154 175 36 421 421 417

Drop-oﬀs zit Astoria 24.8 16.9 45 24 14 30 0 0 0 15 12 39 141 114 141 Battery Park City-Lower Manhattan 132.7 152.2 83 73 65 68 0 3 0 135 145 54 437 437 261 Brooklyn Heights-Cobble Hill 15.0 15.2 15 13 12 14 0 0 0 11 11 9 73 73 60 Carroll Gardens-Columbia Street-Red Hook 14.6 13.7 17 13 12 15 0 0 0 9 9 11 71 71 63 Central Harlem North-Polo Grounds 16.2 14.7 20 11 9 14 0 0 0 13 12 17 81 61 81 Central Harlem South 24.8 25.8 22 15 13 17 0 1 0 22 23 17 89 84 89 Central Park 68.6 88.1 19 43 34 17 0 3 0 73 92 12 208 208 88 Chinatown 76.1 75.3 78 68 57 89 0 1 0 53 54 44 396 362 396 Clinton 192.1 218.4 125 99 84 104 0 13 0 195 209 83 541 541 466 DUMBO-Vinegar Hill-Downtown Brooklyn-Boerum Hill 26.8 26.2 28 19 17 24 0 0 0 21 21 20 110 110 104 East Harlem North 30.8 33.3 24 14 13 16 0 1 0 30 32 20 143 143 85 East Harlem South 46.4 51.7 33 20 16 23 0 8 0 48 51 26 154 154 118 East Village 142.7 146.6 133 124 119 135 0 4 0 94 99 78 580 580 577 East Williamsburg 14.0 8.8 27 16 10 20 0 0 0 7 5 23 87 67 87 Fort Greene 9.6 8.3 13 9 8 11 0 0 0 6 5 10 53 53 49 Gramercy 121.2 138.0 78 70 60 76 0 8 0 117 126 45 320 320 317 Greenpoint 17.8 13.4 29 18 14 22 0 0 0 9 7 23 96 77 96 Hamilton Heights 11.1 9.1 16 8 6 10 0 0 0 9 7 15 71 47 71 Hudson Yards-Chelsea-Flatiron-Union Square 455.4 546.6 222 241 188 200 0 27 0 507 563 136 1269 1269 886 Hunters Point-Sunnyside-West Maspeth 28.9 25.6 37 17 12 24 0 3 0 23 22 31 151 80 151 JFK Airport 34.6 44.0 11 26 24 16 0 0 0 34 41 4 137 137 118 La Guardia Airport 56.6 71.2 19 49 46 33 0 0 0 58 75 2 217 217 187 Lenox Hill-Roosevelt Island 200.8 241.2 97 105 80 90 0 19 0 221 240 59 490 490 425 Lincoln Square 180.6 224.5 68 112 96 63 0 9 0 192 224 41 659 659 286 Lower East Side 45.6 46.1 44 32 30 37 0 1 0 37 38 32 174 158 174 Manhattanville 7.4 7.0 9 5 4 6 0 0 0 7 7 7 39 38 39 Midtown-Midtown South 833.4 1049.2 282 477 362 225 0 46 0 896 1044 204 2164 2164 1067 Morningside Heights 51.9 59.2 33 27 22 28 0 2 0 56 61 23 200 200 131 Murray Hill-Kips Bay 236.8 279.6 128 121 90 121 0 11 0 265 289 73 497 487 497 North Side-South Side 40.0 32.6 59 39 31 48 0 0 0 24 19 44 199 174 199 Park Slope-Gowanus 24.5 20.8 34 25 22 29 0 0 0 13 12 23 140 140 118 Queensbridge-Ravenswood-Long Island City 8.5 8.3 9 4 4 6 0 0 0 8 8 8 30 26 30 SoHo-TriBeCa-Civic Center-Little Italy 236.4 279.5 126 130 104 126 0 7 0 255 283 72 596 588 596 Stuyvesant Town-Cooper Village 20.6 21.4 18 16 16 16 0 0 0 15 16 12 80 80 80 Turtle Bay-East Midtown 315.7 388.8 129 180 144 118 0 19 0 342 390 80 924 924 504 Upper East Side-Carnegie Hill 336.8 438.2 78 217 164 74 0 13 0 373 463 48 866 866 371 Upper West Side 234.3 284.7 106 142 124 98 0 12 0 244 290 66 800 800 480 Washington Heights South 16.7 15.5 20 9 7 13 0 0 0 15 14 17 119 119 71 West Village 315.1 362.1 195 217 201 210 0 9 0 295 320 106 1039 1039 894 Yorkville 145.8 168.0 89 94 88 85 0 9 0 136 158 50 462 462 432

yit - pickups in neighborhood i in the 15-minute time period t. zit - drop-offs in neighborhood i in the 15-minute time period t. Summary statistics are based on observations from January-March 2013. Interval a contains 6,210 15 minute time periods between 6am and 11pm. The first interval each day is calculated as the number of pickups that occured between 6:00am and 6:15am, the last interval is the number of pickups between 10:45pm and 11:00pm. Other time intervals are defined analogously. Interval b contains 8,640 15 minute time periods between 11pm and 6am.

7 3 Benchmark Model

In this section I introduce the model proposed by Lagos (2000) and analyzed by Lagos (2003). First I describe the model and main result as shown in Lagos (2000). I then consider equilibrium characteristics under alternative pricing rules. Denote locations by i = 1, 2,...,N. Assume that there are large populations of taxicabs and passengers, denoted by v and u, respectively. I focus on the steady-state outcome of an inﬁnite-horizon discrete time game. In each period, passengers wish to transition from P location i to j with probability aij, with j aij = 1. The transition probability of passengers is captured 3 by the Markov matrix A, and its steady-state distribution is denoted by µ = (µ1, µ2, . . . , µN ) . The meeting process between passengers and cabs in location i is frictionless, and meetings occur according to

mi = min{ui, vi}, (3.1) with mi being the number of meetings in location i. Note that the failure of cabs and passengers to contact each other can occur only because of the location choices of the cab drivers. Assuming that meetings are random, the probability that a cab meets a passenger is given by pi = min{1/θi, 1} and the probability that a passenger is matched with a cab is given by piθi, where θi = vi/ui.

Assumption 1 (Profit Under Two-Part Tariff). The passenger is charged a two part tariff: an initial "flag-drop" rate b and a per-mile charge c¯. Taxis incur a fixed per-mile cost c. Let π =c ¯ − c. Then a taxi taking a passenger from i to j earns a profit πij = b + πδij, where δij is the distance (in miles) between locations i and j,

In every period there is a meeting session. Let Vi denote the value function of a cab in location i before the meeting session. If the cab does not match with a passenger it may relocate to any other location for the next meeting session. Let β be the discount factor and Ui = β maxj{Vj}j=1,2,...,N be the value function of an unmatched cab. Then

X Vi = pi aij max{πij + βVj,Ui} + (1 − pi)Ui. (3.2) j

A steady-state equilibrium is a time-invariant distribution of passengers and cabs such that the cabs have no incentive to relocate.

Deﬁnition 1 (Steady-State Equilibrium). A steady-state equilibrium is a time-invariant distribution n P P of passengers and cabs across locations {ui, vi}i=1 such that i ui = u, i vi = v, Vi = Vn for all i and P P j aijmi = j ajimi. 3For simplicity, assume the time-invariant distribution is unique.

8 Pn P Proposition 1 (Equilibrium Outcomes). Let φi = πi/( j=1 µjπj), where πi = j aijπij, and deﬁne n φ = min{φi}i=1. Let θ = v/u be the aggregate market tightness. Label locations so that

π1 ≥ π2 ≥ ... ≥ πk = ... = πN . (3.3)

Hence, locations labeled k and higher have the lowest conditional proﬁt from rides. Then Lagos (2000) shows that the following holds in equilibrium. • If θ > 1/φ, then there is a unique equilibrium in which all locations exhibit excess supply.

• If θ = 1/φ there is a unique equilibrium in which locations 1, 2, . . . , k − 1 exhibit excess supply, and the market clears in locations k, . . . , N.

• If θ < 1/φ and k < n, there exists a continuum of equilibria with excess supply only in locations 1, . . . , k −1 and excess demand in at least one of the remaining locations. If k = N the equilibrium is unique and location N exhibits excess demand and all other locations exhibit excess supply.

3.1 Model Parametrization

I calculate the transition matrices for each time period, A(a) and A(b) directly from the data following the method described in Lagos (2003). Distances between neighborhoods are computed as the average of the distances of the rides that occurred between the two neighborhoods. According to the New York City Taxi and Limousine Commission 2012 Fact Book the average fuel economy of the taxi ﬂeet was 29 mpg. The average per gallon gas price in New York City in January 2013 was $3.704. Hence, I assume that the cost of driving one mile is 12. Lagos (2000) uses data on 22,604 trips from 1988 to calibrate the model assumes all medallions are¢ active throughout the day. I use the data to calculate the average number of active medallions for each of the time intervals (a): 6am-11pm and (b): 11pm-6am. On an average day, 380 trips per minute occurred during time interval (a), with the average trip duration being 11.44 minutes. The corresponding numbers for interval (b) are 183 trips per minute with an average trip duration of 11.02 minutes. 12,921 medallions were observed on average during time period (a), and 12,534 during time period (b). Using these numbers we can calculate taxi availability during an average minute in intervals (a) and (b). For time interval (a) we have v(a) = 12921 − 11.44 × 380 = 8574, and for interval (b) v(b) = 12534 − 11.02 × 183 = 10517.

Let α = b/π. The current fare rates of New York yellow cabs yield b = 2.50 and c¯ = 2, which yields P (a) α+ j a(a)ij δij (int) (int) N α = 1.05. We can then write φi = P . Remembering that φ = min{φi }i=1, we α+ i,j µia(a)ij δij 4source: https://www.nyserda.ny.gov/Researchers-and-Policymakers/Energy-Prices/Motor-Gasoline/Monthly- Average-Motor-Gasoline-Prices

9 have for interval (a), φ(a) = 0.71 and corresponds to Upper East Side-Carnegie Hill. For interval (b), φ(b) = 0.75 and corresponds to Gramercy. Since the aggregate number of meetings given the frictionless matching is min{u, φv}, it follows that u(a) = 380 and u(b)=183. This yields the following estimates of aggregate market tightness for periods (a) and (b): θ(a) ∼ 16 and θ(b) ∼ 43. Even assuming that not all observed taxi medallions are active throughout the time interval, this parametrization puts market tightness above the no-frictions frontier for both time intervals and implies excess supply in all locations. (a) α+1.81 (b) α+2.31 We have φ (α) = α+2.40 and φ (α) = α+2.93 .

Remark 2 (Changing Two-Part Tariff). We have (φ(0)(a))−1 = 1.33 and (φ(0)(b))−1 = 1.26. Also, (a) −1 (b) −1 limα→∞(φ(0) ) = limα→∞(φ(0) ) = 1 Since v/u > is equal to 16 and 43 for time periods (a) and (b), respectively, changes in the two-part tariff don’t affect the equilibrium number of matches.

Figure 2: No-Frictions Frontier with Two-Part Tariﬀ

3.2 Demand-Driven Pricing

Now suppose that pricing is demand-driven. Specifically, suppose that the two-part tariff defined by the parameters b and c¯ now potentially varies by location and depends on the relative volume of demand in the location as compared to other locations.

10 Assumption 2 (Demand-Sensitive Pricing). Let the two-part tariﬀ for rides originating in location i be given by bi = bfb(µi), c¯i =cf ¯ c(µi), where µi is the steady state fraction of demand in location i.

We can then write P αfb(µi) + fc(µi) j aijδij φi = P P , (3.4) α i µifb(µi) + i,j fc(µi)aijδij where α = b/c¯. Note that unlike the case with a fixed two-part tariff, where the location i with the lowest value φi does not vary with α, this location is potentially different for different values of the policy parameters b, c¯, fb and fc. Consider for example the following policies:

• fb(µi) = κµi - short rides are more incentivized in locations with high demand.

• fc(µi) = κµi - long rides are more incentivized in locations with high demand.

• fb(µi) = fc(µi) = κµi - both long and short rides are incentivized more in locations with high demand. As seen in Figures 3 (c) and (d), in these cases the no frictions frontier is substantially higher and there is excess demand in at least one location.

As argued by Lagos (2003), evidence suggests that v and u do not respond much to fare increases. The calibrated ratio of market tightness puts the city above the no-frictions frontier, thus confirming the results of Lagos (2003). Changes in the two-part tariff have no effect on the aggregate number of matches in a setting with frictionless matching, and the equilibrium of oversupply of taxis in each location does not change. Demand dependent pricing has an effect on the aggregate number of meetings if the no-frictions frontier rises above the current ratio of aggregate market tightness.

11 Figure 3: No-frictions frontier for diﬀerent pricing mechanisms

(a) Interval (a) (b) Interval (b)

12 −1 Table 2: πi and φi for intervals (a) and (b)

−1 πi φi interval (a) (b) (a) (b) Astoria 11.08 10.50 1.10 1.10 Battery Park City-Lower Manhattan 12.09 12.47 1.33 1.27 Brooklyn Heights-Cobble Hill 12.54 12.09 1.31 1.26 Carroll Gardens-Columbia Street-Red Hook 12.32 11.84 1.29 1.25 Central Harlem North-Polo Grounds 10.02 9.74 1.28 1.24 Central Harlem South 9.35 10.07 1.27 1.23 Central Park 7.48 8.89 1.26 1.22 Chinatown 8.64 9.28 1.24 1.21 Clinton 7.58 9.00 1.24 1.21 DUMBO-Vinegar Hill-Downtown Brooklyn-Boerum Hill 11.77 11.12 1.23 1.20 East Harlem North 9.22 9.50 1.22 1.19 East Harlem South 8.44 9.41 1.21 1.19 East Village 7.73 8.76 1.20 1.18 East Williamsburg 10.01 10.20 1.20 1.18 Fort Greene 11.65 11.75 1.19 1.17 Gramercy 7.22 8.17 1.18 1.17 Greenpoint 9.51 9.68 1.18 1.16 Hamilton Heights 12.40 11.67 1.17 1.16 Hudson Yards-Chelsea-Flatiron-Union Square 7.26 8.51 1.17 1.15 Hunters Point-Sunnyside-West Maspeth 10.43 10.68 1.16 1.15 JFK Airport 42.36 42.93 1.16 1.15 La Guardia Airport 26.76 25.36 1.15 1.14 Lenox Hill-Roosevelt Island 7.69 8.99 1.15 1.14 Lincoln Square 7.41 8.92 1.15 1.14 Lower East Side 8.61 9.48 1.14 1.13 Manhattanville 10.17 9.94 1.14 1.13 Midtown-Midtown South 7.51 8.53 1.14 1.13 Morningside Heights 9.27 9.54 1.13 1.13 Murray Hill-Kips Bay 7.23 8.20 1.13 1.12 North Side-South Side 9.86 10.10 1.13 1.12 Park Slope-Gowanus 11.65 12.26 1.13 1.12 Queensbridge-Ravenswood-Long Island City 8.72 9.93 1.12 1.12 SoHo-TriBeCa-Civic Center-Little Italy 8.61 9.19 1.12 1.11 Stuyvesant Town-Cooper Village 7.98 8.89 1.12 1.11 Turtle Bay-East Midtown 7.55 8.49 1.12 1.11 Upper East Side-Carnegie Hill 6.90 8.44 1.11 1.11 Upper West Side 7.71 9.41 1.11 1.11 Washington Heights South 15.61 13.19 1.11 1.10 West Village 7.43 8.71 1.11 1.10 Yorkville 8.25 9.55 1.11 1.10

13 4 Matching with Frictions

The model presented and calibrated in the previous section is idealized - it is reasonable to assume that matching in the New York yellow cab market is not frictionless, as done by for example Frechette et al. (2015) and Buchholz (2016). In this section I argue that matching with frictions better describes that taxi-passenger meeting process. I then propose a novel way of inferring taxi availability in a given neighborhood and time period. Then, based on taxi arrival rates and matching mechanisms proposed in the literature, I estimate customer arrival rates and and time-specific local market tightness, i.e. the ratio of supply to demand in each neighborhood and time period. I analyze the variability of this measure throughout the day for different neighborhoods and compare my findings with existing literature.

Frechette et al. (2015) show that the fraction of time taxis spend searching is almost never lower than thirty percent and shows substantial variation throughout the day, ranging up to 65%. Under the current system of essentially ﬁxed fares, most inter-temporal variation in driver and customer welfare comes from varying search/wait times. Frechette et al. (2015) show that a simple linear model reveals that waiting time for passengers explains about 60% of the variation in hourly wages for drivers, which supports the theory that matching is not frictionless. In this section I propose an algorithm to estimate market tightness in the presence of matching frictions. Unlike Frechette et al. (2015) and Buchholz (2016), I do not assume a general equilibrium model. Instead I allow customer and taxi arrival rates to be diﬀerent in each observed time period, and estimate them using observed data.

As previously, I consider neighborhoods i = 1, 2,...,N and time periods t = 1, 2,...,T . Denote the set of all neighborhoods by I. Let dit denote demand for taxi rides in neighborhood i and time period t, and let yit denote the number of rides (taxi-passenger matches) in location i and time period t.

Assumption 3 (Customer and Taxi Arrival Rates). Customers and empty taxis arrive deterministically C T at location i during time period t with rates λit and λit, respectively. Note that vacant taxis in location i and time period t are composed of vacant taxis that transition from other neighborhoods and taxis that drop a passenger in i during t

T C Assumption 4 (Matching Rate). Customers are matched to taxis at a rate µit = µ(λit, λit ), hence C yit = λit µit.

Following Buchholz (2016), I assume the following functional form of the matching function,

" C # λit T 1 yit = λ 1 − 1 − T . (4.1) γλit

As discussed by Buchholz (2016), the function exhibits several properties desirable in the context of the

14 T C T C taxi market. For small values of λit and λit , the function is bounded below by yit = min{λit, λit }, which means that matching becomes frictionless. This implies that smaller values of supply and demand occur when the matching area is small so that taxis and customers can easily ﬁnd each other. Further, the function exhibits constant returns to scale for larger values of supply and demand, which will prove im- portant in inferring unmet demand as I show below. Matching eﬃciency is represented by the parameter γ, with larger values of γ generating fewer matches, everything else constant.

Note that the notion of “supply” of taxis in a neighborhood i during a time interval t is not straight- forward. For example, would a supply of 1 mean that there was 1 taxi at some point during t, or that there was a taxi throughout the entire interval of t? Instead, I introduce a measure of taxi availability in location i throughout time period t.

Deﬁnition 2 (Taxi Slack). Taxi availability in neighborhood i during time period t is measured by taxi slack τit, with one unit of τit representing the state of a taxi that is vacant and in neighborhood i during the entire time period t.

For example, suppose that there was one vacant taxi circulating in i for the entire time period t.

Then τit = 1. If the taxi was vacant for only one third or t, and there were no other taxis in the neighborhood, then τit = 1/3, and so on.

T C Given the customer matching rate, vacant taxis accumulate at a rate λit − µitλit , and the total slack T C in i and time period t is given by the area of a triangle with base 1 and height λit − µitλit ,

T C τit = 0.5(λit − µitλit ). (4.2)

We can now derive the vacant taxi arrival rate.

T Remark 3. The vacant taxi arrival rate in location i and time period t is given by 2τit + yit = λit.

Further, note that C 1 T C λit = µ(λit, λit ) T . (4.3) 2τit/yit + 1 λit Given the matching function in (4.1), the customer matching rate is

" C # T λit T C λ 1 µ(λit, λit ) = C 1 − 1 − T . (4.4) λit γλit

C λit T C Since this function is approximately constant for a given ratio T , we can write µ(λit, λit ) ≈ p(θit), λit

15 C λit 0 where θit = T is the relative demand intensity and p(θ) is monotonous with p (θ) < 0. Then λit

1 = p(θit)θit. (4.5) 2τit/yit + 1

C Lemma 1 (Inferring Demand). We can infer customer arrival rates λit using equations (4.3), (4.5) and the fact that p(θ)θ is strictly monotonous.

4.1 Calculating τˆit

In this section I describe the algorithm I use to approximate τit. I assume that the taxi takes the shortest route from one neighborhood to another. Speciﬁcally, I represent neighborhoods as an undirected graph

G = {gij}i,j∈I , where gij = gji = 1 if neighborhoods i and j share a border or a corner, and gij = 0, otherwise. Let Ωij be the set of shortest paths from i to j, where the length of a path is equivalent to the number of vertices of G it contains, and let κij be the cardinality of Ωij.

I consider all cases where the time between a taxi dropping off a passenger and picking up the next one is shorter than 1 hour for day shifts and 1 hour 30 minutes for night shifts. I calculate τît in 15-minute intervals starting at each full hour, and I assume that each vacant taxi contributes 1 to the supply during a 15-minute interval. For example, suppose a taxi drops off a passenger in i at pm and picks up another passenger in i at 3:16pm. I then assume the taxi spent the time 3-3:15pm in i, and thus, the taxi contributes 1 to the supply of vacant taxis in i in this time period. If the taxi pick up the passenger at 3:06pm instead, it contributes 1/3 to the supply of vacant taxis in i during 3-3:15pm and so on.

Now consider the case when a taxi drops oﬀ a passenger in i at 3:05pm and pick sup another passenger in j at 3:35pm. Suppose there are 2 shortest paths from i to j, so that κij = 2 and suppose the routes are (i, k, j) and (i, l, j). I calculate the supply contribution of the taxi for each area for each of the routes and weight it by κij as described below.

Let ai denote the area of neighborhood i. Consider the path (i, k, j). The taxi was vacant during 30min, and I assume that the time the driver spend in each neighborhood in the path is equal to

(ai, ak, aj)/(ai + ak + aj) × 30 min, i.e. proportional to the are of the neighborhood relative ot the other areas. Suppose this equals to (7, 13, 10) min, so the taxi is assumed to bin in i from 3:05pm to 3:12pm, in k from 3:12pm to 3:25pm and in j from 3:25pm to 3:35pm. The taxi then contributes (7/15)/κij to the supply in i for the time period 3-3:15pm, (3/15)κij to the supply in k calculated for the time period 3-3:15pm, and (10/15)κij to the supply for k in the time period 3:15-3:30pm, (5/15)κij to the supply in j for the time period 3:15-3:30pm, and ﬁnally, (5/15)κij to the supply in j for the time period

16 3:30-3:45pm. I repeat these calculations for the other route, and proceed analogously for all observations where the time between a drop-oﬀ and a subsequent pickup satisﬁes the above-mentioned criteria.

Remark 4 (Acknowledgment of shortcomings). Assuming that the taxi driver took one of the shortest routes according to the number of vertices in G is a simpliﬁcation and might not be optimal in some circumstances. An improved version of the algorithm would use Google Maps API to calculate the optimal route between any given pair of locations. However, due to the quota on Google Maps API calls, I do not consider this approach at the moment.

4.2 Market Tightness and Frictions

T C I use the results from Section 4 to infer the taxi and customer arrival rates λit and λit . I approximate τit ˆT ˆC by τît, calculated as described in Section 4.1. Then I obtain the estimates λit and λit . The estimates of customer arrival rates depend on the efficiency parameter γ of the matching function. Buchholz (2016) estimates the parameter γ of the matching function to be 1.3. My neighborhood definitions are similar in size to those used by Buchholz (2016), hence, assuming a similar value of γ seems reasonable. In ˆC what follows I present values of λit obtained by assuming γ = (1, 1.3, 1.6). Figure 4 shows how the number of taxi-passenger matches varies for different levels of matching efficiency. Higher values of γ imply lower matching efficiency and lead to higher estimates of demand arrival rates, as illustrated in Figure 5. Below I present preliminary summary statistics and compare my results to those of Buchholz (2016).

I estimate taxi and customer arrival rates for each time period and each value of γ. Buchholz (2016) assumes that taxi and customer arrival rates are the same for any 5-minute time interval on weekdays, and estimates arrival rates for for example 3-3.05pm on Tuesdays etc. Since I estimate date and time- speciﬁc arrival rates, averaging them across dates allows me to compare my results to those of Buchholz (2016).

Let ι1, ι2, . . . , ι96 denote unique 15-minute time intervals during 24 hours, with ι1 being 12:00-12:15am and so on. Remembering that t = 1, 2,...,T denote dated 15-minute time intervals, for example, 12:00-

12:15am January 1st 2013, let tι denote the time portion of t, for example 1ι is 12:00-12:15am. Let Tιk denote the set of all date-time intervals t with tι = ιk. Finally, deﬁne the average taxi arrival rate for ¯T 1 P ¯C neighborhood i for the time of day ιk as λiι = t∈T λit, and deﬁne λiι analogously. k |Tιk | ιk k

In Table 3 I present summary statistics of the estimated values of customer and taxi arrival rates for each time of the day. In Figure 5 I present estimates of taxi and customer arrival rates for diﬀerent ˆ(γ) ˆT ˆC ˆ(1.3) values of γ. Let θit = λit/λit . Figure 6 shows a plot of θit for Midtown-Midtown South and West

17 T Figure 4: Number of matches for taxi arrival rate λit = 100 and diﬀerent levels of matching eﬃciency γ

Village for a representative week. Similar to Buchholz (2016), I ﬁnd that there is an oversupply of taxis in Midtown during morning rush hours, and a slight undersupply of taxis in the afternoon. The opposite is true for West Village, which is also in line with the results of Buchholz (2016). This is an example of spatial misallocation. This evidence is anecdotal and should not be treated as conclusive evidence. There is uncertainty involved both in the parameter values and the estimates of demand and supply arrival rates. The main point I want to make is to show my results corroborate the ﬁndings of Buchholz (2016) and point to frictions that result in misallocation.

18 Table 3: Estimated values of taxi and customer arrival rates for diﬀerent parameter values of the matching function

matching function parameter γ = 1 γ = 1.3 γ = 1.6 λ¯ˆT λ¯ˆC λ¯ˆC /λ¯ˆT λ¯ˆC λ¯ˆC /λ¯ˆT λ¯ˆC λ¯ˆC /λ¯ˆT iιk iιk iιk iιk iιk iιk iιk iιk iιk iιk 6am-11pm mean 294.5 200.1 0.7 260.2 0.9 320.3 1.1 std 442.0 295.6 0.2 384.3 0.3 473.0 0.4 min 4.4 1.5 0.1 2.0 0.1 2.5 0.2 25% 26.5 11.6 0.5 15.2 0.7 18.7 0.8 50% 121.4 56.1 0.7 73.0 0.9 90.0 1.1 75% 395.0 307.0 0.8 399.2 1.1 491.4 1.3 max 2741.2 2119.0 1.8 2754.9 2.4 3390.7 3.0 11pm-6am mean 151.0 94.1 0.7 122.4 0.9 150.7 1.0 std 240.4 153.5 0.2 199.5 0.3 245.6 0.4 min 3.1 1.3 0.2 1.8 0.2 2.3 0.3 25% 21.1 8.9 0.5 11.7 0.7 14.4 0.8 50% 57.4 25.2 0.6 32.8 0.8 40.5 1.0 75% 173.3 116.5 0.8 151.5 1.0 186.6 1.2 max 2187.1 1346.2 1.8 1750.2 2.4 2154.1 3.0 The summary statistics for the time period 6am-11pm are based on 2,720 observations of 40 neighborhoods over 68 15-minute time intervals. The summary statistics for the time period 11pm-6am are based on 1,120 observations of 40 neighborhoods over 28 15-minute time intervals.

19 Figure 5: Estimated taxi and customer arrival rates for diﬀerent values of the matching function parameter γ

20 Figure 6: Spatial misallocation

21 4.3 Local market tightness regression

Finally, I consider a simple dynamic model.

P ˆ(γ) X ˆ(γ) 0 θit = γi + βpθi,t−p + γ zt + δt + υit, (4.6) p=1 where δt are time effects and zt are weather conditions, i = 1, 2,..., 40 and t = 1, 2,..., 2976 (all 15- minute time intervals in January 2013). Note that during the considered time period weather conditions do not vary notably as shown in Table 4. Parameter estimates for model (4.6) are presented in Table ˆ(γ) 5. The results do not vary notably if different lag orders of θit are included. The results indicate that demand pressure increases in the mornings and during periods with increased precipitation. The latter is interesting as it is in line with earlier findings, see for example Farber (2015) and Kamga et al. (2015). Farber (2015) suggests that rain does not only drive up the demand for taxis, it also drives down the supply of drivers, making the problem worse from both angles.

Table 4: Summary statistics

Statistic Mean St. Dev. Min Pctl(25) Median Pctl(75) Max

yit 123.49 202.27 1 8 31 163 1,834 τˆit 68.11 114.04 0.004 7.47 25.28 81.07 1,043.67 ˆT λit 259.70 418.88 1.01 24.28 89.48 327.33 3,453.54 ˆC λit , γ = 1 173.95 288.65 1.00 10.03 41.07 231.61 2,804.00 ˆC λit , γ = 1.3 226.23 375.25 1.30 13.11 53.50 301.20 3,645.35 ˆC λit , γ = 1.6 278.51 461.86 1.60 16.20 65.90 370.80 4,486.71 ˆ(γ) θit , γ = 1 2.53 2.74 0.13 1.33 1.76 2.62 84.60 ˆ(γ) θit , γ = 1.3 1.93 2.10 0.10 1.02 1.35 2.00 64.99 ˆ(γ) θit , γ = 1.6 1.57 1.70 0.08 0.83 1.10 1.62 52.76 precipitation 0.003 0.02 0.00 0.00 0.00 0.00 0.33 wind speed (m/s) 5.99 3.84 0 3 6 8 23 temperature (F) 34.50 11.54 0 28 36 43 64 Precipitation is measured in total accumulation in units of millimeters at the Central Park station during a 60-minute period.

5 Conclusions

In a market with frictionless matching and the current two-part tariff there should be excess supply in all locations. This is still true if the two-part tariff is modified so that the ratio of flag-drop rate to per-mile fare lies in the range of (0, ∞). Demand-driven pricing implemented in such a way that

22 Table 5: Parameter estimates for model (4.6)

ˆ(γ) Dependent variable: θit

matching efficiency γ = 1 γ = 1.3 γ = 1.6 ˆ(γ) ∗∗∗ ∗∗∗ ∗∗∗ θi,t−1 0.279 0.280 0.263 (0.024) (0.024) (0.029) ˆ(γ) ∗∗∗ ∗∗∗ ∗∗∗ θi,t−2 0.222 0.222 0.196 (0.015) (0.015) (0.018) ˆ(γ) ∗∗∗ ∗∗∗ ∗∗∗ θi,t−3 0.151 0.151 0.121 (0.009) (0.009) (0.014) 7am-10am −0.262∗∗∗ −0.200∗∗∗ −0.151∗∗∗ (0.065) (0.050) (0.039) 5pm-9pm 0.028 0.022 0.026 (0.034) (0.026) (0.021) 12am-6am 0.051 0.036 0.023 (0.043) (0.033) (0.022) temperature (F) −0.0003 −0.0002 −0.0001 (0.001) (0.0004) (0.0003) wind speed (m/s) −0.0003 −0.0003 −0.0002 (0.001) (0.001) (0.001) precipitation† −0.400∗ −0.306∗ −0.304∗∗ (0.219) (0.167) (0.132) Standard errors in parentheses. ∗, ∗∗ and ∗∗∗ denote statistical significance at the 10%, 5% and 1% levels, respectively. † - precipitation is measured in total accumulation in units of millimeters at the Central Park station during a 60-minute period. Neighborhood fixed effects are included in all models, balanced panel with N = 40, T = 2, 976 The results do not change notably if different lag orders of θˆγ are included. high-demand locations have higher fares than low demand locations can result in excess demand in at least one location depending on the degree of price discrimination. In this paper specific functional forms of demand-driven pricing are considered. A formal characterization of equilibria for general forms of the pricing function is beyond the scope of this paper and left for future research.

Data-driven estimation of taxi availability provides evidence for spatial misallocation, which implies excess demand or supply depending on the time of the day and location. Market tightness decreases in the mornings and during periods of higher precipitation, which is in line with earlier ﬁndings in the literature. In continued research I plan to consider the above results in the framework of a spatial general equilibrium model and analyze the implications of a demand-driven pricing algorithm in the context of matching with frictions.

23 References

Aﬁan, A., A. Odoni, and D. Rus (2015). Inferring unmet demand from taxi probe data. In Intelligent Transportation Systems (ITSC), 2015 IEEE 18th International Conference on, pp. 861–868. IEEE.

Buchholz, N. (2016). Spatial Equilibrium, Search Frictions and Eﬃcient Regulation in the Taxi Industry. Working paper, 1–64.

Farber, H. S. (2015). Why you can’t ﬁnd a taxi in the rain and other labor supply lessons from cab drivers. The Quarterly Journal of Economics 130 (4), 1975–2026.

Frechette, G. R., A. Lizzeri, and T. Salz (2015). Frictions in a Competitive, Regulated Market Evidence from Taxis. SSRN Electronic Journal.

Kamga, C., M. A. Yazici, and A. Singhal (2015). Analysis of taxi demand and supply in new york city: implications of recent taxi regulations. Transportation Planning and Technology 38 (6), 601–625.

Lagos, R. (2000). An alternative approach to search frictions. Journal of Political Economy 108 (5), 851–873.

Lagos, R. (2003). An analysis of the market for taxicab rides in new york city. International Economic Review 44 (2), 423–434.

24 Appendix A Data

The data set contains the following information for each taxi ride.

• Medallion id

• Anonymized hack license

• Vendor ID - code indicating the TPEP provider that provided the record (Creative Mobile Tech- nologies or VeriFone)

• Pickup date/time - date and time when the meter was engaged

• Drop-oﬀ date/time - date and time when the meter was disengaged

• Passenger count

• Trip distance in miles reported by the taximeter

• Pickup longitude and latitude

• Drop-oﬀ longitude and latitude

• RateCodeID - Standard rate, JKF, Newark, Nassau or Westchester, Negotiated fare or group ride.

• Store and forward ﬂag - ﬂag that indicates whether the trip record was held in vehicle memory before sending to the vendor, aka “store and forward”, because the vehicle did not have a connection to the server.

• Payment type - credit card, cash, no charge, dispute, voided or unknown

• Time-and-distance fare calculated by the meter

• Extras and surcharges. Currently, this only includes the $0.50 and $1 rush hour and overnight charges.

• MTA_tax - $0.50 MTA tax that is automatically triggered based on the metered rate in use. item Improvement_surcharge - $0.30 improvement surcharge assessed trips at the ﬂag drop. The improvement surcharge began being levied in 2015.

• Tip amount - only takes into account card tips, not cash.

• Tolls - amount of tolls paid in the trip

• Total amount charged to passengers (does not include cash tips)

25 A.1 Neighborhood Tabulation Areas

Figure A7: Neighborhood Tabulation Areas

New York City Neighborhood Tabulation Areas* North Riverdale- Woodlawn- Fieldston- Wakefield Riverdale

Eastchester- Spuyten Duyvil- Edenwald- Kingsbridge Baychester Williamsbridge- Van Norwood Olinville Co-op Bronx Cortlandt City Village

Bedford Park- Marble Fordham North Allerton- Hill- Kingsbridge Pelham Inwood Heights Bronxdale Gardens Fordham Belmont Washington South Heights Pelham North University Mount Parkway Heights-Morris Hope Heights Washington Van Nest-Morris East Heights Claremont- Park-Westchester Tremont South Bathgate Square Pelham Bay- Highbridge Country Club- City Island West Parkchester Crotona Farms- Park East Bronx River East Concourse- Westchester- Concourse Unionport Hamilton Village Morrisania- Soundview- Bruckner Heights West Melrose Concourse Schuylerville- Melrose Throgs Neck- Longwood Soundview-Castle Edgewater Park Manhattanville South-Mott Hill-Clason Haven North Point-Harding Park Central Harlem North-Polo Hunts Morningside Grounds Point Heights Mott Haven- Central Port Morris Harlem South East Harlem Manhattan North Upper East Rikers Queens West Harlem Island Whitestone Side South Ft. Totten- Bay Terrace- Clearview College Yorkville Upper Steinway Point Lincoln LaGuardia East Side- Square Airport Carnegie Hill Old Astoria Murray Hill Lenox Hill- Bayside- Roosevelt Clinton East Bayside Douglas Manor- Island Elmhurst Douglaston- Midtown- Astoria Hills Midtown Flushing Little Neck South Queensbridge- Jackson Turtle Ravenswood- Heights Bay-East Long Island City East North Midtown Flushing Glen Oaks- Corona Floral Park- Woodside Auburndale New Hyde Park Murray Hudson Yards- Hill- Hunters Point- Elmhurst Queensboro Kips Bay Chelsea-Flatiron- Sunnyside- Corona Hill Union Square West Maspeth Elmhurst- Maspeth Oakland Gramercy Fresh Gardens Bellerose West Pomonok- Meadows- Village Stuyvesant Flushing Utopia Town-Cooper Rego Heights-Hillcrest East Village Greenpoint Kew Maspeth Park Village Gardens Hills SoHo-TriBeCa- Forest Civic Center- Hills Jamaica Estates- Little Italy Lower East Middle Holliswood East North Williamsburg Village Queens Side Side- Briarwood- Village Chinatown South Side Jamaica Battery Park Hills Hollis City-Lower Kew Gardens Manhattan Text Ridgewood Glendale Williamsburg Bushwick Jamaica North Bushwick Brooklyn Fort Richmond South Cambria South Heights- Greene Hill Heights Bedford Jamaica St. Cobble Hill Albans Stuyvesant Woodhaven DUMBO-Vinegar Heights Hill-Downtown Clinton Cypress Brooklyn-Boerum Hill Hill Hills- City Line Carroll Gardens- Prospect Baisley South Columbia Street- Ocean Park Heights Ozone Ozone Laurelton Red Hook Crown Hill Heights Park Park Springfield North Park Slope- Gardens North Gowanus Crown Heights South Brownsville East New York Springfield Brooklyn (Pennsylvania East Prospect Gardens South- Ave) New Rosedale Lefferts Lindenwood- Brookville York Gardens-Wingate Howard Beach Windsor Rugby- Sunset Terrace Remsen Park West Village Starrett City John F. Kennedy Erasmus Sunset International Airport West New Brighton- Park East New Brighton- Kensington- East St. George Ocean Flatbush- Parkway Farragut Port Flatbush Canarsie Mariner's Harbor- Richmond Arlington-Port New Brighton- Borough Ivory-Graniteville Silver Lake Park

Bay Flatlands Ridge Dyker Heights Georgetown-Marine Midwood Park-Bergen Grymes Hill- Westerleigh Ocean Beach-Mill Basin Clifton- Parkway Fox Hills Bensonhurst South Stapleton- West Rosebank New Springville- Bloomfield-Travis Bath Madison Far Beach Bensonhurst Grasmere- Rockaway- East Arrochar- Homecrest Bayswater Ft. Wadsworth

Hammels- Staten Sheepshead Bay- Arverne- Gerritsen Beach- Gravesend Edgemere Todt Hill-Emerson Old Town- Manhattan Beach Hill-Heartland Village- Dongan Hills- Island Lighthouse Hill South Beach West Brighton Seagate- Brighton Beach Coney New Dorp- Island Midland Beach

Oakwood- Oakwood Beach Breezy Point- Belle Harbor-Rockaway Arden Park-Broad Channel Heights Great Kills

Rossville- Woodrow Annadale- Huguenot-Prince's Bay-Eltingville

Charleston- Richmond Valley- Tottenville * Neighborhood Tabulation Areas or NTAs, are aggregations of census tracts that are subsets of New York City's 55 Public Use Microdata Areas (PUMAs). Primarily due to these constraints, NTA boundaries and their associated names may not definitively represent neighborhoods.

Source: Population Division-New York City Department of City Planning