The Pennsylvania State University

The Graduate School

Department of Economics

ESSAYS ON EMPIRICAL INDUSTRIAL ORGANIZATION

A Dissertation in

Economics

by

Bo Bian

© 2018 Bo Bian

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

August 2018

The dissertation of Bo Bian was reviewed and approved∗ by the following:

Mark Roberts

Professor of Economics

Dissertation Advisor, Chair of Committee

Charles Murry

Assistant Professor of Economics

Peter Newberry

Assistant Professor of Economics

Guangqing Chi

Associate Professor of Rural Sociology and Demography and Public

Health Sciences

Barry Ickes

Professor of Economics

Head of the Department of Economics

∗Signatures are on file in the Graduate School.

ii

Abstract

This dissertation consists of two chaperts on empirical industrial organization.

My research focuses on market efficiency and welfare analysis. In both chapters,

I build structural model to estimate demand and supply decisions of the market

and conduct policy experiments to analyze market efficiency.

Chapter 1: Search Frictions, Network Effects and Spatial Com-petition: Taxis versus Uber

In this chapter, I model the search and matching process among passengers,

taxis and Uber drivers in New York City to analyze the matching efficiency

taking into account network effects and supply competition. Drivers make

dynamic spatial search decisions to supply rides across locations (platforms)

and passengers make static discrete choice decisions among taxi and Uber. Net-

work effects occur if increased participation of one side impacts searches of the

other side in the same location. I model network effects by adding demand and

supply to both sides’ decisions. I use the nonstationary oblivious equilibrium

to estimate the dynamic model and analyze frictions as mismatches between

drivers and passengers. I find significant network effects. Then, I show that

network effects and supply competition, in addition to fixed pricing structure

(of taxi), have extensive effects on frictions and welfare in three counterfactual

scenarios. The first eliminates the Uber surge multiplier, the second improves

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traffic conditions and the third decreases Uber drivers by 30 percent. I find

that without surge pricing, Uber’s mismatches increase by 3,152 in a day shift.

Improving traffic condition reduces matching frictions for both taxis and Uber. It

increases searches of drivers and increases taxis’ pickups by 10.6 percent. Taxis’

profit increases by $ 231,100 and Uber’s increases by $5,110. Restricting Uber’s

supply increases frictions for both taxis and Uber due to less competition. But it

increases taxis’ pickups by 1,660 ($ 34,300) compared to 7,004 ($ 119,320) loss

of Uber’s trips. Consumers are worse off after the regulatory policy but better

off in the first two scenarios. Most importantly, with or without accounting for

network effects generates different simulation results and could lead to opposite

conclusions.

Chapter 2: Vertical Relationship and Merger Effects in the U.S.Beer Industry

In this paper, I study the MillerCoors joint venture of 2008 in the U.S. beer

industry. In particular, I focus on impacts of the cost efficiency (in terms of

shipping distance and production cost) and increased market power of this

merger and importantly how they are affected by the vertical market structure.

With vertical relationship, the upstream shock does not fully pass through to

downstream retail price because both upstream and downstream will adjust

markups to the shock. Thus, merger analysis in the beer industry depends

on concentration of both upstream and downstream markets. I use random

coefficient model to estimate demand for beer and price elasticities. In the supply

side, I model the double marginalization problem of beer retailers and brewers

by assuming linear pricing contracts between upstream and downstream firms.

Cost saving of the merger is estimated by comparing pre- and post-merger

implicit marginal costs. I simulate the two markups in the post-merger period

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without joint venture to quantify and disentangle the merger effects. I find that

average cost saving of producing a 12 oz serving is 2 cents for Coors light and

1.6 cents for Miller lite. Cost saving through shipping distance is at most 7.4

cents for Coors and 2.2 cents for Miller. Market power of MillerCoors increases

brewers’ markups which dominate the cost saving. However, retailers’ markups

decreases to mitigate the impact on retail prices especially for more concentrated

downstream markets. Social welfare increases after the joint venture.

v

Table of Contents

List of Figures ix

List of Tables x

Acknowledgments xi

Chapter 1Search Frictions, Network Effects and Spatial Competition: Taxis

versus Uber 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 A One-Period, Two-Islands Model of Search and Matching . . . . 8

1.3.1 Monopoly Model . . . . . . . . . . . . . . . . . . . . . . . . 91.3.2 Duopoly Model . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.4 Industry Background . . . . . . . . . . . . . . . . . . . . . . . . . . 151.5 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.5.1 Sample Construction . . . . . . . . . . . . . . . . . . . . . . 181.5.2 Sample Overview . . . . . . . . . . . . . . . . . . . . . . . . 21

1.6 Empirical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.6.1 Passengers’ Choice Problem . . . . . . . . . . . . . . . . . . 301.6.2 Drivers’ Choice Problem . . . . . . . . . . . . . . . . . . . . 341.6.3 Matching Function . . . . . . . . . . . . . . . . . . . . . . . 381.6.4 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1.7 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421.7.1 Pre-estimation Discussion . . . . . . . . . . . . . . . . . . . 44

1.7.1.1 Number of Taxi and Uber Drivers . . . . . . . . . 441.7.1.2 Passengers’ Destinations . . . . . . . . . . . . . . 45

1.7.2 Two-Step Estimation . . . . . . . . . . . . . . . . . . . . . . 451.7.2.1 Step 1: Estimating Nonlinear Parameters . . . . . 451.7.2.2 Step 2: Estimating Linear Parameters . . . . . . . 48

vi

1.7.3 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 491.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

1.8.1 Estimates outside mean utilities . . . . . . . . . . . . . . . 511.8.2 Estimates in mean utilities . . . . . . . . . . . . . . . . . . 601.8.3 Benchmark Welfare . . . . . . . . . . . . . . . . . . . . . . . 61

1.9 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681.9.1 Eliminating surge multiplier . . . . . . . . . . . . . . . . . 691.9.2 Improving traffic conditions . . . . . . . . . . . . . . . . . . 731.9.3 Regulating Uber’s supply . . . . . . . . . . . . . . . . . . . 76

1.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Chapter 2Vertical Relationship and Merger Effects in the U.S. Beer Industry 812.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812.2 Background of the U.S. Beer Industry . . . . . . . . . . . . . . . . 852.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

2.3.1 Nielsen Retail Data . . . . . . . . . . . . . . . . . . . . . . . 882.3.2 ACS&QCEW . . . . . . . . . . . . . . . . . . . . . . . . . . 892.3.3 Shipping distance . . . . . . . . . . . . . . . . . . . . . . . . 892.3.4 Market Definition . . . . . . . . . . . . . . . . . . . . . . . . 90

2.4 Preliminary analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 922.5 Structural Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

2.5.1 Beer Demand . . . . . . . . . . . . . . . . . . . . . . . . . . 992.5.2 Beer Supply . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

2.5.2.1 Retailers . . . . . . . . . . . . . . . . . . . . . . . . 1032.5.2.2 Manufacturers . . . . . . . . . . . . . . . . . . . . 104

2.6 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072.6.1 Demand estimation . . . . . . . . . . . . . . . . . . . . . . . 1072.6.2 Supply estimation . . . . . . . . . . . . . . . . . . . . . . . . 1082.6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

2.6.3.1 Simple logit demand . . . . . . . . . . . . . . . . . 1092.6.3.2 Random Coefficient Model . . . . . . . . . . . . . 1112.6.3.3 Supply estimates . . . . . . . . . . . . . . . . . . . 113

2.7 Counterfactuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1172.8 Conclusion and extension . . . . . . . . . . . . . . . . . . . . . . . 122

Appendix AProofs of chaper 1 124A.1 Proof of proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . 124A.2 Proof of proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . 125

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Appendix BSelected MSAs for chapter 2 128B.1 Selected MSAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

Bibliography 131

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List of Figures

1.1 40 select markets and 79 spots to collect Uber surge multiplier . . 211.2 Comparison of traffic speed in 2010 and 2016 . . . . . . . . . . . . 261.3 Distribution of expected profits of taxi and Uber . . . . . . . . . 271.4 Hyperbolic function for perfect matching . . . . . . . . . . . . . . 401.5 Overview of the estimation process . . . . . . . . . . . . . . . . . . 431.6 Uber drivers’ working schedule table cited from Chen et. al.(2017) 451.7 Dynamics of search values before matching process . . . . . . . . 551.8 Dynamics of expected profits conditional on being matched . . . 571.9 Dynamics of expected continuation values conditional on being

unmatched . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581.10 Heterogeneous expected continuation values conditional on be-

ing unmatched . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591.11 Aggregate frictions and matches of taxis& Uber over time . . . . 651.12 Demand, supply and matches in a location of Queens . . . . . . . 651.13 Demand, supply and matches in a location of Brooklyn . . . . . . 661.14 Demand, supply and matches in Times Square . . . . . . . . . . . 661.15 Demand, supply and matches in Financial District . . . . . . . . . 67

2.1 Average price per serving by brand over 50 markets . . . . . . . . 932.2 Distribution of HHI increases of post-merger . . . . . . . . . . . . 942.3 Distance(miles) between breweries and markets for pre/post-

merger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

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List of Tables

1.1 Trip and share by firm, shift, and area . . . . . . . . . . . . . . . . 231.2 Distribution of dropoffs in day shift by firm . . . . . . . . . . . . . 241.3 Summary statistics of key variables . . . . . . . . . . . . . . . . . . 251.4 Estimates of nonlinear parameters . . . . . . . . . . . . . . . . . . 531.5 Statistics in equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 541.6 Linear regression of mean utility . . . . . . . . . . . . . . . . . . . 611.7 Baseline welfare statistics . . . . . . . . . . . . . . . . . . . . . . . 641.8 Eliminating surge multiplier . . . . . . . . . . . . . . . . . . . . . 721.9 Traffic improvement . . . . . . . . . . . . . . . . . . . . . . . . . . 751.10 Restricting Uber’s supply . . . . . . . . . . . . . . . . . . . . . . . 78

2.1 OLS regression of retail price(12oz) on HHI . . . . . . . . . . . . . 982.2 Demand estimates from simple logit model . . . . . . . . . . . . . 1102.3 Demand estimates from random coefficient model . . . . . . . . . 1132.4 Own and cross price elasticity (average over markets) . . . . . . . 1142.5 Statistics on estimated markups and costs(average over products) 1162.6 OLS regression on marginal cost(12oz) . . . . . . . . . . . . . . . . 1182.7 Couterfactuals: average cost and markups by firm and HHIchain . 121

B.1 The 50 MSAs with average statistics over 20 quarters . . . . . . . 128

x

Acknowledgments

I am deeply indebted to my advisor Mark Roberts for his constant support

and guidane without what this work would not be accomplished. I am always

inspired and encouraged by him to persist in excellent research work. I am

also thankful to him for supporting me to attend conference and to present my

work.

I also express my gratitude to my committee members, Peter Newberry,

Charles Murry and Guangqing Chi. They provide many valuable comments to

my work. They are very generous sharing their wisdom and research ideas for

me to improve my work.

My research has greatly benefited from discussions and comments from

participants in Brownbag seminar and IIOC conference including Paul Grieco,

Daniel Grodzicki, Joris Pinkse, Lixiong Li and Alon Eizenberg.

Lastly, my gratitudes goes to my parents for their love. Without their sacrifice

and support, I cannot pursue my career and persist until today’s achievement.

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Dedication

To my parents: Yanxiang Bian and Lan Yao

xii

Chapter 1 |Search Frictions, Network Effects andSpatial Competition: Taxis versus Uber

1.1 Introduction

Frictions play an important role in explaining the failure of market clearing.

When sellers and buyers meet and trade with each other, information imper-

fections about potential trading partners, heterogeneities, slow mobility and

congestion from large numbers can prevent some potential traders on one side

of the market from contacting potential traders on the other side, leaving some

buyers and sellers unable to trade. The early search and matching literature use

a reduced form matching function to capture effects of frictions on equilibrium

outcomes of bilateral trades1. The source of frictions underling such a function

is not explicitly modeled.

In more recent literature, the microfoundation of the matching function is

studied. Lagos (2000) builds a model of taxis’ spatial search for passengers and

finds that even without imperfection information and random search assump-

tion, aggregate mismatches over locations arise endogenously as outcomes of

drivers’ optimal search decisions. Specifically, when one location is more prof-

itable than another, taxis may overcrowd that location leaving another location

with unserved passengers. Similar to the idea in Lagos (2000), Buchholz (2016)

1Blanchard and Diamond (1989), Pissarides (1990), and Mortensen and Pissarides (1994) areexamples.

1

empirically studies search frictions in the taxi industry as consequence of price

regulation which fails to coordinate cross-market demand and supply leaving

empty taxis in some areas and excess demand in other areas. However, both

Lagos (2000) and Buchholz (2016) emphasize the prices as a source of spacial

mismatches and mainly focus on the supply side of the matching process.

This paper studies the matching efficiency in the taxi and ridesharing in-

dustry 2. I contribute to previous literature by developing a richer demand

side accounting for network effects in the way that decisions of both drivers

and passengers depend on the size of the other side of the market. Treating

a location as a platform, such feedback loop is called indirect network effect

(INE) in the literature3. I study how this non-price factor influences matching

efficiency of the market. In details, on the supply side, drivers make spatial

search decisions among locations by choosing the one with the highest expected

profit taking into account both demand and supply in the location. The demand

positively affects expected profit by increasing matching probability, whereas the

supply competition negatively affects expected profit by decreasing matching

probability. On the demand side, passengers make a static discrete choice deci-

sion among taxi, Uber and an outside option. From the passengers’ perspective,

the supply of cars changes the matching probabilities and waiting time which

affects their utility and choice decisions. This interdependence between demand

and supply, if exists, has effects on matching efficiencies. For instance, if the INE

is positive, an increase of supply in a location with excess supply will increase

demand which further attracts more drivers. Supposing the increased demand

is less (more) than increased supply, excess supply will be larger (smaller) at

new equilibrium than without network effects. In other words, network effects

provide an extra channel which may exacerbate or alleviate matching frictions

2Taxi industry is well known for existence of matching frictions such that some areas haveexcess demand whereas some have excess supply. This industry is ideal for analyzing searchand matching frictions for several reasons. First, search decisions are made by decentralizedindividuals without coordination. Second, the taxi market is highly regulated in fares andmedallions. Third, there is no preference heterogeneity among drivers and passengers.

3I refer to cross sides externality as indirect network effect (INE) and the same side externalityas direct network effect (DNE) for the rest of this paper.

2

caused by inefficient prices.

Instead of modeling only taxi drivers’ search decisions as in Buchholz (2016),

I further allow the model to include ridesharing company Uber. Taxis and Uber

compete for passengers in each location by providing products with different

prices and qualities (i.e. waiting time, matching probability). I also allow the

matching technology within location to differ between taxis and Uber. The

benefits of modeling Uber are twofold. First, in addition to the DNE within

taxis that matching probability decreases in number of taxi drivers, Uber drivers

affect taxis’ profits in a different way by affecting the demand for taxis. Second,

with the rapid growth of ridesharing industry, there are many real world debates

about the influence of Uber on traditional taxis’ profits and its regulation. My

duopoly model can simulate several policy outcomes and makes suggestions to

the policy makers.

To empirically analyze the model, I use data on trip records of taxis and Uber

from the New York City Taxi and Limousine Commission(TLC) and collected

Uber’s surge multiplier in April 2016. This dataset provides detailed information

on taxis’ trips including pickup/dropoff locations and time for trips and brief

information on Uber’s trips including only pickup areas and time. This data

is very limited since it does not provide information on supply and demand

levels in the matching process. I borrows the strategy from Buchholz (2016)

to estimate equilibrium demand and supply out of a dynamic spatial search

model for both taxi and Uber drivers. Due to the large number of drivers in

this dynamic game, I apply the concept of nonstationary oblivious equilibrium

proposed by Weintraub, Benkard and Jeziorski (2008) to solve the equilibrium.

The idea of OE is that, instead of competing with each other, taxi and Uber

drivers are atomistic and compete against deterministic paths of distribution of

other drivers in equilibrium.

Finally, as implication of my model estimates, I simulate several counterfac-

tuals for the interests of both matching efficiency of the market and policy issues

in the real world. During the sample period of April 2016, Uber is growing

3

rapidly and the total Uber licensed drivers outnumber the taxis4. There are

mainly two complaints about the growth of Uber. First, people blame that it

contributes to traffic congestion. Second, it causes the taxis’ profits to drop5. In

2015, the city governor proposed to solve these problems by capping the growth

of Uber though not implemented. Now, city governor thinks of regulating Uber

again and they also propose to charge congestion pricing to improve traffic in

Manhattan6.

Thus, I focus three main counterfactuals. In the first counterfactual, I elimi-

nate Uber’s surge multiplier to study to what extent the flexible pricing improves

spatial matching efficiency. In the second one, I improves the traffic condition

to study the magnitude of traffic condition’s impact on matching efficiency. In

the third one, I simulate the regulatory policy of restricting Uber’s supply and

analyze how competitiveness affects matching efficiency and profit changes of

taxis. In each simulation, I predict and compare market outcomes with and

without network effect. But, I do not endogenously model traffic conditions so

that the simulation results are partial effects.

I find that without surge multiplier, Uber’s cross location mismatches in-

crease whereas taxis’ mismatches decrease. Lower price of Uber make the

market more competitive and competition improves taxi’s matching efficiency.

After improving traffic condition, I find that matching efficiencies increase

for both firms. Pickups of taxis increase by 10.6% whereas Uber’s pickups

decrease by 2.21%. Though I do not endogenously model traffic condition

in this paper, the second simulation suggests importance of traffic speeds in

spatial matching efficiency. In the last counterfactual, after restricting Uber’s

supply, taxis’ demand and pickups increase slightly in comparison to decline

of Uber’s pickups. The cross location mismatches of taxis increase a bit. All

4There are 26, 000 Uber’s licensed vehicles in comparison to 13, 000 taxi medallions. Ubercompletes 4.6 million trips and taxis complete 13 million in the sample month

5For example, the auction price of an independent unrestricted medallion dropped from $0.7 million in 2011 to $0.5 million in 2016.

6https://www.timeout.com/newyork/news/the-city-council-finally-remembered-that-uber-needs-to-be-regulated-in-nyc-030218

4

results indicate the importance of network effects on the simulation outcomes

and policy conclusions.

The rest of this paper is organized as follows. Section 2 discusses prior

literature in detail. In section 3, I present a simplified model demonstrating why

the network effects matter for matching efficiency. Section 4 and 5 introduce

industry background and the data separately. Section 6 presents the empirical

model. Estimation strategy is in section 7 and the results are in section 8. In

section 9, I simulate and discuss counterfactuals. Section 10 concludes this

paper.

1.2 Literature

This paper is built upon two streams of literature, network effects and search and

matching. This paper contributes to the network effects literature by modeling

both DNE and INE. DNE measure the externalities of other agents from the

same side of market on agent’s decision. For example, other drivers in the same

location would decrease the chance of being matched. INE measures the impact

of agents from the other side of market on agent’s decision. For example, high

demand increases supply of drivers and more drivers will increase passengers’

choice probability of taxi(or Uber). If INE is bilateral, it forms a feedback loop

for evolution of both sides. The theoretical literature of network effects begins

with Katz and Shapiro(1985) and follows by Farrell and Saloner (1986), Chou

and Shy (1990), Church and Gandal (1992), Rochet and Tirole(2003, 2006) and

Amstrong (2006).

The empirical works on network effects begin with Gandal (1994), Saloner

and Shepard (1995) and grow rapidly in recent years. For instance, Gandal,

Kende, and Rob (2000) develop a dynamic model of consumer’s adoption of

CD player and software entry to estimate the feedback in CD industry. Ohashi

(2003) and Park (2004) study network effects in the U.S. home VCR market. Nair,

Chintagunta, and Dube(2004) quantify the network effects in the PDA market.

5

Clements and Ohashi (2005), Corts and Lederman (2009) focus on network

effects in the video game industry. Rysman (2004) estimates the network effects

in Yellow Pages market and how it is related to market concentration and

antitrust policy. Ackerberg and Gowrisankaran (2006) estimate the importance

of network effect in the ACH banking industry. Dubé, Hitsch, and Chintagunta

(2010) study network effects in video game market and its tipping effects. Lee

(2013) also studies game industry but focus on software exclusivity. Luo (2016)

studies network effects in smartphone industry and how it affects carriers’

dynamic penetration pricing strategy.

Most of these empirical works focus on indirect network effect of a two-sided

platform and ignore the direct network effects. Or they use network size of

one side to estimate joint effects of INE and DNE. Goolsbee and Klenow (2002)

is one paper focusing on only direct network effect in the diffusion of home

computers. Chu and Manchanda (2016) is one recent paper trying to estimates

and distinguish both direct and indirect network effects in e-commerce platform

(Alibaba). My paper contributes to the literature by quantifying both direct

and indirect network effects. I allow the sizes of agents from both sides of the

market to affect decisions of individuals on either side.

This paper also contributes to the search and matching literature by adding

network effects to the model. Early search and matching model use reduced

form matching function to introduce frictions that prevent the market from clear-

ing (Blanchard and Diamond(1989), Pissarides(1984), Mortensen and Pissarides

(1999)). Microfoundations of the matching function are introduced, for example,

as coordination failures in ball-and-urn problem (Butters (1977) and Burdett,

Shi and Wright (2001)). Lagos (2000) develops a spacial search model of taxis

without imperfect information and random search assumptions showing that

frictions arise in the aggregate matching function endogenously as outcomes of

drivers’ search decisions. Specifically, when prices are fixed and one location is

more lucrative than other locations, drivers will overcrowd that location leaving

other locations undersupplied. Coexistence of excess demand and excess supply

6

reflect frictions in the aggregate matching function. Buchholz (2016) extends

Lagos (2000) and builds an empirical model with non-stationary drivers’ dy-

namics and price-sensitive demand. He shows that price regulation of NYC

leads to inefficient matching because drivers making dynamic search decisions

prefer searching locations with high profitability. Fixed pricing structure of taxis

prevents the market from clearing on prices.

This paper follows the approach of Buchholz (2016) and extend his model.

My contributions are twofold. First, I build a richer demand model that is not

only sensitive to prices, but also sensitive to supply/demand to incorporate

both INE and DNE. For instance, each geographic location can be deemed as a

platform. Drivers’ search decisions among locations are analogous to software

providers’ choosing platforms. High demand of passenger in one location

attracts more drivers and more drivers increase the choice probability of pas-

sengers. Frechette, Lizzeri and Salz (2016) also includes supply in passenger’s

demand function in the form of a simulated waiting time. But they do not model

drivers’ location choices. Second, I model cross-firm competition between taxi

and Uber drivers for passengers. The first extension allows me to study non-

price factors that influence matching efficiency. The second extension provides

richer competition form between drivers and allows me to study regulation of

Uber’s supply on matching efficiencies of taxis, profits and consumer welfare.

A very similar work to this paper is by Shapiro (2018) which however focuses

on Uber’s welfare contribution to the New York City without emphasizing the

network effects in the matching efficiency.

This paper also contributes to empirical literature with dynamic oligopoly

models. When there are a large number of firms within the market, Weintraub et

al.(2007,2008) propose the concept of oblivious equilibrium(OE) to approximate

Markov-perfect equilibrium in order to avoid the curse of dimensionality. In

oblivious equilibrium, the firm is assumed to make the decision based only

on its own state and deterministic average industry state rather than states of

other competitors. In this paper, I assume drivers compete with the distribution

7

of other drivers throughout the day. Under the OE assumption, only the

distribution path at equilibrium is calculated. There are empirical papers

using stationary OE (Xu(2008), Saeedi(2014)) and nonstationary OE (Qi(2013),

Buchholz(2016)) to solve equilibrium of a model with large number of agents.

Finally, there are many works related to the taxi and ride-sharing industry.

Some use the same trip records dataset as this paper. Early work studying NYC

taxi industry include Farber (2005, 2008), Crawford and Meng (2011) which

study taxy drivers’ labor supply decisions. Frechette, Lizzeri and Salz (2016)

study taxi drivers’ labor supply decisions with matching frictions. In recent

years, research on ride-sharing industry also grows. For example, Chen et

al.(2017) study flexible labor supply of Uber drivers and Chen and Sheldon

(2015) study surge pricing of Uber. Other work related to traffic condition and

government regulation worth to mention is by Kreindler (2018) which studies

road congestion pricing policy in India.

1.3 A One-Period, Two-Islands Model of Search and

Matching

In this section, I build two simplified models to show the influence of network

effects and duopoly competition on matching efficiency. These are the two

main contributions of this paper to the literature. Both models are built under

an environment of drivers searching for passengers among two islands in one

period. The prices are fixed in both models. There are only taxis in the first

model and there are taxis & Uber in the second. In the first model, I study how

network effects influence matching efficiency by changing supply coefficient

in the demand equation. In the second model, I study how competition and

regulation affect matching by changing the total number of Uber cars. These

exercises help to understand the mechanisms underling the dynamic structural

model of this paper.

8

1.3.1 Monopoly Model

There are a fixed number of taxis, Ny, searching for passengers among two

isolated islands i = 1, 2 in one period7. The fare in each island is denoted as pi

and is fixed. Supply and demand of each island is denoted as vi and ui. For

simplification, I use a linear demand function in each island as a reduced form

of aggregate demand over passengers’ decisions8

ui = −αui + βvi + di, ∀i (1.1)

The coefficient −α on demand ui, assumed negative, measures DNE of other

passengers in the same island9. The coefficient β on supply, assumed positive,

measures INE of supply on demand. The di captures island fixed effects such as

population size and price. Since prices are fixed and the purpose of this exercise

is not to model prices, I add prices to di. The goal of this exercise is to study

how β affects equilibrium matching outcomes. A taxi chooses which island

to serve in order to maximize his expected profit. The driver’s optimization

problem is:

i∗ = arg maxi

mi

vipi (1.2)

where mi is matches in island i obtained from mi = min{ui, vi} which means

perfect matching within island. Assume all passengers and drivers make

simultaneous decision and Nash equilibrium satisfies the conditions E1-E4:

m∗1v∗1

p1 =m∗2v∗2

p2 (E1)

u∗i =β

1 + αv∗i +

11 + α

di (E2)

7I use y as index for yellow taxis and x as index for UberX in this paper.8One can think this demand equation as linear approximation for discrete choice model with

one product and one outside option.9The direct network effect could be positive or zero as well.

9

m∗i = min{u∗i , v∗i } (E3)

v∗1 + v∗2 = Ny (E4)

Condition E1 means the expected profits of the two islands are equal and drivers

have no incentive to deviate. Condition E2 means that demand ui is calculated

according to equation (3.1). E3 follows perfect matching assumption. Finally, E4

means the total number of taxis is fixed at Ny.

Proposition 1: There exists a Nash equilibrium such that one island exhibits

excess demand and the other island exhibits excess supply. (see appendix for

proof).

I consider one special equilibrium such that there is excess supply in one

island(w.l.o.g. island 1) and excess demand in the other(island 2). The parameter

values required for existence of this equilibrium are given in proposition 1. The

equilibrium demand and supply are:

v∗1 =p1

p2u∗1 (supply in island 1)

u∗1 =d1

1 + α− βp1

p2

(demand in island 1)

v∗2 = Ny − v∗1 (supply in island 2)

u∗2 =β

1 + αv∗2 +

d2

1 + α(demand in island 1)

In this equilibrium, the price in island 1 is greater than price in island 2,

p1 > p2. The excess supply in island 1 is v∗1 − u∗1 and excess demand in island 2

is u∗2 − v∗2 . The aggregate matching friction is measured as:

mismatch = min{v∗1 − u∗1 , u∗2 − v∗2} (1.3)

Expression 3.3 is derived by subtracting taxis’ aggregate pickups , u∗1 + v∗2 , from

the minimum of total demand and supply, min{u∗1 + u∗2, v∗1 + v∗2}. It counts

10

the number of extra matches that could be made in an efficient matching. Our

interest in this exercise is to do static comparative analysis of β on the friction

min{v∗1 − u∗1, u∗2 − v∗2}. However, one thing to notice is that (3.3) is a good

measure of efficiency when both aggregate demand and supply are fixed. In

the model, aggregate demand is not fixed. Thus, the discussion below is within

certain domain.

The excess supply in island 1 is v∗1 − u∗1 = (p1

p2− 1)

d1

1 + α− βp1

p2

which

increases in β. The intuition is as follows: when β increases, demand is more

sensitive to supply and therefore increases. Increased demand makes island 1

more profitable to drivers. However, in island 2 the increase in demand does not

increase profit because matching probability is already 1 due to excess demand.

Thus, some drivers switch to search island 1. In the new equilibrium, both

demand and supply in island 1 increase proportionally such that v∗1 = p1/p2u∗1 .

The excess supply in island 1, v∗1 − u∗1 , increases.

The excess demand in island 2 also changes in the new equilibrium. In-

creasing β has two opposite effects on demand in island 2. First, it positively

affects demand as coefficient on supply. Second, supply in island 2 decreases

which in return decreases demand in island 2. The first order derivative of u∗2w.r.t. β is

v∗21 + α

+β

1 + α

dv∗2dβ

. The first order derivative of excess demand u∗2 − v∗2

w.r.t. β isv∗2

1 + α+ (

β

1 + α− 1)

dv∗2dβ

> 0 becausedv∗2dβ

< 0 and β < 1 + α10. Since

both excess supply in island 1 and excess demand in island 2 increase in β, the

matching friction becomes larger when β is larger. Thus, if a network effect

was present (β > 0) in the real world, but ignored (β = 0) in the model, our

measure of friction in equilibrium and policy simulation are incorrect. In the

next subsection, I extend this model by adding Uber and show how supply

competition affects matching friction at equilibrium.

10β < 1 + α is equilibrium condition as one can see in u∗1 . The denominator 1 + α− βp1

p2> 0.

Due to p1 > p2, we must have 1 + α > β

11

1.3.2 Duopoly Model

In this subsection, I extend the monopoly model by adding Uber with fixed

number of cars Nx. The demand function is modified such that there are cross

elasticities. The new demand equation is:

uyi = −αuyi + βvyi + γuxi − θvxi + dyi︸ ︷︷ ︸Dyi

, ∀i (3.4.1)

uxi = −αuxi + βvxi + γuyi − θvyi + dxi︸ ︷︷ ︸Dxi

∀i (3.4.2)

where y indicates taxi, x indicates Uber and i indicates island11. The parameters

α and β measure DNE and INE of each firm as in previous model. The new

parameters γ and θ measure cross elasticity of demand to the supply/demand

of the other product. This equation can be deemed as linear approximation

for discrete choice demand. I denote the last three terms as Dyi and Dxi for

convenience in analogy to di in the monopoly model. However, Dyi and Dxi

are endogenous here. The equilibrium conditions in this case are similar to

monopoly model:

m∗f 1

v∗f 1p f 1 =

m∗f 2

v∗f 2p f 2 ∀ f = y, x (E1)

u∗f i =β

1 + αv∗f i +

D∗f i

1 + α∀i = 1, 2, f = y, x (E2)

m∗f i = min{u∗f i, v∗f i} ∀i = 1, 2, f = y, x (E3)

v∗f 1 + v∗f 2 = N f ∀ f = y, x (E4)

The competition comes from D f i such that opponent’s supply decreases firm’s

demand and opponent’s demand increases firm’s demand. As mentioned above,

11For the rest of this paper, I denote y as yellow taxis and x as UberX.

12

I consider this relationship as linear form of a simple logit demand model with

two products such that demand of one product depends on utilities of all

products. In this exercise, I focus on an equilibrium with excess supply for

taxis in island 1, excess demand for taxis in island 2 and excess supply of Uber

in both islands. The goal of this exercise is to study how the supply of Uber

N2 affect taxis’ matching friction. I choose equilibrium that Uber has excess

supply in both island for two reasons. First, if Uber has excess demand in both

islands, there will be multiple equilibria. Second, since I only study taxis friction

in this exercise, it is not necessary to analyze equilibrium in which Uber also

has friction (i.e. one island with excess demand and one with excess supply).

Existence of such equilibrium is proved in proposition 2.

Proposition 2: There exists a Nash equilibrium such that one island exhibits

excess demand and the other island exhibits excess supply for taxis. Both

islands have excess supply of Uber (see appendix for proof).

To simplify the solutions, I impose one important assumption that γ = 012.

The competition still remains in θv f i. Then, the equilibrium demand and supply

satisfy:

v∗y1 =py2

py1u∗y1 =

py2

py1

−θv∗x1 + dy1

1 + α− βpy1/py2(3.5)

u∗y2 =β

1 + αv∗y2 +

−θv∗x2 + dy2

1 + α(3.6)

v∗x1 =−θv∗y1 + dx1

−θNy + dx1 + dx2Nx (3.7)

v∗x2 =−θv∗y2 + dx2

−θNy + dx1 + dx2Nx (3.8)

Solving explicit form of demand and supply as function of parameters requires

complex algebra and the intuition will be mixed. These equations look like best

response functions in Cournot model and I will discuss the intuition based on

12I also impose px1 = px2 which is irrelevant to study taxis’ friction .

13

these equations. When Nx decreases due to regulation, supply of Uber in both

islands decrease according to (3.7)(3.8). From (3.5), decreasing vx1 will increase

demand of taxis in island 1 which further increases taxis drivers’ incentive

to search island 1 and therefore vy1 increases. More taxis in island 1 further

decreases supply of Uber in island 1 as shown in (3.7). Due to the proportional

increases of demand and supply of taxis in island 1, excess supply of taxis

in island 1 increases. Since more taxis switch to island 1, taxi supply vy2 in

island 2 decreases. Supply of Uber in island 2 has ambiguous change. The

downside force to Uber’s supply in island 2 is drop of Nx. The upside force is

decreased supply of taxis in island 2 and switch of Uber drivers from island 1 to

island 2. Supposing that vx2 decreases, derivative of u∗y2 − v∗y2 w.r.t. Nx ,that is

(β

1 + α− 1)

dv∗y2

dNx− θ

1 + α

dv∗x2dNx

, is negative. In this case, both excess demand and

excess supply of taxis increase after Nx decreases. It implies matching efficiency

is worse off under supply regulation of Uber. However if vx2 increases, it offsets

the effect of decreased taxi supply in island 2. Whether excess demand of taxis

increases or decreases is ambiguous. So does aggregate matching friction of

taxis in this case.

To summarize, in this section, I build two simple spatial search models

illustrating two findings. First, the interdependence of demand and supply

in search and matching process (network effects) affects aggregate matching

friction. Second, in a duopoly model, competition also affects the matching

friction of each firm. Especially, when decreasing the supply of Uber, taxis’

aggregate matching friction may increase or decrease depending on elasticities

of demand. In the next section, I introduce the background of NYC taxi industry

in which I empirically study matching efficiencies in a fully developed dynamic

version of the search model.

14

1.4 Industry Background

My model application is based on the New York City taxi industry. In NYC,

there are mainly two ways to get a ride, taxi or for-hire-vehicle(FHV). Taxis

can only pick up street hails and FHV can only pick up pre-arranged ride

requests. These two markets are strictly separated under the regulation of NYC

government. Running a taxi requires a medallion attached to the vehicle. The

total number of medallions available is fixed by regulation which is 13,587 in

2015. Medallion owners can trade medallions through auction. Along with

yellow taxis, there are 7,676 boro taxis introduced to the city in 2013. Boro

taxis follow the same rules as yellow taxis except for that they can only pick up

passengers in Northern Manhattan, the Bronx, Brooklyn, Queens and Staten

Island. Moreover, the boro taxis can only pick up passengers at the airport

that prearranged. Yellow and boro taxis follow the same pricing rule under

the regulation of Taxi and Limousine Commission (TLC). The medallion owner

can either operate the taxi himself or lease to other licensed drivers. In 2015,

there are 38,319 active taxi drivers running 13,587 vehicles. Usually, one driver

operates the vehicle for a shift of the day. The day shift starts at 6 a.m. and night

shift starts at 4 p.m. such that the expected revenues are equal between shifts.

Part of the medallions are owned by individual owners and part are owned by

fleets. Regardless of medallion ownership, the operation of the vehicle is by an

individual driver who either owns or leases the car.

The FHV also has different types, black car, livery or luxury limousine. Only

black cars can provide contracted service through a smartphone app. Other

types of FHV can only provide for-hire service by pre-arrangement. All FHV

vehicles are required to be affiliated with black car, livery or limousine bases.

Unlike taxis which have a fixed number of medallions FHV is allowed for entry.

Black cars include ridesharing companies such as Uber, Lyft and Via13. Uber

13Uber and Lyft also have black car bases. UberX drivers need to be affiliated with one ofUber black car bases in NYC. However, Uber vehicles are not physically dispatched from thebases such as luxury cars.

15

is a technology firm that provides a mobile app which creates a two-sided

market for on-demand transportation. Riders send a request for a ride to Uber

drivers through the Uber app. The information provided in the mobile app

includes fare (calculated on distance and time of the trip), and waiting time

before passengers are picked up. Active Uber drivers nearby receive the request

and they can choose either to take the order or not14. However, Uber drivers do

not know the destination before accept the request. If one driver doesn’t take

the request, it will be forwarded to another driver and so on. When demand

for Uber is high but supply is low, Uber charges passengers the regular fare

multiplied by a surge multiplier. By raising the fare, it intends to attract more

Uber drivers to compensate the demand and supply gap.

Unlike taxis, most Uber drivers work part time and use their own cars to

provide ride services. This makes it difficult to study Uber supply without

proprietary data that I will discuss later. Uber also provides different services

such as UberX, UberTaxi, UberPool, UberXL, SUV, etc. In this paper, I do not

distinguish car types of Uber. I treat all trips completed by Uber cars affiliated

with black car bases as identical.

1.5 Data

The data used in this paper comes from three sources. The main information

about taxis and Uber cars comes from trip records provided by the New York

City Taxi and Limousine Commission (TLC)15. The taxis trip records include all

trips completed by yellow taxis since 2009 and by boro taxis since 2013. Each

trip is an observation in the data including pick-up and drop-off date/time,

geographic location, trip distance and fare. One can calculate the interval

between pick-up and drop-off time to figure out trip time. One important

14An active Uber driver means that a driver opens Uber app and is willing to pick uppassengers.

15In the past years, the data is available to public by filing FOIL re-quest to TLC. Now, all trip records are accessible from TLC’s website,http://www.nyc.gov/html/tlc/html/about/trip_record_data.shtml.

16

limitation of the data is that there is no identifier of the taxi vehicle for each

trip. Moreover, I cannot tell where the vacant taxis are located until they pick

passengers up. Because of this, supply of taxis at any time-location is not

directly observed. Similarly, given only pickups data, I can not tell how many

passengers who want rides fail to match a taxi .

The other part of TLC data is FHV trip records which include trips by black

cars and luxury limousine. The method of collecting FHV data is different

from taxis which is submitted by FHV bases. Each observation in the FHV data

includes the base id that dispatches the vehicle for this trip, pick-up date/time

and taxi zone area of the pick-up16. I obtain the Uber trips according to base

numbers that the vehicle is affiliated with. The qualities of the data submitted by

bases also differ across companies. For example, only trip records submitted by

Uber bases include the pick-up zone. Thus, I only model Uber as competitor to

taxis without Lyft as a player. Lyft is not an effective player at that time. Out of

all black car trips, Uber accounts for 72.6% and Lyft accounts for 11.6%. Unlike

the taxi records, drop-off, trip distance, fare and trip time are not observed

for Uber. I solve the problem of trip time and distance by assuming the travel

distance and time between two locations are the same as taxis’ trips between

the same locations at the same time. The fare of Uber is calculated according to

Uber’s price rule after knowing travel time and distance. The drop off locations

of Uber are generated by my structural model.

The second source of data that supplements the main trip record is Uber’s

surge multiplier. Uber’s fare during a normal time is calculated based on trip

distance and time. However, during rush hours or when Uber’s supply is less

than demand, Uber applies surge pricing which multiplies the regular fare by a

surge multiplier. To calculate Uber’s trip fare, I use Uber’s API for developer to

collect the real time surge multiplier every 10 minutes at 79 selected location

spots across the city from November 2015 to June 2016. Each request via the

API returns the surge multiplier of different types of Uber products at that time16The taxi zones are not accurate as geographic locations which are areas defined by the TLC.

There are about 263 taxi zones in the NYC.

17

and I use multiplier of UberX as representative. Combining with trip records

data by matching location and time, I can calculate approximate fare of Uber

trips.

The third data I use is subway riderships obtained from Metropolitan Trans-

portation Authority (MTA) of the city. This data is used to calculate the number

of potential riders of a given location-time, a measure of market size. The

ridership data includes information on weekly aggregate entrances to each

station of the NYC subway. For a given station, the riderships are sorted by

various types of MetroCards that the customers swipe such as 30 day pass,

student, and full fare. I only count those paying full fare as potential passengers

of taxis and Uber since they are more likely to have the same travelling patterns

as taxi&Uber passengers compared to commuters. Thus, the market size of a

location at a given time is defined as the sum of taxi and Uber pickups and full

fare riderships. Those who choose subway as the outside option and who fail to

match a car comprise full fare riderships. To divide weekly aggregate subway

riderships, first I allocate ridership evenly to all locations near the station, then

I divide subway riderships of each location evenly for 7 days, and finally I

proportionally divide the daily riderships of a location based on taxi and Uber

pickups distribution over time of day.

1.5.1 Sample Construction

In the empirical part of this paper, I model drivers’ dynamic search across

locations over daytime of a representative weekday. I choose April of 2016 as my

sample period. My model focuses on equilibrium evolution of pickups over a

day and therefore for a given location-time I average pickups over all weekdays

of April 2016 as steady state pickups of this market17. The time period within a

17I do not model daily search and matching since computing (unobserved) supply anddemand of all days requires solving dynamic equilibrium many times which is computationallycostly. In the data, I find that pickups distributions over all weekdays are quite similar andby averaging across all weekdays I have good approximation of how pickups evolve within arepresentative day.

18

day in my sample is restricted to 6 a.m. to 4 p.m. Hence, my empirical model

studies search and matching during 6 a.m.-4 p.m. of a representative weekday

of April 2016. The main reason for doing this is that I do not have information

about how many active Uber drivers at a given time of day. Uber drivers have

much more flexible work time than taxis due to free entry and exit18 . Given

that I have no real-time data on active Uber drivers, I cannot model weekends

and night shift of weekdays when part-time Uber drivers are more likely to be

active. The implicit assumption I make is that during 6 a.m.-4 p.m. of weekdays,

the number of active Uber drivers is fixed (full-time drivers) such that supply is

tractable. The time period also covers the day shift of taxis such that the number

of taxis is also fixed.

I discretize time and space in the following ways. I define every 10 minutes

as a time period and 60 periods in total. Within each period, passengers and

drivers randomly meet only once within a location and successful contacts

become pickups of that location-period. In other words, each driver only

supplies once in a period19. I divide the city and select 40 geographic locations

as shown in figure 1.1. I define the area of each market by combining small

taxi zones and comparing pickups. For example, the area sizes of locations in

Queens and Brooklyn are large compared to those in Manhattan because the

pickups in outer boroughs are quite less. I exclude central park from this map

since all pickups within it is on the boundaries of the park and I assign pickups

in central park to locations nearby. The combination of location-period pair is

defined as a market (platform) in this paper. Finally, the pickups of a market are

calculated as monthly average pickups of the same market over all weekdays in

Aprial 2016.

The variables constructed from the data include trip distance, trip time,

fares and trip distribution. In a period, for a trip between any two locations, I

18One can check studies on labor supply by Chen et al.(2017) and Hall and Krueger (2016) forUber and by Farber(2008) and Frechette et al. (2016) for taxi

19Under this assumption that each driver only supplies once in a period the model couldunderestimate supply if the length of the defined period is long. For example, drivers couldcomplete a trip within 10 minutes and pick up another passenger.

19

calculate monthly average trip distance and trip time over all taxis’ trips between

the same two locations and of the same period20. I use this average trip distance

and time of any given origin-destination-period to calculate average fares of

taxis and Uber using their respective pricing structures. I multiply Uber’s

regular fare by monthly average surge multiplier of the same origin-period to

calculate the final Uber fare. The location spots I choose to collect the surge

multiplier are shown in figure 1.1. The trip time in minute is transformed into

number of 10-minute periods. For example, a 25 minutes trip takes 3 periods to

complete.

For any well defined market as a location-period combination, I construct

market size and distribution of passengers’ destinations. Market size is widely

used in discrete choice demand model to control substitution among inside

products to outside option when price increases. In my demand model, the

outside option of demand is subway. The population of a market is calculated

as sum of subway riderships and taxis & Uber pickups. Note that, these subway

riderships include both travellers who choose subway when making discrete

choice and those who choose taxis & Uber but fail to match one. I calculate the

market size in the following way. First, I divide weekly aggregate riderships

of a station by seven as daily average riderships. Many stations are located at

intersection corner of locations. I evenly assign riderships of a station to nearby

locations. Then I assume the subway riderships follow the same trendency

of taxis & Uber pickups over the time of day and divide subway riderships

proportionally over time of day21.

Finally, I calculate the trip pattern of all travellers. I do not have data of

distribution of all passengers’ destinations. Instead, I calculate the dropoff

pattern of taxis in November 2010 as proxy for population travelling pattern22.

There are two implicit assumptions in order to use this pattern as population

20This can only be calculated from taxis’ trips since data of Uber dropoffs is not available. Iassume the trip distance and time are same for Uber.

21By doing this, I retain the variations of subway market share across locations but not overtime of day.

22The reason of choosing November 2010 is that Uber and boro taxis are not available.

20

transportation pattern. First, I assume travellers paying full fare for subway

follow the same travelling pattern to taxis’ passengers in 2010. Second, the

travelling pattern of 2010 and 2016 are the same after Uber’s entry. The trip

pattern is defined for each market as shares of destinations. In other words, taxis’

distribution of dropoffs in 2010 is deemed as travelling pattern of population

in 2016 and distribution of taxis’ dropoffs in 2016 is outcomes of travellers’

discrete choice demand. In the next subsection, the sample and data overview

are provided.

Figure 1.1: 40 select markets and 79 spots to collect Uber surge multiplier

1.5.2 Sample Overview

The table B.1 shows monthly aggregate statistics of weekday pickups in Novem-

ber 2010 (22 days) and April 2016 (21 days). It demonstrates the distribution

of pickups by area, firm and shift. In April 2016, taxis’ monthly aggregate

pickups during day shifts is 3.7 million. Almost 93% of the total pickups are

21

in Manhattan, 4.59% are in JFK and Laguardia airports. My sample of 40

locations cover 99.38% of all taxis’ pickups during day shifts. Outer boroughs

has 2.24% pickups in total. Comparing pickups of taxis between 2010 and 2016,

I can observe huge decrease of pickups from 4.6 million to 3.7 million for day

shifts. The pickups distribution also has small differences that share of airport

increases from 3.42% to 4.59% and share of Manhattan drops from 93.67% to

93.17%. More differences can be investigated if I collapse Manhattan in many

smaller zones and compare the shares of pickups. This indicates that taxis’

supply and demand pattern changes slightly after Uber’s entry. Table B.1 also

includes Uber’s and Lyft’s pickups distribution in April 2016. Uber has different

distribution in comparison to taxis that 59.5% pickups are in Manhattan. The

share of Uber’s pickups in outer boroughs is 36.58% quite larger than taxis.

It indicates that during my sample period, only half of Uber’s pickups have

direct competition with taxis. The share of Uber’s pickups covered by my 40

locations is 77.63%. Lyft as second largest FHV firm has 0.2 million pickups

far less than Uber. Similarly, most of Lyft pickups are in outer boroughs. In

my demand model, I exclude Lyft from choice set. The variation of pickup

shares of taxi and Uber across locations as shown in table B.1 helps estimate

demand model similar to BLP demand model, in which variation of market

shares among products both within the same market and cross markets helps

identify price elasticities, product fixed effects and mean utility. The complexity

in my model is that pickup shares are not exactly demand shares considering

mismatches within market.

In random coefficient discrete choice model, we use market demographics

to identify random price coefficient. In my model, the demographics come

from exogenous travelling patterns of passengers defined by distribution of

destinations conditional on any given market. I use taxis’ dropoffs data of

November 2010 to approximate market demographics. I do not use dropoffs in

2016 as market demographics because it is endogenous outcomes of passengers’

discrete choice among taxi, Uber and outside option. Table 2.1 provides a

22

rough overview of distribution of dropoffs. The distribution is calculated using

pickups and dropoffs in day shift of weekdays. The first panel tells that 95.11%

of pickups in Manhattan are delivered within Manhattan and 3% to airports.

Trips originating from airports have 73.45% ending up in Manhattan and 6.37%

of them are inter-airport. Comparing 2010 and 2016, the dropoff distributions

are slightly different that trips originating from airports to Manhattan decrease

from 73.45% to 71%. Table 2.1 only shows travelling patterns among three

highly aggregate areas, Manhattan, Airport and Other. More variations of

travelling patterns can be discovered at the market level, which helps identify

random coefficient of prices. For instance, given two markets with same prices,

market size and supplies, differences in demands reflect differences in travelling

patterns. Finally, the destination distribution of taxis in 2016 also helps with

my demand estimation such that model predicted dropoffs of taxis match

observations in the data.

Table 1.1: Trip and share by firm, shift, and area

Firm&Shift Total Manhattan Airports Other 40 mktYellow Taxi 2010.11(22)Day shift 4,627,258 93.67% 3.42% 2.91% 98.93%Night shift 5,139,146 92.91% 3.46% 3.63% 98.99%Yellow Taxi 2016.04(21)Day shift 3,730,326 93.17% 4.59% 2.24% 99.38%Night shift 4,279,262 92.04% 4.94% 3.02% 99.27%Uber 2016.04Day shift 1,322,507 59.5% 3.92% 36.58% 77.63%Night shift 1,989,054 64.15% 4.1% 31.75% 82.43%Lyft 2016.04Day shift 215,240 40.10% 2.46% 57.44% 59.56%Night shift 301,577 49.64% 2.84% 47.52% 40.44%

23

Table 1.2: Distribution of dropoffs in day shift by firm

Obs. Manhattan Airports Queen&Brooklyn not in 40Yellow Taxi 2010.11(22)Manhattan 4,334,266 95.11% 3% 0.98% 0.89%Airports 158,410 73.45% 6.37% 8.15% 12.01%Queen&Brooklyn 84,925 47.53% 4.43% 42.13% 5.88%not in 40 49,657 41.50% 3.2% 9.04% 46.24%Yellow Taxi 2016.04(21)Manhattan 3,475,467 94% 3% 0.97% 1.17%Airports 171,407 71% 3.2% 10.73% 14.69%Queen&Brooklyn 60,274 42.6% 4.26% 44.89% 8.2%not in 40 23,178 45% 3.9% 17.3% 32.8%Uber 2016.04Manhattan 786,854Airports 51,855Queen&Brooklyn 187,912not in 40 295,886

24

At last, table 2.2 shows the statistics of key variables in my sample construc-

tion discussed in section 5.1. Given 40 locations and 60 periods in my sample,

there are 2,400 well defined markets. Uber’s surge multiplier varies from 1 to

1.37 as 90% quantile. Taxi and Uber prices are calculated at origin-destination-

time level which has 96,000 observations (i.e. 40 destinations of each market).

Uber’s fare on average is higher than taxi for the following reasons: 1, Uber

charges both trip time and distance; 2, there is surge multiplier; 3, Uber charges

minimum fare $7 which is higher than taxis for short trips.

Table 1.3: Summary statistics of key variables

variable Obs mean 10%ile 90%ile S.D.trip distance 3,643,011 2.61 0.6 5.6 3.34trip time 3,636,906 15.1 4.4 29.38 11.63trip fare 3,643,011 12.53 5 23.5 9.6final sample variablessurge 2,400 1.14 1 1.37 0.18taxi matches 2,400 72.28 8.80 163.02 57.34Uber matches 2,400 20.37 8.33 34.95 10.25taxi fare 96,000 17.68 7.92 28.4 10Uber fare 96,000 22.39 9.12 37.95 12.48trip distance 96,000 5.07 1.19 9.88 4.10trip time 96,000 23.78 8.97 39.11 12.35

In figure 1.2, it displays the comparison of trip time in 2010 and 2016. The

difference in distributions implies worse traffic condition in 2016. For example,

the median of trip time in 2010 is 18.73 minutes. The median of trip time in

2016 is 22.62 minutes. The trip time in terms of periods of 2016 is also higher

than 2010. In 2010, more than half of trips take less than two periods to deliver.

However, more than half of trips in 2016 takes 3 or more periods to deliver. In

the second counterfactual of this paper, I replace the trip time of my sample

by the trip time of 2010 to study how traffic improvement affects the matching

efficiency in new equilibrium.

In order to show the differences of expected profits across markets, I calculate

the expected profit conditioning on randomly picking up a passenger for each

25

Figure 1.2: Comparison of traffic speed in 2010 and 2016

26

Figure 1.3: Distribution of expected profits of taxi and Uber

27

market. I obtain 2400 (40 ∗ 60) expected profits in total. The distributions

of expected profits for taxi and Uber are shown in figure 1.3. For taxis, the

average expected profit is 15.27 and it ranges from less than 10 dollors to

almost 60 dollors. The distribution for Uber has mean of 13.94 dollars without

surge multiplier and 18.21 dollars with surge multiplier. It implies that Uber

driver’s expected profit is higher than taxi in general. This high heterogeneity

in profitability as shown in figure 1.3 illustrates the incentive of drivers’ search

decisions and why some markets are oversupplied than others. However, the

expected profit calculated here is static flow profit. Drivers’ search decisions are

made based on dynamic search values. In the following sections, I will build a

dynamic model and with the estimates I can compare the differences in search

values across markets.

1.6 Empirical Model

The structural model fully extends the search and matching model discussed

in section 3. Taxi and Uber drivers make dynamic spatial search decisions

among I locations over T periods in a day. Potential passengers make static

discrete choice decision among Uber, taxi and subway. Drivers and passengers

have perfect information about the size of either side in a given market. When

making supply/demand decision, the agent accounts for both the indirect

network effects from the other side of the market and direct network effect from

the same side. This supply sensitive demand specification is one contribution of

this paper relative to Buchholz (2016). The model allows two types of frictions

that prevent the market from clearing. First, within location I allow taxis and

passengers to not fully contact with each other due to coordination failure as in

Burdett, Shi and Wright (2001). However, I assume perfect matching of Uber

within the market. Matching is perfect in airports for both taxis and Uber. In

other words, I simplify the matching process within a market by assuming a

matching process with an explicit functional form. Second, across locations

28

because of drivers’ endogenous search decisions there are locations exhibiting

excess supply along with other locations with excess demand. Both frictions

result in inefficient matching at the city aggregate level.

Before delving into demand and supply decisions, I assume the timeline

within a market is as follows. At the beginning of each period, part of taxis and

Uber cars will arrive at their destinations. If the car has a passenger on board

(employed), it arrives at the dropoff location. If the car is vacant (unemployed),

it arrives at the location based on the driver’s search decision in the last decision

period. Some of the cars either employed or unemployed are still on their way

to the destinations and will not necessarily arrive at a location in this period.

All arriving cars become supply to that market in this period23. A passenger in

this market has perfect information about fares and beliefs on demand/supply,

how likely he will find a taxi or Uber car, and how long it takes to match24.

Passengers make static discrete choice decision. Aggregating all passengers’

decisions returns demand for each firm in this market. Then matches are made

within market and firm. Unmatched passengers either due to excess demand or

matching friction leave with subway. Employed drivers deliver passengers to

their destinations and unemployed drivers choose next locations to search.

23It assumes that a driver must stay in this location for at least one period.24Uber’s supply can be perfectly learned by app which shows how many cars around and

how long to wait. Taxis’ supply is hard to directly observe. However, my model studies demandand supply only in equilibrium such that passengers are fully experienced and know how likelyto get a car without necessarily knowing how many cars nearby.

29

(un)Employed

drivers ar-

rive and

become

supply.

Passengers

make

choices.

Matches

are made

between

drivers

and pas-

sengers

within the

market.

Unmatched

passen-

gers leave

with

subway.

Employed

drivers

deliver

passengers

and un-

employed

drivers

make

search

decisions.

timing of supply, demand and match of a market

1.6.1 Passengers’ Choice Problem

In a market defined by a location-period combination, a group of potential

travellers (market size) make discrete choice among taxis, Uber and subway

conditional on their exogenous destination with knowledge on prices, product

qualities, supply and demand. In this model, Uber is denoted as x (UberX),

taxi as y (yellow taxi) and outside option as o. The utility of a passenger c in

location i at period t choosing firm f = x, y, o to travel to j prior to matching

process is:

Uijc f t,pre = G(τf (ui

f t, vif t), ui

f t, vif t, pij

f t, Xif t, εi

c f t)

= τif tU

ijc f t,post + (1− τi

f t)Uijcot,post

(1.4)

where uif t is market demand for firm f , vi

f t is firm f ’s supply and pijf t is the price

from i to j. The function τif t = τf (ui

f t, vif t) is the probability of being matched

by choosing firm f determined by the firm specific demand and supply level in

30

the market. The matching probability does not differ for different destinations j

under the implicit assumption that drivers cannot reject a ride. The probability

τ(uif t, vi

f t) can be written as m(vif t, ui

f t)/uif t with matching function m(vi

f t, uif t).

The function form of m will be discussed later. In addition to effects of uif t, vi

f t

on matching probability, they could also affect the utility through classical

direct network effects. For example, the user base uif t in the market could

affect individual’s choice decision as outcome of consumers learning from each

other or herd behaviors (Goolsbee and Klenow (2002)). The supply vif t affects

choices through indirect network effect25. Higher vif t could increase utility

by decreasing waiting time after conditioning on being matched. I assume

Ucot,post = 0 which implies that unmatched passengers end up with zero utility

by taking subway. Furthermore, I assume the logarithm of Uijc f t,post is linear

such that (1.4) can be rewritten as :

ln(Uijc f t,pre) = ln(τi

f t) + ln(Uijc f t,post)

= θ1 ln(vif t) + θ2 ln(ui

f t) + dx + di + t + ξ if t︸ ︷︷ ︸

δif t

+αij ln(pijf t) + ε

ijc f t

(1.5)

Equation (1.5) is obtained by: 1, transforming τif t as a linear combination of

ln uif t, ln vi

f t; 2, assuming ln(Uijc f t,post) is linear in ln ui

f t, ln vif t and other chara-

teristics including price pijf t, Uber fixed effect dx, market fixed effect di, time

fixed effect dt, unobserved demand shock ξ if t and idiosyncratic shock ε

ijc f t. The

benefit of these assumption is that all endogenous variables of the model uif t, vi

f t

are contained in parameter δif t such that demand is simple to solve. In other

words, unobserved endogenous demand u and supply v which need to be

solved through structure are separated from estimating price coefficients26. The

25In this paper, I misuse the concepts of indirect network effect and cross-network effect sothat they are interchangeable.

26In details, given values δif t and αij, demands are fixed when I iteratively solve equilibrium

supply. If matching probabilities interacts with price, update of supply requires update ofdemand as well. More details are in section 7.

31

drawback of log-linearity assumption of τ is that coefficients θ in (1.5) measures

the joint effect of vif t or ui

f t without distinguishing channels through matching

probability or through classic network effects (i.e. product variety, word-of-

mouth.). The price coefficients αij depends on travel distance and trip type

which are parameterized as:

αij = ∑k=1,2,3

αk1{distij ∈ Ik}+ α41{distij ∈ IJFK} (1.6)

where I1 is for trip distance less than 3 miles, I2 is for distance between 3 and

6 miles, I3 is for distance greater than 6 miles and IJFK is trips between JFK

airport and Manhattan which charges flat rate. Finally, I assume the utility of

choosing subway before the matching process as:

ln(Uijcot,pre) = δi

ot + εijc0t (1.7)

where δiot is normalized to zero. Since the subway fare is fixed for single trip

regardless of trip length, there is not price in 1.7.

I allow substitution between taxi and Uber by assuming a nested logit

demand model such that:

εijc f t = ζ

ijcgt + (1− β)ν

ijc f t (1.8)

where ζijcgt is common to taxi and Uber which are categorized as one group,

and subway alone as the other group. Variable νijc f t is assumed to follow type

I extreme value distribution. The distribution of ζijcgt satisfies that ε

ijc f t is also

an extreme value random variable. The parameter β measures substitution

between taxi and Uber. When β = 0, it is equivalent to the simple logit demand

model. Larger β implies stronger substitution pattern between taxi and Uber.

Then, the choice probability conditioning on route ij at time t becomes product

of choice probability within group and probability across group. Within the

group of taxi and Uber, the choice probability is:

32

sijy|gt =

exp((δif t + αij ln(pij

f t))/(1− β))

exp((δiyt + αij ln(pij

yt))/(1− β)) + exp((δixt + αij ln(pij

xt))/(1− β))

(1.9)

Let us denote the denominator of equation 1.9 as:

Dg = exp((δiyt + αij ln(pij

yt))/(1− β)) + exp((δixt + αij ln(pij

xt))/(1− β)) (1.10)

The probability of choosing the group of taxi and Uber is:

sijgt =

D1−βg

1 + D1−βg

(1.11)

Then the choice probability becomes sijf t = sij

f |gt ∗ sijgt.

In the traditional way, I can estimate demand by matching choice probabil-

ities of to the market shares obtained by dividing demand uijf t by the size of

people travelling from i to j as Berry (1994). However, there are two obstacles to

do this in this paper. First, I can only observe pickups mijf t rather than demand

uijf t. Thus, I cannot calculate market share of demand. Second, even though

assuming matches equal to demand such that uif t = mi

f t, I cannot calculate

uijxt for any j of Uber without knowing the destination distribution of Uber

trips. In other words, I can not directly estimate equation (1.5) at the route level

{i, j, t}. Instead, I treat the choice probability as the model prediction for the

conditional (on destination) market share and aggregate sijf t over j to calculate

the unconditional market share.

The exogenous distribution of passengers’ destination in a market {i, t} is

denoted as Ait = {a

ijt }∀j where aij

t is the probability that a passenger from this

market travels to j. The unconditional market share predicted by the demand

model is:

33

sif t = ∑

jaij

t sijf t (1.12)

Denote the market size as λit. I can calculate the potential demand before

matching process as:

uif t = λi

tsif t (1.13)

In comparison to the exogenous distribution of travellers’ destinations Ait, I

can also calculate the dropoffs distribution of each firm Aif t as outcomes of

passengers’ discrete choice using Bayes’ rule. Thus, the model predicted firm

specific destination distribution becomes:

aijf t =

aijt sij

f t

sif t

(1.14)

I put tilde and firm index f in aijf t to distinguish from aij

t .

To summarize the demand side, I assume passengers make demand decision

before matching process but with belief of demand and supply level as proxy

for matching probability, waiting time, and network effects. Given a set of

demand parameter values, the demand model can predict two main things.

First, the model predicts market shares sif t and demand ui

f t. Second, it predicts

endogenous distribution of firm’s dropoffs A f . Though, I cannot directly

observe demand and supply in the data, in the estimation section, I will discuss

how to solve supply/demand by fitting model predicted pickups to pickups

observed in the data.

1.6.2 Drivers’ Choice Problem

At the end of each period, if the driver is employed, he will travel to the

destination requested by the passengers. Drivers can not refuse to deliver a

passenger once being matched. The probability of an employed car of firm f

34

in location i at time t travelling to destination j is aijf t which is obtained from

equation (1.14). Search decisions are made only by unmatched drivers at the

end of each period.

If the driver is unmatched after the current period, he makes a decision on

which location to search for passengers in the next period. Drivers are identical

within firm and make individual decisions without coordination of the firm.

Similar to passengers, when drivers consider a location to search in the next

period, they know the matching probability, expected profit conditional on

being matched and continuation value if not matched in that location. In order

to know the matching probability, drivers need to have rational expectation

of demand and supply distribution across locations in the future. A standard

dynamic oligopoly model is inappropriate for this game due to the large number

of drivers in the game. For example, the number of possible states of allocating

N drivers into I locations will be CI−1N+I−1 which is large when N is large27. The

model would be intractable and computationally infeasible if drivers’ expected

profits are taken over all possible market states. Instead, I assume drivers make

search decision only on their own state and knowledge of the deterministic

market evolution of demand and supply distributions. This concept comes

from oblivious equilibrium (Weintraub et al.(2008)) when players are atomistic

and individual decision does not measurably impact aggregate market state.

In equilibrium, drivers’ belief is consistent with realized supply and demand

distributions.

At the end of a period, an unmatched driver of firm f in location i makes a

search decision after observing supply shocks {εj}∀j by choosing the location

with maximum value:27This number is obtained by counting the number of outcomes of putting N balls in I

different urns CI−1N+I−1 =

(N + I − 1)!(I − 1)!(N)!

allowing for empty urns.

35

j∗ = arg maxj{V j

f t+χijt− cij

t + ρ f (Vj

f t+χijt−min

l{V l

f t+χilt}︸ ︷︷ ︸

∆jf t

)1χ

ijt =1

+ εjf } (1.15)

where cijt is the cost of travelling from i to j calculated as cij

t = 0.75 ∗ distanceijt .

The cost per mile is set to be 0.75 dollars. V j

f t+χijt

is driver’s ex-ante value of

searching location j in period t + χijt before the matching process in period

t + χijt . The number of periods travelling from i to j at t is χ

ijt which is time cost

compared to cijt . Drivers are assumed not to pick up passengers along his way

to the search location. When the driver chooses j which is far from i, he has to

account for the loss of not searching for passengers until the next χijt periods.

This time costs plays two important roles in the model. First, it contributes to

mismatches across locations due to mobility. For example, a location i has many

vacant cars at the end of period t, while in t + 1 there are many passengers

in j far from i. This may result in excess supply in locations near j but excess

demand in j at t + 1. Second, I can study benefits of traffic improvement by

changing χijt . Both cij

t and χijt are allowed to vary over periods t and route i, j,

but common to Uber and taxis. These two variables can be directly calculated

from the data. At last, the parameters ρ f measures extra benefits of searching

locations that are close to current location i, χijt = 1. The difference of V j

f t+χijt

minus the minimal values guarantee non-negative benefit. The ex-ante value is

defined as:

V jf t = φ

jf t

(∑

lajl

f t(pjlf t − cjl

t + V lf t+χ

jlt))+

(1− φjf t)Eε

[max

l{V l

f t+χjlt− cjl

t + ρ f ∆jf t1χ

ijt =1

+ εlf }]. (1.16)

In equation (1.16), φjf t denotes the matching probability of drivers, φ

jf t = mj

f t/vjf t.

Conditional on being matched, the expected profit is obtained by averaging over

36

all possible destinations l with weights ajlf t. Recall that ajl

f t measures firm specific

destination distribution obtained in (1.14). The profit conditional on completing

trip jl includes the fare of the trip, cost of travelling, and continuation value in

location l after dropoff in t + χjlt period.

The second part of (1.16) is the continuation value of not being matched in

j. The interpretation of each variable is the same as (1.15). Since drivers do

not observe realized supply shock ε’s until the end of period, the continuation

value takes expectation over all possible supply shocks. I assume the supply

shock ε f to follows i.i.d T1EV distribution with scale parameter σf for each firm

f such that the continuation value of unmatched has an explicit form:

Eε maxl{V l

f t+χjlt− cjl

t + ρ f ∆jf t1χ

ijt =1

+ εl}

= σ log(Σl exp((V l

f t+χjlt− cjl

t + ρ f ∆lf t1χil

t =1)/σf ))

(1.17)

Given the feature of supply shock’s distribution, I can calculate deterministic

transition probability of unemployed drivers such that the probability of an

unemployed driver of firm f in location i searching j in the next period is:

πijf t =

exp((V j

f t+χijt− cij

t + ρ f ∆jf t1χ

ijt =1

)/σf )

Σl exp((V lf t+χil

t− cil

t + ρ f ∆lf t1χil

t =1)/σf )(1.18)

The scale parameter σf controls for incentives of drivers searching certain

locations captured by continuation values other than shocks. For example, large

σf implies that drivers’ search decisions are largely driven by random supply

shocks which leads to an even allocation of drivers’ searches across locations.

Recall the transition of employed cars following the dropoffs distribution of

passengers {aijf t} calculated in (1.14). Combining the transition of employed cars

A f and the policy function of unemployed cars Π f of equation (1.18) gives the

law of motion for state transition. The state includes the status of all in-transit

cars. The state at the beginning of period t is a collection of {Sit}∀i where Si

t

37

is a collection of {vif t,k} f ,k with vi

f t,k indicating the number of cars for firm f

that will arrive at location i in the next k periods. When k = 1, it implies that

the supply at period t satisfies vif t = vi

f t,k=1. At the end of each period, the

transition of employed and unemployed cars update the state such that:

vif t+1,k = vi

f t,k+1 + Σjmjf t a

jif t1χ

jit =k

+ Σj(vjf t −mj

f t)πjif t1χ

jit =k

, ∀ f , i, k (1.19)

To interpret (1.19), at beginning of period t + 1, the number of firm f drivers

that will arrive at location i in k periods is composed of three parts: (1) those

who will arrive at i in k + 1 periods at the beginning of period t; (2) those

who pickup passengers at time t and will arrive at i in k periods; (3) those

unemployed drivers of period t who decide to search location i next but will

arrive in k periods. In the next section, I discuss the matching function applied

to calculate matches in the demand and supply decisions.

1.6.3 Matching Function

During the matching process in each period within a location, I use an explicit

functional form to predict the matching outcomes. In the works of Buchholz

(2016) and Frechette et al.(2016) studying NYC taxi industry, they all assume a

matching process with friction for taxis within a location. Frechette et al.(2016)

simulate the process of taxis searching over grids within a location for pas-

sengers. Buchholz (2016) assumes an urn-ball random matching process and

a corresponding explicit functional form can be derived by Burdett, Shi and

Wright (2001). I use the same functional form as Buchholz (2016) and Burdett,

Shi and Wright (2001) with a modification to reflect heterogeneity in frictions

across locations. This matching process is only applied to taxis within locations

outside two airports. For taxi in airports and Uber in all locations, I assume

perfect matching within the location. I will discuss both functions below.

First, I introduce the random matching of taxis in locations other than

38

airports. Given taxis’ demand uiyt and supply vi

yt in location i at period t, I

assume that passengers randomly visit the taxis and of those visiting the same

car only one can be successfully matched. Other unmatched passengers will

leave with the subway. I do not distinguish where passengers and cars are

located within the market such that all cars are identical to the passengers. That

means a passenger has equal probability visiting any car. Each car receives a

passenger’s visit with probability 1/viyt. Therefore, the probability of a taxi not

receiving a visit is (1− 1/viyt)

uiyt . The probability of a taxi being matched is

1− (1− 1/viyt)

uiyt . However, in locations with larger size of area, it is different

to know the exact location of cars. Thus, I add an location specific parameter γi

such that the probability of a car being matched becomes 1− (1− 1/(γiviyt))

uiyt .

Higher value of γi will decrease the probability of being matched. To be specific,

I define γi = γ1{i ∈ CentralManhattan}+ γ2{i ∈ OuterBorough}. Since taxis

within i have the same probability of being matched, and therefore the number

of matches is:

m(uiyt, vi

yt) = viyt

(1− (1− 1

γiviyt)ui

yt)

≈ viyt(1− exp(−

uiyt

γiviyt))

(1.20)

Function (1.20) itself allows matching friction due to coordination failures such

that there is possibility that some cars receive no visits and some passengers are

not matched.

As for Uber and aiports, the matching between drivers and passengers is

assumed to be frictionless. Uber use mobile technology to assign passengers

and drivers into a one-to-one pair without coordination failure as above. As for

airport, drivers are waiting in a queue to match passengers one by one without

coordination failure as well. However, I do not model the queueing process as

Buchholz (2016) for simplicity. The explicit functional form of perfect matching

39

Figure 1.4: Hyperbolic function for perfect matching

is mixt = min{ui

xt, vixt}. However, one drawback of this function is that it is not

always invertible given any two variables for the third variable. For example,

when mixt = vi

xt the solution of uixt is not unique. Instead, I use a hyperbolic

function to approximate perfect matching as shown in figure 1.4. When the

demand-to-supply ratio is greater than 1, the matching probability of drivers

approaches 1. When the ratio is less than 1, the matching probability approaches

45 degree line that is mixt ≈ ui

xt. The explicit matching function form of figure 4

is obtained by solving mixt from (with small value of ε):

(mi

xt

vixt− 1)(

mixt

vixt− ui

xt

vixt) = ε (1.21)

Even when mixt = vi

xt, it can returns an uixt though its value depends on the

curvature rather than any economic assumption. In the next section, I will

discuss equilibrium of the model in details.

1.6.4 Equilibrium

I use the equilibrium concept of OE such that unemployed drivers make search

decision based on his own state and knowledge about state evolution of the

40

market. The key information about the market state is the distribution of supply

and destination distribution of in-transit cars. Driver’s own state is denoted as

st which includes his location at time t. The state of the city at time t is denoted

as collection {S it}i∈I . For any i, S i

t includes information about arrival of cars

in next K periods, hence collection {vif t,k} f ,k∈K. In OE, drivers make optimal

search decisions according to {st, {S it}∀i,t}. Drivers’ belief on the evolution

of market state (i.e. supply distribution) is consistent with the realized state

in equilibrium28. Given the deterministic evolution of supplies, equilibrium

demand can be simply calculated for each market due to the static discrete

choice assumption. The definition of equilibrium is summarized as follows:

Definition Equilibrium is a sequence of supply {vif t}, beliefs of state transition

{vif t,k}, policy function of unemployed cars {πij

f t}, transition of employed cars

{aijf t} for ∀i, t, f and given initial distribution of supply {vi

f t=1} such that:

1. At the beginning of each period t, in any location i, passengers make

discrete choice between firms based on (1.4)-(1.11). Market demand is

calculated from (1.13).

2. Matches are made randomly between supply and demand for each firm,

location and time. Within location, the matching process follows (1.20) for

taxis and (1.21) for Uber and taxi in airport.

3. Transition of employed cars follows {aijf t} obtained by Bayes’ rule (1.14).

4. At the end of each period, unemployed drivers follow policy function πijf t

calculated in (1.18) based on beliefs of state transition {vif t+1,k}.

5. Realized state transition is obtained by combining both employed {aijf t}

and unemployed cars {πijf t}. State of next period is updated to vi

f t+1,k by

(1.19).

28Another way to understand the OE in this model is that instead of knowing evolution ofsupply distribution, drivers know the evolution of ex-ante search values {Vi

f t}∀i,t. Knowingsupply distribution or search values are interchangeable given one step calculation of (6.8).

41

6. At the beginning of next period, both employed and unemployed cars

arrive and form the new supply vif t,k=1 = vi

f t.

7. Drivers’ belief is consistent such that vif t+1,k = vi

f t+1,k for all i, t, f , k

My model’s equilibrium is quite similar to Buchholz(2016) and still satisfies

finite horizon and finite action-space for existence of equilibrium. In the next

section, I will explain estimation process. The main idea of estimating this

model is to solve unobserved equilibrium demand and supply such that the

equilibrium model-generated matches fit the pickups observed in the data for

all well defined markets {i, t}i∈I,t∈T.

1.7 Estimation

In this section, I will discuss the estimation process of my model in detail.

The key feature of this estimation is that supply and demand level in any

given market are not directly observed in the data. Instead, the data only

has observation of pickups, which are the outcome of underlining matching

process given supply and demand. Thus, estimation of the model is searching

for parameter values, equilibrium demand and supply that generate outcomes

fitting the data. The demand side parameters include mean utility {δif t}∀ f ,t,i,

price coefficients {α1, α2, α3, α4}, and substitution parameter β. The supply

side parameters include supply shock parameter σf , bonus of searching nearby

locations ρ f . Finally, there are parameters defining the matching function of

taxis {γ1, γ2}. Given the values of these parameters, I can solve equilibrium

supply v f and demand u f , f = 1, 2. Then parameters in δ can be estimated

using linear regression.

This process of estimating these parameters can be summarized as figure

1.5. Given demand parameter values and market size, market demand can be

calculated. Then, given supply side parameters values and drivers’ optimal

decisions I can calculate supply using backward induction due to the finite time

42

of the model. Finally, the matching function can predict pickups given supply

and demand above. The model is estimated once the model predicted pickups

equal pickups in the data and model generated transitions of employed taxis

follow the same dropoff distribution of taxis in the data.

Initialguess of{α, β, γ, σ, ρ}

guessmean

utitiliy δ

calculatedemand u

solve fixedpoint

supply v

calculatematches m

calculatedropoffdistribu-tion of

taxis Ay

ivreg δequation

for θ

α, β σ, ρ

γ

δ

update δ′

ifmi

f t 6= mif t,

∀ f , t, i

estimate{α, γ, σ, β, ρ}NLLS‖my(Ay −Ay)‖

Figure 1.5: Overview of the estimation process

In general, the process is similar to estimating a random coefficient discrete

choice model but with more complexities. Given a set of nonlinear parameter val-

ues {α, γ, σ, β, ρ}, I solve the fixed point for mean utilities δ such that the model

predicted shares of pickups equal shares in the data29. Given δ(α, γ, σ, β, ρ; m),

I estimate nonlinear parameters using nonlinear least square estimation to di-

minish the difference between model predicted dropoffs of taxis to the dropoffs

in data. Parameters within δ are estimated using linear IV regression because

of endogeneity of supply v and demand u in demand equation. The instrument

29The definition of nonlinear parameters here follows Nevo (2000). He denotes parametersoutside mean utilities as nonlinear parameters and parameters within mean utilities as linearparameters.

43

variable I use for supply and demand is dropoffs of cars from the same and

opponent firm in the market and market size. Recall that supply of a market

comprises arrivals of employed and unemployed drivers. Demand shock influ-

ences arrival of unemployed drivers but employed drivers drop passengers off

according to exogenous destination of passengers regardless of the demand in

that destination. In the following subsections, I first discuss NLLS estimation as

step 1 followed by IV regression as step 2.

1.7.1 Pre-estimation Discussion

1.7.1.1 Number of Taxi and Uber Drivers

In order to predict the supply distribution over locations and time, I have to fix

the total number of cars both for taxis and Uber. The supplies are intractable

if drivers can enter or exit in any location and at any time. Even with fixed

number of cars, I need to assume an initial supply distribution of cars at period

1. I assume the fixed number of taxis in my model as 13,587 which is the total

number of medallions30. As for Uber, though there are around 26,000 Uber

affiliated cars, most of them only work part-time or in weekends. In Chen et al.

(2017), they have detailed data about Uber drivers’ working hours. They define

types of driving schedules of Uber drivers into evening, morning, late-night,

weekend and infrequent categories and find a transition matrix of Uber drivers

among these types of schedule across weeks as cited in figure 1.6. For example,

in the first row, 11.0% of evening driver in this week will switch to morning

drivers in the following week. In my paper, working patterns of individual

drivers is irrelevant since I do not distinguish identities. I obtain the fixed

number of daytime drivers by calculating the stationary distribution of the

markov chain in figure 1.6. In the stationary distribution, there are 10% morning

drivers which is equivalent to around 3,000 Uber cars in NYC. Thus, I assume

30Buchholz (2016) uses the number of medallions as total taxis in his model. Frechette etal.(2016) also find that almost 80% of minifleets and 70% of self-owned taxi medallions areactive during day shift hours.

44

the number of active Uber cars in my sample hours from 6 am to 4 pm to be

3,000.

Figure 1.6: Uber drivers’ working schedule table cited from Chen et. al.(2017)

1.7.1.2 Passengers’ Destinations

As mentioned in the sample construction, in the demand side I need to know

the exogenous destinations of the travelling population composed of taxi &

Uber passengers and subway passengers paying full fare. It is important to

note that travellers with subway pass or taking other transportation tools (i.e.

bike, bus, and walking) are not considered. There is no data available on the

city transportation pattern. Thus, I use taxis’ pickup-dropoff pattern of 2010

as proxy for the population travelling pattern in my model. The two implicit

assumptions here are that: first, the pattern doesn’t change due to Uber’s entry;

second, subway passengers paying full fare follow the same travelling pattern

as taxi passengers. Thus, the destination distribution of population, denoted as

{Ait} in the model, conditional on markets of origin can be nonparametrically

calculated using taxis trip records in 2010.

1.7.2 Two-Step Estimation

1.7.2.1 Step 1: Estimating Nonlinear Parameters

The first step is to estimate {δ, α, β, γ, σ, ρ}. The estimation process can be

further broken into two procedures. First, given the parameter values of

45

{α, β, γ, σ, ρ}, I need to solve equilibrium demand as function of mean utilities

δ and supply such that model generates the same pickups as observed in the

data. Second, in the outer loop of first procedure, I update {δ, α, β, γ, σ, ρ} to

minimize deviation of model predicted distribution of dropoffs for matched

taxis to the dropoff distribution in data. The first procedure is similar to Buch-

holz (2016) with an extra calculation due to the introduction of discrete choice

demand to the model. In Buchholz (2016), he searches for equilibrium demand

u which generates pickups in the sample. Instead of solving for demand u, I am

solving for fixed mean utilities δ which have one-to-one mapping to demand

according to BLP contraction mapping. Solving mean utilities is necessary to

generate destinations of matched passengers for each firm A f which forms

objective function of the second procedure.

In details, the first procedure is as follows. Given parameter values {α, σ, γ, ρ, β},I make initial guess of all mean utilities {δi

f t}∀ f ,t,i which are obtained by using

pickups as demands to calculate market share and applying BLP contraction

mapping to back out mean utilities. Given the initial guess mean utilities and

demands, I need to figure out corresponding equilibrium supplies {vif t}∀ f ,t,i.

Instead of an arbitrary guess of supplies, I use backward induction to calculate

my starting point for equilibrium supply. In details, from the last period T,

given the demand distribution and zero search values Vif t = 0, ∀t > T, I cal-

culate continuation values {Vif T} for an arbitrary supply distribution {vi

f T}31.

For period T − 1, given the search values {Vif T} and demands {ui

f T−1}, I can

calculate search values {Vif T−1} and updated supplies of next period {vi

f T} for

an arbitrary supply distribution {vif T−1}. Repeat this process backward until

period t = 1. The supply distribution in period 1 is assumed to be proportional

to pickups distribution of period 1. This process returns my starting values of

supplies v. I iterate the process of updating supplies and search values from

31The day ends for taxi drivers in period T due to shifts. However, Uber drivers have no shifts.Uber drivers may continue to work after period T with positive search values. In this estimation,I assume search values are equal over locations for t > T and normalized to 0. Normalizationwon’t affect transition probabilities since constants are cancelled out by equation 1.18.

46

Algorithm 1 Solve Equilibrium Supply

1: Set parameter values for {σ, α, γ, ρ, β} and {δif t}∀ f ,i,t

2: Guess supply {vif T} f ,i, calculate {ui

f T} f ,i, {Vif T} f ,i

3: for τ = T − 1 to 14: Guess {vi

f τ} f ,i, reset state of in-transit cars {vif t,k}t>τ = 0

5: for t = τ to t = T6: Compute market share {si

f t} and demand {uif t}

7: Compute matches mif t = m(ui

f t, vif t)

8: Compute transition of employed cars {aif t}

9: Compute transition policy of unemployed cars {πif t}

10: Update {vif t+1,k} based on {πi

f t}, {aif t}

11: Update value {Vif t} of current period

12: Update supply of next period vif t+1 = vi

f t+1,k=113: end14:end15:Fix τ = 116: Iterate step 5 to 1317: Stop until step 11 and 12 won’t update under certain tolerance level.

t = 1 forward to t = T until supplies and search values stop updating such

that equilibrium supplies are obtained. The whole procedure is summarized

in algorithm 1 below. I find starting point of supplies for iteration in step 2-14.

Step 15-17 is the iteration for equilibrium supplies32. This procedure generates

mapping from mean utilities to equilibrium demands u = u(δ) and supplies

denoted as v = Γ(δ). The pickups generated by model are m = m(u(δ), Γ(δ)).

In order to fit pickups to the monthly average pickups m, I need to update mean

utilities in the outer loop of the procedure above. The outer loop is summarized

in algorithm 2.

The second procedure follows the first one to estimate {α, σ, γ, ρ, β} given

the transition probability of matched cars {Aiyt}. For each of the 60 time

periods, the transition probabilities form a 40 by 40 matrix. Instead of matching

32This process does not satisfy contraction mapping. In order to find the fixed point solution,I applies iterative method of average damping.

47

Algorithm 2 Solve Fixed Points of Mean Utility

1: Guess demand {uif t}0 based on observed pickups {mi

f t}2: Calculate market share si

f t and guess initial {δif t}0

3: Iterate BLP contraction mapping to solve for {δif t}1 to match market shares

4: Plug {δif t}1 into algorithm 1 to solve for {vi

f t}5: Invert matching function with {vi

f t, mif t} for {ui

f t}6: a: vi

f t > mif t, update ui

f t7: b: vi

f t ≤ mif t, don’t update ui

f t8: Given updated {ui

f t}1, solve BLP contraction mapping for {δif t}2 and {Ai

yt}9: a: Σ f ui

f t < λit, update δi

f t10: b: Σ f ui

f t ≥ λit, set ui

xt = uif tm

ixt/Σ f ui

f t and uiyt = λi

t − uixt, update δi

f t11: Repeat step 4 to 1012: Until |δk+1 − δk| < ε13: Report {Ai

yt}, transition of employed taxis

the probabilities point-to-point to probabilities in the data, I aggregate the

pickups and dropoffs over locations and periods and recalculate the transition

probabilities in larger areas over 20 half hours. This process applies to both data

and model generated transitions. Then I calculate the sum of squared deviations

between model generated transition of taxis to the observed transition of taxis

in data as my nonlinear least squares objective function. Estimators are defined

as 1.22 below:

{α, σ, γ, ρ, β} = arg minα,σ,γ,ρ,β

Σt,i(mi

yt(Aijyt − Aij

yt(α, σ, γ, ρ, β)))2 (1.22)

1.7.2.2 Step 2: Estimating Linear Parameters

Given the estimates of {Θ, m, δ, u, v} with Θ = {α, σ, γ, ρ, β} in step 1. I can

calculate variables in mean utility equation that are not directly obtained in

data such as market demand and supply in equation (1.5). In the specification

of mean utility, the coefficient on demand measures direct network effect and

coefficient on supply measures indirect network effect. An OLS regression of

48

equation (1.5) suffers endogeneity problem since demand and supply are all

correlated with unobserved demand shock ξ if t. For supply vi

f t, I use arrival of

employed cars of firm f at the beginning of period as instrument. The argument

is that these cars visit location i because of their passengers’ destination. It is

reasonable to assume that demand shock of current period is not correlated with

the destination of passengers picked up from other locations in previous periods.

One exception to this assumption could be that some passengers visit location

i to pick someone up and leave i immediately. This instrument is correlated

with supply as it constitute supply together with arrival of unemployed cars.

To solve to endogenous problem of demand, I use two instruments, market size

λit and arrival of opponent’s cars. Market size is exogenous and correlated with

demand as in (1.13). Arrival of opponent’s cars are uncorrelated with demand

shocks following the same argument above. Moreover, it also correlates with

demand by affecting the choice probability of passengers.

1.7.3 Identification

The parameters are identified by variation of pickups, the travelling pattern of

population and the pattern of taxi passengers’ dropoffs over locations and time

in the data. Given a set of nonlinear parameter values, mean utilities {δif t} are

identified by the variation of pickups across firms and markets. The mapping

from mean utilities to pickups follows algorithm 1&2 in which I firstly map mean

utilities to demands and corresponding dynamic supply distributions followed

by calculating matches given supply and demand. Consider two identical

markets (i.e. same market size, travelling pattern and prices) with different

pickups m1 > m2. In a static model, market 1 with higher pickups implies a

higher demand and supply than market 2 and therefore δ1 > δ2. However,

in a dynamic model, the corresponding supplies for given mean utilities are

more complicated than in static model. In the dynamic model, supply may not

fully respond to demand variation across locations due to mobility restriction

of cars conditional on their locations in the previous period. However, given

49

the one-to-one mapping from inter-period demands to dynamic supplies, the

dynamic pickup patterns in the data helps to identify mean utilities.

Identification of price coefficient α comes from variation of population

travelling patterns over markets. For example, two markets with same mean

utility δif t = δ

jf t and market size λi

t but with different destination distributions of

passengers Aif t 6= Aj

f t will have different unconditional(on destination) demand

uif t 6= uj

f t. The demand level relative to subway riderships also helps identifying

price coefficient. As for supply shock parameter σ, it controls for transition

of unemployed drivers. Given the search values over locations Vif t, ∀i, high σ

implies equal probability of search in each location i.

Identification of matching function parameters γ is not quite intuitive. They

are crucial to connect the mapping from δ to pickups. Different γ do not

affect equilibrium supply as much as equilibrium demand. The reason is that

drivers’ matching probability does only depend on successful pickups rather

than potential demand. Given the pickups generated by model equal those

of data in estimation, matching efficiency does not change probability much.

However, given supply level fixed, inefficient matching of γ affects estimated

mean utilities δ. For example, given fixed number of pickups and supply, a

large γ (less efficient) will generate high potential demand and corresponding

high δ. The mean utilities further affects destinations of passengers in equation

(1.14) and drivers’ profits. Since ex-ante search values Vif t depend not only

on matching probability but also on profits, equilibrium supply also reacts to

change of γ. Thus, in order to identify the {δif t} with restriction to γ, I use the

dropoffs of taxis in the data such that model predicted dropoffs of taxis match

the data. The reason is that different magnitudes of δ, which is shifted by γ, not

only affect market shares relative to outside option but also affects distribution

of firm specific dropoffs as in (1.14). High δ could dominate heterogeneous

price effects on utilities over different routes and making the distribution of

taxis’ dropoffs close to destinations of market population33. Hence, I use taxis’

33For a given market i, t, the mean utility δif t is common for all destinations j. It shifts the

50

dropoffs to identify the matching function parameters.

Finally, linear parameters in δ are estimated using instrument variables.

Since both demand and supply are endogenous and correlate with demand

shocks, I need to find instrument for demand and supply. I choose arrival of

employed cars from the same and opponent firm as instruments which are

correlated with supply and demand but uncorrelated with demand shocks. The

estimation result is in next section.

1.8 Results

1.8.1 Estimates outside mean utilities

The estimation results are listed in table 1.4. The estimates of price coefficients

for different trip distance are {αk}k=1,2,3,4 as specified in (1.6). The price co-

efficient for trip distance less than 3 miles is -0.81 and becomes less sensitive

for long distance trip. The estimate α4 = −0.26 is for trips between JFK and

Manhattan which charges flat rate for taxi passengers. The estimate of another

demand parameter β ∈ [0, 1] in nested logit demand defined in (1.8) is equal to

0.38. When β→ 1, demand shocks for taxi and Uber are highly correlated and

when β→ 0 they are independent as in a simple logit model.

There are two sets of parameters from the supply side. First, the estimates

of supply shocks’ scales σf , f = y, x for taxi and Uber are 7.67 and 12.65. These

two parameters affect the transition probability of unemployed cars as in (1.18).

Larger σf implies less effect of profit differences (without accounting for supply

shocks) across locations on transition probability πijf t. The other way around,

a smaller σf will enlarge the difference in profits among locations such that

drivers have higher likelihood to search high profit area. The estimates means

that taxi drivers have higher incentive to search for locations with higher search

values than Uber drivers. Furthermore, controlling for profit differences across

conditional shares on routes uniformly. In the extreme case of taxis’ mean utility large enough,destination of taxis’ passengers is exactly same to population’s.

51

locations, these two estimates implies a higher chance that taxi drivers will

overcrowd high profit areas and leave low profit areas undersupplied. In

other word, σf enhance the role of profit gap caused by regulated price on

matching frictions across locations. Second set of supply parameters are ρ f

which measures the incentive of unmatched drivers to search locations nearby

in the next period. This extra bonus from current location i to search location j

is measured proportionally to V j

f t+χijt−minl{V l

f t+χilt} if χ

ijt = 1 (see 1.15). This

proportion for taxi is 0.38 and for Uber is 0.27. Taxi’s higher ρy means taxi

drivers have slightly higher incentive to search locations nearby than directly

visiting a location far away.

Table 1.4 also reports the estimates for random matching function 1.20.

The γi = γ1{i ∈ CentralManhattan}+ γ2{i ∈ OuterBorough} measures within

market matching efficiency for taxis in non-airport locations. I distinguish

the efficiency in central Manhattan and outer Borough (Northern Manhattan,

Brooklyn and Queens). Higher value of γ means less efficient matching within

the market. For instance, given a fixed number of supply and demand, higher γ

generate less successful matches. The estimates for this parameter in Manhattan

area is 1.11 in comparison to other locations which is 3.67. Given these estimates,

it indicates that the within market matching is less efficient in Outer Borough. It

is reasonable considering on the large area sizes of defined markets in Queens

and Brooklyn.

Finally, there are 4800 mean utilities {δif t}∀ f ,t,i to estimate and the statistics

for taxi or Uber is listed in the bottom of table 1.4. The mean of taxis’ {δiyt} is

1.21 with maximum value at 4.90 and minimum value at −1.79. Uber’s mean

utilities {δixt} are less than taxis’ after controlling for prices. It is because Uber’s

supply and demand are still far less than taxis. Market share of taxis are still

much higher than that of Uber. Even controlling for prices, higher market share

of taxis corresponds to higher mean utility level. One novel interpretation is that

the number of taxi riders and drivers have strong network effects on passengers’

choice between taxi and Uber. By the specification of δif t in (1.5), taxis’ high

52

Table 1.4: Estimates of nonlinear parameters

panel 1: nonlinear parameter estiamtes std errordemand side parametersα1 -0.81 (0.042)**α2 -0.58 (0.029)**α3 -0.41 (0.040)**α4 -0.26 (0.031)**β 0.38 (0.026)**supply side parametersσy 7.67 (0.245)**σx 12.65 (0.513)**ρy 0.38 (0.023)**ρx 0.27 (0.025)**matching functionγ1 1.11 (0.015)**γ2 3.67 (0.345)**mean utilities mean min/maxδi

yt 1.21 -1.79/4.90δi

xt 0.30 -1.62/4.02** 1-percent or * 5-percent level significant

mean utility could result from network effects.

Along with the parameter estimates, the statistics of three key variables

solved in equilibrium including demand, supply, and search values are shown

in table 1.5 for taxi and Uber respectively. The mean of taxis’ demand in

2400 markets(location-period) is 118.13 with maximum demand of 531.61 and

minimum of 1.66. In comparison to taxis, Uber’s potential demand is less

with 20.92 on average. The average supply of taxis for each market is 174.21

ranging from 3.02 to 1779.3. The average supply of Uber is 34.46. Finally,

the ex-ante search values across markets for taxis have the maximum value of

$194.33 dollars at the beginning of the day (6 a.m.). Uber’s maximum search

values is $273.27 dollars at the beginning of the day and the average value is

$128.75 dollars. In general, Uber drivers have higher expected profit than taxis.

This high profitability of Uber could be the result of surge pricing, matching

efficiency and competition within firm. Specifically, the minimum fare $7 and

53

surge multiplier make the expected profit of Uber conditional on being matched

higher than taxis. Technology makes the matching probability of Uber higher

than taxi controlling for supply and demand in a market. In addition, the

number of active Uber cars are much less than taxis such that within firm

cannibalization is smaller than taxis.

Table 1.5: Statistics in equilibrium

demand mean min/maxui

yt 118.13 1.66/531.61ui

xt 20.92 1.06/136.65supplyvi

yt 174.21 3.02/1779.3vi

xt 34.46 4.45/227.7$ search valuesVi

yt 98.25 1.10/194.33Vi

xt 128.75 4.87/273.27

Table 1.5 only shows the statistics of demand, supply and search values over

both locations and periods. Given the dynamic feature of this model, search

values follow a decreasing trend over t which is not revealed in simple statistics.

Thus, I draw four figures to demonstrate four key values by firm, by location

over time. The first one is figure 1.7 which shows the values of Vif t over t. Each

line represents a location i and there are 40 lines. Given the finite periods of

this dynamic game, the values decrease over time. Uber’s values are generally

larger than taxis’ due to its higher conditional expected profit and probability

of being matched.

By 1.16, the search value is sum of two parts: expected profit of being

matched and expected continuation value of not being matched. I separately

show each of the two conditional expected values in figure 1.8, 1.9. There are

two findings by comparing these two figures with figure 1.5. First, by comparing

figure 1.5 and 1.8, I find that conditional expected profits on being matched are

more dispersed than search values Vif t. It implies that matching probability plays

54

Figure 1.7: Dynamics of search values before matching process

a role to shrink the gaps of profitability among locations and therefore leads to

much more close search values of them. For instance, drivers are self-motivated

to search locations with high conditional expected profits which decrease the

matching probability of that location such that search value of a location with

high conditional expected profit approaches search value of a low profitable

location. Second, by comparing figure 1.8 and 1.9, I find that expected values

55

conditional on being matched are higher than continuation values conditional

on being unmatched. It means that drivers are always willing to be matched

than to be unmatched in any market. This finding is not redundant given the

assumption of my model since it does not hold in certain instances. For example,

my model assumes that drivers arriving at a market at the beginning of the

period must attend the matching process of that market. If a driver drops off

a passenger in a market where he has a higher probability to pick up a new

passenger travelling to a destination with a quite low search value, he would

rather to be unmatched and make search decisions.

In order to compare the differences of V j

f t+χijt− cij

t + ρ f ∆jf t1χ

ijt =1

across

destination j for a given location i, I draw figure 1.10. The differences of

V j

f t+χijt− cij

t + ρ f ∆jf t1χ

ijt =1

directly determine the search choices of drivers based

on equation (1.18). For any market i, t, unmatched driver needs to choose a

location to search based on optimization decision 1.15. I calculate two times

standard deviation, 2 ∗ stdj{Vj

f t+χijt− cij

t + ρ f ∆jf t1χ

ijt =1}, to represent the differ-

ences in incentives of drivers to search among locations. A small value of this

difference means drivers have equal incentive to search any of the 40 locations.

In figure 1.10, the horizontal axis is time periods and vertical axis is the differ-

ence. Each line represents a location i over t and the variation of continuation

values a driver face if unmatched. The figure shows that when unmatched

drivers make search decisions, they face a heterogeneous values among search

options. The 2*standard deviation of these values range from $6 to $14 in t = 1

among 40 markets for taxis. For Uber, the standard deviation changes largely

over time and is greater than taxis. To interpret the comparison, after controlling

for scale parameter of supply shock, σf , Uber drivers have more incentive than

taxis to search certain locations.

56

Figure 1.8: Dynamics of expected profits conditional on being matched

57

Figure 1.9: Dynamics of expected continuation values conditional on beingunmatched

58

Figure 1.10: Heterogeneous expected continuation values conditional on beingunmatched

59

1.8.2 Estimates in mean utilities

Given previous estimation results, I run a linear regression of mean utilities

{δif t} on variables in equation (1.5). The coefficients of interest are θ1, θ2. The

supply coefficient measures indirect network effects from the other side of the

market. It is a net effect of supply on utility of choosing product including, but

not limited to, impact via matching probability and waiting time. Likewise, the

coefficient on demand captures net effect of demand on utility. One possible

channel is that the demand decreases the chance of being matched and therefore

negatively affect utility. The other way around, it can also positively affect

utility of choices via consumers learning from each other, herding and culture.

The cause of this joint effects, as discussed in section 6.1, is approximation of

matching probability and log linear assumption of ex-post utility, see 1.5.

I use market size, arrival of drivers from the same and opponent firm as

instruments for ln u, ln v. The OLS and 2SLS regression results are shown in

table 6. In the regression, I add interaction term of Uber dummy with logarithm

of demand and supply levels. The estimates show that both positive effects of

demand and supply on utility. Moreover, the effects are larger for utility of

choosing taxis than for Uber. The fixed effect of Uber on mean utility is positive

which equals 1.21. The positive sign of supply coefficient means that higher

supply level increases the choice probability of taxi(or Uber) and thus demand

level. Since demand will positively affect supply as implicitly imposed in supply

side structure, these two effects form the positive feedback loop between drivers

and passengers34. It is a little surprised that the coefficient on demand is also

positive. Demand is expected to negatively affect matching probability after

controlling for supply level. One way to explain this negative sign is that there

exists strong positive direct network effect among passengers which offset the

negative effect on probability. For example, if my neighbor, colleague or friend

34In the supply side, I do not parameterize and estimate the effects of demand on drivers’supply decisions. Instead, the positive effect is “imposed" because matching probabilityof drivers increases in demand AND conditional expected profit is higher than expectedcontinuation value as discussed.

60

uses taxi (or Uber), I would also like to choose taxi (or Uber). To highlight

early, the coefficients on demand and supply in the mean utility are important

for forming feedback loop in two sided market. In the counterfactual of this

model, I compare the scenarios with or without network effect by allowing the

mean utility to react to changes of demand and supply or not. This exercise

will generate two different equilibria for understanding the consequences of

ignoring network effects.

Table 1.6: Linear regression of mean utility

Dependent variable δif t

OLS 2SLSIVln v 0.054 0.496

(0.019)** (0.07)**ln v× dx -0.053 -0.224

(0.039) (0.11)*ln u 0.53 0.249

(0.021)** (0.06)**ln u× dx -0.014 -0.086

(0.038) (0.08)Uber dummy dx 0.19 1.21

(0.054)** (0.18)**constant -2.226 -3.71location fixed effects YES YEStime fixed effects YES YES** 1-percent or * 5-percent level significant

1.8.3 Benchmark Welfare

In this section, I will discuss and analyze the matching efficiency of this industry

given the model backed out demand, supply and observed matches, prices and

so on. The key factors that I am interested in are the two types of mismatches

in the model, within location friction and cross location friction. Within location

friction is partly reflected by the mismatches between drivers and passengers

of the same firm in the matching process. Since the matching process within

a market is assumed, this type of friction is mainly driven by the functional

61

form (1.20) though introducing γ adds flexibility to the function. Cross location

mismatches means in the same period some locations have more drivers than

demand whereas some locations have more demand than supply before the

matching process within locations. Excess supply of a location can be counted

as max{vif t − ui

f t, 0} and likewise excess demand is counted as {u f t − v f t, 0}.These expressions does not account for the mismatches due to random matching

within market such that I can distinguish these two types of frictions. In

period t, the city level aggregate demand is Σiuif t and aggregate supply is

Σivif t. The maximum aggregate matches that can be made without type 1

friction are Σi min{uif t, vi

f t}. Given the aggregate demand and supply level

fixed, the efficient matches should be min{Σiuif t, Σivi

f t} from the city aggregate

perspective35. The difference is:

min{Σiuif t, Σivi

f t} − Σi min{uif t, vi

f t}

= min{Σiuif t − Σi min{ui

f t, vif t}, Σivi

f t − Σi min{uif t, vi

f t}}

= min{Σi max{0, uif t − vi

f t}︸ ︷︷ ︸aggregate excess demand

, Σi max{vif t − ui

f t, 0}︸ ︷︷ ︸aggregate excess supply

}(1.23)

Expression 1.23 counts the minimum of aggregate excess supply and demand.

Unlike assumed within location friction, this friction is mainly driven by the

endogenous supply and demand decisions of drivers and passengers. To be

a good measure of friction, we should be able to compare efficiencies of two

scenarios by their index values. There are three limitations for the validity of

(1.23) as a measure of friction. First of all, it only counts the static mismatches

in a given period. An less efficient matches of current period could make better

matches in the next period considering the mobility of drivers across locations.

Second, it only counts the number. But passengers and trips are not identical. I

35Lagos (2000) treats this expression as efficient aggregate matches and aggregate matchingfunction generating less matches has friction. However, in his paper, the demand is exogenousand there is no demand-supply feedback loop.

62

improves this measure by weighting number by its dollar value. Third, even

without previous two limitation, this index is invalid if aggregate excess supply

is larger than aggregate excess demand. The reason is that aggregate demand is

not a fixed number as aggregate supply does. A large value of this index could

still end up with a large number of aggregate matches.

The welfare statistics are listed in table 1.7. The first panel displays type

1 mismatches both in terms of counts and dollar values. For example, there

are totally 95,547 within location mismatches for all 40 locations from 6 a.m.-

4 p.m. of a weekday. These mismatches could generate 1.3 million for taxis

if within location matching is perfect. In other words, without coordination

failure within market, drivers could make 50% more profits. For now, taxi

drivers’ daily total profit is 2.5 million. The within location mismatches for Uber

is negligible. Though I assume perfect matching for Uber within market, the

hyperbolic function still generate slight friction than perfect matching. The cross

location mismatches as measured by 1.23 are shown in second panel. There

are totally 14,738 type 2 mismatches for taxis which could make $203,530 trip

fares. Uber has a far less cross location mismatches which is 1,850 in counts and

$34,450 in money value. The revenue made by all taxi drivers in a day shift is

2.5 million and Uber drivers make $ 779,380. Consumer welfare is evaluated by

inclusive value of logarithm utility. In the counterfactuals, I will compute the

compensating variation to compare consumer welfare changes.

The dynamics of frictions over periods are provided in figure 1.11. It shows

how the aggregate frictions and matches over locations for any given period

evolve. Taxi pickups increase sharply after the first hour in the morning and

decrease until t = 30 at 11 a.m.. Uber’s aggregate pickups are more flat than

taxis which only increases slightly during rush hours of morning. Notably, the

cross location mismatches reach the daily highest level during the morning

rush hours. In other words, during rush hours, taxi drivers are more likely to

overcrowd some areas and leave others undersupplied. At last, I show several

figures for selected locations about their demand, supply and pickups of taxi

63

Table 1.7: Baseline welfare statistics

within-location mismatchesΣi,t min{ui

yt, viyt} − mi

yt 95,547$1,286,400

Σi,t min{uixt, vi

xt} − mixt 635

$10,517cross-location mismatchesΣt min{Σi max{ui

yt − viyt, 0}, Σi max{vi

yt − uiyt, 0}} 14,738

$203,530Σt min{Σi max{ui

xt − vixt, 0}, Σi max{vi

xt − uixt, 0}} 1,850

$34,450Profits and welfaretaxi profit $ 2,510,400Uber profit $ 779,380consumer welfare 505,210matches: data v.s. model generated data modelΣi,tmi

yt 173,490 173,230Σi,tmi

xt 48,897 47,738

and Uber over time, see figure 1.12 to 1.15. One interesting finding by comparing

Queens or Brooklyn with central Manhattan areas is that there are excess taxis’

supply in Manhattan almost all the time during the daytime. In comparison,

Queens and Brooklyn are more likely to have excess demand. Especially during

the morning hours from 7 am to 9 am. It is harder for passengers to hail a taxi.

Another finding is that Uber serves outer boroughs much in comparison to taxis.

The number of Uber drivers in selected location of Brooklyn is close to that in

Times Square. In next section, I will simulate several counterfactuals to learn

how they affect the matching efficiency of this market.

64

Figure 1.11: Aggregate frictions and matches of taxis& Uber over time

Figure 1.12: Demand, supply and matches in a location of Queens

65

Figure 1.13: Demand, supply and matches in a location of Brooklyn

Figure 1.14: Demand, supply and matches in Times Square

66

Figure 1.15: Demand, supply and matches in Financial District

67

1.9 Counterfactuals

In the previous sections, I estimate a dynamic search and matching model

of taxi & Uber drivers and passengers. The results show that: 1, there exists

feedback loop (indirect network effect) between demand and supply in a market

(platform) and direct network effect within the same side; 2, when drivers make

search decisions, they face a very heterogeneous search values among locations;

3, drivers are more likely to oversupply high profitable location and leaving

other locations undersupplied such that cross location mismatches exist; 4, the

low matching probability due to oversupply in high profitable location reduces

the ex-ante value of that location such that Vif t are close for different locations

i. This paper focuses on the “mis-allocation" of drivers, therefore the type 2

friction, because type 1 friction is driven by the random matching assumption.

In order to understand what factors and to what extent they affect the matching

efficiency and social welfare, I simulate two counterfactuals at the beginning of

this section, followed by counterfactuals of regulatory policy. First, I analyze

how Uber surge pricing affects efficiency of matching. Second, I study to what

extent traffic condition matters for matching. As for the policies, I study the

government’s proposal to cap Uber in 2015 and its effects. I also simulate the

congestion pricing policy that the NYC government is thinking of to reduce the

congestion in Manhattan.

Before discussing each simulation, the simulation process that applies to

all counterfactual scenarios is listed below. The different between with or

without network effect is whether or not to update mean utility δf for the

new equilibrium demand and supply. Not updating mean utility means that

passengers will not respond to the change of demand and supply level so

that feedback loop between two sides is shut down. This case is similar to

Buchholz 2016 without taking into account of network effects. With network

effect, the mean utilities will also adjust to any change of supply levels and so

does demand. Furthermore, the supply will respond to the change of demand

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and so forth until new equilibrium is reached. One note is that in the new

equilibrium, I assume the demand shocks ξ f backed out from linear regression

are fixed.

Simulation Algorithm Without Network Effects

1: Fix parameter values as estimates {σ, α, γ, ρ, β, θ} and δ

2: Given {δ, α, β}, calculate new eq demand u′ and transition of passengersA f3: Run the iteration process in Algorithm 1 to solve for new eq supplies v′

Simulation Algorithm With Network Effects

1: Fix parameter values as estimates {σ, α, γ, ρ, β, θ}2: Set initial guess of δ0 = δ3: Iterate from k = 03: Given {δk, α, β}, calculate new eq demand uk and transition of passengersAk

f4: Run the iteration process in Algorithm 1 to solve for vk

f5: Plug {vk

f , ukf , ξ, θ} in to mean utility 1.5 and update δk+1

6: Stop until ‖δk+1 − δk‖ < ε7: New equilibrium v∗f , u∗f

1.9.1 Eliminating surge multiplier

In this section, I want to study whether Uber’s surge pricing improves matching

efficiency across locations. Unlike fixed fare of taxis, Uber use surge multiplier

to efficiently adjust drivers’ search incentives of different locations. When some

locations have higher demand than supply, Uber tends to charge a higher price

than regular one to motivate more drivers to come. This higher price is product

of surge multiplier and regular price. To investigate the effect of flexible pricing

of Uber on matching efficiency, I eliminate Uber’s surge multiplier such that all

Uber’s trips are calculated using the normal pricing structure. By comparing

69

the new equilibrium with the benchmark, it could tell, to some extent, the role

of flexible pricing in matching of this industry. The results are listed in table 1.8.

First of all, we can compare the new equilibrium without network effects to

the baseline. After decline of Uber’s prices, the aggregate searches of drivers

do not change much for both taxi and Uber. Demand are more sensitive to this

change such that Uber’s demand increases by 8,150 (16%). Taxis’ total demand

decreases by 5,510 (1.9%) due to the price competition. As a result of demand

change, taxis’ pickups also declines slightly by 1.39% whereas Uber’s pickups

increases by 9.11%. We are more interested in comparing the frictions in the

second panel. The type 1 friction (within market mismatches) of taxi decreases

due to the decreased demand and supply. Uber’s type 1 friction is not quite

meaningful to discuss since it results from the error of using hyperbolic function

to approximate perfect matching. Most interesting findings are the cross location

mismatches. Taxi’s cross location friction decreases by 1,894 (12.8%) whereas

Uber’s friction increases by 2,811 (152%) trips. The increased type 2 friction

of Uber is worth $ 30,455 fares. The decreased cross location mismatches of

taxis may result from the competition effect, since Uber’s product becomes

more competitive with lower price. Without the help of surge pricing, Uber’s

misallocation of drivers makes its matching less efficient. As for the last panel,

taxis’ profits decrease due to price competition by $ 30,300. Though Uber’s

demand increases due to lower price, its total revenue decreases by $ 57,990.

The welfare gain of passengers measured by inclusive value of expected utility

prior to choices and matching process is 511,140 which is worth $ 120,400.

Then, the last column reports equilibrium with network effects such that

demand and supply levels will change not only prices but also mean utilities in

passengers’ choice problem. I find that both supply and demand of taxi and

Uber change further more than without network effect in the same direction.

For example, the total supply of taxis decreases by 3,240 which is more than

previous case. The demand of Uber increases to 62,065 compared to 58,374. This

finding reflects the positive feedback loop in two sided market. After Uber’s

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price decreases, demand for Uber increases which further increases utility of

choosing Uber through direct network effect and so forth. As a result, the total

pickups of taxis decreases more and Uber’s pickups increase more than without

network effect. To conclude, existence of network effect could expand the effect

of price drop on market share in this counterfactual.

As for frictions, taxis’ within location friction decreases. This is mainly due

to the further decreased demand and supply of taxis. Cross location mismatches

of taxis and Uber have opposite results as well. Taxi’s type 2 friction decreases

by 2,573 and Uber’s increases by 3,152. Finally, in the last panel, taxis’ profits

decreases slightly more than the case without network effect. Uber drivers make

more money after allowing network effect because it make more demand for

Uber to compensate the price drop. However, consumer welfare gain decreases

from $ 120,400 to $ 96,977 due to network effects.

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Table 1.8: Eliminating surge multiplier

supply, demand, match Benchmark w/o network with networkΣi,tvi

yt 418,100 417,230 414,860Σi,tvi

xt 82,707 83,375 84,219Σi,tui

yt 283,510 278,000 273,730Σi,tui

xt 50,224 58,374 62,065Σi,tmi

yt 173,230 170,810 168,470Σi,tmi

xt 47,738 52,088 54,371two type frictionwithin f rictiony 95,547 94,343 93,092

$ 1,286,400 $ 1,272,300 $ 1,256,800within f rictionx 635 758 786

$ 10,517 $ 10,516 $ 10,804cross f rictiony 14,738 12,844 12,165

$ 203,530 $ 178,120 $ 169,460cross f rictionx 1,850 4,661 5,002

$ 34,450 $ 64,905 $ 66,603welfare$taxipro f it $2,510,400 $2,480,100 $2,452,900$Uberpro f it $779,350 $721,360 $744,330consumer wel f are 505,210 511,140 510,020∆$consumer wel f are NA $120,400 $ 96,977∆$social wel f are NA $32,110 $4,457

Note: within f rictiony is Σi,t min{uiyt, vi

yt} − miyt.

cross f rictiony is Σt min{Σi max{uiyt − vi

yt, 0}, Σi max{viyt − ui

yt, 0}}.

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1.9.2 Improving traffic conditions

In this section, I simulate equilibrium after improving traffic conditions. To do

so, I replace the trip time {χijt }∀i,j,t from location i to j in period t computed

using 2016 sample by the trip time of the same route in 2010 (the year before

Uber’s entry)36. I have shown in figure 1.2 that traffic in 2010 is relatively faster

than 2016. Thus, by solving new equilibrium with traffic condition in 2010 can

suggest the role of traffic condition on matching efficiency. But, in this paper, I

do not build any relationship between traffic condition and supply of vehicles.

Thus, all counterfactuals only provide a partial effect or first order response of

factor change on equilibrium. The new equilibrium and welfare in comparison

to benchmark is provided in table 1.9.

First we can compare the efficiency change without network effects. Ag-

gregate demand for taxi and Uber do not change in the new equilibrium37.

Daily aggregate supply of both taxi and Uber increase. For example, total

supply/searches of taxi drivers increase by 68,610 (16.4%) and Uber’s increase

by 10,963 (13.25%). As consequence, the total pickups of taxis increase by

7,110 (4.1%) and of Uber increase by 971 (2.03%). The two types of friction

also changes. Both frictions of taxi decrease especially for the cross location

mismatches. The total number of friction 2 of taxis decreases by 6,142 (41.67%)

which is equivalent to $ 80,620 trip fares. As for Uber, the within location

friction is negligible due to perfect matching assumption. Uber’s cross location

mismatches also decrease by 1,014 trips and the loss of fare decreases by $

18,618. The total revenue of taxis increases by $ 107,400 (4.2%) and of Uber

increases by $ 17,830 (2.28%). The welfare gain to consumers as measured by

compensating variation (CV) is zero because inclusive value of their expected

utility prior to matching does not change without network effect. However,

consumer welfare after matching process changes.

36The trip time for any route ij at t of a representative weekday of 2010 can be calculated inthe same way as 2016

37The marginal change is due to computation error between δf ↔ u f

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Then, the last column of table 1.9 shows the equilibrium with network

effect which means demand will respond to the change of supply. The total

supply of taxis increases further than without network effect. Uber’s supply

also increases compared to the benchmark however less than without network

effect. There could be two possible explanations for the smaller supply of Uber

than without network effect. One reason is that choice decisions of passengers

change after responding to network effect. As consequence, not only the market

share/demand changes, but also the destinations of Uber’s passengers change

such that Uber’s passengers tend to travel a long distance. The other reason is

that the search values of Uber changes due to the demand change and Uber

drivers are more likely to search a location far away. Both reasons make Uber

drivers spend more time on travelling than searching. Taxi’s demand increases

more than without network effect and Uber’s demand drops. One reason is

that taxis have stronger network effect than Uber and increased mean utility of

choosing taxis is higher than Uber. As results, taxi’s pickups increase by 18,470

(10.6%) which is quite larger than 4.1% without network effect. It is interesting

that Uber’s pickups decreases in new equilibrium rather than increase in the

previous case which implies that we could even have opposite conclusions with

or without network effect.

As for frictions, the type 1 friction of taxis increases both in numer and

money value. It is because of both increased demand and supply of taxis, and

the random matching assumption. The type 2 friction of taxis also decreases

compared to benchmark but is slight larger than the case without network effect.

The same finding applies to Uber’s type 2 friction. This finding implies that

network effects actually make the matching across locations less efficient in this

counterfactual. I have discussed the ambiguous impact of network effects on

matching efficiency across locations earlier in section 3.

At last, the total profits of taxi and Uber increase after traffic improvement.

However, taxis’ profits are higher than without network effect whereas Uber’s

profits are less than without network effect. Consumer welfare increases by $

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748,900 benefiting from traffic improvement via the network effects in utilities.

Table 1.9: Traffic improvement

supply, demand, match Benchmark w/o network with networkΣi,tvi

yt 418,100 486,710 498,920Σi,tvi

xt 82,707 93,670 91,857Σi,tui

yt 283,510 283,030 300,120Σi,tui

xt 50,224 50,182 48,391Σi,tmi

yt 173,230 181,340 191,700Σi,tmi

xt 47,738 48,709 46,681two type frictionwithin f rictiony 95,547 93,090 98,923

$ 1,286,400 $ 1,252,900 $ 1,328,200within f rictionx 635 635 611

$ 10,517 $ 10,531 $ 10,406cross f rictiony 14,738 8,596 9,501

$ 203,530 $ 122,910 $ 134,920cross f rictionx 1,850 836 1,097

$ 34,450 $ 15,832 $ 21,807welfare$taxipro f it $2,510,400 $2,617,800 $2,741,500$Uberpro f it $779,350 $797,180 $784,460consumer wel f are 505,210 505,210 536,070∆$consumer wel f are NA $0 $ 748,900∆$social wel f are NA $ 125,230 $ 985,110

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1.9.3 Regulating Uber’s supply

In this counterfactual, I study the proposed regulatory policy of NYC govern-

ment on Uber in summer 2015. At that time, the number of Uber’s affiliated

vehicles is growing at a monthly rate of 3%. The total number of licensed

Uber vehicles was 26,000 which outnumber the total medallions, though not all

Uber vehicles are on the street together. Since the government blames Uber for

contributing to traffic congestion, it proposed to restrict the growth of Uber to

1% annually. To simulate the result of this policy, I decrease the assumed total

number of Uber vehicles in my model by 30%. This 30% comes from a simple

calculation of ten months growth rate 3% ∗ 10 from mid 2015 to my sample

April 2016. Similarly, I simulate two equilibria with or without network effect

in this scenario. The results are in table 1.10.

First, compare the second and the first column. After dropping 30% Uber

vehicles, the total supply of Uber cars decrease by 17,377 (21%). The total

number of taxis’ supply does not change without network effect. The reason

is that demand for taxis in this case does not change due to fixed mean utility.

Given the unchanged distribution of demand for taxis, the equilibrium supply

of taxis does not change as well. Similarly, demand for Uber is also unchanged.

But due to decline of Uber’s supply, total pickups of Uber decrease by 3,387

(7.1%). As for the frictions, we only need to compare Uber’s type 2 friction.

Uber’s cross location mismatches increases by 3,020 which is worth $ 56,702

fares. The increase is because of unchanged Uber demand and the decreased

supply of Uber. However, demand of passengers should respond to change of

supply as it affects matching probability and waiting time. The importance of

accounting for network effect is reflected in this example. Finally, taxis are not

affected in this case without network effect. The total profit of Uber decrease by

$ 63,250.

Next, compare the last column that allows network effect with first two

columns. Total supply of taxis does not change much but its demand increases

by 3,790. However, the decline of Uber’s demand is 6,353 (12.6%) which is

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greater than increased taxi’s demand. The total pickups of taxi increase by

1,660 and pickups of Uber decrease by 7,004 more than without network effect.

The difference is because that utility of choosing Uber declines due to less

supply of Uber cars. As for frictions, taxis type 1 friction increases a bit due to

increased demand for taxis. Moreover, its type 2 friction also increases from

14,738 to 15,595. Though the difference is small, it reflects the direction that

taxis’ matching friction may go if there is less competition from Uber. Uber’s

cross location mismatches is small than without network effect as expected, but

it is still greater than benchmark. In terms of profits, taxis make $ 34,300 more

money in a day shift after regulating Uber compared to $ 119,320 profit loss of

Uber. Moreover, passengers are worse off by $ 98,829 after this regulation.

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Table 1.10: Restricting Uber’s supply

supply, demand, match Benchmark w/o network with networkΣi,tvi

yt 418,100 418,120 417,610Σi,tvi

xt 82,707 65,330 64,622Σi,tui

yt 283,510 283,030 287,300Σi,tui

xt 50,224 50,182 43,871Σi,tmi

yt 173,230 173,070 174,890Σi,tmi

xt 47,738 44,351 40,734two type frictionwithin f rictiony 95,547 95,596 96,812

$ 1,286,400 $ 1,287,100 $ 1,304,800within f rictionx 635 700 602

$ 10,517 $ 11,670 $ 9,994cross f rictiony 14,738 14,367 15,595

$ 203,530 $ 198,620 $ 215,750cross f rictionx 1,850 4,870 2,534

$ 34,450 $ 91,152 $ 46,764welfare$taxipro f it $2,510,400 $2,507,800 $2,544,700$Uberpro f it $779,350 $716,100 $660,030consumer wel f are 505,210 505,210 501,540∆$consumer wel f are NA $0 $ -98,829∆$social wel f are NA $-65,850 $-183,849

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1.10 Conclusion

In this paper, I study the role of network effects on matching friction with an

application to taxi and Uber drivers searching for passengers in New York City.

To be specific, I model Uber and taxi drivers’ dynamic search decisions among

40 defined locations in NYC and passengers’ static choice decision. I focus on a

day shift of a representative weekday in April 2016. In this industry, due to the

fixed pricing structure of taxis, market is not cleared in prices leaving spatial

mismatches across locations such that some areas have waiting passengers

(excess demand) and some have vacant cars (excess supply). In additional

of inefficient pricing, I also add network effects in the model and study its

impact on matching efficiency. If we treat a market (location-time) as a platform,

network effects exist if there are externalities between drivers and passengers

when they make search decisions in this market (platform). The source of

network effects could be passengers’ preference to high matching probability

and short waiting time, and drivers’ preference to hight matching probability

and less vacant time. I allow both direct and indirect network effects in demand

side by adding supply and demand into utility function of passengers.

Estimates of the model show the existence of network effects and positive

feedback loop between drivers and passengers. There is also positive exter-

nalities among passengers. Then, I study how network effects affect spacial

mismatches of drivers and passengers in counterfactuals and whether ignoring

it would cause inaccurate conclusions. I simulate three counterfactual scenarios

with the model. First, I study whether Uber’s surge pricing improves matching

efficiency by eliminating it. I find a significant increase of Uber’s mismatches

without surge pricing. However, lower price without surge pricing would

make more pickups for Uber by 6,633 in total of a daytime. Second, I study

to what extent traffic condition matters for matching efficiency by using the

traffic speed in 2010. In the new equilibrium of better traffic, both Uber and

taxis have less mismatches by 33.71% and 40,7% respectively. Their profits also

79

increase. However, without considering network effect, Uber’s pickups are

predicted to increase whereas it decreases with network effects. Third, I study

the regulatory policy of capping Uber’s number of vehicles. I reduces number

of Uber cars by 30%. I find that taxis’ pickups increases by 1,660 far less than the

decrease of Uber’s pickups 7,004. Interestingly, due to less competition, taxis’

mismatches increases. Uber’s matching efficiency decreases. All counterfactuals

show different results either in magnitude or sign for whether network effects

are considered.

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Chapter 2 |Vertical Relationship and Merger Ef-fects in the U.S. Beer Industry

2.1 Introduction

This paper studies the mega merger between the second and the third largest

beer firms, SABMiller and Molson Coors, in the U.S. beer industry1. This merger

was completed in summer 2008. At that time, the market share of Miller is 18%

and of Coors is 11% which makes the joint firm MillerCoors have 29% market

share in comparison to 49% market share of the largest firm Anheuser-Busch.

To evaluate the merger effect, it is standard to analyze and compare the two

opposite effects, cost saving and increased market power. On the one hand, cost

saving will decrease the post-merger price and on the other hand consolidation

will increase price.

In the literature, there are mainly two types of merger study. First, a merger

can be studied in a retrospective way with both pre- and post-merger data.

Usually a retrospective study uses a reduced form analysis. Or, a structural

model approach is applied to predict a merger effects with only pre-merger data.

However, the prediction assumes fixed market environment or fixed unobserved

1The conclusions drawn from the Nielsen data provided by the Kilts Center for MarketingData Center at The University of Chicago Booth School of Business are those of the researchersand do not reflect the views of Nielsen Company (US), LLC. Nielsen Company holds thecopyright © 2018, however is not responsible for, had no role in, and was not involved inanalyzing and preparing the results reported herein.

81

shocks after the merger. My paper is a mixture of both types of studies. I build

a structural model to analyze the MillerCoors merger with both pre- and post-

merger data. The benefits are twofold. First, with both pre- and post-merger

data, I can estimate and capture changes of unobserved demand and supply

shocks which can not be obtained with only pre-merger data. Second, with

structural model approach, I can quantify and disentangle the welfare changes

of this merger in terms of implicit marginal costs, markups and consumer

welfare in comparison to a reduced form analysis. Most importantly, I can study

the impact of vertical relationship and market structure on the merger effects

which can be extended to understand merger in other industries.

Specifically, I build a model with both demand and supply side decisions.

In the demand side, I model consumers’ discrete choices among differentiated

beer brands. In the supply side, I model two stage pricing of upstream brewers

and downstream retailers. In the second stage, downstream retailers set opti-

mal retail prices given the whole sale prices from upstream. In the first stage,

upstream firms set optimal wholesale prices anticipating the best response of

retailer prices. Given the demand estimates, I can calculate double marginaliza-

tion and joint implicit marginal costs of retailers and brewers without observing

wholesale prices using the approach of Villas-Boas (2007). Then I can estimate

the cost saving by comparing pre- and post-merger implicit marginal costs.

Cost saving through shipping is estimated via the variation of distance between

breweries and markets. Cost saving through production is estimated by adding

interaction of merger dummy and brand dummies in the linear equation of

marginal costs. Given the model estimates, I simulate the scenario of no merger

for the post- merger period to understand: 1, cost saving effects; 2, market

power effects; and how different downstream concentration transfers upstream

shocks differently2.

The contribution of this paper to literature is threefold. First, it contributes to

the reduced form analysis of this merger by Ashenfelter, Hosken and Weinberg2The reason of simulating no merger scenario for the post-merger period to compare with

post-merger data is similar to the difference in differences idea.

82

(2015). In their paper, they also study the MillerCoors merger and they use

reduced form analysis to study how increased market power (measured by

change of Herfindahl-Hischman index (HHI)) and cost saving (measured by

reduced shipping distance) affect final retail prices of beer. However, change

of retail prices does not fully reflect the change of marginal costs and change

of markups. For example, given the double marginalization model, one dollar

decrease of marginal cost will not decrease the final price by one dollar because

firms will adjust markups (Hellerstein 2008, Goldberg and Hellerstein (2013)).

With structural model, I can quantify the cost saving and markups and their

pass-through to final prices, in other words, the underlying mechanism of price

change. Moreover, I can disentangle the cost saving and market power effects

on price.

Second, I contribute to the structural merger analysis with both pre- and

post-merger data. As pointed out by Nevo and Whinston (2010), the limitation

of merger prediction with pre-merger data is that it relies on assumption of

unchanged market environment after the merger. For instance, if the estimated

demand shocks or supply shocks change after the merger, the structural model

can not account for them. There are several studies about the accuracy of merger

simulation such as Peter (2006), Houde (2012), Weinberg (2011) and Hosken and

Weinberg (2013). With a long sample period covering this merger, I can account

for the change of unobserved shocks and simulate the no merger scenario for

the post merger period such that the merger analysis does not suffer from the

limitation above. Moreover, this paper contributes to the merger analysis by

considering vertical relationship in the supply side rather than one stage supply

decision (Nevo (2000, 2001), Fan (2013)).

Third, the most important contribution of this paper is to study how down-

stream market concentration affects the transition of upstream shocks, which

is merger in this paper, in a vertical relationship. There are many empirical

literature on vertical relationship of supply side. Chen (2014), Asker (2016) and

Lee (2013) study the exclusive contracts between upstream and downstream

83

firms. Villas-Boas (2007) develops a model with double marginalization to study

different vertial relationships between manufactureres and retailers. Murry

(2017) study the advertising efforts between dealers and manufacturers in auto-

mobile industry. Yang (2017) studies product innovation in vertical relationship

of smart phone industry.

There are several works close to this paper which also study beer industry

including Hellerstein (2008), Goldberg and Hellerstein (2008), Dearing (2016),

Miller and Weinberg (2017), Sweeting and Tao (2017). Hellerstein (2008), Gold-

berg and Hellerstein (2008) study the pass-through of cost shocks to retailer

prices in the beer industry. Similar to their idea, my paper studies the pass-

through of cost saving and market power due to upstream merger to retail

prices. Moreover, my paper emphasizes the heterogeneity of the pass-through

due to different downstream concentration. Dearing (2016) studies how up-

stream affects downstream chain’s setting uniform retail price across stores

within the chain. In comparison, Villas-Boas (2009) studies welfare effects of

uniform wholesale pricing. Miller and Weinberg (2017), Sweeting and Tao

(2017) study the merger of MillerCoors in the aspect of collusion or incomplete

information on marginal costs. However, all these works model at most one

firm in the downstream market such that they do not study the downstream

market concentration effects.

One work quite close to this paper is by Manuszak (2010) which studies the

impact of upstream mergers on downstream market in gasoline industry. How-

ever in his paper, downstream retailers are affiliated with upstream suppliers

unlike beer industry in which a retailer chain sells brands from all upstream

brewers. Due to the exclusive relationship between downstream stations and

upstream suppliers, upstream merger mainly affect participating firms and

associated downstream stations in Manuszak (2010). In my paper, upstream

merger affects all downstream retailers.

The rest of this paper is structured as follows. Section 2 introduces the

background of the U.S. beer industry. Section 3 introduces the data used in

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this paper and section 4 shows preliminary analysis. The empirical model is

discussed in section 5 with estimation results in section 6. In section 7, I simulate

counterfactuals and analyze welfare change of the merger. Section 8 concludes

the paper.

2.2 Background of the U.S. Beer Industry

The U.S. beer industry has a long history and is quite mature in modern years.

Unlike other industry, the beer industry is highly regulated by government.

After the repeal of Prohibition (1919-1933), when individual state was given the

right to regulate its beer sales, the policies on beer consumption differ across

states. Even so, there are laws in common for almost all states. The most

important one is the “three-tier distribution system" feature of beer distribution.

In the three-tier system, beer manufacturers are not allowed to sell beer

directly to consumers, retailers, restaurants or bars. Instead, they must sell their

beer through state licensed beer wholesalers who thereafter sell beer to retailers,

restaurants or bars. Exception adopted by some states allows small craft brewers

to sell beer directly to retailers, given that their annual output does not exceed

certain limits3. Almost all the U.S. states adopt this three-tier system. The main

intent of this system is to avoid over-consumption and alcohol abuse, which led

to the Prohibition (1919 to 1933). In principle, brewers are free to choose the beer

distributor/wholesaler and distributor is free to choose the brands portfolio

to carry. Finally, it is up to the retailers who decide which brands to put on

the shelves. Within the three-tier system, any kind of vertical integration is

discouraged. However, some manufacturers still try to build special relationship

with their distributors. For example, Anheuser-Busch has some contracted

exclusive wholesalers who can only sell Anheuser-Busch brands. Chen (2014)

studies the foreclosure effect of the Anheuser-Busch exclusive wholesalers on3In this paper, local craft beer is not included in the sample. Thus, all brands considered are

sold through the vertical framework.

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entry costs of rival brewers. The three-tier distribution system which is in

common across states justifies why I model the vertical relationship in the

supply side.

At retail level, given each state has its own regulation on alcohol consump-

tion, they can be categorized into control or non-control states. In control states,

wine and especially spirits are not allowed to sell in grocery stores. Instead, they

can be sold only in liquor stores (some are state-owned). Though regulation

on beer sales is less restricted, some states do not allow grocery stores to sell

beer (i.e. Delaware, New Jersey, and North Dakota) or only allow beer with less

alcohol (ABW<3.2%) to be sold in groceries (i.e. Colorado, Kansas, Minnesota,

Oklahoma and Utah.). Beer sales in gas station, convenience store, or pharma-

cies also vary across states. At the wholesale level, there are many wholesalers

serving each state. Each wholesaler has exclusive territory to distribute beer. In

most states, wholesalers form alliance or association. Uniform wholesale prices

to retailers within states are encouraged by state or wholesaler association. In

this paper, since wholesalers data is not available, for simplification I integrate

the manufacturers and wholesalers as one layer such that manufacturers set

wholesale price to retailers.

As for the style of beer sold in the U.S., they can be categorized into larger,

light, ales, porter, and stout. The distinction is how each style is brewed.

Usually the ale, porter and stout have dark color, bitter taste and high alcohol

by volume(abv). Light and lager are quite similar except that light has lower

calories. Among these styles, light and lager beer account for most of the beer

sales by volume, approximately 92.7%. Most of the national brands brewed by

large manufacturers are lager or light beer. Ale, porter and stout are mostly

brewed by craft breweries and have quite small market share. During the data

period 2007-2011, the U.S. beer industry is highly concentrated. It is dominated

by three large domestic breweries before the merger including Anheuser-Busch,

Miller and Coors followed by two large imported beer companies, Heineken and

Grupo Modelo. In June 2008, the second and third largest brewers Miller and

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Coors created a joint venture named MillerCoors, in which Miller owns 58% and

Coors owns 42% of the joint firm. After this merger, Anheuser-Busch has 49%

market share, while MillerCoors has 30%. Since this merger almost turns U.S.

beer industry from oligopolies into duopoly, it is very interesting and important

to evaluate this merger approved by Department of Justice (DOJ). As the DOJ

stated in its closing statement, the Division verified that the joint venture is

likely to produce substantial and credible savings that will significantly reduce

the companies costs of producing and distributing beer. One goal of this paper

is to quantify the cost savings and markup change due to this mega-merger.

2.3 Data

In this paper, I choose sample period from 2007 to 2011 which covers 6 quarters

of pre-merger and 14 quarters of post-merger. The data come from several

sources. The beer prices and sales data come from Nielsen retail scanner data,

which records the weekly sales of all beer in more than half U.S. retail stores

(in sales volume) across the country. The demographics data is from American

Community Survey. These two datasets are used for demand estimation. The

third dataset comes from Quarterly Census of Employment and Wages (QCEW)

of Bureau of Labor Statistics. The QCEW dataset includes average weekly wages

in each geographic area. I also add the median gross rent (from ACS) of each

geographic area. I use local wages and gross rent to control for retailer costs of

each geographic market. In addition, I collect beer characteristics from brewers’

websites for demand estimation and collect hop, malt prices to control for

brewer’s cost. Shipping distance between breweries to markets are calculated

using arcGIS. The details of each dataset and how I construct the sample is

described below.

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2.3.1 Nielsen Retail Data

The Nielsen retail scanner dataset is at weekly level which records beer sales of

participating stores. In other words, one observation in the data is for weekly

sales of a Universal Product Code (UPC) in a store. The product comes at

the UPC level, which differs in pack size, container and volume per container

for the same brand. A store is uniquely identified by store id and 3-digit zip

code, county, state. Each store also has a parent code to identify the ownership

or chain it belongs to such that I can tell the number stores of a chain in a

geographic area. The chains are categorized as different channels including

food store, drug store, mass merchandiser, liquor store and convenience store.

The coverage of Nielsen across channel is different. Since the coverage rate for

liquor and convenience store is quite low, I only consider food chains in the

paper.

For each observation, I know the price, quantity sold in a week, UPC

information and brand information. Brand information includes the type of the

beer (i.e. lager, light, ale, stout or porter) and the brand name. I supplement

the product characteristics by collecting abv, carb, calorie, whether domestic or

imported and firm it belongs to. I aggregate the UPC into brand-package size

level regardless of the container or volume per serving. The reason to distinguish

package size is that price per 12 oz serving is quite different between large pack

and small pack4. Given the variety of pack size, I only distinguish large size

(> 12 packs) and small size (≤ 12). Furthermore, I aggregate sales of a given

brand-size across stores into chain level. It implicitly assumes that chain sets

uniform retail prices across stores which is studied by Dearing (2016). If I allow

store to set individual price, the number of “products" will be quite large and

the market becomes more competitive than price setting by chains. Thus, a well

defined product in my paper is a brand-size-chain combination in a geographic

markets. I divide the area of the market by number of stores of a chain as proxy

4In general, large pack has smaller price per serving than small pack. By this definition, Ihave two products for a brand.

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for travelling cost to buy a product or how easily to access to a chain.

Finally, I aggregate weekly level into quarterly level to avoid effects of

temporary store discounts or household storage behavior (Hendel and Nevo

(2016)) on demand estimation. In sum, one observation in the sample is quarterly

sale of a brand-size-chain during 2007-2011.

2.3.2 ACS&QCEW

The American Community Survey data from U.S. census are used to simulate

households’ demographics in each geographic market. For every quarter of

a year, I randomly draw demographics of residents in a geographic market

including ratio of income to poverty level, age, education and race based on

the distribution of demographics provided in ACS. The benefit of using income

to poverty level is that it measures “richness" per capita rather than household

income which is not discounted by household size in ACS. Usually, researchers

use Current Population Survey(CPS) to generate demographics. However, CPS

is not appropriate to analyze geography smaller than a state5.

I use ACS and QCEW to collect data on local retailer costs. From ACS, I

collect gross rent in the market as proxy for commercial rent of retail chains. I

also collect average wage in supermarket industry from QCEW to control for

retailer costs. I also collect malt and hop prices to control for production costs

of beer.

2.3.3 Shipping distance

One important cost factor is the shipping distance from breweries to the geo-

graphic markets which is an argument of cost saving for MillerCoors merger.

Ashenfelter, Hosken and Weinberg (2015) finds the reduced shipping distance

significantly accounts for post-merger price change. I use the same method of

5The comparison between ACS and CPS is listed in https://www.census.gov/topics/income-poverty/poverty/guidance/data-sources/acs-vs-cps.html

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them to calculate the shipping distance. First, I locate all plants of Anheuser-

Busch, Miller, Coors and other domestic brewers6. Then, I use arcGIS to compute

the distance between geographic market and closest plant of a brewer as ship-

ping distance. It is implicitly assumed that a plant of a brewer produces the

whole product line of brands. Given the fact that I include selected nation wide

brands in my sample, this assumption is plausible. For small brewers in the

sample, such as Yuengling, Sierra Nevada and New Belgium brewery, though

they are not sold nation wide, they only have few plants and the assumption

still holds. As for imported brands, I follow Miller and Weinberg (2017) to

calculate distance of markets to the ports. But in the estimation, I simply use

fixed effect for imported brands to control for shipping costs. In the post-merger

periods, I combine Coors and Miller’s plants as MillerCoors plants to calculate

the post-merger shipping distance and therefore the reduced distance.

2.3.4 Market Definition

Information about store location in Nielsen includes 3-digit zipcode, county and

state. I define a market as a metropolitan statistics area(MSA) which comprises

several central/outlying counties. The reason of using MSA as a market is that

residents in each MSA rarely travel outside to purchase beer and MSA seems

to have the proper area size for retailers and brewers to make strategic pricing

decision. Ashenfelter, Hosken and Weinberg (2015) also uses MSAs as separate

geographic markets. I aggregate quarterly beer sales of Nielsen stores in a MSA

as market size of the MSA in the quarter. This definition of market size includes

all the observed beer sales in Nielsen dataset including all channels such as

food store and drug store. The big concern of this market size definition is the

coverage rate of Nielsen. Though Nielsen covers, on average, 50% food stores

in the U.S., the coverage rate varies a lot across locations7. If the missing data

comes from stores of the same chains in Nielsen, I could probably use in-sample

6Anheuser-Busch has 12 plants over the country. Miller has 6 plants and Coors has 2 plants.7Nielsen provides the coverage rate by channel at Scantrack markets level.

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share as mirror projection to the market share. However, if the missing data

comes from chains that do not cooperate with Nielsen and if those chains are

big players in the market, my definition of the market size could overestimate

the market power of chains in the sample. This issue also occurs to Miller and

Weinberg (2017) when they use IRI data. They scale the observed beer sales in

data by 1.5 as the market size which is equivalent to normalizing outside market

share. An alternative way of defining market size is Hellerstein (2008) which

scales the population by beer consumption per capita. However, the problem of

applying this method is that I do not know the beer consumption per capita

in food store channel which varies across MSAs. Second, it would generate a

quite large outside market share which could underestimate concentration of

retailers.

Instead, I borrow this idea of Hellerstein (2008) to select MSAs included in

my final sample. The selection criteria is that the per capital consumption of

beer (calculated by dividing Nielsen beer sales by MSA population) is greater

than 2 servings per month. Furthermore, I select the MSAs with market share of

beer sold through food channel greater than 70% and population larger than 0.2

million. According to these criteria, only MSAs with high food store coverage

and large market share of food channel are left. These MSAs are idea for the

analysis of this paper because firstly I need high coverage rate of my sample in

order to measure the downstream concentration and secondly I do not model

competition of food chains with drug stores or convenience stores. In the end, I

have 50 MSAs over 20 quarters from 2007-2011 in my sample. Table B.1 shows

the 50 MSAs and corresponding market information including the number

of chains, the number of products (brand-size-chain), the total market share

of inside products, market size (sales observed in Nielsen) and food channel

coverage of the DMA8.

8DMA is Nielsen Designated Marketing Areas. The document provided by Nielsen does notshow the coverage for all DMAs. Usually DMA is larger than MSA which means that coveragerate of a MSA could be larger or smaller than the coverage of a DMA it belongs to.

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2.4 Preliminary analysis

In this section, I start the analysis by showing some key variables in the data

and preliminary regression results on retail prices. First of all, figure 2.1 shows

the dynamics of retail price per 12 oz serving for selected brands by package

size(large or small). For a given time period, the price is averaged over MSAs

and package sizes and therefore the change is not quite obvious. However, it

still illustrates that on average the price of Bud light, Budweiser, Coors light

and Miller Lite increases by 10 cents (12.5%) per serving for small packs. The

increase is smaller for large packs. After the merger point, both MillerCoors

and Anheuser-Busch brand increase prices in comparison to imported beer such

as Heineken and Corana. The increase of prices could result from increased

market power after merger or increased production cost of domestic brewing.

The two key factors that change after the merger are upstream concentration

and shipping distance. Figure 2.2 and 2.3 demonstrate these two variables for

50 markets.

To obtain 2.2, I calculate the proxy for HHI change such that ∆HHIbrewer ≈(smiller + scoors)2− s2

miller − s2coors = 2 ∗ smiller ∗ scoors which is used in Ashenfelter,

Hosken and Weinberg (2015). For each MSA-quarter, I calculate the HHI change

and the histogram of all MSA-quarter in post-merger periods are shown in

figure 2.2. The variation of ∆HHIbrewer is large across markets ranging from 0.01

to 0.07. Given the HHI of national market share 0.492 + 0.182 + 0.112 = 0.28,

after merger brewers’ HHI increases more than 10% for most markets. Figure 2.3

illustrates the reduction of shipping distance between 50 MSAs to MillerCoors

breweries. The horizontal axis is shipping distance before merger and vertical

axis is shipping distance after the merger. A 45 degree line is used as reference

such that the vertical distance from spot to 45 degree line is the reduced shipping

distance. As it shows, the merger primarily reduce the shipping distance for

Coors than Miller. The reason is that Coors only have 2 plants before the merger

and Miller has 6 over the country. Out of the 50 MSAs, only 5 markets have

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slightly shorter distance after the merger.

Figure 2.1: Average price per serving by brand over 50 markets

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Figure 2.2: Distribution of HHI increases of post-merger

94

Note: distance is calculated as shortest distance of MSA to breweries.

Figure 2.3: Distance(miles) between breweries and markets for pre/post-merger

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To understand the merger effects on retailer prices and vertical relationship

in the supply side, I run two specifications on logarithm of price per serving.

log(pjcmt) = α1HHIbrewermt + α2HHIretailer

mt + α3HHIbrewermt × HHIretailer

mt

+ postmerger× (β1HHIbrewermt + β2HHIretailer

mt + β3HHIbrewermt × HHIretailer

mt )

+ dlarge + γ log(distance) + djmt + ε jcmt (2.1)

and the second specification

log(pjcmt) = α∆HHIbrewermt + βHHIretailer

mt × ∆HHIbrewermt

+ dlarge + γ log(distance) + djmt + ε jcmt (2.2)

where the subscript j stands for brand j; c stands for chain c; m is geographic

market; t is time period. On the left hand side of both equations 2.1 and 2.2

is retailer price of brand j sold in chain c in market m at time t. On the right

hand side of 2.1, I use HHIbrewermt to control for brewer markup and HHIretailer

mt

to control for retailer markup. Importantly, I add interaction term of two

HHI to estimate the vertical relationship between upstream and downstream

markets. In other words, the interaction term measures how downstream market

concentration affects the transition(slope) of upstream HHI to retail price. For

flexibility, I also interact the HHIs with post-merger dummy. Furthermore,

dummy for large pack, logarithm of shipping distance, local wage, rent and

dummies for market, time and brand are included. The second specification

uses change of HHI instead of HHI level similar to Ashenfelter, Hosken and

Weinberg (2015). However, I add interaction of HHIretailer with ∆HHIbrewer in

difference to Ashenfelter, Hosken and Weinberg (2015) in order to study how

downstream HHI affects the transition of market power to price.

The regression results are given in table 2.1. The first column is regression

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result of equation 2.1 without interaction terms of post-merger dummy. The

second column is full specification of 2.1. First, the result shows that both

HHIbrewer and HHIretailer positively affect retail prices. Coefficient on brewer

HHI means increase of HHI by 0.01 points will increase retail price per 12

oz by 0.43%. According to the histogram of figure 2.2, increasing HHI by

0.03 after the merger will increase retail price by 1.23%. The estimate of HHI

interaction term is negative for both column 1 and 2. To interpret, increase

of upstream concentration will raise the final retail price less for market with

more concentrated downstream market. In other words, market with a severe

competition in the downstream market has less power to dampen the upstream

shocks. Estimates of other coefficient are negative for large packs and positive

for shipping distance. As distance is a key factor in merger, the coefficient

means that reduction of shipping distance by 1% will decrease the price by

0.031%.

In column 3 of table 2.1, it shows regression result of 2.2. Similar to the first

specification, increase of upstream concentration will positively affect retail price.

However, the effect is mitigated by the downstream concentration according to

the negative coefficient −1.232 of interaction term. The interpret is the same to

the first specification. In order to quantify changes of marginal cost, markups

and vertical relationship in the merger rather than their reduced reflection in

price, I build a demand and supply side model in the next sections.

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Table 2.1: OLS regression of retail price(12oz) on HHI

log(price)HHI-brewer 0.463 0.244

(0.144)** (0.148)HHI-retailer 0.279 0.062

(0.149) (0.152)HHI-brewer ×HHI-retail -1.47 -0.871

(0.413)** (0.418)*post-merger×

HHI-brewer 0.193(0.038)**

HHI-retailer 0.208(0.043)**

HHI-brewer ×HHI-retailer -0.675(0.147)**

∆ HHI-brewer 1.762(0.26)**

HHI-retailer × ∆ HHI-brewer -1.232(0.60)*

large pack -0.659 -0.67 -0.659(0.002)** (0.147)** (0.002)**

log(Distance) 0.031 0.031 0.031(0.001)** (0.001)** (0.001)**

Year dummies X X XSeason dummies X X XBrand dummies X X XMarket dummies X X XR-square 0.92Observation 155,973** 1-percent or * 5-percent level significant

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2.5 Structural Model

2.5.1 Beer Demand

I model a consumer’s decision for purchasing one 12 oz standard serving of

beer using a discrete choice model following Berry (1994), Berry et al. (1995),

and Nevo (2001). In each MSA market of year-quarter, a consumer’s choice

set includes all brands sold in all in-sample chains of the market and outside

option. A product is defined as a brand-size-chain combination. Stores within

the same chain set uniform price for the same brand-size. I do not distinguish

stores and products sold by stores within the same chain9. The utility function

of a consumer i, in market and period mt, of choosing brand-size j in chain c is:

uijcmt = δjcmt + εijcmt (2.3)

with:

δjcmt = αpjcmt + βxjcmt + λjcmt + ξ jcmt (2.4)

where the first term δjcmt is mean utility of product which comprises the follow-

ing variables: pjcmt is price per 12 oz of brand j sold in chain c; xjcmt includes

product characteristics such as logarithm of the radius (mile2) per store of the

chain as measure of travelling distance and dummy for package size; λjcmt is

full set of fixed effects including brand dummies λj, market-chain dummies λcm,

year and season dummies λt. Brand characteristics such as abv, calorie, carb,

dummy for light beer and dummy for domestic beer are not shown up in δjct,

because they are fixed for any given brand and therefore are fully accounted

in the brand dummies. ξ jcmt is unobserved demand shock. In Nevo(2001),

parameters in δjct are referred as linear parameters Θ1 ≡ {α, β, λ}. The last term

9As mentioned before, the uniform retail price within chain is studied by Dearing (2016).He finds that upstream adjustment will significantly dampen the profit gains of retailer bydeviating from uniform pricing to store-level pricing.

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εijcmt of utility captures the idiosyncratic preference shock, which is assumed

to follow Type 1 extreme-value distribution. This is the standard simple logit

demand model.

The random coefficient discrete choice model adds another term to equation

2.3 such that:

uijcmt = δjcmt + µijcmt + εijcmt (2.5)

with:

µijct = [pjcmt, xjcmt](ΠDi + Σvi) (2.6)

This additional term µijct includes consumer demographics to make the sub-

stitution among products more flexible than simple logit model to solve I.I.A.

problem. In µijct, together with price xjcmt are product characteristics that

consumers with different demographics have heterogeneous tastes to. In the es-

timation, I include ABV, dummy for light beer, and dummy for domestic beer in

xjmct; Di are consumer demographics which captures consumers’ heterogeneous

preference over product characteristics. I use income and age as demographics

variables in the estimation; vi are consumer i’s idiosyncratic preference, which

is assumed to follow standard normal distribution in the estimation. The matrix

Θ2 ≡ {Π, Σ} are nonlinear parameters, which measures the different preferences

of consumers.

The mean utility of choosing outside option is:

ui0mt = δ0mt + µi0mt + εi0mt (2.7)

the utility of choosing outside good is normalized to be ui0t = εi0t for both

simple and mixed logit model.

Consumer with demographics {Di, vi, εi} chooses the option which gives her

the highest utility such that jc∗ = argmaxjc uijcmt. Denote the set of consumers

choosing product (j, c) as Ajct = {Di, vi, εi|uijct > uij′c′t, ∀j′, c′}. Then, the

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market share for product (j, c) is:

sjcmt =∫

Ajcmt

dP∗m(Di, vi, εi) (2.8)

where P∗m is the joint probability distribution function of {Di, vi, εi}. Given the

T1EV distribution assumption on εi, this formula can be rewritten as:

sjcmt =∫

Di,vi

exp(δjcmt(Θ1) + µijcmt(Di, vi; Θ2))

1 + ∑j′ exp(δj′cmt(Θ1) + µij′cmt(Di, vi; Θ2))dPm(Di, vi) (2.9)

In the special case of Θ2 = 0, it becomes simple logit model and the market

share is:

sjcmt =exp(δjcmt(Θ1))

1 + ∑j′ exp(δj′cmt(Θ1))(2.10)

to back out δjcmt of simple logit model easy such that:

δjcmt = log(sjcmt)− log(s0mt) = αpjcmt + βxjcmt + λjcmt + ξ jcmt (2.11)

Since market share and outside share are observed in data, I can simply construct

the left hand side of equation 2.11 and regress on the variables on the right

hand side.

Back to the full random coefficient model, BLP proves that the contraction

mapping can help recover mean utility δ from equation 2.9). To be more specific,

given each pair of parameter values, I randomly draw ns persons’ (Di, vi) from

“known" distribution of Pm, such that I can calculate the monte carlo simulated

share as:

sjcmt =1ns ∑

i

exp(δjcmt + µijcmt)

1 + ∑j′ exp(δj′cmt + µij′ct)(2.12)

BLP proves that there is a unique vector of δ that can match the simulated

market share and observed market share in data. The iteration process for δ is:

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δh+1mt = δh

mt + log smt − log s(pmt, xmt, δhmt, Pm; Θ2) (2.13)

where the first vector smt is data and the second vector s is calculated based

on simulation. After backing out δ, I can simple run linear regression on mean

utility to estimate Θ1. One problem occurs to both simple and mixed logit

model that pjcmt is endogenously correlated with unobserved demand shock

ξ jcmt. It is because that when manufacturers and retailers set optimal strategic

price, they observe unobserved product characteristics and account for it in

price setting. In the estimation, I instrument prices with cost side variables such

as local wage, rent, hop and malt prices.

2.5.2 Beer Supply

The three-tier system of beer distribution includes beer manufacturers, distribu-

tors and retailers. To decompose the price setting, it is ideal if I could model all

three tiers in the supply side. However, there are more than 3300 licensed beer

wholesalers throughout the U.S. with each of them carrying multiple brands,

sharing different territories, having different storage and shipping capacities.

To collect detailed information on those wholesalers is hard and the data is not

available. Since I don’t have data on beer distributors or even the number of

distributors in a given MSA, I simply follow the literature (Hellerstein (2008),

Goldberg and Hellerstein (2013)) by integrating manufacturers and distributors

into one price setting stage which sets whole sale price, and retailer is the second

stage setting retail price. In the following discussion, I use brewer or manufac-

turer to represent brewer-distribution integration. Brewers sets wholesale prices,

while retailers set retail prices. As shown in the preliminary regression, the

retail price consists of brewers’ markup, retailers’ markup and joint marginal

cost of firms. The supply model solves double markups given estimates of price

elasticities in the demand side. Then total marginal cost of brewer and retailer

is recovered by subtracting markups from retail price.

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In order to calculate the double markups, the price setting is assumed to

follow Bertrand-Nash linear pricing game between upstream and downstream

firms. Linear pricing contract between upstream and downstream is assumed

in Hellerstein (2008), Goldberg and Hellerstein (2013) and Dearing (2016). Most

recently, there is a paper by Faheem and Gayle (2017) studying the nonlinear

pricing contract between brewers and retailers and its fitness to the data. Sine

my paper focuses on the downstream market concentration on upstream merger

shocks, I simply assume linear pricing contract.

At first stage, beer brewer sets wholesale price for its differentiated brands

accounting for the downstream retailers’ best response retail prices. At the

second stage, after observing the wholesale prices of all brands by all brewers,

the retailers set optimal retail prices for the brands they carry. I do not model

retailers’ choosing product portfolio in this paper which could be an interesting

extension. Instead, I take the brands sold by each chain retailer as exogenously

given and retailers only set endogenous retail prices. This assumption is rea-

sonable since I only include “popular" brands in the sample. I use backward

induction to solve this two stage game.

2.5.2.1 Retailers

The retailer c which is a food chain in a market m at period t chooses retail price

pjcmt to maximize its profit10:

Πct = Σjc∈Jct

[pjct − pωjt −mcr

jct]sjct(pt) (2.14)

where Jct is the set of products sold by chain c; pωjt is wholesale price of brand

j; mcrjct is marginal cost of chain c for selling product (j, c). To avoid the

duplication of script, I use r instead of c and ω to distinguish retailer and

manufacturer; sjct is market share of product (j, c). The wholesale price doest

not have c in the subscript, because wholesalers are assumed to charge uniform10To simplify the notation, I drop m and use t to represent market.

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wholesale price to different retailers due to state law or distributor association.

Retailer c chooses optimal price vector pct to satisfy first order conditions:

sjct + Σj′,c∈Jct[pj′ct − pω

j′t −mcrj′ct]

∂sj′ct

∂pjct= 0 (2.15)

for all (j, c) ∈ Jct. If I write all products (j, c) of market t into vector, the first

order conditions can be rewritten as:

pt − pωt −mcr

t = −(Tr ∗ ∆rt)−1st(pt) ≡ mkupr

t (2.16)

with Tr as the retailer’s ownership matrix. The dimension of matrix Tr equals

the number of products in the market, say Nt. The element Tr(i, j) equal to 1

when both product i and j are sold by the same chain and 0 otherwise. ∆rt(i, j)

is Nt by Nt matrix containing the first derivatives of all the shares with respect

to all retail prices, with element ∆rt(i, j) = ∂sjt/∂pit. The values in 2.16 are the

retailer markups.

2.5.2.2 Manufacturers

The manufacturer sets optimal wholesale price pωjt for brand j taking retailers’

optimal pricing strategy of 2.16 into account. manufacturer ω maximizes profit

function:

Πωt = Σj∈Jωt

[pωjt −mcω

jt ]sjt(p∗(pω)) (2.17)

where Jωt is the set of brands owned by manufacturer ω; p∗(pω) is best response

function of retailers on wholesale prices pω; sjt is the total market share of

brand j sold by all chains, which equals Σcsjct11. The first order condition of

manufacturer’s profit w.r.t. pωjt become:

11The market share of brands and market share of products(brand-chain) use the samenotation s which is confusing. But I distinguish them by adding c to the subscript or not.

104

sjt + Σj′∈Jωt [pωj′t −mcω

j′t]∂sj′t

∂pωjt= 0 (2.18)

Similarly, let Tω be a matrix of ownership for the manufacturers. The dimension

of matrix Tω is different to the dimension of Tr because number of brands is

less than number of products. Manufacturers do not distinguish brand sold

in different chains. Thus, the dimension of matrix Tω equals the number of

brands available in the market, say NUt with element Tω(i, j) = 1 if brand i and

j belongs to the same manufacturer.

Let ∆ωt be the manufacturer’s response matrix with element ∆ωt(i, j) =

∂sjt/∂pωit which has the dimension of NU

t by NUt . To obtain the matrix ∆ωt, I

need to calculate the derivatives of optimal retail prices with respect to wholesale

prices, because

∂sjt

∂pωit= ΣcΣk

∂sjct

∂pkt

∂pkt∂pω

it(2.19)

Define matrix ∆pt with element (i, j) = ∂pjt/∂pωit such that dimension of ∆pt

is NUt by Nt matrix. Once I get ∆pt, I can construct matrix with derivatives of

all product market shares with respect to all wholesaler prices ∆pt∆rt, which

is a NUt by Nt matrix. To simplify notation, I drop the subscript t and c in the

following derivation. To get the expression for ∆p, I totally differentiate first

order condition of optimal retail price 2.15 for a given product j with respect to

all retail prices (dpk, ∀k = 1, . . . , N) and wholesale price pωF such that:

ΣNk=1 [

∂sj

∂pk+ ΣN

i=1(Tr(i, j)∂2si

∂pj∂pk(pi − pω

i −mcri )) + Tr(k, j)

∂sk∂pj

]︸ ︷︷ ︸g(j,k)

dpk−

Σ f∈FTr( f , j)∂s f

∂pj︸ ︷︷ ︸h(j,F)

dpωF = 0 (2.20)

105

putting all products j together, let G be the matrix with element g(j, k) and

let HF be the Nt-dimensional vector with element h(j, F). I can rewrite 2.20 in

matrix form Gdp− HF dpωF = 0. Then I get ∆′p = G−1 ∗ [H1H2 . . . HNU ] with

dimension N by NU. Finally, according to 2.19 ∆ωt = ∆pt∆rtU, where matrix U

is a Nt by NUt matrix with element U(i, j) = 1 if product i is brand j. Matrix U

is used to aggregate product market share sjcmt into brand market share sjmt.

Similar to retailer markup, wholesaler markup is :

pωt −mcω

t = −(Tω ∗ ∆ωt)−1st(p) ≡ mkupω

t (2.21)

Note that the vector of brand market share in 2.21 has NUt element in difference

to the product market share vector in 2.16.

Calculating the two markups in 2.16 and 2.21 only requires simulated market

share and first/second order derivatives of market share with respect to retail

prices. The derivatives of market share w.r.t retail prices can be calculated

once price elasticities are estimated in the demand side. Since I do not observe

wholesale prices pωt , it is impossible to calculate marginal costs respectively

using 2.16 and 2.21. However, by combing these two equations, I can recover

the joint costs of retailer and manufacturer such that:

pt −mkuprt −mkupω

t = mcrt + mcω

t (2.22)

By moving markups to the right hand side, this equation is analogous to

specification 2.1 in the preliminary analysis. The difference between 2.22 and 2.1

is that HHI is a measure for markups but fixing HHI in 2.1 is not equivalent to

fixing markups of 2.22. Therefore, the coefficients of cost variables in 2.1 are not

the same to those in regressing mcrt + mcω

t on cost variables. Once I back out

marginal costs for both pre- and post-merger periods, I can estimate cost saving

through reduced shipping distance and production rather than their effects on

prices.

106

2.6 Estimation

2.6.1 Demand estimation

Estimation of the model has two steps. First, I estimate the random coefficient

demand model in the way of past literature. For any given values of Θ2, I use

contraction mapping to solve for fixed point of mean utility δ(Θ2) such that

model predicted market share equals observed share in data. Then, I use the

mean utility equation 2.4 to back out unobserved demand shock ξ(Θ1, Θ2). Due

to price endogeneity, I use instruments Z = [z1, . . . , zL] and GMM estimation to

estimate parameters {Θ1, Θ2}. The moment conditions are:

E[zlξ] = E[zl(δ(Θ2)− αp− βx− λ)] = 0, l = 1, . . . , L (2.23)

with the GMM estimator being:

Θ = argmin ξ(Θ)′ZWZ′ξ(Θ) (2.24)

where W is weight matrix. Following Nevo (2001), the estimation can be

simplified by substituting the estimator Θ1 given guessed parameter values Θ2 :

Θ1 = (X′ZWZ′X)−1(X′ZWX′δ(Θ2)) (2.25)

into the GMM estimation such that the estimation algorithm only search over

Θ2 rather than {Θ1, Θ2} to minimize the objective function. For simple logit

model, δ can be calculated using market shares and the estimator for Θ1 above

is equivalent to 2sls iv estimator. Matrix X is product characteristics including

retail price, logarithm of the radius per store, dummy for package size, and full

set of dummies for brand, market-chain, year and season.

As for the instruments, I primarily use cost shifters and market demograph-

ics. To be specific, I use local retailer’s costs such as local average wage in

supermarket industry and local gross rent. I also use manufacturers’ costs in-

107

cluding shipping distance between brewery and market, malt and hop prices. I

interact malt and hop prices with firm dummies to allow heterogeneous produc-

tion costs across manufacturers. Hellerstein (2008) and Goldberg and Hellerstein

(2008) also use input prices as instrument when they study the pass through

rate of cost in the U.S. beer industry. Following Miller and Weinberg (2017), I

also use mean demographics interacting with exogenous product characteristics

in X as instrument for estimating parameters Π in the random coefficients.

2.6.2 Supply estimation

Once the demand side is estimated, I can calculate the partial derivative of

market shares to retail prices. Based on 2.16 and 2.21, I can calculate markups

for retailers and manufacturers. Then the joint marginal cost can be recovered by

subtracting markups from retail price based on 2.22. Then I use OLS regression

to estimate cost function:

mcr + mcw = α1 log(distance) + α2 log(rent) + α3 log(wage)

+ λbrand + λmerge × λbrand × λmillercoors + λmt + ν (2.26)

where the coefficient α1 measures shipping cost and interaction terms of dum-

mies λmerge × λbrand × λmillercoors (MillerCoors brand dummies after merger)

measure the average cost saving after the merger other than shipping cost. For

example, if the production cost of MillerCoors brand decreases after the merger,

I will have negative coefficients on this set of dummies. One thing to note is that

I do not add brand dummies interacting with merger dummy for other brewers.

As discussed earlier in the paper, estimation of the cost function and cost saving

of the merger can only be achieved when I back out marginal costs in the left

hand side of 2.26 and the sample period covers both pre- and post-merger

periods. In the counterfactual of this paper, I simulate the scenario of no merger

for post-merger period to disentangle cost saving and increased market power

108

of the merger. The cost without merger is calculated using the estimates of cost

function 2.26 above.

2.6.3 Results

2.6.3.1 Simple logit demand

I start with the simple logit demand model and estimate the mean utilities on

product characteristics using OLS and 2sls estimation. The regression results are

listed in 2.2. The price coefficients are negative which means utility of choosing

a product decreases in the price. Since price is endogenous and positively

correlated with demand shock, OLS estimation will underestimate the price

elasticity. Comparing the estimates of OLS and IV regression, the absolute value

of price coefficient is higher in IV regression which means that the cost shifters

address the price endogeneity problem. The second product charateristics is

the logarithm of radius per store. This variable is calculated by dividing MSA

area by the number of stores in the chain that product brand-chain belongs to.

If a chain has fewer stores than the other in the same market, it will have a

larger value of radius such that the travelling cost of consumers to purchase

the brand-chain is higher. The coefficient on this variable has negative sign as

expected which implies that 1% increase of radius will decrease utility by 0.0168.

The third variable is dummy for large package size. I define package size less

or equal to 12 (regardless of the volume per serving in the pack) as small pack

such that dummy equals 1 if pack size is greater than 12. The estimate of large

size on utility is -0.25 which implies that controlling for other characteristics

on average consumers are less likely to purchase large size. It makes sense

since the moving cost, storage cost of large size is higher for consumers not to

mention about that beer is perishable goods. Finally, the estimates of selected

brand fixed effects are listed. Flagship brands such as bud light, coors light and

miller lite have higher utility of cheap brand such as Busch light. Due to the

limited substitution effects and I.I.A problem of simple logit demand model, I

109

estimate the random coefficient model with market demographics in the next

section.

Table 2.2: Demand estimates from simple logit model

variable OLS IVprice -3.941 -5.79

(0.025)** (0.172)**log(radius per store) -1.716 -1.684

(0.004)** (0.005)**large size -0.043 -0.253

(0.005)** (0.020)**Bud light 1.652 0.991

(0.021)** (0.064)**Budweiser 0.868 0.204

(0.021)** (0.064)**Natural light -0.315 -1.315

(0.023)** (0.094)**Busch light -0.833 -1.858

(0.024)** (0.097)**Miller lite 0.753 0.090

(0.021)** (0.064)Miller high life -0.820 -1.814

(0.023)** (0.094)**Coors light 0.993 0.341

(0.021)** (0.063)**Heineken 1.014 1.099

(0.019)** (0.021)**Corona extra 1.448 1.451

(0.019)** (0.020)**constant 7.451 9.335

(0.099)** (0.200)**Year dummies X XSeason dummies X XBrand dummies X XMarket-Chain dummies X Xmin.brand dummy -1.97 -3.10max.brand dummy 1.65 1.45** 1-percent or * 5-percent level significant

110

2.6.3.2 Random Coefficient Model

In the random coefficient model, I add the interaction terms of consumer’s

demographics and product characteristics according to 2.5. For each market,

I randomly draw 300 consumers and their demographics from known joint

distribution of income to poverty ratio and age. The product characteristics

which interact with demographics and i.i.d standard normal variable v include

retail price, dummy for light beer, dummy for domestic beer and ABV. The

purpose of adding these interaction terms is to account for the heterogeneous

tastes of consumers with different demographics on product characteristics so

that substitution effects among products with similar characteristics are stronger.

Identification of coefficients on these interaction terms comes from the different

consumption patterns for markets with different demographics. For example, if

consumers in market A has higher income than consumers in market B, and we

observe increase of one brand’s price in both markets does not affect the market

share of that brand in market A as much as in market B. That implies that

consumers with higher income level are less sensitive to price so that coefficient

on income interacting price is positive.

The estimates of random coefficient model is shown in table 2.3. I use the

same instruments in 2slsiv regression. The first column of table 2.3 is estimates

of Θ1 in comparison to table 2.2. Estimates of Θ2 are provided in the last

3 columns. Since I add brand dummies in product charateristics which are

linearly correlated with dummy for light beer, dummy for domestic beer and

ABV, I apply the minimum-distance estimation following Chamberlain (1982)

and Nevo (2000). To interpret the results, fist of all, the price coefficient is -11.308

which means that without considering demographics in the random coefficient,

one dollar increase of a brand’s price will decrease utility of choosing the brand

by 11.30812. The interaction term of income and price has estimated coefficient

1.034 which means that the price coefficient of consumer with higher income

12In the estimation, I do not demean the demographics. Otherwise, the estimates of coefficienton price represents the average effect of price on indirect utility over consumers.

111

level is smaller in absolute value. The interaction of income with light, domestic

dummies and ABV are alll negative such that high income consumers are less

likely to buy light beer, domestic beer and high alcoholic beer. As for elderly

consumers, they are more likely to buy light beer and domestic beer but less

likely to buy high alcoholic beer. The estimates of demographics in random

coefficient provides more flexible substitution among products.

The estimates of Θ1 are similar to 2slsiv. The coefficient on radius of chain

stores is -1.688 similar to -1.684 in 2slsiv. The coefficient on size dummy is

still negative. The coefficient on light dummy, domestic dummy and ABV are

retrieved from minimum-distance estimation. In the bottom of table 2.3 I also

report the statistics of estimated own price elasticity. The concern is that random

coefficient model may have positive price coefficient due to the interaction terms

of demographics and price.

The average own price elasticity and cross price elasticity by brand are

provided in table 2.4. These numbers are obtained firstly by aggregating market

share of a given brand over size and chain in a market, then calculating partial

derivatives of brand shares to brand prices from a representative chain, and

finally averaging over MSAs and time periods. The first panel shows own and

cross price elasticities for flagship brands in the industry. For example, the first

rows shows percentage change of demand for Bud light to price increase of

other brands. To interpret, if the price of Bud light increase by 1%, its demand

will drop by 4.92%. If the price of Coors light increase by 1%, demand for

Bud light will increase by 0.75%. The elasticities are quite reasonable such that

substitution among light beer such as Bud light, Coors light and Miller Lite

is stronger than substitution between light and lager. Moreover, substitution

among domestic brands are stronger than imported brands. Finally, the second

panel of table 2.4 lists almost all the 50 brands in my sample including large

brewers and top craft brewers such as New Belgium, Yuengling and Boston

brewing.

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Table 2.3: Demand estimates from random coefficient model

Interaction with:variable mean in population unobservable income agePrice -11.308 0.943 1.034 0.793

(1.237)** (0.650) (0.301)** (0.638)Large size -0.360 0.898

(0.058)** (0.249)**Light 4.175 0.863 -0.578 0.625

(0.129)** (0.419)* (0.125)** (0.161)**Domestic 5.221 0.753 -0.140 0.722

(0.120)** (0.167)** (0.105) (0.249)**ABV -0.148 1.030 -0.107 -0.179

(0.015)** (0.055)** (0.055)* (0.136)log(radius per store) -1.688

(0.011)**Bud light 1.414

(0.429)**Budweiser -0.128

(0.497)Miller lite 0.513

(0.430)Coors light 0.770

(0.429)Heineken 1.124

(0.026)**Corona extra 1.432

(0.091)**constant 14.583

(1.175)**Year dummies XSeason dummies XBrand dummies XMarket-Chain dummies Xown price elasticity> 0 0%own price elasticity> −1 0.0064%Obervations 155,973** 1-percent or * 5-percent level significant

2.6.3.3 Supply estimates

With demand estimates, I calculate the markups of retailer and manufacturer,

and implicit marginal costs for all products (j, c, m, t) according to the optimal

pricing strategy 2.16, 2.21 and 2.22. The average statistics of markups and costs

113

Table 2.4: Own and cross price elasticity (average over markets)

Cross-price elasticity

Bud light Budweiser Coors light Corona extra Heineken Miller LiteBud light -4.924 0.364 0.757 0.096 0.066 0.644Budweiser 0.832 -5.071 0.455 0.225 0.179 0.390Coors light 1.362 0.363 -5.593 0.096 0.066 0.644Corona extra 0.479 0.495 0.255 -6.084 0.361 0.227Heineken 0.468 0.549 0.250 0.488 -6.465 0.221Miller Lite 1.366 0.364 0.758 0.096 0.066 -5.644

Own-price elasticity

Anheuser-BuschNatural light -4.602 Michelob light -6.059Natural ice -4.563 Stella Artois -7.118Busch light -4.506 Rolling rock -5.387Michelob amber bock -5.717 Beck’s -6.643Michelob ultra light -6.091 Bud ice -5.291Budweiser select light -5.601 Bud light lime -6.512Budweiser select -5.216 Busch -4.298CoorsKeystone light -5.593 George killians -6.086Coors banquet -5.549 Blue moon -6.434HeinekenTecate -5.900 Dos equis especial -6.306Newcastle brown ale -6.748MillerMiller genuine draft -5.455 Milwaukee’s best -3.879Miller genuine draft light -5.573 Miller chill light -6.459Miller high life light -4.722 Steel reserve 211 -4.011Milwaukee’s best light -4.155 Icehouse -4.909Milwaukee’s best ice -4.052ModeloCorona light -6.814 Pacifico -6.670Modelo especial -6.287New belgiumFat tire amber ale -6.879Pabst brewingPabst blue ribbon -4.354Sierra nevadaSierra nevada pale ale -6.703YuenglingYuengling -5.060Boston brewingSamuel adams -6.366

114

by brewers for pre- and post-merger periods are given in 2.5. The number is

obtained by unweighted averaging key variables over all brands, chains, markets

and periods of each firm for pre- and post-merger respectively. For example,

in the pre-merger periods (6 quarters) the average marginal cost of one 12 oz

serving of Anheuser-Busch beer (regardless of brands) is 10 cents. On average,

a retailer’s profit of selling one serving of Anheuser-Busch product is 36 cents.

Anheuser-Busch’s profit per serving is 26 cents.

In order to understand the merger effect, first I compare the marginal costs.

Comparing the pre- and post-merger marginal costs for all brewers in the first

column, it is clear that in the post-merger periods marginal cost of selling beer

brands increases in general. For example, after MillerCoors merger, the cost of

Anheuser-Busch increases from 10 cents to 19 cents. This indicates a national

level cost shock in the post-merger period. However, the amount of increased

marginal costs is smaller for Coors which can be explained by the cost saving of

the merger especially the significant reduced shipping cost of Coors. Without

estimating cost function, it is hard to tell cost saving due to merger from the

common supply shock.

As for the effect of increased market power, I compare the markups of

retailers and brewers for Miller and Coors before and after the merger. I find

that on average, retailer’s profit of selling one serving of Miller or Coors beer

decreases by 2 cents. The markup of Coors increases from 15 cents to 19

cents and Miller’s increases from 16 cents to 19 cents. The conclusions are

twofold. First, upstream brewers’ profits increase in their market power. Second,

downstream retailers may sacrifice their profits as a buffer to partially offset the

positive shock of upstream on retail price. It is very important to note that the

decrease of retailer markup is reduced response to both changes of brewer’s

markup and marginal cost. For example, even without significant change

of brewer’s markup, retailer’s markup of selling Anheuser-Busch, Heineken,

Modelo, Boston and Sierra Nevada decreases. In the counterfactual analysis,

I disentangle effects of cost and market power by releasing one effect while

115

controlling for the other. The last column of table 2.5 provides average quarterly

profits of brewers. Miller and Coors profits increase by 4.3 million and 2.2

million after the merger. Profits of Anheuser-Busch also increases by 0.8 million

which is mainly due to the shift of demand to Anheuser-Busch due to higher

MillerCoors prices.

Table 2.5: Statistics on estimated markups and costs(average over products)

marginal cost retailer markup brewer markup qtrly profitFirm Name mean sd mean sd mean sd (in $ 107)

Anheuser-Busch(pre) 0.10 0.51 0.36 0.46 0.26 0.044 5.35Anheuser-Busch(post) 0.19 0.44 0.34 0.38 0.25 0.043 5.43

Coors(pre) 0.25 0.49 0.35 0.44 0.15 0.018 0.70Coors(post) 0.27 0.43 0.33 0.38 0.19 0.033 1.13Miller(pre) 0.08 0.52 0.35 0.47 0.16 0.033 2.32

Miller(post) 0.14 0.43 0.33 0.38 0.19 0.036 2.54Heineken(pre) 0.56 0.44 0.37 0.42 0.17 0.016 0.30

Heineken(post) 0.58 0.37 0.35 0.35 0.17 0.016 0.31Modelo(pre) 0.59 0.46 0.38 0.45 0.18 0.015 0.43

Modelo(post) 0.60 0.37 0.35 0.36 0.17 0.015 0.42Boston(pre) 0.59 0.48 0.41 0.46 0.17 0.011 0.06

Boston(post) 0.66 0.39 0.38 0.38 0.17 0.012 0.07New belgium(pre) 0.74 0.27 0.31 0.29 0.16 0.016 0.01

New belgium(post) 0.78 0.37 0.37 0.36 0.17 0.018 0.02Pabst(pre) 0.05 0.49 0.35 0.48 0.12 0.006 0.05

Pabst(post) 0.14 0.40 0.33 0.38 0.12 0.005 0.08Yuengling(pre) 0.25 0.29 0.32 0.28 0.14 0.006 0.06

Yuengling(post) 0.29 0.28 0.32 0.27 0.14 0.007 0.07Sierra Nevada(pre) 0.66 0.49 0.41 0.48 0.17 0.013 0.04

Sierra Nevada(post) 0.73 0.39 0.39 0.38 0.17 0.012 0.05markupr < 0 0%markupw < 0 0%

mc < 0 13%obs 155,973

Given the recovered implicit cost, the OLS regression result of cost equation

2.26 is shown in table 2.6. The coefficient on distance is 0.013 which measures

how cost per serving is correlated with shipping distance. In the bottom of

table 2.6 I calculate the maximum cost saving per serving across MSAs due to

reduced shipping distance of the merger. For Miller, merger reduces shipping

cost per serving by at most 2.2 cents and for Coors it reduces shipping cost by

116

7.4 cents. The results corresponds to 2.3 that Coors benefits more than Miller

in terms of shipping distance. The estimates of changes of brand dummies

after merger are listed in 2.6 for selected brands. For example, Coors light

has 2 cents cost reduction after merger and Miller Lite has 1.6 cents reduction.

These cost reductions other than shipping cost may come from synergy of

production after the merger. Most importantly, they can not be estimated

without backed out cost level and sample covering both pre- and post-merger.

Without information about these estimates (i.e. with only pre-merger data),

merger simulation may be less accurate under the fixed environment assumption.

Another factor that could affect merger simulation is the residual of the cost

regression. The residual that measures unobserved cost is not constant before

and after merger which also affects merger simulation. With all these precise

estimates of unobserved demand and supply shocks, shipping cost and cost

synergy, I can simulate counterfactual without merger in the post-merger period

similar to a retrospective analysis in order to, firstly disentangling merger effects

and secondly understanding vertical relationship in upstream merger.

2.7 Counterfactuals

In this section, I simulate several counterfactual scenarios and solve double

marginalizations in each counterfactual. In the first counterfactual, I calculate

marginal cost in the post-merger period without MillerCoors merger. To do

that, I subtract cost saving through shipping distance and production from the

backed out marginal cost. I treat this scenario as benchmark. In the second

counterfactual, I analyze the cost saving of merger without consolidation by

changing the marginal cost but fixed the ownership matrix of brands. And

the third scenario is what I observed and estimate in the sample that both cost

saving and upstream consolidation occurs. Moreover, I simulate two scenarios

without vertical relationship such that brewer sets retail price. These two

simulations help to compare merger effects with or without vertical relationship.

117

Table 2.6: OLS regression on marginal cost(12oz)

mcrjcmt + mcω

jmtlog(Distance) 0.013

(0.0006)**log(Gross rent) -0.04

(0.002)**log(Wage) 0.02

(0.015)post-merger×

Coors light -0.02(0.005)**

Coors Banquet -0.02(0.005)**

Blue moon -0.019(0.007)**

George killian -0.017(0.008)*

Miller lite -0.016(0.005)**

Miller high life -0.008(0.005)

Miller chill light -0.13(0.008)

Miller genuine draft -0.003(0.005)

Year dummies XSeason dummies XBrand dummies XMarket dummies XR-square 0.90Observation 155,973cost saving through ∆log(Distance) max($ per 12oz)Coors brand(12oz) -0.074Miller brand(12oz) -0.022** 1-percent or * 5-percent level significant

Moreover, it shows that welfare analysis would be inaccurate if supply side is

improperly specified.

The simulation results are listed in table 2.7. Each column represents a

scenario with the first column as benchmark without consolidation and the

third column as “observed" merger in the sample. The values in the table

for key variables (i.e. cost, markups) are calculated by firm and by concentra-

tion of downstream retailers. For instance, Coors(low) means (unweighted)

118

average statistics over all Coors products sold in markets with HHIchain less

than 0.28 where 0.28 is the median value of HHIchain across markets. Compar-

ing brewer(high) and brewer(low) illustrates the heterogeneous responses to

upstream shocks for markets with different downstream concentration.

First of all, comparing column (1) and (2) shows the change of key variables

after cost saving. In the first panel, merger saves the marginal cost of Coors

beer by 2.8 cents per 12 oz serving. It also saves the marginal cost of Miller

by 1.3 cents in markets with high concentrated downstream and 0.9 cents in

less concentrated ones. The differences in costs are mainly due to location of

markets rather than vertical relationships. The second panel shows changes of

retailer markups with cost saving. The changes are not quite obvious probably

due to the averaging. In the third panel, brewer’s markups increase after the

cost saving. For instance, Coors increases markups by 0.3 cents and 0.2 cents

in response to 2.8 cents cost saving per serving. This finding means that cost

saving is significant for Coors after the merger, while it does not fully pass

through to retail price due to the slight increase of Coors markup. Interestingly,

Anheuser-Busch also decreases its markup in order to compete with lower price

of MillerCoors.

Column (2) and (3) demonstrate the changes due to increased market power.

Marginal costs are the same in the third column to the second column. After

increasing market power, retailer markups in low concentrated market on

average increases by 0.1 cents while in high concentrated market decrease by

0.1 cents for Coors and decrease by 0.3 cents for Miller13. Comparing “low"

and “high" markets for other brewers, I find that retailers of markets with high

concentrated downstream have more power to adjust retail markups than those

in “low" markets. As for brewer markups, Miller and Coors markups increase

further with more market power. By comparing (1) and (3), it is obvious that

increased brewer markups of Miller and Coors dominate the cost saving of the

13The change of average retailer markups seems tiny even in percentage. One way to improvethe comparison could be calculating the change of each market and showing percentile ratherthan mean.

119

merger.

In the two panels at the bottom of table 2.7, I calculate the changes of brewers’

and retailers’ total profits of selling MillerCoors brands and all brands. The

second column shows that with cost saving the total profits of MillerCoors

increases by 22 million dollars and retailers’ profits incresse by 73 million

dollars. The third column shows profits’ changes when MillerCoors maximizes

joint profits. MillerCoors’ profit increases further, whereas retailers’ profits

decrease significantly. One reason is that the total consumption of Miller and

Coors decreases (by 3.27 ∗ 108 servings) due to higher prices and the other

reason could be decreased retailers’ markups. In the last panel, it shows the

changes of surplus and social welfare. Column (2) shows that total profits of

all brewers decrease (by 1.81 ∗ 107) with cost saving of MillerCoors, though

MillerCoors’ profits increase (by 2.2 ∗ 107). Beer consumption shifts from other

brands to Miller and Coors due to cost saving and consumer welfare increases.

After considering change of market power as in column (3), all brewers’ profits

increase and consumption shifts from MillerCoors to other brands. Retailers’

profits and consumer welfare decrease. By summing up column (2) and (3),

it implies the joint effects of cost savings and market power. Consumers and

retailers are worse off in this merger which is dominated by the increase of

brewers’ profits. The social welfare increases.

Finally, the last two columns show brewer markups with only one stage

price setting. The findings are three-fold. First, the markups in one stage price

setting are much less than those in two stages which corresponds to the reason

of building three-tier beer distribution system to discourage beer consumption.

Second, brewers’ markups are higher in one stage price setting. The reason is

that retailers’ markups decrease the marginal revenue of oligopolistic prices

and therefore brewers charge small markups in a two stage price setting system.

Third, similar to the second finding, the effect of increased market power on

retail price is smaller with vertical relationship which indicates that downstream

market restricts the increase of brewers’ markups after the merger.

120

Table 2.7: Couterfactuals: average cost and markups by firm and HHIchain

two tiers one tierBrewer name no merger costsaving costsaving+power costsaving costsaving+power

marginal costcoors(low) 0.440 0.412 0.440 0.412

coors(high) 0.158 0.130 0.158 0.130miller(low) 0.318 0.305 0.318 0.305

miller(high) 0.003 -0.006 0.003 -0.006AB(low) 0.341

AB(high) 0.055heineken(low) 0.669

heineken(high) 0.493retailer markups

coors(low) 0.225 0.224 0.225coors(high) 0.457 0.457 0.456miller(low) 0.213 0.213 0.214

miller(high) 0.446 0.447 0.444AB(low) 0.224 0.225 0.224

AB(high) 0.455 0.456 0.452heineken(low) 0.250 0.251 0.249

heineken(high) 0.481 0.483 0.478brewer markups

coors(low) 0.159 0.162 0.194 0.177 0.212coors(high) 0.150 0.152 0.203 0.171 0.228miller(low) 0.156 0.156 0.189 0.170 0.206

miller(high) 0.173 0.172 0.199 0.192 0.222AB(low) 0.249 0.243 0.253 0.263 0.273

AB(high) 0.260 0.254 0.266 0.284 0.296heineken(low) 0.171 0.171 0.171 0.189 0.188

heineken(high) 0.174 0.175 0.173 0.197 0.196Only for MillerCoors (2)-(1) (3)-(2) (5)-(4)

total brewer profits$ 2.2 ∗ 107 4.5 ∗ 107 5.6 ∗ 107

total retailer profits$ 7.3 ∗ 107 −1.78 ∗ 108

total cost saving$ −3.53 ∗ 107 2.34 ∗ 107

total servings 1.49 ∗ 108 −3.27 ∗ 108 −3.8 ∗ 108

All firm (2)-(1) (3)-(2) (5)-(4)

total brewer profits$ −1.81 ∗ 107 1.28 ∗ 108 1.68 ∗ 108

total retailer profits$ 2.56 ∗ 107 −5.40 ∗ 107

total cost saving$ −4.46 ∗ 107 2.86 ∗ 107

total servings 3.99 ∗ 107 −7.86 ∗ 107 −5.52 ∗ 107

total consumer welfare$ 5.7 ∗ 107 −1.17 ∗ 108 −1.78 ∗ 108

total welfare$ 6.45 ∗ 107 −4.3 ∗ 107 −1.00 ∗ 107

Note: “high" indicates HHIchain > 0.28 where 0.28 is the median HHI over markets in post-merger

121

2.8 Conclusion and extension

In this paper, I study and quantify the impacts of cost synergy and increased

market power of upstream consolidation in the U.S. beer industry. I use Nielsen

retail data of beer sales in food stores from 2007-2011 to estimate demand

for beer in 50 selected MSA markets. With the estimates of demand, I model

vertical relationship in the supply side and assume a Bertrand-Nash linear

pricing game between upstream brewers and downstream retailers to estimate

double marginalizations. Implicit costs for both pre- and post-merger periods

are backed out by subtracting markups from retail price. By regressing recovered

costs on supply side shifters such as distance and interaction of brand dummies

with merger, I can estimate cost saving through reduced shipping distance

and production cost. I find that on average MillerCoors joint venture reduces

production cost of Coors light by 2 cents per 12 oz serving, and cost of Miller

lite by 1.6 cents. The shipping cost of Coors decreases by 7.4 cents per serving

at maximum and shipping cost of Miller decreases by 2.2 cents at maximum.

In order to disentangle cost saving and market power effects of the merger,

I simulate several counterfactual scenarios. I find that brewer will increase

markups in both scenarios of cost saving and increased upstream market power.

Retailers in markets with high concentrated downstream are more likely to

adjust retail markups to dampen the shocks from upstream. In the simulation, I

find that MillerCoors increase markups after the merger which dominates the

cost saving. In terms of welfare, the mega-merger increases MillerCoors profits

but hurt retailers’ profits markedly. The total consumption of MillerCoors beer

for all 50 markets from mid-2008 to 2011 decrease by 1.78 ∗ 108 servings. As for

change of total surplus, consumers and retailers are worse off due to the merger

which is offset by the increased brewers’ profits. The social welfare increases

due to MillerCoors joint venture.

In this paper, I only focus on brewers’ and retailers’ price setting. One

possible extension is to study how upstream merger affects retailers’ choosing

122

portfolio of brands. It is also interesting to study how this merger and price

rising affect entry or profits of “small" brewers. For example, I find non-

participating brewers’ profits also increase after the merger as in table 2.5 due

to the positive cross price elasticity and shift of demand. Another interesting

question to study is about effects of merger on advertising and introducing

new products14. In a recent work by Chandra and Weinberg (2017), they find

positive effect of market concentration on advertising expenditure. If merger

increases marginal revenue of advertising, it may contribute to introducing

new products by decreasing learning cost through intensive advertisement.

Moreover, if positive spillover effect of advertising exists, merger can further

increase firms’ incentive to introduce new products.

14Usually, firms advertise new products for informative reason or to encourage learning.

123

Appendix A|Proofs of chaper 1

A.1 Proof of proposition 1

In order to have one island with excess supply and one island with excess

demand in equilibrium, the model parameters should have two properties. First,

the price in island 1 is greater than island 2, p1 > p2. This is also condition in

Lagos (2000) such that one island is more profitable. Second, the population in

island 2 must be greater to offset or even dominate the negative effect of low

supply on demand. This second condition requires that islands are not only

heterogeneous in price but also in market size such that d2 of island 2 is large

enough to make u2 > v2. Given p1 > p2, suppose in equilibrium v∗1 > u∗1 and

v∗2 < u∗2 . By condition E3, we have m∗1 = u∗1 and m∗2 = v∗2 . Plugging equilibrium

matches in to condition E1, we have v∗1 =p1

p2u∗1 . Then solving demand equation

of island 1, we can get explicit form of equilibrium supply and demand in

island 1:

v∗1 =p1

p2u∗1

u∗1 =d1

1 + α− βp1

p2

We can solve equilibrium supply in island 2 by condition E4. Then plugging

124

supply in island 2 into demand equation in island 2 solves equilibrium demand

in island 2 which are:

v∗2 = Ny − v∗1

u∗2 =β

1 + αv∗2 +

d2

1 + α

In order to sustain this equilibrium, parameter values of {pi, di, Ny, α, β} need to

satisfy the following conditions. First condition is by default such that demand

is positive. The second condition needs to make island 1 more profitable than

island 2. The third inequality guarantees demand is positive in equilibrium

if thick market effect β is relatively smaller than congestion or direct network

effects α. The last inequality derives from excess demand in island 2. It requires

that d2 need to be large enough such that u∗2 > v∗2 in equilibrium.

d1, d2 > 0

p1 > p2

1 + α− βp1

p2> 0

u∗2 − v∗2 =d2

1 + α+ (

β

1 + α− 1)(Ny −

p1

p2u∗1) > 0

A.2 Proof of proposition 2

The demand equation can be rewritten as in (3.4):

uyi = −αuyi + βvyi + γuxi − θvxi + dyi︸ ︷︷ ︸Dyi

∀i

uxi = −αuxi + βvxi + γuyi − θvyi + dxi︸ ︷︷ ︸Dxi

∀i

125

We can deem Dyi as di in proposition 1 above. The equilibrium in which taxis

have excess supply in island 1 and excess demand in island 2, while Uber has

excess supply in both islands satisfies:

v∗y1 =py1

py2u∗y1 (T1)

u∗y1 =Dy1

1 + α− βpy1

py2

(T2)

v∗y2 = Ny − v∗y1 (T3)

u∗y2 =β

1 + αv∗y2 +

Dy2

1 + α(T4)

for taxis. These four equations are obtained similar to proposition 1. The only

different is that Dyi contains supply and demand of opponent firm Uber within

the same island i. As for Uber, assuming equal prices of Uber in both island, we

haveu∗x1v∗x1

=u∗x2v∗x2

such that drivers’ probabilities of matching are same in both

islands. Together with Uber’s demand equations, we can solve expression for

Uber’s demands and supplies as below.

v∗x1 =Dx1

Dx1 + Dx2Nx (X1)

u∗x1 =β

1 + αv∗x1 +

Dx1

1 + α(X2)

v∗x2 =Dx2

Dx1 + Dx2Nx (X3)

u∗x2 =β

1 + αv∗x2 +

Dx2

1 + α(X4)

Given the eight equations (T1-T4, X1-X4) and defined D f i, we can solve eight un-

knowns {u∗f i, v∗f i} after some algebra. To make such equilibrium exist, the solved

equilibrium and demands as explicit form of parameters {N f , d f i, pyi, α, β, γ, θ}

126

must satisfy u∗y2 > v∗y2 and u∗xi < v∗xi, ∀i1. Without solving the explicit forms, the

intuition for existence of such equilibrium is as follows. First, excess supply of

Uber in both islands can be achieved when Nx is large enough. For example,

v∗x1 − u∗x1 = (1− β

1 + α)v∗x1 −

Dx1

1 + αwith Dx1 ≡ γuy1 − θvy1 + dx1. Larger Nx

makes both v∗x1 and u∗x1 larger. As long as u∗y1 and Dx1 do not increase as fast as

increase of v∗x1(i.e. γ = 0), difference v∗x1 − u∗x1 increase in Nx. Second, to guar-

antee taxis’ demand in island 2 large than supply u∗y2 − v∗y2 > 0, it still requires

dy2 large enough as in proposition 1. Large dy2 increases demand of taxis in

island 2 as show in T4 such that demand exceeds supply. Moreover, increased

demand uy2 will not affect Uber’s equilibrium conditions X1-X4 through Dx2 as

long as γ is small or even equals zero.

1 Excess supply of taxi in island 1 is guaranteed given py1 > py2 and condition T1.

127

Appendix B|Selected MSAs for chapter 2

B.1 Selected MSAs

Table B.1: The 50 MSAs with average statistics over 20 quarters

Market No.

chains

No. prod-

ucts

Inside

share

Market

size(107 oz)

DMA

food

coverage

Asheville 1 77 0.63 9.56 0.77

Augusta 3 202 0.88 5.50

Boise City 2 135 0.71 6.21

Charleston 3 198 0.87 9.84

Charlotte 3 215 0.85 33.4 0.86

Charlottesville 3 210 0.77 4.06

Chattanooga 2 134 0.76 3.96

Chicago 2 131 0.66 86.7 0.65

Cincinnati 1 73 0.86 21.8 0.64

Columbia 2 137 0.84 9.32

Columbus 2 139 0.81 18.5 0.67

Davenport 1 72 0.81 5.18

Durham 3 200 0.79 8.16 0.77

Fayetteville 1 68 0.79 3.86 0.77

128

continued from previous page

Market No.

chains

No. prod-

ucts

Inside

share

Market

size(107 oz)

DMA

food

coverage

Florence 3 176 0.87 1.94

Fresno 4 220 0.61 8.61

Greensboro 2 142 0.88 10.9

Greenville 3 191 0.86 9.23 0.77

Hickory 2 98 0.71 3.54 0.86

Houston 3 153 0.71 47.2 0.50

Jacksonville 2 137 0.62 12.3 0.47

Kingsport 3 204 0.83 3.38

Knoxville 3 173 0.71 9.82

Lafayette 3 179 0.79 2.53

Lake Havasu 3 204 0.82 6 0.84

Las Vegas 3 198 0.77 21.7 0.76

Lynchburg 2 137 0.87 4

Manchester 3 197 0.67 12.1 0.83

Medford 3 179 0.68 1.88

Milwaukee 2 105 0.81 20.9 0.72

Myrtle Beach 3 199 0.90 7.74

Nashville 2 131 0.76 12.1 0.60

Oxnard 3 180 0.60 12 0.52

Phoenix 3 207 0.79 58.2 0.84

Prescott 3 201 0.81 3.59 0.84

Raleigh 2 146 0.74 21.1 0.77

Richmond 2 138 0.80 19.5 0.81

Roanoke 2 142 0.86 5.81

Salinas 3 160 0.64 3.94

San Francisco 2 110 0.57 35.5 0.48

Santa Barbara 3 173 0.54 6.61

129

continued from previous page

Market No.

chains

No. prod-

ucts

Inside

share

Market

size(107 oz)

DMA

food

coverage

Santa Rosa 3 146 0.65 6.09 0.48

Shreveport 2 120 0.67 3.38

Spartanburg 3 200 0.88 3.99 0.77

Tampa 2 143 0.72 26.3 0.29

Toledo 1 72 0.76 5.09

Tucson 3 197 0.72 14.1

Virginia Beach 2 146 0.72 33.3

Wilmington 2 142 0.89 9.77

Winston 2 141 0.88 6.44

130

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136

VitaBo Bian

Education• Ph.D. Economics, Pennsylvania State University, 2018.• M.Phil. Economics, Tilburg University (Cum Laude), 2012.• B.A. Economics, Nankai University (with honors), 2010.

Research Fields• Primary: Industrial Organization• Secondary: Applied Microeconomics, Applied Econometrics

Working Papers• Search Frictions, Network Effects and Spatial Competition: Taxis versus

Uber• Vertical Relationship and Merger Effects in the U.S. Beer Industry

Teaching Experience• Instructor, Labor Economics (online course), summer 2017.• Teaching Assistant, Intermediate Microeconomic Analysis (undergrad)• Teaching Assistant, Industrial Organization (undergrad)• Teaching Assistant, Introduction to Econometrics (undergrad)• Teaching Assistant, Statistical Foundations for Econometrics (undergrad)

Research Experience• Research Assistant, Prof. Peter Newberry, Summer 2014.

Languages & Computer Skills• Language: Mandarin Chinese (native), English (fluent).• Software: Matlab, Stata, Python, ArcGIS, LATEX, MS Office.