Business, Sauder School of
Operations and Logistics (OPLOG), Division of
DSpace
UBCV
Wang, Kun
Doctor of Philosophy - PhD
University of British Columbia
This dissertation focuses on three major topics in transportation. The first one is related to the seaports adaptation to climate change related disasters (Chapter 2). We investigate the disaster adaptation investments made by two landlord ports with each serving its captive markets while competing for a common hinterland. The impact of “Knightian uncertainty” of disaster occurrence on port adaptation investment is investigated. We also investigate the impacts of inter-port and intra-port competition and cooperation on the port adaptation investment. The second topic is related to competition between airlines and high-speed rail (HSR) (Chapter 3). We investigate, both theoretically and empirically, the effect of HSR speed on airline traffic and price, taking into account the degree of air-HSR service substitutability. We consider two countervailing effects of HSR speed on airlines, i.e., the “travel time” effect and the “safety” effect. A rare natural experiment in HSR speed reduction in China is used to empirically test the theoretical findings. The incident is a rare quasi-natural experiment of HSR speed change as it was forced by the government due to safety concern and implemented system-wide regardless of market heterogeneity. A difference-in-differences method is used for estimation of the HSR speed effect on airlines as well as for verification of the theoretical predictions. The last topic addresses two important issues in the air transport economics, aiming to provide new insights. In Chapter 4, we develop a structural discrete-choice model to study airline competition in Chinese domestic market, explicitly taking into account the potential effects of “legacy” regulation on airlines’ competition behavior. Finally, in Chapter 5, we explore the effect of airport congestion on airport’s concession revenue. We model and empirically test two countervailing effects of airport congestion on airport concession demand: namely a “dwell time” effect (passenger spends more, due to longer dwell time within the airport) and a “stress” effect (passenger spends less when he/she feels stressful because of the congestion). The implications on airport optimal pricing and social welfare are investigated.
Essays on Economics of Transport Infrastructure: Pricing, Investment and Competition by Kun Wang A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Business Administration) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) August 2018 © Kun Wang, 2018 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled: Essays on Economics of Transport Infrastructure: Pricing, Investment and Competition submitted by Kun Wang in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Business Administration Examining Committee: Anming Zhang, Sauder School of Business Supervisor Robin Lindsey, Sauder School of Business Supervisory Committee Member Ralph Winter, Sauder School of Business Supervisory Committee Member Kevin Milligan, Vancouver School of Economics University Examiner Thomas Davidoff, Sauder School of Business University Examiner Additional Supervisory Committee Members: Tae Hoon Oum, Sauder School of Business Supervisory Committee Member iii Abstract This dissertation focuses on three major topics in transportation. The first one is related to the seaports adaptation to climate change related disasters (Chapter 2). We investigate the disaster adaptation investments made by two landlord ports with each serving its captive markets while competing for a common hinterland. The impact of “Knightian uncertainty” of disaster occurrence on port adaptation investment is investigated. We also investigate the impacts of inter-port and intra-port competition and cooperation on the port adaptation investment. The second topic is related to competition between airlines and high-speed rail (HSR) (Chapter 3). We investigate, both theoretically and empirically, the effect of HSR speed on airline traffic and price, taking into account the degree of air-HSR service substitutability. We consider two countervailing effects of HSR speed on airlines, i.e., the “travel time” effect and the “safety” effect. A rare natural experiment in HSR speed reduction in China is used to empirically test the theoretical findings. The incident is a rare quasi-natural experiment of HSR speed change as it was forced by the government due to safety concern and implemented system-wide regardless of market heterogeneity. A difference-in-differences method is used for estimation of the HSR speed effect on airlines as well as for verification of the theoretical predictions. The last topic addresses two important issues in the air transport economics, aiming to provide new insights. In Chapter 4, we develop a structural discrete-choice model to study airline competition in Chinese domestic market, explicitly taking into account the potential effects of “legacy” regulation on airlines’ competition behavior. Finally, in Chapter 5, we explore the effect of airport congestion on airport’s concession revenue. We model and empirically test two countervailing effects of airport congestion on airport concession demand: namely a “dwell time” effect (passenger spends more, due to longer dwell time within the airport) and a “stress” effect (passenger spends less when he/she feels stressful because of the congestion). The implications on airport optimal pricing and social welfare are investigated. iv Lay Summary This dissertation studies three major topics emerging in today transport sector, especially in the fast-growing markets. The first topic is on seaport adaptation to climate change related disasters. It shows how the disaster uncertainty, and port competition and cooperation can affect optimal port adaptation investment, and the resultant implication to social welfare. The second topic is about the airlines and high-speed rail competition, in which we examine how the HSR speed can affect airline demand and price. Last topic is to explore how the government regulation can restrict airlines competition and the effect on airfare; and how airport congestion can affect passengers’ concession consumption at the airport. Overall, our findings can contribute to a better understanding on these emerging issues in transportation, provide both policy and managerial implications, and open avenues for future studies as well. v Preface A version of Chapter 2 has been accepted for publication. Wang, K., Zhang, A. (2018). Climate change, natural disasters and adaptation investments: Inter- and intra-port competition and cooperation. Transportation Research Part B: Methodological, forthcoming. Anming Zhang and I came up with the initial research question. I conducted the initial modeling analysis and all mathematical derivations. The first draft of the manuscript was written by me, and Anming Zhang made major revisions on later versions. Chapter 3 is a joint work with Anming Zhang, Wenyi Xia and Qiong Zhang. A version of this chapter has been published. Wang, K., Xia, W., Zhang, A., Zhang, Q. (2018). Effects of train speed on airline demand and price: Theory and empirical evidence from a natural experiment. Transportation Research Part B: Methodological, 114, 99-130. Anming Zhang came up with the original research question. I proposed both theoretical economic model and econometric specification. I derived the basic theoretical economic model solutions, and worked with Wenyi Xia for further modeling extensions. The econometric part was exclusively done by myself. Anming Zhang made revisions on manuscript writing, and Qiong Zhang is responsible for data collection. Chapter 4 is unpublished work jointly with Tae Hoon Oum and Xiaowen Fu. I came up with the research idea, derived the methodology, collected data and conducted estimation. Tae Hoon Oum and Xiaowen Fu helped on result interpretation and manuscript writing. A version of this chapter has also been awarded the “Best Graduate Student Paper” at the 58th US Transportation Research Forum. Chapter 5 is unpublished work with Wenyi Xia, Tae Hoon Oum and Leonardo Corbo. I and Tae Hoon Oum came up with the research idea, developed and solved the economic model. Wenyi Xia and I conducted the empirical estimation. Leonardo Corbo collected data and contributed on manuscript writing. Tae Hoon Oum made major revision on the manuscript writing. vi Table of Contents Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface ............................................................................................................................................ v Table of Contents .......................................................................................................................... vi List of Tables .................................................................................................................................. x List of Figures .............................................................................................................................. xii Acknowledgements ..................................................................................................................... xiv Dedication .................................................................................................................................... xiv Chapter 1. Introduction ................................................................................................................ 1 1.1 Port adaptation investment to climate change related disasters ..................................... 1 1.2 Air-HSR competition ........................................................................................................... 3 1.3. Air transport management and policy .............................................................................. 5 Chapter 2. Climate Change, Natural Disasters and Adaptation Investments ......................... 8 2.1 Introduction .......................................................................................................................... 8 2.2 Basic Model ......................................................................................................................... 12 2.3 Analysis ............................................................................................................................... 19 2.3.1 Port pricing .................................................................................................................... 20 2.3.2 Adaptation investment .................................................................................................. 25 2.4 Effects of Port Competition Intensity ............................................................................... 37 vii 2.5 Concluding Remarks ......................................................................................................... 40 Chapter 3. Effects of High-Speed Rail Speed on Airline Demand and Price ........................ 42 3.1 Introduction ........................................................................................................................ 42 3.2 Literature Review............................................................................................................... 44 3.2.1 Air-HSR competition .................................................................................................... 45 3.2.2 Interactions of horizontal differentiation and vertical differentiation ........................... 47 3.3 A Natural Experiment in HSR Speed Reduction ............................................................ 47 3.4 Analytical Model ................................................................................................................ 50 3.4.1 Demand side .................................................................................................................. 50 3.4.2 Supply side .................................................................................................................... 53 3.5 Empirical Methodology and Data .................................................................................... 60 3.6 Empirical Results ............................................................................................................... 70 3.7 Concluding Remarks ......................................................................................................... 84 Chapter 4. Modeling Airline Competition in Markets with Legacy Regulation ................... 87 4.1 Introduction ........................................................................................................................ 87 4.2 Background on the Chinese Airline Market .................................................................... 89 4.3 Model and Estimation Method ......................................................................................... 91 4.3.1. Travel demand side and passenger utility .................................................................... 92 4.3.2 Modeling of airline competition ................................................................................... 94 4.4 Variables, Data, and Instrument Variables (IVs) Selection ......................................... 101 4.5 Model Estimation Results ................................................................................................ 106 viii 4.5.1 Demand estimation based on the demand moment conditions only ........................... 106 4.5.2 Joint estimation of demand and marginal cost functions ............................................ 111 4.6 Conclusion and need for further study .......................................................................... 122 Chapter 5. Airport pricing when airport congestion affects passengers’ concession ......... 124 5.1 Introduction ...................................................................................................................... 124 5.2 Theoretical model ............................................................................................................. 127 5.2.1 Airline problem ........................................................................................................... 133 5.2.2 Private Congested Airport ........................................................................................... 134 5.2.3 Public Congested Airport ............................................................................................ 136 5.3 Empirical estimation ........................................................................................................ 138 5.3.1 The econometric model ............................................................................................... 138 5.3.2 Data description .......................................................................................................... 144 5.5 Summary and concluding remarks ................................................................................ 153 Chapter 6. Conclusion ............................................................................................................... 155 References .................................................................................................................................. 159 Appendices ................................................................................................................................. 177 Appendix A: Appendix for Chapter 2 .................................................................................. 177 A.1 Optimal terminal operators’ prices and port authorities’ concession fee ...................... 177 A2. Best response function of optimal adaptation investments ........................................... 180 A3. Expressions of equilibrium port adaptation investments and comparative statics ........ 183 A4. The Effects of Port Competition Intensity on equilibrium adaptation .......................... 189 ix Appendix B: Appendix for Chapter 3 .................................................................................. 191 B1. Proof of Proposition 3.1 ................................................................................................ 191 B2. Proof of Proposition 3.2 ................................................................................................ 192 B3. Proof of Proposition 3.3 ................................................................................................ 193 B4. Airline demand and price equation estimation .............................................................. 200 Appendix C: Appendix for Chapter 4 .................................................................................. 204 C1. Reduced form demand equation estimation .................................................................. 204 C2. Derivative of product share to price (Bertrand) ............................................................ 205 C3. Derivative of price to product share for the Nash-Cournot ........................................... 206 C4. Proof of existence and uniqueness of Fixed Point problem .......................................... 206 Appendix D: Appendix for Chapter 5 .................................................................................. 208 D1. Different effects of runway and terminal congestion .................................................... 208 D2. The effect of concession price on aeronautical charge for private and public airports . 211 D3. Proof of Propositions 5.2 a and 5.2 b ............................................................................ 212 D4. Proof of Proposition 5.3 ................................................................................................ 215 x List of Tables Table 2.1 Notational glossary......................................................................................................... 17 Table 2.2 The summary of the Nash equilibrium of different inter-port competition and intra-port coordination regimes ...................................................................................................................... 33 Table 3.1 Expressions of elasticities to HSR speed………………………………………………63 Table 3.2 Summary of the treated routes before and after the HSR speed reduction .................... 65 Table 3.3 Estimation results for airline traffic equation ................................................................. 71 Table 3.4 Estimation results for airline price equation .................................................................. 73 Table 3.5 Estimated HSR speed effect ........................................................................................... 75 Table 3.6 Expressions of elasticities to HSR speed ....................................................................... 78 Table 3.7 Estimation results for airline traffic equation ................................................................. 79 Table 3.8 Estimation results for airline price equation .................................................................. 80 Table 3.9 Estimated elasticities of airline price and demand to HSR speed reduction and overall HSR competition effect .................................................................................................................. 82 Table 3.10 River-Vuong test for the assumed functional forms .................................................... 84 Table 4.1 Summary Statistics of Major Variables………………………………………………105 Table 4.2 Demand Function Estimation and Robust Test with IV and OLS Demand Estimation ...................................................................................................................................................... 107 Table 4.3 Median price elasticity and willingness to pay for product attributes.......................... 109 Table 4.4 BLP joint estimation of demand and marginal cost functions ..................................... 115 Table 4.5 Estimated airline profit margin and demand elasticity of the three competition conducts ...................................................................................................................................................... 119 Table 4.6 Yield comparison between Chinese and US airlines from accounting data ................ 120 xi Table 5.1 Summary statistics ....................................................................................................... 146 Table 5.2 The estimation for the demand equation ...................................................................... 148 Table 5.3 The estimation for the aeronautical price equation ...................................................... 150 Table 5.4 The estimation of concession pricing equation ............................................................ 151 Table B1 Estimation results for airline traffic equation .............................................................. 195 Table B2 Estimation results for airline price equation ................................................................. 197 Table B3 The estimated HSR speed effect ................................................................................... 199 Table B4 GMM estimation results for airline demand equation ................................................. 201 Table B5 GMM estimation results for airline price equation ...................................................... 203 Table D1 Sample airports ............................................................................................................. 213 xii List of Figures Figure 2.1 The market structure of the two-port system ................................................................ 14 Figure 2.2 The timeline of the decisions of different parties ......................................................... 15 Figure 2.3 Shipper’s utility at each port after completion of adaptation investments ................... 17 Figure 2.4 Numerical values of I̅i a(t′)Ĩi a(t′) and I̅i t(t′)Ĩi t(t′) ............................................................................ 38 Figure 2.5 Numerical values of Îi a(t′)I̅i a(t′) and Îi t(t′)I̅i t(t′) ............................................................................ 39 Figure 3.1 Evolution of airline traffic and yield for the treated (HSR) and control (no HSR) routes (quarterly data from Quarter 1 of 2010 to Quarter 3 of 2013) ....................................................... 68 Figure 3.2 Evolution of airline traffic and yield for treated routes shorter and longer than 850 km and control (no HSR) routes ........................................................................................................... 69 Figure 4.1 Market price elasticity distribution ............................................................................. 110 Figure 4.2 Factors considered by Chinese air passenger for air product choice in the year 2010 ...................................................................................................................................................... 111 Figure 4.3 Average route-level airline HHI for different density markets from August to December of 2010 ........................................................................................................................ 113 Figure 4.4 Average route-level yield (in USD$) for different density markets from August to December 2010 ............................................................................................................................ 114 Figure 4.5 Price Reduction distribution by dliminating price collusiveness on Top 25% dense markets (in 100 USD) .................................................................................................................. 122 Figure 5.1 The distribution of a representative passenger’s willingness to pay for airport concession service ........................................................................................................................ 128 Figure 5.2 Plot of airport passenger volume and concession revenue per passenger .................. 132 xiii Figure 5.3 Estimated inverted U-shaped curve between airport passenger volume and concession revenue per passenger .................................................................................................................. 152 Figure A1 The impact of increased port authority adaptation Iia on the best response functions of competing port authorities’ concession fee at operation stage ..................................................... 179 Figure A2 The best response adaptation investment functions for port authority and terminal operators at the same port ............................................................................................................. 181 Figure A3 The best response adaptation investment functions for port authorities ..................... 183 Figure D1 The relation between number of passenger per runway and per passenger concession revenue…………………………………………………………………………………………..209 Figure D2 The relation between number of passenger per terminal square meter concession revenue per passenger .................................................................................................................. 210 Figure D3 Average flight delay and the average passenger per runway for the US sample airports ...................................................................................................................................................... 211 xiv Acknowledgements I am deeply grateful and indebted to Prof. Anming Zhang, my thesis supervisor, for his always insightful and patient guidance on me to finish the major parts of my thesis. His enthusiasm in research and life inspired me all the way. I also would like to express my sincere appreciation to Prof. Tae Hoon Oum who was my chief supervisor in the first two years of my PhD study. He led me into the academic research, and always offers me the strongest support, both morally and financially. Using them as my role models, I have learnt the essence of integrity and hardworking to be a true scholar. I would also express my sincere gratitude to Prof. Robin Lindsey and Prof. Ralph Winter, for their insightful advices provided to me on this dissertation and the PhD study, and spending their valuable time on serving as my thesis committee members. I also very indebted to Wenyi Xia, Prof. Xiaowen Fu for their great support and help on my work and provided advices on the chapters included in this dissertation, as well as Elaine Cho who has provided a wide range of timely and detailed administrative supports. My enduring gratitude also goes to my wife and parents who always love and support me unconditionally. Dedication xv To my wife, Rongwen Jia 1 Chapter 1. Introduction This dissertation includes three major research topics in transportation economics: (i). seaport investments for adaptation to climate change related disasters; (ii). airline and high-speed rail (HSR) competition; and (iii). airline competition and airport pricing. These issues are studied in four essays, which are Chapter 2 to 5 in this manuscript style dissertation. The three topics in this dissertation are all motivated by current major challenges and recent development in the transport sector: the global climate change threat, the intermodal transport competition with dramatic HSR development, and newly emerging issues on aviation management. As the transport sector contributes significantly to the well-being of the society (i.e., employment, tax revenue, investment and economic output), and also provides indispensable inputs to other sectors such as logistics and trade, well developed and coordinated transport systems are of critical importance to the modern society. Major policy options and market competition strategies around the three topics have been implemented or proposed. Despite aiming to promote social welfare or improve financial performance, many of them have not been sufficiently studied. For some of the adopted policies and strategies, their ultimate effects, and underlying mechanisms remain unclear. For some of them proposed, there is a need to quantify the effects and benchmark with alternatives ex ante. This dissertation, therefore, aims to investigate the abovementioned three topics through rigorous economic modeling and econometric approaches, with the hope that optimal policies and strategies can be identified. 1.1 Port adaptation investment to climate change related disasters Chapter 2 is the first topic. This research is motivated by the fact that the climate change has threated the resilience of the transport systems and the global supply chain, and seaports are especially vulnerable to climate changed related disasters. Given over 80 percent of global trade by volume and more than 70 percent of its value being carried by maritime shipping (UNCTAD, 2017), a better adaptation to climate change related disaster is vital to maintain the function of global supply chain and international trade. The past decade has witnessed more frequent extreme weather events and natural disasters around the world, resulting in increasing economic and social 2 costs, e.g., Katrina (occurred in 2005), Sandy (in 2012) and, most recently, Harvey (in 2017) on the US (United States) coastline. Scientific studies suggest that climate change might lead to an increase in both the occurrence and the strength of weather-related natural disasters in the near future (e.g., IPCC, 2013; Keohane and Victor, 2010; Min et al., 2011). However, in spite of its growing importance of port adaptation, the research on this issue has been underdeveloped and provided limited insights on how to adapt port services to climate change related threats. In particular, the majority of existing literature focuses on environmental effects of transportation (especially the mitigation to reduce emissions of transport sector on climate change; see, e.g., Zhang et al., 2004; Wang et al., 2015; Liu et al., 2017). And a research line on the interplays between ports and their hinterlands is emerging (e.g. De Borger and Proost, 2012; Wan et al., 2016, 2017). However, these studies focus on the issues of port and hinterland pricing and capacity investment (Basso and Zhang, 2007; De Borger and De Bruyne, 2011). The impacts of the disaster uncertainty, inter- and intra- port competition and cooperation on port adaptations have been largely left untouched. In Chapter 2, we develop an economic model to study disaster adaptation investments made by two landlord ports that serve their own respective captive markets while compete for a common hinterland. Each port consists of a private port authority (landlord owning the port infrastructure and land) and a private terminal operator (tenant owning the superstructure and handling the cargos). This landlord type port is the most common port structure in the world. We model the probability of a natural disaster, which is induced by climate change, to be ambiguous prior to an adaptation investment, but will be known after the adaptation investment, i.e., a “Knightian uncertainty” (Knight, 1921). 1 We assume this Knightian uncertainty of disaster probability in the sense that probability of the disaster occurrence is uncertain (a random variable) and not accurately knowable. In Chapter 2, we find that (i). with Knightian uncertainty assumption, a higher expectation of the disaster occurrence probability encourages the adaptation, but the variance of the disaster occurrence probability can discourage the adaptation. This analytical result may provide a sound explanation for why in practice adaptation is much more difficult to implement than mitigation: it 1 Knightian uncertainty refers to ambiguity in which decision maker has to make decisions when the relevant probabilities are unknown. 3 might be because our present knowledge about climate change and related disasters is far from reasonable accuracy; (ii). inter-port competition also results in more adaptation investments (i.e., the “competition effect”); (iii). there is free-riding on adaptation investments between the port authority and the terminal operator (i.e. the “free-riding effect”) within each port. Their intra-port coordination can increase the adaptation by removing such free-riding effect; and (iv). these two effects can be strengthened by a higher expectation and larger variance of the disaster occurrence probability, and by a more intense inter-port competition (less service homogeneity). Overall, this chapter has shown the complexity for port adaptation decision. On one hand, the great uncertainty of the disaster occurrence makes it difficult for ports to justify the adaptation investment. On the other hand, the port market structure (both vertical and horizontal relationships among the entities) has further complicated the strategic adaptation efforts. Besides the climate change disaster challenge, the following Chapters 3-5 examine the other major emerging issues on the transport sector. Same as Chapter 2, the following chapters also demonstrate very complex strategic interactions within transport sector among many involved entities. 1.2 Air-HSR competition Chapter 3 addresses the intermodal competition between the airlines and the high-speed rail (HSR). This research was motivated by the recent phenomenal HSR expansions, especially in China. By the end of 2017, the length of HSR network under operation in China has reached 25,000 kilometers (km), greater than the sum of the rest of the world. China recently announced its plan to further expand its HSR network to a total length of 38,000 km by 2025, when all Chinese cities with more than half million population will have HSR linkage. At least a yearly investment of 800 billion RMB (about 115 billion USD) is required from 2017 to 2025 to maintain the pace of HSR expansion. This HSR development has intensified air-HSR competition dramatically. There have been several studies focusing on air-HSR competition in the European markets, where the HSR has longer history of development (e.g. González-Savignat, 2004; Behrens and Pels, 2012; Dobruszkes, 2011; Capozza, 2016). However, recently, intense air-HSR competition is mainly observed in the Chinese market, evidenced by the fact that the airlines were forced to cut prices and withdrew from several important routes (Fu et al., 2012; Jiang and Li, 2016). For example, air ticket price has dropped by 80% in the market between Wuhan and Xiamen, two provincial capital 4 Chinese cities recently linked by HSR. Spring Airlines, the largest of the low-cost carriers (LCCs) in China, withdraw all capacities from the routes less than 800 km to avoid head-to-head competition with HSR (Wang et al., 2017). The HSR has already outpaced the air transport growth in China, as the HSR passenger traffic grew at an annual rate more than 30% for the 2008-2016 period, while the air transport grew at only about 10% during the same period (Chinese Statistics Yearbook 2017). However, in spite of the growing air-HSR competition, several issues have not been well addressed by existing literature. Especially we find there have been few studies to explicitly examine the HSR speed effect on airline demand and traffic. The answers to this question is of great policy relevance and managerial implications in that many countries are lifting the HSR speed. For example, China has decided to raise the HSR speed from current 300 km/hr (kilometers per hour) to its design speed at 380 km/hr, and the US, Japan and China are also developing maglev HSR with speed more than 500 km/hr. Furthermore, the HSR speed increase can also cause safety concern, which is an important factor for travel mode choice in developing countries where the HSR technology is immature. However, there are very limited studies that explicitly investigate how the HSR speed could affect air-HSR competition (in terms of airline traffic and price). To fill these research gaps, in Chapter 3, we develop an analytical model to study HSR speed effects on airline traffic and price, explicitly accounting for the potential impact of intermodal substitutability between airline and HSR services in different markets. The model incorporates two countervailing effects of HSR speed on airlines, namely the “travel time” effect and “safety” effect, in that an increase in HSR speed reduces HSR travel time but may harm public confidence in HSR safety. Following the analytical model predictions, we empirically test and quantify the HSR speed effects on airlines using an event of HSR speed reduction in China. We utilize a quasi-natural experiment of the HSR speed reduction in China due to a fatal accident in 2011 for estimation. This speed reduction is an exogenous shock as it was implemented system-wide and enforced by the government rather than being a market competition outcome. A difference-in-differences method is employed to estimate equations of airline traffic and price. In line with theoretical analysis, we identify the varying HSR speed effects when airline and HSR services are differently substitutable. The theoretical model shows that (i). air-HSR substitutability reinforces the HSR speed effect on airlines; (ii). HSR speed has a larger impact on airline traffic than on airline price; and (iii). HSR speed effect can be moderated by the intensity of inter-airlines competition. The empirical results 5 are largely consistent with the theoretical propositions. Specifically, we find that (i). the HSR speed reduction increased both airline traffic and price, implying that the travel-time effect dominates the safety effect of a HSR speed change; and more importantly (ii). the estimation shows that the HSR speed effect on airlines is much stronger on short-haul routes than on long-haul routes, where airlines and HSR are less substitutable. 1.3. Air transport management and policy The last parts of the dissertation aim to add to two emerging yet nascent research line on air transport economics: one is the airline competition under legacy regulation (Chapter 4), and the other is the impact of airport congestion on airport concession demand and pricing (Chapter 5). Chapter 4 is motivated by the fact that the air transport is growing dramatically in developing countries, especially with China becoming the world’s second largest aviation market since 2005. However, most airline markets in the developing countries are still subject to restrictive regulations, such as route entry, airport slot allocation, capacity expansion etc. They lag far behind the developed countries, such as the US and the EU, in market liberalization. It is important to understand how such legacy regulations can distort airline competition and pricing in these developing countries. The presented research can help evaluate possible deregulation’s effects on airlines pricing and passenger’s surplus. we find that existing econometric approaches on airline studies assume a certain competition type, i.e. Cournot, Bertrand or collusion, and thus are unable to account for a wide range of airline competition behaviors under regulatory constraints. So in Chapter 4, we propose an improved econometric model to fill this research shortage. Besides, Chapter 5 is based on two dramatic trends in nowadays airport business: one is the increasing share of concession service revenue (i.e., services of retail, food and beverage, car rental, land rentals, car parking and advertising) in airport total revenue (Oum et al., 2004); and the other is the deteriorating airport congestion in major airports around the world (D’Alfonso et al., 2013; Wan et al., 2015). The interaction of these two factors (airport concession business and congestion) has been largely ignored, while there can be very essential implications on airport operation and pricing. On one hand, airport congestion can make passenger to stay longer at airport (increasing dwell time), thus increasing their chance to consume concession (D’Alfonso et al., 2013), but on the other hand, airport congestion can cause stress which may discourage the concession 6 consumption. The two countervailing effects of airport congestion on concession business have not been well explored. Specifically, in Chapter 4, we develop a structural discrete-choice model to study airline competition in Chinese domestic market, explicitly taking into account the potential effects of legacy regulation on airlines’ competition behavior. This work constitutes an improved econometric approach that allows researchers to identify a range of competitive regimes for different group of routes. This allows us to measure possible effects of the legacy regulation and to benchmark the results obtained under restrictive Bertrand or Cournot competition. The results show that (i). Chinese airlines set prices collusively on the densest (with highest traffic volume) routes where regulatory control is stricter and airport congestion is severer; by contrast, they compete more aggressively on less travelled routes with lighter regulatory control; and (ii). on model side, strong evidence exists that the presented new approach performs better than the existing competition models in terms of obtaining better results on estimation and prediction. This suggests that simply assuming a particular type of competition regime for a market may yield biased estimation. Our proposed econometric model may be also applied to other airline markets with legacy regulations, to identify the airlines competition behavior and for counterfactual analysis of possible market liberalization. Finally, in Chapter 5, we explore the effect of airport congestion on airport’s concession revenue, and optimal airport pricing on both aeronautical and concession services. We conduct both analytical and empirical investigations, proposing two countervailing effects of airport congestion on concession demand: (i). the “dwell-time” effect: passengers consume more when airport congestion forces them to stay longer at airport and (ii). the “stress” effect: passengers are unwilling to spend at airport when they are under stress caused by the flight delay or crowdedness. We propose an overall curvilinear effect of airport congestion on concession demand. Specifically, dwell time effect dominates when airport congestion is moderate, while stress effect prevails when airport congestion is severe. We then investigate the optimal aeronautical and concession charges of two types of airports: a private profit-maximizing airport and a public social-welfare maximizing airport. Our results suggest that (i). when airport congestion is severe and the stress effect prevails, it is possible that public airports charge a higher aeronautical price than private airports. This finding complements previous studies, which ignore airport congestion effect on concession demand and suggest that public airport always charges lower aeronautical price; (ii) empirical 7 evidence supports the existence of both dwell-time and stress effects of airport congestion on concession demand and price; and (iii) runway congestion contributes more to dwell time effect while terminal congestion contributes more to stress effect. 8 Chapter 2. Climate Change, Natural Disasters and Adaptation Investments 2.1 Introduction The past decade has witnessed more frequent extreme weather events and natural disasters around the world, with increasing economic and social costs. The examples include the impacts of hurricanes Katrina (occurred in 2005), Sandy (in 2012) and, most recently, Harvey (in 2017) on the US (United States) coastline. In particular, Harvey brought an estimated $75 billion economic loss2, and Sandy caused an estimated $36.1 billion loss. Scientific studies suggest that climate change might lead to an increase in both the occurrence and the strength of weather-related natural disasters in the near future (e.g., IPCC, 2013; Keohane and Victor, 2010; Min et al., 2011). According to Morgan Stanley research, until 2015, among the top-ten most costly hurricanes hitting the US, eight occurred after year 2000.3 Such increasing frequency and strength of hurricanes in North Atlantic Basin can be attributed to temperature rise of the ocean due to global warming (IPCC, 2013). In addition to such “one shot” disasters, there is an increasing risk of coastal and marine natural disasters (in terms of frequency and intensity) such as the sea level rise (SLR) owing to climate change. By the end of this century the sea level may be 75-80 centimeters (cm) higher than today’s level (Schaeffer et al., 2012). Seaports are highly vulnerable to coastal and marine natural disasters, and are exposed to climate hazards such as SLR and resultant flooding and storms due to climate change (OECD, 2016). For example, Kafalenos and Leonard (2008) estimate the vulnerability of ports in the US Gulf Coast to SLR, and Nicholls et al. (2008) assess the exposure to flooding for 136 large port cities around the globe. Stenek et al. (2011) and Scott et al. (2013) gauge the vulnerability for port system sub-components to climate-change, including navigation, berthing, material handling, vehicle movement, goods storage and transportation. The increasing risk of natural disasters to seaports may trigger substantial social, economic loss and may lead to shifts in freight transport and passenger flow (Koetse and Rietveld, 2009). Crucially, many ports play a critical role in global supply chains, so that any significant loss or degradation of service due 2 Unless specified otherwise, the dollar amount in this chapter is in US$. 3 The details about top ten most costly hurricanes in the US can be found in the link http://www.businessinsider.com/hurricane-irma-costliest-hurricanes-us-history-map-2017-9. 9 to disaster occurrence would have significant knock-on effects on global supply chain performance (OECD, 2016). Unlike rich literature on the environmental effects of transportation (especially the mitigation of transport sector on climate change; see, e.g., Zhang et al., 2004; Wang et al., 2015; Liu et al., 2017), there is a lack of research on the adaptation of ports to climate change related disasters. 4 Xiao et al. (2015) is one exception that models the port adaptation investment by both port authority and terminal operator under the uncertainty of disaster occurrence. They find that there is a free-riding effect of adaptation efforts between the two entities, and that the information of the disaster occurrence is essential for the timing of adaptation investments (the “invest now or later” question). It is noted that Xiao et al. (2015) consider port adaptation of a single port and so they did not consider inter-port competition 5. They further treat port demand and pricing being exogenous to adaptation investments. However, port adaptation and resilience to natural disaster can essentially affect port competitiveness and the port choice decision by shippers. For instance, port disruption can cause serious reputational and direct economic losses on shippers (Zhang and Lam, 2015), leading to their switching to a better adapted port for services (Chang, 2000).6 Therefore, an improved theoretical model on port adaptation need to endogenize the shipper’s demand and port pricing decisions, and incorporate the inter-port competition as well.7 4 There are several studies on post-disaster relief, and transport and logistics system resilience (e.g. Chen and Yu, 2016; Huang et al., 2013; Rawls and Turnquist, 2010; Sheu, 2014), while the studies on adaptation strategies are few. In addition, these studies mainly adopt engineering approaches to analyze optimal cargo flow and to strengthen the important segment of the supply chain or network for enhancing the network resilience, and the economic analysis is not well implemented. 5 Port competition and cooperation was recently also analyzed in disaster prevention by Liu et al. (2017), in which the ports can be either substitutes or complements. They focused on the case of mitigation rather than adaptation, however. 6 For example, Chang (2000) empirically studied the impact of the 1995 Great Hanshin earthquake on the port of Kobe (Japan), which was shut down post the disaster and only recovered after two years. She found that due to the earthquake damage, the Kobe port lost most of transshipment cargo to competing Asian ports, in both the short- and long-term. 7 Theoretical analyses on port competition and the interplays between ports and their hinterlands are emerging. Wan et al. (2018) reviewed recent theoretical studies in the area, and found that these studies mainly focus on the port and hinterland capacity investments, and on port congestion pricing (De Borger et al., 2008; Zhang, 2008; De Borger and Proost, 2011; Wan and Zhang, 2013). Some recent studies discussed the emission control of marine transport, such as Homsombat et al. (2013), Wang et al. (2015), Sheng et al. (2017) and Dai et al. (2018). However, none of these papers have considered port adaptation to climate-change risks. 10 Furthermore, despite a rich theoretical literature on traffic demand uncertainty modelling, 8 uncertainty about climate change-related disasters and the associated costs have not been well modeled in existing maritime transport studies. Uncertainty regarding their occurrence and outcomes can be very high (IPCC, 2013; OECD, 2016), due to limited scientific knowledge and to forecast complexity. In contrast, traffic demand can be more accurately forecasted with the availability of rich historical traffic data and other economic and demographic variables. Therefore, to model uncertainty of climate change-related disasters, one needs to account for the large ambiguity at the adaptation planning and investment stage, noting that adaptation projects usually are lengthy in duration and very costly. Xiao et al. (2015) modelled the disaster uncertainty in a two-period setting, assuming a uniformly distributed disaster occurrence probability in the first period but, with information learning, a more accurate (a more narrowly-bounded uniform distribution) probability in the second period. There is thus an option value in delaying investment, owing to better information about the disaster occurrence probability. However, this assumption of uniformly-distributed disaster occurrence probability could be restrictive. In this chapter, we propose a model allowing a general distribution of the disaster occurrence probability, which can capture the “ambiguity” notion of disaster uncertainty that is absent in Xiao et al. (2015). Taken together, the present chapter contributes to existing literature by developing a more general analytical framework to analyze port adaptation to climate change-related disasters. More specifically, we model the climate change-related disaster occurrence probability to have Knightian uncertainty (Knight, 1921) at an early adaptation investment stage when two ports make adaptation decisions. Knightian uncertainty refers to ambiguity in which a decision maker must make decisions when the relevant probabilities are unknown. This is used to capture the fact that the probability of disaster occurrence is very uncertain (is subject to a probability distribution) at the adaptation planning stage. Our Knightian uncertainty is general and covers a wider family of probability distributions of natural disaster occurrence, which are not limited to the specific 8 See, for example, the studies by Kraus (1982), D’Ouville and McDonald (1990), Proost and Van der Loo (2010), and Xiao et al. (2013). Kraus (1982) considered highway pricing and capacity choice under demand uncertainty, and found that both capacity and price are greater than those under an expected value of demand. D’Ouville and McDonald (1990) also studied the optimal capacity and toll of urban highways under demand uncertainty, and found that a social planner who simultaneously chooses the capacity and congestion toll to maximize the expected welfare will choose a larger capacity relative to the mean level of road use. Proost and Van der Loo (2010) examined capacity choice by modeling a social planner’s decision on transport infrastructure capacity when the future demand can be either high or low, with different tolls being set for each case to maximize welfare. Xiao et al. (2013) analyzed the effects of demand uncertainty on airport capacity choices. 11 assumptions in Weitzman (2009) and Xiao et al. (2015). 9The effects of this Knightian uncertainty on port adaptation are investigated. Moreover, the present chapter will explicitly examine the impacts of both inter-port competition and intra-port cooperation on port adaptation by explicitly modelling the endogenous port pricing and shippers’ demand together with port adaptation. It is the first chapter, to our best knowledge, that analytically examines how inter-port competition would affect port adaptation.10 We find, with Knightian uncertainty assumption, port adaptation investment increases with the expectation of the disaster occurrence probability but decrease with its variance. In other words, a higher expectation of the disaster occurrence probability encourages the adaptation, but the variance of the disaster occurrence probability can discourage the adaptation. This analytical result is general and not limited to the specific disaster occurrence probability distributions assumed in Weitzman (2009) and Xiao et al. (2015), and it may provide a nice explanation for why in practice adaptation is much more difficult to implement than mitigation, owing to the fact that our present knowledge about climate change and related disasters is far from reasonable accuracy. Inter-port competition also results in more adaptation investments (i.e., the “competition effect”). This is an important supplementary finding to Xiao et al. (2015) who ignore the inter-port competition and its possible effect on port adaptation investment. There is free-riding on adaptation investments between the port authority and the terminal operator (i.e. the “free-riding effect”) within each port. Their intra-port coordination can increase the adaptation by removing such free-riding effect. These two effects can be strengthened by a higher expectation and larger variance of the disaster occurrence probability, and by a more intense inter-port competition (less service homogeneity). The chapter is organized as follows. Section 2.2 introduces the basic economic setup. Section 2.3 derives the analytical results for optimal port adaptation with different inter-port competition and intra-port coordination conditions. Section 2.4 examines the effects of inter-port competition 9 As can be seen later in the model set-up for the adaptation investment stage, this Knightian uncertainty on the disaster occurrence probability can be integrated with the uncertainty of the disaster occurrence (Bernoulli trial) together, keeping the modeling set-up the same. Thus we can regard that the shippers are faced with an uncertain absolute level of disaster damage because of the total disaster uncertainty, including both the Knightian uncertainty on the disaster occurrence probability and the occurrence of the disaster. Thys, alternatively, we may use only one random variable to capture such total disaster uncertainty. 10 Different from Xiao et al. (2015) with a multi-period investment model, the present paper abstracts away the issue of adaptation investment timing (the option value to choose to invest early or late). 12 intensity (port service homogeneity) on adaptation investments, and Section 2.5 contains the concluding remarks for this chapter. 2.2 Basic Model We consider two nearby ports sharing a common hinterland that are subject to a threat of common but uncertain disaster (shown in Figure 2.1). The ports are of the landlord type, each consisting one port authority owning the port basic infrastructure, and a terminal operator as a tenant to own the port superstructure and directly handles cargo transport (Liu 1992).11 The landlord port is the the most predominant type of ports in the world (Becker et al., 2012; Xiao et al., 2015). For landlord type port, the terminal operators are private entities. For example, PSA International, Hutchison Port Holding, APM terminals, DP World and China Merchant Holding are the major terminal operator corporations operating worldwide 12 . Port authorities are also assumed to be private entities to maximize profit, which is similar to Chen and Liu (2014) and Liu et al. (2018). Since 1990s, there is trend around the world to privatize port authority from public sector, aiming to relieve government’s heavy financial burden, and to upgrade port operation efficiency (Liu, 1995; Cullinane et al., 2005). Port authority privatization was pioneered by the UK Thatcher’s government in 1990s (Baird and Valentine, 2006). Later, corporatization of port authorities has been widely applied around the world, especially in Asia and Oceania (Everett, 2005; World Bank, 2011). Even without full privatization, most of port authorities have been corporatized, with government controlling partial share. Meanwhile, port governance has also been transferred from the national/state governments to local ones who are responsible for own financial performance 11 There is no universally accepted framework for port classification. A widely adopted classification is by Liu (1992) to categorize port into four types: service port, tool port, landlord port and private port. A service port is if the port authority is responsible for the provision of all port facilities; a tool port is if the port authority is public and provides the infrastructure and superstructure, while the provision of services is licensed to private operators; a landlord port is in which the domain of the port authority (public or private) is restricted to the provision of the infrastructure, while investment in the superstructure and port operation is the responsibility of licensed private companies; a private port is if the provision of all the facilities and services is left to one single private entity. 12 These operators are international corporations having business in many ports around the world. One operator may operate in two nearby ports at the same time (for example, Hutchison Port Holding operates in both Hong Kong and Shenzhen ports). One port can also have multiple terminal operators. To make the model tractable and to focus on the main trade-off issues, we assume that there is only one terminal operator for each port and that the two operators are independent. 13 (Cheon et al., 2010).13 As a result, the port authorities would be profit-oriented, resembling a private entity to certain degree. The two ports can belong to competing port authorities. Such inter-port competition is exemplified by the Pearl River Delta with Hong Kong port competing against Shenzhen port to be the gateway for South China. The other example may be the west European ports, especially the Hamburg-Le Havre (HLH) port range with several ports competing as the gateway to West and North Europe. One monopoly port authority to control multiple ports is also common. For example, Port Authority of New York and New Jersey controls port of Newark, Port of Perth Amboy and Port of New York. Georgia Ports Authority controls Port of Savannah and Port of Brunswick on the east coast of the US. For landlord port, port authority signs concession contract with private terminal operator, stipulating the duration, concession fee scheme and other terms to lease the port land and basic facility to terminal operator (Trujillo and Nombela, 2000). Notteboom (2006) summarizes common types of concession contracts between port authority and terminal operator. Detailed concession fee scheme varies among the ports, but commonly, port authority charges a concession fee to the terminal operator based on the throughput it handled i.e. a unit concession fee, such that the total concession fee is proportional to the cargo volume.14 Analogous to Basso and Zhang (2007), Pels and Verhoef (2004) 15, it is assumed that port charges within a port are determined in a vertical structure: the port authority decides a unit charge (unit concession fee) on the terminal operator first, and then the terminal operator chooses its unit service charge to be paid by shippers. 13 According to Cheon et al. (2010), in 1991, 42% of the world’s major hub and gateway ports were managed by national or state government bodies; by 2004, the percentage dropped to mere 32%. Corporatized port authorities accounted for less than 1/3 in 1991, but by 2004, the number became 45%. 14 De Monie (2005) specifies three most common port authority concession fee schemes: unit fee, fixed fee and two-part tariff. Chen and Liu (2014) and Liu et al. (2018) analytically discuss and compare these three schemes for a port authority to maximize profit. They find that unit fee is most likely to be preferred by a profit maximizing port authority. 15 Basso and Zhang (2007) study revelry between two congested facilities considering the upstream as the provider of the facility infrastructure and downstream carrier to use the facility. The pricing is determined in a vertical structure with downstream carrier charges the end customer, while upstream facility infrastructure provider charges carrier. 14 Figure 2.1 The market structure of the two-port system In this study, we model the impact of port authority inter-port competition and monopoly, and intra-port cooperation between port authority and terminal operator within one port, on port adaptation. A multi-stage game is used to model both an “adaptation investment stage” for the ports, and an “operation stage” when port charges are determined, conditional on adaptation investments.16 The timeline of economic model is demonstrated in Figure 2.2. The probability of disaster occurrence is assumed to be ambiguous at adaptation investment stage, which is a Knightian uncertainty (Knight, 1921; Camerer and Weber, 1992; Gao and Driouchi, 2013; Nishimura and Ozaki, 2007). Knightian uncertainty suggests disaster occurrence probability x can be a random variable at adaptation investment stage, with a density function (pdf) 𝑓(𝑥), expectation 𝛺 and variance 𝛴. But this probability only becomes realized later at operation stage when ports decide price and shipper chooses port. This improvement in information reflects a likely setting in which a better knowledge on climate change and related disasters is accumulated during the lengthy period of adaptation investment. At adaptation investment stage, port authorities and terminal operators at the two ports simultaneously determine their adaptation investment 𝐼𝑖𝑎 , 𝐼𝑖𝑡 . Once decided, the adaptation 16 A multi-stage game is a widely adopted approach to model the capacity investment at early stage and pricing at later stage for transport infrastructure (e.g., marine ports and airports) such as Luo et al. (2012) and Xiao et al. (2013). 15 investments are assumed to be fixed since any adjustment would require additional complex evaluation and funding approval, thus causing major delay in completion. We do not consider the case where the disaster occurs during the period of adaptation constructions. However, this does not alter strategic behavior of the ports since both port authorities and terminal operators do not adjust pricing until the port adaptation is installed to take effect to reduce disaster damage. Figure 2.2 The timeline of the decisions of different parties At operation stage, following Basso and Zhang (2007) and Wan et al. (2016), as shown in Figure 2.3, we adopt an infinite linear city model to derive shipper demand conditional on port service charges 𝑝𝑖 and port adaptation investments 𝐼𝑖𝑎, 𝐼𝑖𝑡 in response to disaster occurrence probability 𝑥. The value to the shipper of using the port service V is exogenous. Shippers have to choose which port to use before observing event of disaster occurrence or not.17 The expected damage incurred 17 Shippers are assumed to make their port choice decisions before observing the realization of disaster occurrence or not. If the disaster occurs, shippers cannot make the decisions to switch ports. This assumption is based on observations in (Magala and Sommons, 2008; Tongzon, 2009) that shippers/shipping lines often sign long-term contract with terminal operators. Ad hoc re-routing and rescheduling to other ports are difficult. Shippers/shipping lines could commit to particular ports/terminals due to integration and investment in hinterland transport, Adaptation Investment Stage Operation Stage 16 on the shipper is 𝑥Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)}. D is the damage without any port adaptation when disaster occurs. 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) is the reduction of damage owing to port authority and terminal operator adaptation. 18 The disaster damage to shippers can include the cargo damage and inventory delay cost. If the disaster does not occur, shippers do not incur any cargo damage. With the disaster occurrence probability 𝑥, the expected damage incurred on shippers is 𝑥Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} 19. Shippers are assumed to be uniformly distributed on the linear city with density 1. Shippers incur a cost of t per unit distance to transport cargo from its location to the port. This transport cost can also capture any horizontal differentiation (service homogeneity) of two ports’ services perceived by the shippers. Shippers choose which port to use, and directly pay the terminal operator. The terminal operator pays port authority a concession fee in exchange to use the port land and basic infrastructure. The port charges within a port are determined in a “vertical structure”: the port authority chooses its concession fee 𝜙𝑖 on the terminal operator first, and then the terminal operator chooses its service charge 𝑝𝑖 on shippers. Table 2.1 summarizes notations and parameters definitions in our economic model. warehousing and other forms of cooperation with port sector (Chang et al., 2008; Wiegmans et al., 2008; Franc and van der Horst, 2010). 18 We assume the disaster imposes the damage cost on shippers. Port authorities and terminal operators can also have damage in their properties and equipment when disaster occurs. However, port authorities and terminal operators within and across the ports interact with each other through the shipper’s demand, thus the specific damage to each entity does not enter the other entities’ FOC. As a result, the specific damage to port authority/terminal operator only affects the magnitude of the adaptation investment, while not qualitatively affect the effects of Knightian uncertainty, and the inter-port/intra-port interactions on adaptations. 19 This linear form of damage reduction by port adaptation is associated with the disasters forms such as the strong wind, rainfall and drought. The adaptations to these disasters can reduce damage to shippers in a proportion of the amount of the adaptation investment. Thus, a linear form of damage function in adaptation investments could be appropriate. Some types of disasters exhibit the all-or-nothing feature depending on whether the adaptation is above a threshold or not (for example, a dike to protect high wave). However, considering this step-wise damage function will dramatically complicate the model, and future studies may be called for. 17 Figure 2.3 Shipper’s utility at each port after completion of adaptation investments Table 2.1 Notational glossary Parameter Definition 𝑉 Utility to shipper of using the port service 𝐷 Level of disaster damage to the shipper, and we assume 𝐷 < 𝑉 𝜂 Effectiveness of adaptation investment to reduce damage 𝑡 Unit distance transport cost for the shipper to move cargo to the port 𝐼𝑖𝑎 Adaptation investment made by port authority at port 𝑖 𝐼𝑖𝑡 Adaptation investment made by terminal operator at port 𝑖 𝑥 Random variable denoting probability of the disaster occurrence 𝛺 The expectation of 𝑥 at adaptation investment stage 𝛴 The variance of 𝑥 at adaptation investment stage 𝛹 The second moment of 𝑥, which is equal to Ω2 + Σ 𝑝𝑖 The service fee charged by terminal operator to shippers 𝜙𝑖 The concession fee charged by port authority to terminal operator 𝑄𝑖 The demand for service at port 𝑖 at the operation stage 𝛱𝑖 Profit of terminal operator in port 𝑖 at operation stage 𝜋𝑖 Profit of port authority in port 𝑖 at operation stage 18 For a shipper located at a point 𝑧 in the two ports’ common hinterland, the utility of using port 1 is 𝑉 − 𝑝1 − 𝑧𝑡 − 𝑥Max{0, 𝐷 − 𝜂(𝐼1𝑎 + 𝐼1𝑡)}, and the utility of using port 2 is 𝑉 − 𝑝2 − (1 − 𝑧𝑡) −𝑥Max{0, 𝐷 − 𝜂(𝐼2𝑎 + 𝐼2𝑡)}. For a shipper located at a point 𝑧 in port 1’s captive hinterland, the utility is 𝑉 − 𝑝1 − |𝑧|𝑡 − 𝑥Max{0, 𝐷 − 𝜂(𝐼1𝑎 + 𝐼1𝑡)}. For a shipper located at a point 𝑧 in port 2’s own hinterland, the utility is 𝑉 − 𝑝2 − (𝑧 − 1)𝑡 − 𝑥Max{0, 𝐷 − 𝜂(𝐼2𝑎 + 𝐼2𝑡)}. We can then derive the marginal shipper’s location 𝑧𝑙, who is indifferent between using port 1’s service and not using the port service at all; the marginal shipper’s location 𝑧𝑚, who is indifferent between using port 1 and using port 2’s service; and the marginal shipper’s location 𝑧𝑟, who is indifferent between using port 2’s service and not using the port services. 20 |𝑧𝑙| =𝑉−𝑝1−𝑥Max{0,𝐷−𝜂(𝐼1𝑎+𝐼1𝑡)}𝑡 (2.1.1) 𝑧𝑟 = 1 +𝑉−𝑝2−𝑥Max{0, 𝐷−𝜂(𝐼2𝑎+𝐼2𝑡)}𝑡 (2.1.2) 𝑧𝑚 =12+𝑝2−𝑝1−𝑥Max{0, 𝐷−𝜂(𝐼1𝑎+𝐼1𝑡)}+𝑥Max{0, 𝐷−𝜂(𝐼2𝑎+𝐼2𝑡)}2𝑡 (2.1.3) The demand for each port at the operation stage is as follows: 𝑄𝑖(𝑝)|(𝑥, 𝐼𝑎 , 𝐼𝑡) =12+2𝑉+𝑝𝑗−3𝑝𝑖+𝑥Max{0, 𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}−3𝑥 Max{0, 𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}2𝑡 (2.2) The profits for terminal operators at operation stage is 𝛱𝑖|(𝑥, 𝐼𝑎, 𝐼𝑡) =(𝑝𝑖 − 𝜙𝑖)𝑄𝑖. Port authorities’ profits at operation stage are 𝜋𝑖|(𝑥, 𝐼𝑎, 𝐼𝑡) = 𝜙𝑖𝑄𝑖. For model tractability, we normalize operating cost of port authorities and terminal operators to be zero. At adaptation investment stage, terminal operators’ expected profits are 𝐸[𝛱𝑖] = [∫𝛱𝑖𝑓(𝑥)𝑑𝑥] − 0.5𝜔𝐼𝑖𝑡2 . Port authorities’ expected profits are 𝐸[𝜋𝑖] = [∫ 𝜋𝑖𝑓(𝑥)𝑑𝑥] − 0.5𝜔𝐼𝑖𝑎2. At adaptation investment stage, port authorities incur adaptation investment cost 0.5𝜔𝐼𝑖𝑎2, and terminal operators incur 0.5𝜔𝐼𝑖𝑡2. The adaptation investment cost for both port authorities and terminal operators is assumed to be in quadratic form, indicating an increasing marginal cost of adaptation as technology requirement is higher and the 20 For infinite decimals in all the formulas, two digits after the decimal points are reported in the chapter to save space. 19 overall difficulty increases to add more adaptation. 𝜔 is the adaptation cost parameter. Port authorities and terminal operators can have different adaptation measures. Port authorities’ adaptations are mainly on port’s basic infrastructure, such as building breakwaters, storm barriers, flood-control gates (Becker et al., 2012). These adaptations are not specific to protect particular terminals but to benefit entire port. Terminal operator’s adaptation is mainly for its own berths and piers, e.g., the elevation of terminal, upgrading the drainage system, redesigning, and retrofitting of the terminal facilities (Becker et al., 2012). For model tractability and to focus on main insights, we assume port authorities and terminal operators to have the same adaptation investment cost structure, i.e., the same cost parameter 𝜔. The consumer surplus for the shipper at the operation stage is as follows: 𝐶𝑆|(𝑥, 𝐼𝑎, 𝐼𝑡) = ∫ [𝑉 − 𝑝1 − 𝑥Max{0, 𝐷 − 𝜂(𝐼1𝑎 + 𝐼1𝑡)} − 𝑧 𝑡]|𝑧𝑙|0𝑑𝑧 + ∫ 𝑧𝑚0[𝑉 − 𝑝1 −𝑥Max{0, 𝐷 − 𝜂(𝐼1𝑎 + 𝐼1𝑡)} − 𝑧 𝑡]𝑑𝑧 + ∫ [𝑉 − 𝑝2 − 𝑥Max{0, 𝐷 − 𝜂(𝐼2𝑎 + 𝐼2𝑡)} −1𝑧𝑚(1 − 𝑧) 𝑡]𝑑𝑧 + ∫ [𝑉 − 𝑝2 − 𝑥Max{0, 𝐷 − 𝜂 (𝐼2𝑎 + 𝐼2𝑡)} − (𝑧 − 1)𝑡]𝑑𝑧𝑧𝑟1 (2.3) The social welfare for the two-port system at operation stage is defined as 𝑆𝑊 = 𝐶𝑆 + ∑ 𝜋𝑖2𝑖=1 +∑ 𝛱𝑖2𝑖=1 . 2.3 Analysis We adopt backward induction to solve the model. First, operation stage is analyzed on shipper port choice decision and pricing behavior of port authorities and terminal operators (Section 2.3.1). At operation stage, disaster occurrence probability 𝑥 is realized, and port adaptation is also completed. Second, we analyze port adaptation decisions at adaptation investment stage, where disaster occurrence probability is ambiguous with a Knightian uncertainty (Section 2.3.2). 20 2.3.1 Port pricing At port operation stage, adaptations 𝐼𝑎, 𝐼𝑡 have been completed, and the disaster occurrence probability x is also realized. The port charges within a port are determined in a “vertical structure”: the port authority decides on its concession fee to terminal operator first as the upstream, and then the terminal operator as downstream chooses its service charge to be paid by shippers. Terminal operators maximize profit by setting service charge 𝑝𝑖 to shippers. They also pay concession fee 𝜙𝑖 to port authorities. The profit function of terminal operator is Max𝛱𝑖𝑝𝑖|(𝑥, 𝐼𝑎, 𝐼𝑡) = (𝑝𝑖 − 𝜙𝑖)𝑄𝑖. 𝑝𝑖(𝜙𝑖 , 𝜙𝑗) = 0.2[(2𝑉 + 𝑡) + 2.57𝜙𝑖 + 0.42𝜙𝑗 − 2.43𝑥Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)}} +0.42Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}] (2.4) It is noted that 𝑝𝑖(𝜙𝑖, 𝜙𝑗) is a function of two port authorities’ concession fees 𝜙𝑖 and 𝜙𝑗 due to the interaction of two ports in the common hinterland. But 𝜙𝑖 has more impact on the port charge 𝑝𝑖(𝜙𝑖, 𝜙𝑗) at the same port. While terminal operators at two ports compete, port authorities may compete or cooperate (monopoly). Pricing rules of port authorities thus depend on inter-competition or cooperation (monopoly). 2.3.1.1 Pricing rule of competing port authorities The objective of each competing port authority is Max𝜙𝑖 𝜋𝑖|(𝑥, 𝐼𝑎 , 𝐼𝑡) =𝜙𝑖𝑄𝑖(𝑝𝑖(𝜙𝑖 , 𝜙𝑗), 𝑝𝑗(𝜙𝑖, 𝜙𝑗)). It is noted that 𝜋𝑖 is a function of 𝑝𝑖(𝜙𝑖, 𝜙𝑗), and 𝑝𝑗(𝜙𝑖 , 𝜙𝑗) because shippers directly pay terminal operators. Substituting 𝑝𝑖(𝜙𝑖, 𝜙𝑗) and 𝑝𝑗(𝜙𝑖, 𝜙𝑗) into 𝜋𝑖 such that port authority has Max𝜙𝑖 𝜋𝑖|(𝑥, 𝐼𝑎 , 𝐼𝑡) = 𝜙𝑖𝑄𝑖(𝜙𝑖, 𝜙𝑗). Solving the first-order conditions (FOCs), ∂𝜋𝑖∂𝜙𝑖= 0 and ∂𝜋𝑗∂𝜙𝑗= 0, the optimal concession fee 𝜙𝑖|(𝑥, 𝐼𝑎, 𝐼𝑡) is as follows. The second-order conditions (SOCs), ∂2𝜋𝑖∂𝜙𝑖2 < 0 and ∂2𝜋𝑗∂𝜙𝑗2 < 0, are also satisfied. 21 ?̅?𝑖|(𝑥, 𝐼𝑎, 𝐼𝑡) = 0.23(2𝑉 + 𝑡) − 𝑥 [0.50Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} − 0.045Max{0, 𝐷 −𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}] (2.5.1) Inserting ?̅?1 |(𝑥, 𝐼𝑎, 𝐼𝑡), and ?̅?2 |(𝑥, 𝐼𝑎, 𝐼𝑡) to 𝑝1(𝜙) and 𝑝2(𝜙), and 𝑄1 (𝑝) and 𝑄2 (𝑝) we have: ?̅?𝑖 = 0.34(2𝑉 + 𝑡) − 𝑥[0.74Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} − 0.066Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}] (2.5.2) and ?̅?𝑖 = 0.16 (2𝑉+𝑡)−𝑥 [0.36Max{0, 𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}−0.032Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}]𝑡 (2.5.3) The following comparative statics are obtained to show the impact of adaptation investment and probability of disaster occurrence on port charges and port demands. Port authority and terminal operator charge more (less) and have more (less) demand if its own port (the other port) makes more adaptation. The disaster occurrence probability 𝑥, however, has two countervailing effects on port charges and demands. On one hand, higher disaster occurrence probability increases the expected damage cost for shippers, decreasing port’s demand and charge ceteris paribus. On the other hand, with two ports competing in a common hinterland, if one port prevails over the other in adaptation (i.e., when Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≤ 0.089), higher disaster occurrence probability makes this much better adapted port more appealing to shippers, such that disaster occurrence probability has a positive effect on port charge and demand. 𝜕?̅?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̅?𝑖𝜕𝐼𝑖𝑡 ≥ 0; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑎 ≤ 0; 𝜕?̅?𝑖𝜕𝐼𝑗𝑡 ≤ 0 𝜕?̅?𝑖 𝜕𝑥≤ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≥ 0.089; 𝜕?̅?𝑖 𝜕𝑥≥ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≤ 0.089 𝜕?̅?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̅?𝑖 𝜕𝐼𝑖𝑡 ≥ 0; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑎 ≤ 0; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑡 ≤ 0 22 𝜕?̅?𝑖 𝜕𝑥≤ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≥ 0.089 ; 𝜕?̅?𝑖 𝜕𝑥≥ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≤ 0.089 𝜕?̅?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̅?𝑖 𝜕𝐼𝑖𝑡 ≥ 0; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑎 ≤ 0; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑡 ≤ 0 𝜕?̅?𝑖 𝜕𝑥≤ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≥ 0.089 ; 𝜕?̅?𝑖 𝜕𝑥≥ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≤ 0.089 2.3.1.2 Pricing rule of monopoly port authority The monopoly port authority maximizes a joint profit at two ports as Max𝜙𝑖,𝜙𝑗∑ 𝜋𝑖2𝑖=1 |(𝑥, 𝐼𝑎, 𝐼𝑡) = ∑ 𝜙𝑖𝑄𝑖(𝜙𝑖, 𝜙𝑗)2𝑖=1 . FOCs are ∂(𝜋𝑖+𝜋𝑗)∂𝜙𝑖= 0 and ∂(𝜋𝑖+𝜋𝑗)∂𝜙𝑗= 0 . SOCs ∂2(𝜋𝑖+𝜋𝑗∂𝜙𝑖2 < 0 and ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗2 < 0 are also satisfied. The optimal concession fees are ?̃?𝑖|(𝑥, 𝐼𝑎, 𝐼𝑡) =0.25(2𝑉 + 𝑡) − 0.5𝑥(Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)}) . Substituting ?̃?𝑖 |(𝑥, 𝐼𝑎, 𝐼𝑡) into 𝑝𝑖(𝜙𝑖, 𝜙𝑗) and also 𝑄𝑖(𝜙𝑖, 𝜙𝑗). 𝑝𝑖 = 0.35(2𝑉 + 𝑡) − 𝑥[0.74Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} − 0.043Max{0, 𝐷 −𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}] (2.6.1) and ?̃?𝑖 =0.15 (2𝑉+𝑡)−𝑥[0.36Max{0, 𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}−0.064Max{0, 𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}]𝑡 (2.6.2) Below are comparative statics of port charges and demands with respect to disaster occurrence probability and port adaptation investment. For monopoly port authority, it increases concession fee at one port when this port increases adaptation i.e., 𝜕?̃?𝑖 𝜕𝐼𝑖𝑎 ≥ 0 ; 𝜕?̃?𝑖 𝜕𝐼𝑖𝑡 ≥ 0 . In addition, with monopoly power, port authority can raise concession fee when disaster occurrence has higher probability i.e., 𝜕?̃?𝑖𝜕𝑥≥ 0. For terminal operator, it can charge more to shipper when its port adapts more i.e., 𝜕?̃?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̃?𝑖𝜕𝐼𝑖𝑡 ≥ 0, but charges less when the other port has more adaptation i.e., 𝜕?̃?𝑖𝜕𝐼𝑗𝑎 ≤23 0; 𝜕?̃?𝑖 𝜕𝐼𝑗𝑡 ≤ 0. Similar to the competing port authorities case, the disaster occurrence probability has two countervailing effects on concession fee and terminal operators’ charge. When Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}< 0.057 holds, which means one port is much better adapted compared to the other port, disaster occurrence has overall positive effect such that port authority and terminal operator at one port can increase charge. 𝜕?̃?𝑖 𝜕𝑥≥ 0; 𝜕?̃?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̃?𝑖 𝜕𝐼𝑖𝑡 ≥ 0; 𝜕?̃?𝑖 𝜕𝐼𝑗𝑎 = 0; 𝜕?̃?𝑖 𝜕𝐼𝑗𝑡 = 0 𝜕?̃?𝑖 𝜕𝑥≤ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≥ 0.057; 𝜕?̃?𝑖 𝜕𝑥> 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≤ 0.057 𝜕?̃?𝑖𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̃?𝑖𝜕𝐼𝑖𝑡 ≥ 0; 𝜕?̃?𝑖𝜕𝐼𝑗𝑎 ≤ 0; 𝜕?̃?𝑖𝜕𝐼𝑗𝑡 ≤ 0 𝜕?̃?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̃?𝑖𝜕𝐼𝑖𝑡 ≥ 0; 𝜕?̃?𝑖 𝜕𝐼𝑗𝑎 ≤ 0; 𝜕?̃?𝑖 𝜕𝐼𝑗𝑡 ≤ 0 𝜕?̃?𝑖 𝜕𝑥≤ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≥ 0.057 ; 𝜕?̃?𝑖 𝜕𝑥≥ 0 if Max{0,𝐷−𝜂(𝐼𝑖𝑎+𝐼𝑖𝑡)}Max{0,𝐷−𝜂(𝐼𝑗𝑎+𝐼𝑗𝑡)}≤ 0.057 Port concession fees and terminal operator charges comparison is ?̅?𝑖 < ?̃?𝑖 ; ?̅?𝑖 < 𝑝𝑖 as shown below, which leads to our Lemma 2.1. ?̃?𝑖 − ?̅?𝑖 = 0.024 × (2𝑉 + 𝑡) − 𝑥[0.0039Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} + 0.044Max{0, 𝐷 −𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}] > 0 𝑝𝑖 − ?̅?𝑖 = 0.015 × (2𝑉 + 𝑡) − 𝑥[0.0058Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} + 0.023Max{0, 𝐷 −𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}] > 0 Lemma 2.1: Conditional on disaster occurrence probability and the adaptation investment at two ports, inter-port competition between two port authorities leads to lower concession fee and lower terminal operator charge. 24 This lemma holds for general functional form (as shown in Appendix A1), suggesting that monopoly price is higher than duopoly competition price. This is because, as concession fees at two ports are strategic complements, the monopoly port authority is able to internalize the externality of concession fee rise at one port on the other port. This leads to a higher concession fee and terminal operator charge at both ports. In addition, our comparative statics demonstrate: 𝜕?̅?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̅?𝑖𝜕𝐼𝑖𝑡 ≥ 0; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑎 ≤ 0; 𝜕?̅?𝑖𝜕𝐼𝑗𝑡 ≤ 0; 𝜕?̅?𝑖 𝜕𝐼𝑖𝑎 ≥ 0; 𝜕?̅?𝑖 𝜕𝐼𝑖𝑡 ≥ 0 ; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑎 ≤ 0 ; 𝜕?̅?𝑖 𝜕𝐼𝑗𝑡 ≤ 0 and 𝜕?̃?𝑖 𝜕𝐼𝑖𝑎 ≥ 0 ; 𝜕?̃?𝑖 𝜕𝐼𝑖𝑡 ≥ 0 ; 𝜕?̃?𝑖 𝜕𝐼𝑗𝑎 = 0 ; 𝜕?̃?𝑖 𝜕𝐼𝑗𝑡 = 0 ; 𝜕?̃?𝑖𝜕𝐼𝑖𝑎 ≥ 0 ; 𝜕?̃?𝑖𝜕𝐼𝑖𝑡 ≥ 0 ; 𝜕?̃?𝑖𝜕𝐼𝑗𝑎 ≤ 0; 𝜕?̃?𝑖𝜕𝐼𝑗𝑡 ≤ 0. These lead to Lemma 2.2 about the impact of port adaptation on port charges. Lemma 2.2: For ports with competing port authorities, concession fee and terminal operator charge increase with own port’s adaptation, but decrease with the other port’s adaptation. For monopoly port authority, concession fee and terminal operator charge also increase with own port’s adaptation, while not affected by the other port’s adaptation. As shown in Figure A1 in Appendix A1, for competing port authorities, when one port increases adaptation (e.g., port 𝑖 ), the best response function of port 𝑗 ’s concession fee 𝜙𝑗(𝜙𝑖) moves outward due to stronger competing pressure from port 𝑖. The best response function of port i’s concession fee 𝜙𝑖(𝜙𝑗) moves downward. Thus, at new equilibrium, concession fee rises at the port with an increased adaptation (port 𝑖), while the concession fee at the other port (port 𝑗) decreases. When one port increases adaptation, terminal operator at this port thus has to pay a higher concession fee and also has larger shipper demand, both imposing positive effects on the terminal operator charge. When the other port increases adaptation, terminal operator at one port faces lower concession fee and also lower shipper demand, thus making it to reduce charge to shipper. For monopoly port authority, when adaptation at one port increases, port authority rises concession fee at this port. Meanwhile, it can internalize the positive externality of concession fee rise on the 25 other port by not reducing the other port’s concession fee. For terminal operator, the impact of adaptation change on its charge is the same. When one port increases adaptation, terminal operator at this port pays higher concession fee while also having larger shipper demand, both having positive effects on its charge. When the other port increases adaptation, terminal operator at one port pays a lower concession fee with lower shipper demand, making it to lower charge to shipper. Taking derivatives of the difference in concession fees and terminal operator charges with respect to adaptation investments, we can see ∂(?̃?𝑖|( 𝑥,𝐼𝑎,𝐼𝑡)−?̅?𝑖 |(𝑥,𝐼𝑎,𝐼𝑡))∂ 𝐼> 0 ; ∂(?̃?𝑖| (𝑥,𝐼𝑎,𝐼𝑡)−?̅?𝑖 |(𝑥,𝐼𝑎,𝐼𝑡))∂ 𝐼> 0, where 𝐼 ∈ {𝐼𝑖𝑎, 𝐼𝑖𝑡 , 𝐼𝑗𝑎, 𝐼𝑗𝑡}. Proposition 2.1: Increased port adaptation at either port would enlarge the differences in both concession fee and terminal operator charge between the competing and cooperative ports. Detailed explanation of Proposition 2.1 is as follows. With adaptation increased at one port, monopoly port authority internalizes the externality to the other port, thus making the concession fee to rise more than that with the competing port authorities. Terminal operator charge increases with concession fee, such that its charge increases with monopoly port authority. Therefore, the difference in concession fee and terminal charge between competing and monopoly port authority is enlarged. On the other hand, when the other port increases adaptation, the monopoly port authority does not change the concession fee at one port, whereas the competing port authorities would reduce concession fee in response. Thus, the difference in concession fee and terminal charge at one port is also enlarged when the other port increases adaptation. 2.3.2 Adaptation investment At adaptation investment stage, disaster occurrence probability 𝑥 has not been realized and has a Knightian uncertainty. Specifically, 𝑥 is a random variable with a pdf 𝑓(𝑥), expectation 𝛺 , variance 𝛴 , and the second moment 𝛹 = 𝐸𝑥2 = 𝛺2 + 𝛴 . Next, analogous to operation stage analyses, we discuss different inter-and intra- port competition and cooperation regimes. Port authorities and terminal operations are assumed to simultaneously make adaptation investment 26 decisions. This is because adaptation projects are lengthy, such that each party makes adaptation decision well in-advance, while only observing completed adaptations by the others after a long-period. 2.3.2.1 Adaptation of competing port authorities The pricing rule follows that of two competing port authorities at operation stage i.e. ?̅?𝑖 and ?̅?𝑖. The expected profits for port authorities at adaptation investment stage are: 𝐸[𝜋𝑖] = [∫ 𝜋𝑖𝑓(𝑥)𝑑𝑥] − 0.5𝜔𝐼𝑖𝑎2 =0.15𝑉2𝑡+ 0.15𝑉 + 0.037𝑡 +1𝑡 { 0.15 [1.1Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} −0.1Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}]2𝛹−0.30𝛺(𝑉 + 0.50𝑡) [1.10Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} −0.10Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}]} − 0.5𝜔𝐼𝑖𝑎2 (2.7.1) The expected profits for terminal operators are: 𝐸[𝛱𝑖] = [∫𝛱𝑖𝑓(𝑥)𝑑𝑥] − 0.50𝜔𝐼𝑖𝑡2 = 0.072𝑉2𝑡+ 0.072𝑉 + 0.018𝑡 +1𝑡 { 0.072 [1.10Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} −0.10Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}]2𝛹 −0.14 𝛺 (𝑉 + 0.5𝑡) [1.10Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} −0.10Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}]} − 0.5𝜔𝐼𝑖𝑡2 (2.7.2) Port authorities and terminal operators maximize expected profits respectively. The constraints 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) ≤ 𝐷 must be imposed in the sense that ports choose not to adapt beyond the total possible level of disaster damage 𝐷: Max𝐼𝑖𝑎E[𝜋𝑖], st. 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) ≤ 𝐷; Max𝐼𝑖𝑡E[𝛱𝑖], st. 𝜂(𝐼𝑖𝑎 +𝐼𝑖𝑡) ≤ 𝐷. 27 To solve above constrained optimization problem, we first assume the constraints are not binding at equilibrium, and then discuss conditions to reach such interior solutions. For port authorities, FOCs with respect to 𝐼𝑖𝑎 are as follows: 𝜕𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎 = 0.33𝜂𝑡 [(𝑉 + 0.50𝑡)𝛺 − 𝐷𝛹] − 0.032 𝜂2𝑡𝛹(𝐼𝑗𝑎 + 𝐼𝑗𝑡) + 0.36 𝜂2𝑡𝛹𝐼𝑖𝑡 +(0.36 𝜂2𝑡𝛹 − 𝜔) 𝐼𝑖𝑎 (2.7.3) The SOCs require ω ≥ 0.36 𝜂2𝑡𝛹. This is to guarantee that port authorities’ expected profits are concave in 𝐼𝑖𝑎. If ω < 0.36 𝜂2𝑡𝛹, port authorities’ expected profit functions are convex in 𝐼𝑖𝑎 such that marginal return of adaptation investment always increases, suggesting port authority to keep investing till reaching the bound 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) = 𝐷. FOCs for terminal operators are as follows: 𝜕𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡 = 0.16𝜂𝑡 [(𝑉 + 0.50𝑡)𝛺 − 𝐷𝛹] − 0.015 𝜂2𝑡𝛹(𝐼𝑗𝑎 + 𝐼𝑗𝑡) + 0.17 𝜂2𝑡𝛹𝐼𝑖𝑎 + (0.17 𝜂2𝑡𝛹 −𝜔)𝐼𝑖𝑡 (2.7.4) SOCs require 𝜔 ≥ 0.17 𝜂2𝑡𝛹 so that terminal operators’ expected profit functions are concave in 𝐼𝑖𝑡 . If 𝜔 < 0.17 𝜂2𝑡𝛹 , marginal return of adaptation investment for terminal operators always increases, such that they keep investing till reaching the bound 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) = 𝐷. The second derivatives indicate 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 ≥ 0; 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 ≤ 0; 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 ≤ 0, and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 ≥ 0; 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 ≤0; 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 ≤ 0. Thus, adaptation of port authority and terminal operator at the same port is strategic complement, while adaptation across ports is strategic substitute. In Appendix A2, we plot best response functions of adaptation 𝐼𝑖𝑎 and 𝐼𝑖𝑡 at the same port, and 𝐼𝑖𝑎 and 𝐼𝑗𝑎 at two different ports. The best response functions of 𝐼𝑖𝑎 and 𝐼𝑖𝑡 are positively sloped while those of 𝐼𝑖𝑎 and 𝐼𝑗𝑎 are negatively sloped. Solving the system equations of FOCs, and imposing symmetry, we obtain following symmetric interior equilibrium adaptation investments with competing port authorities. 28 𝐼?̅? 𝑎 = 𝐼?̅? 𝑎 = 𝜂 [(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.1 𝜔𝑡−3𝛹𝜂2≥ 𝐼?̅? 𝑡 = 𝐼?̅? 𝑡 = 𝜂 [(2𝑉+𝑡) 𝛺−2𝐷𝛹]2.1 (6.1 𝜔𝑡−3 𝛹𝜂2) (2.7.5) To have finite adaptation investment implies 𝜔 > 0.49𝜂2𝑡𝛹, which to make the denominator to be positive. Existence of interior solution requires 𝜔 ≥0.48 𝛺(𝑉+0.50𝑡)𝜂2 𝐷𝑡. It is noted that when constraint 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) ≤ 𝐷 binds at equilibrium, i.e., 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) = 𝐷, there would be an infinite number of Nash equilibria of adaptation investment (see Appendix A2 for discussion). This happens when 𝜔 ≤0.48 𝛺(𝑉+0.50𝑡)𝜂2 𝐷𝑡 such that adaptation is not costly enough, such that ports adapt as much as possible to achieve a “full insurance”. This case of infinite Nash equilibria with binding constraint makes comparison between 𝐼?̅? 𝑎 and 𝐼?̅? 𝑡 and other implications of Knightian uncertainty unclear. In addition, in practice, port adaptation is likely to be extremely costly (OECD, 2016) and as a result, ports seldom fully adapt to a potential disaster (see survey in Becker et al. (2012)). Therefore, to simplify our discussion and to reflect real practice, we exclude discussion on the multiple equilibria under binding constraint. Taking total derivatives of the FOCs (𝜕𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎 = 0 and 𝜕𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡 = 0) to 𝛺 and 𝛴 respectively, and imposing the symmetry assumption, the expressions of 𝜕𝐼?̅? 𝑎 𝜕𝛺, 𝜕𝐼?̅? 𝑡 𝜕𝛺 and 𝜕𝐼?̅? 𝑎 𝜕𝛴, 𝜕𝐼?̅? 𝑡 𝜕𝛴 are shown in Appendix A3: 𝜕𝐼?̅? 𝑎 𝜕𝛺≥ 0 ; 𝜕𝐼?̅? 𝑡 𝜕𝛺≥ 0 ; 𝜕𝐼?̅? 𝑎 𝜕Σ≤ 0 ; 𝜕𝐼?̅? 𝑡 𝜕Σ≤ 0 Proof of the above comparative statics is in Appendix A3. The sign of 𝜕𝐼?̅? 𝑎 𝜕𝛺 and 𝜕𝐼?̅? 𝑡 𝜕𝛺 is determined by 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω. As a higher expectation of disaster occurrence probability increases the marginal expected profit of port authority and terminal operator to their own adaptation, i.e., 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω≥ 0 and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω≥ 0, the equilibrium port adaptation also increases with the expectation of disaster occurrence probability, i.e., 𝜕𝐼?̅? 𝑎 𝜕𝛺≥ 0 and 𝜕𝐼?̅? 𝑡 𝜕𝛺≥ 0. In addition, the sign of 𝜕𝐼?̅? 𝑎 𝜕Σ and 𝜕𝐼?̅? 𝑡 𝜕Σ is determined by 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ. As larger variance of disaster occurrence probability decreases 29 the marginal expected profit of port authority and terminal operator to their own adaptation, the equilibrium port adaptation decreases with the variance of disaster occurrence probability as a result, i.e., 𝜕𝐼?̅? 𝑎 𝜕Σ≤ 0 and 𝜕𝐼?̅? 𝑡 𝜕Σ≤ 0. 2.3.2.2 Adaptation of monopoly port authority The pricing rule at operation stage follows that of monopoly authority regime, i.e., ?̃?𝑖 and 𝑝𝑖. For monopoly port authority, the expected joint profit is as follows: 𝐸[𝜋𝑖 + 𝜋𝑗] = [∫(𝜋𝑖 + 𝜋𝑗)𝑓(𝑥)𝑑𝑥] − 0.50𝜔(𝐼𝑖𝑎2 + 𝐼𝑗𝑎2) = 0.30𝑉2𝑡+ 0.30𝑉 + 0.15 −0.075𝑡+1𝑡[0.18 (Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)})2−0.064 Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)} + 0.18 (Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)})2]𝛹 − (0.15 +0.45𝑉𝑡)𝛺[ Max{0, 𝐷 − 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡)} + Max{0, 𝐷 − 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡)}] − 0.50𝜔(𝐼𝑖𝑎2 + 𝐼𝑗𝑎2) (2.8.1) Monopoly port authority maximizes the expected joint profit by choosing adaptation at two ports together: Max𝐼𝑖𝑎, 𝐼𝑗𝑎𝐸[𝜋𝑖 + 𝜋𝑗], st. 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) ≤ 𝐷 and 𝜂(𝐼𝑗𝑎 + 𝐼𝑗𝑡) ≤ 𝐷. FOCs for the monopoly port authority are as follows. SOCs require that 𝜔 ≥ 0.36 𝜂2𝑡𝛹. 𝜕𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎 = 0.30𝜂𝑡 [(𝑉 + 0.50𝑡)𝛺 − 𝐷𝛹] − 0.064 𝜂2𝑡𝛹(𝐼𝑗𝑎 + 𝐼𝑗𝑡) + 0.36 𝜂2𝑡𝛹𝐼𝑖𝑡 +(0.36 𝜂2𝑡𝛹 − 𝜔)𝐼𝑖𝑎 (2.8.2) Terminal operators maximize their expected profit as Max𝐼𝑖𝑡E[𝛱𝑖]; s. t. 𝜂 (𝐼𝑖𝑎 + 𝐼𝑖𝑡) ≤ 𝐷. FOCs are as follows. The SOCs require 𝜔 ≥ 0.18 𝜂2𝑡𝛹. 30 𝜕 𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡 = 0.15𝜂𝑡 [(𝑉 + 0.5𝑡)𝛺 − 𝐷𝛹] − 0.031 𝜂2𝑡𝛹(𝐼𝑗𝑎 + 𝐼𝑗𝑡) + 0.18 𝜂2𝑡𝛹𝐼𝑖𝑎 −(𝜔 − 0.18 𝜂2𝑡𝛹)𝐼𝑖𝑡 (2.8.3) The second derivatives show 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 ≥ 0 ; 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 ≤ 0 ; 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 ≤ 0 and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 ≥ 0 ; 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 ≤ 0; 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 ≤ 0. The adaptations of port authority and terminal operators within the same port are thus strategic complements, while adaptations across ports are strategic substitutes. Solving the system equations of FOCs for symmetric interior Nash equilibrium, following solution is obtained. 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.70𝜔𝑡−3𝛹𝜂2≥ 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6𝛹𝜂2 (2.8.4) To make sure a finite adaptation investment requires 𝜔 > 0.45 𝜂2𝑡𝛹, while the interior solution requires 𝜔 ≥0.22 Ω(𝑉+0.5𝑡)𝜂2𝐷𝑡. Taking total derivative of the FOCs (𝜕𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎 = 0 and 𝜕 𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡 = 0) to 𝛺 and 𝛴 respectively, and imposing the symmetry assumption, 𝜕𝐼𝑖 𝑎 𝜕𝛺, 𝜕 𝐼𝑖 𝑡 𝜕𝛺 and 𝜕𝐼𝑖 𝑎 𝜕𝛴, 𝜕 𝐼𝑖 𝑡 𝜕𝛴 are shown in Appendix A3: 𝜕𝐼𝑖 𝑎 𝜕𝛺≥ 0 ; 𝜕 𝐼𝑖 𝑡 𝜕𝛺≥ 0 ; 𝜕𝐼𝑖 𝑎 𝜕𝛴≤ 0 ; 𝜕 𝐼𝑖 𝑡 𝜕𝛴≤ 0 Proof of the above comparative statics is also in Appendix A3. The sign of 𝜕𝐼𝑖 𝑎 𝜕𝛺 and 𝜕 𝐼𝑖 𝑡 𝜕𝛺 depends on 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω, 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω. 𝜕𝐼𝑖 𝑎 𝜕𝛺≥ 0 and 𝜕 𝐼𝑖 𝑡 𝜕𝛺≥ 0, as 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω≥ 0 and 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω≥ 0. That is, as a higher expectation of disaster occurrence probability increases the marginal expected profit of terminal operator, and marginal joint expected profit of the monopoly port authority to own adaptation, the equilibrium adaptation increases as a result. The sign of 𝜕𝐼𝑖 𝑎 𝜕𝛴 , 𝜕 𝐼𝑖 𝑡 𝜕𝛴 depends on 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ. 𝜕𝐼𝑖 𝑎 𝜕𝛴≤ 0 and 𝜕 𝐼𝑖 𝑡 𝜕𝛴≤ 0, as 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ≤ 0 and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0. That is, as larger variance of disaster occurrence probability decreases the marginal expected profit of terminal operator, and marginal 31 expected joint profit of the monopoly port authority to own adaptation, the equilibrium port adaptation decreases as a result. 2.3.2.3 Adaptation of competing port authorities with intra-port coordination In this regime, port authorities compete with each other, but they can coordinate with terminal operators at each port on adaptation decision. Pricing rule at operation stage follows that of competing port authorities i.e. ?̅?𝑖 and ?̅?𝑖. Port authority and terminal operator at the same port now jointly maximize a total expected profit at one port: Max𝐼𝑖𝑎,𝐼𝑖𝑡𝐸[𝜋𝑖 + 𝛱𝑖], s. t. 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) ≤ 𝐷. FOCs for this intra-port coordination problem are as follows. SOCs require 𝜔 ≥ 0.53𝜂2𝑡𝛹. 𝜕𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎 =𝜕𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡 = 0.48𝜂𝑡 [(𝑉 + 0.50𝑡)𝛺 − 𝐷𝛹] − 0.048 𝜂2𝑡𝛹(𝐼𝑗𝑎 + 𝐼𝑗𝑡) +0.53 𝜂2𝑡𝛹 𝐼𝑖𝑡 + (0.53 𝜂2𝑡𝛹 −𝜔)𝐼𝑖𝑎 (2.9.1) The second derivatives show 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 ≥ 0 ; 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 ≤ 0 ; 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 ≤ 0 .The adaptation investment of port authority and terminal operator at the same port is strategic complement, while adaptation investment across ports is strategic substitute. Solving the system equations of above FOCs, symmetric interior Nash equilibrium is obtained as follows: 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂 [(2𝑉+𝑡) 𝛺−2𝐷𝛹]4.1 𝜔𝑡−4 𝛹𝜂2 (2.9.2) To make sure finite adaptation investment requires 𝜔 > 0.98 𝜂2𝑡𝛹. The interior Nash equilibrium requires 𝜔 ≥0.97 Ω(𝑉+0.5𝑡)𝜂2 𝐷𝑡. The derivatives of 𝐼𝑖 𝑎 and 𝐼𝑖 𝑡 to 𝛺 is as follows. Taking total derivative of the FOCs (𝜕𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎 = 0 and 𝜕𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡 = 0) to 𝛺 and 𝛴 respectively, and imposing the symmetry assumption, 𝜕𝐼𝑖 𝑎 𝜕𝛺, 𝜕𝐼𝑖 𝑡 𝜕𝛺 and 𝜕𝐼𝑖 𝑎 𝜕𝛴, 𝜕𝐼𝑖 𝑡 𝜕𝛴 can be obtained as shown Appendix A3: 32 𝜕𝐼𝑖 𝑎 𝜕𝛺≥ 0 ; 𝜕𝐼𝑖 𝑡 𝜕Ω≤ 0 ; 𝜕𝐼𝑖 𝑎 𝜕Σ≥ 0 ; 𝜕𝐼𝑖 𝑡 𝜕Σ≤ 0 Proof of the above comparative statics is also in Appendix A3. The sign of 𝜕𝐼𝑖 𝑎 𝜕𝛺 and 𝜕𝐼𝑖 𝑡 𝜕Ω depends on 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω. 𝜕𝐼𝑖 𝑎 𝜕𝛺≥ 0 and 𝜕𝐼𝑖 𝑡 𝜕Ω≥ 0, as 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω≥ 0 and 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω≥ 0. That is, as a higher expectation of disaster occurrence probability increases the marginal expected joint profit of port authority and terminal operator at one port to their own adaptation, the equilibrium adaptation thus increases. The sign of 𝜕𝐼𝑖 𝑎 𝜕Σ , 𝜕𝐼𝑖 𝑡 𝜕Σ depends on 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ. 𝜕𝐼𝑖 𝑎 𝜕Σ≤ 0 and 𝜕𝐼𝑖 𝑡 𝜕Σ≤ 0, as 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ≤ 0 and 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0. That is, as a larger variance of disaster occurrence probability decreases the marginal expected joint profit of port authority and terminal operator to their own adaptation at one port, the equilibrium port adaptation decreases as a result. Table 2.2 summarizes the interior equilibrium adaptation, SOCs, finite adaptation investment condition and condition of interior equilibrium adaptation for the three regimes discussed above. The comparative statics of equilibrium adaptation to the expectation and variance of the disaster occurrence probability are as follows. Proposition 2.2. is obtained on the impact of Knightian uncertainty on port adaptation. 𝜕𝐼?̅? 𝑎𝜕 𝛺≥ 0; 𝜕𝐼𝑖 𝑎𝜕𝛺≥ 0 ; 𝜕𝐼𝑖 𝑎𝜕𝛺≥ 0 and 𝜕𝐼?̅? 𝑎𝜕𝛴≤ 0; 𝜕𝐼𝑖 𝑎𝜕𝛴≤ 0 ; 𝜕𝐼𝑖 𝑎𝜕𝛴≤ 0 𝜕𝐼?̅? 𝑡𝜕 𝛺≥ 0; 𝜕𝐼𝑖 𝑡𝜕𝛺≥ 0 ; 𝜕𝐼𝑖 𝑡𝜕𝛺≥ 0 and 𝜕𝐼?̅? 𝑡𝜕𝛴≤ 0; 𝜕𝐼𝑖 𝑡𝜕𝛴≤ 0 ; 𝜕𝐼𝑖 𝑡𝜕𝛴≤ 0 Proposition 2.2: Higher expectation of disaster occurrence probability increases adaptation, while larger variance of disaster occurrence probability reduces adaptation. 33 Table 2.2 The summary of the Nash equilibrium of different inter-port competition and intra-port coordination regimes Regimes Port authority adaptation Terminal operator adaptation SOCs and finite adaptation Interior solution requirement Competing Port Authorities 𝐼?̅? 𝑎 = 𝜂 [(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹]6.1𝜔𝑡 − 3𝛹𝜂2 𝐼?̅? 𝑡 = 𝜂 [(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹]2.1 (6.1 𝜔𝑡 − 3 𝛹𝜂2) 𝜔 ≥ 0.49 𝜂2𝑡𝛹 𝜔 ≥0.48 𝛺(𝑉 + 0.5𝑡)𝜂2 𝐷𝑡 Monopoly Port Authority 𝐼𝑖 𝑎 = 𝜂 [(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹]6.7𝜔𝑡 − 3 𝛹𝜂2 𝐼𝑖 𝑡 = 𝜂 [(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹]13.7 𝜔𝑡 − 6.1 𝛹𝜂2 𝜔 ≥ 0.45 𝜂2𝑡𝛹 𝜔 ≥044 𝛺(𝑉 + 0.5𝑡)𝜂2𝐷𝑡 Competing Port Authorities with Intra-port Coordination 𝐼𝑖 𝑎 = 𝜂 [(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹]4.1𝜔𝑡 − 4 𝛹𝜂2 𝐼𝑖 𝑡 = 𝜂 [(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹]4.1𝜔𝑡 − 4 𝛹𝜂2 𝜔 ≥ 0.98 𝜂2𝑡𝛹 𝜔 ≥0.97 𝛺(𝑉 + 0.5𝑡)𝜂2 𝐷𝑡 This analytical result may provide a sound explanation for why in practice port adaptation is much more difficult to implement than “mitigation”, because our present knowledge about climate change and related disasters is far from reasonable accuracy. For example, Becker et al. (2012) and Ng et al. (2016) find that most surveyed ports cite the “inadequate information” and need to know more about the issue as a major reason for slow development of adaptation. On the other hand, the relatively low probability of the climate change related disaster also discourages the port’s motivation to adapt. This is exemplified by Gulfport’s (Mississippi US) decision to exclusively use the post-Katrina grant ($ 570 million) allocated by federal government to expand capacity, while canceling terminal elevation project to help protect against another Katrina-like hurricane. Although not severely affected by the most recent Hurricanes Harvey and Irma in August 2017, this port has been alerted that disaster occurrence probability may not be as low as it once perceived. The increase in expectation or risk of disaster occurrence probability stimulates adaptation investment. Ng et al. (2016) survey 21 Canadian ports’ adaptation and find that ports subject to higher climate change risk adapt more. Our Proposition 2.2 is also consistent with existing economics and decision science literature. Camerer and Weber (1992) model a subjective expected utility (SEU) with Knightian uncertainty on event occurrence probability. They find people prefer to bet on events they know more about, even when their beliefs are held constant as 34 people are averse to ambiguity about the probability. Nishimura and Ozai (2007) investigate the effect of “Knightian uncertainty” on project investment decisions. It is found that ambiguity of Knightian uncertainty decreases the value of irreversible investment while the increase in risk increases it. The ranking of adaptation is 𝐼𝑖 𝑎 ≥ 𝐼?̅? 𝑎 ≥ 𝐼𝑖 𝑎, which is because: 𝐼𝑖 𝑎 − 𝐼?̅? 𝑎 =0.079×𝜂(2𝑉Ω−2𝐷Ψ+Ω𝑡)(𝜔𝑡+0.51Ψ𝜂2)(𝜔𝑡−0.97Ψ𝜂2)(𝜔𝑡−0.48Ψ𝜂2)> 0; 𝐼?̅? 𝑎 − 𝐼𝑖 𝑎 =0.0132×𝜂(2𝑉Ω−2𝐷Ψ+Ω𝑡)𝜔𝑡(𝜔𝑡−0.48Ψ𝜂2)(𝜔𝑡−0.45Ψ𝜂2)> 0 Analogously, one can show 𝐼𝑖 𝑡 ≥ 𝐼?̅? 𝑡 ≥ 𝐼𝑖 𝑡 . Proposition 2.3: Port authorities’ competition leads to higher adaptation (the competition effect), i.e., 𝐼?̅? 𝑎 ≥ 𝐼𝑖 𝑎; 𝐼?̅? 𝑡 ≥ 𝐼𝑖 𝑡. Intra-port coordination between port authority and terminal operator at each port also increases adaptation i.e., 𝐼𝑖 𝑎 ≥ 𝐼?̅? 𝑎; 𝐼𝑖 𝑡 ≥ 𝐼?̅? 𝑡. Thus, without intra-port coordination, port authority and terminal operator at the same port “free-ride” on each other adaptation by investing in less adaptation (the free-riding effect). Adaptation across ports is strategic substitute such that an increase in one port’s adaptation imposes negative externality on the other port’s expected profit. When two ports are controlled by a monopoly port authority, they coordinate to internalize such negative externality through reducing adaptation investment at two ports. Thus, inter-port competition between private terminal operators increase port adaptation investments of two ports (the competition effect). On the other hand, port authorities’ adaptation and terminal operator’s adaptation within one port is strategic complement such that an increase in adaptation by one party benefits the other. As a result, port authority and terminal operator free-ride on each other with a less incentive to adapt (the free-riding effect). The ratio of the adaptation between competing port authorities and monopoly port authority is 𝐼?̅? 𝑎𝐼𝑖 𝑎 =1.09 ×(𝜔𝑡−0.45Ψ𝜂2)(𝜔𝑡−0.49Ψ𝜂2), which measures the degree of the competition effect. 𝜕𝜕𝛺(𝐼?̅? 𝑎𝐼𝑖 𝑎) =0.085 Ω𝜂2𝜔𝑡(𝜔𝑡−0.49Ψ𝜂2)2> 0 ; 𝜕𝜕Σ(𝐼?̅? 𝑎𝐼𝑖 𝑎) =0.042 Ω𝜂2𝜔𝑡(𝜔𝑡−0.485Ψ𝜂2)2> 0 . Analogously, 𝜕𝜕𝛺(𝐼?̅? 𝑡𝐼𝑖 𝑡) > 0 , 𝜕𝜕Σ(𝐼?̅? 𝑡𝐼𝑖 𝑡) > 0 . The ratio of the adaptation between intra-port coordination and no coordination for competing port 35 authorities is 𝐼𝑖 𝑎𝐼?̅? 𝑎 = 1.49 ×(𝜔𝑡−0.49Ψ𝜂2)(𝜔𝑡−0.97Ψ𝜂2) , which measures the degree of the free-riding effect. 𝜕𝜕𝛺(𝐼𝑖 𝑎𝐼?̅? 𝑎) =1.44 Ω𝜂2𝜔𝑡(𝜔𝑡−0.97Ψ𝜂2)2> 0 ; 𝜕𝜕Σ(𝐼𝑖 𝑎𝐼?̅? 𝑎) =0.72 Ω𝜂2𝜔𝑡(𝜔𝑡−0.97Ψ𝜂2)2> 0 . Analogously, it can be proved that 𝜕𝜕𝛺(𝐼𝑖 𝑡𝐼?̅? 𝑡) > 0; 𝜕𝜕Σ(𝐼𝑖 𝑡𝐼?̅? 𝑡) > 0. Proposition 2.4: Higher expectation and larger variance of disaster occurrence strengthen both the competition effect and the free-riding effect. Proposition 2.4 suggests that a higher expectation and larger variance of disaster occurrence probability enhance the competition effect and the free-riding effect. For the competition effect, when two port authorities compete on adaptation, if the expectation of disaster occurrence probability increases, they have a stronger incentive to adapt compared to the monopoly port authority, strengthening the competition effect. When the variance of disaster occurrence probability increases, as suggested by Proposition 2.2, two ports reduce adaptation investment. However, when port authorities compete, they reduce adaptation less compared to that of monopoly port authority. As a result, an increased variance of disaster occurrence probability also enlarges difference in adaptation for competing port authorities and monopoly port authority, enhancing the competition effect. For the free-riding effect, when the expectation of disaster occurrence probability increases, the marginal expected profit of adaptation investment is larger, such that one party (port authority or terminal operator) benefits more from the other party’s adaptation, thus enhancing the free-riding incentive. When the variance of disaster occurrence probability increases, each party reduces adaptation. Without coordination, such reduction is more significant, thus also enlarging the difference with and without intra-port coordination. This strengthens the free-riding effect. Last, we investigate the implications of inter-port competition and intra-port cooperation on the expected social welfare of the two-port system. 𝐸[𝑆𝑊̅̅̅̅̅] is the expected social welfare with competing port authorities; 𝐸[𝑆?̃?] is the expected social welfare with monopoly port authority; 𝐸[𝑆?̂?] is the expected social welfare with competing port authorities and with intra-port coordination. The expression of 𝐸[𝑆?̂?] − 𝐸[𝑆𝑊̅̅̅̅̅] is as below. 36 𝐸[𝑆?̂?] − 𝐸[𝑆𝑊̅̅̅̅̅] =0.048𝜔(𝑡2𝜔2−0.96Ψ𝜂2𝑡𝜔+0.068Ψ2𝜂2)𝜂2(2Ω𝑉−2𝐷Ψ+Ω𝑡)2(𝜔𝑡−0.49Ψ𝜂2)2(𝜔𝑡−0.97Ψ𝜂2)2> 0 The sign of 𝐸[𝑆?̂?] − 𝐸[𝑆𝑊̅̅̅̅̅] is determined by the term 𝑡2𝜔2 − 0.96𝛹𝜂2𝑡𝜔 + 0.068𝛹2𝜂2 in the numerator, which is a convex quadratic function of 𝜔. The two solutions of 𝑡2𝜔2 − 0.96𝛹𝜂2𝑡𝜔 +0.068Ψ2𝜂2 = 0 are 0.096 𝜂2𝑡𝛹 and 0.86 𝜂2𝑡𝛹. The finite adaptation investment condition for 𝐼𝑖 𝑎 and 𝐼𝑖 𝑡 suggests 𝜔 > 0.98𝜂2𝑡𝛹, such that 𝑡2𝜔2 − 0.96𝛹𝜂2𝑡𝜔 + 0.068Ψ2𝜂2 > 0. Thus 𝐸[𝑆?̂?] −𝐸[𝑆𝑊̅̅̅̅̅] > 0. The expression of 𝐸[𝑆𝑊̅̅̅̅̅] − 𝐸[𝑆?̃?] is as below, which is apparently positive. 𝐸[𝑆𝑊̅̅̅̅̅] − 𝐸[𝑆?̃?] =0.0056×𝜔2𝜂2𝑡(2Ω𝑉−2𝐷Ψ+Ω𝑡)2(𝜔𝑡−0.47Ψ𝜂2)(𝜔𝑡−0.445Ψ𝜂2)2(𝜔𝑡−0.49Ψ𝜂2)2> 0 The ranking of expected social welfare is 𝐸[𝑆?̂?] > 𝐸[𝑆𝑊̅̅̅̅̅] > 𝐸[𝑆?̃?]. Proposition 2.5: The expected social welfare increases with the port adaptation. Intra-port coordination between port authorities and terminal operators results in the highest expected social welfare by overcoming the free-riding effect. Monopoly port authority, on the contrary, leads to the smallest expected social welfare with the lowest level of port adaptation. Proposition 2.5 may have several policy implications. First, from the social welfare perspective, with uncertain natural disaster threat, it is better to have ports controlled by different port authorities. Inter-port competition between port authorities results in more adaptation, and higher expected total social welfare. Regulators should avoid granting monopoly power to a single port authority in a multiple-port region. Second, intra-port coordination on adaptation between port authority and terminal operator should be encouraged to address the free-riding effect on adaptation. Unlike anti-trust concern on pricing collision, regulators should allow and even facilitate intra-port coordination between port authority and terminal operator to jointly plan port adaptation. When the revenue-sharing mechanism can be figured out between port authority and terminal operator, they have incentive to coordinate adaptation as the total expected profit is 37 maximized. The experience of the port of San Diego 21 can be learnt by more ports to better develop framework and mechanism to involve terminal operators to discuss, plan and implement port adaptation. 2.4 Effects of Port Competition Intensity Ports’ service differentiation can moderate inter-port competition (Wang et al., 2012), thus affecting port adaptation investment. Ports with more homogenous services should compete more fiercely. For example, Shenzhen and Hong Kong port both focus on container cargo as gateway to the South China, making their competition intense. And ports with more differentiated services compete less intensely. For example, the largest port in Europe, port of Rotterdam (the Netherlands), focuses on container cargo, while the other port in the same region, the port of Antwerp (Belgium), mainly handles bulk cargo. The two ports thus do not compete head-to-head. In this section, we explicitly model such inter-port competition intensity by allowing the shippers in the common hinterland to have a different transport cost parameter compared to each port’s captive catchment area. Specifically, we let the shipper in the common hinterland have a different transport cost, 𝑡′ , compared to the transport cost, 𝑡 , for shippers in two ports’ own captive catchment. The parameter 𝑡′ thus helps capture port service heterogeneity in the common hinterland market. A smaller 𝑡′ suggests a less port service heterogeneity, equivalent to a more intense inter-port competition. With this new parameter 𝑡′, the pricing rule at operation stage and optimal adaptation investment at the adaptation investment stage can be solved first. The new equilibrium adaptation with competing port authorities is obtained as 𝐼?̅? 𝑎(𝑡′) and 𝐼?̅? 𝑡(𝑡′) . The equilibrium adaptation with monopoly port authority is obtained as 𝐼𝑖 𝑎(𝑡′) and 𝐼𝑖 𝑡(𝑡′) (the expressions of these equilibria are shown in Appendix A4). The competition effect is measured by ratio 𝐼?̅? 𝑎(𝑡′)𝐼𝑖 𝑎(𝑡′) and 𝐼?̅? 𝑡(𝑡′)𝐼𝑖 𝑡(𝑡′). The comparative statics 𝜕𝜕𝑡′(𝐼?̅? 𝑎(𝑡′)𝐼𝑖 𝑎(𝑡′)) and 𝜕𝜕𝑡′(𝐼?̅? 𝑡(𝑡′)𝐼𝑖 𝑡(𝑡′)) shed light on the impact of inter-port competition intensity (port service 21 The Port of San Diego (California) led a multi-stakeholder effort, The Climate Mitigation and Adaptation Plan, with the port terminal operators, nearby communities (Becker et al., 2013). 38 homogeneity) on the competition effect of port adaptation. However, 𝐼?̅? 𝑎(𝑡′)𝐼𝑖 𝑎(𝑡′) and 𝐼?̅? 𝑡(𝑡′)𝐼𝑖 𝑡(𝑡′) are high order polynomial of 𝑡′, such that the analytical result on comparative statics 𝜕𝜕𝑡′(𝐼?̅? 𝑎(𝑡′)𝐼𝑖 𝑎(𝑡′)) and 𝜕𝜕𝑡′(𝐼?̅? 𝑡(𝑡′)𝐼𝑖 𝑡(𝑡′)) is difficult to reach. Numerical simulation is conducted with the parameter values 𝛹 = 0.1, 𝜂 = 2, 𝜔 = 25, 𝑡 = 0.1. Figure 2.4 shows the numerical values of 𝐼?̅? 𝑎(𝑡′)𝐼𝑖 𝑎(𝑡′) and 𝐼?̅? 𝑡(𝑡′)𝐼𝑖 𝑡(𝑡′) with changes in 𝑡′. When 𝑡′ increases, the values of ratios 𝐼?̅? 𝑎(𝑡′)𝐼𝑖 𝑎(𝑡′) and 𝐼?̅? 𝑡(𝑡′)𝐼𝑖 𝑡(𝑡′) decrease. That is, when two ports are more competitive, or port services are more homogenous, the competition effect on port adaptation is strengthened. Robustness check has also been done with a wide range of the different parameter values, and our conclusions keep consistent qualitatively. 22 Figure 2.4 Numerical values of ?̅?𝒊 𝒂(𝒕′)?̃?𝒊 𝒂(𝒕′) and ?̅?𝒊 𝒕(𝒕′)?̃?𝒊 𝒕(𝒕′) with changing 𝒕′ (𝜳 = 𝟎. 𝟏, 𝜼 = 𝟐, 𝝎 = 𝟐𝟓, 𝒕 = 𝟎. 𝟏) Note: Larger values of ?̅?𝒊 𝒂(𝒕′)?̃?𝒊 𝒂(𝒕′) and ?̅?𝒊 𝒕(𝒕′)?̃?𝒊 𝒕(𝒕′) suggest a stronger competition effect on port adaptation. 22 The results of the robustness check with alternative parameter values are available upon request. They are not reported in the manuscript to save space. 39 In addition, the equilibrium adaptations with competing port authorities but allowing intra-port coordination are solved as 𝐼𝑖 𝑎(𝑡′) and 𝐼𝑖 𝑡(𝑡′) with the expressions in Appendix A4. The free-riding effect is reflected by the ratio 𝐼𝑖 𝑎(𝑡′)𝐼?̅? 𝑎(𝑡′) and 𝐼𝑖 𝑡(𝑡′)𝐼?̅? 𝑡(𝑡′). The inter-port competition intensity (port service homogeneity) might also affect incentive of the port authority and terminal operator to free-ride each other on adaptation within one port. Numerical simulation demonstrates the relation between values of 𝐼𝑖 𝑎(𝑡′)𝐼?̅? 𝑎(𝑡′) , 𝐼𝑖 𝑡(𝑡′)𝐼?̅? 𝑡(𝑡′) and the parameter 𝑡′ (as Figure 2.5). It is noted when 𝑡′ increases, the values of ratios 𝐼𝑖 𝑎(𝑡′)𝐼?̅? 𝑎(𝑡′) , 𝐼𝑖 𝑡(𝑡′)𝐼?̅? 𝑡(𝑡′) decrease as well. This suggests that more intense inter-port competition (more service homogeneity) can strengthen the free-riding effect on adaptation between port authority and terminal operator at the same port. This finding makes sense since when two ports compete more fiercely in the common hinterland market, one port’s adaptation contributes more to gain competitive advantage in this competing market. Therefore, within one port, port authority and terminal operator have stronger incentive to free-ride on each other on adaptation. We summarize the effect of inter-port competition intensity (port service homogeneity) on the competition effect and free-riding effect on adaptation as Proposition 2.6. Figure 2.5 Numerical values of ?̂?𝒊 𝒂(𝒕′)?̅?𝒊 𝒂(𝒕′) and ?̂?𝒊 𝒕(𝒕′)?̅?𝒊 𝒕(𝒕′) with changing 𝒕′ (𝜳 = 𝟎. 𝟏, 𝜼 = 𝟐, 𝝎 = 𝟐𝟓, 𝒕 = 𝟎. 𝟏) Note: Larger values of 𝐼𝑖 𝑎(𝑡′)𝐼?̅? 𝑎(𝑡′) and 𝐼𝑖 𝑡(𝑡′)𝐼?̅? 𝑡(𝑡′) suggest a stronger free-riding effect on port adaptation. 40 Proposition 2.6: More intense inter-port competition (less service heterogeneity) strengthens both the competition effect on adaptation between two ports, and the free-riding effect on adaptation between port authority and terminal operator within one port. 2.5 Concluding Remarks With more than 80% of the global trade carried by international shipping, coastal ports resilience to climate change related disaster is important to maintain reliable global supply chain. Ports around the world are increasingly aware of adaptation to threat of such disasters. This chapter contributes to existing literature in port adaptation on several aspects. First, we model the climate-change related disaster to have a general-form Knightian uncertainty (Knight 1921) in the sense that the probability of the disaster occurrence is per se a random variable and not accurately knowable. Our Knightian uncertainty captures a more general and wider family of probability distributions, not limited to the specific assumptions in Weitzman (2009) and Xiao et al. (2015). The other strand of contributions is to explicitly examine the impacts of inter-port competition, intra-port cooperation on port adaptation investment. We also explicitly model endogenous port pricing and shippers’ demand with port adaptation. The study answers how inter-port competition, and intra-port cooperation can increase or decrease the port adaptation. We find, with Knightian uncertainty assumption, the port adaptation investments increase with the expectation of the disaster occurrence probability but decrease with its variance. In other words, a higher expectation of the disaster occurrence probability encourages port adaptation, but the variance of the disaster occurrence probability discourages port adaptation. Inter-port competition results in more adaptation investment (i.e., the competition effect). There is free-riding between the port authority and the terminal operator (i.e., the free-riding effect) within each port. Their coordination can increase the adaptation by removing such free-riding effect. The expected social welfare of the two-port region increases with ports’ adaptation, such that inter-port competition, and intra-port coordination lead to higher expected social welfare. We also find that the competition and free-riding effects on port adaptation can be strengthened by a higher expectation and larger 41 variance of disaster occurrence probability, and by increasing inter-port competition intensity (less port service homogeneity). This chapter also opens new avenue for future research. First, the market structure of private terminal operators needs better exploration. We assume each port has a single terminal operator, which can be restrictive. One port can have more than one terminal operator, either private or owned by port authority. Some shipping lines also operate dedicated terminals. In addition, multinational terminal operators such as PSA International, Hutchison Port Holding, APM terminals, DP World and China Merchant Holding can simultaneously operate in several nearby ports. Such intra- and inter-port competition, and inter-port cooperation among private terminal operators can be better accounted for in the future study when analyzing port adaptation. Second, public ownership of port authority and its implication on port adaptation may be also investigated. Although we have explained in the study that most of the port authorities have been corporatized and financially self-responsible, port authority may also partially bear social responsibility. It is reasonable to conjecture that public port authority could invest more on adaptation, especially when port adaptation can have positive externality to protect nearby neighbourhood community and contribute to a more resilient local economy beyond protecting shippers’ economic benefits. In addition, public ownership may also reduce port authorities’ free-riding effect on terminal operator, as public port authority also accounts for terminal operator’s profit in its objective function. Last our study exclusively focuses on the disaster adaptation decision, while port can have multi-dimensional long-term decisions, such as capacity expansion, facilities upgrading etc. With a limited resource, port may need to trade off among adaptation, capacity expansion and other development projects. A more comprehensive economic model is therefore called for to consider port optimal resource allocation for multi-dimension decisions.42 Chapter 3. Effects of High-Speed Rail Speed on Airline Demand and Price 3.1 Introduction With a significantly increased train speed, high-speed rail (HSR) has become an effective competitor of air transport. Studies on intermodal competition show mixed results on the competitive distance of HSR. Adler et al. (2010) find that HSR is most competitive in markets of 750 km or less distance. Chen (2017) finds that the impact of HSR on airlines is the greatest on route distance between 500 km to 800 km. Wan et al. (2016) show that in China, HSR services with a maximum speed of 300 km/hr produce much stronger negative impacts on routes above 800 km than those with a maximum speed of 200 km/h. Therefore, HSR speed plays a critical role in shaping HSR’s service substitutability with airlines. In fact, HSR speed is an important service quality that contributes to the vertical differentiation between HSR and air transport (Xia and Zhang, 2016). Furthermore, vertical differentiation in speed may co-exist with passengers’ heterogeneous taste in mode preference (i.e., horizontal differentiation). More specifically, given the quality factor (e.g., speed), passengers may not reach consensus on the modal choice. The perceptions and attitudes, habitual behaviors, lifestyle choices, and cultural factors can affect travel mode choice over airlines or HSR (Bennett et al., 1957; Thøgersen, 2006; Blainey et al., 2012). For instance, passengers can have divergent perceptions on airlines and HSR in terms of safety concern, comfort level, and in-vehicle service (Li et al., 2015). The heterogeneous tastes may lead to different substitutability between airlines and HSR. When route distance increases, passengers spend longer time in traveling. As a result, their personal tastes on service characteristics of different modes can be amplified, they may increasingly regard airline and HSR services as different and less substitutable. On the other hand, airline and HSR services become more substitutable on short-haul routes. For instance, by using survey data from Taiwan’s HSR market Li and Schmöcker (2017) find that airline and HSR services are more substitutable on the short-haul routes with HSR travel time between one to two hours. 43 When the two modes are more substitutable and thus compete more fiercely, HSR speed, as a quality attribute, may have different effects on airlines in terms of price and traffic volume. An increasing number of analytical studies have investigated the intermodal competition between airlines and HSR (Yang and Zhang, 2012; D’Alfonso et al., 2015, 2016; Jiang and Zhang 2016; Talebian and Zou, 2016), but there are no studies, to our best knowledge, that explore how the air-HSR substitutability can moderate the HSR speed impacts on airline traffic and price. Furthermore, while an increased HSR speed reduces travel time it may, on the other hand, raise safety concern as the existing trains are already at a very high level. This appears the case especially in emerging HSR markets such as China, where the HSR operation experience is still being accumulated and technologies are being fast developed. The speed increase can cause suspicion over the railway safety among travellers, especially after China’s “7.23 rear-ending” crash accident in July 2011 (the details of the accident will be discussed in Section 3.3 below). This safety concern may be ongoing, affecting negatively HSR demand. In this chapter we develop an analytical model to study HSR speed effects on airline traffic and price, explicitly accounting for the potential impact of intermodal substitutability. Our model incorporates, following the above discussion, two countervailing effects of HSR speed on airlines, namely the travel time effect and safety effect, where an increase in HSR speed reduces HSR travel time but may harm public confidence in HSR safety. Apart from investigating whether and how the air-HSR service substitutability can moderate the HSR speed effect, the present chapter is also the first study to analytically incorporate the safety effect of HSR speed. As a natural and important extension of the analytical model, we empirically test, and quantify, the HSR speed effects on airlines using an event of HSR speed reduction in China. The exercise also allows to verify the theoretical findings. As will be elaborated in Section 3.3, this HSR speed reduction in China in 2011 largely alleviates the endogeneity concern over HSR speed effect estimation. Briefly, this is because the reduction was enforced by the government rather than being a market competition outcome, and it was implemented system-wide (independent of any route heterogeneity). A difference-in-differences (DID) method is employed to estimate equations of 44 airline traffic and price.23 In line with theoretical analysis, we identify varying HSR speed effects when airline and HSR services are differently substitutable. The theoretical model shows that the air-HSR substitutability reinforces the HSR speed effect on airlines, and that the speed effect depends further on the relative dominance of the travel-time and safety effects. A HSR speed reduction increases airline traffic and price when the travel-time effect dominates, while it reduces airline traffic and price when the safety effect dominates. Moreover, HSR speed has a larger impact on airline traffic than on airline price. Finally, our analysis suggests that the speed effect can be moderated by the intensity of inter-airlines competition. The empirical results are largely consistent with the theoretical findings. Specifically, the HSR speed reduction increased both airline traffic and price, implying that in the Chinese market we examined, the travel-time effect dominates the safety effect of a HSR speed change. More importantly, the estimation shows that the HSR speed effect on airlines is much stronger on short-haul routes than on long-haul routes, where airlines and HSR are less substitutable. This result is robust with alternative econometric specifications. By conducting model selection tests, we find that the HSR speed effect on airlines declines with route distance but increases with HSR speed in a square relation. The HSR speed effect is thus very responsive to air-HSR substitutability. The remainder of this chapter is organized as follows. Literature review is provided in Section 3.2. Section 3.3 briefly discusses HSR development in China and the system-wide HSR speed reduction in 2011, which is used as a natural experiment to estimate HSR speed effects. Section 3.4 develops a theoretical model, and Section 3.5 specifies the econometric model and discusses data sources and variables. Estimation results are presented in Section 3.6. The last section, Section 3.7, summarizes this chapter. 3.2 Literature Review This literature review consists of two parts. The first part reviews major studies on air-HSR competition, focusing on the travel time and safety issues. The second part discusses the literature 23 See Ashenfelter and Card (1985) for the details on the DID estimation method and application. 45 on the interactions of horizontal and vertical differentiation, with an emphasis on the research gaps in the context of air-HSR competition. 3.2.1 Air-HSR competition One stream of the literature analytically investigates the effects of air-HSR competition. Yang and Zhang (2012), using an adapted Hotelling model, find that both airfare and rail fare fall as HSR put more weight on social welfare in the objective function. D’Alfonso et al. (2015) analyze the environmental impact of air-HSR competition and show that the introduction of HSR may have a negative effect on the environment. Jiang and Zhang (2016) investigate the long-term impacts of HSR competition on airlines and find that the airline, faced with stronger competition from HSR, will more likely move towards a hub-and-spoke network. Talebian and Zou (2016) find that the HSR operator focusing more on social welfare will benefit passengers through reduced fare and higher frequency. However, some gaps exist among the current analytical studies on air-HSR competition. First, Yang and Zhang (2012), D’Alfonso et al. (2015) and Talebian and Zou (2016) have modeled HSR speed as a decision variable. D’Alfonso et al. (2015) focus on the environmental effect of HSR speed while the other two focus on the travel time effect of HSR speed. However, the safety effect of HSR speed has not yet been explicitly considered. Second, existing analytical studies on air-HSR interactions largely deal with a duopoly market (i.e., one HSR and one airline), for example, Yang and Zhang (2012), D’Alfonso et al. (2015, 2016), Jiang and Zhang (2016), and Talebian and Zou (2016). However, inter-airlines competition within the air sector in the presence of HSR has rarely been modeled. Another stream of literature empirically investigates air-HSR competition, focusing on the travel-time effect. For instance, González-Savignat (2004) analyzes the potential for HSR to compete with airlines in the Madrid-Barcelona market, and finds that the impact on airlines depends on HSR travel time. Dobruszkes (2011) considers HSR travel time as a key competitive factor. Behrens and Pels (2012) study the travelers’ behavior in the London-Paris market and find that HSR market share is influenced by total travel time. Capozza (2016) tests how HSR travel time affects airfare using the market data of Italy and finds that airlines set, on average, higher fares as rail travel time increases. Zhang et al. (2017) find that airline demand falls as HSR travel time becomes shorter in 46 the Chinese market. However, the endogeneity issue has not been well addressed in the above-mentioned studies. For instance, cross-sectional data is used in Capozza (2016), so the route-level unobservables cannot be controlled. Zhang et al. (2017) adopt panel data, but the fixed-effect model cannot be used to control the route-level unobservables, because HSR travel time is time-invariant during the sample period. In addition, the safety concern due to HSR speed change may not be trivial, as empirical literature demonstrates that travellers demand higher safety when choosing transport modes. Janic (2003) evaluates HSR, Maglev and air transport in Europe using multiple criteria and finds that safety is related to the perceived risk of injury and/or death due to an accident, and is of particular interest for the users of high-speed systems. Chou and Kim (2009) analyze the actual riding experience on the Taiwan HSR (THSR) and Korea Train eXpress (KTX) and find that rider security is one of the key factors of service quality that affects customer satisfaction. Chou et al. (2011) evaluate HSR service quality and performance by interviewing THSR and KTX passengers, and find that the top importance measurement indicator for TSHR passengers is the safety of the HSR. Kuo and Tang (2013) show that satisfaction directly affects travel behaviors, and maintain transportation safety are essential considerations, especially in an aging society. Chou et al. (2014) find that safety is one of the service quality dimensions that affect customer satisfaction and loyalty for THSR services. Wang et al. (2017b) survey more than 300 Chinese inter-urban travellers and find that the perception on the mode safety is one of the most important factors in determining their modal choice among coach, conventional train, HSR and airlines. In addition, Banister (2011) points out that the growth in travel distance needs to be reassessed with a view to reduce it, as shorter distances and slower travel have positive co-benefits for the environment (including safety), energy (and carbon), social inclusion, wellbeing (including health) and the economy. Givoni and Banister (2012) also argue that more important than average speed is the journey reliability, comfort, security and safety and service frequency, all of which make up the journey experience, while achieving high quality for these components that include a rail segment might often mean compromising on the maximum speed. However, the safety effect due to HSR speed change is omitted in the existing literature of air-HSR competition. More importantly, very few studies have directly and systematically verified the HSR speed effect on airlines, as well as the magnitude, if such impacts do exist. One possible reason is 47 that there is little variation in HSR speed in countries that operate HSR over the years. As will be discussed in Section 3.3, the system-wide HSR speed reduction in China in 2011 provides a rare natural experiment to unbiasedly estimate the HSR speed effect on airlines. 3.2.2 Interactions of horizontal differentiation and vertical differentiation The interactions of product substitutability (horizontal differentiation) and service quality (vertical differentiation) have been well studied in industrial organization literature. For instance, Neven and Thisse (1990) analyze a duopoly model with both horizontal (variety) and vertical (quality) differentiation and find that firms choose maximum differentiation along one of the characteristics and minimum differentiation along the other. Degryse (1996) shows that more closely located (more substitutable) banks compete more fiercely on the service quality. Ferreira and Thisse (1996) adopt a revised Hotelling model to investigate the product vertical-horizontal differentiation interaction. The product substitutability is shown to enhance the impact of vertical differentiation on firms’ equilibrium price and profit. In the context of the airline-HSR competition, HSR speed, as a service quality, presumably has a stronger effect on airlines when the two modes are more substitutable (e.g., on shorter haul routes), while the effect may diminish when the services are less substitutable (e.g., on longer haul routes). We are not aware of any studies on air-HSR competition that analytically investigate and empirically test the interactions of horizontal differentiation (air-HSR substitutability based on distance) and vertical differentiation (service quality based on speed). 3.3 A Natural Experiment in HSR Speed Reduction To modernize the country’s railway transport system and to alleviate rail capacity constraint, China announced a “Mid-to-Long-Term Railway Network Plan” in 2004 and laid out a blueprint of 48 building a “4+4” HSR network with a total length of 16,000 km by 2020.24 By the end of 2017, China has already built 25,000 km HSR, longer than the combination of all the other countries. The dramatic HSR construction in the first several years raised significant safety concern. In April 2011, Ministry of Railway planned to slow down HSR operating speed due to reasons that China only had 3 years of experience in HSR operation, and the HSR network was expanding too fast to be totally free of technical flaws. On July 1st 2011, the maximum operating speed on Wuhan-Guangzhou, Zhengzhou-Xi’an, Shanghai-Nanjing HSR lines slowed from 350 km/hr to 300 km/hr. On July 23, a serious crash happened due to signal failures on the Yong-Wen HSR track, where one train collided with another stopped train, killed 40 passengers. The 7.23 rear-ending accident showed some weaknesses in HSR planning and monitoring, which triggered the decision to slow HSR speed system-wide, affecting 498 pairs of trains belonging to 18 railway sub-bureaus, with the maximum operating speed for trains of 350 km/hr reduced to 300 km/hr, 250 km/hr reduced to 200 km/hr, and 200 km/hr reduced to 160 km/hr. For instance, the Beijing-Tianjin, Shanghai-Hangzhou HSR reduced speed from 350 km/hr to 300 km/hr soon after the accident. The Beijing-Shanghai HSR inaugurated on July 1, 2011 and runs at a speed of 300 km/hr, despite the designed maximum speed of 380 km/hr. The decision was designed to accumulate safety management experience, which increases passengers’ travel time, but “half an hour is a good price to pay for safety” as stated by the Ministry of Railways.25 This major overall drop in HSR speed represents the first time that China’s railway authorities have gone against the long-standing policy of acceleration (with a total of six times of rail speed increase since 1997). This speed reduction in China has provided a rare natural experiment to study effects of HSR speed on competing airlines’ market demand and price.26 As already explained, such speed reduction is exogenous as it is of safety concern instead of a market competition outcome. The 24 The four vertical HSR corridors are Beijing-Shanghai, Beijing-Guangzhou-Shenzhen, Beijing-Harbin, and Hangzhou-Fuzhou-Shenzhen, whereas the four horizontal HSR corridors are Qingdao-Taiyuan, Xuzhou-Lanzhou, Shanghai-Wuhan-Chengdu, and Shanghai-Kunming. 25 The HSR operator did not shorten the stopping time at each railway station to make up for the travel time loss due to the speed reduction. 26 Bilotkach et al. (2012) investigate the sensitivity of prices to demand shocks in a natural experiment that occurred in the San Francisco Bay Area where a freeway interchange collapse after an accident, making OAK airport a less attractive choice than SFO airport. The study reveals that the surface road infrastructure disruption reduced airfare by 6-7% at the affected airports. 49 speed reduction was mandated by the government and implemented on all HSR routes almost at the same time, which makes it independent of route heterogeneous characteristics. Potential endogeneity of HSR speed is minimized to the largest extent for empirical estimation. This speed reduction effect has been ongoing since its implementation in 2011. The maximum operating speed on Beijing-Shanghai line, however, resumed to 350km/hr in September 2017, after accumulating HSR operation experience and going through rigorous evaluation on current HSR safety standard. HSR price in China is strictly regulated. Although China’s Railway Corporation announced in March 2017 that the price of some HSR lines will be adjusted based on market condition, the exact timeline has not yet been settled.27 The HSR baseline price is 0.45 RMB per km (about 0.07 USD), applied to every route.28 Even when the speed was reduced in 2011, HSR price remained almost the same, 29 while HSR in Europe has much autonomy to set price, taking into account the heterogeneous market conditions. The 7.23 rear-ending accident could also result in confidence loss and panic in traveling by HSR. This panic can also divert travel demand from HSR to airlines in the short term, which might create a confounding factor on the speed reduction effect. For example, Wei et al. (2017) find that, on the newly opened Beijing-Shanghai HSR line, airline price increased by 27.4% within the first half month immediately post the accident. Thus, our empirical estimation must disentangle the speed reduction (HSR service quality) effect from the potential short-term panic effect.30 Unlike the speed effect that can be persistent over time, this panic effect could attenuate fast. This nature helps us identify them separately. 27 See the article from China Daily at http://www.chinadaily.com.cn/opinion/2017-03/27/content_28686754.htm. 28 See the article from Xinhua News Agency of China at http://news.xinhuanet.com/politics/2016-02/28/c_128758428.htm. 29 The ticket price of some HSR lines was reduced by at most 5% after the speed reduction: http://news.xinhuanet.com/politics/2016-02/28/c_128758428.htm. 30 This is similar to Ito and Lee (2005) who find that the impact of “9-11” on the US air travel demand consists of: i) a negative “transitory” shock (over 30%); and ii) an “ongoing” negative demand shock. The latter is due to the increased security measures. In particular, the stringent new security requirements that were implemented as a direct result of the September 11th terrorist attacks have made pre-departure procedures more cumbersome and time-consuming, an effect often referred to as the “hassle factor.” Ito and Lee (2005) are able to empirically detect this hassle factor. 50 3.4 Analytical Model 3.4.1 Demand side Suppose that a representative passenger maximizes the following net utility from travelling by airlines and HSR: 31 Max{𝑞𝐴,𝑞𝐻}𝑈 (𝑞𝐴, 𝑞𝐻) − ?̅?𝐴𝑞𝐴 − ?̅?𝐻𝑞𝐻 (3.1) where 𝑈(𝑞𝐴, 𝑞𝐻) is the gross utility of travel in the sense that it excludes the generalized travel costs, which consist of out-of-pocket money, time-related and safety-related costs involved in travel. ?̅?𝑖 and 𝑞𝑖 represent the generalized travel costs and the quantity of travel mode 𝑖, with 𝑖 =𝐴 or 𝐻 standing for airlines or HSR, respectively. The generalized travel costs perceived by travelers are: ?̅?𝐴 = 𝑃𝐴 (3.2.1) ?̅?𝐻 = 𝑃𝐻 + 𝒯(𝑠𝐻(?̅?𝐻)) + 𝒮(?̅?𝐻) (3.2.2) where 𝑃𝑖 is the ticket price of transport mode 𝑖, ?̅?𝐻 is the maximum HSR operating speed, and 𝑠𝐻 is the average HSR operating speed. 𝒯 and 𝒮 capture, respectively, the travel-time effect and safety effect of HSR speed, measured in monetary term. The travel time that passengers experience is a factor of the average HSR speed, which depends on the maximum HSR speed, the number of stops on the HSR line, the percentage of the line on which the maximum speed can be achieved, as well as weather conditions (Givoni and Banister, 2012).32 In this analysis, we assume that average speed 𝑠𝐻 is a monotonically increasing function of maximum speed ?̅?𝐻 and treat the other factors as given. This could be a reasonable assumption, because in general higher average speed is usually 31 We assume the representative passenger to represent the average travel utility of possibly different types of passengers in response to the travel modes’ characteristics. 32 Since the function 𝒯(𝑠𝐻(?̅?𝐻)) is quite general, it can capture the access/egress travel time effect (which is treated as constant), besides the in-vehicle travel time in our analysis. 51 achieved on HSR lines with higher maximum operating speed. On the other hand, passengers may perceive HSR with a higher maximum speed as less safe, because faster speed is usually associated with higher risk of an accident and casualties.33 The function 𝒮(?̅?𝐻) may not be linear in the sense that when speed is low, an increase of HSR speed limit may not raise much safety concern, while when speed is fast (e.g., 300 km/hr or above), an increase of maximum HSR speed may raise sufficient safety concern. Therefore, a HSR with faster speed limit enhances the total travel time advantage of HSR relative to air transport but may cause disutility due to the perceived safety concern. Hence, 𝜕𝒯 𝜕?̅?𝐻⁄ < 0 34 and 𝜕𝒮 𝜕?̅?𝐻⁄ > 0. We obtain the inverse demand function of travel mode 𝑖 by solving Eq. (3.1): 𝑃𝐴 = 𝜌𝐴(𝑞𝐴, 𝑞𝐻) (3.3.1) 𝑃𝐻 = 𝜌𝐻(𝑞𝐴, 𝑞𝐻) − 𝒯(𝑠𝐻(?̅?𝐻)) − 𝒮(?̅?𝐻) (3.3.2) where 𝜌𝑖(𝑞𝐴, 𝑞𝐻) =𝜕𝑈(𝑞𝐴,𝑞𝐻)𝜕𝑞𝑖, which stands for the marginal utility with respect to 𝑞𝑖. Differentiating Eq. (3.3.1) and Eq. (3.3.2) with respect to ?̅?𝐻 and solving for the partial derivatives of demand with respect to ?̅?𝐻 yield Eq. (3.4.1) and Eq. (3.4.2) 35: 𝜕𝑞𝐴𝜕?̅?𝐻= −(𝜕𝒯𝜕?̅?𝐻⏞<0+𝜕𝒮𝜕?̅?𝐻⏞>0)𝜕𝜌𝐴𝜕𝑞𝐻⏞<0𝜕𝜌𝐻𝜕𝑞𝐻𝜕𝜌𝐴𝜕𝑞𝐴−𝜕𝜌𝐻𝜕𝑞𝐴𝜕𝜌𝐴𝜕𝑞𝐻⏟ >0 (3.4.1) 33 We assume safety effect is a function of maximum HSR speed instead of average HSR speed, because passengers may not have full information of the average operating speed, but are fully aware of the maximum speed. 34 𝜕𝒯𝜕?̅?𝐻=𝜕𝒯𝜕𝑠𝐻⏟<0𝜕𝑠𝐻𝜕?̅?𝐻⏟>0< 0. 35 The HSR speed effect in our analysis refers to the effect of HSR maximum speed, corresponding to the natural experiment in China, where the speed limit was adjusted. However, for the sake of brevity, we use the phrase “HSR speed effect” instead of “HSR maximum speed effect” in the following analysis. 52 𝜕𝑞𝐻𝜕?̅?𝐻=(𝜕𝒯𝜕?̅?𝐻⏞<0+𝜕𝒮𝜕?̅?𝐻⏞>0)𝜕𝜌𝐴𝜕𝑞𝐴⏞<0𝜕𝜌𝐻𝜕𝑞𝐻𝜕𝜌𝐴𝜕𝑞𝐴−𝜕𝜌𝐻𝜕𝑞𝐴𝜕𝜌𝐴𝜕𝑞𝐻⏟ >0 (3.4.2) Assuming 𝑈 to be strictly concave in (𝑞𝐴, 𝑞𝐻), we have two properties: (i). definiteness 𝜕𝜌𝐻𝜕𝑞𝐻𝜕𝜌𝐴𝜕𝑞𝐴−𝜕𝜌𝐻𝜕𝑞𝐴𝜕𝜌𝐴𝜕𝑞𝐻> 0; and (ii). slutsky symmetry 𝜕𝜌𝐻𝜕𝑞𝐴=𝜕𝜌𝐴𝜕𝑞𝐻 (Dixit, 1986). Given the diminishing marginal utility of travel, suggested by a downward sloping demand curve, we have 𝜕𝜌𝐴𝜕𝑞𝐻< 0 and 𝜕𝜌𝐴𝜕𝑞𝐴< 0. Therefore, when travel-time effect dominates safety effect (𝜕𝒯 𝜕?̅?𝐻⁄ + 𝜕𝒮 𝜕?̅?𝐻⁄ < 0), we have 𝜕𝑞𝐴𝜕𝑠𝐻< 0 and 𝜕𝑞𝐻𝜕𝑠𝐻> 0, while when safety effect dominates (𝜕𝒯 𝜕𝑠?̅?⁄ + 𝜕𝒮 𝜕?̅?𝐻⁄ > 0), 𝜕𝑞𝐴𝜕𝑠𝐻> 0 and 𝜕𝑞𝐻𝜕𝑠𝐻< 0. Thus, an increasing HSR speed can increase or decrease HSR/airline demand, depending on which effect (travel-time vs. safety) dominates. By assuming symmetry (𝜕𝜌𝐻𝜕𝑞𝐻=𝜕𝜌𝐴𝜕𝑞𝐴) and from the two properties (definiteness and Slutsky symmetry), we have |𝜕𝜌𝐴𝜕𝑞𝐴| > |𝜕𝜌𝐴𝜕𝑞𝐻|. Comparing Eq. (3.4.1) and Eq. (3.4.2), we obtain |𝜕𝑞𝐻𝜕?̅?𝐻| > |𝜕𝑞𝐴𝜕?̅?𝐻|. Thus, HSR speed has a larger impact on HSR demand than on airline demand. As discussed in Section 3.3 since HSR price is fixed in China36, we can derive the partial derivative of airline price to ?̅?𝐻 in Eq. (3.5) by taking 𝑃𝐻 as given. The effect of HSR speed on airline price again depends on the sign of 𝜕𝒯 𝜕?̅?𝐻⁄ + 𝜕𝒮 𝜕?̅?𝐻⁄ as: 𝜕𝑃𝐴𝜕?̅?𝐻=𝜕𝜌𝐴𝜕𝑞𝐻⏞<0𝜕𝜌𝐻𝜕𝑞𝐻⏟<0 (𝜕𝒯𝜕?̅?𝐻⏞<0+𝜕𝒮𝜕?̅?𝐻⏞>0) (3.5) 36 Assuming fixed HSR price is not a strong assumption. Besides China, HSR price in several regions is largely fixed and does not vary as much as airfares. For example, in Japan, the price on Tokaido line is fixed, despite of only a JPY200 discount during off-peak season. In Taiwan, HSR operator offers only a limited quantity of early bird discount, but when the early bird tickets are sold out, regular and fixed fares apply. In South Korea, the HSR prices from Seoul to Daegu, Daejeon and Busan are fixed. 53 It should be noted that the demand and price here are not the equilibrium resulting from market competition outcome. After taking into account the supply side in the next subsection, we will show that the same result holds for the equilibrium traffic and price. 3.4.2 Supply side Airlines are assumed to be symmetric in cost structure and provide homogenous air service. We assume that N airlines engage in Cournot competition.37 However, since HSR price is assumed to be fixed regardless of speed change, it is impossible to explicitly model the competition between airlines and HSR, as well as the cost structure of HSR through speed variation.38 The HSR speed effect on airlines is thus only through the demand side. This analysis thus should be better interpreted as partial equilibrium, without fully accounting for possible strategic behavior of the HSR operator. We write the inverse airline demand function as 𝑃𝐴(𝑞𝐴, ?̅?𝐻) . A single airline maximizes the profit with respect to its own quantity qjA. 39 Max𝑞𝑗𝐴 𝜋𝑗𝐴 = (𝑃𝐴(𝑞𝐴, ?̅?𝐻) − 𝑐) 𝑞𝑗𝐴 (3.6) where 𝑞𝐴 = ∑ 𝑞𝑗𝐴𝑁𝑗=1 is the total air traffic, and c is the airline’s common constant marginal cost. The first-order condition (FOC) of Eq. (3.6) with respect to 𝑞𝑗𝐴 gives: 37 Empirical evidence suggests that rivalry between oligopoly airlines may be consistent with Cournot behavior (e.g., Brander and Zhang, 1990, 1993; Oum et al., 1993; Lijesen and Behrens, 2017). In addition, Cournot behavior among airlines has been assumed in theoretical studies in airline alliance (e.g., Park, 1997; Brueckner, 2001; Zhang and Zhang, 2006a; Bilotkach, 2007; Brueckner and Proost, 2010), airport congestion pricing (e.g., Zhang and Zhang, 2006b; Basso and Zhang, 2007; Basso, 2008; Zhang and Zhang, 2010) and airline-HSR cooperation (Xia and Zhang, 2016). 38 Empirical evidence also confirms the positive relation between HSR speed and operating cost, since maintaining higher speed requires more energy consumption (Kemp, 2004; Andersson and Lukaszewicz, 2006; Álvarez, 2010; Bosquet et al., 2013; D’Alfonso et al., 2016). However, we abstract away the potential mechanism that the HSR operating cost changes due to speed variation, which could be reflected on HSR price through its strategic interaction with airlines. 39 We also examined more general cases other than Cournot competition. We define ∂q−jA∂qjA =(N − 1)∂qhA∂qjA , with the conjectural variation δ=∂qhA∂qjA∈ [0,1] (h≠j ), as in Brander and Zhang (1990; 1993) and Oum et al. (1995). The values of 0 and 1 for 𝛿 represent the Cournot and cartel airline competition, respectively. The larger the 𝛿, the more collusion or less competition among the airlines. The result with a positive δ gives similar results, indicating that our analysis is not constrained to Cournot competition among airlines. The detailed derivations and results are available upon request from the authors. 54 (𝑃𝐴 − 𝑐) + 𝑞𝑗𝐴 𝜕𝑃𝐴𝜕𝑞𝐴= 0 (3.7) By imposing symmetry and totally differentiating FOC with respect to ?̅?𝐻, we can obtain how the equilibrium airline traffic 𝑞𝐴∗ changes with ?̅?𝐻: 𝑑𝑞𝐴∗𝑑?̅?𝐻= −𝜕𝑃𝐴𝜕?̅?𝐻+𝑞𝐴N𝜕2𝑃𝐴𝜕𝑞𝐴𝜕?̅?𝐻(1 +1N)𝜕𝑃𝐴𝜕𝑞𝐴+𝑞𝐴N𝜕2𝑃𝐴𝜕𝑞𝐴2⏟ <0 (3.8) In case of linear demand, 𝜕2𝑃𝐴𝜕𝑞𝐴𝜕?̅?𝐻= 0 . In case of non-linear demand, if 𝜕2𝑃𝐴𝜕𝑞𝐴𝜕?̅?𝐻 is small in magnitude, the sign of 𝑑𝑞𝐴∗𝑑?̅?𝐻 follows the sign of 𝜕𝑃𝐴𝜕?̅?𝐻 (Eq. (3.5)). As a result, 𝜕𝑞𝐴∗𝜕𝑠𝐻< (>)0 if 𝜕𝒯 𝜕?̅?𝐻⁄ + 𝜕𝒮 𝜕?̅?𝐻⁄ < (>)0. Therefore, the equilibrium airline demand decreases (increases) with HSR speed when travel-time (safety) effect is dominant. Next, we write the airline demand function as 𝑞𝐴(𝑃𝐴, ?̅?𝐻) . Rearranging the FOC and totally differentiating it with respect to ?̅?𝐻, we obtain how the equilibrium airline price 𝑃𝐴∗ changes with ?̅?𝐻: 𝑑𝑃𝐴∗𝑑?̅?𝐻= −1𝑁𝜕𝑞𝐴𝜕?̅?𝐻+ (𝑃𝐴 − 𝑐)𝜕2𝑞𝐴𝜕𝑃𝐴𝜕?̅?𝐻(1 +1𝑁)𝜕𝑞𝐴𝜕𝑃𝐴+ (𝑃𝐴 − 𝑐)𝜕2𝑞𝐴𝜕𝑃𝐴2⏟ <0 (3.9) Similar as the discussion for Eq. (3.8), in case of linear demand, 𝜕2𝑞𝐴𝜕𝑃𝐴𝜕?̅?𝐻= 0; or in case of non-linear demand, if 𝜕2𝑞𝐴𝜕𝑃𝐴𝜕?̅?𝐻 is small in magnitude, the sign of 𝜕𝑃𝐴∗𝜕?̅?𝐻 follows the sign of 𝜕𝑞𝐴𝜕?̅?𝐻 (Eq. (3.4.1)). As a result, 𝜕𝑃𝐴∗𝜕?̅?𝐻< (>)0 if 𝜕𝒯 𝜕?̅?𝐻⁄ + 𝜕𝒮 𝜕?̅?𝐻⁄ < (>)0. Therefore, the equilibrium airline price decreases (increases) with HSR speed when travel-time (safety) effect is dominant. We summarize the above discussion in Proposition 3.1, and the detailed proof is relegated to Appendix B1. 55 Proposition 3.1: When HSR travel-time effect dominates the safety effect, i.e., 𝜕𝒯 𝜕?̅?𝐻⁄ +𝜕𝒮 𝜕?̅?𝐻⁄ < 0, airline traffic and price decrease with HSR speed; while when the safety effect dominates travel-time effect, i.e., 𝜕𝒯 𝜕?̅?𝐻⁄ + 𝜕𝒮 𝜕?̅?𝐻⁄ > 0, airline traffic and price increase with HSR speed. Although Proposition 3.1 is intuitive, the analysis incorporates the trade-off between the travel-time and safety effects, contrary to the existing analytical literature that only examines the HSR travel-time effect on airlines (e.g., Yang and Zhang, 2012; D’Alfonso et al., 2015; Talebian and Zou, 2016; Xia and Zhang, 2016, 2017). As discussed earlier, this consideration is especially important in emerging HSR markets, such as China, where HSR technology is just being introduced and fast developed before maturity. In order to investigate how the air-HSR substitutability can alter the HSR speed effect on airline traffic and price, we introduce a quadratic utility function as in Singh and Vives (1984) and Vives (1999, Chapter 6) 40: 𝑈(𝑞𝐴, 𝑞𝐻) = 𝛼𝐴𝑞𝐴 + 𝛼𝐻𝑞𝐻 − (12𝛽𝐴(𝑞𝐴)2 +12𝛽𝐴(𝑞𝐻)2 + 𝛾𝑞𝐴𝑞𝐻) (3.10) This approach has been widely used in transport literature (e.g., Fu et al., 2006; Flores-Fillol and Moner-Colonques, 2007; Oum and Fu, 2007; Clark et al., 2009, 2011; Socorro and Betancor, 2010; Socorro and Viecens, 2013; Jiang and Zhang, 2014; D’Alfonso et al., 2015, 2016; Talebian and Zou, 2016). However, our model has several distinctions. First, we consider an industry with two sectors (air sector and rail sector) producing differentiated goods, and the air sector consists of multiple firms producing homogeneous goods, while the above studies mainly consider a duopolistic industry with two firms. Second, we introduce both horizontal and vertical differentiation in the sense that consumers have heterogeneous preference over air and rail services ceteris paribus, but they uniformly prefer the safer and faster transport mode given the same price. We thus analyze the interactions between vertical and horizontal differentiation in the context of 40 Singh and Vives (1984) focus on the duality of price and quantity competition in a differentiated duopoly, and analyze the dominant strategy for each firm given the substitutability (complementarity) of products. Vives (1999, Chapter 6) considers both quantity and price competition, and focuses on the existence and uniqueness of quantity and price equilibria, as well as characterizes and compares those equilibria. 56 air-HSR competition, which has not been examined before. Third, the safety effect of HSR speed has yet been explicitly modeled in the existing analytical studies. 𝛼𝐴 and 𝛼𝐻 in Eq. (3.10) measure the potential market size for airlines and HSR, respectively. 𝛾 ∈[0,1] measures the air-HSR substitutability. A small value of 𝛾 implies that airline and HSR are less substitutable, while a large value of 𝛾 suggests that HSR and airlines services are more homogenous and substitutable. As discussed earlier, we expect that airlines and HSR are more substitutable on short-haul routes. Substitutability 𝛾 captures horizontal differentiation, while 𝒯(𝑠𝐻(?̅?𝐻)) and 𝒮(?̅?𝐻) indicate vertical differentiation (i.e., quality offered by HSR due to speed variation). Our model thus introduces the interaction of both service substitutability and quality. For simplicity, we assume 𝛽𝐴 = 𝛽𝐻 = 1 (i.e., price sensitivities of demands is 1). However, this assumption is without loss of generality, because all the results hold when 𝛽𝐴𝛽𝐻 −𝛾2 > 0, which is true due to the definitiveness of the quadratic utility function (Dixit 1986). The travel demand with the quadratic utility is derived as follows: 𝑞𝐴 =𝛼𝐴 − 𝑃𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) 1 − 𝛾2 (3.11.1) 𝑞𝐻 =𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮) − 𝛾(𝛼𝐴 − 𝑃𝐴)1 − 𝛾2 (3.11.2) Before taking into account the supply side of airline competition, the elasticity of airline demand 𝑞𝐴 with respect to ?̅?𝐻 (conditional on the price which may not be the equilibrium) is derived in Eq. (3.12). Thus, the sign of εqA,?̅?𝐻 still depends on the relative dominance of the travel-time and safety effect of HSR speed change, i.e., 𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻. 𝜀𝑞𝐴,?̅?𝐻 =𝜕𝑞𝐴𝜕?̅?𝐻?̅?𝐻𝑞𝐴=𝛾 ?̅?𝐻(𝜕𝒯𝜕?̅?𝐻⏞<0+𝜕𝒮𝜕?̅?𝐻⏞>0)𝛼𝐴 − 𝑃𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮))⏟ >0 (3.12) With the quadratic utility function, the equilibrium individual airline traffic 𝑞𝑖,𝐴∗ , the equilibrium total airline traffic 𝑞𝐴∗ , and the equilibrium airline price 𝑃𝐴∗ are derived as follows: 57 𝑞𝑖,𝐴∗ =𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐(1 − 𝛾2)(1 + 𝑁) (3.13.1) 𝑞𝐴∗ = 𝑁𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐(1 − 𝛾2)(1 + 𝑁) (3.13.2) 𝑃𝐴∗ =𝑁𝑐 + 𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮))1 + 𝑁 (3.13.3) We next investigate how equilibrium airline traffic 𝑞𝑖,𝐴∗ and price 𝑃𝐴∗ change with HSR speed ?̅?𝐻. 𝑑𝑞𝑖,𝐴∗𝑑?̅?𝐻=𝛾(𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻)(1 − 𝛾2)(1 + 𝑁) (3.14.1) 𝑑𝑞𝐴∗𝑑?̅?𝐻=𝑁𝛾(𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻)(1 − 𝛾2)(1 + 𝑁) (3.14.2) 𝑑𝑃𝐴∗𝑑?̅?𝐻=𝛾(𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻)1 + 𝑁 (3.14.3) Consistent with the discussion of Eq. (3.8) and (3.9), the signs of Eq. (3.14.1) - (3.14.3) depend on the relative dominance of travel-time and safety effect, i.e., 𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻. We can obtain the elasticity of equilibrium airline traffic with respect to ?̅?𝐻 and the elasticity of equilibrium airline price with respect to ?̅?𝐻 in Eq. (3.15.1) and Eq. (3.15.2), respectively: 𝜀𝑞𝐴∗ ,?̅?𝐻 = 𝜀𝑞𝑖,𝐴∗ ,?̅?𝐻 =𝑑𝑞𝐴∗𝑑?̅?𝐻?̅?𝐻𝑞𝐴∗ =?̅?𝐻𝛾(𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻)𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐⏟ >0 (3.15.1) 𝜀𝑃𝐴∗ ,?̅?𝐻 =𝑑𝑃𝐴∗𝑑?̅?𝐻?̅?𝐻𝑃𝐴∗ =?̅?𝐻𝛾(𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻)𝑁𝑐 + 𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮))⏟ >0 (3.15.2) 58 Comparing the magnitudes of elasticities with respect to HSR speed, we obtain Eq. (3.16), which indicates that HSR speed change has a larger effect on airline traffic than on airline price. We thus have Proposition 3.2. |𝜀𝑞𝐴∗ ,?̅?𝐻| − |𝜀𝑃𝐴∗ ,?̅?𝐻|=𝑐?̅?𝐻𝛾(1 + 𝑁) |𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻|(𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐)(𝑁𝑐 + 𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)))> 0 (3.16) Proposition 3.2: With quadratic utility function, the magnitude of elasticity of airline traffic with respect to HSR speed is larger than that of airline price, i.e., |𝜀𝑞𝐴∗ ,?̅?𝐻| > |𝜀𝑃𝐴∗ ,?̅?𝐻|. As shown in Appendix B2, Proposition 3.2 can be proved without imposing specific functional forms. The result is driven by Cournot competition and the assumption that the sensitivity of price to demand is not a function of HSR speed (i.e., ∂(∂𝑃𝐴 ∂𝑞𝐴⁄ )∂?̅?𝐻= 0). We have empirically verified Proposition 3.2 in Section 3.6. We next examine how the substitutability of airlines and HSR moderate the HSR speed effect on airlines. Taking derivative of Eq. (3.12) with respect to 𝛾, we obtain Eq. (3.17): 𝜕|𝜀𝑞𝐴,?̅?𝐻|𝜕𝛾=?̅?𝐻(𝛼𝐴 − 𝑃𝐴) |𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻|(𝛼𝐴 − 𝑃𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)))2 > 0 (3.17) The positive sign indicates that the air-HSR substitutability measured by 𝛾 reinforces the HSR speed effect (vertical differentiation) on airlines, no matter which quality effect (travel-time or safety) is dominant. In addition, we obtain how the elasticity of equilibrium airline traffic/price changes with 𝛾: 𝜕|𝜀𝑞𝐴∗ ,?̅?𝐻|𝜕𝛾=?̅?𝐻(𝛼𝐴 − 𝑐) |𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻|(𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐)2> 0 (3.18.1) 59 𝜕|𝜀𝑃𝐴∗ ,?̅?𝐻|𝜕𝛾=?̅?𝐻(𝑐𝑁 + 𝛼𝐴) |𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻|(𝑁𝑐 + 𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)))2> 0 (3.18.2) It can also be shown that 𝜕|𝜀𝑞𝐴∗ ,?̅?𝐻|𝜕𝛾−𝜕|𝜀𝑃𝐴∗ ,?̅?𝐻|𝜕𝛾> 0 in Appendix B3. Combining with Eq. (3.17), Eq. (3.18.1) and Eq. (3.18.2), we have Proposition 3.3. Proposition 3.3: With quadratic utility function, the magnitude of the elasticities of airline traffic and price with respect to HSR speed increases with air-HSR substitutability 𝛾. 𝛾 has larger impact on the elasticity of airline traffic with respect to HSR speed than on the elasticity of airline price with respect to HSR speed. Lastly, we examine how the number of airlines moderates the HSR speed effect. The comparative statics of the equilibrium results with respect to the inter-airlines competition, measured by the number of airlines 𝑁, are given in Eq. (3.19.1)-Eq. (3.19.3): 𝜕𝑞𝑖,𝐴∗𝜕𝑁= −𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐(1 − 𝛾2)(1 + 𝑁)2< 0 (3.19.1) 𝜕𝑞𝐴∗𝜕𝑁=𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐(1 − 𝛾2)(1 + 𝑁)2> 0 (3.19.2) 𝜕𝑃𝐴∗𝜕𝑁= −𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐(1 + 𝑁)2< 0 (3.19.3) Eq. (3.19.1)-Eq. (3.19.3) show that the equilibrium total airline traffic increases with the number of competing airlines 𝑁, but the equilibrium airline price and equilibrium individual airline traffic decrease with 𝑁. By taking derivative of 𝜀𝑃𝐴∗ ,?̅?𝐻 with respect to 𝑁, we obtain Eq. (3.20), which can be directly signed. As from Eq. (3.15.1), 𝜀𝑞𝐴∗ ,?̅?𝐻 is not a function of 𝑁. Proposition 3.4 is reached. 𝜕|𝜀𝑃𝐴∗ ,?̅?𝐻|𝜕𝑁=−𝑐?̅?𝐻𝛾 |𝜕𝒯𝜕?̅?𝐻+𝜕𝒮𝜕?̅?𝐻|(𝑁𝑐 + 𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)))2< 0 (3.20) 60 Proposition 3.4. With quadratic utility function, the elasticity of airline price with respect to HSR speed decreases with the level of inter-airlines competition measured by the number of competing airlines 𝑁. Proposition 3.4 suggests that the HSR speed effect on equilibrium airline price can be negatively moderated by the inter-airlines competition. However, the elasticity of equilibrium airline traffic to HSR speed, 𝜀𝑞𝐴∗ ,?̅?𝐻, is not a function of 𝑁. Thus, the inter-airlines competition does not affect 𝜀𝑞𝐴∗ ,?̅?𝐻. It should also be cautioned that in the above discussion we assume the number of airlines N is exogenous to the HSR speed change. This might be true when the HSR speed variation is small, thus not triggering airlines’ entry and exit. To endogenize the number of airlines and the degree of collusion, more sophisticated airline entry model is called for. 3.5 Empirical Methodology and Data In this section, we empirically quantify the HSR speed effect on airlines and verify our analytical findings through the natural experiment of HSR speed reduction in China. A DID method is adopted to compare airline market outcomes between the treated and control groups, both before and after the HSR speed reduction. The treated group consists of the airline routes with the presence of HSR. The control group consists of the airline routes without HSR presence. The speed effect is detected by the exogenous HSR speed reduction and the resultant variation in HSR competition effect on airlines. The analytical model derives the impact of air-HSR service substitutability on HSR speed effect (Proposition 3.3). We thus specify the airline traffic and price equations in Eq. (3.21), which is in a log-linear form that allows nonlinear airline traffic and price functions, while guaranteeing easy identification of elasticities of airline traffic and price with respect to HSR speed (e.g., Borenstein, 61 1989; Schipper et al., 2002). The subscript 𝑖 represents the route, and 𝑡 represents the quarter and the year of the observation. ln𝑞𝑖𝑡∗ = 𝛼0 + 𝛼1 × 𝑓(𝑠𝑖𝑡) × 𝐻𝑆𝑅𝑖𝑡 + 𝛼21𝑃𝑜𝑠𝑡_𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡𝑖𝑡× 𝐻𝑆𝑅𝑖𝑡 + 𝛼3ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i+ 𝛼4ln𝐻𝐻𝐼𝑖𝑡 + 𝛼5ln𝑃𝑜𝑝𝑖𝑡 + 𝛼6ln𝐼𝑛𝑐𝑜𝑚𝑒𝑖𝑡 + 𝛼7 𝐿𝐶𝐶𝑖𝑡+ 𝛼8𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖𝑡 + 𝛼9𝑆𝑝𝑟𝑖𝑛𝑔𝑡 + 𝛼10𝑆𝑢𝑚𝑚𝑒𝑟𝑡 + 𝛼11𝐴𝑢𝑡𝑢𝑚𝑛𝑡 + 𝛼12𝑌𝑒𝑎𝑟𝑡+ 𝛼13𝐻𝑆𝑅𝑖𝑡 + 𝜓𝑖 + 𝜉𝑖𝑡 ln𝑃𝑖𝑡∗ = 𝛽0 + 𝛽1 × 𝑓(𝑠𝑖𝑡) × 𝐻𝑆𝑅𝑖𝑡 + 𝛽21𝑃𝑜𝑠𝑡_𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡𝑖𝑡×𝐻𝑆𝑅𝑖𝑡 + 𝛽3ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟𝑖 + 𝛽4ln𝐻𝐻𝐼it+ 𝛽5ln𝑃𝑜𝑝𝑖𝑡 + 𝛽6ln𝐼𝑛𝑐𝑜𝑚𝑒𝑖𝑡 + 𝛽7𝐿𝐶𝐶𝑖𝑡 + 𝛽8𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖𝑡 + 𝛽9𝑆𝑝𝑟𝑖𝑛𝑔𝑡+ 𝛽10𝑆𝑢𝑚𝑚𝑒𝑟𝑡 + 𝛽11𝐴𝑢𝑡𝑢𝑚𝑛𝑡 + 𝛽12𝑌𝑒𝑎𝑟𝑡 + 𝛽13𝐻𝑆𝑅𝑖𝑡 + 𝜏𝑖 + 𝜈𝑖𝑡 (3.21) where • 𝑞𝑖𝑡∗ is the number of airline passengers on route 𝑖 at time 𝑡; • 𝑃𝑖𝑡∗ is the average airline yield on route 𝑖 at time 𝑡; • HSRit is a dummy variable equaling to one if HSR is present on route 𝑖 at time 𝑡; • sit is HSR speed on route 𝑖 at time 𝑡; • Post_Accidentit is the number of quarters after the 7.23 rear-ending accident; • Dist_Airi is the flying distance of route 𝑖; • Popit is the geometric average population of the endpoint cities of route 𝑖 at time 𝑡; • Incomeit is the geometric average income per capita of the endpoint cities of route 𝑖 at time 𝑡; • Tourismi is the dummy variable to indicate the tourism status of route 𝑖; • Springt, Summert, and Autumnt are the quarter dummy variables; • HHIit is the Herfindahl-Hirschman index, which captures the inter-airlines competition, on route 𝑖 at time 𝑡; • LCCit is the dummy variable which indicates low-cost carrier (LCC) presence on route 𝑖 at time 𝑡; • Yeart is the yearly dummy variable. 62 To capture the HSR speed effect on airlines, we introduce a term 𝑓(𝑠𝑖𝑡) × 𝐻𝑆𝑅𝑖𝑡, where 𝑓(𝑠𝑖𝑡) is a function of the HSR speed 𝑠𝑖𝑡, and 𝐻𝑆𝑅𝑖𝑡 is a dummy variable of HSR presence on this route. The interaction term 𝑓(𝑠𝑖𝑡) × 𝐻𝑆𝑅𝑖𝑡 measures HSR speed effect on airline traffic and price. HSR speed reduction led to variation in HSR speed, resulting in variation in air-HSR competition intensity on the treated routes. This is reflected in the term 𝑓(𝑠𝑖𝑡) × 𝐻𝑆𝑅𝑖𝑡, enabling us to identify the HSR speed effect. For 𝑓(𝑠𝑖𝑡), we have tried alternative functional forms: 𝑠𝑖𝑡, 𝑠𝑖𝑡2, √𝑠𝑖𝑡. Since the control group is not subject to HSR competition, the route-specific fixed effect is controlled for possible heterogenous characteristics between the treated and control routes. The fixed effect of the treated routes is controlled by the dummy variable HSRit. The DID method is applied to compare the differences in airline traffic and price between the control and the treated airline routes before and after the HSR speed reduction. The fixed effect also controls other time-invariant variables on the route-level. The route distance is thus controlled by the route fixed effect, such that the HSR travel time variation due to the speed reduction is captured through the change in HSR speed variable 𝑓(𝑠𝑖𝑡). It is also noted that, in the empirical model, we are able to disentangle the speed effect from the travel-time and safety sides because these two effects are confounding. Therefore, the estimation on the HSR speed variation should be interpreted as the “net HSR speed effect”, which depends on the relative dominance of the travel time and safety effects suggested by the analytical model. With the above specification, elasticities of airline traffic and price with respect to HSR speed can be calculated as follows. Table 3.1 summarizes the expressions of the elasticities with alternative functional forms of 𝑓(𝑠𝑖𝑡). 𝜀𝑞𝐴∗ ,𝑠𝐻 =∂ln𝑞𝑖𝑡∗∂lnsit =∂ln𝑞𝑖𝑡∗∂sit ×sit=α1×𝑓′(sit)×sit 𝜀𝑝𝐴∗ ,𝑠𝐻 =∂ln𝑝𝑖𝑡∗∂lnsit =∂ln𝑝𝑖𝑡∗∂sit ×sit=𝛽1×𝑓′(sit)×sit (3.22) 63 Table 3.1 Expressions of elasticities to HSR speed with assumed forms of 𝒇(𝒔𝒊𝒕) 𝑓(𝑠𝑖𝑡) 𝑠𝑖𝑡 𝑠𝑖𝑡2 √𝑠𝑖𝑡 𝜀𝑞𝐴∗ ,𝑠𝐻 α1𝑠𝑖𝑡 2α1𝑠𝑖𝑡2 12α1√𝑠𝑖𝑡 𝜀𝑝𝐴∗ ,𝑠𝐻 𝛽1𝑠𝑖𝑡 2𝛽1𝑠𝑖𝑡2 12𝛽1√𝑠𝑖𝑡 In Eq. (3.21), we also include a term 1Post_accidentit× HSRit to capture passengers’ immediate but short-term panic of 7.23 rear-ending accident. Such short-term panic can shift travel demand from HSR to airlines. This suggests a positive 𝛼2 in the airline traffic volume equation, and positive 𝛽2 in airline price equation. We assume the panic effect is proportional to the reciprocal of the number of periods post the accident, similar to the approach by Ito and Lee (2005) which captures the panic after the 911 event.41 Other explanatory variables include the route flying distance, population, income, tourism, airline market HHI index, and LCC presence dummies. The error terms consist of a time-invariant route specific fixed effect 𝜓𝑖 and 𝜏𝑖, and white noise 𝜉𝑖𝑡 and 𝜈𝑖𝑡. Fixed-effect model is used to control potential correlation between these time-invariant error terms and the explanatory variables. The Eq. (3.21) are in reduced-form as we express the airline traffic and price by all the exogenous variables from airline demand and supply (airlines competition) side. This is to measure the HSR speed effect on the market equilibrium airline traffic and price. In addition, we can specify the airline demand and price equations in the structural approach, where airline demand is a function of price and airline price is a function of airline demand. The system equations of airline demand and price and the estimation results will be discussed in Appendix B4. We collect route-level airline price and traffic data for China’s Big Three full service carriers namely, Air China, China Eastern, and China Southern Airlines, from January 2010 to June 30, 41 For example, within the first period post the accident, the percentage change on the airline yield is calculated as e𝛽2 − 1. Let us assume the airline yield is P1 when Post_accidentit = 1, and the airline yield is P0 without the accident. Thus P1−P0P0=P1P0− 1 = e𝛽2 − 1. Similarly, in the n-th period post the accident, the percentage change on airline yield is e𝛽2/𝑛 − 1, and this term converges to zero when n is increasing. 64 2013, a total of 14 quarters. These three airlines are the largest in China, and dominate market with more than 80% of total domestic traffic (Zhang et al., 2014). The sample period covers observations prior to and post the HSR speed reduction occurred on July 1, 2011 and August 28, 2011, as well as the 7.23 rear-ending accident on July 23, 2011. A total of 74 routes are included in our sample, including the ones linking Beijing, Shanghai and Guangzhou to all the provincial capital cities in China, except Lhasa.42 Among the 74 airline routes, HSR is present on 9 routes that all experienced the HSR speed reduction in Quarter 3 of 2011. The description of these 9 routes can be found in Table 3.2. The 9 routes compose our treated group, with the other 65 routes as control group. As these sample routes are the ones linking three Chinese airline hubs (Beijing, Guangzhou and Shanghai) with major Chinese cities, the controlled and treated routes have similar characteristics, such as passenger volume, route distance, airport size etc. 42 We exclude the origin-destination (OD) routes along the Beijing-Shanghai HSR line which opened on July 1st 2011, because this HSR line opened at the same time of the speed reduction. The maximum design speed of this line is 380 km/hr, but it only allows to operate at a maximum speed of 300 km/hr. Thus, there is no direct comparison of the outcomes before and after the HSR speed reduction for these routes, which make the route not suitable for the DID estimation. 65 Table 3.2 Summary of the treated routes before and after the HSR speed reduction Route HSR Route Distance (km) Date of speed reduction Speed before reduction Speed after reduction HSR in-Vehicle Travel Time (mins) HSR Total Travel Time (mins) Shanghai-Hefei 456 28-Aug, 2011 233 186 128 202 Beijing-Taiyuan 513 28-Aug,2011 250 200 152 242 Shanghai-Zhengzhou 651 28-Aug,2011 250 200 239 318 Guangzhou-Changsha 726 01-Jul,2011 350 300 137 225 Shanghai-Wuhan 826 28-Aug,2011 240 192 260 355 Shanghai-Fuzhou 883 28-Aug,2011 250 200 264 346 Guangzhou-Wuhan 995 01-Jul,2011 350 300 218 306 Shanghai-Xiamen 1109 28-Aug,2011 250 200 381 495 Guangzhou-Hefei 1427 01-Jul,2011 325 275 401 468 Notes: 1. The Shanghai-Hefei HSR line passes through Shanghai-Nanjing intercity railway segment (with design speed of 250 km/hr before the speed reduction) and Nanjing-Hefei passenger-railway segment (with design speed of 200 km/hr before the speed reduction). The HSR speed on the Shanghai-Hefei line is thus calculated by taking a weighted average based on distance of the two segments. The same applies to the lines of Shanghai-Wuhan and Guangzhou-Hefei. 2. The HSR total travel time adds the access and egress time between HSR stations and the city centers to the HSR in-vehicle time. 3.The HSR total travel time and in-vehicle time are the time after the HSR speed reduction. The HSR in-vehicle time before the HSR speed reduction was not available. Airfare data is obtained from the Chinese Airfare Information Network. Route distance is collected from Statistical Data on Civil Aviation of China (CAAC, 2014). Each city’s per capita income, population and GDP are collected from the city statistical yearbook. The list of the 25 most important tourism cities is released by Forbes China every year, using which we construct the tourism dummy variable. We define a route as a tourism route, if at least one of the endpoint airport city is one of the 25 most developed cities for tourism in mainland China, released by Forbes China every year. The data on the HSR speed, and route distance are obtained from two websites: www.12306.cn (the official online booking site for all trains in China) and www.gaotie.cn (the 66 website summarizing HSR information in China).43 Our airfare and passenger volume data are available on daily basis. Given most of our control variables, such as population, income and HHI, are only available at the quarterly basis, we aggregate the daily price and traffic data into the quarterly basis. The quarterly passenger volume is the aggregate of the daily data, and the quarterly average price is calculated by dividing the quarterly aggregate airline revenue by the quarterly passenger volume. 44 The analytical model suggests HSR speed effect varies with the intermodal substitutability. We thus divide the 9 treated routes (see Table 3.2) into two groups based on the HSR route distance: 5 short-haul routes (<850 km: Shanghai-Hefei, Beijing-Taiyuan, Shanghai-Zhengzhou, Guangzhou-Changsha), and 4 medium-to-long-haul routes (>850 km: Shanghai-Fuzhou, Guangzhou-Wuhan, Shanghai-Xiamen, Guangzhou-Hefei). Our estimations are run for the two subsamples separately. As suggested by Proposition 3.3, it is expected to observe stronger HSR speed effect on the short-haul routes (<850 km) as air-HSR services are more substitutable. In addition, we have tried to divide the treated routes based on total HSR travel time to differentiate the air-HSR service substitutability: 4 short-haul routes (< 5 hours: Shanghai-Hefei, Beijing-Taiyuan, Guangzhou-Changsha, Guangzhou-Wuhan) and 5 medium-to-long-haul routes (>5 hours: Shanghai-Zhengzhou, Shanghai-Wuhan, Shanghai-Fuzhou, Shanghai-Xiamen, Guangzhou-Hefei), the results of which are relegated to Table B1-B3 of Appendix B. Before formal estimation, we plot average quarterly airline traffic and yield for both treated and control group (see Figure 3.1). 45 The accident and HSR speed reduction occurred at the 7th quarter (the season 7) of the sample period. The figure clearly shows that our treated and control groups have a common time trend before HSR speed reduction, satisfying the DID requirement. As shown in Figure 3.1 (a), airline traffic increased significantly post HSR speed reduction on the treated 43 The two websites are in Chinese language. 44 When calculating the average ticket price and air traffic, we removed the observations of “first-class” and “business-class”, to focus on airline demand and price of the “economy class” observations. 45 The airline yield is calculated by dividing the airfare by the flying distance. The average yield of each route for the treated and control groups is calculated using each airline’s passenger volume as the weight on the route. 67 routes. 46 For airline price in Figure 3.1 (b), the HSR speed effect is much less obvious. But between the 9th and 14th quarter, airline yield on the treated routes seems less volatile and did not plummet as the control group did. This may indicate a positive effect of HSR speed reduction on airfare. In Figure 3.2, we further distinguish observations for the two subsamples of treated group: routes shorter, or longer than 850 km. The airline traffic on the routes shorter than 850 km increases more significantly than that on the routes longer than 850 km does. This may suggest stronger HSR speed effect on short-haul routes when airline and HSR services are more substitutable. For the airline yield, no clear change is observed post the speed reduction. 46 There is a drop of airline traffic for the control routes after Quarter 3 of 2011, which was when the speed reduction occurred. This traffic drop is purely due to the seasonal cycle of air travel demand in China. Quarter 3 of 2011, i.e. the summer season, is the peak air travel period in China, whereas the demand is much weaker in the following winter season, i.e., Quarter 4. Therefore, without the HSR speed reduction, the airline traffic in the control group routes dropped at Quarter 4. 68 Figure 3.1 Evolution of airline traffic and yield for the treated (HSR) and control (no HSR) routes (quarterly data from Quarter 1 of 2010 to Quarter 3 of 2013) (a). Airline traffic (b). Airline yield Note: the vertical lines represent the time of speed reduction. 80000900001000001100001200001300001400001500001600001700001 2 3 4 5 6 7 8 9 10 11 12 13 14Air TrafficSeasonControlTreated00.00020.00040.00060.00080.0010.00120.00141 2 3 4 5 6 7 8 9 10 11 12 13 14Yield (US dollar)SeasonTreatedControl69 Figure 3.2 Evolution of airline traffic and yield for treated routes shorter and longer than 850 km and control (no HSR) routes (quarterly data from Quarter 1 of 2010 to Quarter 3 of 2013) (a). Airline traffic (b). Airline yield Note: the vertical lines represent the time of speed reduction. 70 3.6 Empirical Results Estimation results of Eq. (3.21) are summarized in Table 3.3 and 3.4 with alternative functional forms of the HSR speed variable (𝑓(𝑠𝑖𝑡)= 𝑠𝑖𝑡, 𝑠𝑖𝑡2, √𝑠𝑖𝑡). The estimations are based on full treated sample, the treated routes shorter than 850 km and longer than >850 km. The HSR speed reduction overall has statistically significant and positive effect on airline traffic and price, suggested by the negative sign of 𝛼1 and 𝛽1. This also implies the travel-time effect dominates safety effect of HSR speed in China. In addition, HSR speed effect manifests on treated routes shorter than 850 km, while not identified on longer than 850 km treated routes. This empirical finding confirms our Proposition 3.3 that HSR speed effect is stronger on short-haul routes when airline and HSR services are more substitutable. Robustness tests have also been done using different distance thresholds to divide sample treated routes, for example, routes shorter or longer than 700 km, 950 km etc. The estimations are qualitatively consistent: the HSR speed effect is only statistically significant on short-haul treated group. In addition, we have tried estimation on subsample treated routes based on the HSR travel time to differentiate the air-HSR service substitutability (shorter vs. longer than 5-hour HSR travel time). The estimation results are collated in Table B1-B3 of Appendix B. It is noted that we obtained very similar estimation results as dividing the treated routes based on distance: the HSR speed effect is only statistically significant on the short-haul routes with total HSR travel time less than 5 hours. 71 Table 3.3 Estimation results for airline traffic equation with 𝒇(𝒔𝒊𝒕) = 𝒔𝒊𝒕, 𝒔𝒊𝒕𝟐 , or √𝒔𝒊𝒕 Airline Traffic All <850km >850km All <850km >850km All <850km >850km 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 𝛼1 -0.0035*** -0.0042*** 0.0100 -5.51× 10−6*** -6.42× 10−6*** -1.84× 10−5 -0.119*** -0.144*** -0.073** (0.001) (0.0008) (0.046) (-2.24× 10−7) (-1.67× 10−6) (7.99× 10−5) (0.039) (0.028) (0.0308) 𝛼2 1.159 1.245 1.227 1.098 1.238 1.216 1.179 1.247 1.219 (5.755) (3.439) (4.051) (5.746) (3.452) (4.058) (5.758) (3.437) (0.314) HHI -0.095** -0.090** -0.096** -0.092** -0.089** -0.1005** -0.096** -0.090** -0.102** (0.046) (0.044) (0.045) (0.047) (0.045) (0.045) (0.046) (0.044) (0.045) Population -1.035 -0.839 -0.254 -1.076 -0.939 -0.317 -0.997 -0.773 -0.360 (0.717) (0.662) (0.714) (0.722) (0.666) (0.709) (0.714) (0.661) (0.710) Income -0.285** -0.361*** -0.367*** -0.283 -0.370*** -0.331 -0.285*** -0.355*** -0.324** (0.136) (0.129) (0.130) (0.137) (0.130) (0.130) (0.136) (0.129) (0.130) LCC -0.027 -0.027 -0.027 -0.027 -0.027 -0.026 -0.027 -0.027 -0.026 (0.065) (0.064) (0.063) (0.065) (0.064) (0.063) (0.065) (0.063) (0.063) Tourism 0.007 0.026 0.061 0.006 0.013 0.087* 0.006 0.030 0.090 (0.050) (0.043) (0.046) (0.051) (0.043) (0.047) (0.050) (0.043) (0.047) Spring 0.717*** -0.240*** 0.687*** 0.719*** -0.243*** 0.698*** 0.716*** -0.237 -0.225*** (0.246) (0.044) (0.239) (0.246) (0.044) (0.238) (0.245) (0.044) (0.044) Summer 0.205 0.199 0.193 0.206 0.198 0.196 0.204 0.199 0.196 (0.165) (0.162) (0.161) (0.166) (0.163) (0.160) (0.165) (0.162) (0.160) Autumn 0.333** -0.610*** 0.319** 0.335** -0.612*** 0.322** 0.332** -0.608*** -0.602*** (0.168) (0.160) (0.163) (0.168) (0.161) (0.163) (0.168) (0.160) (0.158) Year2011 0.149*** 0.153*** 0.145*** 0.150*** 0.156*** 0.141*** 0.149*** 0.151*** 0.141*** (0.030) (0.029) (0.029) (0.030) (0.029) (0.029) (0.030) (0.029) (0.029) Year2012 0.837*** 0.840*** 0.820*** 0.838*** -0.094 0.817 0.836*** 0.836*** 0.818*** (0.164) (0.161) (0.160) (0.164) (0.165) (0.159) (0.164) (0.161) (0.159) Year2013 0.348*** 0.357*** 0.335*** 0.350*** 0.363*** 0.328*** 0.347*** 0.353*** 0.328*** (0.043) (0.041) (0.042) (0.043) (0.041) (0.042) (0.043) (0.041) (0.042) Constant 20.600*** 20.942*** 15.951*** 20.820*** 21.573*** 16.215*** 20.417*** 20.611*** 18.515*** 72 Airline Traffic All <850km >850km All <850km >850km All <850km >850km 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 (4.529) (4.197) (4.762) (4.562) (4.223) (4.499) (4.515) (4.189) (4.539) Time trend fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ No. of Observations 1,036 980 966 1,036 980 966 1,036 980 966 Note: 1. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 2. ***<0.01, **<0.05, *<0.10. 3. Standard errors are in parentheses. 73 Table 3.4 Estimation results for airline price equation with assumed functional forms of 𝒇(𝒔𝒊𝒕) = 𝒔𝒊𝒕, 𝒔𝒊𝒕𝟐 , or √𝒔𝒊𝒕 Airline price All <850km >850km All <850km >850km All <850km >850km 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 𝛽1 -0.0008** -0.0016*** -0.0217 -1.64× 10−6* -3.11× 10−6*** -6.46× 10−7 -0.028* -0.049*** 0.225 (0.0004) (0.0003) (0.0189) (9.02× 10−7) (6.71× 10−7) (3.27× 10−6) (0.05) (0.011) (1.24) 𝛽2 -0.034 -0.023 0.031 -0.037 -0.033 0.032 -0.038 -0.013 0.020 (0.051) (0.031) (0.037) (0.060) (0.043) (0.037) (0.062) (0.031) (0.022) HHI 0.1120*** 0.1036*** 0.106*** 0.116*** 0.104*** 0.108*** 0.116*** 0.103*** 0.108*** (0.018) (0.018) (0.018) (0.018) (0.018) (0.018) (0.018) (0.018) (0.018) Population 0.811*** 0.641*** 0.847*** 0.881*** 0.592** 0.895*** 0.916*** 0.663*** 0.906*** (0.277) (0.267) (0.292) (0.290) (0.267) (0.290) (0.288) (0.267) (0.290) Income 0.081 0.094* 0.098* 0.085 0.088* 0.084 0.085 0.096* 0.083 (0.054) (0.052) (0.053) (0.055) (0.052) (0.053) (0.055) (0.052) (0.053) LCC 0.0042 0.003 0.003 0.004 0.003 0.0032 0.004 0.003 0.003 (0.0261) (0.025) (0.025) (0.026) (0.025) (0.025) (0.026) (0.025) (0.025) Tourism 0.0049 0.005 -0.0014 0.004 0.003 -0.008 0.002 0.004 -0.008 (0.0199) (0.0174) (0.019) (0.020) (0.017) (0.019) (0.020) (0.017) (0.019) Spring -0.0371** -0.034* 0.407*** 0.409*** -0.036** 0.403*** 0.408*** -0.033* -0.035** (0.0183) (0.0178) (0.097) (0.099) (0.017) (0.097) (0.099) (0.017) (0.018) Summer 0.170** 0.167** 0.168*** 0.173*** 0.167** 0.167*** 0.173*** 0.167*** 0.167** (0.066) (0.065) (0.065) (0.066) (0.065) (0.065) (0.066) (0.065) (0.065) Autumn -0.187*** -0.189*** 0.253*** 0.258*** -0.190*** 0.252*** 0.258*** -0.188*** -0.185*** (0.065) (0.064) (0.066) (0.067) (0.064) (0.066) (0.067) (0.064) (0.064) Year2011 0.0127 0.013 0.010 0.011 0.014 0.012 0.011 0.012 0.012 (0.012) (0.011) (0.012) (0.012) (0.011) (0.012) (0.012) (0.011) (0.012) Year2012 -0.213*** 0.234*** 0.226*** 0.227*** -0.207*** 0.226*** 0.226*** 0.233*** 0.226*** (0.067) (0.065) (0.065) (0.066) (0.066) (0.065) (0.066) (0.065) (0.065) Year2013 -.0515*** -0.0491*** -0.057*** -0.054*** -0.046*** -0.054*** -0.055*** -0.050*** -0.055*** (0.017) (0.016) (0.0172) (0.017) (0.016) (0.017) (0.017) (0.016) (0.017) Constant -7.143*** -6.025*** -7.418*** -8.135*** -5.690*** -8.107*** -8.340*** -6.147*** -8.101*** 74 Airline price All <850km >850km All <850km >850km All <850km >850km 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 (1.752) (1.693) (1.945) (1.695) (1.840) (1.837) (1.822) (1.695) (1.858) Time trend fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ No. of Observations 1,036 980 966 1,036 980 966 1,036 980 966 Note: 1. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 2. ***<0.01, **<0.05, *<0.10. 3. Standard errors are in parentheses. 75 Table 3.5 collates the estimated elasticities and percent changes in airline traffic and price to HSR speed reduction. On shorter than 850 km routes, our HSR speed effect estimates seem robust with assumption on 𝑓(𝑠𝑖𝑡) . The estimates are conducted for 250 km/hr HSR and 350 km/hr HSR respectively. Specifically, for shorter than 850 km routes, with 250 km/hr HSR, the elasticities of airline traffic and price to HSR speed are estimated to be -0.802 to -1.13, and -0.38 to -0.4, respectively. HSR speed dropped by 20% from 250 km/hr to 200 km/hr. HSR speed reduction thus increased airline traffic and price by 16% to 22%, and 7.6% to 8%, respectively. When HSR speed is 350 km/hr, elasticities of airline traffic and price to HSR speed are larger than those of 250 km/hr speed HSR. HSR speed dropped by 14.3% from 350 km/hr to 300 km/hr. HSR speed reduction increased airline traffic and price by 21% to 22% and 5.7% to 10.8% on the 350 km/hr HSR routes. With the estimated HSR speed effect, we are also able to construct the estimate on HSR entry effect on airlines. The percentage change of airline traffic and price before and after a HSR entry can be calculated as 𝑞𝑖𝑡∗ | 𝐻𝑆𝑅=1− 𝑞𝑖𝑡∗ |𝐻𝑆𝑅=0𝑞𝑖𝑡∗ | 𝐻𝑆𝑅=0= 𝑒𝛼1×𝑓(𝑠𝑖𝑡) − 1, and 𝑃𝑖𝑡∗ | 𝐻𝑆𝑅=1− 𝑃𝑖𝑡∗ |𝐻𝑆𝑅=0𝑃𝑖𝑡∗ | 𝐻𝑆𝑅=0= 𝑒𝛽1×𝑓(𝑠𝑖𝑡) − 1. It can be seen, for routes shorter than 850 km, HSR entry can cause more dramatic decrease in airline traffic and price, similar to the findings in Wan et al. (2016). Table 3.5 Estimated HSR speed effect with assumed functional forms of 𝒇(𝒔𝒊𝒕) = 𝒔𝒊𝒕, 𝒔𝒊𝒕𝟐 , or √𝒔𝒊𝒕 (a) For 250 km/hr HSR lines <850 km 𝑓(𝑠𝑖𝑡) 𝑠𝑖𝑡 𝑠𝑖𝑡2 √𝑠𝑖𝑡 Elasticity to HSR speed 𝜀𝑞𝐴∗ ,𝑠𝐻 -1.05 -0.802 -1.13 𝜀𝑝𝐴∗ ,𝑠𝐻 -0.40 -0.38 -0.38 Impact of HSR speed reduction Traffic Change % 21% 16% 22% Price Change % 8% 7.6% 7.6% Impact of HSR entry Traffic Change % -65% -33% -89% Price Change % -33% -18% -54% Note: For >850 km routes, the items for the functional form 𝑠𝑖𝑡 and 𝑠𝑖𝑡2 are not calculated, because the coefficients of the HSR speed variables are not statistically significant. 76 (a) For 350 km/hr HSR lines <850 km 𝑓(𝑠𝑖𝑡) 𝑠𝑖𝑡 𝑠𝑖𝑡2 √𝑠𝑖𝑡 Elasticity to HSR speed 𝜀𝑞𝐴∗ ,𝑠𝐻 -1.47 -1.57 -1.44 𝜀𝑝𝐴∗ ,𝑠𝐻 -0.56 -0.76 -0.411 Impact of HSR speed reduction Traffic Change % 21% 22% 21% Price Change % 5.7% 10.8% 5.8% Impact of HSR entry Traffic Change% -71% -54% -90% Price Change % -43% -32% -93% Note: For >850 km routes, the items for the functional form 𝑠𝑖𝑡 and 𝑠𝑖𝑡2 are not calculated, because the coefficients of the HSR speed variables are not statistically significant. The estimates of other coefficients seem to be reasonable. First, the airline traffic is higher when airline market is less concentrated, since airline competition can reduce the airline price. Second, the airline price increases with the market population and income level. In addition, the short-run accident effect is, however, not identified (i.e., the estimated 𝛼2 and 𝛽2 are statistically insignificant). This is probably because the accident effect could attenuate fast over time, most likely within the quarter in which it occurred. Our quarterly data thus cannot accurately capture it. Since our ticket data is for the flights departing on particular day, not the booking price on that day, some observations after the accident could be the tickets booked before the event, thus confounding the accident effect estimation. Wei et al. (2017) find significant short-term panic effect: the airline price rose by 27.4% immediately within the first half month after the accident. This is because they only examined a very short-term period. And their ticket information is for the booking on each day, not the tickets flying on the day.47 The coefficients of LCC variable are insignificant in both the airline traffic and price equations. This is because the LCCs penetration in China is still very low, with less than 10% of market share (Fu et al., 2015; Wang et al., 2018). Fu et al. (2015a) and Wang et al. (2018) find that LCCs have little impact on the route average ticket price and traffic. 47 The estimated coefficient for the 𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖𝑡 is insignificant. This is probably because the list of top 25 most developed tourism cities by Forbes China has not been changed significantly from 2010 to 2012, thus the values of 𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖𝑡 on each route does not change significantly over time. As we have controlled the route-level fixed effect, the coefficients for the relatively time-invariant variables cannot be significantly identified. 77 It is somewhat surprising to obtain a statistically insignificant coefficient estimate on population variable and a statistically significant and negative coefficient estimation on the average personal income variable in our airline traffic and price equations. This result is likely to be driven by our sample route selection criteria, which consider the routes linking Beijing, Shanghai, and Guangzhou with provincial capital cities of China. Many provincial capital cities, e.g., Chengdu, Xi’an, Kunming, are in western and central China, with lower population and lower average personal income. However, these cities are relatively geographically remote to the economic centers, i.e., Beijing, Shanghai and Guangzhou, thus relying heavier upon air transport to be linked. Moreover, despite the lower average personal income, the income disparities in such cities are higher than Beijing, Shanghai and Guangzhou. As air travel is consumed by the population group with high income, the share of population traveling by air can be higher in these cities compared to cities with higher average personal income. The estimates of the quarterly and yearly dummies suggest that summer is the peak season of the air travel in China, and air traffic and price increase over years. HSR speed effects are only statistically significant on treated routes shorter than 850 km or shorter than 5-hour HSR travel time (Table B1-B3 of Appendix B), which supports our Proposition 3.3 that air-HSR substitutability reinforces the HSR speed effect. To directly account for the different degree of air-HSR substitutability for different route distance, we construct a term ℎ(𝑠𝑖𝑡, 𝐷𝑖) × 𝐻𝑆𝑅𝑖𝑡, as specified in Eq. (3.23), to allow HSR speed effect to decrease with route distance 𝐷𝑖. Specifically, we try sit𝐷𝑖, (sit𝐷𝑖)2 and √sit𝐷𝑖 for ℎ(𝑠𝑖𝑡, 𝐷𝑖). In this way, the HSR speed effect could be negatively moderated by the HSR route distance as an indicator of air-HSR service substitutability. ln𝑞𝑖𝑡∗ = 𝛼0 + 𝛼1 × ℎ(𝑠𝑖𝑡, 𝐷𝑖) × 𝐻𝑆𝑅𝑖𝑡 + 𝛼21𝑃𝑜𝑠𝑡_𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡𝑖𝑡× 𝐻𝑆𝑅𝑖𝑡 + 𝛼3ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i+ 𝛼4ln𝐻𝐻𝐼𝑖𝑡 + 𝛼5ln𝑃𝑜𝑝𝑖𝑡 + 𝛼6ln𝐼𝑛𝑐𝑜𝑚𝑒𝑖𝑡 + 𝛼7 𝐿𝐶𝐶𝑖𝑡+ 𝛼8𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖𝑡 + 𝛼9𝑆𝑝𝑟𝑖𝑛𝑔𝑡 + 𝛼10𝑆𝑢𝑚𝑚𝑒𝑟𝑡 + 𝛼11𝐴𝑢𝑡𝑢𝑚𝑛𝑡 + 𝛼12𝑌𝑒𝑎𝑟𝑡+ 𝛼13𝐻𝑆𝑅𝑖𝑡 + 𝜓𝑖 + 𝜉𝑖𝑡 (3.23) 78 ln𝑃𝑖𝑡∗ = 𝛽0 + 𝛽1 × ℎ(𝑠𝑖𝑡, 𝐷𝑖) × 𝐻𝑆𝑅𝑖𝑡 + 𝛽21𝑃𝑜𝑠𝑡_𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡𝑖𝑡×𝐻𝑆𝑅𝑖𝑡 + 𝛽3ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟𝑖+ 𝛽4ln𝐻𝐻𝐼it + 𝛽5ln𝑃𝑜𝑝𝑖𝑡 + 𝛽6ln𝐼𝑛𝑐𝑜𝑚𝑒𝑖𝑡 + 𝛽7𝐿𝐶𝐶𝑖𝑡+ 𝛽8𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖𝑡 + 𝛽9𝑆𝑝𝑟𝑖𝑛𝑔𝑡 + 𝛽10𝑆𝑢𝑚𝑚𝑒𝑟𝑡 + 𝛽11𝐴𝑢𝑡𝑢𝑚𝑛𝑡 + 𝛽12𝑌𝑒𝑎𝑟𝑡+ 𝛽13𝐻𝑆𝑅𝑖𝑡 + 𝜏𝑖 + 𝜈𝑖𝑡 The elasticities of airline traffic and price to HSR speed can be derived as follows: 𝜀𝑞𝐴∗ ,?̅?𝐻 =∂ln𝑞𝑖𝑡∗∂lnsit =∂ln𝑞𝑖𝑡∗∂sit ×sit=α1×ℎ′(𝑠𝑖𝑡, 𝐷𝑖)×sit 𝜀𝑝𝐴∗ ,?̅?𝐻 =∂ln𝑝𝑖𝑡∗∂lnsit =∂ln𝑝𝑖𝑡∗∂sit ×sit=𝛽1×ℎ′(𝑠𝑖𝑡, 𝐷𝑖)×sit (3.24) The expressions of the elasticities are summarized in Table 3.6 for different forms of ℎ(𝑠𝑖𝑡, 𝐷𝑖). With ℎ(𝑠𝑖𝑡, 𝐷𝑖) = (sit𝐷𝑖)2, the airline traffic and price elasticities with respect to HSR speed decrease at a faster rate with an increasing HSR distance 𝐷𝑖 or decreasing HSR speed 𝑠𝑖𝑡 , while, with ℎ(𝑠𝑖𝑡, 𝐷𝑖) = √sit𝐷𝑖, the airline traffic and price elasticities with respect to HSR speed decrease at a slower rate with an increasing HSR route distance 𝐷𝑖 or decreasing HSR speed 𝑠𝑖𝑡. Table 3.6 Expressions of elasticities with respect to HSR speed with assumed functional forms of 𝒉(𝒔𝒊𝒕, 𝑫𝒊) =sit𝑫𝒊, (sit𝑫𝒊)𝟐 or √sit𝑫𝒊 ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 𝜀𝑞𝐴∗ ,𝑠𝐻 α1sit𝐷𝑖=α1𝑇it 2α1 (sit𝐷𝑖)2=2α1𝑇𝑖𝑡2 12α1√sit𝐷𝑖=12α1√𝑇it 𝜀𝑝𝐴∗ ,𝑠𝐻 𝛽1sit𝐷𝑖=𝛽1𝑇it 2𝛽1(sit𝐷𝑖)2=2𝛽1𝑇𝑖𝑡2 12𝛽1√sit𝐷𝑖=12𝛽1√𝑇it 79 The estimation results of the airline traffic and price equations with the alternative functional forms of ℎ(𝑠𝑖𝑡, 𝐷𝑖) are collated in Table 3.7 and 3.8. First, it is found that HSR speed reduction significantly increased airline traffic and price, suggested by the statistically significantly negative sign of 𝛼1 and 𝛽1. This again confirms that travel-time effect dominates the safety effect of the HSR speed on airlines. Table 3.7 Estimation results for airline traffic equation with assumed functional forms of 𝒉(𝒔𝒊𝒕, 𝑫𝒊) =sit𝑫𝒊, (sit𝑫𝒊)𝟐 or √sit𝑫𝒊 Airline Traffic ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 𝛼1 -1.899*** -1.765*** -2.813*** (0.437) (0.424) (0.612) 𝛼2 -0.001 0.014 -0.063 (0.101) (0.078) (0.081) HHI -0.092** -0.093** -0.091** (0.044) (0.044) (0.044) Population -0.876 -0.946 -0.811 (0.664) (0.665) (0.663) Income -0.352*** -0.354*** -0.351*** (0.130) (0.130) (0.130) LCC -0.027 -0.028 -0.028 (0.064) (0.064) (0.064) Tourism 0.018 0.015 0.022 (0.043) (0.043) (0.044) Spring -0.237*** -0.239*** -0.237*** (0.044) (0.044) (0.044) Summer 0.198 0.198 0.199 (0.163) (0.163) (0.163) Autumn -0.609*** -0.611*** -0.608*** (0.160) (0.161) (0.161) Year2011 0.153*** 0.155*** 0.152*** (0.029) (0.030) (0.030) Year2012 0.840*** 0.843*** 0.838*** (0.162) (0.162) (0.162) Year2013 0.356*** 0.360*** 0.354*** (0.041) (0.042) (0.041) Constant 21.099*** 21.523*** 20.764*** 80 Airline Traffic ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 (4.207) (4.215) (4.201) Time trend fixed effect ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ No. of Observations 1,036 980 966 Note: 1. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 2. ***<0.01, **<0.05, *<0.10. 3. Standard errors are in parentheses. Table 3.8 Estimation results for airline price equation with assumed functional forms of 𝒉(𝒔𝒊𝒕, 𝑫𝒊) =sit𝑫𝒊, (sit𝑫𝒊)𝟐 or √sit𝑫𝒊 Airline Price ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 𝛽1 -0.656*** -0.580*** -0.993*** (0.169) (0.171) (0.247) 𝛽2 -0.019 0.052* 0.022 (0.032) (0.031) (0.034) HHI 0.111*** 0.103*** 0.103*** (0.017) (0.018) (0.018) Population 0.551** 0.603** 0.651*** (0.261) (0.269) (0.268) Income 0.108** 0.097* 0.098* 0.051 (0.052) (0.052) LCC 0.004 0.003 0.003 81 Airline Price ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 (0.025) (0.026) (0.026) Tourism -0.001 -0.0007 0.0025 (0.017) (0.017) (0.017) Spring -0.031* -0.034* -0.033* (0.017) (0.018) (0.018) Summer 0.184*** 0.167** 0.168** (0.064) (0.066) (0.066) Autumn -0.198*** -0.189*** -0.188*** (0.063) (0.065) (0.064) Year2011 -0.038 0.014 0.012 (0.011) (0.012) (0.012) Year2012 0.245 0.235*** 0.233*** (0.064) (0.066) (0.065) Year2013 -0.048 -0.048*** -0.050*** (0.016) (0.017) (0.017) Constant -5.649 -5.854*** -6.102*** (1.659) (1.704) (1.698) Time trend fixed effect ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ No. of Observations 1,036 980 966 Note: 1. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 2. ***<0.01, **<0.05, *<0.10. 3. Standard errors are in parentheses. We construct the elasticities estimate and the percent changes in airline traffic and price with respect to the HSR speed reduction for three categories of routes which have distinct air-HSR service substitutability: 500 km, 850 km, and 1,100 km (as shown in Table 3.9). It is found that the estimates for the 500-km route are relatively robust across different forms of ℎ(𝑠𝑖𝑡, 𝐷𝑖). HSR speed 82 reduction raised airline traffic by 17.7% to 19.9% when HSR speed is 250 km/hr, and by 16.8% to 34.6% when HSR speed is 350 km/hr. And the airline price rose by 5.8% to 7.0% when HSR speed is 250 km/hr, and by 5.9% to 8.1% when HSR speed is 350 km/hr. When route distance is extended to 850 km and 1,100 km, the HSR speed effects decrease while the magnitudes largely depend on the specific functional form of ℎ(𝑠𝑖𝑡, 𝐷𝑖). Table 3.9 Estimated elasticities of airline price and demand to HSR speed reduction and overall HSR competition effect (a). For 250 km/hr HSR lines ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 Route Distance 500 km 850 km 1100 km 500 km 850 km 1100 km 500 km 850 km 1100 km 𝜀𝑞𝐴∗ ,𝑠𝐻 -0.95 -0.56 -0.43 -0.88 -0.31 -0.18 -0.99 -0.76 -0.67 𝜀𝑝𝐴∗ ,𝑠𝐻 -0.33 -0.19 -0.15 -0.29 -0.10 -0.06 -0.35 -0.27 -0.24 Traffic Change % 19.0% 11.2% 8.6% 17.7% 6.1% 3.6% 19.9% 15.3% 13.4% Price Change % 6.6% 3.9% 3.0% 5.8% 2.0% 1.2% 7.0% 5.4% 4.7% (b). For 350 km/hr HSR lines ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 Route Distance 500 km 850 km 1100 km 500 km 850 km 1100 km 500 km 850 km 1100 km 𝜀𝑞𝐴∗ ,𝑠𝐻 -1.33 -0.78 -0.60 -1.73 -0.60 -0.36 -1.18 -0.90 -0.79 𝜀𝑝𝐴∗ ,𝑠𝐻 -0.46 -0.27 -0.21 -0.57 -0.20 -0.12 -0.42 -0.32 -0.28 Traffic Change % 19.0% 11.2% 8.6% 34.6% 8.6% 5.1% 16.8% 12.9% 11.3% 83 ℎ(𝑠𝑖𝑡, 𝐷𝑖) sit𝐷𝑖 (sit𝐷𝑖)2 √sit𝐷𝑖 Route Distance 500 km 850 km 1100 km 500 km 850 km 1100 km 500 km 850 km 1100 km Price Change % 6.6% 3.9% 3.0% 8.1% 2.8% 1.7% 5.9% 4.6% 4.0% To determine which form of ℎ(𝑠𝑖𝑡, 𝐷𝑖) fits our data better, a Rivers-Vuong model selection test is conducted (Rivers and Vuong, 2002). This test is based on a lack-of-fit criterion (Bonnet and Dubois, 2010; Doi and Ohashi, 2018). 𝐽𝑛ℎ(𝑏ℎ) =1𝑛∑(?̂?𝑖𝑡ℎ)2 (3.25) where 𝑏ℎ is the set of parameters, 𝑛 is the number of observations, and ?̂?𝑖𝑡ℎ are the residuals from the regressions ( 𝜉𝑖𝑡ℎ for the airline traffic equation, and ?̂?𝑖𝑡ℎ for the airline price equation). The alternative model can have the parameters 𝑏ℎ′. Under the null-hypothesis that 𝐽𝑛ℎ(𝑏ℎ) and 𝐽𝑛ℎ′(𝑏ℎ′) are the same, the test statistics 𝑇 follows an asymptomatically normal distribution: 𝑇 =√𝑛?̂?𝑛ℎℎ′{𝐽𝑛ℎ(?̂?ℎ) − 𝐽𝑛ℎ′(?̂?ℎ′)} (3.26) where ?̂?ℎ is the estimate of 𝑏ℎ and ?̂?𝑛ℎℎ′is the estimator of the asymptotic variance of the difference between 𝐽𝑛ℎ(?̂?ℎ) and 𝐽𝑛ℎ′(?̂?ℎ′). The selection procedure is to compare the sample value of 𝑇 with critical values of standard normal distribution. We compare pair-wise the three competing forms of ℎ(𝑠𝑖𝑡, 𝐷𝑖): sit𝐷𝑖, (sit𝐷𝑖)2 and √sit𝐷𝑖. The results from the River-Vuong test are shown in Table 3.10. For both airline traffic and price equations, the model with (sit𝐷𝑖)2 significantly outperforms the other two, by producing the smallest overall residuals 𝐽𝑛ℎ(?̂?ℎ). This suggests that HSR speed effect can diminish fast with route distance, i.e., air-HSR substitutability. 84 Table 3.10 River-Vuong test for the assumed functional forms of 𝒉(𝒔𝒊𝒕, 𝑫𝒊) =sit𝑫𝒊, (sit𝑫𝒊)𝟐 or √sit𝑫𝒊 (a). For airline traffic volume equation Model 𝒉 \ Model ℎ′ sit𝐷𝑖 √sit𝐷𝑖 (sit𝐷𝑖)2 -2.657*** -8.064*** sit𝐷𝑖 -10.09*** (b). For airline price equation Model 𝒉 \ Model ℎ′ sit𝐷𝑖 √sit𝐷𝑖 (sit𝐷𝑖)2 -10.771*** -11.771*** sit𝐷𝑖 -11.972*** Note: A more negative statistic suggests the superiority of one model to the other. The *** suggests that the Type I error to reject the null hypothesis that the two models are the same is less than 1%. 3.7 Concluding Remarks This study investigates, both theoretically and empirically, the effects of HSR speed on airline traffic and price, taking into account the degree of the substitutability between airlines and HSR on different markets. To the best of our knowledge, this is the first study to explore how airline and HSR service substitutability can alter HSR speed effect on airline traffic and price. In addition, our model incorporates two countervailing effects of HSR speed on airlines, namely the travel-time effect and the safety effect: increasing HSR speed reduces HSR travel time but may bring about 85 safety concern, which is especially true in emerging HSR markets such as China. This is also the first study to incorporate the safety effect of HSR speed analytically. The theoretical model suggests that HSR speed effect is stronger when airline and HSR services are more substitutable (i.e., on short-haul routes). The HSR speed effect depends on the relative dominance of travel-time and safety effect. HSR speed reduction increases airline traffic and price when travel-time effect dominates, while it reduces airline traffic and price when safety effect dominates. In addition, HSR speed has a larger impact on airline traffic volume than on airline price. Lastly, HSR speed effect can be moderated by inter-airlines competition, suggesting that more intense competition among the airlines in one market can reduce HSR speed effect on airlines. The natural experiment of China’s HSR speed reduction helps unbiasedly estimate HSR speed effect on airline traffic volume and price. The estimation indicates that HSR speed reduction increased both airline traffic and price, suggesting the dominance of the travel-time effect. More importantly, the empirical evidence confirms that HSR speed effect is stronger when airline and HSR services are more substitutable. This result is robust with alternative econometric specifications. By conducting model selection tests, it is found that the HSR speed effect on airlines declines with the route distance but increases with HSR speed in a square fashion. The HSR speed effect thus diminishes fast with air-HSR substitutability. We also tried to identify the 7.23 rear-ending short-term accident. The accident effect is, however, statistically insignificant with the use of quarterly data, as the accident effect attenuated probably very fast within a short period. This chapter also opens avenue for future research. First, HSR price is fixed in China, so that the strategic behavior of HSR cannot be modeled. This analysis should be regarded as a partial equilibrium without fully accounting for competition behavior and cost structure of HSR. Future study is thus called for on those markets with HSR being free to decide price. The HSR speed effect on HSR operating cost and its full impact on air-HSR competition can then be identified. Second, we have not considered airline and HSR frequencies adjustment. Yang and Zhang (2012) and D’Alfonso et al (2015) model airline and HSR competing on frequencies. Airline and HSR frequencies could be important service quality. HSR speed change could also change airline and HSR schedules and frequencies. The frequency and schedule information of airline and HSR in 86 China is difficult to retrieve. Future effort is suggested to take into account frequency and schedule for HSR speed effect estimation. 87 Chapter 4. Modeling Airline Competition in Markets with Legacy Regulation: The case of the Chinese domestic markets 4.1 Introduction Competition analysis is at the core of industrial organization economics (Dixit, 1979; Bresnahan, 1981, 1987; Singh and Vives, 1984). Economic analysis for the airline industry is no exception. Empirical studies have been conducted to identify the type of competition between airlines (i.e. Cournot, Bertrand or cartel). Brander and Zhang (1990; 1993) estimate conduct parameters for airlines providing homogenous services. They show that American Airlines and United Airlines competed close to a Cournot type in the duopoly markets out of Chicago O’Hare airport. Oum et al. (1993) also include oligopoly routes at the same airport and conclude that airlines’ conducts differentiate with each other’s and are affected by market share distribution and route distance. Berry, Carnall, and Spiller (BCS 1996) adopt the Berry, Levinsohn and Pakes (BLP 1995) structural model to estimate a general type of airline competition with differentiated products in the US domestic market. Airlines are assumed to conduct Bertrand competition. Berry and Jia (2010) adopt the same model as BCS (1996) to study the evolution of air travel demand and airline cost structures in the US airline markets. This BLP type structural model with assumed Bertrand competition has been commonly used in other airline competition studies such as Lee’s (2013) analysis of the Delta and Northwest Airlines merger and Yan and Winston’s (2014) study on the welfare effect of possible airport privatization in the San Francisco Bay Area. Aguirregabiria and Ho (2012) extend the method and incorporate dynamic elements in airline competition analysis. In fully deregulated aviation markets, such as those in the US, the assumption of Bertrand or Cournot competition may be justified, because airlines are able to compete freely on fares, flight frequencies and route entries (Dresner et al., 1996; Windle and Dresner, 1999). However, aviation markets in many countries are still subject to various legacy regulations. Although China became the world’s second largest aviation market since 2005, its domestic market has been dominated by a few state-owned airlines with various regulations on airline competition, route entry, airport slot 88 allocation, and input procurements such as aircraft, fuel and pilots (Fu et al., 2015a, b). Unlike the fully deregulated US market, airlines in China are not always allowed to compete freely. Compared to state-owned airlines based in mega hubs such as Shanghai, Beijing and Guangzhou, private airlines based in other airports often face stricter regulations on route entry and airport slot acquisition. Although since 1997 Chinese airlines have been allowed to freely discount the ‘standard’ fares set by the government, airlines’ attempts at aggressive pricing have been repeatedly warned and penalized by the Civil Aviation Administration of China (CAAC), the regulator and de facto owner of the largest state carriers. Zhang and Round (2011) find that in the absence of effective anti-trust laws in China, state-owned carriers are suspected to collude on price in selected markets. Airlines in China, therefore, may not compete freely in price (Bertrand) or quantity (Cournot). Applying a standard BLP method to markets with legacy regulation may yield biased estimation. Given that a large number of aviation markets in the world that have yet to be fully deregulated,48 there is a need to explicitly incorporate possible constraints on airlines’ competition decisions in empirical studies. Nevo (2001) incorporates “perfect collusive pricing” into the BLP structural model, considering the hypothetical case in which a monopolist maximizes the joint profit of all products in the market. The price-cost margin predicted under such a perfect collusion model can be compared to the Nash-Bertrand outcome. The model that produces a better prediction (i.e., one that more closely matches the firm’s real accounting data) is identified as the preferred method. Such an approach is known as the “menu” method in the literature. Hu et al. (2014) apply this method to study the Chinese passenger-vehicle industry, and find that the competition resembles more of a Bertrand competition than perfect price collusion. However, the assumption of perfect price collusion in Nevo (2001) can be very restrictive to exclude all intermediate collusion types. Ciliberto and Williams (2014) thus model intermediate degrees of airline price collusion by constructing and incorporating an index of airline multi-market contacts into the BLP specification. A more flexible approach is proposed by Sudhir (2001), who develops a weighted profit model for the US auto-mobile market. A firm is assumed to internalize 48 Whereas legacy regulations are present in most developing countries’ domestic markets, even many international routes between developed economies, such as those between Hong Kong, Japan, Korea, and Australia, still face various capacity, route entry and flight frequency regulations. For discussions on the regulation and liberalization of international markets, see for example Fu et al. (2010), Adler et al. (2014). 89 part of its rivals’ profits. Firms are identified as being more collusive when they put more weight on other firms’ profits. Building on previous studies, this chapter proposes an empirical approach to analyzing airline competition by accounting for possible regulation effects. With a general specification, a range of competition regimes (e.g., Bertrand, Cournot, or collusion) can be considered and empirically identified in the BLP framework. As regulations restrict airlines’ ability to compete freely, we analyze market equilibrium using a competition model that resembles the weighted profit model (Sudlhir, 2001). We also adopt the “menu” approach (Nevo, 2001) to benchmark the performance of the proposed model against the models in which airlines are assumed to compete a la Cournot or Bertrand. Such a framework is applied to the Chinese domestic markets, for which better estimation and prediction results are obtained compared with BLP methods under standard Bertrand or Cournot competition. This study not only provides rich empirical results on the Chinese aviation industry in terms of passenger preference and airline competition, but also constitutes a new approach for modeling firm competition in the presence of possible regulatory constraints. It may also be extended for the analysis of markets with other types of constraints such as the limits of airport slots and air space, airport curfew, or international markets that are not fully liberalized. The remainder of this chapter is organized as follows. Section 4.2 briefly reviews the background and current status of the Chinese airline industry. Section 4.3 establishes the econometric model and explains the algorithms used in the estimation. Section 4.4 describes the data sources, variable definitions, and selection of Instrument Variables (IVs) for the generalized method of moments (GMM) estimation. Estimation results and interpretations are given in Section 4.5. Section 4.6 summarizes and concludes the study. 4.2 Background on the Chinese Airline Market The Chinese aviation industry has experienced rapid growth, achieving an average annual growth over 10% between 1990 and 2015 in terms of number of passengers (CAAC 2015). In 2005, China became the world’s second largest aviation market in terms of scheduled capacity. Despite such phenomenal growth and some deregulation policies, much commercial regulation remains in the 90 Chinese domestic markets. Airfare and route entry had been strictly regulated until 1997, when airlines were allowed to provide discounts off the standard fares set by the government, which effectively relaxed price control. This has been the most influential deregulation to promote airline competition and has led to widespread price competition and substantial price reduction (Zhang and Round, 2011; Fu et al., 2015b). However, continuous price wars in the following years led to serious financial losses among airlines owned by state and local governments. As a response, CAAC coordinated consolidations of the nine largest state-owned carriers into three big airline groups in 2002, namely the so called “big three” including Air China, China Eastern and China Southern. The claimed policy objective is to reduce excessive competition and help carriers achieve economies of scale. The formed big-three airline groups are balanced in terms of network geographic coverage, capitalization and market shares, so that none of them owns a significant market power over the other two (Zhang and Round, 2009; Zhang and Zhang, 2017). As another measure to stabilize the domestic market and limit fierce competition among state-owned carriers, route entry has remained regulated for a long time, especially for services to the large hub airports. This restriction has been partially relaxed since 2006. Prior approval is no longer required for most airports, whereas regulations have been retained for routes out of the eight busiest airports (Fu et al., 2015a). Since 2010, only routes involving the four mega-hubs have needed formal approval (i.e. Beijing Capital, Shanghai Hongqiao, Shanghai Pudong, and Guangzhou Baiyun). On the input acquisition side, airline’s fleet expansion plans need prior approval from CAAC to ensure “orderly” industry growth. Among others, airlines need to achieve certain utilization thresholds such as load factor and daily aircraft operation hours. Although such measures do increase the industry capital utilization rates, they also restrict the overall supply of industry capacity and thus prevent large scale price wars. With the CAAC’s 2005 approval of private sector participation in the civil aviation industry, a few private airlines have been formed including Okay Airways, United Eagle Airlines and Spring Airlines. Spring Airlines positions itself as a low-cost carrier (LCC) and achieved sustained growth in scale and profit with an annualized average growth rate of more than 10%. Still, private airlines play a minor role in the sector with a combined market share of less than 10% (Wang et al., 2017). Fu et al. (2015b) find that private airlines face stricter restrictions to entering and expanding capacity on major routes. Despite being one of the most successful LCCs in China and in the region, 91 Spring Airlines has never exceeded a 20% market share in the most travelled routes such that it has not imposed significant competitive pressure on the full-service carriers as overseas LCCs. That said, Fu et al. (2015a, b) note an increasing deregulation trend in China since year 2006. Regulations on pricing, capacity and route entry have been largely removed on routes other than those linked to major hub airports. Private and low-cost carriers are granted more freedom to compete against the state-owned carriers in secondary domestic routes and selected international markets. With their generally higher efficiency and lower cost, for example, private and low-cost airlines have initiated services on thin routes to small to medium airports, where they claimed large market shares or even monopoly. To summarize, although the Chinese aviation market has become much more liberalized than it was decades ago, substantial regulations are still present in areas such as route entry, slot allocation and fleet acquisition. These regulations are likely to limit airlines’ ability to compete freely as carriers do in fully deregulated markets in North America and Europe. These constraints are not universally imposed in the whole domestic markets, with secondary routes being much more liberalized compared to routes linked to hub airports. Therefore, simply assuming Chinese airlines engage in a particular type of competition is likely to yield biased estimation results. There is a need to develop an econometric approach that allows for alternative types of competition, and the flexibility for one airline’s strategy and behavior to differ across the routes on which it competes. 4.3 Model and Estimation Method This section first specifies passenger preference and demand modeling. It then discusses alternative modeling methods on airline competition and the corresponding market equilibria that followed these alternative competition specifications. 92 4.3.1. Travel demand side and passenger utility The specification of air travel demand is in the spirit of BCS (2006), Berry and Jia (2010), Ciliberto and Williams (2014). The utility of consumer i when consuming product j in market t is given by Eq. (4.1): uijt=xjtβ-α pjt+ξjt+νit(λ)+λϵijt (4.1) where • xjt is a vector of observable product characteristics including route distance, airline brand and tourism destination, etc.; • β is a vector of coefficients of product characteristics; • α is the marginal disutility of a price increase for the passenger; • ξjt is the product characteristics unobservable to the researchers; • λ is the nested logit parameter which is between 0 and 1, and νit(λ) is the nested logit error. 49 As in Berry and Jia (2010), a nested logit model is adopted under the assumption that the error term in Eq. (4.1) follows a Generalized Extreme Value (GEV) distribution. A closed-form demand (market share) function can be derived as follows: 50 νit(λ)+λ ϵijt (4.2) Specifically, conditional on choosing air travel, the proportion of consumers who purchase product j in market t is given: e(xjtβ-αpjt+ξjt) λ⁄Dt (4.3) where the denominator Dt is defined by: 49 There are two nests considered, which include the outside good of no air travel and all the airline products. 50 Berry (1994) shows the derivation of this nested logit specification from a purely random coefficient discrete choice model using the mean utility approach. 93 Dt=∑ e(xjtβ-αpjt+ξjt) λ⁄j (4.4) The proportion of consumers who choose air travel is: st(xt,pt,ξt,θd)=Dtλ1+Dtλ (4.5) The overall market share of product j in market t is as defined by: sjt(xt,pt,ξt,θd)=exjtβ-αpjt+ξjtλDt×Dtλ1+Dtλ (4.6) The demand parameters θd include the taste for product characteristics β, the disutility of price α, and the nested logit parameter λ. The unobservable characteristics ξjt can be expressed as below by inverting the demand function. ξjt=s-1(xt,pt,st,θd) (4.7) With the contraction mapping method proposed by BLP (1995), through numerical iterations, we can calculate the value of ξjt with Eq. (4.8) 51: ξjt M=ξjt M-1+λ[lnsjt-lnsjt(xt,pt,ξt,θd)] (4.8) With the value of ξjt, GMM method can be utilized based on the moment conditions between the demand IVs and the unobservable ξjt, as Eq. (4.9) suggests. The next section describes the selection of IVs. E (h(zt)ξ(xt,pt,st,θd))= 0 (4.9) 51 The initial 𝜉𝑗𝑡0 is set to be a zero vector with the dimension of number of markets. The iteration stops when difference between the two iterated 𝜉 values small then pre-set threshold. 94 Using the nested logit demand function, a reduced-form IV regression can be derived to estimate demand parameters (see Appendix C1), 52 which provides a robustness check for the sophisticated BLP method. If the numerically simulated GMM weight matrix of BLP works well, the demand estimations from the two methods should be close to each other as both estimators are consistent asymptotically. 4.3.2 Modeling of airline competition 4.3.2.1 Bertrand equilibrium Bertrand competition assumes that each airline competes in price to maximize the total profit of its products. Suppose that there are a total of F airlines on route t, each of which produces Jft different products where f ∈{1,…,F}. It is also assumed that airlines have constant marginal costs, thus the profit for airline f at market t is: Πft=∑(pjt-mcjt)Mtsjt(pt,xt,ξt;θd)Jftj=1-FCft (4.10) where sjt(pt,xt,ξt;θd) is the market share of product j at market t, a function of all other airline products on that route; Mt is the market size, and 𝐹𝐶𝑓𝑡 is the fixed cost which does not enter the first order condition. Li and Huh (2011) prove the existence of a pure-strategy Nash-Bertrand equilibrium for the nested logit model. At equilibrium the price pjt of product j by firm f at market t must satisfy the first-order condition: 𝑠𝑗𝑡 (𝑝𝑡, 𝑥𝑡, 𝜉𝑡; 𝜃𝑑) + ∑ (𝑝𝑟𝑡 −𝑚𝑐𝑟𝑡)𝑟∈𝐽𝑓𝑡𝜕𝑠𝑟𝑡(𝑝𝑡, 𝑥𝑡, 𝜉𝑡; 𝜃𝑑)𝜕𝑝𝑗𝑡= 0 (4.11) 52 For details about this reduced regression, see for example Berry (1994), and Yan and Winston (2014).. 95 This set of equations implies the price-cost margins for each product. The markups can be solved for explicitly by defining Vjrt=-∂ srt ∂⁄ pjt , where 𝑗, 𝑟 = 1, … , 𝐽𝑡 and 𝐽𝑡 = ∑ Jft Ff=1 is the total products of air travel in market t: Ωjrt= { Vjrt, if {r,j}⊂ {1,…,Jft}0, otherwise (4.12) The derivations of Vjrt is reported in Appendix C2. Denote Ωt to be a Jt×Jt matrix. In vector notation the first-order conditions become: st(pt)-Ωt(pt-mct)=0 (4.13) where st(∙), 𝑝𝑡, and 𝑚𝑐𝑡 are 𝐽𝑡 × 1 vectors of mark shares, prices, and marginal cost, respectively. This implies a markup Eq. (4.14): (pt-mct)= Ωt-1st(pt) (4.14) We assume a linear form of marginal cost as follows: mct=wtψ+ωt (4.15) where • wt is a vector of observed cost characteristics; • ψ is a vector of cost parameter; • ωt is an unobserved cost shock. and thus, one has: ωt=pt-Ωt-1st(pt)-wtψ (4.16) With the estimated value of ωt, we can use exogenous variables 𝑧𝑡 that are mean independent with ωt to construct the moment conditions as: 96 E (g(zt)ωt(xt,pt,st;θd,ψ))=0 (4.17) These additional moment conditions of Eq. (4.17) from the supply side can be added to those from the demand side (see Eq. (4.9)) for a joint estimation of parameters θd, ψ. The demand parameters θd also enter the supply side moment conditions to improve the estimation efficiency of θd. 4.3.2.2 Cournot equilibrium The Cournot equilibrium conditions for the BLP model are also derived in this section. Despite empirical evidence that airlines do compete in Cournot in selected markets (see for example Brander and Zhang 1990), to our best knowledge Cournot equilibrium has not been developed and applied in structure BLP models in the literature. This is the first BLP study to model Cournot competition with product differentiation in oligopoly markets. To obtain the first order condition for the Cournot equilibrium, we first derive the inverse demand function as Eq. (4.18), expressing airline ticket prices as a function of the market shares of all products and the outside goods s0= 11+Dt λ (derivation details in Appendix C3). pjt=1α[xjtβ+ξjt+(λ-1)ln(sts0)-λ ln(sjt)+λ ln(s0)] (4.18) Cournot competition assumes that airlines compete in quantity (market share in our case, as market size Mt is constant for each market) to maximize the total profit of its products portfolio. It is assumed again that there are F airlines on route t and each of them has a constant marginal cost. The profit of airline f is: Πft=∑(pjt(st,xt,ξt;θd)-mcjt)MtsjtJftj=1-FCft (4.19) 97 This set of equations imply price-cost margins for each air travel product. The markups can be solved for explicitly by defining Rjrt=-∂ prt ∂⁄ sjt, 𝑗, 𝑟 = 1,… , 𝐽𝑡: Γjrt= { Rjrt, if {r,j}⊂{1,…,Jft}0, otherwise (4.20) The derivations of 𝑅𝑗𝑟𝑡 is shown in Appendix C3. 𝛤𝑡 is a 𝐽𝑡 × 𝐽𝑡 matrix and in vector notation the first-order conditions become: (pt(st)-mct)+Γtst=0 (4.21) where 𝑝𝑡(∙) and 𝑚𝑐𝑡 are 𝐽𝑡 × 1 vectors of prices, and marginal cost, respectively. This implies a markup equation: pt-mct=-Γtst (4.22) and so ωt=pt-wtψ+Γtst (4.23) As in the Bertrand equilibrium, with estimated value of ωt from Eq. (4.23), the exogenous variables 𝑧𝑡 that are mean independent with ωt are used to construct the moment conditions: E (g(zt)ωt(xt,pt,st;θd,ψ))=0 (4.24) 4.3.2.3 Weighted profit equilibrium As discussed in Section 4.2, legacy regulations on route entry, fleet expansion and airport slot acquisition are present in China. Although many such regulations are not meant to directly 98 intervene in airlines’ pricing strategies, they are expected to prevent airlines from competing with each other freely. To model such market conditions, it is considered that Chinese airlines maximize their profits subject to the constraint that their rivals’ profits are also above a threshold. This is likely to be the case especially for the most travelled routes where CAAC is keen to maintain the profitability of major state-owned airlines, an “orderly” market outcome desired by the regulator. If an airline competes aggressively and disturbs the so-called “market order”, it may be penalized with its slots at hub airports confiscated, or forbidden to serve other lucrative routes in the future (Zhang and Round, 2011). Since these regulations are mainly imposed on densely travelled routes, the effects on competition should be most prominent in these markets. On the other hand, in the absence of effective anti-trust laws airlines in China may form self-enforcing cartels without regulator’s intervention. Major Chinese airlines, especially the “Big Three” (i.e. Air China, China Southern, China Eastern), are balanced in market power and thus are likely to sustain a cartel. If this is the case, such a cartel can be nation-wide covering both dense and thin markets. The cartel is likely to be more stable in the more concentrated routes with fewer number of airlines. 53 As in the cases of Bertrand and Cournot equilibria, consider F airlines competing on the route, each produces Jft different travel products and has a constant marginal cost. Firm f’s rivals are denoted as f -∈{1,…,F}/f. Airline f decides its ticket prices to maximize its profit, with a constraint that its rivals’ profits cannot be less than a minimum level Πf -t: Max pjt Πft=∑(pjt-mcjt)Mtsjt(pt,xt,ξt;θd)Jftj=1-FCft s.t. Qf--t(pt-mct)-FCf--t≥ Πf -t (4.25) where 𝑄𝑓−𝑡 is a (F-1)×Jt matrix, 𝑝𝑡 −𝑚𝑐𝑡 is a 𝐽𝑡 × 1 vector, and 𝐹𝑓−𝑡 and 𝛱𝑓−𝑡 are (𝐹 − 1) × 1 vectors. Each row vector of 𝑄𝑓−𝑡 represents rivals’ products: 53 We expect more concentrated industries to benefit from cartel formations for two reasons. First, in a static setting, as the number of firms rises, we expect the free-rider problem to worsen (Rodrik, 1986). Second, in a super-game setting, we expect that the ability to maintain a cooperative outcome deteriorates as the number of firms increases (Friedman, 1971). 99 Qfj= { qj if product j belongs to firm f 0 otherwise (4.26) Transforming the above constrained profit maximization problem into a Lagrange function with the Lagrange multipliers Φ=[ϕ1,…,ϕF-1]' gives: Max pjt,Φ Πft=∑(pjt-mcjt)Mtsjt(pt,xt,ξt;θd)Jftj=1-FCft+ { Qf-t(pt-mct)-Ff--tΠf−t}' Φ =∑(pjt-mcjt)Mtsjt (pt,xt,ξt;θd)Jftj=1-FCft +∑{ϕg[ ∑(pit-mcit) Mtsit(pt,xt,ξt;θd)Jgti=1- FCgt]}g≠f (4.27) Solving the above Lagrange function is equivalent to maximizing an airline’s own profit plus others’ profit, weighted by the Lagrangian multiplier vector 𝜙. This leads to the weighted profit model as in Sudhir (2001). The larger the value of the Lagrangian multipliers, the more restrictive constraints are (i.e., stricter regulations or stronger price collusion). The first order condition with respect to 𝑝𝑗𝑡 is as in Eq. (4.28): ∂Πft∂pjt=Mt {sjt+∑(pjt-mcjt)∂sjt∂pjtJftj=1+∑ ϕg[∑(pit-mcit)∂sit∂pjtJgti=1]g≠f}=0 (4.28) In theory, the value of ϕ can be airline-pair and route specific. However, allowing such specificity can create an extreme burden on model identification.54 To make the empirical estimation feasible 54 For example, F airlines to compete on one route, which will lead to a total 𝐹(𝐹 − 1) values of ϕg to estimate for each market. With more than 1,000 routes, the vector ϕ will be of dimension 1000𝐹(𝐹 − 1). Even we only distinguish ϕg by the airline, not the market, suppose we have more than 8 airlines (which will be shown in the later 100 while still allowing useful implications to be drawn, we simplify by letting ϕ to be dependent on route traffic level. We classify markets into four categories based on their ranks of traffic volumes, and assign different values of ϕ to each category. Specifically, markets are grouped into four categories per their traffic volumes: (i) the top 25%. (ii) top 25%-50%. (iii) top 50%-75%. (iv). others. If policy interventions in the dense markets are effective, one would expect the values of ϕ to be more significantly positive. If airlines maintain a tacit or even explicit collusion without government intervention, the values of ϕ can be significantly positive for all the route categories, especially on concentrated routes. Define Vjrt=-∂ srt ∂⁄ pjt, j,r=1,…,Jt, and Hjrt= { Vjrt, if {r=j}⊂{1,…,Jft}ϕmVjrt, Otherwise (4.29) where ϕm, m=1,2,3,4 represents the weight of the route categories for the top 25%, top 25%-50%, top 50%-75% and other markets respectively. 𝛨_𝑡 is a 𝐽𝑡 × 𝐽𝑡 matrix. In vector notation the first-order conditions become: st(pt)-Ht(pt-mct)=0 (4.30) where 𝑠𝑡(∙) , 𝑝𝑡 , and 𝑚𝑐𝑡 are 𝐽𝑡 × 1 vectors of market shares, prices, and marginal cost, respectively. This implies the following markup equation: pt-mct=Ht-1st(pt) (4.31) then, we have ωt=pt-Ht-1st(pt)-wtψ (4.32) data description section), as almost any two of them have direct contact in some markets. We will have as many as 8 × 7 = 56 values of ϕg to estimate. 101 With the estimated value of 𝜔𝑡 from Eq. (4.32), we can use the exogenous variables 𝑧𝑡 (same as in the Bertrand and Cournot models) that are mean independent with 𝜔𝑡 to construct the moment conditions as: E (g(zt)ωt(xt,pt,st;θd,ψ))=0 (4.33) 4.4 Variables, Data, and Instrument Variables (IVs) Selection Analogous to Berry and Jia (2010), in the demand function the following characteristics are included in the vector xjt in addition to airfare Fare: route flying distance Distance (for connecting flights, it is defined as the sum of every segment’s distance); distance squared Distance_squared; number of connections Connection; flight frequency No. of Departure; the average number of destinations the airline serves out of the two endpoint airports No. of Destination; the tour route dummy Tour 55 ; the airport congestion as reflected by its slot controlled status Slot_control ; and the income level of the endpoint cities on the route Income 56. In the marginal cost function specified for different competition regimes, we consider the following variables in vector wt: flying distance Distance; the number of connection Connection; a hub variable defined as the airline’s market shares in the endpoint airports Hub; and the slot control variable Slot_control. Airlines’ marginal costs can significantly differ between short-to-medium haul routes and long-haul routes due to different aircraft sizes, on-board services and crew costs. Therefore, similar to Berry and Jia (2010) and Lee (2015), we also allow two sets of cost parameters: one for routes shorter than 2,400 km, and the other for routes longer than 2,400 km. 55 The tour dummy is defined for popular tourist destinations in China. A similar definition was used by Zhang and Round (2009), Fu et al, (2015). 56 The impact of the income on air travel utility is two-fold. First, people with higher income should attach higher utility on the air travel. Second, since the air travel is a derived demand, the air travel derived from the economic activity of more prosperous markets implies higher utility to passengers. 102 Airline-route specific data are compiled from the PaxIS database of the International Air Transport Association (IATA). The PaxIS database is a GDS (Global Distribution System) that records airlines’ ticket booking information. Monthly directional itinerary data are retrieved which contains ticket price and passenger number for each reporting Chinese airline in each origin-destination (OD) market. The airfare data in PaxIS is an aggregate average for all different fare classes and all flights operated by each airline. 57 PaxIS nevertheless distinguishes direct and connecting flights as distinct products. A market is defined as a city-pair, whereas a product is defined as a unique combination of directional airport-pair, airline, and direct/connecting flight. 58 Direct and connecting flights provided by the same airline are treated as different products. Two connecting flights transferred via different third airports are also regarded as different products. The Official Airline Guide (OAG) data are supplemented for airline route-specific flight frequency. The OAG reports airlines’ scheduled flight frequency for each direct OD segment. The flight frequency variable is constructed for connecting flights reported in PaxIS. Without detailed airline flight schedules within the 24-hour cycle, it is impossible to match connection flights individually. We thus use the minimum flight frequency among all segments of the connecting flight frequency, a similar approach as those used in Adler and Smilowitz (2007) and Adler et al. (2014). Route distance and airlines’ airport presence (market share in the airport, and the number of routes originating from the airport) are also obtained from the OAG data. Other socioeconomic data are compiled from various databases and sources. The city level population and personal income (GDP per capita) data are available from the city statistical yearbooks published by city census bureaus. Cities’ monthly rainfall and temperature data are also acquired from the National Meteorological Centre of China, which are used as additional cost 57 In addition, ticket price reported by PaxIS does not count tax, airport charges and fuel surcharge. 58 For the cities with more than one airport, flights to different airports are treated as different products. There are only two cities that have more than one airport: Hongqiao (SHA) and Pudong (PVG) airports in Shanghai; and Beijing Capital (PEK) and Nanyuan (NAY) airports in Beijing. 103 instruments to improve estimation efficiency. Airport slot control status is collected from Fu and Oum (2015) 59. It is suspected that, in some very thin markets, passenger preference and airline competition behaviors could be very different. We thus filter out very small regional markets to only consider the routes linking cities with more than four million population, which are the top 100 populous cities in China. Such a dataset covers more than 90% of the passenger travels in the domestic markets. Airlines included in this study are Air China (CA), China Eastern (MU), China Southern (CZ), Hainan (HU), Shanghai (FM), Shenzhen (ZH), Xiamen (MF), with other small-sized airlines grouped into one category as “Other”. 60 We acquired data for the five-month period during August to December in 2010. The moment conditions for the GMM estimation are not affected by serial dependence of error terms ξt and ωt, because the same route at different months can be regarded as different markets. Because data are collected for a relatively short period, passenger demand and airline competition pattern do not change significantly over the five months. 61 Per the above sample selection criteria, we end up with a total of 5,944 markets and 18,349 airline products in the sample. Instrument variables (IVs) must be specified for both the demand and pricing moment conditions. Any factor that is correlated to the observed variables but uncorrelated with demand or supply disturbances ξt and ωt can be appropriate IVs. Following previous studies (BCS, 2006; Berry and Jia, 2010; Yan and Winston; 2014; Lee, 2015; Luo, 2015), the following instruments are used for the demand moments with strong exogeneity assumption E(ξt|zt)= 0. • The number of products in each market; 59 Slot controlled Chinese airports include Beijing (PEK), Shanghai Pudong (PVG), Guangzhou (CAN), Xi’an (XIY), Shanghai Hongqiao (SHA), Chongqing (CKG), Shenzhen (SZX), Chengdu (CTU), Wuhan (WUH), Hangzhou (HGH), Nanjing (NKG), Qingdao (TAO), Xiamen (XMN), Dalian (DLC), Changsha (CSX), Haikou (HAK), Urmuqi (URC), Tianjin (TSN), Fuzhou (FOC) and Sanya (SYX). 60 Spring Air, the largest private airline in China, is not included in the PaxIS dataset, as it uses its own ticket reservation system and is not obliged to report ticket itinerary information to the IATA. 61 We tried to run our estimation using each month data separately. The estimation results are generally consistent, albeit with reduced estimation efficiency . 104 • The percentage of rivalry products that offer direct flights in the market; • The number of rivalry products available in the market; • The number of carriers in the market; • The Hub status of each airline in the market; • The 25th % percentile and 75th % percentile of fitted fares in a market. 62 • The market size measured by the geometric means of the endpoint cities’ population. The characteristics of the rival airlines in the same market are included as IVs because they are excluded in the passenger utility function derived from consuming one particular product (uijt is the utility to consume product 𝑗 , which does not directly depend on the product characteristics of the other products, 𝑥𝑟𝑡). These variables are nevertheless correlated with the price of the consumed product via the markups in the first-order conditions of airline competition (Berry, 1994). These IVs are not as the traditional ones from the cost side, which shifting the price due to higher operating cost, while not directly affecting demand. That is, with imperfect firm competition, demand-side instruments can be variables that affect markups as well as variables that affect marginal cost (Berry, Levinsohn and Pakes, 1995). For example, the IV, the percentage of rivalry products that offer direct flights in the market is to affect the markup as it indicates the airline competition intensity, while this variable may also indicate the level of marginal cost as direct flight is more expensive to operate. Thus, no matter affecting operating cost or market up due to imperfect competition, these IVs should be valid. The strong exogeneity condition E(ξt|zt)=0 implies the mean independence E(g(zt)ξt)=0 for the functional forms of the chosen IVs. To create the vector of IVs used for the estimation, we basically adopt the same set of IVs as Berry and Jia (2010), with additional functional forms of the IVs, and also select the ones that have the small empirical correlation with the simulated disturbance ξt. Airline flight frequency may be subject to endogeneity concern since it can also be correlated with the unobservable product characteristics ξt, and it is also because flight frequency is also affected by increasing air travel utility and demand (airlines increase flight frequency to accommodate 62 Quantile regression on the ticket price is conducted to generate the predicted values of 25% and 75% quantiles of the ticket price in the market. 105 higher air travel demand), i.e., a simultaneous relationship (Berry and Jia, 2010; Fu et al, 2014). To address the endogeneity of the flight frequency, we first regress the flight frequency on characteristics of the end cities, and then replace the frequency variable with the fitted values (Fu et al., 2014). For the marginal cost shifter ωt, our IVs include some of the demand instruments as well as additional exogenous cost shifter IVs such as monthly average rainfall and temperature in cities. The summary statistics is shown in Table 4.1. Table 4.1 Summary Statistics of Major Variables Variable Mean Std. Dev. Min Max Unit Product share 0.00033 0.00051 4.20E-08 0.0072428 Unit Fare 132.07 46.37 24 761 USD Distance 1,314.89 603.66 159 3922 Kilometer Connection 0.17 0.24 0 1 Unit No. Departure 90.45 92.83 30 630 Weekly No. Destination 17.83 18.22 1 86 Unit Tour 0.04 0.19 0 1 Dummy Slot_control 0.83 0.37 0 1 Dummy Income 51.04 14.35 15.49 91.09 RMB 1,000 Hub 0.21 0.18 0 1 Unit Hub_connect 0.14 0.23 0 1 Unit Market Population 9,995,725 3,560,943 4,190,057 25,800,000 Person No. of Carrier 3.53 1.56 1 8 Unit No. of Product 4.70 3.33 1 33 Unit 106 Variable Mean Std. Dev. Min Max Unit Temperature 12.47 9.46 -20.74 26.04 Centigrade Rainfall 77.88 64.61 1.51 342.34 mm 4.5 Model Estimation Results We first report the demand estimates based on the demand moment conditions only, then present the joint demand and airline cost estimates using both the demand and airline competition moment conditions. The joint estimates with different airline competition conducts, namely Bertrand, Cournot and weighted profit, are benchmarked for inferences and comparisons. 4.5.1 Demand estimation based on the demand moment conditions only The demand estimates using both BLP and reduced-form regression are collated in Table 4.2. For reduced-form regressions, we adopt an ordinary least squares (OLS) approach and an IV approach to instrument the endogenous price variable. Our BLP and IV models produce very similar results, indicating the validity of the BLP method and the necessity to control for the price endogeneity. The OLS produces a positive price coefficient estimate, showing a strong price endogeneity due to the positive correlation between the unobservable characteristics ξt and the airfare. 63 Our BLP and IV logit demand estimates are overall sensible with expected signs. Table 4.3 shows the median market price elasticity and the traveler’s willingness to pay for the different product characteristics. These values can be directly compared to the US market estimates of Berry and Jia (2010), and Yan and Winston (2014). 63 This can happen when the unobservable product characteristics, ξt, contains some unobservable quality factors associated to a higher airfare. 107 Table 4.2 Demand Function Estimation and Robust Test with IV and OLS Demand Estimation Demand Variables BLP IV Logit OLS Logit Fare -0.8501*** -0.7555*** 0.0559** (0.0808) (0.0591) (0.0222) Connection -1.2957*** -1.4284*** -1.3315*** (0.0187) (0.0114) (0.0104) Constant -11.0717*** -9.1751*** -9.541*** (0.1141) (0.0573) (0.0526) No. Destination 0.1223*** 0.2921*** 0.2846*** (0.0494) (0.0467) (0.0433) No. Departure 0.0281*** 0.0267*** 0.0387*** (0.0014) (0.0016) (0.0014) Distance 1.7262*** 0.8753*** 0.1326*** (0.1192) (0.072) (0.0512) Distance_squared -0.4147*** -0.1444*** -0.0613*** (0.0332) (0.0169) (0.0149) Tour 0.9873 0.4355*** 0.4616*** (0.0521) (0.0396) (0.0368) Slot_control -0.5276*** -0.1706*** -0.0371* (0.0370) (0.0231) (0.0214) Income 0.0579*** 0.0222*** 0.0245*** 108 Demand Variables BLP IV Logit OLS Logit (0.0020) (0.0006) (0.0005) 𝛾 0.6431 0.748*** 0.6215*** (0.0102) (0.0525) (0.0040) Carrier Dummy OT 0.0065 (0.0782) CA 0.2981*** 0.2103*** -0.2143*** (0.0817) (0.0492) (0.0452) MU 0.3609*** 0.2095*** 0.0488 (0.0759) (0.0410) (0.0381) CZ 0.4719*** 0.3323*** 0.0729* (0.0770) (0.0405) (0.0374) HU 0.3082*** 0.3443*** 0.3362*** (0.0813) (0.0487) (0.0454) FM 0.2691*** 0.2033*** 0.0352 (0.0830) (0.0517) (0.0479) ZH 0.1876*** 0.3089*** 0.1386*** (0.0832) (0.0479) (0.0444) MF 0.3556*** 0.0951* -0.0425 (0.1310) (0.0494) (0.0457) No. of Obs 18,349 18,349 18,349 109 Note: * Significant at the 10% level; **Significant at the 5% level; *** Significant at the 1% level. Table 4.3 Median price elasticity and willingness to pay for product attributes BLP IV Logit Berry and Jia (2010) Yan and Winston (2014) Brons et al. (2002) Median price elasticity -1.022 -0.9083 -1.55 -1.54 -1.146 Willingness to pay (US$) Additional weekly flight frequency 3.31 3.53 6.75 2.28 Additional one destination valuation 0.14 0.38 1.17 0.20 Airport without slot control 62.1 22.6 77.4 24.0 Direct flight with no connection 152.4 189.1 224 212 Our estimated price elasticity is -1.02 (BLP model) and -0.91 (IV regression model). The distribution of the route price elasticities is shown in Figure 4.1. These elasticity results on Chinese airline markets are similar to those of the developed countries (Berry and Jia, 2010; Yan and Winston, 2014). Zhang et al. (2013) use reduced-regression approach and find similar price elasticity of about -0.9 on the major Chinese routes out of Beijing, Shanghai, and Guangzhou. A meta-analysis in Brons et al. (2002) and a survey of Oum et al. (1992) show that air travel price elasticity is in the range of -0.8 to -2.0 for the liberalized markets of the developed countries. Despite the much lower average personal income in China, the air travel price elasticity is actually very close to the markets in developed economies. Such low price elasticity is in line with the findings of Chinese air travelers survey. Air travelers in China have much higher personal income than the average population, with half of them traveling for business purpose, and more than 40% of passengers having their airfares paid for by a third party (CAMIC, 2010). 110 Figure 4.1 Market price elasticity distribution Note: the IV-2sls is the IV logit model with 2 stage-least square estimation Chinese air travelers also value high flight frequency. The willingness to pay for one additional flight per week is 3.31 US$ by BLP model (3.53 US$ by our IV regression model). They are very close to the values in Yan and Winston (2014) for the US San Francisco market. The CAMIC (2010) survey reveals that more than 30% of survey respondents in China consider flight scheduling and frequency as the most important factors for their air travel choice, close to the price factor. We also find air passengers in China to value the airline hub status and to be willing to pay for it. Specifically, when airlines fly one more destination, they can charge 0.14 US$ higher per ticket. This finding is also consistent with Yan and Winston (2014). Overall, our demand estimate clearly shows that China has a very similar air travel demand pattern to those of the US. 111 Figure 4.2 Factors considered by Chinese air passenger for air product choice in the year 2010 Source: CAMIC report 2010. Note: the percent represents the frequency with which the factor is expressed as the most important factor when the surveyed passengers choose air service product. 4.5.2 Joint estimation of demand and marginal cost functions The joint estimations of demand and marginal cost are reported in Table 4.4 for the three models with different competition patterns: Bertrand, Cournot and weighted profit. Across the three models, our estimated marginal cost coefficients all seem to have the reasonable signs. The airline marginal cost increases with the distance, more significant for the short-and-medium haul flights. Connecting flight has a lower marginal cost because of the economies of density effects. Airlines also have a lower marginal cost when they have larger scale operations in the endpoint airports. The slot control seems not significant in increasing airlines’ marginal cost. We also test other cost specifications, for example, not distinguishing flights by short and long hauls; removing the airport slot control variable; including the airline’s number of departures as suggested by Lee (2015). 0%5%10%15%20%25%30%35%40%FrequencyandSchedulingPrice Airline FFP AircrafttypeDirect orconnectngOthers112 None of the cost parameter estimates change significantly, suggesting our estimates of marginal cost to be fairly robust. We are most interested in the estimated values of the Lagrangian multiplier vector ϕ under the weighted-profit model. We find for the most densely travelled markets (the top 25%), ϕ1 is estimated to be 0.45 and statistically significant. This indicates that each airline internalizes almost half of the rivals’ profit when making its own pricing decision. For the rest of the route categories, none of the ϕ values is significant. We thus only detect price collusion on the densest domestic routes. This is probably in line with our conjecture that the regulations imposed on the densest routes and the airport slot control by the regulator can lead to airline collusion. On other less traveled routes where regulations are relatively light, Chinese airlines compete intensely close to a Bertrand competition mode. 64 Figure 4.3 and 4.4 plot the average route-level concentration (the Herfindahl-Hirschman Index) and the average prices for the route markets with different traffic density. The most travelled routes (the top 25%) are much less concentrated because the demand is large enough to sustain more airlines. This probably explains the fact that yields on these routes are actually lower than those on medium-sized routes. There is higher market concentration on the thin routes (e.g. ‘other’ routes or the bottom 25% least travelled routes), which leads to average yields comparable with those on the most travelled routes. However, our tests on type of competition suggest that there are some degrees of collusion among carriers on the densely travelled routes, which raised price above the level that would have prevailed in a Bertrand competition equilibrium. On the thin routes, airline competition is actually closer to the Bertrand equilibrium. The observed price collusion on the densest market is likely due to regulatory effects instead of self-enforcing cartel, because such 64 It is possible that the dense routes have lower operating cost due to economies of density, thus contributing to the observed higher profit margin. It is also likely that the dense route can be more congested, raising airline operating cost. To rule out these confounding factors from the cost side, in the airline cost function estimation, we have also controlled for the effects of economies of density and airport congestion on airlines’ cost and thus airlines’ profit margin. Specifically, the variable “Hub” is included in the cost function to capture the economies of density when the routes have large traffic volume when linking major airline hubs in China. The estimation in Table 4.4 indicates that for routes with hub endpoint airport, the marginal operating cost is lower. Besides, the variable “slot_control” is included to capture the airport congestion effect on airline operating cost. The sign of this variable is positive in all the estimations, while only significant in Cournot model. After controlling the operating cost differences among dense and thin markets, it is safer to attribute the higher profit margin on the dense routes to airlines’ collusive behaviors. 113 collusion patterns were not detected in other markets, especially those highly concentrated routes that are easier to sustain a cartel. Figure 4.3 Average route-level airline HHI for different density markets from August to December of 2010 Note: (1). The regions between dashed lines represent the 95% confidence interval. (2). The route passenger number is used as weight to calculate the average HHI for each category of markets. 114 Figure 4.4 Average route-level yield (in USD$) for different density markets from August to December 2010 Note: (1). The yield is calculated by dividing the airfare with the flying distance. (2). The regions between dashed lines represent the 95% confidence interval. (3). The route passenger number is used as weight to calculate the average yield for each category of markets. As the GMM method relies on a numerical calculation of a weight matrix, which can affect the estimation stability, we also try to use the same numerical weight matrix of the Bertrand, Cournot models for the weighted profit model. Estimates do not significantly change and the price collusion is again detected in the densest routes (i.e. top 25%) but not the others. Although no restriction is put to force the estimated ϕ to be in the sensible range [0, 1], all estimated ϕ are within this range. All these results provide support to the validity of the model and estimation. 115 Table 4.4 BLP joint estimation of demand and marginal cost functions Demand Variables Bertrand Model Cournot Model Weighted Profit Model Fare -1.2605*** -1.4533*** -0.9232*** (0.0545) (0.0554) (0.0560) Connection -1.3205*** -1.34715*** -1.3331*** (0.0175) (0.01675) (0.01705) Constant -10.8620*** -10.7260*** -10.8290*** (0.1113) (0.1099) (0.1078) No. Destination 0.1548*** 0.2060*** 0.1081*** (0.0443) (0.0431) (0.0436) No. Departure 0.0275*** 0.0269*** 0.0286*** (0.0012) (0.0012) (0.0012) Distance 1.9977*** 2.1280*** 1.7554*** (0.1000) (0.1011) (0.0992) Distance_squared -0.4189*** -0.4230*** -0.4065*** (0.0306) (0.0309) (0.0300) Tour 0.9326*** 0.8264*** 0.8811*** (0.0503) (0.0499) (0.0501) Slot_control -0.5181*** -0.5004*** -0.5183*** (0.0358) (0.0356) (0.0350) Income 0.0549*** 0.0508*** 0.0527*** (0.0019) (0.0018) (0.0019) 116 Demand Variables Bertrand Model Cournot Model Weighted Profit Model 𝛾 0.6416 0.6609*** 0.6504*** (0.0093) (0.0088) (0.0093) Cost Variables Constant_short -0.7253*** -0.9119*** -1.0354*** (0.0463) (0.0510) (0.0734) Distance_short 0.6685*** 0.6689*** 0.6637*** (0.0075) (0.0075) (0.0076) Connection_short -0.0504*** -0.0346*** -0.0500*** (0.0043) (0.0044) (0.0053) Constant_long 0.1959 0.0832 -0.0380 (0.1565) (0.1618) (0.1781) Distance_long 0.2392*** 0.2097*** 0.2233*** (0.0538) (0.0546) (0.0570) Connection_long -0.0269 -0.0096 -0.0530*** (0.0229) (0.0233) (0.0252) Hub -0.0704*** -0.1316*** -0.0574*** (0.0163) (0.0163) (0.0180) Slot_control 0.0048 0.0129* -0.0021 (0.0088) (0.0088) (0.0096) 𝜙1 0.4489*** 117 Demand Variables Bertrand Model Cournot Model Weighted Profit Model (0.2127) 𝜙2 0.0487 (0.3450) 𝜙3 0.3497 (0.4409) 𝜙4 0.4592 (0.4292) Note: * Significant at the 10% level; **Significant at the 5% level; *** Significant at the 1% level. Next, we benchmark our weighted profit model with the estimates under the assumption of Bertrand and Cournot competition (henceforth referred to as Bertrand model and Cournot model). Such a “menu” approach (Nevo, 2001) allows us to decide which model is more reasonable. Specifically, we first compare the estimated price elasticities derived from the three models to those obtained from the consistent demand estimation based on the demand moments only. Second, we benchmark the predicted price-cost margins of the three models with our Chinese airlines’ accounting data. Table 4.5 summarizes the estimated values of price elasticities and airlines’ price-cost margins. First, the median price elasticity estimated by the weighted profit model is -1.11, very close to the consistent estimate using only the demand moments (1.02 as reported in the last column). The Bertrand and Cournot models, however, over-estimate the price elasticities with values of -1.51 and -1.74, respectively. For the predicted price-cost margins, Cournot model yields higher values than Bertrand model, in line with the theoretical conclusions obtained by Li and Huh (2011). This 118 is because the quantity competition is overall less intense than price competition.65 Weighted profit model produces the highest price-cost margin estimates among the three models, which makes sense. Berry and Jia (2010) find the price-cost margin to be about 0.60 for the US domestic markets. 66 Chinese airlines are expected to achieve higher price-cost margin than the US carriers, because airfare levels are comparable in the two countries (see Table 4.6) but Chinese carriers enjoy lower unit operating cost (Wang et al, 2014). Among the three models, only the weighted profit model predicts estimates higher than that in the US market. In sum, the model incorporating possible legacy regulation effect (weighted profit model) provides better estimates and more reasonable results than the Bertrand and Cournot models. Without explicitly modeling such possible effects of regulation, simply assuming Bertrand or Cournot competition would lead to biased estimates, as discussed above for the cases of demand and airline competition analysis. 65 It should be cautioned that if products are differentiated, it is possible for some firms to have lower profit margin in Cournot competition than Bertrand competition, because Cournot competition does not necessarily improve every firm’s profitability. Hackner (2000) proves that the high-quality firms can earn higher profits under price competition than under quantity competition. 66 Note in the calculation of price-cost margin marginal cost per flight or passenger is used. Fixed cost such as aircraft capital, depreciation, airport and ground handling cost are not included. That is, only variable costs are included which lead to higher margin at route level. 119 Table 4.5 Estimated airline profit margin and demand elasticity of the three competition conducts Profit Margin Bertrand Model Cournot Model Weighted Profit Model Berry and Jia (2010) Overall 0.484 0.621 0.660 0.60 Direct Flight 0.531 0.677 0.712 0.66 Connecting Flight 0.377 0.503 0.561 0.56 CA 0.405 0.547 0.592 MU 0.462 0.599 0.648 CZ 0.487 0.612 0.650 HU 0.497 0.634 0.687 FM 0.461 0.610 0.674 ZH 0.473 0.632 0.666 MF 0.509 0.664 0.697 SC 0.523 0.677 0.712 Top 25% market 0.684 25%-50% market 0.644 50%-75% market 0.628 other market 0.661 Price Elasticity Bertrand Model Cournot Model Weighted Profit Model Demand Side (BLP) Market Aggregate -1.5113 -1.7405 -1.1092 -1.022 Note: (1). Berry and Jia (2010) assumes airline Bertrand competition. 120 (2). the 95% confidence intervals of each profit margin statistic have been obtained using the bootstrap method. They are not reported to save space, but the intervals are very tight so that the profit margins of each model does not overlap with each other. Table 4.6 Yield comparison between Chinese and US airlines from accounting data (a) Average yield for different categorized Chinese domestic routes (US$/Kilometer) Route Category 2008-Q4 2009-Q1 2009-Q2 2009-Q3 2009-Q4 2010-Q1 2010-Q2 Top 1- Top 50 0.096 0.101 0.101 0.118 0.111 0.109 0.122 Top 51- Top 150 0.098 0.105 0.104 0.117 0.110 0.110 0.117 others 0.117 0.119 0.119 0.130 0.124 0.124 0.130 All 0.114 0.117 0.116 0.128 0.122 0.122 0.128 Note: The yield is calculated by dividing ticket price by flying distance. The fare data is from PaxIS; Flying distance is from OAG. The data are for Air China, China Eastern and China Southern airlines only. (b) Average yield for US Carriers (USD/kilometer) (c) Airline Group 2008-Q4 2009-Q1 2009-Q2 2009-Q3 2009-Q4 Regional 0.121 0.117 0.103 0.098 0.104 Low-Cost 0.084 0.075 0.071 0.071 0.078 Network 0.083 0.075 0.068 0.070 0.075 21-Carrier Total 0.085 0.077 0.071 0.071 0.078 Source: Wang et al (2014) 121 We also conduct a counterfactual analysis by eliminating the collusive pricing on the densest routes. This simulates the hypothetic case in which constraints on airlines, such as the legacy regulation and possible airport slot limits, are removed. We first set ϕ1=0 for the top 25% routes which correspond to Bertrand competition. The new equilibrium price vector pt* is a fixed-point solution to the following first-order condition which is a unique solution (see the proof in Appendix C4). pt=Ωt-1(pt)st(pt;xt,ξt,θd)+mct(ωt,wt,ψ) (4.34) With the initial pt0 set to be the current airfare, the new equilibrium price vector is obtained with the following numerical iterations until the convergence defined by Eq. (4.35) is reached. The prices on the top 25% densest routes in the counterfactual case are reduced by 30 US$ on average, which is about one quarter of the current price. The distribution of the price changes is plotted in Figure 4.5. This counterfactual analysis indicates a major gain in consumer surplus if competition can be promoted in these most travelled markets. 67 ptM=Ωt-1(ptM-1) st(ptM-1;xt,ξt,θd)+mct(ωt,wt,ψ) (4.35) 67 However, this counterfactual analysis assumes that air travel product characteristics other than price, such as flight frequency, number of destinations served out of airports, airport slot control, all remain unchanged. In reality, airlines can adjust flight frequency and make changes to network configuration in response to deregulation and airport capacity expansion. 122 Figure 4.5 Price Reduction distribution by dliminating price collusiveness on Top 25% dense markets (in 100 USD) 4.6 Conclusion and need for further study Many studies use BLP-type models to analyze airline rivalry under the assumption of Bertrand competition. Such an assumption is unlikely to hold in the presence of market constraints such as legacy regulations and/or airport slot controls. Although the ‘menu approach’ has been used to test collusive behaviors in selected markets, a specific competition type still needs to be assumed. This study proposes an improved econometric approach that allows for a range of competition types that can be empirically identified for different (groups of) routes. Such generality and flexibility allow us to model possible legacy regulatory effects in the Chinese domestic market. Estimates obtained from the new model are benchmarked to those obtained from models with restrictive assumptions such as Bertrand or Cournot competition, and are compared to airlines’ actual financial/accounting data. Overall, we find strong evidence that our new approach performs better than existing models in terms of obtaining better estimation and prediction results. Our study suggests that simply assuming a particular type of competition for a market may lead to biased estimates, especially in the presence of competition/operational constraints. Therefore, it is advisable to conduct empirical tests using an approach similar to that proposed in this study. 123 In addition to the methodological improvements, our study is among the first to empirically estimate a BLP type model for the airline markets in China. Rich results have been obtained. Specifically, there is clear evidence of collusive pricing among Chinese airlines on the routes with strict legacy regulations and airport congestion, while no significant evidence of collusive pricing is observed on less travelled routes with light regulation. Our demand estimate show that Chinese air passengers exhibit similar preferences as those in developed countries in terms of the price elasticity, valuation of flight frequency and degree of aversion to airport congestion.68 Although our study highlights the importance to explicitly model the possible effects of competition/operational constraints such as legacy regulation and airport slot limitation, we have not clearly identified the source and cause of the observed pattern, that is, to what extent do specific constraints affect airline competition and market equilibrium in selected (groups of) routes. This problem could have been addressed if detailed regulatory rules can be obtained for each (groups of) route(s). However, as discussed the existing regulatory policies in the Chinese domestic market are quite ad hoc. We hope our study could lead to more in-depth investigations on this important but under-studied market. 68 Although these results may be somewhat unexpected given China’s lower per capita income compared to developed economy, it is consistent with some of the estimates in previous studies on the same market (see for example, Wang et al. 2014a, Fu et al. 2015a, Wang et al., 2017a). Per a survey of CAMIC (2010), more than half of air travels in China have yearly income over US$ 20,000, and 40% of the passengers’ fares are paid by the third-party (e.g. company or government agencies). All these suggest that air travel in China are still mostly consumed by high-income customers who are not be price-sensitive. Thus, a systematic demand estimate is essential for the Chinese airline market. 124 Chapter 5. Airport pricing when airport congestion affects passengers’ concession consumption 5.1 Introduction Airports generate revenues from both aeronautical and non-aeronautical businesses. The former refer to aeronautical activities related to take-offs and landings, aircraft parking and terminal usage, whereas the latter refer to commercial activities on the airport land and buildings including concession services of retail, food and beverage, car rental, and other non-concessional services such as office and land rentals, car parking and advertising (Oum and Yu, 2004). Concession revenue has become the most important source of many airports’ income. For example, the shares of concession revenues were 49%, 27% and 20% of the total revenue for Hong Kong, Atlanta and Copenhagen airports respectively, while the shares of total non-aeronautical revenue for those airports were 76%, 67% and 60%, respectively (ATRS, 2014). For most airports, concession is, by far, the most important non-aeronautical service activity. Given that there is a strong demand complementarity between aeronautical services and concession services (Oum et al., 2004), airports may be regarded as a platform providing a two-sided market which derives revenues from both aeronautical and concession services (Kaiser and Wright, 2006). The implications of the demand complementarity on airports’ aeronautical and concession service charges have been discussed extensively (see for example Starkie, 2001; Zhang and Zhang, 2003; Oum et al., 2004; Fu and Zhang, 2010; Zhang et al., 2010). Due to the substantial growth in air traffic over the last few decades, major airports around the world are operating close to capacity. A natural consequence of airport saturation is congestion. For instance, 21% of the US domestic flights were delayed in 2013, and only 68.4% of Chinese domestic flights departed on time in 2014. Extensive literature has been developed on market mechanisms such as congestion pricing, slot trading and slot allocation to address the increasing airport congestion problem (Brueckner, 2002, 2009; Zhang and Zhang, 2003; Basso and Zhang, 2010; Verhoef, 2010). Most of these studies, however, focus on the effect of airport congestion on air travel demand and airport pricing issues, ignoring the potential impact of congestion on 125 passengers’ concession demand. Furthermore, airport congestion is often referred to as runway congestion, and terminal congestion is often not explicitly taken into account. Interesting exceptions include D’Alfonso et al. (2013), who assume that airport congestion can increase passengers’ concession demand due to their longer dwell time in the airport (i.e. the time after completing the security check but before boarding), and Wan et al. (2015), who further distinguish runway- and terminal-related congestions, arguing that the latter can increase concession consumption. Both D’Alfonso et al. (2013) and Wan et al. (2015) assume a positive relation between airport congestion and concession demand because of passengers’ longer dwell time in the airport. Despite their modeling of this positive congestion effect on concession demand, the actual pattern of such effects is still ambiguous. Thus, the objective of this chapter is to extend the airport economics literature by establishing a direct analytical and empirical link between airport congestion and concession demand while treating endogeneity between these two variables properly. Although, in principle, longer dwell time due to congestion may increase passengers’ chance to consume concession goods, some consumer behavior studies also find that crowdedness, inconvenience and mental stress can discourage consumers’ consumption (Harrell et al., 1980; Yüksel, 2007; Li et al., 2009). In the context of airport concession services, airport congestion, and especially the terminal congestion, deteriorates service quality, responsiveness and friendliness of staff, availability of waiting area and washrooms, cleanliness of the facilities, and ease of finding connecting flights (Yang and Fu, 2015). A recent survey of 15 world’s largest airports, found that a 0.1 unit increase, on a 5-point scale, in overall satisfaction of airport quality brings 0.8 USD more concession revenue per enplaned passenger (DKMA, 2013). Bohl (2013) surveyed 294 travelers within the Budapest airport, and found that the airport retail store environment and passengers’ time pressure significantly influence their visiting and consumption. In an effort to reconcile these juxtaposing effects, we hypothesize that a nonlinear relationship exists between airport congestion and concession demand, and then analyze such effect on airport optimal aeronautical and concession pricing. This study complements the existing airport pricing studies, especially, by recognizing the possible negative effect of airport congestion on concession demand in the analysis of congestion effect on airport pricing. 126 The present study first models the concession demand as a function of airport congestion, which in turn is a function of the passenger volume, runway and terminal capacity. By doing so, we can analyze the airport congestion effect on airport pricing by endogenzing its effect on passenger’s concession demand. Next, an econometric estimation is conducted to verify the findings obtained from the model. Specifically, a system of equations of the airport demand, aeronautical price, and concession price are estimated, utilizing operational and financial panel data for 61 of the world’s largest and congested airports in North America, Asia-Pacific and Europe, from 2008 to 2012. It should be also noted that the majority of existing airport pricing studies still remain theoretical, and the recent empirical studies have focused exclusively on aeronautical pricing (Bel and Fageda, 2010; Bilotkach et al., 2012; Choo, 2014). Systematic empirical investigation on the determinants of airport concession pricing is lacking. To our knowledge, Van Dender (2007) is the only empirical study that estimates airport’s concession pricing equation using panel data of 55 major US airports from 1998 to 2002. Our empirical analysis hopes to extend the work of Van Dender (2007) by explicitly measuring airport congestion effect on concession demand and airport pricing. In addition, our data also include the European and Asia-Pacific airports, thus can shed additional light on the effects of different airports’ ownership and governance structures. The rest of the chapter is organized as follows. In Section 5.2, the airport pricing model is proposed to generate the propositions. In Section 5.3, we specify the system of econometric equations to perform the empirical estimation. This section also discusses the data sources, variable constructions and the estimation strategies. The estimation results are presented in Section 5.4. Section 5.5 summarizes the study. 127 5.2 Theoretical model Our airport pricing model draws on the work of Zhang and Zhang (2003, 2010) and D’Aflonso et al. (2013) to assume an aggregate utility of air travel, B(Q), where Q is the airport passenger volume. The market equilibrium is reached at 69: B'(Q)=p+v D(Q, K) (5.1) 𝑃 is the airline ticket price, v D(Q, K) is the representative passenger’s congestion cost, which is a product of the congestion disutility parameter v and airport congestion D(Q, K) . Airport congestion D(Q, K) is a function of airport total passengers Q and airport capacity K. Airport capacity K includes both runway and terminal capacity. Air passengers are assumed to incur congestion disutility from runway flight delay and from terminal congestion. It is assumed that one representative passenger’s willingness to pay for the concession service is randomly distributed in a fixed interval [0, e], follows a cumulative distribution function G(x), and a corresponding density function g(x). Airports can decide the concession price r. The probability to consume concession service by the representative consumer is thus 1-G(r), as shown in Figure 5.1. The total airport concession demand is Q(1-G(r)). This air travel demand specification assumes that air travelers are myopic whose travel decision is primarily driven by the air ticket price not the concession price. This assumption is more widely adopted by most analytical airport pricing studies, recognizing the fact that air travelers may not easily obtain the concession price information before arriving at the airport, or compared to the air ticket price, the concession price is at much smaller amount. There is, however, an emerging literature to account for possible foresight behavior of the air travelers who may consider airport concession price at the travel planning stage (e.g. Czerny, 2006; Bracaglia et al., 2014; Czerny et 69 In this setup, we assume the marginal passenger indicated by Eq. (5.1) is representative, such that it represents the average utility change of air passengers to the airport congestion, i.e., the dwell time and stress effects. This is a simplification assumption indeed, as passengers can have heterogenous tastes and vary in the response to the dwell time and stress caused by airport congestion. Several studies have considered the impact of different types of passengers on airport pricing and possible discriminating pricing possibly adopted by airports (Czerny and Zhang, 2011, 2014, 2015). 128 al., 2016; D’Alfonso et al., 2017). This is driven by the easier acquisition of concession price information on airline and booking agencies’ websites (bundling products). But this foresight behavior is out of scope this chapter and leaves as a future avenue to explore. Figure 5.1 The distribution of a representative passenger’s willingness to pay for airport concession service We assume airport congestion to have two countervailing effects on passengers’ concession demand. First, congestion leads to longer passenger dwell time which could induce passengers to consume more concession products (Torres et al., 2005; Castillo-Manzano, 2010; D’Alfonso et al., 2013; Wan et al., 2015). Second, congestion leads to greater crowdedness which on the other hand could dampen passengers’ willingness to shop due to increasing stress and declining airport service quality (Entwistle, 2007; Bohl, 2013). Combining the abovementioned two effects, we model the congestion effect on concession consumption in the following expression: 70 70 In the United States, car rental accounts for a significant proportion of airport concession revenues. Some US airports derive more than half of their concession revenues from car rental services. Airport congestion may have a lower effect on the car rental service than on other concession services, such as food and retail shopping. But severe airport congestion could discourage car rental consumption per person if passengers are worried about the long and unexpected time spent on going through the car rental process. 129 𝑑 [1 − 𝐺(𝑟 |𝑇(𝐷), 𝑆(𝐷)]𝑑𝐷=𝜕(1 − 𝐺)𝜕𝑇⏟ >0𝑑𝑇𝑑𝐷⏟>0+ 𝜕(1 − 𝐺)𝜕𝑆⏟ <0𝑑𝑆𝑑𝐷⏟>0 (5.2) In Eq. (5.2), T denotes the passenger’s dwell time at an airport, and S is the passenger’s “stress” from airport congestion. The “stress” is used as a general term to describe airport service quality deterioration and passengers’ mental stress from an increased airport congestion. 71 The first term on the right-hand side, ∂(1-G)∂T⏟>0dTdD⏟>0, implies that congestion lengthens a passenger’s dwell time, and longer dwell time can increase the concession demand 72. The second term on the right-hand side ∂(1-G)∂S⏟<0dSdD⏟>0 implies that congestion also contributes to a passenger’s stress, and stress can reduce a passenger’s concession demand. Torres et al. (2005) find empirical evidence on a decreasing marginal effect of dwell time on a passenger’s concession consumption. Thus, the concession demand per passenger 1-G should be a concave function in T (e.g. ∂(1-G)2∂2T⏟ <0). On the other hand, we assume 1-G to be also a concave function of the stress level S (e.g. ∂(1-G)2∂2S⏟ <0). This can happen when passengers become increasingly more resistant to consume concession services as they experience more stress or when the service quality deteriorates. In addition, although both dwell time T and stress S increase with congestion D, it is expected that stress S rises faster than dwell time T with the congestion D (equivalent to the elasticity comparison 𝑑ln𝑆𝑑ln𝐷>𝑑ln𝑇𝑑ln𝐷 | D). This can be true when passengers are more sensitive to the perception of service quality deterioration than the physically increasing dwell time length. Such relation is likely to hold because the longer dwell time per se also contributes to a passenger’s stress (Torres et al., 2005). 71 The stress effect is described to be negative on concession consumption due to airport service quality deterioration and passenger’s anxiety to miss the flight. It is possible passengers may consume more concession to relieve stress, but we can attribute this to the dwell time effect. 72 Here, the dwell time refers to the waiting time of the departing passengers. Therefore, the flight departure delay is more relevant for a longer dwell time. Normally, passenger leaves the airport after landing, thus the arrival delay has little relevance with the dwell time effect. 130 When airport congestion is low or moderate, we will have 𝑑 [1−𝐺(𝑟|𝑇(𝐷),𝑆(𝐷) ]𝑑𝐷=𝜕(1−𝐺)𝜕𝑇⏟ >0𝑑𝑇𝑑𝐷⏟>0+ 𝜕(1−𝐺)𝜕𝑆⏟ <0𝑑𝑆𝑑𝐷⏟>0> 0, because ∂(1-G)∂T⏟>0 is significantly larger than ∂(1-G)∂S⏟<0 in absolute magnitude when both T and S are small. Passengers are still feeling relaxed and are willing to consume more concession when staying marginally longer at the airport, leading to ∂1-G(x, D)∂D>0 (which is equivalent to the First Order Stochastic Dominance (FOSD) condition, 1 − 𝐺(𝑥|𝑇( 𝐷), 𝑆(𝐷)) ≤ 1 −𝐺(𝑥| 𝑇(?̅?), 𝑆(?̅?)), ∀ D<D̅ and ∀ x∈[0,e], which is in line with D’Alfonso et al. (2013)). In this scenario, the dwell time effect dominates the stress effect. As ∂(1−𝐺)2𝜕2T⏟ <0 and ∂(1−𝐺)2𝜕2S⏟ <0, when T and S further increase with the congestion D, ∂(1-G)∂T⏟>0 turns to be smaller than ∂(1-G)∂S⏟<0 in absolute magnitude. In addition, we also have d𝑆2𝑑2𝐷≥d𝑇2𝑑2𝐷 | D so that S increases faster than T. Therefore, if airport becomes too congested, the stress effect will turn to dominate the dwell time effect, leading to d [1-G( T,S | r)]dD=∂(1-G)∂T⏟>0dTdD⏟>0+ ∂(1-G)∂S⏟<0dSdD⏟>0< 0 . 73 This is equivalent to the FOSD condition, 1 − 𝐺(𝑥|𝑇( 𝐷), 𝑆(𝐷)) ≥ 1 − 𝐺(𝑥| 𝑇(?̅?), 𝑆(?̅?)), , ∀ D>D̅ and ∀ x∈[0,e]. To summarize, we should observe the concession demand to have an inverted U-shaped relationship with airport congestion. When congestion is low, dwell time effect outweighs the stress effect such that concession demand increases with airport congestion. But when congestion is high, stress effect becomes dominant, reducing concession demand. 74 Given the fixed airport capacity K, we have the following result as Eq. (5.3): 73 The increasing congestion at the check-in counters and security check points can also decrease the dwell time for passengers. 74 However, it should be noted that our assumption is based on a reasonable degree of airport congestion. In reality, in case flights are seriously delayed or even cancelled, passengers may be forced to consume additional meals or to arrange accommodation at the airport. In this way, dwell time effect always dominates stress effect. Nevertheless, such extremely long flight delays should account for a small proportion in airport operations. 131 𝑑 [ 1 − 𝐺(𝑟 | 𝑇(𝐷(𝑄, 𝐾)), 𝑆(𝐷(𝑄, 𝐾)))]𝑑𝑄=𝑑 [1 − 𝐺(𝑟 | 𝑇(𝐷(𝑄, 𝐾), 𝑆(𝐷(𝑄, 𝐾)))]𝑑𝐷(𝑄, 𝐾)𝑑𝐷(𝑄, 𝐾)𝑑𝑄 (5.3) Since 𝑑𝐷(𝑄,𝐾)𝑑𝑄> 0, 𝑑 [ 1−𝐺(𝑟 | 𝑇(𝐷(𝑄,𝐾)),𝑆(𝐷(𝑄,𝐾)))]𝑑𝑄 and 𝑑 [1−𝐺(𝑟 | 𝑇(𝐷(𝑄,𝐾),𝑆(𝐷(𝑄,𝐾)))]𝑑𝐷(𝑄,𝐾) have the same sign. Thus, given airport capacity K, concession demand also first increases with airport passenger volume and then decreases. The plotted relationship between the airport passenger volume and the airport concession revenue per passenger of our sampled airports appears to support this conjecture. In Figure 5.2, airport concession revenue per passenger seems to exhibit an inverted U-shape with airport passenger volume. However, airport capacity is not controlled. A rigorous investigation is thus called for to verify such prediction. In the above discussion we aggregate the runway and terminal congestion as D(Q,K), and consider how this aggregate congestion affects concession demand. In Appendix D1, we further distinguish runway and terminal congestion, and investigate how runway capacity Kr and terminal capacity Kt can affect concession demand differently. In the remaining part of this section, we examine the impact of dwell time effect and stress effect on airport pricing. To simplify the notation for the next analytical derivation, we will use 1 − 𝐺(𝑟, 𝐷) to replace 1 − 𝐺(𝑟 | 𝑇(𝐷(𝑄, 𝐾), 𝑆(𝐷(𝑄, 𝐾)) as the concession demand. 132 Figure 5.2 Plot of airport passenger volume and concession revenue per passenger (a). Asian Pacific Airports (b) European Airports 133 (c) US Airports 5.2.1 Airline problem Consider the case where each airline maximizes its profit in a Cournot competition game: Maxqi (p− c − τ) qi (5.4) The airline is assumed to be symmetric in cost structure and provides homogenous products, and c denotes the airline marginal operating cost. 𝜏 is the airport aeronautical charge to the airline. The First Order Condition (FOC) implies the following: p =c+ τ − qi B''(Q)+qiv D'(Q,K) (5.5) 134 This is the stylized airline pricing rule in a congested airport. − qiB''(Q) is the mark-up for the airline market power, and qiv D'(Q,K) is the self-internalization of the congestion cost by the airline. Substituting p=B'(Q)-v D(Q, K), indicated by Eq.(5.1), we obtain, τ = B'(Q) − v D(Q,K) − c+QN (B''(Q) − v D'(Q,K))=M(Q) (5.6) From the above derived inverse airport demand function, we can get the derived demand function by converting Eq. (5.6): Q=M −1(τ) (5.7) Totally differentiating both sides of Eq. (5.6) with respect to 𝜏 and rearranging terms we obtain the expression for ∂Q∂τ, we have the following Eq. (5.8): dQdτ=dM −1(τ)dτ−1(1+1N) (v D'(Q) − B''(Q))+QN (v D''(Q,K) − B'''(Q))<0 (5.8) Eq. (5.8) shows that the airport’s derived demand decreases with its aeronautical price τ. 5.2.2 Private Congested Airport An airport maximizes its profit by choosing both the aeronautical charge 𝜏 and the concession price 𝑟. The objective of such airport can be formulated as follows: Max τ, r(τ− c1)Q+(r− c2)(1− G(r,D(Q,K))) Q (5.9) 135 where c1 is the airport marginal operating cost of aeronautical service, and c2 is the airport marginal operating cost of concession service. From FOC., the aeronautical charge 𝜏 can be written as, τ=c1+ (1+1N) [vQD'(Q,K)B''(Q)Q]+Q2N(vD''(Q,K) − B'''(Q)) − (r− c2) [(1− G(r,D)) − Q∂G∂D∂D∂Q] (5.10) where (r-c2)[(1-G(r,D))-Q∂G∂D∂D∂Q] is the term from airport concession operation. If ∂G∂D<0 (i.e. ∂1-G∂D>0) as we assumed to be the case when airport congestion is low, airport congestion increases the concession demand, making (r− c2) [(1− G(r,D)) − Q∂G∂D∂D∂Q]>0 . Therefore, airport concession operation exerts a downward pressure on aeronautical price. But, if ∂G∂D>0 (i.e., ∂1-G∂D<0), it is possible that (r-c2) [(1-G(r,D))-Q∂G∂D∂D∂Q]<0, such that τ can be higher to reduce congestion so as to increase concession demand. The optimal r for a private airport is given by: r=c2+1∂G∂r(1− G(r,D)) (5.11) The derivative of r with respect to Q is as follows: ∂r∂Q=∂G∂D∂D∂Q+(r − c2)∂2G∂r∂D∂D∂Q−[2∂G∂r+(r − c2)∂2G∂r2] (5.12) 136 The denominator is −[2∂G∂r+(r− c2)∂2G∂r2]<0 from the Second Order Condition (SOC) of airport profit with respect to r. Therefore, when ∂G∂D< 0 and ∂2G∂r∂D<0, in the case where the concession consumption increases with congestion, we obtain ∂r∂Q> 0. When ∂G∂D> 0 and ∂2G∂r∂D>0, in the case where the concession consumption increases with congestion, we obtain ∂r∂Q< 0. 5.2.3 Public Congested Airport The public airport’s objective is to maximize social welfare as shown below: Maxτ,rSW=B(Q) − Qv D(Q,K) − (c+c1)Q+(∫ xg(x,D)1-G(r,D)dx− c2)(1 − G(r,D))Qer (5.13) It can be shown that the aeronautical charge 𝜏 is equal to: τ=c1+QNB''(Q)+(1−1N)vQD'(Q) − [E(x| x>r, D) − c2] [1−G(r,D) − Q∂G∂D∂D∂Q] − [∂D∂Q∂∂DE(x |x>r, D)] (1− G(r,D))Q (5.14) ∂∂DE(x |x>r, D)>(<)0 if ∂G∂D<(>)0. Thus, when congestion is low or moderate, airport concession operation creates a downward pressure on aeronautical price, whereas when congestion is severe, the airport sets a higher aeronautical price to alleviate congestion and to stimulate passengers’ concession consumption. The optimal r for public airport is equal to: −rg(r,D)+c2∂G(r,D)∂r=0 (5.15) 137 Since ∂G(r,D)∂r=g(r,D), we thus have r=c2 for a public airport. The concession price is independent of airport congestion level. For public airports, as shown in Appendix D2, we can conclude that ∂τ∂r< 0 when congestion is low or moderate, and ∂τ∂r> 0 when congestion is severe. From Eq. (5.10) and Eq. (5.14), we have following Proposition 5.1. Proposition 5.1. For both private and public airports, when airport congestion is low or moderate and the concession consumption increases with airport congestion (dwell time effect is dominant), there is a cross-subsidization such that the airport lowers its aeronautical charge to induce a higher traffic volume and a demand increase for concession services. When airport congestion is severe and concession consumption decreases with airport congestion (stress effect is dominant), it is possible for an airport to charge a higher aeronautical price to alleviate congestion and to stimulate concession consumption. Proposition 5.1 highlights a possibility for airports to charge a higher aeronautical price in the presence of concession operations. This proposition extends the stylized analytical findings of Zhang and Zhang (2003, 2010), Oum et al. (2004) and Fu and Zhang (2010), and the empirical findings of Choo (2014) on cross-subsidization between aeronautical and concession services. This is because if one acknowledges the adverse stress effect of airport congestion on concession demand, in order to gain optimal profit or social welfare, airports can increase their aeronautical charges to decrease congestion in order to stimulate concession demand. To compare the aeronautical and concession prices between private and public airports, we present the following set of Propositions 5.2 a and 5.2 b, derived in Appendix D3. Proposition 5.2 a. When airport congestion is low or moderate (dwell time effect is dominant), a public airport charges lower aeronautical charges than a private airport. However, when congestion is severe (stress effect is dominant), it is possible for a public airport to charge a higher aeronautical price than a private airport. 138 Proposition 5.2 b: A public airport should charge a lower concession price than a private airport regardless of the airport congestion level. Existing research with stylized airport pricing models indicates that private airports charge a higher aeronautical price than public airports (e.g. Zhang and Zhang, 2003). The reasons are twofold. First, as a monopoly, private airports charge a markup on aeronautical price to maximize profit. Second, a welfare maximizing public airport has to lower its aeronautical charges to subsidize airlines with market power in the downstream. Our Proposition 5.2 suggests that when airport congestion can adversely affect passenger concession demand, public airports can have stronger incentives to raise aeronautical charges to alleviate airport congestion so as to guarantee more surplus gain from passengers’ concession consumption. It is thus possible for a public airport to set a higher aeronautical price. Such pricing rules narrow the aeronautical price gap between public and private airports. In addition, from Eq. (5.12), we generate the following Proposition 5.3. Proposition 5.3: When we model airport congestion as a function of passenger volume, we predict that given airport capacity, airport concession price and passenger volume should have an inverted U-shaped relationship. 5.3 Empirical estimation 5.3.1 The econometric model In this section, we carry out an econometric estimation to verify the dwell time and stress effects, and to test our propositions. We refer to our economic model for the variable choices. We also include other factors that are not explicitly included in the theoretical model, such as airport competition and the weather conditions. Log-linear equations are adopted so as to simplify the identification and estimation, while allowing the nonlinearity of functions. Specifically, our system of equations includes: (i). the airport demand equation; (ii). the aeronautical price equation; and 139 (iii). the concession price equation. The subscript i stands for the airport, j stands for the country, k stands for the continent (North America, Asia-Pacific and Europe), and t stands for the year. Since existing airport data do not allow us to identify the airport concession price, we use the airport concession revenue per passenger, the variable conrevpaxijkt, as a proxy. The concession revenue per passenger is equivalent to the term r (1-G), which is the product of concession price 𝑟 and individual passenger’s probability for concession consumption 1-G. We show in Appendix D4 that our Proposition 5.3 still holds after replacing the concession price 𝑟 with the concession revenue per passenger term r(1-G).75 Although our propositions are related to airport congestion (the variable 𝐷), there is no available data to measure terminal congestion. For runway congestion (which can be measured by airport average flight delay), the data is unavailable for most of the European and Asian airports. Thus, our empirical tests need to rely on airport capacity K and traffic volume Q, since D is a function of K and Q. This functional relation may be implied by plotting the airport flight delay against the number of passengers per runway for our US airports sample whose flight delay data are available. As shown in Figure D1 of Appendix D, the average flight delay in the US airports has a positive linear relationship with the number of passengers per runway. Similarly, since terminal congestion is not directly observable, we also utilize terminal size and passenger number to infer terminal congestion. The airport demand equation is built based on Eq.(5.6) and Eq. (5.7). lnpsgtotalijkt=α0+α1 lnaeroatmijkt+α2 lngdpijkt+ α3 lnpop ijkt+ α4 lncluster ijk+ α5 lndominant ijkt+ α6 LCCijkt+ α7 lnintershare ijkt+ϕ1j+η1k+ν1t+ψ1i+ε1ijkt (5.16) From Eq. (5.7), the airport demand psgtotalijkt is a function of airport aeronautical price aeroatmijkt. The sign of the parameter α1 is the price elasticity of derived air travel demand with respect to 75 From Proposition 5.2 b, we know that a public airport charges a lower concession price 𝑟 than does a private airport. However, for concession revenue per passenger r (1-G(r,D)), a public airport may have a higher value, since the chance of concession purchase (1-G(r,D)) increases with lower 𝑟. 140 airport aeronautical charge, which should be negative according to Eq. (5.8). Since we assume air travel demand to be independent of airport concession price with “myopic” passengers (Zhang and Zhang, 2003; Oum et al., 2004) as in Eq. (5.1), the concession price does not enter Eq. (5.16). 76 To control for airport competition with nearby airports, we count the number of airports located within 100-km radius for each sampled airport using the variable clusterijk.77 The variables gdpijkt and pop ijkt are the GDP and the population of the city where the airport is located. dominant ijkt is the dominant airline’s market share in the airport. LCCijkt is a dummy that captures the presence of LCCs in the airport. Both dominant ijkt and LCCijkt are used to capture the airline market structure and its impact on airport demand. Finally, intershare ijkt measures the share of international passengers. The airport aeronautical price equation Eq.(5.17) is based on Eq. (5.10) and Eq. (5.14). lnaerotamijkt= β0+β1 lnpsgtotalijkt+ β2 lnconrevpaxijkt+ β3 lnunitcostijkt+ β4 Publicijk + β5 lnrunways ijkt+ β6 lnterminalsize ijkt+ β7 lncluster ijk+ β8 lnpop ijkt+β9 lngdpijkt + β10 lndominant ijkt + β11 LCCijkt+ β12 lnintershare ijkt+ β13 Pricecapijk+ β14 RORijk + β15 Singletillijk+β16 Dualtillijk+ϕ2j+η2k+ν2t+ψ2i+ε2ijkt (5.17) To measure aeronautical price, we use the aeronautical revenue per aircraft movement (Bilotkach et al., 2012; Van Dender, 2007).78 Following Eq. (5.10) and Eq. (5.14), the aeronautical price is a 76 Czerny (2006) models the airport travel demand as a function of the airport concession price. This implies that passengers, especially business passengers, may well decide upon traveling based on entire trip costs for both tickets and concession price. Czerny et al. (2016), for instance, find empirical evidence that one-dollar increase in daily car rental price reduces 0.36% airport demand by studying 199 US airports. 77 Small regional airports with yearly passenger number smaller than 150,000 are not counted (Bel and Fageda, 2010). 78 Airport aeronautical revenue consists mainly of landing charge and terminal fee. The landing charge is on aircraft movement basis, and the terminal fee is normally on per passenger basis. Since the landing charge is the major component of the aeronautical revenue, we use the aeronautical revenue per aircraft movement (ATM) to measure aeronautical price. 141 function of both airport passenger volume and airport concession price. Proposition 5.1 suggests that the concession price can have different effects on aeronautical price, depending on airport congestion levels. Thus, the sign of β2 is uncertain. Following Proposition 5.2, public ownership also has a mixed effect on airport aeronautical price, making the sign of β4 uncertain as well.79 In addition, we control for the effect of airport price regulations: the price cap, rate-of-return, single-till, and dual-till. The airport concession price equation Eq. (5.18) is based on Eq. (5.11) and Eq. (5.15) and can be written as follows. lnconrevpaxijkt= λ0 + λ1 lnpsgtotalijkt + λ2 lnpsgtotal_2ijkt+ λ3 lnrunwaysijkt + λ4 lnterminalsizeijkt + λ5 lngdpijkt+ λ6 LCCijkt+ λ7 lnintershare ijkt+ λ8 Publicijk + λ9 Pricecapijk+ λ10 RORijk+ λ11Singletillijk+ λ12 Dualtillijk + ϕ3j+ η3k+ ν3t+ ψ3i+ ε3ijkt (5.18) Proposition 5.3 indicates that concession price has an inverted U-shaped relationship with airport passenger volume. We thus expect a positive λ1 and negative λ2 in Eq. (5.18). In Appendix D1, we also show that an increase in runway capacity should negatively affect concession price (a negative λ3 ), and larger terminal size should positively affect concession price (a positive λ4 ). Airport ownership and price regulation are also controlled for in the concession price equation Eq. (5.18). The proposed system of equations can be re-written as follows. lnpsgtotalijkt=α1 lnaeroatmijkt+X1ijktδ1+Z1ijktτ1+ϕ1j+η1k+ν1t+ ψ1i+ε1ijkt (5.19) 79 In order to directly verify Propositions 5.1 and 5.2, we need to incorporate interaction terms between lnconrevpaxijkt, Publicijk and airport congestion variables measured by lnpsgtotalijkt, lnrunways ijkt and lnterminalsize ijkt. The signs of these interaction terms could indicate how airport congestion moderates the effect of concession price and public ownership on aeronautical price, as stated in Propositions 5.1 and 5.2. However, the variables lnconrevpaxijkt, lnpsgtotalijkt and lnterminalsize ijkt are all endogenous, making the interaction terms also endogenous in the system of equations. The inclusion of these additional endogenous interaction terms actually fails our identification condition for the aeronautical price equation. Therefore, our estimation of β2 and β4 in Eq. (5.17) should be interpreted as the overall effect of concession price and airport public ownership on aeronautical prices, conditional on the average congestion levels among our sample airports. 142 lnaeroatmijkt=β1 lnpsgtotalijkt+ β2 lnconrevpaxijkt+ β3 lnterminalsizeijkt+X2ijkt δ2 +Z2ijkt τ2+ϕ2j+η2k+ ν2t+ψ2i+ε2ijkt (5.20) lnconrevpaxijkt=λ1 lnpsgtotalijkt+ λ2 lnpsgtotal_2ijkt + λ4 lnterminalsizeijkt +X3ijkt δ3+Z3ijkt τ3+ϕ3j+η3k+ν3t+ψ3i+ε3ijkt (5.21) These three equations can be written in the following matrix form. [1 −α1 0−β11 −β2−λ1 −λ2 1 0−β3−λ4 00−λ2]Yijkt= [X1ijktX2ijktX3ijkt Z1ijktZ2ijktZ3ijkt] [δ1 δ2τ1 τ2 δ3 τ3]+ [ϕ1j+η1k+ν1t+ψ1i+ε1ijktϕ2j+η2k+ν2t+ψ2i+ε2ijktϕ3j+η3k+ν3t+ψ3i+ε3ijkt] (5.22) The airport traffic volume, psgtotalijkt, aeronautical price, aeroatmijkt , concession price, conrevpaxijkt, are endogenous given their simultaneity relationship indicated in our model. Squared passenger number, psgtotal_2ijkt, is also endogenous as function of airport traffic volume. Terminal size, terminalsizeijkt is also treated as endogenous since airports have some flexibility to adjust it in relatively shorter term through expansion or renovation. Runway capacity instead is more fixed since runway investment is lumpy and takes a long time (Oum and Zhang, 1990; Xiao et al., 2013; Xiao et al., 2017). Thus, the number of runways is treated as exogenous. Xijkt=[X1ijkt, X2ijkt, X3ijkt, Z1ijkt, Z2ijkt, Z2ijkt]' are exogenous variables satisfying the mean independence condition E[Xijkt εijkt]=0, where εijkt=[ε1ijkt, ε2ijkt, ε3ijkt ]'. Xijkt are the exogenous variables included in all the three equations, while Zijkt are the exogenous variables only included in one of the equations so that they can serve as instrument variables for endogenous variables in the other equations. The demand equation, Eq.(5.16), only contains one endogenous variable, the 143 aeronautical price; aeronautical pricing equation, Eq.(5.17) contains three endogenous variables: airport passenger volume, concession price and terminal size. Concession pricing equation, Eq. (5.18) contains three endogenous variables, airport passenger volume, squared passenger volume and terminal size. We do not assume mean independence between Xijkt and ϕj, ηk, νt. Country, continent and year dummies are used to control for the fixed effect of ϕj, ηk and νt . However, it is assumed that E[Xijkt ψi]=0 , and thus the airport specific unobservables are orthogonal to our independent variables. Yet, because most time-invariant unobservables such as country, continent, and the time-variant year effects have been controlled, the airport specific unobservable ψi could be orthogonal to a large degree. 80 The identification condition is satisfied for each equation. To estimate the equations, we try both a system GMM (three-stage least square) and an equation-by-equation GMM estimation strategies (two-stage least square). 81 For Eq. (5.16), Z2ijkt and Z3ijkt can be used as instruments for the endogenous variable. For Eq. (5.17), Z1ijkt and Z3ijkt can be used as instruments for the endogenous variables. For Eq. (5.18), Z1ijkt and Z2ijkt can be used as instruments for the endogenous variables. To improve efficiency of the estimation, we also include additional exogenous variables, for example, the yearly average rainfall and snowfall of the airports, as instrument variables. 80 Although a fully fixed effect model (FE) can control for airport specific unobservable ψi, thus relaxing the assumption E[Xijkt ψi]=0, the FE model does not allow us to identify coefficients of several time-invariant factors such as ownership and airport regulation. 81 Three-stage least square (3SLS) is used to estimate the equations simultaneously with the optimal GMM weight matrix incorporating information from all three equations, whereas a two-stage least square (2SLS) method is applied to each equation individually with random effect (RE), which is a GMM method but only utilizing equation-by-equation information. Both 3SLS and 2SLS estimators should be consistent under our assumption, while 3SLS can produce more efficient estimates. 144 5.3.2 Data description Air Transport Research Society (ATRS) airport database is our primary source for the detailed airport operational and financial data. It includes a large sample of North American, European and Asia Pacific airports.82 Specifically, the airport financial data we retrieved include the airport aeronautical revenues, concession revenues and operating expenses. The airport traffic data include the airport total passenger number, cargo volume, aircraft movements and the share of international passengers. The general airport information includes the number of runways, terminal size and airport ownership. Since we study the congested airports, we complement the ATRS data with information gathered from the Airline Business magazine database which collects statistics on the top 100 world busiest airports. These airports are capacity constrained and subject to some degree of airport congestion. We choose the airports that are present in both the ATRS and Airline Business databases for the period 2008-2012, leading to an unbalanced dataset of 253 observations for a total of 61 sample airports (16 Asia-Pacific airports, 13 European airports, and 32 North American airports). The list of the 61 sample airports is provided in Table D1 of Appendix D. All the Asian, European and Canadian airports are categorized as the level 3 slot-coordinated airports by IATA (International Air Transport Association), which means that these airports are highly congested and thus strict rules of slot allocation are required. 83 Some very congested US airports such as JFK, EWR, LAX, MCO, ORD and SFO, are also categorized as Level 2 and 3 slot coordinated by IATA. The other selected US airports also experience considerable congestion problems. 82 Each year, ATRS collects airport data and performs a due diligence check through the airport annual reports, industry reports and even direct contact with the airports. Since year 2002, ATRS annually publishes the ATRS Global Airport Benchmarking Report ranking the sampled airports around world in operational efficiency. In its annual ATRS World Conference, the award airports were recognized. For the more details about ATRS and its published report and database, please check its official website: http://www.atrsworld.org/. 83 Based on the IATA’s Worldwide Slot Guideline (WSG), Level 2 airports are airports where there is potential for congestion during some periods of the day, week or season which can be resolved by schedule adjustments mutually agreed between the airlines and facilitator. A facilitator is appointed to facilitate the planned operations of airlines using or planning to use the airport. Level 3 airports are airports where capacity providers have not developed sufficient infrastructure, or where governments have imposed conditions that make it impossible to meet demand. A coordinator is appointed to allocate slots to airlines and other aircraft operators using or planning to use the airport as a means of managing the declared capacity. 145 The Airline Business magazine database reports the market shares of the top three airlines in each airport. Airports with a significantly dominant airline are more likely to face a concentrated downstream airline market, and more likely to be an important hub for the dominant carrier. Our GDP and population data for different countries and regions were obtained from different sources. The population and GDP are collected from the US Bureau of Economic Analysis (BEA) and the US Census Bureau for the US airports, from Statistics Canada for Canadian airports, from EuroStat for European airports, and finally from the OECD and the World Bank databases for airports in the other countries. Data on airport ownership was also taken from the ATRS database. Among the 61 sample airports, 20 airports are fully or partially privatized. For the airport regulation regimes, we searched for the price regulation types of each airport, i.e. price-cap, rate-of-return (ROR) or light-handed (no specific regulation). We then distinguish the scope of such price regulation assessing whether concession side is included in the price regulation, i.e. single-till or dual-till regulation. 84 The civil aviation authority websites, airport annual reports, industry reports, and academic papers on airport regulation were used to collect and verify information on price regulation for our sampled airports. The detailed variable definition and summary statistics are reported in Table 5.1. 84 In the US instead of the single and dual till regulation, some airports adopt residual cost-plus rule which is equivalent to single-till while other airports adopt a compensatory cost-plus rule which corresponds to dual-till regulation (Oum et al., 2004). 146 Table 5.1 Summary statistics Variables Brief description Obs. Mean Std. Dev. Min Max Endogenous variables psgtotalijkt Total annual passengers in millions 253 35.2 16.3 13.0 90.0 aeroatmijkt Aeronautical revenue (in USD) per aircraft movement 253 924.4 792.4 130.6 4851.4 conrevpaxijkt Concession revenue (in USD) per passenger 253 3.58 3.27 0.43 19.14 terminalsize ijkt Terminal size (in m2) 253 3,75,530 251,746 12,888 1,400,000 Exogeneous variables gdpijkt Annual GDP (billions USD) of the airport metropolitan area 253 339 349 30 1500 pop ijkt Total population (millions) of the airport metropolitan area 253 7.24 6.65 1.1 35 cluster ijk The number of other airports within 100 km radius area 253 2.22 1.07 1 5 dominant ijkt Market share of the largest dominant airline 253 35.25% 0.132 11.12% 84.92% LCCijkt Dummy (1 = one of the top three dominant carriers is a low-cost carrier) 253 0.241 0.429 0 1 intershare ijkt Share of the international passengers (percentage) 253 37.79% 0.339 0.2% 100% unitcostijkt Total operating expenses (USD) per passenger 253 9.40 6.24 1.83 36.36 147 Variables Brief description Obs. Mean Std. Dev. Min Max publicijk Dummy (1 = 100% publicly owned airport) 253 0.67 0.47 0 1 runwaysijkt The number of runways 253 3.31 1.43 1 7 pricecapijk Dummy (1 = airport subjected to price-cap regulation; 0 = airport subjected to rate-of-return regulation or no regulation) 253 0.18 0.38 0 1 RORijk Dummy (1 = airport subjected to rate-of-return regulation; 0 = airport subjected to price-cap regulation or no regulation) 253 0.07 0.26 0 1 singletillijk Dummy (1 = airport adopt single-till approach; 0 = airport adopt dual-till approach or no regulation) 253 0.57 0.50 0 1 dualtillijk Dummy (1 = airport adopt dual-till approach; 0 = airport adopt single-till approach or no regulation) 253 0.23 0.42 0 1 148 5.4 Empirical estimation results Demand equation estimations are summarized in Table 5.2. Aeronautical charge has a negative and statistically significant effect on passenger volume with both two-stage least square (2SLS) and three-stage least square (3SLS) estimations. But the magnitude of the price elasticity estimate is very small, probably because airport charge accounts for only a very small fraction of airline total costs. Airport competition, indicated by the number of nearby airports, also has a significantly negative effect on airport passenger demand. In addition, airline dominance in the airport seems to stimulate airport passenger volume. This result could be attributed to the fact that a major hub can consolidate and connect more passengers. The share of international passengers has a significantly positive effect. GDP and population are found to contribute to higher air travel demand. It is also noted that LCC variable in 3SLS is significantly negative. This is as expected as the demand function is derived from passenger’s utility function, and LCC provides inferior service quality compared to full service carrier (FSC) after we have controlled for the other demand variables. 85 Table 5.2 The estimation for the demand equation 2SLS 3SLS Explanatory Variables Coef. Std. Err. Coef. Std. Err. Aeronautical price -0.310*** 0.089 -0.144** 0.063 GDP 0.536*** 0.069 -0.117 0.129 Population -0.112 0.103 0.368*** 0.137 Nearby airports -0.175* 0.101 -0.222*** 0.054 Dominant airline share 0.104* 0.056 0.094* 0.060 LCC 0.004 0.033 -0.174*** 0.055 % of international passenger 0.048** 0.023 0.181*** 0.028 Year 2009 -0.023 0.015 -0.040 0.056 Year 2010 0.003 0.017 0.013 0.057 Year 2011 0.019 0.019 0.055 0.058 Year 2012 0.029 0.021 0.200*** 0.068 EU airports 0.647** 0.329 -0.965*** 0.234 NA airports -0.397** 0.194 -0.251 0.136 85 The LCC variable may be subject to endogeneity concern as LCC may self-select to enter uncongested airports charging lower airport charges. We have checked the simple correlations between the LCC dummy variable and the airport traffic and number of passenger per runway and terminal size, and airport pricing. And all these correlation values have absolute magnitude smaller than 0.2. There is no strong empirical evidence the LCC presence is due to airline self selection. Instead, it is more likely due to regional unbalanced LCC development condition and local air travel demand structure affecting LCC dominance at one airport. 149 Note: 1. *** for 1%, ** for 5% and * for 10% significance level. 2. To make a clear expression, the variables that are specified in logarithm form in the estimation are omitted in the table. 3. Coefficients estimates for the country and continent dummies are removed for parsimony. The estimation results for the aeronautical price equation are reported in Table 5.3. First, the concession price is found to negatively affect aeronautical charges. Overall, airport congestion for our sampled airports has not seriously dampened the concession demand and thus has not motivated the congested airports to charge higher aeronautical price in presence of concession operation (highlighted in Proposition 5.1). Thus, the stylized findings of cross-subsidization between aeronautical and concession prices still hold among our sampled congested airports. In line with Proposition 5.2, public airports appear to charge a lower aeronautical price as indicated by our 3SLS result. Although we assume a public airport to maximize social welfare without cost recovery constraint, in reality, most public airports are supposed to be self-financed and to reach a break-even (Zhang and Zhang, 2010; Yang and Fu, 2015). Such budget constraint imposed upon the public airports can result in a pricing behavior lying between a purely social welfare-maximizing public airport and a purely profit-maximizing private airport. In addition, the airport unit cost is found to be an essential determinant of the aeronautical charge. This contributes an important addition to the existing empirical airport studies (Bel and Fageda, 2010; Bilotkach et. al, 2012; Van Dender, 2007) which were not able to explicitly control for airport cost due to data availability. From the 3SLS estimation, we find that price-cap regulation lowers airport aeronautical charges, while the effect of the ROR regulation is statistically insignificant. Both single-till and dual-till regulations lower aeronautical price, while single-till has a stronger effect because concession profit is also considered in determining aeronautical pricing. The effects of airport capacity variables, number of runways and terminal size, on airport aeronautical charges are not statistically significant. As in both Bel and Fageda (2010) and Van Dender (2007) we also do not find significant impact of the dominance of airlines on the airport aeronautical charge. 150 Table 5.3 The estimation for the aeronautical price equation 2SLS 3SLS Explanatory variables Coef. Std. Err. Coef. Std. Err. Airport passenger volume 1.087 0.847 0.403 0.306 Concession price -0.642** 0.301 -0.343*** 0.111 Unit operating cost 1.321*** 0.383 1.279*** 0.069 Public ownership 0.716 0.680 -1.730* 0.969 Number of runways -0.440 0.399 0.144 0.105 Terminal size -0.035 0.146 -0.224 0.251 Nearby airports 0.213 0.168 -0.027 0.058 Population -0.209 0.209 -0.162 0.166 GDP -0.073 0.209 0.132 0.212 Dominant airline share -0.136 0.152 0.030 0.068 LCC 0.060 0.675 0.140 0.061 % of international passengers 0.072* 0.043 0.159*** 0.034 Pricecap regulation 0.287 0.628 -1.754* 0.969 ROR regulation -0.186 0.789 -0.303 0.555 Singletill regulation -0.908** 0.447 -0.713*** 0.211 Dualtill regulation -0.873* 0.498 -0.615*** 0.173 Year 2009 0.109* 0.057 0.093 0.060 Year 2010 0.120** 0.048 0.104* 0.061 Year 2011 0.121*** 0.449 0.092 0.062 Year 2012 0.127** 0.055 0.120 0.078 EU airports -0.847 0.573 -0.321 0.555 NA airports -1.337 0.620 0.482 1.043 Note: 1. *** for 1%, ** for 5% and * for 10% significance level. 2. To make a clear expression, the variables that are taken logoritim in the estimation are not specifically claimed in the table. 3. Coefficients estimate for the country and continent dummies are removed for parsimony. Table 5.4 collates the estimation results of our concession price equation, which help verify the existence of dwell time and stress effects. Both the 2SLS and 3SLS estimations confirm Proposition 5.3. The concession price first increases with airport passenger volume and then decreases, with an existence of the inverted U-shaped relationship between concession price and airport passenger volume given the airport capacity. Using the estimated coefficients, we draw the inverted U-shaped relation between airport passenger volume and concession price as shown in Figure 5.3. The concession price reaches its peak when airport passenger number reaches around 30 million per year. This is about the median passenger volume for our 61 sample airports. 151 Table 5.4 The estimation of concession pricing equation 2SLS 3SLS Explanatory variables Coef. Std. Err. Coef. Std. Err Airport passenger volume 3.759*** 0.176 2.821** 1.143 Squared passenger volume -1.560** 0.546 -1.237*** 0.422 Terminal Size 0.616*** 0.176 0.665*** 0.148 Number of runways -0.435** 0.183 -0.412*** 0.155 GDP 0.063 0.074 0.066 0.063 LCC 0.296*** 0.100 0.281*** 0.086 % of international passengers -0.163* 0.088 -0.133* 0.072 Public ownership 1.350** 0.649 2.359 1.348 Pricecap regulation 0.716 0.764 1.638** 0.792 ROR regulation 0.776* 0.446 2.040*** 0.473 Singletill regulation -1.530*** 0.319 -1.431*** 0.266 Dualtill regulation -1.963*** 0.353 -1.872*** 0.296 Year 2009 0.001 0.102 -0.016 0.086 Year 2010 -0.081 0.103 -0.086 0.878 Year 2011 -0.039 0.104 -0.041 0.890 Year 2012 -0.061 0.127 -0.053 0.108 EU airports 1.160*** 0.375 -0.266 0.497 NA airports -0.909 0.592 -1.989*** 0.597 Note: 1. *** for 1%, ** for 5% and * for 10% significance level. 2. To make a clear expression, the variables that are taken logoritim in the estimation are not specifically claimed in the table. 3. Coefficients estimate for the country and continent dummies are removed for parsimony. 152 Figure 5.3 Estimated inverted U-shaped curve between airport passenger volume and concession revenue per passenger The concession price estimations also show that runway capacity has a significantly negative effect on concession price while terminal capacity has a significantly positive effect on concession price. Such results are consistent with the predictions in Appendix D1. Runway congestion contributes mainly to the dwell time effect which increases the concession demand. Terminal congestion is more associated with the stress effect, leading to lower concession demand. In addition, for airports with significant LCC presence, concession price increases, implying a higher concession demand for leisure rather than for business passengers. Higher share of international passengers has a negative effect on concession demand, probably because international flights involve more connection passengers who have time constraint to shop and have no car rental demand. 86 86 Unfortunately, we are unable to access the detailed data about the airport transfer-passenger share, preventing us to explicitly control for this flight transfer effect. 153 5.5 Summary and concluding remarks This chapter investigates the airport congestion effect on concession demand, and its impact on airports’ optimal aeronautical and concession service pricing. In particular, we identify two countervailing effects of airport congestion on concession demand: the dwell time effect and the stress effect. The dwell time effect draws on previous work by D'Alfonso et al. (2013) and Wan et al. (2015) arguing that the airport congestion can lengthen passengers’ stay at the airport, and thus, increase their concession consumption. For the first time, this chapter identifies the stress effect, which has a negative effect on concession demand. This stress effect can be attributed to mental stress and service quality deterioration when airports become overcrowded. The empirical evidences of the 61 congested airports worldwide support the existence of both dwell time effect and stress effect. Because of the presence of the stress factor, we propose and find an inverted U-shaped relation between passenger volume and the concession demand and price. In addition, runway and terminal congestions have opposite effects on concession demand and price. Runway congestion contributes more to the dwell time effect, raising concession demand and price. But terminal congestion generates more stress and thus affects negatively concession demand and price. For the sample covered, the airport concession pricing reaches its peak for a 30-million-passenger airport as revealed by our estimation. In addition, complementing the existing airport pricing studies, we conclude that, when the stress effect dominates, it is possible for an airport to charge a higher aeronautical price in order to reduce airport congestion, and thereby, to stimulate concession demand. This adds to the stylized findings on the cross-subsidization of aeronautical services by concession operation (Zhang and Zhang, 2003, 2010; Oum et al. 2004). Second, we argue that it is also possible for a public airport to charge higher aeronautical price when the stress effect of airport congestion prevails, contrary to previous studies sustaining a lower aeronautical price for public airports. This chapter also raises several other issues and avenues for future research. First, we assume that airports directly stipulate concession price. In practice, airports can be the landlord signing rental and revenue sharing contracts with concession service providers such as car rental companies, duty 154 free stores, and other retail chains. Therefore, the market structure of the concession service providers and the vertical relationships can affect the concession price. However, the data on concession service market structure are not available. Future studies are called for to tackle this issue. Second, because the data on terminal congestion are unavailable, and the runway congestion data are not accessible for the European and Asian airports, we empirically test the congestion effect using the airport capacity and passenger volumes variables. Future studies could be carried out for an accurate measurement of airport terminal congestion, and then directly test the airport congestion effect on airport concession demand and price. 155 Chapter 6. Conclusion This dissertation explores three major research topics in transportation economics: (i). seaport investments for adaptation to climate change related disasters; (ii). airline and high-speed rail (HSR) competition; and (iii). airline competition and airport pricing. The dissertation contributes to the related literature by providing rigorous theoretical analysis and empirical evidences to a few important problems that have been overlooked or not well studied. First, we model the port adaptation to climate change related disasters, considering the inter- and intra- port competition and cooperation. More importantly, we adopt the Knightian uncertain to describe the disaster occurrence uncertainty, which is able to capture a more general and wider family of probability distributions, not limited to the specific assumptions in Weitzman (2009) and Xiao et al. (2015). We also explicitly model endogenous port pricing and shippers’ demand with port adaptation. The chapter is essential to add to literature by answering how inter-port competition and intra-port cooperation can affect port adaptation besides the impact of disaster uncertainty. We find, with Knightian uncertainty assumption, the port adaptation investments increase with the expectation of the disaster occurrence probability but decrease with its variance. Inter-port competition results in more adaptation investment (i.e., the competition effect). There is free-riding between the port authority and the terminal operator (i.e., the free-riding effect) within each port. Their coordination can increase the adaptation by removing such free-riding effect. The expected social welfare of the two-port region increases with ports’ adaptation, such that inter-port competition, and intra-port coordination lead to higher expected social welfare. The second topic of this dissertation is on the air-HSR competition. Specifically, we investigate, both theoretically and empirically, the effect of HSR speed on airline traffic and price, taking into account the degree of air-HSR service substitutability. This is the first study to explore how airline and HSR service substitutability can alter HSR speed effect on airline traffic and price. We also consider two countervailing effects of HSR speed on airlines, i.e., travel-time and safety effect. The empirical evidence from a rare natural experiment in HSR speed reduction in China is used to empirically verify the theoretical findings. We find that HSR speed effect is stronger when airline and HSR services are more substitutable (i.e., on short-haul routes). The HSR speed effect depends on the relative dominance of travel-time and safety effect. And HSR speed reduction increases 156 airline traffic and price when travel-time effect dominates, while it reduces airline traffic and price when safety effect dominates. The last topic addresses two important issues in the air transport economics, namely the airlines competition under legacy regulation, and airport concession pricing with airport congestion. First, a structural discrete-choice model is developed to study airline competition in Chinese domestic market, explicitly taking into account the potential effects of legacy regulation on airlines’ competition behavior. This work constitutes an improved econometric approach that allows researchers to identify a range of competitive regimes for different group of routes. This allows us to measure possible effects of the legacy regulation and to benchmark the results obtained under restrictive Bertrand or Cournot competition. We find that Chinese airlines set prices collusively on the densest (with highest traffic volume) routes where regulatory control is stricter and airport congestion is severer; by contrast, they compete more aggressively on less travelled routes with lighter regulatory control. There is also strong evidence that the presented new approach performs better than the existing competition models in terms of obtaining better results on estimation and prediction. This may suggest that simply assuming a particular type of competition regime for a market may yield biased estimation. Second, we explore the effect of airport congestion on airport’s concession revenue, and optimal airport pricing on both aeronautical and concession services. We conduct both analytical and empirical investigations, proposing two countervailing effects of airport congestion on concession demand, i.e., dwell-time effect that passengers consume more when airport congestion forces them to stay longer at airport, and the stress effect that passengers are unwilling to spend at airport when they are under stress caused by the flight delay or crowdedness. The optimal aeronautical and concession charges of two types of airports: a private profit-maximizing airport and a public social-welfare maximizing airport are investigated. We find that when airport congestion is severe, and the stress effect prevails, it is possible that public airports charge a higher aeronautical price than private airports. This finding complements previous studies, which ignore airport congestion effect on concession demand and suggest that public airport always charges lower aeronautical price. In addition, empirical evidence supports the existence of both dwell-time and stress effects of airport congestion on concession demand and price. We also find that runway congestion contributes more to dwell time effect while terminal congestion contributes more to stress effect. 157 This dissertation also opens avenues for future research on several related issues. For the first topic, we assume that each port has a single terminal operator, which could be restrictive. One port can have more than one terminal operator, either private or owned by port authority. Some shipping lines also operate dedicated terminals. In addition, multinational terminal operators such as PSA International, Hutchison Port Holding, APM terminals, DP World and China Merchant Holding can simultaneously operate in several nearby ports. Such intra- and inter-port competition, and inter-port cooperation among private terminal operators can be better accounted for in the future study when analyzing port adaptation. Second, public ownership of port authority and its implication on port adaptation may be also investigated. Although we have explained in Chapter 2 why we focus on private port authorities, the port authority can also be publicly owned and bear social responsibility. It is reasonable to conjecture that public port authority could invest more on adaptation, especially when port adaptation can have positive externality to protect nearby neighborhood community and contribute to a more resilient local economy beyond protecting shippers’ economic benefits. For the second topic, the HSR price is treated as fixed as we are using Chinese market data where government regulates the HSR price. This prevents the investigation on the strategic behavior of HSR. Future study is thus called for on those markets with the HSR being free to decide price. The HSR speed effect on HSR operating cost and its full impact on air-HSR competition can then be identified. Second, we have not considered airline and HSR frequencies adjustment. Yang and Zhang (2012) and D’Alfonso et al (2015) model airline and HSR competing on frequencies. Airline and HSR frequencies are important service quality variables. HSR speed change could also change airline and HSR schedules and frequencies. The frequency and schedule information of airline and HSR in China is difficult to retrieve. Future effort is suggested to take into account frequency and schedule for HSR speed effect estimation. For the last topic, in Chapter 4, although our econometric model highlights the importance to explicitly model the possible effects of competition/operational constraints such as legacy regulation and airport slot limitation, we have not clearly identified the source of the observed pattern, that is, to what extent do specific constraints affect airline competition and market equilibrium in selected (groups of) routes. This problem could have been addressed if detailed regulatory rules can be obtained for each (groups of) route(s). For the airport congestion on 158 concession demand and pricing, we assume that airports directly stipulate concession price. In practice, airports can be the landlord signing rental and revenue sharing contracts with concession service providers such as car rental companies, duty free stores, and other retail chains. Therefore, the market structure of the concession service providers and the vertical relationships can affect the concession price. 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International Journal of Industrial Organization, 29(4), 361-372. 177 Appendices Appendix A: Appendix for Chapter 2 A.1 Optimal terminal operators’ prices and port authorities’ concession fee For the competing port authorities, the FOCs satisfy ∂𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖= 0 . For the monopoly port authority, the FOCs satisfy ∂𝜋𝑖(?̃?𝑖,?̃?𝑗)∂𝜙𝑖⏟ <0+∂𝜋𝑗(?̃?𝑖,?̃?𝑗)∂𝜙𝑖⏟ >0= 0. With the monopoly port authority setting concession fee at one port, it internalizes the positive externality of higher concession fee on the other port i.e. ∂𝜋𝑗(?̃?𝑖,?̃?𝑗)∂𝜙𝑖⏟ >0 and ∂𝜋𝑖(?̃?𝑖,?̃?𝑗)∂𝜙𝑗⏟ >0. In addition, the second-order derivative ∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖 ∂𝜙𝑗> 0, as concession fee at ports is strategic complement. The second-order derivative ∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖2 < 0 as required by SOC. Because of the symmetry, we have ?̃?𝑖 = ?̃?𝑗 and ?̅?𝑖 = ?̅?𝑗. In magnitudes it is true that |∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖2 | > |∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖 ∂𝜙𝑗|. In other words, the second-order derivative ∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖2 is the main effect. Because ∂𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖= 0 and ∂𝜋𝑖(?̃?𝑖,?̃?𝑗)∂𝜙𝑖< 0 , we have ?̃?𝑖 = ?̃?𝑖 > ?̅?𝑖 = ?̅?𝑗 . Terminal operators’ charge 𝑝𝑖(𝜙𝑖, 𝜙𝑗) and 𝑝𝑗(𝜙𝑖, 𝜙𝑗) are increasing function of 𝜙𝑖 and 𝜙𝑗 , such that 𝑝𝑖(?̃?𝑖 , ?̃?𝑖) > 𝑝𝑖(?̅?𝑖 , ?̅?𝑗) and 𝑝𝑗(?̃?𝑖 , ?̃?𝑖) > 𝑝𝑗(?̅?𝑖, ?̅?𝑗). Taking total derivatives of FOCs of competing port authorities with respect to 𝐼𝑖𝑎: ∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖 ∂𝐼𝑖𝑎 +∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖2∂?̅?𝑖∂𝐼𝑖𝑎 +∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖 ∂𝜙𝑗∂?̅?𝑗∂𝐼𝑖𝑎 = 0 ∂2𝜋𝑗(?̅?𝑖,?̅?𝑗)∂𝜙𝑗 ∂𝐼𝑖𝑎 +∂2𝜋𝑖(?̅?𝑖,?̅?𝑗)∂𝜙𝑖 ∂𝜙𝑗∂?̅?𝑖∂𝐼𝑖𝑎 +∂2𝜋𝑗(?̅?𝑖,?̅?𝑗)∂𝜙𝑗2∂?̅?𝑗∂𝐼𝑖𝑎 = 0 Solving ∂?̅?𝑖∂𝐼𝑖𝑎 as follows: ∂?̅?𝑖∂𝐼𝑖𝑎 =−( ∂2𝜋𝑗∂𝜙𝑗2 ∂2𝜋𝑖∂𝜙𝑖 ∂𝐼𝑖𝑎)+∂2𝜋𝑖∂𝜙𝑖 ∂𝜙𝑗 ∂2𝜋𝑗∂𝜙𝑗 ∂𝐼𝑖𝑎∂2𝜋𝑖∂𝜙𝑖2 ∂2𝜋𝑗∂𝜙𝑗2−∂2𝜋𝑖∂𝜙𝑖 ∂𝜙𝑗 ∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗> 0 178 The denominator ∂2𝜋𝑖∂𝜙𝑖2⏟<0 ∂2𝜋𝑗∂𝜙𝑗2⏟<0−∂2𝜋𝑖∂𝜙𝑖 ∂𝜙𝑗⏟ >0 ∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗⏟ >0 is positive, as |∂2𝜋𝑖∂𝜙𝑖2| > |∂2𝜋𝑖∂𝜙𝑖 ∂𝜙𝑗| and |∂2𝜋𝑗∂𝜙𝑗2 | >|∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗| . The numerator −( ∂2𝜋𝑗∂𝜙𝑗2⏟<0 ∂2𝜋𝑖∂𝜙𝑖 ∂𝐼𝑖𝑎⏟ >0) +∂2𝜋𝑖∂𝜙𝑖 ∂𝜙𝑗 ⏟ >0 ∂2𝜋𝑗∂𝜙𝑗 ∂𝐼𝑖𝑎⏟ <0 is also positive, as |∂2𝜋𝑗∂𝜙𝑗2| > |∂2𝜋𝑖∂𝜙𝑖 ∂𝜙𝑗 | and |∂2𝜋𝑖∂𝜙𝑖 ∂𝐼𝑖𝑎 >∂2𝜋𝑗∂𝜙𝑗 ∂𝐼𝑖𝑎 |. Therefore ∂?̅?𝑖∂𝐼𝑖𝑎 > 0. Solving ∂?̅?𝑗∂𝐼𝑖𝑎 as follows: ∂?̅?𝑗∂𝐼𝑖𝑎 =∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗 ∂2𝜋𝑖∂𝜙𝑖 ∂𝐼𝑖𝑎−∂2𝜋𝑖∂𝜙𝑖2 ∂2𝜋𝑗∂𝜙𝑗 ∂𝐼𝑖𝑎∂2𝜋𝑖∂𝜙𝑖2 ∂2𝜋𝑗∂𝜙𝑗2−∂2𝜋𝑖∂𝜙𝑖 ∂𝜙𝑗 ∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗 The denominator of ∂?̅?𝑗∂𝐼𝑖𝑎 is the same as ∂?̅?𝑖∂𝐼𝑖𝑎 , which is positive. Numerator ∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗 ⏟ >0 ∂2𝜋𝑖∂𝜙𝑖 ∂𝐼𝑖𝑎⏟ >0−∂2𝜋𝑖∂𝜙𝑖2⏟<0 ∂2𝜋𝑗∂𝜙𝑗 ∂𝐼𝑖𝑎⏟ <0 has uncertain sign, which depends on the relative magnitude of ∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗 ∂2𝜋𝑖∂𝜙𝑖 ∂𝐼𝑖𝑎 and ∂2𝜋𝑖∂𝜙𝑖2∂2𝜋𝑗∂𝜙𝑗 ∂𝐼𝑖𝑎 . As shown in following Figure A1, when 𝐼𝑖𝑎 increases, the best response function 𝜙𝑗(𝜙𝑖) moves outward, and the best response function 𝜙𝑖(𝜙𝑗) moves downward. If 𝜙𝑖(𝜙𝑗) does not move too much with 𝐼𝑖𝑎, the new equilibrium concession fees increase for both 𝜙𝑖 and 𝜙𝑗. If 𝜙𝑖(𝜙𝑗) moves more with 𝐼𝑖𝑎 , the new equilibrium concession fee 𝜙𝑖 will still increase, but concession fee 𝜙𝑗 will decrease. With the functional form imposed in this study, we can derive that ∂?̅?𝑗∂𝐼𝑖𝑎 < 0. 179 Figure A1 The impact of increased port authority adaptation 𝑰𝒊𝒂 on the best response functions of competing port authorities’ concession fee at operation stage Analogously, we are able to prove ∂?̅?𝑖∂𝐼𝑖𝑡 > 0, and the sign ∂?̅?𝑗∂𝐼𝑖𝑡 depends on the relative magnitude of ∂2𝜋𝑗∂𝜙𝑖 ∂𝜙𝑗 ∂2𝜋𝑖∂𝜙𝑖 ∂𝐼𝑖𝑡 and ∂2𝜋𝑖∂𝜙𝑖2∂2𝜋𝑗∂𝜙𝑗 ∂𝐼𝑖𝑡. With our functional form, it can be derived that ∂?̅?𝑗∂𝐼𝑖𝑡 < 0. Taking total derivatives of FOCs of monopoly port authority with respect to 𝐼𝑖𝑎: ∂2(𝜋𝑖(?̃?𝑖,?̃?𝑗)+𝜋𝑗(?̃?𝑖,?̃?𝑗))∂𝜙𝑖 ∂𝐼𝑖𝑎 +∂2(𝜋𝑖(?̃?𝑖,?̃?𝑗)+𝜋𝑗(?̃?𝑖,?̃?𝑗))∂𝜙𝑖2∂?̃?𝑖∂𝐼𝑖𝑎 +∂2(𝜋𝑖(?̃?𝑖,?̃?𝑗)+𝜋𝑗(?̃?𝑖,?̃?𝑗))∂𝜙𝑖 ∂𝜙𝑗∂?̃?𝑗∂𝐼𝑖𝑎 = 0 ∂2(𝜋𝑖(?̃?𝑖,?̃?𝑗)+𝜋𝑗(?̃?𝑖,?̃?𝑗))∂𝜙𝑗 ∂𝐼𝑖𝑎 +∂2(𝜋𝑖(?̃?𝑖,?̃?𝑗)+𝜋𝑗(?̃?𝑖,?̃?𝑗))∂𝜙𝑖 ∂𝜙𝑗∂?̃?𝑖∂𝐼𝑖𝑎 +∂2(𝜋𝑖(?̃?𝑖,?̃?𝑗)+𝜋𝑗(?̃?𝑖,?̃?𝑗))∂𝜙𝑗2∂?̃?𝑗∂𝐼𝑖𝑎 = 0 Solving ∂?̃?𝑖∂𝐼𝑖𝑎, ∂?̃?𝑖∂𝐼𝑖𝑎 =−( ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗 ∂𝐼𝑖𝑎⏞ <0 ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗⏞ >0) +∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝐼𝑖𝑎⏞ >0∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗2⏞ <0(∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗)2−(∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖2 )(∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗2 )⏟ <0> 0 180 The denominator (∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗)2 − (∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖2 ) (∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗2 ) < 0 , as suggested by the Hessian condition for monopoly port authority to maximize profit. For the numerator, |∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗2 | >|∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗|, and |∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝐼𝑖𝑎 | > |∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗 ∂𝐼𝑖𝑎 |, such that the numerator is positive as well. Solving for ∂?̃?𝑖∂𝐼𝑗𝑎: ∂?̃?𝑖∂𝐼𝑗𝑎 =∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗 ∂𝐼𝑖𝑎⏞ <0 ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖2⏞ <0 − ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗⏞ >0 ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝐼𝑖𝑎⏞ >0(∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗)2−(∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖2 )(∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗2 )⏟ <0 The denominator (∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗)2 − (∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖2 ) (∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗2 ) < 0 . For numerator, |∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗 ∂𝐼𝑖𝑎 | <|∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝐼𝑖𝑎 | and |∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖2 | < |∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗|, thus the sign of the numerator is uncertain. We thus have to depend on our functional setup to determine the sign of ∂?̃?𝑖∂𝐼𝑗𝑎 with the result as ∂?̃?𝑖∂𝐼𝑗𝑎 = 0. Analogously, it can be shown that ∂?̃?𝑖∂𝐼𝑖𝑡 > 0 and the sign of ∂?̃?𝑗∂𝐼𝑖𝑡 depends on the relative magnitude of ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑗 ∂𝐼𝑖𝑎 ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖2 and ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝜙𝑗 ∂2(𝜋𝑖+𝜋𝑗)∂𝜙𝑖 ∂𝐼𝑖𝑎 . The signs of derivatives of 𝑝𝑖(?̅?𝑖 , ?̅?𝑗 , 𝐼) ; 𝑝𝑗(?̅?𝑖, ?̅?𝑗 , 𝐼) and 𝑝𝑖(?̃?𝑖, ?̃?𝑖 , 𝐼); 𝑝𝑗(?̃?𝑖, ?̃?𝑖, 𝐼) to 𝐼𝑖𝑎 and 𝐼𝑖𝑡 can only be judged with functional setup. A2. Best response function of optimal adaptation investments With competing port authorities, for port authority 𝑖 , the best response function of its own adaptation investment 𝐼𝑖𝑎 to 𝐼𝑖𝑡 conditional on the other port’s adaptation investment 𝐼𝑗𝑎 and 𝐼𝑗𝑡 is as: 𝐼𝑖𝑎|𝐼𝑗𝑎, 𝐼𝑗𝑡 =0.33𝜂 [(𝑉+0.50𝑡)𝛺−𝐷𝛹]−0.032 𝜂2𝛹(𝐼𝑗𝑎+𝐼𝑗𝑡)𝜔𝑡−0.36 𝜂2𝛹+0.36 𝜂2𝛹𝜔𝑡−0.36 𝜂2𝛹𝐼𝑖𝑡 = 𝐴 + 𝐵𝐼𝑖𝑡 181 where 𝐴 =0.33𝜂 [(𝑉+0.5𝑡)𝛺−𝐷𝛹]−0.032 𝜂2𝛹(𝐼𝑗𝑎+𝐼𝑗𝑡)𝜔𝑡−0.36 𝜂2𝛹 and 𝐵 =0.36 𝑡𝜂2𝛹𝜔𝑡−0.36 𝜂2𝛹. For terminal operator 𝑖, the best response function of its own adaptation investment in response to 𝐼𝑖𝑎 is as: 𝐼𝑖𝑡|𝐼𝑗𝑎, 𝐼𝑗𝑡 =0.16𝜂 [(𝑉+0.5𝑡)𝛺−𝐷𝛹]−0.015 𝜂2𝛹(𝐼𝑗𝑎+𝐼𝑗𝑡)𝜔𝑡−0.17𝜂2𝛹+0.17 𝜂2𝛹𝜔𝑡−0.17 𝜂2𝛹𝐼𝑖𝑎 = 𝐶 + 𝐹𝐼𝑖𝑎 where 𝐶 =0.16𝜂 [(𝑉+0.5𝑡)𝛺−𝐷𝛹]−0.015 𝜂2𝛹(𝐼𝑗𝑎+𝐼𝑗𝑡)𝜔𝑡−0.17𝜂2𝛹 and 𝐹 =0.17 𝜂2𝛹𝜔𝑡−0.17 𝜂2𝛹. 𝐵 and 𝐹 are positive as the SOCs suggest 𝜔 > 0.36 𝜂2𝑡𝛹. The two best response functions are positively sloped, suggesting that the port adaptation investment at the same port is strategic complement. The best response functions are plotted as follows. Figure A2 The best response adaptation investment functions for port authority and terminal operators at the same port As shown in above figure, if 𝜔 <0.48 Ω(𝑉+0.5𝑡)𝜂2 𝐷𝑡, the binding constraint 𝜂(𝐼𝑖𝑎 + 𝐼𝑖𝑡) = 𝐷 indicated by the orange line cuts two best response lines inside of the interior Nash equilibrium. Any point 182 on the orange line is a Nash equilibrium, as port authority 𝑖 and terminal operator 𝑖 have the incentive to increase adaptation investment but already reaching constraint 𝜂 (𝐼𝑖𝑎 + 𝐼𝑖𝑡) = 𝐷. Each party does not have incentive to deviate from its adaptation investment on the constraint. Thus, there are infinite Nash equilibria if the constraint 𝜂 (𝐼𝑖𝑎 + 𝐼𝑖𝑡) ≤ 𝐷 is binding. For the port authority 𝑖, the best response function to the adaptation investment of the other port authority 𝐼𝑗𝑎, conditional on two ports’ terminal operators’ adaptation investments is as: 𝐼𝑖𝑎|𝐼𝑖𝑡, 𝐼𝑗𝑡 =0.33𝜂 [(𝑉+0.5𝑡)𝛺−𝐷𝛹]+0.032 𝜂2𝛹(11𝐼𝑖𝑎−𝐼𝑗𝑡)𝜔𝑡−0.36 𝜂2𝛹−0.032 𝜂2𝛹𝜔𝑡−0.36 𝜂2𝛹𝐼𝑗𝑎 = 𝐺 + 𝐻𝐼𝑗𝑎 where 𝐺 =0.33𝜂 [(𝑉+0.5𝑡)𝛺−𝐷𝛹]+0.032 𝜂2𝛹(11𝐼𝑖𝑎−𝐼𝑗𝑡)𝜔𝑡−0.36 𝜂2𝛹 and 𝐻 = −0.032 𝜂2𝛹𝜔𝑡−0.36 𝜂2𝛹. For the port authority 𝑗, the best response function to the adaptation investment of that of port authority 𝑖 is as, 𝐼𝑗𝑎|𝐼𝑖𝑡, 𝐼𝑗𝑡 =0.33𝜂 [(𝑉+0.5𝑡)𝛺−𝐷𝛹]+0.032 𝜂2𝛹(11𝐼𝑗𝑎−𝐼𝑖𝑡)𝜔𝑡−0.36 𝜂2𝛹−0.032 𝜂2𝛹𝜔𝑡−0.36 𝜂2𝛹𝐼𝑖𝑎 = 𝐽 + 𝐾𝐼𝑗𝑎 where 𝐽 =0.33𝜂 [(𝑉+0.5𝑡)𝛺−𝐷𝛹]+0.032 𝜂2𝛹(11𝐼𝑗𝑎−𝐼𝑖𝑡)𝜔𝑡−0.36 𝜂2𝛹 and 𝐾 = −0.032 𝜂2𝛹𝜔𝑡−0.36 𝜂2𝛹. 𝐻 and 𝐾 are negative as SOCs suggest 𝜔 > 0.36 𝜂2𝑡𝛹 . The two best response functions are negatively sloped, suggesting that the port authorities’ adaptation investments at two different ports are strategic substitutes. In addition, the finite adaptation investment condition indicates that 𝜔 > 0.49 𝜂2𝑡𝛹. Therefore |𝐻| < 1 and |𝐾| < 1. 183 Figure A3 The best response adaptation investment functions for port authorities at two ports A3. Expressions of equilibrium port adaptation investments and comparative statics The expressions of 𝜕𝐼?̅? 𝑎 𝜕𝛺, 𝜕𝐼?̅? 𝑡 𝜕𝛺 and 𝜕𝐼?̅? 𝑎 𝜕𝛴, 𝜕𝐼?̅? 𝑡 𝜕𝛴 can be obtained as follows: 𝜕𝐼?̅? 𝑎 𝜕𝛺=(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎)(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≥ 0 𝜕𝐼?̅? 𝑡 𝜕𝛺=(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω−(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎)(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≥ 0 𝜕𝐼?̅? 𝑎 𝜕Σ=(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎)(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≤ 0 𝜕𝐼?̅? 𝑡 𝜕Σ=(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ−(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎)(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≤ 0 184 The expressions of 𝜕𝐼𝑖 𝑎 𝜕𝛺, 𝜕 𝐼𝑖 𝑡 𝜕𝛺 and 𝜕𝐼𝑖 𝑎 𝜕𝛴, 𝜕 𝐼𝑖 𝑡 𝜕𝛴 can be solved as follows: 𝜕𝐼𝑖 𝑎 𝜕𝛺=(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≥ 0 𝜕 𝐼𝑖 𝑡 𝜕𝛺=(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω−(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≥ 0 𝜕𝐼𝑖 𝑎 𝜕𝛴=(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≤ 0 𝜕 𝐼𝑖 𝑡 𝜕𝛴=(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ−(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≤ 0 The expressions of 𝜕𝐼𝑖 𝑎 𝜕𝛺, 𝜕𝐼𝑖 𝑡 𝜕𝛺 and 𝜕𝐼𝑖 𝑎 𝜕𝛴, 𝜕𝐼𝑖 𝑡 𝜕𝛴 can be obtained as follows: 𝜕𝐼𝑖 𝑎 𝜕𝛺=(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≥ 0 𝜕𝐼𝑖 𝑡 𝜕Ω=(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≤ 0 𝜕𝐼𝑖 𝑎 𝜕Σ=(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≥ 0 𝜕𝐼𝑖 𝑡 𝜕Σ=(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 )−(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 )(𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 )≤ 0 185 Taking 𝜕𝐼?̅? 𝑎 𝜕𝛺 and 𝜕𝐼?̅? 𝑎 𝜕Σ as example for the proof of 𝜕𝐼?̅? 𝑎 𝜕𝛺≥ 0, 𝜕𝐼?̅? 𝑡 𝜕𝛺≥ 0 and 𝜕𝐼?̅? 𝑎 𝜕Σ≤ 0, 𝜕𝐼?̅? 𝑡 𝜕Σ≤ 0. 𝜕𝐼?̅? 𝑎 𝜕𝛺= ( 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡⏞ ≥0+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡⏞ ≤0⏞ ≥0) 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω⏞ ≥0−( 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2⏞ ≤0+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡⏞ ≤0⏞ ≤0) 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω⏞ ≥0( 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2⏟ ≤0+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎⏟ ≤0⏟ ≤0 ) ( 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2⏟ ≤0+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡⏟ ≤0⏟ ≤0 ) −( 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎⏟ ≤0+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎⏟ ≥0⏟ ≥0 ) ( 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡⏟ ≥0+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡⏟ ≤0⏟ ≥0 ) ⏟ ≥0≥ 0 For the denominator (𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2+𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎) (𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 ) − (𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 +𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 ) (𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 +𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 ), the second-order derivatives suggest 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2≤ 0, 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 ≤ 0, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2≤ 0, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 ≤ 0, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎 ≤ 0 , 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 ≥ 0 , 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 ≥ 0 , 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 ≤ 0 . |𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎 | = |𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡 | and |𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎2| ≥ |𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡 | , |𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2| ≥ |𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 | and |𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡 | = |𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎 |. Thus, it is concluded that the denominator is positive. The sign of 𝜕𝐼?̅? 𝑎 𝜕𝛺, therefore, depends on the sign of 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω . The proof of 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω≥ 0 is as follows. Substituting 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω, 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω=𝜂[0.26𝜔𝑡2+[(0.12𝜓−0.24Ω2)𝜂2+(0.5𝑉−0.99𝐷Ω)𝜔]𝑡+(0.48Ω2−0.24𝜓)𝑉𝜂2]1.60𝜔𝑡−0.75𝜂2𝜓. The denominator of 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω is 1.60𝜔𝑡 − 0.75𝜂2𝜓 > 0. For the numerator, it is an increasing function in𝜔. The finite adaptation investment condition requires 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡 . When 𝜔 =0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω=0.16(2𝑉+𝑡)𝜂𝑡> 0. Therefore, 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Ω> 0 when 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. 186 Similarly, one can also show 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω≥ 0 . Substituting 𝐼𝑖 𝑎 = 𝐼𝑗𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω=𝜂[0.24(𝑉+0.5𝑡)(2Ω2−𝜓)𝜂2+(0.5𝑉+0.25𝑡−𝐷Ω)𝜔𝑡]3.2𝜔𝑡−1.6𝜂2𝜓, with the denominator 3.2𝜔𝑡 − 1.6𝜂2𝜓 to be positive, and numerator as an increasing function in 𝜔. The finite adaptation investment condition requires 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡 . When 𝜔 =0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω=0.15(2𝑉+𝑡)𝜂𝑡> 0. Therefore, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω> 0 when 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. Similarly, it can also been shown that the signs of 𝜕𝐼?̅? 𝑎 𝜕Σ and 𝜕𝐼?̅? 𝑡 𝜕Σ depend on 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ. The proof of 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ≤ 0 is as follows. Substituting 𝐼𝑖 𝑎 = 𝐼𝑗𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ, 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ=𝜂[0.48(𝑉+0.5𝑡)Ω𝜂2−𝐷𝜔𝑡]𝑡(3.1𝜔𝑡−1.5𝜓𝜂2). The denominator 𝑡(3.1𝜔𝑡 − 1.5𝜓𝜂2) is positive, and the numerator is a decreasing function in 𝜔. The finite adaptation investment condition requires 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡 . When 𝜔 =0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ= 0 . Therefore, 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0 when 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. Similarly, one can also show 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0 . Substituting 𝐼𝑖 𝑎 = 𝐼𝑗𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ=𝜂[0.48(𝑉+0.5𝑡)Ω𝜂2−𝐷𝜔𝑡]𝑡(6.4𝜔𝑡−3.1𝜓𝜂2). The denominator 𝑡(6.4𝜔𝑡 − 3.1𝜓𝜂2) is positive, and the numerator is a decreasing function in 𝜔. The finite adaptation investment condition requires 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡 . When 𝜔 =0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ= 0 . Therefore, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0 when 𝜔 ≥0.48 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. Analogously, the sign of 𝜕𝐼?̅? 𝑡 𝜕Σ also depends on 𝜕2𝐸[𝜋𝑖]𝜕𝐼𝑖𝑎𝜕Σ and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ, which is negative. Taking 𝜕𝐼𝑖 𝑎 𝜕𝛺 and 𝜕𝐼𝑖 𝑎 𝜕Σ as an example for the proof of 𝜕𝐼𝑖 𝑎 𝜕𝛺≥ 0, 𝜕𝐼𝑖 𝑡 𝜕𝛺≥ 0 and 𝜕𝐼𝑖 𝑎 𝜕Σ≤ 0, 𝜕𝐼𝑖 𝑡 𝜕Σ≤ 0. 187 𝜕𝐼𝑖 𝑎 𝜕𝛺= ( 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡⏞ ≥0+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡⏞ ≤0⏞ ≥0) 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω⏞ ≥0−( 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2⏞ ≤0+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡⏞ ≤0⏞ ≤0) 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω⏞ ≥0( 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎2⏟ ≤0+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎⏟ ≤0⏟ ≤0 ) ( 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡2⏟ ≤0+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡⏟ ≤0⏟ ≤0 ) −( 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎⏟ ≤0+𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎⏟ ≥0⏟ ≥0 ) ( 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡⏟ ≥0+𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡⏟ ≤0⏟ ≥0 ) ⏟ ≥0≥ 0 It can be shown that the sign of 𝜕𝐼𝑖 𝑎 𝜕𝛺 depends on sign of 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω. The proof of 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω≥ 0 is as follows. Substituting 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω, 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω=𝜂[0.25t2𝜔+[(0.11𝜓−0.22Ω2)𝜂2+(0.5𝑉−𝐷Ω)𝜔]𝑡+0.223(Ω2−𝜓)𝑉𝜂2]𝑡(1.67𝜔𝑡−0.74𝜂2𝜓), with the denominator to be positive, and with numerator as an increasing function in 𝜔 . The finite adaptation investment condition requires 𝜔 ≥0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡 . When 𝜔 =0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω=0.15(2𝑉+𝑡)𝜂𝑡. Therefore, 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Ω≥ 0 when 𝜔 ≥044 𝛺(𝑉+0.5𝑡)𝜂2𝐷𝑡. Similarly, one can show 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω≥ 0 . Substituting 𝐼𝑖 𝑎 = 𝐼𝑗𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω=𝜂[0.25t2𝜔+[(0.11𝜓−0.22Ω2)𝜂2+(0.5𝑉−𝐷Ω)𝜔]𝑡+0.223(Ω2−𝜓)𝑉𝜂2]𝑡(3.43𝜔𝑡−1.53𝜂2𝜓), with the denominator to be positive, and the numerator as an increasing function in ω. The finite adaptation investment condition requires 𝜔 ≥0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. When 𝜔 =0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω=0.15(2𝑉+𝑡)𝜂𝑡. Therefore, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω≥ 0 when 𝜔 ≥044 𝛺(𝑉+0.5𝑡)𝜂2𝐷𝑡. It can also been shown that the sign of 𝜕𝐼𝑖 𝑎 𝜕Σ and 𝜕𝐼𝑖 𝑡 𝜕Σ depends on 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ and 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ. The proof of 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ≤ 0 is as follows. Substituting 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ, 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ=𝜂[0.446(𝑉+0.5𝑡)Ω𝜂2−𝐷𝜔𝑡]𝑡(3.33𝜔𝑡−1.49𝜓𝜂2), with the denominator to be positive, and the numerator as a decreasing function in ω. The finite adaptation investment condition requires 𝜔 ≥188 0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. When 𝜔 =0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝜋𝑖+𝜋𝑗]𝜕𝐼𝑖𝑎𝜕Σ= 0 . Therefore, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0 when 𝜔 ≥044 𝛺(𝑉+0.5𝑡)𝜂2𝐷𝑡. Similarly, one can also show 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0 . Substituting 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝜂[(2𝑉+𝑡) 𝛺−2𝐷𝛹]6.7𝜔𝑡−3𝛹𝜂2, 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂[(2𝑉+𝑡)𝛺−2𝐷𝛹]14𝜔𝑡−6.𝛹𝜂2 into 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ. 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ=𝜂[0.446(𝑉+0.5𝑡)Ω𝜂2−𝐷𝜔𝑡]𝑡(6.86𝜔𝑡−3.06𝜓𝜂2), with the denominator to be positive, and the numerator as a decreasing function in ω . The finite adaptation investmentcondition requires 𝜔 ≥0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. When 𝜔 =0.44 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ= 0. Therefore, 𝜕2𝐸[𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0 when 𝜔 ≥044 𝛺(𝑉+0.5𝑡)𝜂2𝐷𝑡. Taking 𝜕𝐼𝑖 𝑎 𝜕𝛺 and 𝜕𝐼𝑖 𝑎 𝜕Σ as example for the proof of 𝜕𝐼𝑖 𝑎 𝜕𝛺≥ 0, 𝜕𝐼𝑖 𝑡 𝜕𝛺≥ 0 and 𝜕𝐼𝑖 𝑎 𝜕Σ≤ 0, 𝜕𝐼𝑖 𝑡 𝜕Σ≤ 0. 𝜕𝐼𝑖 𝑎 𝜕𝛺= ( 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡⏞ ≥0+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡⏞ ≤0⏞ ≥0) 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω⏞ ≥0−( 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2⏞ ≤0+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡⏞ ≤0⏞ ≤0) 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω⏞ ≥0( 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎2⏟ ≤0+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑎⏟ ≤0⏟ ≤0 ) ( 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡2⏟ ≤0+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑡⏟ ≤0⏟ ≤0 ) −( 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑗𝑎⏟ ≤0+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕𝐼𝑖𝑎⏟ ≥0⏟ ≥0 ) ( 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑖𝑡⏟ ≥0+𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕𝐼𝑗𝑡⏟ ≤0⏟ ≥0 ) ⏟ ≥0≥ 0 It can be shown that the sign of 𝜕𝐼𝑖 𝑎 𝜕𝛺 depends on the sign of 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω and 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω. The proof of 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω≥ 0 is as follows. Substituting 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂 [(2𝑉+𝑡) 𝛺−2𝐷𝛹]4.1 𝜔𝑡−4 𝛹𝜂2 into 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω=𝜂[0.25t2𝜔+[(0.48Ω2−0.24𝜓)𝜂2+(0.5𝑉−𝐷Ω)𝜔]𝑡+0.48(2Ω2−𝜓)𝑉𝜂2]𝑡(𝜔𝑡−𝜂2𝜓), with the denominator to be positive, and the numerator to be an increasing function in 𝜔. The finite adaptation investment condition requires 𝜔 ≥0.97 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡 . When 𝜔 =0.97𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω=0.24(2𝑉+𝑡)𝜂𝑡. Therefore 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω≥ 0 when 𝜔 ≥0.97 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. In addition, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Ω=𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Ω≥ 0. 189 It can also been shown that the sign of 𝜕𝐼𝑖 𝑎 𝜕Σ and 𝜕𝐼𝑖 𝑡 𝜕Σ depends on the sign of 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ and 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ. The proof of 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ≤ 0 is as follows. Substituting 𝐼𝑖 𝑎 = 𝐼𝑗 𝑎 = 𝐼𝑖 𝑡 = 𝐼𝑗 𝑡 = 𝜂 [(2𝑉+𝑡) 𝛺−2𝐷𝛹]4.1 𝜔𝑡−4 𝛹𝜂2 into 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ=𝜂[0.97(𝑉+0.5𝑡)Ω𝜂2−𝐷𝜔𝑡]𝑡(2.1𝜔𝑡−2𝜓𝜂2), with the denominator to be positive, and the numerator to be a decreasing function in 𝜔. The finite adaptation investment condition requires 𝜔 ≥0.97 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. When 𝜔 =0.97 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ= 0 . Therefore 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ≤ 0 when 𝜔 ≥0.97 𝛺(𝑉+0.5𝑡)𝜂2 𝐷𝑡. In addition, 𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑎𝜕Σ=𝜕2𝐸[𝜋𝑖+𝛱𝑖]𝜕𝐼𝑖𝑡𝜕Σ≤ 0. A4. The Effects of Port Competition Intensity on equilibrium adaptation The new equilibrium adaptation with competing port authorities is obtained as follows: 𝐼?̅? 𝑎(𝑡′) = 𝐼?̅? 𝑎(𝑡′)= 𝜂(4𝑡′ + 𝑡)(4𝑡′ + 3𝑡)(2𝑡′ + 𝑡)(128𝑡′4 + 256𝑡′3𝑡 + 156𝑡′𝑡𝑡2 + 28𝑡′𝑡3 + 𝑡4)[(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹](4𝑡′ + 3𝑡)(4𝑡′ + 𝑡)2(16𝑡′2 + 18𝑡′𝑡 + 3𝑡2)(16𝑡′2 + 14𝑡′𝑡 + 𝑡2)2𝜔𝑡 − 8(6𝑡′2 + 6𝑡′𝑡 + 𝑡2)(8𝑡′2 + 8𝑡′𝑡 + 𝑡2)(2𝑡′ + 𝑡)(128𝑡′4 + 256𝑡′3𝑡 + 156𝑡′𝑡𝑡2 + 28𝑡′𝑡3 + 𝑡4)𝛹𝜂2 𝐼?̅? 𝑡(𝑡′) = 𝐼?̅? 𝑡(𝑡′)= 𝜂(2𝑡′ + 𝑡)(8𝑡′2 + 8𝑡′𝑡 + 𝑡2)2(128𝑡′4 + 256𝑡′3𝑡 + 156𝑡′𝑡𝑡2 + 28𝑡′𝑡3 + 𝑡4)[(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹](4𝑡′ + 3𝑡)(4𝑡′ + 𝑡)2(16𝑡′2 + 18𝑡′𝑡 + 3𝑡2)(16𝑡′2 + 14𝑡′𝑡 + 𝑡2)2𝜔𝑡 − 8(6𝑡′2 + 6𝑡′𝑡 + 𝑡2)(8𝑡′2 + 8𝑡′𝑡 + 𝑡2)(2𝑡′ + 𝑡)(128𝑡′4 + 256𝑡′3𝑡 + 156𝑡′𝑡𝑡2 + 28𝑡′𝑡3 + 𝑡4)𝛹𝜂2 The equilibrium adaptation with monopoly port authority is obtained as follows: 𝐼𝑖 𝑎(𝑡′) = 𝐼𝑗 𝑎(𝑡′) = 0.25𝜂(4𝑡′+3𝑡)(2𝑡′+𝑡)(4𝑡′+𝑡)[(2𝑉+𝑡) 𝛺−2𝐷𝛹](4𝑡′+3𝑡)(4𝑡′+𝑡)2𝜔𝑡−(6𝑡′2+6𝑡′𝑡+𝑡2)(2𝑡′+𝑡)𝛹𝜂2 𝐼𝑖 𝑡(𝑡′) = 𝐼𝑗 𝑡(𝑡′) = 0.25𝜂(2𝑡′+𝑡)(8𝑡′2+8𝑡′𝑡+𝑡2)[(2𝑉+𝑡) 𝛺−2𝐷𝛹](4𝑡′+3𝑡)(4𝑡′+𝑡)2𝜔𝑡−(6𝑡′2+6𝑡′𝑡+𝑡2)(2𝑡′+𝑡)𝛹𝜂2 In addition, the equilibrium adaptation with competing port authorities but allowing intra-port coordination is solved as follows: 190 𝐼𝑖 𝑎(𝑡′) = 𝐼𝑗 𝑎(𝑡′) = 𝐼𝑖 𝑡(𝑡′) = 𝐼𝑗 𝑡(𝑡′)=[ 4𝜂(2𝑡′ + 𝑡)(6𝑡′2 + 6𝑡′𝑡 + 3𝑡2)(8𝑡′2 + 8𝑡′𝑡 + 3𝑡2)(128𝑡′4 + 256𝑡′3𝑡 + 156𝑡′𝑡𝑡2 + 28𝑡′𝑡3 + 𝑡4)[(2𝑉 + 𝑡) 𝛺 − 2𝐷𝛹]][(4𝑡′ + 3𝑡)(4𝑡′ + 𝑡)2(16𝑡′2 + 18𝑡′𝑡 + 3𝑡2)(16𝑡′2 + 14𝑡′𝑡 + 𝑡2)2𝜔𝑡 −16(6𝑡′2 + 6𝑡′𝑡 + 𝑡2)(8𝑡′2 + 8𝑡′𝑡 + 𝑡2)(2𝑡′ + 𝑡)(128𝑡′4 + 256𝑡′3𝑡 + 156𝑡′𝑡𝑡2 + 28𝑡′𝑡3 + 𝑡4)𝛹𝜂2] 191 Appendix B: Appendix for Chapter 3 B1. Proof of Proposition 3.1 By imposing symmetry and totally differentiating FOC (Eq. (3.7)) with respect to ?̅?𝐻, we obtain Eq. (B.1). (𝜕𝑃𝐴𝜕?̅?𝐻+𝜕𝑃𝐴𝜕𝑞𝐴𝜕𝑞𝐴∗𝜕?̅?𝐻) +1N𝜕𝑞𝐴∗𝜕?̅?𝐻𝜕𝑃𝐴𝜕𝑞𝐴+𝑞𝐴N(𝜕2𝑃𝐴𝜕𝑞𝐴2𝜕𝑞𝐴∗𝜕?̅?𝐻+𝜕2𝑃𝐴𝜕𝑞𝐴𝜕?̅?𝐻) = 0 (B.1) Rearrange Eq. (B.1), we have Eq. (3.8). The second-order condition (SOC) with respect to 𝑞𝑗𝐴 must hold for the existence of optimal airline quantity. Thus, we have: 2𝜕𝑃𝐴𝜕𝑞𝐴+ 𝑞𝑗𝐴 𝜕2𝑃𝐴𝜕𝑞𝐴2 < 0 (B.2) When 𝑁 = 1, the denominator of Eq. (3.8) is exactly Eq. (B.2). When 𝑁 > 1 and the demand is linear (i.e., 𝜕2𝑃𝐴𝜕𝑞𝐴2 = 0), the denominator of Eq. (3.8) is also negative. In addition, when the carriers’ decision variables are strategic substitutes (Bulow et al., 1985; Zhang and Zhang, 2010; Lin and Zhang, 2017), the denominator of Eq. (3.8) is again negative. The FOC of airline competition can be re-written as follows: (𝑃𝐴 − 𝑐)𝜕𝑞𝐴(𝑃𝐴, ?̅?𝐻)𝜕𝑃𝐴+𝑞𝐴𝑁(𝑃𝐴, ?̅?𝐻) = 0 (B.3) Totally differentiate Eq. (B.3) with respect to ?̅?𝐻, we have: 𝜕𝑃𝐴∗𝜕𝑠𝐻𝜕𝑞𝐴𝜕𝑃𝐴+ (𝑃𝐴 − 𝑐) (𝜕2𝑞𝐴𝜕𝑃𝐴2𝜕𝑃𝐴∗𝜕𝑠𝐻+𝜕2𝑞𝐴𝜕𝑃𝐴𝜕𝑠𝐻) +1𝑁𝜕𝑞𝐴𝜕𝑃𝐴𝜕𝑃𝐴∗𝜕𝑠𝐻+1𝑁𝜕𝑞𝐴𝜕𝑠𝐻= 0 (B.4) 192 Rearrange Eq. (B.4), we have Eq. (3.9). Substituting −𝜕𝑞𝐴𝜕𝑃𝐴(𝑃𝐴 − 𝑐) for qjA in Eq. (B.2) from the FOC, and then multiplying both sides of Eq. (B.2) by (𝜕𝑞𝐴𝜕𝑃𝐴)2, we have 2𝜕𝑞𝐴𝜕𝑃𝐴−𝜕2𝑃𝐴𝜕𝑞𝐴2(𝜕𝑞𝐴𝜕𝑃𝐴)3(𝑃𝐴 −𝑐) < 0. Since 𝜕2𝑞𝐴𝜕𝑃𝐴2 = −𝜕2𝑃𝐴𝜕𝑞𝐴2(𝜕𝑞𝐴𝜕𝑃𝐴)3 by implicit function theorem,87 the following inequality holds. 2𝜕𝑞𝐴𝜕𝑃𝐴+ (𝑃𝐴 − 𝑐)𝜕2𝑞𝐴𝜕𝑃𝐴2 < 0 (B.5) When 𝑁 = 1, the denominator of Eq. (3.9) is exactly Eq. (B.5). When 𝑁 > 1 and the demand is linear (i.e., 𝜕2𝑃𝐴𝜕𝑞𝐴2 = 0), the denominator of Eq. (3.9) is also negative. B2. Proof of Proposition 3.2 We prove Proposition 3.2 using more general functional forms. Assume the sensitivity of price to demand is not a function of HSR speed. That is 𝜕(𝜕𝑃𝐴(𝑞𝐴,?̅?𝐻)𝜕𝑞𝐴) 𝜕?̅?𝐻⁄ = 0 . We have 𝑑𝑞𝐴∗𝑑?̅?𝐻= −𝑁𝜕𝑃𝐴𝜕?̅?𝐻(N+1)𝜕𝑃𝐴𝜕𝑞𝐴 and 𝑑𝑃𝐴∗𝑑?̅?𝐻= 𝜕𝑃𝐴𝜕𝑞𝐴𝑑𝑞𝐴∗𝑑?̅?𝐻+𝜕𝑃𝐴𝜕?̅?𝐻=𝜕𝑃𝐴𝜕?̅?𝐻N+1. Thus, 𝑑𝑞𝐴∗𝑑?̅?𝐻𝑑𝑃𝐴∗𝑑?̅?𝐻𝜕𝑞𝐴𝜕𝑃𝐴= −𝑁 (B.6) 87 Since 𝑃𝐴 is a function of 𝑞𝐴 and vice versa, i.e., 𝑃𝐴 = 𝑓(𝑞𝐴) and 𝑞𝐴 = 𝑓−1(𝑃𝐴) , we have 1 =𝜕𝑓(𝑞𝐴)𝜕𝑞𝐴𝜕𝑞𝐴𝜕𝑃𝐴. Differentiating both sides with respect to 𝑃𝐴 gives 0 =𝜕2𝑓(𝑞𝐴)𝜕𝑞𝐴2 (𝜕𝑞𝐴𝜕𝑃𝐴)2 +𝜕𝑓(𝑞𝐴)𝜕𝑞𝐴𝜕2𝑞𝐴𝜕𝑃𝐴2. Thus, 𝜕2𝑞𝐴𝜕𝑃𝐴2 = −𝜕2𝑓(𝑞𝐴)𝜕𝑞𝐴2 (𝜕𝑞𝐴𝜕𝑃𝐴)2𝜕𝑓(𝑞𝐴)𝜕𝑞𝐴=−𝜕2𝑃𝐴𝜕𝑞𝐴2(𝜕𝑞𝐴𝜕𝑃𝐴)2𝜕𝑃𝐴𝜕𝑞𝐴= −𝜕2𝑃𝐴𝜕𝑞𝐴2 (𝜕𝑞𝐴𝜕𝑃𝐴)3. 193 A well-known result from Cournot competition: 𝜀𝑞𝐴∗ ,𝑃𝐴∗ = −1𝑁𝑃𝐴∗𝑃𝐴∗ − 𝑐 (B.7) Since 𝑑𝑞𝐴∗𝑑?̅?𝐻=𝜕𝑞𝐴𝜕𝑃𝐴𝑑𝑃𝐴∗𝑑?̅?𝐻+𝜕𝑞𝐴𝜕?̅?𝐻, we divide both sides by 𝑑𝑃𝐴∗𝑑?̅?𝐻 and multiply both sides by 𝑃𝐴∗𝑞𝐴∗ . We obtain: 𝜀𝑞𝐴∗ ,?̅?𝐻𝜀𝑃𝐴∗ ,?̅?𝐻=𝑑𝑞𝐴∗𝑑?̅?𝐻?̅?𝐻𝑞𝐴∗𝑑𝑃𝐴∗𝑑?̅?𝐻?̅?𝐻𝑃𝐴∗= (𝜕𝑞𝐴𝜕𝑃𝐴+𝜕𝑞𝐴𝜕?̅?𝐻𝑑𝑃𝐴∗𝑑?̅?𝐻)𝑃𝐴∗𝑞𝐴∗ =𝜕𝑞𝐴𝜕𝑃𝐴𝑃𝐴∗𝑞𝐴∗ (1 +𝜕𝑞𝐴𝜕?̅?𝐻𝑑𝑃𝐴∗𝑑?̅?𝐻𝜕𝑞𝐴𝜕𝑃𝐴) = 𝜀𝑞𝐴∗ ,𝑃𝐴∗𝑑𝑞𝐴∗𝑑?̅?𝐻𝑑𝑃𝐴∗𝑑?̅?𝐻𝜕𝑞𝐴𝜕𝑃𝐴=𝑃𝐴∗𝑃𝐴∗ − 𝑐> 1 The last equality is by Eq. (B.6) and Eq. (B.7). Thus, the magnitude of 𝜀𝑞𝐴∗ ,?̅?𝐻 must be larger than the magnitude of 𝜀𝑃𝐴∗ ,?̅?𝐻. B3. Proof of Proposition 3.3 From Eq. (3.18.1) and Eq. (3.18.2), we have: 𝜕|𝜀𝑞𝐴∗ ,𝑠𝐻|𝜕𝛾−𝜕|𝜀𝑃𝐴∗ ,𝑠𝐻|𝜕𝛾=𝑐?̅?𝐻(1 + 𝑁) |𝜕𝒯𝜕𝑠?̅?+𝜕𝒮𝜕?̅?𝐻| (−𝑐2𝑁 + 𝑐𝛼𝐴(𝑁 − 1) + 𝛼𝐴2 − 𝛾2(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮))2)(𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) − 𝑐)2(𝑁𝑐 + 𝛼𝐴 − 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)))2 (B.8) Since 𝛼𝐴 − 𝑃𝐴 > 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) due to the positive demand in Eq. (3.11.1), we have 𝛼𝐴 − 𝑐 > 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)). Since 𝛾(𝛼𝐴 − 𝑃𝐴) < 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) due to the positive demand in Eq. (3.11.2), we have 𝛾2(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) < 𝛾(𝛼𝐴 − 𝑃𝐴) < 𝛼𝐻 − 𝑃𝐻 −(𝒯 + 𝒮). Since 0 < 𝛾 < 1, we have (𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) > 0. 194 The sign of 𝜕|𝜀𝑞𝐴∗ ,𝑠𝐻|𝜕𝛾−𝜕|𝜀𝑃𝐴∗ ,𝑠𝐻|𝜕𝛾 is determined by the term −𝑐2𝑁 + 𝑐𝛼𝐴(𝑁 − 1) + 𝛼𝐴2 −𝛾2(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮))2. We have the following relation: −𝑐2𝑁 + 𝑐𝛼𝐴(𝑁 − 1) + 𝛼𝐴2 − 𝛾2(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮))2> −𝑐2𝑁 + 𝑐𝛼𝐴(𝑁 − 1) + 𝑐(𝛼𝐴 + 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)))> 𝑐 (𝑁(𝛼𝐴 − 𝑐) + 𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)))= 𝑐(𝑁 + 1)𝛾(𝛼𝐻 − 𝑃𝐻 − (𝒯 + 𝒮)) > 0 (B.9) 195 Table B1 Estimation results for airline traffic equation with assumed functional forms of 𝒇(𝒔𝒊𝒕) = 𝒔𝒊𝒕, 𝒔𝒊𝒕𝟐 , or √𝒔𝒊𝒕 with subsamples based on HSR total travel time (including access and egress time between HSR stations and city centers) Airline Traffic All < 5 hours > 5 hours All < 5 hours > 5 hours All < 5 hours > 5 hours 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 𝛼1 -0.0027*** -0.0041*** -0.0182 −4.01 × 10−6*** -6.28× 10−6*** 3.39 × 10−6 -0.081** -0.157*** -0.0721 (0.0010) (0.0009) (0.044) (1.89 × 10−6) (1.62× 10−6) (1.19 × 10−5) (0.026) (0.021) (0.735) 𝛼2 -0.137 -0.119 -0.104 -0.136 -0.119 -0.054 -0.137 -0.144* -0.115 (0.110) (0.074) (0.095) (0.110) (0.074) (0.095) (0.109) (0.074) (0.095) HHI -0.0824* -0.081* -0.0883** -0.081* -0.081* -0.088** -0.083* -0.082** -0.088** (0.044) (0.042) (0.043) (0.044) (0.043) (0.043) (0.044) (0.042) (0.043) Population -0.585 -0.777 -0.542 -0.605 -0.884 -0.491 -0.549 -0.636 -.488 (0.656) (0.632) (0.684) (0.657) (0.635) (0.683) (0.655) (0.630) (0.682) Income -0.332** -0.367*** -0.298 -0.329*** -0.372*** -0.298** -0.334*** -0.357*** -0.297** (0.128) (0.122) (0.124) (0.128) (0.123) (0.124) (0.128) (0.122) (0.124) LCC -0.021 -0.020 -0.020 -0.021 -0.021 -0.020 -0.021 -0.020 -0.020 (0.062) (0.061) (0.060) (0.062) (0.061) (0.060) (0.062) (0.061) (0.060) Tourism 0.015 0.028 0.045 0.0114 0.016 0.053* 0.012 0.035 0.056 (0.048) (0.041) (0.044) (0.048) (0.041) (0.048) (0.047) (0.041) (0.049) Spring -0.171*** -0.182*** -0.219*** -0.171*** 0.752*** -0.219*** -0.229*** -0.236*** -0.218*** (0.045) (0.043) (0.042) (0.045) (0.235) (0.042) (0.043) (0.042) (0.042) Summer 0.232 0.230 0.234 0.233 0.229 0.234 0.231 0.230 0.234 (0.161) (0.158) (0.155) (0.161) (0.159) (0.155) (0.161) (0.157) (0.155) Autumn -0.571*** -0.578*** -0.626 -0.571*** 0.358** -0.626** -0.629*** -0.633*** -0.626*** (0.161) (0.158) (0.153) (0.161) (0.161) (0.153) (0.158) (0.155) (0.153) Year2011 0.148*** 0.152*** -0.208 0.148*** 1.093*** -0.209*** 0.759*** 0.762*** 0.756*** (0.029) (0.028) (0.157) (0.029) (0.233) (0.157) (0.158) (0.155) (0.153) Year2012 0.854*** 0.865*** 0.848*** 0.854*** 0.869*** 0.846*** 0.853*** 0.858*** 0.846*** (0.160) (0.157) (0.154) (0.160) (0.157) (0.154) (0.159) (0.156) (0.154) Year2013 -0.038 -0.028 -0.104 -0.038*** 0.913*** -0.106*** -0.096*** -0.092*** -0.106*** (0.166) (0.163) (0.158) (0.166) (0.161) (0.158) (0.163) (0.160) (0.158) 196 Airline Traffic All < 5 hours > 5 hours All < 5 hours > 5 hours All < 5 hours > 5 hours 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 Constant 18.842*** 20.460*** 18.723*** 18.912*** 20.179*** 18.028*** 18.902*** 20.170*** 18.310*** (4.177) (4.014) (4.514) (4.187) (4.033) (4.349) (4.171) (4.002) (4.328) Time trend fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ No. of Observations 1,036 966 980 1,036 966 980 1,036 966 980 Note: 1. The treated routes included in <5 hours total HSR travel time (including access and egress time between HSR stations and city center) subsample are Shanghai-Hefei, Beijing-Taiyuan, Guangzhou-Changsha, Guangzhou-Wuhan. The treated routes included in > 5 hours subsample are Shanghai-Zhengzhou, Shanghai-Fuzhou, Shanghai-Wuhan, Shanghai-Xiamen, Guangzhou-Hefei. 2. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 3. ***<0.01, **<0.05, *<0.10. 4. Standard errors are in parentheses. 197 Table B2 Estimation results for airline price equation with assumed functional forms of 𝒇(𝒔𝒊𝒕) = 𝒔𝒊𝒕, 𝒔𝒊𝒕𝟐 , or √𝒔𝒊𝒕 with subsamples based on HSR total travel time (including access and egress time between HSR stations and city centers) Airline price All < 5 hours > 5 hours All < 5 hours > 5 hours All < 5 hours > 5 hours 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 𝛽1 -0.0015** -0.0016*** -0.013 −3.01 × 10−6*** -3.12× 10−6*** −1.29 × 10−7 -0.0368*** -0.066*** 0.070 (0.0004) (0.0003) (0.018) (7.73× 10−7) (6.61× 10−7) (4.99× 10−6) (0.0009) (0.011) (0.726) 𝛽2 -0.052 -0.023 0.0004 -0.051 -0.023 0.046 -0.012 -0.051 0.0012 (0.045) (0.030) (0.040) (0.045) (0.030) (0.040) (0.030) (0.045) (0.040) HHI 0.109*** 0.104*** 0.109*** 0.110*** 0.104*** 0.109*** 0.103*** 0.109*** 0.109*** (0.018) (0.017) (0.018) (0.018) (0.017) (0.018) (0.017) (0.018) (0.018) Population 0.605** 0.626*** 0.906*** 0.584** 0.572** 0.922*** 0.671*** 0.625** 0.927*** (0.268) (0.258) (0.286) (0.268) (0.258) (0.285) (0.259) (0.269) (0.285) Income 0.110** 0.100** 0.096* 0.110** 0.096* 0.095* 0.104** 0.112** 0.095* (0.052) (0.050) (0.051) (0.052) (0.050) (0.051) (0.050) (0.052) (0.051) LCC 0.0045 0.0038 0.004 0.004 0.0038 0.004 0.003 0.004 0.004 (0.025) (0.025) (0.025) (0.025) (0.025) (0.025) (0.025) (0.025) (0.025) Tourism -0.0004 0.005 0.003 0.003 0.003 0.002 0.004 -0.005 0.003 (0.019) (0.016) (0.018) (0.019) (0.016) (0.020) (0.017) (0.019) (0.020) Spring 0.021 0.018 -0.032* 0.021*** 0.438*** -0.032** -0.031* -0.030* -0.0320* (0.018) (0.017) (0.017) (0.018) (0.095) (0.017) (0.017) (0.018) (0.017) Summer 0.187*** 0.183*** 0.184*** 0.188*** 0.183*** 0.184*** 0.183*** 0.187*** 0.184** (0.066) (0.064) (0.065) (0.065) (0.064) (0.065) (0.064) (0.066) (0.065) Autumn -0.149** -0.151** -0.199** -0.150** 0.269*** -0.199*** -0.202*** -0.201*** -0.199*** (0.066) (0.064) (0.064) (0.066) (0.065) (0.064) (0.063) (0.065) (0.064) Year2011 0.012 0.012 -0.204*** 0.012 0.435*** -0.204*** 0.289*** 0.290*** 0.284*** (0.012) (0.011) (0.065) (0.012) (0.094) (0.065) (0.063) (0.065) (0.064) Year2012 0.247*** 0.248*** 0.239*** 0.248*** 0.250*** 0.238*** 0.246*** 0.247*** 0.238*** 198 Airline price All < 5 hours > 5 hours All < 5 hours > 5 hours All < 5 hours > 5 hours 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡 𝑓(𝑠𝑖𝑡) = 𝑠𝑖𝑡2 𝑓(𝑠𝑖𝑡) = √𝑠𝑖𝑡 (0.065) (0.064) (0.064) (0.065) (0.064) (0.064) (0.064) (0.065) (0.064) Year2013 -0.256*** -0.252*** -0.312*** -0.255*** 0.171*** -0.312*** -0.306*** -0.308*** -0.313*** (0.068) (0.066) (0.066) (0.068) (0.065) (0.066) (0.065) (0.067) (0.066) Constant -6.051*** -6.031*** -7.638*** -5.926*** -6.101*** -7.975*** -6.110*** -6.046*** -8.041*** (1.711) (1.642) (1.888) (1.711) (1.642) (1.819) (1.645) (1.713) (1.811) Time trend fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ No. of Observations 1,036 966 980 1,036 966 980 1,036 966 980 Note: 1. The treated routes included in <5 hours total HSR travel time (including access and egress time between HSR stations and city center) subsample are Shanghai-Hefei, Beijing-Taiyuan, Guangzhou-Changsha, Guangzhou-Wuhan. The treated routes included in > 5 hours subsample are Shanghai-Zhengzhou, Shanghai-Fuzhou, Shanghai-Wuhan, Shanghai-Xiamen, Guangzhou-Hefei. 2. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 3. ***<0.01, **<0.05, *<0.10. 4. Standard errors are in parentheses199 Table B3 The estimated HSR speed effect with assumed functional forms of 𝒇(𝒔𝒊𝒕) = 𝒔𝒊𝒕, 𝒔𝒊𝒕𝟐 , or √𝒔𝒊𝒕 (a) For 250 km/hr HSR lines < 5 hours 𝑓(𝑠𝑖𝑡) 𝑠𝑖𝑡 𝑠𝑖𝑡2 √𝑠𝑖𝑡 Elasticity to HSR speed 𝜀𝑞𝐴∗ ,𝑠𝐻 -1.03 -0.79 -1.24 𝜀𝑝𝐴∗ ,𝑠𝐻 -0.40 -0.39 -0.52 Impact of HSR speed reduction Traffic Change % -20.5% -15.7 % -24.8% Price Change % -8% -7.8% -10.3% Impact of HSR entry Traffic Change % -64% -32% -92% Price Change % 33% -18% -65% Note: For total HSR travel time> 5 hours, the HSR speed effects are not calculated, because the estimated coefficients of 𝑓(𝑠𝑖𝑡) are statistically insignificant. (b) For 350 km/hr HSR lines < 5 hours 𝑓(𝑠𝑖𝑡) 𝑠𝑖𝑡 𝑠𝑖𝑡2 √𝑠𝑖𝑡 Elasticity to HSR speed 𝜀𝑞𝐴∗ ,𝑠𝐻 -1.44 -1.54 -1.47 𝜀𝑝𝐴∗ ,𝑠𝐻 -0.57 -0.76 -0.62 Impact of HSR speed reduction Traffic Change % 20% 22% 21% Price Change % 8 % 11 % 9 % Impact of HSR entry Traffic Change% -76% -54% -95% Price Change % -43% -32% -71% Note: For total HSR travel time> 5 hours, the HSR speed effects are not calculated because the estimated coefficients of 𝑓(𝑠𝑖𝑡) are statistically insignificant. 200 B4. Airline demand and price equation estimation The airline demand equation can be regarded as a function of airline price 𝑃𝑖𝑡. The coefficient 𝜌1 is the impact of HSR speed on airline demand conditional on the airline price. This is a measurement of direct HSR speed effect on passengers’ utility. For airline price equation, it is from the supply side which is a function of airline demand. Speed effect variable is not included in the airline price equation because the HSR speed only has a direct effect on airline demand, and its impact on airline price has been controlled by the airline traffic variable in the price equation (referring to Eq. (3.7) of the theoretical model). ln𝑞𝑖𝑡 = 𝜌0 + 𝜌1 × 𝑓(𝑠𝑖𝑡) × 𝐻𝑆𝑅𝑖𝑡 + 𝜌21𝑃𝑜𝑠𝑡_𝑎𝑐𝑐𝑖𝑑𝑒𝑛𝑡𝑖𝑡× 𝐻𝑆𝑅𝑖𝑡 + 𝜌3ln𝑃𝑖𝑡+ 𝜌4ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟𝑖 + 𝜌5ln𝑃𝑜𝑝𝑖𝑡 + 𝜌6ln𝐼𝑛𝑐𝑜𝑚𝑒𝑖𝑡 + 𝜌7 𝐿𝐶𝐶𝑖𝑡+ 𝜌8𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖 + 𝜌9𝑆𝑝𝑟𝑖𝑛𝑔𝑡 + 𝜌10𝑆𝑢𝑚𝑚𝑒𝑟𝑡 + 𝜌11𝐴𝑢𝑡𝑢𝑚𝑛𝑡+ 𝜌12𝑌𝑒𝑎𝑟𝑡 + 𝜌13𝐻𝑆𝑅𝑖𝑡 + 𝜒𝑖 +𝜛𝑖𝑡 ln𝑃𝑖𝑡 = 𝜂0 + 𝜂1ln𝑞𝑖𝑡 + 𝜂2ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟𝑖 + 𝜂3ln𝐻𝐻𝐼𝑖𝑡 + 𝜂4ln𝑃𝑜𝑝𝑖𝑡 + 𝜂5𝑙𝑛𝐼𝑛𝑐𝑜𝑚𝑒𝑖𝑡+ 𝜂6𝐿𝐶𝐶𝑖𝑡 + 𝜂7𝑇𝑜𝑢𝑟𝑖𝑠𝑚𝑖 + 𝜂8𝑆𝑝𝑟𝑖𝑛𝑔𝑡 + 𝜂9𝑆𝑢𝑚𝑚𝑒𝑟𝑡+ 𝜂10𝐴𝑢𝑡𝑢𝑚𝑛𝑡 + 𝜂11𝑌𝑒𝑎𝑟𝑡 + 𝜂12𝐻𝑆𝑅𝑖𝑡 + 𝜍𝑖 + 𝜊𝑖𝑡 (B.10) The GMM estimation results of the above system of equations are summarized in Table B4 and B5. First, the estimated coefficients for the HSR speed variable 𝑓(𝑠𝑖𝑡) in the airline demand function are larger than those in the airline traffic equation. This is because HSR speed reduction can also cause airline price to rise, thus have a negative moderation on the airline traffic in the reduced-form airline traffic equation, which lowers the HSR speed effect on airline traffic. Second, the airline demand elasticity to price is found to be around -0.8, which is close to airline demand’s price elasticity estimated by Wang et al. (2018).201 Table B4 GMM estimation results for airline demand equation with assumed functional forms of 𝒇(𝒔𝒊𝒕) = 𝒔𝒊𝒕, 𝒔𝒊𝒕𝟐 , or √𝒔𝒊𝒕 Airline Traffic All <850km >850km All <850km >850km All <850km >850km 𝑓(𝑠𝑖𝑡) 𝑠𝑖𝑡 𝑠𝑖𝑡2 √𝑠𝑖𝑡 𝜌1 -0.0041*** -0.0055*** -0.00778 -6.56× 10−6*** -8.69× 10−6*** -1.22× 10−5 -1.131*** -1.431*** -1.929 (0.0013) (0.442) (0.048) (2.46× 10−6) (2.22× 10−6) (-8.32× 10−6) (0.341) (0.279) (1.241) 𝜌2 1.986 2.135 2.103 1.882 2.123 2.083 2.043 2.137 2.087 (9.865) (5.896) (6.944) (9.850) (5.917) (6.957) (9.871) (5.892) (6.962) Yield -0.733* -0.784* -0.820** -0.711* -0.772* -0.840** -0.744* -0.797* -0.846*** (0.410) (0.442) (0.061) （0.408） (0.441) (0.432) (0.411) (0.443) (0.432) Population -0.287 -0.285 0.499 -0.377 -0.442 0.502 -0.159 -0.101 0.494 (0.817) (0.747) (0.834) (0.814) (0.741) (0.839) (0.822) (0.756) (0.841) Income -0.228* -0.288** -0.283** -0.227 -0.298** -0.262* -0.229 -0.273* -0.258* (0.146) (0.141) (0.142) (0.146) (0.141) (0.141) (0.146) (0.141) (0.142) LCC -0.017 -0.018 -0.0179 -0.017 -0.018 -0.017 -0.017 -0.017 -0.017 (0.066) (0.065) (0.065) (0.066) (0.066) (0.065) (0.066) (0.065) (0.065) Tourism 0.0105 0.033 0.0602 0.008 0.019 0.077 0.007 0.039 0.079* (0.0519) (0.044) (0.048) (0.052) (0.044) (0.049) (0.051) (0.044) (0.049) Spring 0.384** 0.375** 0.382** 0.381** 0.371** 0.391** 0.385** 0.381** 0.392** (0.188) (0.188) (0.188) (0.188) (0.189) (0.187) (0.188) (0.188) (0.188) Summer 0.375** 0.374*** 0.377** 0.372** 0.372** 0.382** 0.375** 0.376** 0.383** (0.177) (0.188) (0.176) (0.177) (0.177) (0.187) (0.177) (0.176) (0.175) Autumn -0.146 -0.153 -0.150 -0.145 -0.154 -0.148 -0.145 -0.151 -0.148 (0.231) (0.229) (0.228) (0.231) (0.230) (0.229) (0.231) (0.229) (0.228) Year2011 0.691*** 0.706*** 0.696*** 0.689*** 0.709 0.697*** 0.691*** 0.703*** 0.697*** (0.184) (0.184) (0.182) (0.183) (0.184) (0.183) (0.184) (0.183) (0.182) Year2012 0.729*** 0.746*** 0.724*** 0.729*** 0.752*** 0.722*** 0.726*** 0.739 0.723*** (0.180) (0.179) (0.177) (0.180) （0.180） (0.178) (0.179) (0.178) (0.178) Year2013 0.306*** 0.317*** 0.287*** 0.310*** 0.325*** 0.281*** 0.302*** 0.306*** 0.280*** (0.053) (0.051) (0.054) (0.053) （0.051） (0.054) (0.053) (0.052) (0.054) Constant 14.564*** 15.109*** 9.957* 15.135*** 16.116*** 9.551 13.969*** 14.580*** 10.510*** 202 Airline Traffic All <850km >850km All <850km >850km All <850km >850km 𝑓(𝑠𝑖𝑡) 𝑠𝑖𝑡 𝑠𝑖𝑡2 √𝑠𝑖𝑡 (5.501) (5.062) (5.697) (5.474) （5.001） (5.682) (5.529) (5.092) (5.803) Time trend fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ No. of Observations 1,036 980 966 1,036 980 966 1,036 980 966 Note: 1. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 2. ***<0.01, **<0.05, *<0.10. 3. Standard errors are in parentheses. 203 Table B5 GMM estimation results for airline price equation Airline Price All <850km >850km Passenger -0.536*** -0.402*** -0.395*** (0.253) (0.176) (0.189) HHI 0.080*** 0.072** 0.074** (0.038) (0.031) (0.031) LCC -0.051** -0.050* -0.03 (0.032) (0.037) (0.036) Tourism -0.025 -0.018 0.026 (0.033) (0.024) (0.028) Spring 0.365*** 0.315*** 0.315*** (0.136) (0.110) (0.109) Summer 0.329*** 0.282*** 0.282*** (0.132) (0.106) (0.105) Autumn -0.031 -0.022 -0.020 (0.159) (0.134) (0.130) Year2011 0.510*** 0.433*** 0.431*** (0.168) (0.129) (0.130) Year2012 0.502*** 0.420*** 0.416*** (0.176) (0.134) (0.136) Year2013 0.132** 0.096*** 0.092* (0.067) (0.048) (0.050) Constant 4.823 3.405 3.287 (3.065) (2.157) (2.315) Time trend fixed effect ✓ ✓ ✓ HSR route fixed effect ✓ ✓ ✓ Individual route fixed effect ✓ ✓ ✓ No. of Observations 1,036 980 966 Note: 1. The coefficient of the time-invariant variable, i.e., the airline route distance variable, ln𝐷𝑖𝑠𝑡_𝐴𝑖𝑟i cannot be identified because the route fixed effect has been controlled. Therefore, we do not report the coefficient for the airline route distance variable in the table. 2. ***<0.01, **<0.05, *<0.10. 3. Standard errors are in parentheses. 204 Appendix C: Appendix for Chapter 4 C1. Reduced form demand equation estimation Given the specific form of error term 𝜀𝑖𝑗𝑡, the market share for each product in the market can be uniquely identified from a simple algebraic calculation. Denote 𝑠0 as the market share of non-air travel, then, s0=11+Dtλ (C.1) Then the log of proportion of product j in market t and no air travel is, ln (SjtS0)=xjtβ-αpjt+ξjtλ+(1-λ) lnDt (C.2) And the log of proportion of air travel and no air travel is, ln(StS0)=λlnDt (C.3) Combining the above two expressions, we can get, ln (SjtS0)=xjtβ-αpjtλ+ (λ-1λ) ln (StS0)+ξjtλ (C.4) Both the 𝜉𝑗𝑡 and ln (𝑆𝑡𝑆0) are endogenous as they are obviously correlated to 𝑥𝑗𝑡 and 𝑝𝑗𝑡. Thus the IV estimation is conducted to estimate 𝛽, 𝛼 and 𝜆. The IVs used here are the same as for the BLP estimation. 205 C2. Derivative of product share to price (Bertrand) For the simplification of our derivation, first we denote: Ajt=exjtβ-αpjt+ξjtλ (C.5) It is straightforward to get the first derivatives for 𝐴𝑗𝑡 and 𝐷𝑡 as: ∂Ajt∂pjt=-αλAjt, ∂Drt∂pjt=-αλAjt, ∂Ajt∂pit=0, ∂Drt∂pit=-αλAit (C.6) Then the derivative of 𝑠𝑗𝑡 in its own price 𝑝𝑗𝑡 is as follows: ∂sjt∂pjt=∂AjtDtλ-11+Dtλ∂pjt=(-αλ) [(Ajt)2(λ-1)Dtλ-2+AjtDtλ-1] (1+Dtλ)+α(Ajt)2(Dtλ-1)2(1+Dtλ)2= (-αλ)AjtDtλ-2[(Dt-Ajt)(1+Dtλ)+λAjt](1+Dtλ)2 (C.7) Then the derivative of 𝑠𝑗𝑡 of the 𝑝𝑖𝑡 is: ∂sjt∂pit=∂AjtDtλ-11+Dtλ∂pit=(-αλ) [AjtAit(λ-1)Dtλ-2](1+Dtλ)+αAjtAit(Dtλ-1)2(1+Dtλ)2=(-αλ)AjtAitDtλ-2[λ-1-Dtλ](1+Dtλ)2 (C.8) 206 C3. Derivative of price to product share for the Nash-Cournot From reduced form in Appendix C1, we have: pjt= 1α[xjtβ+(λ-1) ln (StS0) -λ ln (SjtS0)+ξjt] (C.9) Then it is easy to get the derivative of 𝑝𝑗𝑡 in its own share 𝑠𝑗𝑡: ∂pjt∂sjt= 1α[(λ-1)1st-1s0-λsjt] (C.10) and the derivative of 𝑝𝑗𝑡 in the share 𝑠𝑗𝑡: ∂pjt∂sit= 1α[(λ-1)1st-1s0] (C.11) C4. Proof of existence and uniqueness of Fixed Point problem Denote function 𝐺:𝐷 → 𝐷, where 𝑝𝑡 ∈ 𝐷. If there exist a constant 𝜌 < 1, such that, in some natural matrix norm: ‖JG(pt)‖≤ ρ, pt∈D (C.12) where 𝐽𝐺(𝑝𝑡) is the Jacobian matrix of function 𝐺 evaluated at 𝑝𝑡, then function 𝐺 has a unique fixed point 𝑝𝑡∗ and fixed-point iteration is guaranteed to converge to 𝑝𝑡∗ for any initial guess 𝑝𝑡0 ∈𝐷. ‖JG(pt)‖=‖(Ωt-1(pt))'st(pt;xt,ξt,θd)+Ωt-1(pt)st'(pt;xt,ξt,θd)‖= ‖1- (Ωt-1(pt))'st(pt;xt,ξt,θd)‖= ‖1+Ωt-1(pt)∂Ωt(pt)∂ptΩt-1(pt)st(pt;xt,ξt,θd)‖<1 (C.13) 207 The last inequality holds because 𝛺𝑡−1(𝑝𝑡) is non-negative matrix because Ω𝑡(𝑝𝑡) is non-negative, and 𝜕Ω𝑡(𝑝𝑡)𝜕𝑝𝑡 is non-positive matrix. 208 Appendix D: Appendix for Chapter 5 D1. Different effects of runway and terminal congestion In this Appendix D1, we disentangle the impact of runway congestion on concession demand from that of terminal congestion. Let Dr denote airport runway congestion, and Dt denote terminal congestion. Dr(Q,Kr) is a function of airport passenger volume and the runway capacity Kr, and Dt(Q, Kt) is a function of airport passenger volume and terminal size Kt. D1.1 Runway congestion Runway congestion results in flight delay and thus contributes more to a passenger’s longer dwell time at the airport after the security check. It is thus more associated with dwell time effect, compared to terminal congestion. Accordingly, the more significant positive dwell time effect of runway congestion helps the term ∂T∂Dr⏟>0 to be larger than ∂S∂Dr⏟>0, making the positive dwell time effect to dominate the negative stress effect. When we only consider the runway congestion, ceteris paribus, one should be more likely to observe an increase in concession demand with the runway congestion. Therefore, we are more likely to observe d(1-G)dDr>0: d(1-G)dDr=∂(1-G)∂T⏟ >0∂T∂Dr⏟>0+∂(1-G)∂S⏟ <0∂S∂Dr⏟>0>0 (D.1) According to Eq. (D.2), we are more likely to observe that concession demand to decrease with the more runway capacity: d(1-G)dKr=d(1-G)dDr⏟ >0dDrdKr⏟<0<0 (D.2) 209 Such conjecture might be supported by the plot of the concession revenue per passenger and the number of passengers per runway as Figure D1, that runway congestion is negatively correlated to concession revenue per passenger. Figure D1 The relation between number of passenger per runway and per passenger concession revenue D1.2 Terminal Congestion Terminal congestion contributes more to stress effect when passengers consume concession services in the terminal. Terminal congestion thus contributes more to stress effect, making ∂S∂Dt⏟>0 more likely to be larger than ∂T∂Dt⏟>0. Therefore, we are more likely to observe the d(1-G)dDt<0, d(1-G)dDt=∂(1-G)∂T⏟ >0∂T∂Dt⏟>0+∂(1-G)∂S⏟ <0∂S∂Dt⏟>0<0 (D.3) According to Eq. (D.4), we are more likely to observe that concession demand to increase with the increased terminal capacity. 051015200 1.00e+07 2.00e+07 3.00e+07 4.00e+07pax per runwayConcession Rev per Pax Fitted values210 d(1-G)dKt=d(1-G)dDt⏟ <0dDtdKt⏟<0>0 (D.4) This relationship might be supported by the following plot in Figure D2, where the concession revenue per passenger is negatively correlated with the number of passengers per terminal square meter. Figure D2 The relation between number of passenger per terminal square meter concession revenue per passenger 0510152050 100 150 200 250 300pax per terminal square meterConcession Rev per Pax Fitted values211 Figure D3 Average flight delay and the average passenger per runway for the US sample airports (as of the 4th quarter of year 2010) Note: The flight delay is the average minutes of delay per flight for the US airports, collected from Bureau of Transportation Statistics (BTS) US, for the 4th quarter of year 2010; the “Pax_ave” in the figure is the passenger number per runway. D2. The effect of concession price on aeronautical charge for private and public airports For a private airport, we have, ∂τ∂r= − [(1− G(r,D))− Q∂G∂D∂D∂Q] (D.5) ATLBOSBWICLTDCADENDFWDTWEWRFLLIADIAHJFKLASLAXLGAMCOMDWMIAMSPORDPHLPHXSANSEASFOSLCTPA681012145000000 1.00e+07 1.50e+07 2.00e+07pax_avedelay Fitted values212 ∂τ∂r<0 when congestion is moderate with ∂G∂D<0; it is possible that ∂τ∂r>0 when congestion is severe with ∂G∂D>0. For a public airport, we have: ∂τ∂r=−∂E(x|x>r,D)∂r(1 − G(r,D)-Q∂G∂D∂D∂Q)+[E(x|x>r,D) − c2] [∂G∂r+Q∂D∂Q∂2G∂D∂r] − [∂D∂Q∂∂r[∂∂DE(x |x>r, D)]] [1-G(r,D)]Q+ [∂D∂Q ∂∂DE(x |x>r, D)] ∂G∂r Q (D.6) The sign of ∂τ∂r is difficult to predict, no matter ∂G∂D<0 or ∂G∂D>0. D3. Proof of Propositions 5.2 a and 5.2 b It is assumed that the higher order D''(Q,K) and B'''(Q) are zero and, ( τprivate− τpublic) | Q,r=2NvQD'(Q) − (1+2N)B''(Q)Q⏟ >0+[E(x |x>r, D)− r][1-G(r,D)-Q∂G∂D∂D∂Q ]+( [∂D∂Q∂∂DE(x |x>r, D)] (1-G(r,D))Q (D.7) The term 2NvQD'(Q)- (1+2N)B''(Q)Q>0, and the term [E(x |x>r, D)-r][1-G(r,D)-Q∂G∂D∂D∂Q]+( [∂D∂Q∂∂DE(x |x>r, D)] (1-G(r,D))Q>0 , when congestion is moderate with ∂G∂D<0, while (τprivate-τpublic) | Q,r < 0 when congestion is severe with ∂G∂D>0. In sum, 213 when congestion is moderate with ∂G∂D<0, a private airport should charge a higher aeronautical price than a public airport, but the opposite happens when congestion is severe with ∂G∂D>0. Table D1 Sample airports Asia-Pacific Airport code Airport name City country Slot control AKL Auckland International Airport Auckland, New Zealand Level 3 BKK Suvarnabhumi Airport Bangkok, Thailand Level 3 BNE Brisbane Airport Brisbane, Australia Level 3 CAN Bai Yun Airport Guangzhou, China Level 3 CGK Jakarta Soekarno-Hatta International Airport Jakarta, Indonesia Level 3 DEL Indira Gandhi International Airport New Delhi, India Level 3 HKG Hong Kong International Airport Hong Kong, China Level 3 HND Haneda Airport Tokyo, Japan Level 3 ICN Incheon International Airport Incheon, Korea Level 3 KUL Kuala Lumpur International Airport Kuala Lumpur, Malaysia Level 3 MEL Melbourne Airport Melbourne, Australia Level 3 NRT Tokyo Narita International Airport Tokyo, Japan Level 3 PEK Beijing Capital International Airport Beijing, China Level 3 PVG Shanghai Pudong International Airport Shanghai, China Level 3 SIN Singapore Changi International Airport Singapore, Singapore Level 3 SYD Sydney Airport Sydney, Australia Level 3 Europe Airport code Airport name City country Slot control AMS Amsterdam Airport Schiphol Amsterdam, The Netherlands Level 3 ATH Athens International Airport Athens, Greece Level 3 BRU Brussels Airport Brussels, Belgium Level 3 CPH Copenhagen Airport Kastrup Copenhagen, Denmark Level 3 DUS Düsseldorf International Airport Düsseldorf, Germany Level 3 LGW London Gatwick International Airport London, England Level 3 LHR London Heathrow Airport London, England Level 3 LIS Lisbon Portela Airport Lisbon, Portugal Level 3 MUC Munich Airport Munich, Germany Level 3 MXP Milan Malpensa Airport Milan, Italy Level 3 STN London Stansted Airport London, England Level 3 VIE Vienna International Airport Vienna, Austria Level 3 ZRH Zurich Airport Zurich, Switzerland Level 3 214 North America Airport code Airport name City country Slot control ATL Hartsfield-Jackson Atlanta International Airport Atlanta, Georgia BOS Boston Logan International Airport Boston, Massachusetts BWI Baltimore Washington International Airport Baltimore, Maryland CLT Charlotte Douglas International Airport Charlotte, North Carolina DCA Ronald Reagan Washington National Airport Washington, DC DEN Denver International Airport Denver, Colorado DFW Dallas Forth Worth International Airport Dallas, Texas DTW Detroit Metropolitan Wayne County Airport Detroit, Michigan EWR Newark Liberty International Airport Newark, New Jersey Level 2 FLL Fort Lauderdale Hollywood International Airport Ft. Lauderdale, Florida IAD Washington Dulles International Airport Washington, DC IAH George Bush Intercontinental Airport Houston, Texas JFK New York-John F. Kennedy International Airport New York, New York Level 3 LAS Las Vegas McCarran International Airport Las Vegas, Nevada LAX Los Angeles International Airport Los Angeles, California Level 2 LGA LaGuardia International Airport New York, New York MCO Orlando International Airport Orlando, Florida Level 2 MDW Chicago Midway Airport Chicago, Illinois MIA Miami International Airport Miami, Florida MSP Minneapolis/St. Paul International Airport Minneapolis, Minnesota ORD Chicago O'Hare International Airport Chicago, Illinois Level 2 PDX Portland International Airport Portland, Oregon PHL Philadelphia International Airport Philadelphia, Pennsylvania PHX Phoenix Sky Harbor International Airport Phoenix, Arizona SAN San Diego International Airport San Diego, California SEA Seattle-Tacoma International Airport Seattle, Washington SFO San Francisco International Airport San Francisco, California Level 2 SLC Salt Lake City International Airport Salt Lake City, Utah STL St. Louis-Lambert International Airport St. Louis, Missouri TPA Tampa International Airport Tampa, Florida YVR Vancouver International Airport Vancouver, British Columbia Level 3 215 YYZ Toronto Lester B. Pearson International Airport Toronto, Ontario Level 3 D4. Proof of Proposition 5.3 In this Appendix D4, we prove that Proposition 5.3 also holds for concession revenue per passenger, r(1-G). For a private airport, ∂r(1-G(D(K,Q),r)∂Q=(1-G(D,r))∂r∂Q-r∂G∂Q=(1-G(D,r))∂r∂Q-r [∂G∂D ∂D∂Q+∂G∂r ∂r∂Q] = (1-G(D,r)-r∂G∂r)∂r∂Q-r∂G∂D ∂D∂Q= (1-G(D,r)-r∂G∂r)∂G∂D∂D∂Q+(r-c2)∂2G∂r∂D∂D∂Q- [2∂G∂r+(r-c2)∂2G∂r2] - r∂G∂D ∂D∂Q=[ (1-G(D,r)-r∂G∂r)- [2∂G∂r+(r-c2)∂2G∂r2]-r ] ∂D∂Q∂G∂D+ (1-G(D,r)-r∂G∂r)(r-c2)∂2G∂r∂D∂D∂Q- [2∂G∂r+(r-c2)∂2G∂r2] (D.8) As long as 1-G(D,r)-r∂G∂r>0, we have the term (1-G(D,r)-r∂G∂r)-[2∂G∂r+(r-c2)∂2G∂r2]-r<0 and (1-G(D,r)-r∂G∂r)(r-c2)∂2G∂r∂D∂D∂Q-[2∂G∂r+(r-c2)∂2G∂r2]>0, thus making the ∂r(1-G(D(K,Q),r)∂Q>0 when ∂G∂D<0, and making it is possible for ∂r(1-G(D(K,Q),r)∂Q< 0 when ∂G∂D>0. For a public airport, 216 ∂r(1-G(D(K,Q),r)∂Q=(1-G(D,r))∂r∂Q-r∂G∂Q=(1-G(D,r))∂r∂Q-r [∂G∂D ∂D∂Q+∂G∂r ∂r∂Q] (D.9) Because ∂r∂Q=0 referring to Eq. (6.15), ∂r(1-G(D(K,Q),r)∂Q=-r∂G∂D ∂D∂Q. Thus 𝜕𝑟(1−𝐺(𝐷(𝐾,𝑄),𝑟)𝜕𝑄> 0 when 𝜕𝐺𝜕𝐷< 0, and 𝜕𝑟(1−𝐺(𝐷(𝐾,𝑄),𝑟)𝜕𝑄< 0 when 𝜕𝐺𝜕𝐷> 0.
Thesis/Dissertation
eng
Business Administration - Transportation and Logistics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Essays on economics of transport infrastructure : pricing, investment and competition
Text