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Essays in environmental economics and international trade Fraser, Alastair Edward Wilson 2018

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Essays in Environmental Economics andInternational TradebyAlastair Edward Wilson FraserB.Sc., The University of Victoria, 2007M.Sc., The University of Alberta, 2010M.A., Queen’s University, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Economics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)October 2018© Alastair Edward Wilson Fraser 2018The following individuals certify that they have read, and recommend to the Faculty of Graduate andPostdoctoral Studies for acceptance, the dissertation entitled:Essays in Environmental Economics and International Tradesubmitted by Alastair Edward Wilson Fraser in partial fulfillment of the requirements forthe degree of Doctorate of Philosophyin EconomicsExamining Committee:Prof Brian Copeland, Vancouver School of EconomicsCo-supervisorProf Werner Antweiler, Sauder School of BusinessCo-supervisorProf Marit Rehavi, Vancouver School of EconomicsUniversity ExaminerProf Richard Barichello, Land and Food SystemsUniversity ExaminerProf Nicholas Rivers, University of OttawaExternal ExaminerAdditional Supervisory Committee Members:Prof Carol McAusland, Land and Food SystemsSupervisory Committee MemberProf Tomasz Swiecki, Vancouver School of EconomicsSupervisory Committee MemberiiAbstractIn Chapter 1, I study how households respond to financial rewards offered for achieving electricityconservation targets. Using an event-study empirical approach, I estimate the short-run and long-runchanges in electricity use. I find that electricity use declines as households join the program and attemptto achieve their conservation targets, but rebounds close to pre-program levels as households leave theprogram. This suggests that households do not make changes that result in persistent electricityconservation, and that the ongoing incentive of the financial rewards is necessary for causing long-runlower electricity use.In Chapter 2, I exploit a discontinuity in the probability that households re-enroll in the same energyconservation program. This provides direct evidence on what determines households’ re-enrollmentdecisions, and permits me to use a fuzzy regression discontinuity empirical strategy to estimate thetreatment effect of re-enrolling. I find households’ decisions whether to re-enroll are sensitive to theirsuccess or failure in achieving their conservation target but, conditional on their success, are largelyindependent of the level of conservation they achieve or their pre-determined characteristics. As aresult, households do not make re-enrollment decisions that are consistent with the incentive structureof the reward program. Importantly for many incentive programs, this suggests households are usingsimple heuristics in making decisions rather than responding to the detailed information provided tothem.In Chapter 3, I show that trade models incorporating multiple transport modes have imposedstrong—and potentially unrealistic—restrictions on substitution patterns across mode-specific tradeflows. In particular, I show that different models have implicitly assumed bilateral trade by air and seato be both complements and substitutes, and this assumption has significant quantitative and qualita-tive implications for counterfactual trade patterns. Using freight costs for U.S. imports I estimate thatthe elasticity of substitution between modes. I find no evidence that transport modes are substitutesand limited evidence they are complements.iiiLay SummaryUsing energy efficiently is an important component of reducing carbon emissions. This dissertationfocuses on two aspects of this challenge. I first consider how households conserve energy in an elec-tricity conservation program that offers them financial rewards. I find that while such rewards causehouseholds to reduce their electricity use, their electricity use rebounds as they leave the program.In addition, households are found to rely on simple rules in making decisions whether to participate- rather than respond as is typically expected from economic theory. The dissertation then showshow prior models of international trade impose unrealistic restrictions on the choice of air vs. oceantransportation, and that there is little potential for substitution between them. This suggests carbonemissions from international aviation and ocean trade can be separately regulated without unintendedconsequences due to interactions between them.ivPrefaceThis dissertation is original, unpublished, independent work by the author, Alastair Fraser.The research in Chapters 1 and 2 was approved by the UBC Behavioural Research Ethics Board underthe project title Household Energy Consumption with Certificate Number H14-03073.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiIntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The Intensive Margin of Electricity Conservation . . . . . . . . . . . . . . . . . . . . 31.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Institutional Setting, Program Design, and Data . . . . . . . . . . . . . . . . . . . . . . 51.2.1 The Team Power Smart Program . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.2 Structure of Additional Conservation Challenges . . . . . . . . . . . . . . . . . . 61.2.3 Data and Household Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 81.2.4 Outcomes During Multiple Conservation Challenges . . . . . . . . . . . . . . . . 91.3 Empirical Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.3.1 Event Study Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.4 Event Study Estimates - Initial Conservation Challenge . . . . . . . . . . . . . . . . . . 171.4.1 Event Study Estimates - Additional Conservation Challenges . . . . . . . . . . . 201.4.2 Seasonal Treatment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261.4.3 Program Effects By Household Characteristics . . . . . . . . . . . . . . . . . . . 261.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 The Extensive Margin of Electricity Conservation . . . . . . . . . . . . . . . . . . . . 302.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2 The Weather Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32viTable of Contents2.3 Re-Enrollment Decisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3.1 By Level of Reductions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4 The Fuzzy Regression Discontinuity Empirical Strategy . . . . . . . . . . . . . . . . . . 362.4.1 First Stage and Reduced Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.4.2 Identifying Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.5 Fuzzy Regression Discontinuity Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . 452.6 Cost Effectiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523 The Choice of Transportation Mode In International Trade . . . . . . . . . . . . . . 543.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.2 A Model of Endogenous Transportation Mode Choice . . . . . . . . . . . . . . . . . . . 583.2.1 Transport Cost Shocks and Trade Changes . . . . . . . . . . . . . . . . . . . . . 603.2.2 The Substitutability of Transport Modes . . . . . . . . . . . . . . . . . . . . . . 613.2.3 Estimating Equation for the Elasticity of Mode Shares . . . . . . . . . . . . . . 643.3 Comparisons to Existing Models of Mode Choice . . . . . . . . . . . . . . . . . . . . . . 643.3.1 The Importance of the Mode Share Elasticity . . . . . . . . . . . . . . . . . . . . 663.4 Estimates of the Elasticity of Substitution Between Modes . . . . . . . . . . . . . . . . 693.4.1 Data - U.S. Imports of Merchandise . . . . . . . . . . . . . . . . . . . . . . . . . 693.4.2 Reduced Form Elasticity Estimates . . . . . . . . . . . . . . . . . . . . . . . . . 703.5 Heterogenous Unit Values and Mode Choice . . . . . . . . . . . . . . . . . . . . . . . . 743.5.1 Differences in Air Shares Across Countries . . . . . . . . . . . . . . . . . . . . . 793.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87AppendicesA Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91A.1 Event Study Estimates: Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . . . 91B Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95B.1 Selection Into a Second Conservation Challenge . . . . . . . . . . . . . . . . . . . . . . 95B.2 Continuity at the Discontinuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95B.3 Fuzzy-RD Robustness Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95C Appendix to Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105C.1 Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105C.1.1 Mode-specific expenditure from nested CES preferences . . . . . . . . . . . . . . 105C.1.2 Elasticities of Trade and Mode Shares . . . . . . . . . . . . . . . . . . . . . . . . 107viiTable of ContentsC.1.3 Difference between CIF and FOB values . . . . . . . . . . . . . . . . . . . . . . . 109C.2 Comparison to Existing Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110C.2.1 Lux (2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110C.2.2 Hummels and Schaur (2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110C.2.3 Shapiro (2016) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110C.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111C.4 Estimated Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111D Appendix to Chapter 1 (II): Table of All Estimates . . . . . . . . . . . . . . . . . . . 113D.1 Event Study Estimates For All Households . . . . . . . . . . . . . . . . . . . . . . . . . 113D.2 Event Study Estimates By Number of Challenges . . . . . . . . . . . . . . . . . . . . . 120viiiList of Tables1.1 Participant and Non-Participant Characteristics . . . . . . . . . . . . . . . . . . 101.2 Probability of Challenge Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.3 Pre-Program Trends in Electricity Use . . . . . . . . . . . . . . . . . . . . . . . . . 161.4 Treatment Effects by Pre-Determined Variables . . . . . . . . . . . . . . . . . . 282.1 Probit Model: Re-Enrolling in a Second Challenge . . . . . . . . . . . . . . . . . 352.2 Fuzzy Regression Discontinuity Estimates of a Second Challenge . . . . . . . . 472.3 Fuzzy Regression Discontinuity Estimates: Additional Covariates . . . . . . . . 492.4 Fuzzy Regression Discontinuity Estimates: Restricted Billing . . . . . . . . . . 502.5 1st Order Bias-Corrected Fuzzy Regression Discontinuity Estimates . . . . . . 513.1 Counterfactual Trade Changes - Complements and Substitutes . . . . . . . . . 673.2 Counterfactual Trade Changes - No Substitution . . . . . . . . . . . . . . . . . . 683.3 Own and Cross-Price Elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723.4 Own and Cross-Price Elasticities - Proxy Rates . . . . . . . . . . . . . . . . . . . 733.5 Differences in Value/Weight Across Modes . . . . . . . . . . . . . . . . . . . . . . 79B.1 Discontinuity Tests of Covariates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99B.2 2nd Order Bias-Corrected Fuzzy Regression Discontinuity Estimates . . . . . 99B.3 Fuzzy Regression Discontinuity Estimates: 6 Month Gap . . . . . . . . . . . . . 101B.4 Fuzzy Regression Discontinuity Estimates: Log Monthly Electricity Use and12 Month Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103B.5 Fuzzy Regression Discontinuity Estimates: Log Monthly Electricity Use and6 Month Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104C.1 Estimated Elasticities: Air Imports . . . . . . . . . . . . . . . . . . . . . . . . . . . 112C.2 Estimated Elasticities: Ocean Imports . . . . . . . . . . . . . . . . . . . . . . . . . 112D.1 Event-Study Point Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113D.2 Event-Study Estimates: Selection Into Challenges . . . . . . . . . . . . . . . . . . 120ixList of Figures1.1 BC Hydro’s Online Member Tool Box . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Decisions in a Conservation Challenge . . . . . . . . . . . . . . . . . . . . . . . . . 81.3 Time Trends in Electricity Use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4 Time Delay Between Conservation Challenges . . . . . . . . . . . . . . . . . . . . 121.5 Distribution of Challenge Start Dates . . . . . . . . . . . . . . . . . . . . . . . . . 131.6 Estimated Program Effects For All Households . . . . . . . . . . . . . . . . . . . 181.7 Single Challenge vs. Two Or More Challenges . . . . . . . . . . . . . . . . . . . . 221.8 Two Challenges vs. Three Or More Challenges . . . . . . . . . . . . . . . . . . . 231.9 Three Challenges vs. Four Or More Challenges . . . . . . . . . . . . . . . . . . . 241.10 Estimated Treatment Effects By Heating Type . . . . . . . . . . . . . . . . . . . 251.11 Seasonal Treatment Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.1 Weather Adjustment Discrepancies . . . . . . . . . . . . . . . . . . . . . . . . . . . 332.2 Probability of Re-Enrolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372.3 First Stage - Probability of Re-Enrolling . . . . . . . . . . . . . . . . . . . . . . . 402.4 Reduced Form - Post-Challenge kWh Changes . . . . . . . . . . . . . . . . . . . . 412.5 Histogram of Credited Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.6 Density Test of the Running Variable - 10% Target . . . . . . . . . . . . . . . . . 443.1 Histogram of Air Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753.2 Log Value/Weight Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773.3 Log Value/Weight Ratio Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . 783.4 Trends in Air Value Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 803.5 Average Air Shares By Country . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 813.6 Average Residual Air Shares By Country . . . . . . . . . . . . . . . . . . . . . . . 823.7 Residual Air Shares and Value to Weight Ratios . . . . . . . . . . . . . . . . . . 83A.1 Estimated Treatment Effects For Participant Households Only . . . . . . . . . 92A.2 Estimated Treatment Effects For All Households . . . . . . . . . . . . . . . . . . 93A.3 Estimated Treatment Effects For All Households — Alternate Baseline . . . . 94B.1 Probability of Continuing to a Second Challenge: Billed Electricity Use . . . 96B.2 Density Test of the Running Variable - 9.5% Threshold . . . . . . . . . . . . . . 97B.3 Continuity of Covariates at The Discontinuity . . . . . . . . . . . . . . . . . . . . 98B.4 First Stage and Reduced Form Discontinuities . . . . . . . . . . . . . . . . . . . . 100xAcknowledgementsA dissertation is never an individual undertaking, but the product of many supportive and thoughtfulvoices. I am deeply grateful to Werner Antweiler, Brian Copeland, Carol McAusland, and TomaszSwiecki for their advice, encouragement, and patience at all stages of this thesis and throughout thePhD. They have been generous with their time and continue to inspire me to be a better economistand researcher. I am particularly indebted to Joshua Gottlieb, Thomas Lemeiux, Vadim Marmer, andKevin Milligan who, despite not being on my thesis committee, were willing to frequently provideimmensely helpful advice on the details and big picture view of my work, and to Patrick Baylis, NicoleFortin, David Green, and Sumeet Gulati for insightful research and career advice. I also recognize theassistance of the department staff and in particular Maureen Chin, who has ever-cheerfully shepherdedme through the graduate school process and into meeting deadlines I would have otherwise missed. Iwould like to single out the regular attendees of the environmental reading group, Richard Barichelloand James Vercammen, and the trade group, Vanessa Alviarez, Matilde Bombardini, Keith Head, HiroKasahara, and John Ries, for listening to many iterations of this work and providing helpful suggestionsat all stages. Too many other professors of the UBC community to name have provided advice inseminars, the hallways, and discussions in their offices: thank you. Beyond UBC, Geoff Steeves, MarkFreeman, and Andrew Leach have been instrumental in inspiring this pursuit of cautious knowledge.They have provided not only mentorship in research, but also deeply appreciated guidance in thoseimportant questions of life and what to do with it. Geoff Steeves taught me my first steps of physicsresearch and then provided much advice over the years since. Mark Freeman, whose lessons in whatcareful thinking and research should and can be are ones I continue to use regularly. I will be forevergrateful to have his counsel and support in thinking through my difficult decision to leave physics.And Andrew Leach, for his willingness to assist my curious but largely uninformed first steps intoeconomics as well as in providing an example of how economics can be an applied discipline focusedon pressing problems. I also count myself extremely lucky to have had the support of such close andtalented friends in my small cohort: Joao da Fonseca, Brad Hackinen, Nouri Najjar, Jose Pescador, andIain Snoddy. And beyond it: Tom Cornwall, Alex Hemingway, Jeff Hicks, Neil Lloyd, Timi Molnar,and Gaelle Simard-Duplain. Finally and most importantly, to my parents Noni and Stirling, and mybrother David, for their love and guidance. Thank you.xiTo my family.xiiIntroductionClimate change is among the central challenges facing society. Important in responding to this challengeis improving the effective use of energy. This motivates the two topics studied in this dissertation:how households respond to financial rewards offered for electricity conservation, and the choice oftransportation method within international trade.Electricity and heat production is the single largest source of carbon emissions, within which thelargest sector is buildings (IPCC, 2014). This has spurred efforts to conserve energy use in buildingsthrough a wide variety of incentive programs, efforts to inform consumers, and direct regulations.Governments and utility companies have many reasons beyond carbon emissions for desiring changesin the use of energy, including other market failures of information asymmetry, transaction costs,principle agent problems, other pollution externalities, and the political costs of raising the price ofenergy. This dissertation evaluates an energy efficiency program to learn whether and how it is effective,and for the insights into how people respond to the general incentives that it provides.In Chapter 1 and 2, I use a confidential dataset of households’ electricity use to study how con-sumers respond to financial rewards offered for achieving electricity conservation targets. Householdsin this program repeatedly choose whether to attempt annual conservation targets; this allows me totrack households’ extensive margin participation decisions and their intensive margin electricity con-servation efforts. This feature provides several insights into how households respond to the financialrewards and use information in making decisions, while the potential for self-selection makes it a chal-lenge to attribute causal treatment effects. To address these challenges, I employ two separate andcomplementary empirical strategies. In Chapter 1, I use an event study empirical approach to estimatethe short-run and long-run changes in electricity use from households participating in the program.Comparing the pattern of estimated reductions over time and across different households providesinsights into their self-selection decisions and the changes made within the home to conserve energy.In Chapter 2, I use the same dataset to examine a different margin of households’ responses—theextensive margin decision whether to re-enroll in the energy conservation program. By exploiting adiscontinuity in the probability that households re-enroll in the program, I provide direct evidence onhouseholds’ re-enrollment decisions. I then use a fuzzy regression discontinuity empirical strategy toestimate the treatment effect from re-enrolling. This approach complements the event study estimatesfrom Chapter 1, and consistent with them, finds that an additional conservation challenge causes lowerelectricity use.These chapters make two separate and important contributions. First, I find that electricity usedeclines as households join the program and attempt to achieve their successive conservation targets,but rebounds close to pre-program levels as they leave the program. This suggests that households donot make changes, such as physical investments or lasting habits, that result in persistent electricity1Introductionconservation, and that the ongoing incentive of the financial rewards is necessary for causing long-runlower electricity use. Second, I find households’ decisions whether to re-enroll are sensitive to theirsuccess or failure in achieving their conservation target but, conditional on their success, are largelyindependent of the level of conservation they achieve. As a result, households do not make re-enrollmentdecisions that are consistent with the incentive structure of the reward program. Importantly for manyincentive programs, this suggests households are using simple heuristics in making decisions ratherthan incorporating the detailed information that is provided to them.Chapter 3 turns to different topic: the choice of transportation mode in international trade. Trans-portation modes differ substantially in freight cost, delivery time, their use across countries and in-dustries, and environmental impacts. With air freight releasing approximately one hundred times thecarbon emissions per tonne-km as ocean freight, the choice of transport mode is particularly importantto the direct effects of international trade on climate change. These differences have been consideredthrough a variety of trade models that incorporate multiple transportation modes, as well as exploitedfor identification of trade elasticities, the value of delivery time, and the importance of distance totrade. This chapter first shows how several tractable models of trade start from different theoreticalmotivations yet impose the same reduced form predictions for counterfactual trade patterns. Thiscommon framework imposes strong, and potentially unrealistic, restrictions on substitution patterns oftrade across modes and countries. In particular, I find models have implicitly treated bilateral trade byair and sea as both substitutes and complements, and that this has significant quantitative and qual-itative implications for counterfactual trade patterns. To evaluate whether these models accuratelyapproximate real trade flows, this chapter then asks whether the empirical evidence on mode choice isconsistent with air and ocean transport being complements or substitutes. By exploiting idiosyncraticvariations in freight rates, I estimate the degree of substitution across transport modes within bilateraltrade. I find little evidence for any substitution between transport modes for products primarily car-ried by air, and some evidence that imports typically carried by ocean transport are complements withair transport. I then revisit the observation—used to motivate the potential for substitution betweenmodes—that many products arrive by both transport modes. I find that this fact can be explainedin part by heterogeneous product quality within detailed product categories. In addition, this unob-served quality is highly correlated with the choice of transport mode across countries, suggesting thata countries specialization in high vs. low quality products may be a major and largely unrecognizeddeterminant of the choice of mode.2Chapter 1The Intensive Margin of ElectricityConservation1.1 IntroductionGovernments and electrical utility companies use a wide variety of incentive and information programsto reduce electricity use and improve energy efficiency. The success of these programs has been mixed.Programs can underperform when consumers do not respond to price schedules and information aspredicted. Their cost-effectiveness can be reduced when consumers are rewarded for changes thatwould have occurred in the absence of the program. How consumers use heuristics and deviate fromneoclassical models of consumer choice is still poorly understood, and this lack of understanding leads toad-hoc program designs. Even when energy is conserved or efficiency improved the long-run persistenceof changes is often uncertain but important for program effectiveness. In addition, many incentiveprograms are voluntary. This leaves them vulnerable to selection biases that can make it difficult toevaluate their cost-effectiveness. As a result of these limitations, the widespread deployment of energyefficiency and conservation programs risks generating few and expensive reductions in energy use. Theseare challenges beyond energy use; ensuring that programs cost-effectively deliver anticipated resultsrequires improved models of how incentives and information affect decisions and the careful evaluationof existing programs.In this chapter, I analyze a novel program that incentivizes energy conservation through repeatedfinancial rewards. BC Hydro’s Team Power Smart program offers households the opportunity toundertake annual electricity conservation “challenges.” Households that successfully reduce their annualelectricity use by 10% relative to their use in the previous 12 months receive a $75 financial reward. Thisreward is worth 10% of the average household’s annual electricity bill. After each annual conservationchallenge, all households have the option of participating in an additional conservation challenge.Importantly, subsequent conservation challenges require an additional 10% reduction in electricity userelative to the previous year and are available to households regardless of their past challenge successor failure.Using an event study empirical strategy, I estimate the short-run reductions and long-run persistenceof changes in electricity use associated with participation in the Team Power Smart program. Thisprovides substantial insight into households’ intensive margin effort and extensive margin participationdecisions. I find that an initial conservation challenge is associated with an immediate 4.3% averagereduction in electricity use which lasts throughout the twelve months of the first challenge. Comparingthe electricity conservation across households I show that there is selection into subsequent challenges31.1. Introductionbased on the level of reductions in electricity use achieved by households. In addition, electricityuse continues to decline among households that re-enroll and rebounds close to pre-program levelsas households end their participation in the program. This rebound occurs primarily in the monthsleading up to a household’s exit from the program and suggests conservation effort stops well beforehouseholds officially end their participation. This shows that these households tend to make only short-run adjustments rather than permanent investments or create persistent habits, and that the ongoingincentive of additional financial rewards is important for causing long-run lower electricity use.There are relatively few papers that have studied programs offering financial rewards for meetingenergy conservation targets.1 Ito (2015) evaluates the financial rewards for energy conservation offeredunder the California 20/20 program. This program, implemented in response to a crisis in electricitysupply, was mandatory for all eligible households and gave customers a 20% rebate on their summerelectricity bill if they reduced electricity use by 20% compared to the previous year. Ito (2015) foundthat the program generated persistent reductions in electricity use for inland customers, but no re-ductions — short run or long run — for households in coastal climactic zones. He attributes thisheterogeneous effect to the higher temperatures, lower income, and increased use of air conditioning ininland regions. Gerard and Costa (2015) study a suite of mandatory incentives introduced in responseto an electricity supply crisis in Brazil. They find the incentives, including fines for overconsumptionand rebates for reductions, caused both a large short-run and then smaller but persistent long-runreduction in energy use. Dolan and Metcalfe (2015) undertake a randomized controlled trial (RCT)and find large financial rewards cause a large conservation over the two months of their treatmentperiod. They find persistent effects over the two post-program months they observe.This chapter differs from the above work in two important ways. First, I find that electricity userebounds as households leave the program and do not find evidence of long-run persistent reductions.In addition, I do not find evidence of significant heterogeneous effects across household types; reduc-tions come primarily from changes in non-heating electricity use. This, along with the heterogeneoustreatment effects found by Ito (2015), suggest that whether households respond to conservation targetswith persistent reductions may depend on the way electricity is used within a home. Alternatively, thecontext in which a financial reward program is offered — during an electricity crisis as in Ito (2015)and Gerard and Costa (2015), or routine electricity use as in Team Power Smart studied in this thesis— may be important to whether households respond with short-run reductions or persistent changes.This chapter’s finding of continued reductions in electricity use when households re-enroll, and a re-bound when they don’t, is similar to the “action and backsliding” found by Allcott and Rogers (2014)in households’ responses to repeated home energy reports. Allcott and Rogers (2014) show these homeenergy reports mailed to households can cost-effectively cause reductions in energy use. Importantly,they also show that electricity use initially rebounds after the arrival of home energy reports, butrepeated reports can cause persistent changes in electricity use.Second, voluntary conservation programs are characterized by potential self-selection into participa-1Several papers, primarily from the psychology literature, have undertaken randomized control trials of financialrewards (Mizobuchi and Takeuchi, 2012; Midden et al., 1983; McClelland and Cook, 1980; Winett et al., 1978). However,these consider very short timeframes, small sample sizes, and unrepresentative electricity users and are of limited use inunderstanding how households respond to financial rewards.41.2. Institutional Setting, Program Design, and Datation. This poses different difficulties for identifying causal program effects than in mandatory programsand different considerations for the program cost-effectiveness. The cost-effectiveness of voluntary pro-grams may be overstated if households self-select into the program to receive credit for reductions inelectricity use that are not additional to what would have occurred in the program absence. This ‘ad-ditionality’ problem is well known and can be substantial. For example, Boomhower and Davis (2014)use several eligibility thresholds in a program offering subsidies for replacing appliances to find thathalf of the participants would have invested in the energy-efficient technology even without the subsidy.Alternatively, self-selection can increase a voluntary programs cost-effectiveness by raising the shareof participant households that respond to the incentive. This is particularly important for electricityconservation as household electricity use, even after controlling for weather changes, exhibits largeidiosyncratic variations over time. As a result, even households that do not respond to the incentivemay still receive rewards for sufficiently large idiosyncratic reductions in electricity use, and this sharecan be substantial in mandatory programs. These two offsetting types of self-selection make it difficultto predict the cost-effectiveness of voluntary programs and necessitates their ex-post evaluation.The remainder of this chapter is organized as follows. Section 1.2 describes the institutional setting,design of the Team Power Smart electricity conservation program, and data. Section 1.3 gives anoverview of the two empirical approaches used in this dissertation and then describes the event studyempirical strategy of this chapter. Section 1.4 presents the empirical results, and I conclude in Section1.5.1.2 Institutional Setting, Program Design, and Data1.2.1 The Team Power Smart ProgramBC Hydro is Canada’s second largest integrated electrical utility company and serves 1.7 millionresidential customers covering 95% of the population in British Columbia (BCH, 2014). BC Hydro isowned and has a mandate set by the provincial government of British Columbia. The B.C. government,through its Clean Energy Act, has required that BC Hydro “[meet] at least 66 per cent of the expectedincrease in demand through conservation and efficiency by 2020” (BCH, 2014). As part of their effortsto achieve this mandate and in response to the Conservation Potential Review, BC Hydro launcheda new conservation initiative — a program targeting ongoing behaviours called Team Power Smart.2Team Power Smart is a voluntary program promoted and summed up by BC Hydro with “Looking tosave money on your electricity bills? Become a member of Team Power Smart and challenge yourselfto reduce your home’s electricity use by 10% in the next year. If you’re successful, you can earn a[$75] reward.”3 This electricity conservation challenge requires households to reduce their aggregateelectricity use over the 12-month challenge by 10% relative to a conservation target. Each household’s2It is possible for households to join Team Power Smart to view their electricity use online without undertaking aconservation challenge. For simplicity, I will use Team Power Smart to refer to those households which also undertake aconservation challenge. I do not observe households which registered online without undertaking a conservation challenge.3BC Hydro Team Power Smart website landing page. The reward value for challenges studied in this thesis is $75which was reduced to $50 in September 2014. I exclude households undertaking a challenge under the new $50 rewardvalue. Accessed June 2017.51.2. Institutional Setting, Program Design, and Dataconservation target is their own annual electricity use over the preceding 12 months, adjusted forchanges in heating degree days to help prevent households from being unduly penalized or rewardedfor changes in weather. Beginning a challenge requires a minimal time cost of registering online.Households can start a challenge in any month of the year as long as they have 12 months of electricityuse in their current home to establish their target. Online signup ensures that all participants can viewtheir progress towards their conservation target through the BC Hydro website and access a varietyof tips and suggestions for reducing their electricity use. The online account provides households withfeedback on both their monthly and cumulative progress towards their annual 10% conservation target;examples of this are shown in Figures 1.2a and 1.2b. Because it is the aggregate annual conservationthat matters for success in a challenge, households can miss their 10% target in any month and stillpass the challenge.Upon completing the 12 months of the challenge BC Hydro undertakes a final evaluation of house-hold’s cumulative conservation. BC Hydro applies the final weather adjustment, accounts for bi-monthly billing and any idiosyncratic factors, and evaluates whether the household passed or failedtheir challenge. While the conservation target advertised to customers is 10%, BC Hydro evaluatesfinal success or failure against a 9.5% conservation threshold. Households that reduced their electricityuse by greater than or equal to 9.5% below their target pass their challenge while the rest fail. BCHydro notifies all customers of their success or failure and gives successful households the choice of arebate through either a cheque or credit applied to their account.1.2.2 Structure of Additional Conservation ChallengesA novel feature of Team Power Smart is that all households have the option of re-enrolling inadditional annual conservation challenges. Upon completion of each challenge both households thatpass and fail their challenge are given the same option to start a subsequent conservation challenge foranother $75 rebate. This process is summarized in Figure 1.2. Each subsequent challenge follows thesame process as the initial conservation challenge; households have a goal of another 10% conservationtarget measured and weather adjusted relative to their previous 12 months of electricity use. Thenew reduction target is independent of whether the prior 12 months contained a challenge or not,and independent of whether the prior challenge was a success or failure. The baseline for a householdimmediately starting an additional challenge would be the 12 months of the just completed challenge,while a household waiting 4 months before starting their next challenge would have a baseline set bythe average of their last 8 months of their previous challenge and the 4 months of the gap prior tostarting their next challenge.Because each additional 10% conservation challenge is evaluated relative to the prior 12 months,the reduction in electricity use achieved by a household during a challenge affects their incentives onwhen and whether to undertake a subsequent challenge. For example, a household that achieves a 20%reduction during their first challenge and immediately undertakes a second challenge will have to reducetheir emissions by a further 10%, for a cumulative 28% reduction, to pass their next challenge and obtainthe rebate. However a household that passes the first challenge with a 10% reduction will only haveto achieve a cumulative 19% reduction for the same second rebate. Under the reasonable assumptionof increasing marginal costs to electricity conservation, the greater the conservation achieved during a61.2. Institutional Setting, Program Design, and DataFigure 1.1: BC Hydro’s Online Member Tool Box(a) Monthly Challenge ProgressNotes: BC Hydro provides households participating in a conservation challenge with an online portal showing theirelectricity use and progress towards their target. The online portal includes information on monthly electricity usecompared to the same month the previous year and their 10% conservation target.(b) Cumulative Challenge ProgressNotes: In addition to monthly electricity use the online portal displays a household’s cumulative progress towards theirannual 10% conservation target.71.2. Institutional Setting, Program Design, and DataFigure 1.2: Decisions in a Conservation ChallengeNotes: This figure summarizes the options available to a household upon completing a conservation challenge. Everyconservation challenge follows the same process independent of how many prior challenges were undertaken or whetherthey were successful.challenge the greater the incentive to postpone a subsequent challenge or leave the program.1.2.3 Data and Household CharacteristicsUnder a non-disclosure agreement with BC Hydro I obtained an anonymized sample of monthly elec-tricity billing records for 10,000 Team Power Smart program participants and 20,000 non-participantsfrom January 2006 to December 2015.4 The panel includes customers’ Team Power Smart programparticipation history including the number of conservation challenges, each challenges start and enddate, whether the challenge was successful, and the building and heating type of the household. BCHydro also provided the weather-adjusted annual electricity use totals used to evaluate a household’ssuccess against the 9.5% conservation threshold. Individual household characteristics from BC Assess-ment including building type, number of bedrooms, assessed value, floor space, and the postal codesForward Sortation Area were merged with the BCH Hydro panel. Removing duplicate accounts, er-roneous data, and dropping households with electricity use more than 5 standard deviations from themean left a sample of 9,817 households participating in Team Power Smart.The sample of households provided by BC Hydro was a random sample of participant householdsfrom the British Columbia Lower Mainland region which covers 60% of the province’s population(BCStats, 2016).5 Temperatures range from a summer average of 18°C to winters averaging 4°C(ECCC, 2017). Electricity use in British Columbia peaks in the winter due to the widespread use ofelectricity for heating and the limited use of air conditioning in the summer, and BC Hydro estimatesthat 46% of residential electricity use in British Columbia comes from electric heating.4I define participant households as those which participate in Team Power Smart prior to the panel end in December2015, and non-participant households as those which do not participate. The sample was selected from households whichdid not move over the panel period.5 Another 18% of the province’s population lives in regions with similar coastal climatic zones.81.2. Institutional Setting, Program Design, and DataTable 1.1 compares the household characteristics of program participants to non-participants. Theprincipal difference is that participants in Team Power Smart are more likely to live in apartmentsor townhouses compared to single family dwellings and are more likely to use non-electric heating.BC Hydro classifies households into heating categories based on surveys of residents and informationon the building where the meter is installed. Non-Electric are households that heat primarily fromsources other than electricity. Electric are households that heat primarily from electricity, and Un-known are unclassified households. Importantly, BC Hydro does not classify households into heatingcategories based on their observed electricity use. Differences in the composition of participant andnon-participant household types cannot be attributed to self-selection into the program. This is be-cause BC Hydro engages in a range of advertising for Team Power Smart that will differently affecthouseholds’ awareness of the program and thus their likelihood of becoming participants. Figure 1.3shows the average electricity use for these households over the panel. Non-participant households havesignificantly higher electricity use, particularly in the winter months, and electricity use is decliningover the period studied among both participants and non-participants. The difference in electricityuse between participants and non-participants is almost entirely a composition effect; after controllingfor building and heating type the average electricity use among participant households is 1.1% higher(p-value 0.08) than non-participants during the pre-program year of 2006. Average monthly electricitybills among participant households are $62 - making the rebate reward of $75 equivalent to 10% of ahousehold’s annual electricity bill in addition to their bill savings.1.2.4 Outcomes During Multiple Conservation ChallengesTable 1.2 summarizes the decisions and outcomes of participant households across multiple chal-lenges. During the initial three challenges approximately 59% of households decide to re-enroll in anadditional challenge.6 Consistent with an increasing difficulty of achieving additional reductions inelectricity use, the unconditional probability of passing a conservation challenge declines with addi-tional challenges. Households are more likely to re-enroll in another challenge if they pass, rather thanfail, their current challenge. In contrast, households are less likely to pass their next challenge if theypassed their previous challenge. This pattern matches the incentive structure previously discussed;passing a challenge requires achieving the 9.5% conservation target, which makes passing the nextchallenge harder.As households choose the start date of subsequent conservation challenges they could strategicallyestablish a new baseline before undertaking their next challenge. Households could in theory increasetheir electricity use (or stop any ongoing efforts to reduce their electricity use) to create a new higherbaseline that would make their subsequent conservation challenge easier to achieve. Figure 1.4 showsno obvious evidence of this; most households, if they continue to additional challenges, begin theirnext challenge in the first 3 months immediately after completing their prior challenge and there is noobvious bunching at 12 months.The option to undertake a subsequent challenge does not expire; households can sign up for anotherchallenge immediately or postpone indefinitely. Figure 1.5 shows the distribution of start dates forchallenges one through four. New households continually enroll in TPS throughout the panel and6 The probability declines with higher challenges in part mechanically due to the limited panel length.91.2. Institutional Setting, Program Design, and DataTable 1.1: Participant and Non-Participant CharacteristicsParticipants Non-ParticipantsN % N %Building Type1 Story Single Family Dwelling 3,796 39 8,764 462 Story Single Family Dwelling 2,716 28 5,088 261.5 Story Single Family Dwelling 400 4 977 5Apartment 1,412 14 1,813 9Townhouse 1,202 12 1,677 9Other 291 3 931 5Heating TypeNon-Electric 5,599 57 9,687 50Electric 2,874 29 7,294 38Unknown 1,344 14 2,269 12Bedrooms0 12 0 12 01 505 5 703 42 1,597 17 2,745 143 3,626 34 6,709 354 2,632 23 4,569 245 ormore 1,814 18 4,512 23Total HH’s 9,817 100 19,250 100Participants All Non-ParticipantsMean SD Mean SDkWh 884 568 972 636AverageMonthlyBill $62 $69Value ($1,000) $664 $467 $721 $575Floor Area (Square Feet) 2025 934 2123 997Notes: This table shows the building characteristics of participant households and non-participant households. Thesehouseholds are chosen from a random selection of British Columbia lower-mainland households, which is primarily anurban and suburban area concentrated around the Vancouver metropolitan area.101.2. Institutional Setting, Program Design, and DataFigure 1.3: Time Trends in Electricity UseNotes: Average monthly electricity use for participant households and the full sample of non-participant households.Table 1.2: Probability of Challenge OutcomesChallenge Households Probability Of Re-Enrolling If Probability Of Passing IfUndertaking All Failed Passed All Failed Prev. Passed Prev.Challenge Challenge Challenge Challenge Challenge1 9,817 0.57 0.50 0.71 0.342 5,638 0.59 0.55 0.70 0.31 0.33 0.283 3,346 0.60 0.56 0.71 0.28 0.30 0.244 2,014 0.54 0.51 0.64 0.26 0.28 0.235 1,091 0.46 0.41 0.60 0.24 0.27 0.176 498 0.38 0.36 0.44 0.24 0.25 0.217 188 0.27 0.26 0.28 0.29 0.28 0.318 50 0.12 0.07 0.33 0.18 0.20 0.139 6 0.00 0.00 0.00 0.33 0.33 0.33Notes: Probability of Re-Enrolling is the probability of re-enrolling in a subsequent conservation challenge, conditionalon being in the current challenge. Probability of Re-Enrolling if Failed [Passed] Challenge is the probability ofre-enrolling conditional on failing [passing] the current challenge. The Probability of Passing is for a household’scurrent challenge, while the Probability of Passing if Failed [Passed] Prev. Challenge is the probability of passing thecurrent challenge conditional on the Fail or Pass status of the previous challenge.111.2. Institutional Setting, Program Design, and DataFigure 1.4: Time Delay Between Conservation ChallengesNotes: These histograms show the number of months households wait between conservation challenges. The majorityof households which continue to additional challenges do so shortly after completing their prior challenge. The medianwait after the 1st challenge is 3 months, 2 months after the 2nd challenge, 2 months after the 3rd challenge, and 1 monthafter the 4th challenge.as time proceeds households that complete challenges continue to subsequent conservation challenges.Several dates show large increases in sign-ups; these are likely due to periods of significant promotionof the TPS program by BC Hydro as they do not coincide with previous months of unusually large orsmall electricity use or unusual changes in weather.121.2. Institutional Setting, Program Design, and DataFigure 1.5: Distribution of Challenge Start DatesNotes: These histograms show the start date for conservation challenges one through four. Several dates show largeincreases in the number of households starting a challenge. Periods of increased sign up do not coincide with unusualweather, seasons, or consumption, and are likely due to promotion of Team Power Smart by BC Hydro.131.3. Empirical Strategies1.3 Empirical StrategiesThere are three principal challenges to estimating the causal effect of repeated conservation chal-lenges. First, as in all voluntary programs, households may self-select into Team Power Smart basedon observable and unobservable time invariant characteristics. This self-selection could make non-participant households an unsuitable counterfactual for electricity use among participant households,had they not participated in the program. Secondly, households may start their first conservation chal-lenge based on shocks to their past electricity consumption or expectations of their future consumption.For example, households may select into the program in response to a particularly cold winter whichcaused a large electricity bill. Households may also take advantage of anticipated reductions in theirelectricity use such as the purchase of an efficient dryer or leaving on holiday. By signing up in advanceor in conjunction with their anticipated reduction in electricity use, a household could receive credit forreductions in electricity use that were not caused by the conservation program. Lastly, all householdshave the option of continuing to additional conservation challenges. This makes the persistence of en-ergy savings and the causal effect of subsequent conservation challenges dependent on the households’decisions to select into additional challenges.To address these challenges I employ two complementary empirical strategies. In Chapter 1 I usean event study research design to estimate the monthly average changes in electricity use associatedwith participation in Team Power Smart. By estimating changes over time within households, thisstrategy identifies program effects independent of self-selection into the program on observable andunobservable time invariant characteristics. For clarity, I use “program effects” to refer to changes inelectricity use that are associated with participation in conservation challenges but which may or maynot be causally due to the program. I restrict “treatment effect” to refer to standard causal effects.Plotting these estimates provides a visual time trend of the changes in electricity use leading up tothe initial conservation challenge, during the months of each challenge, and over the months after ahousehold leaves the program. These trends provide insight into potential self-selection into the pro-gram based on households’ expectations of future electricity use and past shocks to their consumption,along with the persistence of reductions in electricity use and the effect of subsequent conservationchallenges. This strategy provides detailed information on households’ electricity conservation deci-sions and self-selection into the program, and finds no evidence that reductions in electricity associatedwith participation are not causally due to the program. However, because self-selection cannot be ruledout it cannot strictly identify causal treatment effects. To identify causal treatment effects, Chapter 2exploits a discontinuity in the probability that households continue to a second conservation challenge.I use this discontinuous probability change in a fuzzy Regression Discontinuity design (fuzzy-RDD) toidentify the Local Average Treatment Effect (LATE) of a second conservation challenge.1.3.1 Event Study Empirical StrategyAn event study model identifies the monthly changes in electricity use associated with a conservationchallenge by comparing participant households to households that have not participated in a challenge(Angrist and Pischke, 2008). With a control group of non-participant households an event study141.3. Empirical Strategiesmodel is a difference-in-difference model generalized to multiple time periods and where the timingof treatment may vary across households. Multiple time periods allow lag and lead program effectsto be estimated and plotted to visually inspect their pattern over time. Lagged program effects —effects occurring after the start of the initial conservation challenge — show how changes in electricityuse evolve over time and can help distinguish short-run and long-run program effects. The patternof lead program effects helps test the validity of the identifying assumptions. When each unit mayhave a unique date of treatment it is intuitive to consider program effects in “event time” instead ofcalendar time. This can be thought of as centering all households in time by their date of treatmentand measuring event time as the elapsed time for each household relative to its individual date oftreatment.The general event study model is of the formyit =T∑τ=−TβτDi,t−τ+1 + αi + dt + it (1.1)where yit is the log of monthly electricity use for individual i in month t, αi is an individual fixedeffect, and dt is an indictor for date t. Di,t−τ+1 is a dummy variable equaling 1 if individual i inmonth t began treatment in month t − τ + 1, where τ is the measure of event time in months.7 Idefine the start of treatment as the month a household undertakes its first conservation challenge,τ = 1. βτ are the non-parametric program effects τ months lag or lead of treatment and cover allperiods in the panel of length T. Event study models can only identify the full set of program effects{βτ}Tτ=−T up to a constant. That is, event study models can only identify changes in program effectsrelative to a baseline level.8 In my preferred specification, I define the baseline as the second yearbefore each household undertakes their initial conservation challenge. Using a baseline of the secondyear allows important pre-treatment trends in the 12 months preceding participation in the programcan be estimated. Results are robust to excluding other time periods; see Figure A.3 in the Appendixfor a baseline of the third year pre-treatment. For the baseline of the second year, I estimate equation(1.1) excluding indicators Di,t−τ+1, τ = [−23..−12] which is equivalent to defining {βτ ≡ 0}−23τ=−12. Thenon-parametric estimates βˆτ identify the average percentage change in monthly electricity use withina household relative to their average electricity use during the baseline period.Identification ChallengesThe identifying assumption for causal treatment effects in the event-study model is that, in theabsence of treatment, treated households would have the same expected outcome as non-participanthouseholds. This assumption could be violated in two ways. First, as shown in Table 1.2, participanthouseholds differ from non-participant households in observable time-invariant characteristics. Thecomposition of participant households could potentially change over time, for example if high electricity7For example, consider an observation in December 2009 for a household that began treatment (began its initialconservation challenge) in October 2009. For this household and observation, t = December 2009 and t − τ + 1 =October 2009. This finds Di,t−τ+1 = 1 only for τ = 3.8This can be seen by adding a constant to all βτ and noting that this constant is then collinear with both the full setof individual and date fixed effects.151.3. Empirical StrategiesTable 1.3: Pre-Program Trends in Electricity Use(1) (2) (3) (4) (5)β1 :Date -0.00012 -0.00024∗∗ -0.00033∗∗∗ -0.00064∗∗∗ -0.00058∗∗∗(0.00016) (0.00011) (0.00009) (0.00007) (0.00006)β2 :Date×Participants 0.00005 -0.00026 -0.00021 -0.00026∗ 0.00016(0.00023) (0.00018) (0.00016) (0.00015) (0.00025)Pre-Program Years 2 3 4 5 6Participant IDs 7182 7182 7182 7182 7182Non-Participant IDs 5083 3782 2914 1943 467Observations 294359 394703 484607 547498 550725Notes: β1 : Date is the pre-program time trend common to participant and non-participant households. β2 : Date ×Participants is the additional time trend specific to participant households. Pre-Program Years is the length of timefor which time trends are estimated and excludes all households that start a challenge within six months after the givenpre-program. The six month period is to avoid pre-treatment trends that could include anticipation effects in the finalmonths pre-treatment. Standard errors in parentheses clustered at the household level. *** p<0.01, ** p<0.05, * p<0.1.consumption households select into the program earlier compared to low consumption households,and bias estimates of βˆτ . This motivates the inclusion of individual fixed effects in (1.1) to controlfor time-invariant characteristics that may change over the panel. With individual fixed effects theidentifying assumption requires treatment to be as good as randomly assigned conditional on time-invariant characteristics. This fails if participant and non-participant households do not have paralleltrends in the absence of treatment. Evidence that the parallel trends assumption holds is obtained bycomparing pre-treatment linear trends between participant and non-participant households. I estimatethe following specification,yit = β0 + β1mt + β2dt × TPSi + β3TPSi + it (1.2)where yit is log monthly electricity use, mt is the date, and TPSi is an indicator equal to one ifhousehold i is a Team Power Smart participant household. The only pre-treatment period availableto all households is the year 2006. To test trends over multiple years I estimate specification (1.2) forseveral different time periods and include only participant households that do not begin a conservationchallenge until 6 months after the initial pre-treatment years indicated. Table 1.3 shows the resultswhere β1 is the percent change per month for non-participant and participant households and β2 is theadditional monthly percent change for participant households. Participant households do not have asignificantly different, at the 5% level, pre-treatment trend from non-participants. The magnitude ofdiverging time trends is also small. Taking the largest point estimate of different trends, βˆ2 = −0.00026,would imply an upper bound to the potential bias in estimated program effects of only 0.3% at theend of the first conservation challenge.Households starting a conservation challenge in response to past consumption shocks or expectationsof future electricity use will also violate the parallel trends assumption. Shocks to past consumptioncan be tested by examining pre-treatment trends. As I discuss in Section 1.4, I find no evidencehouseholds begin a conservation challenge in response to increases in their past consumption such as161.4. Event Study Estimates - Initial Conservation Challengelarge electricity bills from unusually cold winters. Whether households begin a challenge based ontheir expected future consumption cannot be tested. For example, it is not possible to distinguishbetween a household participating in a conservation challenge which causally reduces their electricityuse from a household purchasing an efficient dryer and the latter participating to take advantage oftheir upcoming decline in electricity use. In this case, reductions in electricity use that coincide withthe start of participation in Team Power Smart would not be causal. Lacking a suitable instrumentfor initial participation or a discontinuity in eligibility for program participation such as used by Ito(2015), self-selection based on expectations of future electricity use cannot be ruled out. Instead, asI discuss below, the pattern of estimated program effects provides evidence that such self-selection isunlikely to be substantial and that the estimated reductions are primarily causally due to the TeamPower Smart program.1.4 Event Study Estimates - Initial Conservation ChallengeThis section presents the results of estimating the event study model, equation (1.3), for all par-ticipant households and a comparison group of non-participant households.9 Estimates are presentedin Table D.1 in the Appendix. To visualize the trend of program effects over event-time τ , I plot theestimates βˆτ in Figure 1.6. The pattern of monthly estimates provides substantial insight into the shortrun and long run reductions in electricity use and whether reductions are causally due to the TeamPower Smart program. The estimates in Figure 1.6 can be separated into three time intervals: the pre-treatment period leading up to the initial conservation challenge (months -60 to 0), the twelve monthsof the initial conservation challenge (months 1 to 12), and the months after the initial conservationchallenge is completed (months 13 to 72).In the second time interval, the twelve months of the initial conservation challenge show a substan-tial average reduction in electricity use of 5.3% relative to the baseline of the second year pre-treatment.BC Hydro measures households’ reductions relative to the twelve months preceding a challenge; house-holds achieve a 4.3% reduction relative to this year and their 10% conservation target. With theexception of the first month, the reductions over the twelve months of the initial challenge are not sta-tistically significantly different from each other at a 5% level. This shows that, on average, householdsare not strongly increasing or decreasing their electricity conservation during the challenge. This stableconservation is consistent with households making either an initial investment that causes persistentreductions throughout the challenge, or maintain a constant conservation effort throughout the chal-lenge. The consistent program effects also indicate that self-selection to take advantage of upcomingshort-term changes in electricity use, such as a holiday, is not a significant cause of participation; ifthey were, reductions in energy use would be expected to spike in the initial months of the challengebefore partially rebounding.In the first time interval, the months leading up to the initial conservation challenge show a gradual9Due to the small sample size for months far from the initial conservation challenge I pool monthly indicators beforeand after the ±5 year estimation window around the initial conservation challenge into separate indicators. Resultsare robust to this simplification. To ensure a closer comparison group of non-participants to participant households, Ialso use a random sub-sample of non-participant households with the same composition of building type and heatingcharacteristics as participant households. Results are robust to including all non-participant households; see Figure A.2in the Appendix.171.4. Event Study Estimates - Initial Conservation ChallengeFigure 1.6: Estimated Program Effects For All HouseholdsNotes: This figure plots estimated program effects βˆτ with 95% confidence intervals from equation (1.3) ordered by event-time τ . Estimates are in Appendix Table D.2. Point estimates in red denote the 12 months of the initial conservationchallenge (τ = [1..12]). The pre-treatment period is denoted by the months prior to Start (τ ≤ 0). The period afterthe initial challenge concludes are the months with τ > 12. The visual gap in estimates between months τ = −11and τ = −23 is the excluded reference period. βˆτ identify the percent change in electricity use relative to the averageelectricity use within a household during this excluded reference year. Estimates include individual and date fixed effectsand I cluster standard errors at the household level.181.4. Event Study Estimates - Initial Conservation Challengedecline in estimated program effects. This pre-treatment trend could arise for two reasons. First,the pre-treatment trend could indicate a violation of the parallel trends assumption — differencesin exogenous trends between the treated and control households — despite the lack of statisticallysignificant different pre-trends estimated previously. To test this, I estimate specification (1.1) withoutnon-participant control households. This identifies the treatment effect by comparing currently treatedhouseholds to a control group composed of households treated at a later date in the panel (Borusyak andJaravel, 2016). I plot estimates in Appendix Figure A.1. Estimates lose precision due to the smaller setof households but continue to show the same pre-treatment trend, showing the pre-treatment declineis not a due to a violation of the parallel trends assumption. Second, the pre-treatment decline couldreflect different time trends among participant households that are not fully controlled for by commondate fixed effects. Figures 1.7 through 1.9 plot the program effects for households undertaking differentnumbers of challenges. This shows that the declining pre-treatment trend is limited to householdsundertaking only one or two challenges and, importantly, does not bias the short or long-run programeffect estimates.A threat to estimated program effects not being causal is households beginning a conservationchallenge in response to a high electricity bill, such as after a cold winter. In this case, reversion tothe mean would result in reductions in electricity use, relative to the previous year, being credited tothe program. If this self-selection occurs it will manifest itself as positive pre-treatment effects in themonths immediately prior to the initial conservation challenge. Instead, the opposite effect is found;the last two months (months τ = [−1..0]) in Figure 1.6 show a decline in electricity use relative to theprevious months. These reductions in electricity use before the program starts do not count towardsthe conservation credited to households and, in addition, make it harder to achieve the financial rewardas they lower the baseline from which the 10% conservation target is measured from. This lack of apositive pre-treatment effect in the months prior to the challenge suggests that households do notself-select into the program based on past consumption shocks.The pre-program decline of months τ = [−1..0] may indicate that households are undertakingelectricity conservation prior to the program start. This could indicate self-selection into Team PowerSmart as a result of making an energy efficiency investments, which would bias the estimated programconservation upwards. There are two reasons such self-selection and bias to the estimated programeffects is unlikely to be large. First, participation in Team Power Smart as a result of making aninvestment would result in persistent reductions in electricity use; in contrast, Subsection 1.4.1 showsthat electricity use rebounds as households leave the program. Second, the pre-program roll-off canresult mechanically from the billing process. During the period of the panel studied in this thesis BCHydro does not record electricity bills on a fixed monthly basis.10 Instead, BC Hydro uses a rollingbilling period where different houses are billed on different days of not more than 62 days and theuse is calendarized to monthly consumption. As a result, reductions that occur after the start of a10BC Hydro began a rolling installation of Smart meters in 2011 which allowed collection of hourly electricity use.The event study estimates of this section includes households beginning their initial challenge prior to February 2013and so will include some households with electricity use recorded at a higher frequency. However, all data provided tothe researcher was harmonized and calendarized by BC Hydro to a monthly level regardless of the recording frequency.As a result, challenges over the period studied are recorded as beginning on the first day of a month regardless of whenduring the month a household signed up for a challenge, or when the electricity meter was read.191.4. Event Study Estimates - Initial Conservation Challengeconservation challenge cannot be separated within a billing cycle from electricity use that occurred priorto the challenge start. This can result in reductions due to a conservation challenge being partiallycredited to up to the last two months before a household begins its challenge.11The third time interval includes all months after the initial challenge completes, months τ = [13..72].Pooling all participant households in estimating (1.1) includes those ending their program participationafter their first challenge, those immediately continuing to additional challenges, and those waitingseveral months to years before starting a subsequent conservation challenge. Estimates βˆτ , τ > 12 arethe average change in electricity use across these households, including any rebound in electricity use,and additional treatment effects from subsequent challenges undertaken by households. While Figure1.6 shows that participation in Team Power Smart is associated with long-run average reductions inelectricity use, this does not distinguish persistent energy savings due to a challenge, from the effects ofsubsequent challenges. To distinguish these effects I modify the event-study model (1.1) and estimate itseparately for households ending their participation and those re-enrolling in subsequent conservationchallenges.1.4.1 Event Study Estimates - Additional Conservation ChallengesComparing the estimated program effects across households that undertake different numbers ofconservation challenges sheds light on both the process of self-selection into additional challenges andthe persistence of energy savings. To do this, I pool households by the number of conservation challengesthey undertake and estimate separate event study models for each group of households, equation (1.3)yit = αi + dt +72∑τ=−59βτDi,t−τ+1 +8∑g=1θgGitg + Preit + Postit + it (1.3)where yit, αi, dt, and Di,t−τ+1 are defined as in the event-study model of equation (1.1). I poolmonthly indicators before and after the ±5 year estimation window around the initial conservationchallenge into, respectively, indicators Preit and Postit. As shown in Figure 1.4, some householdsundertaking multiple conservation challenges have a gap in time between when their previous challengecompletes and they re-enroll in a subsequent challenge. To account for this variable gap I include theindicatorGitg in equation (1.3). Gitg is 1 if household i in month t has completed challenge g but has notyet re-enrolled in challenge g+ 1. This indicator is not necessary for estimating the event study model;instead, it simplifies the comparison of program effects across households with different gap lengths. Forhouseholds undertaking two or more challenges, including Gitg defines the coefficients βτ , τ = [12..23]as the program effects of the twelve months of the second conservation challenge regardless of thelength of gap between conservation challenges. For households ending their participation after a singlechallenge, βτ , τ = [12..23] are the post-program effects for the first 12 months immediately followingthe initial challenge. Similarly, including Gitg defines βτ , τ = [24..35] as the program effects during athird conservation challenge for households that re-enroll, and as the second year post-program effectsfor households that end their participation. In my preferred specifications I pool all households that11Households could also potentially begin reducing their electricity use in response to a conservation challenge but notcomplete their online registration until some weeks later.201.4. Event Study Estimates - Initial Conservation Challengere-enroll within 12 months of completing their previous challenge and exclude households with longergaps between challenges; results are robust to alternate gap lengths between challenges.Estimates for Additional Conservation ChallengesI separately estimate equation (1.3) for six subsets of households depending on how many conser-vation challenges they undertake; these subsets are not mutually exclusive. Estimates are presented inTable D.2 in the Appendix. In Figure 1.7 I plot estimates βˆτ for households that end their programparticipation at a single challenge, and separately for households that re-enroll in a second conserva-tion challenge. These two household groups show significant differences. Households that end theirprogram participation after the initial challenge have average reductions during the challenge of 0.5%.Households that re-enroll in a second conservation challenge have average reductions during their firstchallenge of 6.5%. This suggests self-selection into additional challenges based on the reductions in elec-tricity use achieved during the initial conservation challenge. Alternatively, it could be that householdswhich are ex-ante likely to continue to additional conservation challenges are also those householdsthat achieve large reductions in energy use.Estimates βˆτ in Figure 1.7 for households that re-enroll are the average program effect includingboth households ending their participation after their second conservation challenge, and those thatre-enroll in a third challenge. Figure 1.8 separates these households and plots estimates βˆτ for thoseundertaking only two conservation challenges against those that re-enroll in a third challenge. Boththese household groups have similar conservation during their first challenge. However, during theirsecond conservation challenge those households that end their participation show a rebound in theiruse over the months of the challenge. Their electricity use returns close to the pre-program levels asthe challenge ends. In comparison, households that continue to a third conservation challenge continueto decrease their electricity use during their second challenge.Figure 1.9 shows this pattern repeats again between households ending program participation afterthe third challenge and those re-enrolling in a fourth challenge. Electricity use remains similar acrossboth groups of households until the last challenge, it continues to decrease among those who re-enroll and rebounds among those who leave the program. This rebound does not return to the pre-program use; electricity use remains persistently lower than pre-program levels by approximately 4%.In addition, the rebound occurs during the months leading up to the end of their final conservationchallenge instead of after the challenge has completed. This is consistent with households stoping theirconservation effort, or “giving up,” prior to the end of the challenge.The reductions in electricity use are not driven by a particular heating type. Figure 1.10 plotsestimated changes for primarily Electric and primarily non-Electric heating households. These havesimilar reductions despite the higher average use among electric heating households. As discussedfurther below, this similarity suggests that reductions are not due primarily to heating-related changessuch as a lower thermostat set point or improved insolation.211.4. Event Study Estimates - Initial Conservation ChallengeFigure 1.7: Single Challenge vs. Two Or More ChallengesNotes: This figure plots estimated program effects βˆτ and 95% confidence intervals from equation (1.3) estimated fortwo mutually exclusive groups of households. Individual monthly estimates are presented in Table D.2 in the Appendixand plotted here as a line for clarity. Estimates in blue are households that undertake a single challenge and then endtheir program participation. Event study estimates in green are for households that undertake at least two conservationchallenges and continue to their second challenge within 12 months of completing their initial challenge. Not shown areestimates θg for electricity use during the gap between the first and second challenges. Months 13-24 are estimates ofthe average change in electricity use among households in their second conservation challenge independent of any gapbetween challenges. Estimates include individual and date fixed effects and I cluster standard errors at the householdlevel.221.4. Event Study Estimates - Initial Conservation ChallengeFigure 1.8: Two Challenges vs. Three Or More ChallengesNotes: This figure plots estimated program effects βˆτ and 95% confidence intervals from equation (1.3) estimated fortwo mutually exclusive groups of households. Estimates are presented in Table D.2 in the Appendix. Estimates in blueare households that end their participation after a second conservation challenge. Estimates in green are householdsthat continue to a third conservation challenge. Estimation sample restricted to households that continue to subsequentchallenges within 12 months. Not shown are estimates θg for electricity use during the gap between challenges. Estimatesinclude individual and date fixed effects and I cluster standard errors at the household level.231.4. Event Study Estimates - Initial Conservation ChallengeFigure 1.9: Three Challenges vs. Four Or More ChallengesNotes: This figure plots estimated program effects βˆτ and 95% confidence intervals from equation (1.3) estimated fortwo mutually exclusive groups of households. Estimates are presented in Table D.2 in the Appendix. Estimates inblue are households that end their participation after a third conservation challenge. Estimates in green are householdsthat continue to a fourth conservation challenge. Estimation sample restricted to households that continue to subsequentchallenges within 12 months. Not shown are estimates θg for electricity use during the gap between challenges. Estimatesinclude individual and date fixed effects and I cluster standard errors at the household level.241.4. Event Study Estimates - Initial Conservation ChallengeFigure 1.10: Estimated Treatment Effects By Heating TypeNotes: This figure plots estimates of βˆτ and 95% confidence intervals from specification (1.3) for all participant andnon-participant households by heating type. Non-Electric Heating households (blue line) are those that do not primarilyheat with electricity while Electric Space Heating households use electricity as the primary heat source. Estimates βˆτ areordered by event-time τ . Point estimates in red denote the 12 months of the initial conservation challenge (τ = [1..12]).The pre-treatment period is denoted by the months prior to Start (τ ≤ 0). The visual gap in estimates between monthsτ = −24 and τ = −36 is the excluded reference period. βˆτ identify the percent change in electricity use relative to theaverage electricity use within a household during this excluded reference year.251.4. Event Study Estimates - Initial Conservation Challenge1.4.2 Seasonal Treatment EffectsElectricity conservation may vary by season depending on how households reduce their electricityuse. Improved insulation, smart thermostats, or reductions in the household temperature will pro-duce larger energy savings in the winter and among households that heat primarily with electricity.More efficient dryers, lightbulbs, or other changes that affect primarily non-seasonal electricity use willgenerate energy savings year round for both household heating types. Comparing when during theyear that reductions in electricity use occur, and between household heating types, sheds light on howhouseholds have responded to the conservation challenge.I estimate the event study model (1.1) separately for each calendar month and household heatingtype, and use the year immediately before the initial conservation challenge as the reference baselineto estimate the reductions in electricity BC Hydro credits to households. In Figure 1.11, I plot theestimated program effects for each month of year during the initial challenge. Both household heatingtypes have similar reductions in the summer months, while Electric Space Heating households havelarger reductions in the winter months. To estimate the fraction of reductions due to heating, I usethe reductions in electricity use over the four warmest summer months as a measure of changes innon-heating use. Comparing this to the reductions over the remainder of the year finds that 13% ofelectricity conservation among non-electric heating households is related to heating, while 48% of theconservation among electric heating households is due to changes that affect heating. That non-electricheating households have reductions due to heating is not unexpected; non-electric heating householdsmay still use after-market baseboard heaters in addition to their non-electric primary heat source.1.4.3 Program Effects By Household CharacteristicsIn Table 1.4, I estimate the program effects over the initial challenge for three household character-istics as well as pre-determined electricity use. To estimate the average change during a conservationchallenge, I use an event study model with annual event-time indicators,yit =∑Υ=−4..−1,1..5θΥDi,t,Υ + αi + dt + Preit + Postit + it (1.4)where yit is log monthly electricity use for household i at date t, and Di,t,Υ is an indicator for ifhousehold i in (monthly) date t is in year Υ pre or post the challenge start date. αi and dt are indicatorand date fixed effects. Preit and Postit are indicators for households outside the ±5 year window. θ1 isthe average change during the initial conservation challenge, relative to the average during the referenceyear. I use the last pre-program year as the reference year, Υ = 0. In panel A, I find that treatmenteffects in percentage terms are not statistically different across quartiles of pre-program use. Thisshows that reductions in absolute electricity use are larger for high-consumption household, but arenot statistically different in percentage terms. In panels B, C, and D I find no statistically significantdifferences in treatment effects across building types, quartiles of assessed value, or quartiles of floorarea. If higher assessed property values and larger floorspace is taken as a proxy for income, the resultsimply that households respond similarly across quartiles of wealth.261.4. Event Study Estimates - Initial Conservation ChallengeFigure 1.11: Seasonal Treatment EffectsNotes: This figure plots estimated changes in electricity use during the initial conservation challenge relative to thesame month in the year prior. Estimates are from equation (1.1) estimated separately for each month of the year. 95%confidence intervals shown by the dashed lines. Non-Electric Heating are households expected by BC Hydro to heatprimarily from sources other than electricity. Electric Space Heating are households whose primary source of heating isexpected to be from electricity.271.4. Event Study Estimates - Initial Conservation ChallengeTable 1.4: Treatment Effects by Pre-Determined VariablesPanel A: Quartiles of Pre-Program Electricity Use1st 2nd 3rd 4thθ1 : Initial Challenge -0.0440∗∗∗ -0.0488∗∗∗ -0.0425∗∗∗ -0.0557∗∗∗(0.00749) (0.00546) (0.00595) (0.00699)Avg. Use in 2006 (kWh) 393 701 1007 1642Panel B: Building Type1 Sty SFD 2 Sty SFD Apartment Townhouseθ1 : Initial Challenge -0.0359∗∗∗ -0.0299∗∗∗ -0.0525∗∗∗ -0.0312∗∗∗(0.00335) (0.00381) (0.00737) (0.00581)Panel C: Quartiles of Assessed Value1st 2nd 3rd 4thθ1 : Initial Challenge -0.0388∗∗∗ -0.0410∗∗∗ -0.0327∗∗∗ -0.0303∗∗∗(0.00454) (0.00420) (0.00414) (0.00448)Avg. Assessed Value ($1,000) $289 $450 $684 $1,208Panel D: Quartiles of Floor Area1st 2nd 3rd 4thθ1 : Initial Challenge -0.0463∗∗∗ -0.0402∗∗∗ -0.0281∗∗∗ -0.0278∗∗∗(0.00517) (0.00398) (0.00404) (0.00452)Avg. Floor Area (sq. ft.) 979 1642 2194 3254Notes: Estimated average change in electricity use from the year pre-program to year of the initial conservation challenge.Panel A: Quartiles of pre-program electricity use determined from households’ average electricity use in the pre-programyear, 2006. Quartiles are defined separately for the balanced set of participant and non-participant households. Estimatesexclude households starting their initial challenge before 2009 to avoid biasing estimates with a reversion to the mean.Panel B: Building type includes the four principal housing types of single story single family dwellings, two story singlefamily dwellings, apartments, and town homes. Panel C: quartiles of assessed value are from the 2010 BC Assessment forindividual units and include both structure and land value. Panel D: quartiles of floor area are in square feet. Standarderrors in parentheses. *** p<0.01, ** p<0.05, * p< Conclusion1.5 ConclusionThis chapter investigates how households respond to financial rewards for achieving electricityconservation targets. I work with a large electrical utility company to study a program that allowshouseholds to participate in successive annual electricity conservation challenges. Using a panel ofmonthly electricity use, I track households’ decisions whether to re-enroll in the program along withchanges in their electricity use. The ten years of the panel allow me to estimate the long-run per-sistence of electricity conservation as households leave the program, as well as the long-run changesamong households that repeatedly re-enroll in the program. By comparing the electricity conservationacross households I provide insights into what changes within the home households made to conserveelectricity, and when conservation occurs. Three findings distinguish this work. First, this chapterundertakes one of the longest studies to date of the persistence of electricity conservation. I do not findthat financial rewards cause persistent changes; instead, electricity use rebounds close to pre-programlevels as households leave the program, and continues to decline among households that re-enroll. Thisshows that the ongoing incentive of successive financial rewards is necessary to cause long-run lowerelectricity use. A potential implication of this is that programs in fields outside energy conservation,such as education, that aim to cause persistent effects should consider incentivizing specific changesknown to be permanent rather than reward a general outcome. Second, despite the programs voluntarynature I find no evidence that households strategically manipulate their participation to receive creditfor conservation that is not due to the program. This supports that voluntary electricity conserva-tion reward programs can be implemented and with a large majority of resulting conservation beingcausally due to the program. The lack of strategic manipulation is supported by the third finding of fewdifferences in electricity conservation across household characteristics. This suggests that segmentingconsumers by type is a less effective margin for improving similar conservation programs compared toincreasing re-enrollment.29Chapter 2The Extensive Margin of ElectricityConservation2.1 IntroductionIn Chapter 1, I documented how households may participate in multiple Team Power Smart conserva-tion challenges, and that electricity use repeatedly diverges between those who leave the program andthose that re-enroll in additional conservation challenges. This suggests that energy use may reboundin the absence of program participation and that voluntary re-enrollment in additional conservationchallenges could cause additional reductions in electricity use. This chapter uses the same Team PowerSmart program to study two aspects of these households’ extensive margin re-enrollment decisions.First, I study the decision to re-enroll. I find that re-enrollment decisions differ little across householdcharacteristics or their level of electricity use. Instead, I find that households’ decisions on whetherto remain in the program are sensitive to their success or failure in a conservation challenge but areinsensitive to their actual effort and reductions in electricity use. As a result, households make theopposite decision from what the program design incentivizes; households facing an increased likelihoodof achieving their next conservation target are less likely to re-enroll and attempt another conserva-tion challenge. Importantly for designing general incentive programs this suggests that households usesimple heuristics in making decisions rather than incorporate the detailed information that is readilyavailable to them.Second, comparisons of electricity conservation across multiple challenges in Chapter 1 comparedhouseholds making different extensive margin re-enrollment decisions. A concern with voluntary re-enrollment is that a selection bias may arise if households differ in a way that determines post-challengeelectricity conservation and is correlated with their decision to remain in the program. For example,households that make a capital investment in energy efficient appliances may, conditional on the re-ductions in energy use achieved in the first challenge, be more likely to continue to a subsequentchallenge than a household which is making only short-run adjustments to behaviour. This potentialself-selection bias prevents the event study estimates of Chapter 1 being interpreted as full programtreatment effects. I address this self-selection by undertaking an instrumental variables estimate of thecausal reductions in electricity use from continuing to a second conservation challenge. Households’success or failure in a conservation challenges creates a discontinuity in the probability they continueto an additional challenge. Using this in a fuzzy regression discontinuity empirical strategy I find thatan additional conservation challenge causes lower electricity use. This is consistent with the eventstudy results of Chapter 1 and shows that voluntary financial reward programs can cause reductions302.1. Introductionin electricity use, but that electricity use tends to rebound in the absence of the financial incentive.Information provision is a ubiquitous feature of energy conservation and other incentive programs,both as a stand alone intervention and bundled with incentives such as price changes or financialrewards. I find that households’ re-enrollment decisions are responsive to passing or failing their annualconservation challenge, but not to the detailed information on their actual conservation effort that isprovided to them.12 This suggests that while households are responding to information, they either donot take the full set of information into account or do not respond to it as a standard neoclassical modelof consumer decisions would predict.13 This is important for programs based on providing consumerswith detailed information. For example, Schleich et al. (2017) undertakes a RCT where households canaccess detailed information on their consumption through an online portal or through mailed reportsand finds this is effective in persistently reducing electricity use. Jessoe and Rapson (2014) use aRCT to find in-home displays on the price and quantity of electricity used increases consumers price-elasticity, while Martin and Rivers (2016) show how similar in-home displays can directly cause energyconservation.14 This chapter’s findings are also consistent with previous work that suggests the arrivalof information, not only the information content itself, can serve as a nudge or reminder on electricityuse. Gilbert and Graff Zivin (2014) show that simply receiving an electricity bill can reduce electricityuse in the short term by 1%, and Sexton (2015) finds that increased billing frequency lowers electricityuse. The responsiveness of households to their passing or failing a challenge but not the incentivestructure is also suggestive that intrinsic motivations for conserving energy may be important (Gneezyet al., 2011). Previous work considering intrinsic motivations include the home energy reports studiedin Allcott (2011) and Allcott and Rogers (2014), and Ito et al. (2015) who directly compare moralsuasion against the incentive of short-term higher prices through two RCTs. They find that whileboth interventions cause lower short-run electricity use, only the short-term price increase generatedpersistent effects.Information also plays an important role in programs that change a price schedule or offer a financialreward. These programs assume consumers are sufficiently informed of their own energy use and theprogram design to respond to the incentive as intended. Programs can fail to deliver anticipatedoutcomes if consumers under-respond to the incentive or do not use information available to them. Ito(2014) exploits a spatial discontinuity among households experiencing different block pricing schedulesand finds that consumers respond to average prices instead of marginal prices. He concludes thatthe nonlinear price schedule is unsuccessful in achieving energy conservation due to this suboptimalresponse. The use of heuristics and inattention to information found in this chapter, whether rationalor a sub-optimal response to the incentive, may be a pervasive feature of consumers’ responses and is12This information is provided to participants both through a letter at the end of their conservation challenge andthrough an online portal. The majority of households regularly log into their online portal (Kassirer et al., 2014) so thistheir lack of response is not not due to a lack of awareness of their progress or success.13An important model of decision making in Psychology is self-efficacy, which refers to an individuals beliefs abouttheir ability to affect outcomes through their actions (Bandura, 1977). Households could observe their success, interpretthis as evidence they can affect the outcome of electricity conservation, and decide to re-enroll due to their updated beliefson their self-efficacy. However, the sharp discontinuity in this setting - and the information provided to households ontheir actual conservation achieved - precludes the concept of self-efficacy from alone explaining households’ behaviour.14There is no a-priori reason that additional information would lead to decreases rather than increases in consumption;Wichman (2017) find that switching from bi-monthly to monthly billing for water increased its use.312.2. The Weather Adjustmentan important consideration in the design of incentive programs.The remainder of Chapter 2 is organized as follows. In Section 2.2 I discuss the weather adjustmentand how changes in electricity use are measured. Section 2.3 analyzes what determines the decisionto re-enroll including the discontinuous effect of success. Section 2.4 introduces the fuzzy regressiondiscontinuity empirical strategy and provides evidence the identifying assumptions hold. I present theestimates in 2.5, discuss the program cost-effectiveness in Section 2.6, and conclude in Section The Weather AdjustmentWeather changes affect households’ electricity use. BC Hydro applies a weather-adjustment algorithmto avoid penalizing or unnecessarily rewarding households for changes in electricity use during a con-servation challenge that are due to idiosyncratic changes in weather, and not their conservation effort.This algorithm is applied to the changes in actual electricity use that customers are billed for; I referto changes in billed electricity use, prior to their weather-adjustment, as billed changes. The weather-adjustment algorithm adjusts billed changes for year-to-year changes in heating degree days, and resultsin a second measure which is the electricity conservation houses receive credit for; I refer to these ascredited changes. Importantly, the weather-adjustment algorithm used by BC Hydro resulted in largeadjustments to households’ electricity conservation beyond those necessary for correcting for weatherchanges.15 Figure 2.1, Credited vs. Billed changes, shows a histogram of the difference in absolutepercentage points between credited and billed changes. These differences are not small; they have amean of -0.43% and a standard deviation of 4.5%. In the second panel, Credited vs. Updated Changes,I show the difference between credited changes used to evaluate a household’s success and changes usingthe updated algorithm where the effect of weather on electricity use has been removed as recommendedby BC Hydro. These have a mean of -0.51% and standard deviation of 5.4%. This shows the adjust-ment caused many households to receive random shocks to their electricity conservation comparable inmagnitude to half of their 10% conservation goal. When households view their online progress towardstheir 10% reduction goal, or the reductions in electricity use they are credited with achieving during achallenge, they are shown the credited — not billed — changes. As a result, households were not awareof the random shock applied to their conservation. As I discuss later, this random conservation shocksignificantly strengthens the fuzzy regression discontinuity identifying assumptions by mechanicallyrandomizing households into and out of success in their conservation challenge.1615Adjusting for weather is not an exact science. Some households heat with electricity more than others, somehouseholds that do not principally heat with electricity - and so are defined as non-electric heat households - still makesignificant use of electric heat via baseboard heaters, and household-specific characteristics like insulation or numberof residents will drive large differences in the use electricity in response to weather changes. The weather-adjustmentalgorithm used to calculate credited changes was improved and updated in 2014; I exclude households that use theupdated weather-adjustment algorithm. The weather-adjustment algorithm, formally available on the BC Hydro TeamPower Smart website, is available from the author.16In theory a household could calculate their own reductions from their billed consumption, and from this, determinethe weather correction applied. This is unlikely to have occurred for many households.322.2. The Weather AdjustmentFigure 2.1: Weather Adjustment DiscrepanciesNotes: The left panel, Credited vs. Billed changes, is a histogram of the absolute differences between the changes inelectricity use credited to a household after applying the first weather-adjustment algorithm, and the changes in theirbilled electricity use. The right panel, Credited vs. Updated Changes, is the histogram of differences between creditedchanges and changes in billed electricity use where the effect of weather has been removed as recommended by BC Hydroand used in the updated algorithm. Differences are in absolute percentage points such that a 10% Absolute Difference isequivalent in magnitude to the 10% conservation target.332.3. Re-Enrollment Decisions2.3 Re-Enrollment DecisionsAll households that participate in Team Power Smart have the option of re-enrolling in additionalconservation challenges. Do households differ in their likelihood of re-enrolling? To explore whatcorrelates with their decision I estimate a Probit model for the probability of re-enrolling. Table 2.1shows the marginal effects. Specification (1) includes households’ electric heating category and buildingtype. I use the most common household type, Single Story Single Family Dwellings that heat primarilywithout electricity, as the reference category; marginal effects show the change in probability of re-enrolling relative to this household type. Specification (1) shows Townhouses are the only householdtype with a statistically significant difference (4.75%) in the probability of re-enrolling. Specification(2) shows that the probability of re-enrolling does not materially differ across the number of bedrooms,household value, or size of the house. Specifications (3) and (4) control for, respectively, householdscredited changes in electricity use and an indicator Success for whether they achieve their conservationtarget. These show households with larger electricity conservation are more likely to re-enroll asare households that pass their conservation challenge. This highlights the importance of success in thechallenge relative to differences across household types. Taking the largest difference in point estimatesacross household types in Specification (4) finds Townhouses are 8.6% more likely to re-enroll thanhomes classified Other. In comparison, households that pass their conservation Challenge are 19.8%more likely to re-enroll. This supports the findings from Subsection 1.4.3 that electricity conservationdoes not differ substantially across household types. Specification (5) includes a household’s Pre-Program use measured in standard deviations from the mean of households’ 2006 electricity use withinheating and building type categories. This shows that households with higher Pre-Program electricityuse are more likely to re-enroll; households three standard deviations above the mean 2006 electricityuse are 5.9% more likely to re-enroll. However, this magnitude is not large compared to the effect ofSuccess — Specification (6) — or differences between Townhomes and Other. Specification (7) showsthe re-enrollment probability differs little between Winter and other seasons. Taken together theseresults show that a households pre-determined characteristics have little direct, or in-direct throughthe electricity conservation, effect on the probability of re-enrolling. This is particularly the case incomparison to the importance of passing the conservation challenge, which I explore in detail below.2.3.1 By Level of ReductionsFigure 2.2 plots the probability of re-enrolling in a second challenge against the credited changes inelectricity use from a household’s initial conservation challenge. This provides several insights intohouseholds’ decisions whether to re-enroll. Among households that fail their initial challenge, theirprobability of continuing to a second challenge is largely independent of their credited changes inelectricity use. Figure 2.2 shows households with large increases in electricity use of around 20%have a similar probability of re-enrolling as households that had no change, and these households areapproximately 7% less likely to re-enroll as those that nearly achieved their 10% target. A similarpattern repeats amongst households that passed their challenge; those that barely pass with reductions∼10% are equally likely to continue as households that achieved reductions of ∼20% or more. In342.3. Re-Enrollment DecisionsTable 2.1: Probit Model: Re-Enrolling in a Second Challenge(1) (2) (3) (4) (5) (6) (7)Dependent variable: Re-enrollment in a second conservation challengeNon-Electric Heat - - - - - -Electric Heat 0.00368 0.00112 0.00273 -0.00646 0.00335 -0.00682(0.0148) (0.0152) (0.0149) (0.0150) (0.0149) (0.0151)Heating Unknown -0.0141 -0.00335 -0.0122 -0.00740 -0.0134 -0.00655(0.0178) (0.0185) (0.0179) (0.0178) (0.0178) (0.0178)1 Story Sfd - - - - - -2 Story Sfd -0.00895 0.00879 -0.00873 -0.00661 -0.00915 -0.00684(0.0147) (0.0160) (0.0147) (0.0149) (0.0147) (0.0149)1.5 Story Sfd -0.0161 0.000633 -0.0157 -0.0190 -0.0162 -0.0194(0.0294) (0.0301) (0.0293) (0.0297) (0.0294) (0.0298)Apartment 0.00710 -0.0438∗ 0.00725 0.00821 0.00796 0.00897(0.0199) (0.0263) (0.0201) (0.0201) (0.0200) (0.0202)Townhouse 0.0475∗∗ 0.0215 0.0510∗∗∗ 0.0569∗∗∗ 0.0476∗∗ 0.0572∗∗∗(0.0187) (0.0206) (0.0187) (0.0187) (0.0187) (0.0187)Other (home type) -0.0361 -0.0501 -0.0334 -0.0294 -0.0362 -0.0295(0.0350) (0.0360) (0.0350) (0.0350) (0.0351) (0.0350)Bedrooms -0.0117(0.00739)Value -0.0195(0.0132)FloorArea -0.0260(0.0239)Credited Changes -0.259∗∗∗(0.0470)Success 0.198∗∗∗ 0.200∗∗∗(0.0114) (0.0114)Pre-ProgramUse -0.0195∗∗∗ -0.0236∗∗∗(0.00567) (0.00570)Winter -Spring 0.0357∗(0.0184)Summer 0.0301∗(0.0165)Fall -0.0207(0.0169)Households 7182 6880 7182 7182 7181 7181 7182Pseudo R2 0.001 0.003 0.010 0.030 0.003 0.031 0.002χ2 12.892 23.482 44.942 273.666 24.662 288.620 16.978Notes: This table shows how differences in household characteristics affect the probability of re-enrolling in a secondconservation challenge. Dependent variable: indicator Ci = 1 if household i re-enrolls, 0 otherwise. All households in thissample begin an initial conservation challenge between February 2007 and February 2013. Estimates for specifications (1)- (6) are relative to the reference category of One Story Single Family Dwellings that are primarily non-electric heating.Specification (7) is relative to Winter. Value and Floor area are natural logs, Credited Changes is the percent change inChallenge 1 electricity conservation credited to households, and Success an indicator equal to 1 if a household achievestheir Challenge 1 conservation target. Pre-program use is the number of standard deviations between a household’selectricity use in 2006 and the average electricity use among households within the same building and heating typecategory. All coefficients are marginal effects at the covariate means. Standard errors in parentheses, *** p<0.01, **p<0.05, * p<0.1.352.4. The Fuzzy Regression Discontinuity Empirical Strategycontrast, there is a sharp discontinuous jump in the probability of continuing to a subsequent challengeat the 9.5% threshold for success.17 This pattern shows that in deciding whether to continue in theprogram, households are responsive to their success or failure in a conservation challenge but are largelyinsensitive to the level of reductions in electricity use they are credited with or achieve.18This insensitivity of re-enrollment to changes in electricity use is not consistent with the incentivestructure of the program. Each conservation challenge is an additional 10% reduction compared to theyear prior; this creates a greater incentive for households that had increases, or smaller reductions, inelectricity use to re-enroll compared to if they had larger reductions. Households with large increasesduring a challenge establish a new higher baseline for their subsequent 10% conservation challenge,while those that decreased their electricity use establish a new lower baseline. Under the reasonableassumption that the marginal cost of electricity conservation is increasing, the greater the electricityconservation achieved in a challenge the more costly, in terms of effort or financial investment, thesubsequent challenge will be.19202.4 The Fuzzy Regression Discontinuity Empirical StrategyThe simplest way to identify the causal treatment effect of a second challenge would be to randomlyassign households that complete the first challenge into and out of the second challenge. Randomassignment would permit causal identification by making households ending their participation a validcounterfactual for those which were randomly re-enrolled. In the absence of random assignment,a discontinuity in the probability of treatment can, under several identifying assumptions, producerandom assignment into treatment for a subset of households. This permits causal identification forthat subset despite potential self-selection, and is the basis of the fuzzy regression discontinuity design(fuzzy-RDD) employed here (Angrist and Pischke, 2008).A fuzzy-RDD requires a threshold in a running variable that, as the running variable increases fromjust below the threshold to just above the threshold, causes a discontinuous change in the probabilityof treatment. If units cannot precisely manipulate the running variable then, at the threshold, theywill be as good as randomly assigned to either side of it (Lee and Lemieux, 2010). As a result, someunits are randomly assigned into and out of treatment by their random assignment to either side of thediscontinuity. Those units that ‘comply’ with the running variable by changing their treatment status,17While similar discontinuities exist after the second and subsequent conservation challenges, the sample of thesehouseholds is too small for instrumental variable estimates.18See Figure B.1 in the Appendix for the comparison to billed reductions.19This is supported by Figure B.1 in the Appendix, which shows the fraction of households that, conditional on re-enrolling, pass their second conservation challenge. Consistent with increasing marginal cost of electricity conservationdescribed above, approximately half of households with billed increases in electricity use of 10-20% pass their secondchallenge; these households are twice as likely to pass as households that had reductions during the first challenge of 10%or larger. This finding also holds when using credited changes.20A potential concern is that households may differ substantially depending on their credited changes in a way thataffects their probability of re-enrolling, and this could offset the incentive to re-enroll caused by smaller reductions.The large weather adjustment makes such an offset unlikely to produce the observed insensitivity of re-enrollmentto conservation. The weather adjustment significantly randomizes households achieving the same actual reduction inelectricity use across the credited changes, increasing the comparability of households with different credited changes.362.4. The Fuzzy Regression Discontinuity Empirical StrategyFigure 2.2: Probability of Re-EnrollingNotes: Credited changes are the annual changes in electricity consumption between the pre-program baseline year andthe year of the first conservation challenge after processing by the BC Hydro weather adjustment algorithm. Creditedchanges are those changes shown to households during their conservation challenges and after their completion. Pointestimates and 95% confidence intervals are the mean probability of re-enrolling among households within 0.75% widthbinds in credited changes. The dashed line is a first order local polynomial fit. The vertical dashed line indicates the9.5% threshold. By definition, households to the left of the dashed line pass their conservation challenge while those tothe right fail.372.4. The Fuzzy Regression Discontinuity Empirical Strategybased on their position above or below the threshold, are called ‘compliers.’ This difference in complierschanging their treatment status across the threshold changes, through the compliers treatment effect,the outcome variable across the threshold. The fuzzy-RD recovers the Local Average Treatment Effect(LATE) for these compliers by dividing the average change in outcome variable by the average changein the number of compliers. This is a Local Average Treatment Effect because it is estimated onlyfor those units with the running variable in the vicinity of the threshold.21 The fuzzy-RD estimate ofthe LATE can be found by dividing two regression discontinuity estimates; the numerator is the RDestimate of the change in outcome across the threshold, and the denominator is the RD estimate of thechange in probability of treatment across the threshold. As Angrist and Pischke (2008) discuss, thiscan be interpreted as a two-stage least squares instrumental variables estimation where the instrumentfor treatment is a binary indicator for a unit being above or below the threshold.I use the discontinuity in the probability of continuing to a second challenge at the 9.5% conserva-tion threshold for success, shown in Figure 2.2, as the instrument for treatment in a second conservationchallenge. The instrumental variable is a binary indicator for success in the initial conservation chal-lenge. The first stage relationship isCi = γ0 + γ11{Ri ≤ R¯}+ γ2Ri + γ31{Ri ≤ R¯}×Ri + γ4Bi + γ5Xi + ηi (2.1)where Ci is a binary indicator for whether a household continues to a second challenge, Ri arehouseholds’ credited changes in electricity use from the first challenge, R¯ is the threshold for successin the challenge and is -9.5%, 1{Ri ≤ R¯} is the dummy variable for success in the initial challenge,Bi are the billed changes from the initial challenge, and Xi is a vector of other controls. In my mainspecification I control for a linear trend in credited reductions and allow this trend to have differentslopes on either side of the discontinuity. The instrument excluded from the second stage is 1{Ri ≤ R¯}.The second-stage relationship isyi = β0 + β1Ci + β2Ri + β31{Ri ≤ R¯}×Ri + β4Bi + β5Xi + i (2.2)where yi is the post-challenge percent change in electricity use.22 yi is definedyi ≡ (ui,τ=2 − ui,τ=1)ui,τ=0(2.3)where ui,τ is household i’ s aggregate electricity use during the year indexed by event-time τ . Forhouseholds that do not undertake a second challenge ui,τ=2 is the total electricity use in the 12 monthsimmediately following the completion of their initial challenge, ui,τ=1 is the total electricity use duringtheir initial challenge, and ui,τ=0 is the use during the pre-challenge year. For households that imme-diately undertake a second conservation challenge with no gap between challenges ui,τ=2 is the totalelectricity use during the second challenge and ui,τ=1 and ui,τ=0 are as before. For households that21In contrast to an Average Treatment Effect which would be the average treatment effect across all units, regardlessof their value of the running variable.22In the Appendix Section B.3 I present an alternative fuzzy-RD specification that uses the log of monthly electricityuse. This finds broadly similar results to using post-challenge percent changes in electricity use. My preferred results usepost-challenge changes due to its parsimonious specification and easy interpretation of estimated coefficients.382.4. The Fuzzy Regression Discontinuity Empirical Strategywait before beginning a second conservation challenge I define ui,τ=2 as the 12 months of electricity useduring their second challenge and ui,τ=1 as the 12 months of electricity use immediately preceding thatsecond challenge. This makes yi a consistent measure of the reductions in electricity use a household istrying to achieve in its second challenge regardless of whether that household waited before undertakinga challenge or began it immediately. I center the billed and credited changes at the 9.5% threshold.β0 is the post-challenge change in billed electricity use at this threshold for households that do notcontinue in the program. β1 is the additional effect on post-challenge billed changes in electricity userelative to households that left the program.2.4.1 First Stage and Reduced FormFigure 2.3 plots the probability that households re-enroll in a second conservation challenge by theircredited changes in the first challenge.23 The solid vertical line shows the 10% target, and the dashedvertical shows the 9.5% threshold for success or failure. Importantly, the discontinuity occurs at the9.5% threshold for determining success or failure, and not at the 10% target that households are tryingto achieve. Figure 2.4 plots yi from equation 2.3 against the same bins of credited changes duringa households’ first conservation challenge. The discontinuity occurs again at the 9.5% threshold, not10% conservation target.2.4.2 Identifying AssumptionsThe fuzzy RD estimation strategy requires that assignment into and out of treatment in the vicinityof the threshold is as good as randomly assigned, such that households on one side of the threshold area suitable counterfactual for households on the other. This assumption is violated if households canprecisely manipulate their assignment into treatment. Such manipulation is a particular concern in thissetup as households are explicitly trying to achieve a 10% conservation target. Sorting at the disconti-nuity could occur if, for example, households are heterogeneous in their attention to their progress andhigh-information type households exert additional effort in the last months of a conservation challengeand self-select into passing their challenge.Sorting discontinuously at the threshold is unlikely for several reasons. Because the weather ad-justment is applied each month and used to update households’ cumulative progress towards their 10%conservation target, households that are attentive to their progress could in theory take the weatheradjustment partially into account in updating their effort over the first 11 months.24 However, house-holds do not know their last month’s conservation until they have completed the challenge and BCHydro applies the final weather adjustment. This final weather adjustment mechanically randomizeshouseholds near the threshold into and out of treatment. I estimate that, within a ±5% windowaround the 10% conservation target, 17.3% of households that are on track to succeed at month 11ultimately fail, while 14.7% of households that are on track to fail ultimately pass their challenge. The23This is similar to Figure 2.2 but plotted on a narrower bandwidth around the 9.5% threshold.24In separate ongoing work I find no evidence that households just succeeding in their challenge update their nextmonths conservation effort differently than those households which are just failing their challenge. This suggests thathouseholds are not precisely targeting the 10% conservation target.392.4. The Fuzzy Regression Discontinuity Empirical StrategyFigure 2.3: First Stage - Probability of Re-EnrollingNotes: Credited changes and the Probability of Re-enrolling are as defined in Figure 2.2. The sold vertical line is at the10% conservation target and the dashed vertical line denotes the 9.5% threshold for success in a Challenge.402.4. The Fuzzy Regression Discontinuity Empirical StrategyFigure 2.4: Reduced Form - Post-Challenge kWh ChangesNotes: Post-Challenge Percent Change in kWh denotes the percentage annual change in electricity use from the yearof the conservation to the post-challenge year. The sold vertical line is at the 10% conservation target and the dashedvertical line denotes the 9.5% threshold for success in a Challenge.412.4. The Fuzzy Regression Discontinuity Empirical Strategycumulative nature of the challenge also makes precise manipulation difficult. A household at a 9%cumulative reduction entering the last month of their challenge would have to double their previousmonthly reductions and reduce their use in the last month by 21% to achieve their 10% target.Most importantly, households were not aware that their success or failure would be evaluated againsta 9.5% threshold instead of the advertised 10% target. This does not remove the potential problemof sorting; households sorting around the 10% target in a way that changed potential outcomes in theabsence of treatment would invalidate the causal interpretation of Regression Discontinuity estimatesat the 9.5% threshold.25 Instead, this feature of a separate threshold and target provides evidence thathouseholds are not sorting at the threshold on either observables or unobservables, despite bunchingbelow the 10% target.Figure 2.5 shows a histogram of credited changes during households’ first conservation challenge.The mass of observations just below the 10% threshold suggests that households may be bunchingaround the 10% target. A density test by McCrary (2008), Figure 2.6, rejects the null hypothesis thatthere is no discontinuity in the density of the running variable at the 10% threshold, supporting thathouseholds are bunching at the 10% target.26Evidence on whether there is sorting on observables can be gained by testing the continuity ofcovariates and pre-determined variables across the 9.5% threshold and 10% target. I find no statis-tically significant changes at either threshold which supports that households are not sorting at thediscontinuity or 10% threshold in a manner correlated with observables (Appendix Table B.1 and Fig-ure B.3). BC Hydro’s separation of the 10% target from the 9.5% threshold for success also providesevidence that households are not sorting on unobservables. If households were sorting around the 10%target, their decision to re-enroll in a second challenge or the post-program outcome would be ex-pected to be discontinuous at the 10% target. Figures 2.3 and 2.4 suggest that these outcomes changediscontinuously only at the 9.5% threshold and not the 10% target.The exclusion restriction requires that the instrument only affect the outcome, yi, through thedecision to continue to a second challenge (Angrist and Pischke, 2008). Conditional on credited andbilled reductions, success in a challenge can have no direct effect on post-program changes in electric-ity use and therefore can be excluded from the second stage. This assumption could be violated ifhouseholds receive a warm-glow effect from succeeding that affects their subsequent effort at reduc-tions independent of continuing, or if the $75 rebate causes an income effect and alters post-programconservation. As $75 is small relative to household’s incomes I assume there is no income effect thatinfluences electricity use. Any warm-glow effect on subsequent conservation effort is likely to be shortlived compared to the effect of the financial incentive, which remains throughout the twelve months ofthe challenge. In addition, if a warm glow effect was substantial it is likely to be particularly strongduring the initial months of the next challenge while a household’s success is still fresh in their minds.The event study estimates of Figure 1.7 indicate that additional program effects during the secondchallenge are consistent throughout the twelve months of challenge. This suggests that there is little25In theory, a sufficiently large number of observations would allow estimation limited to bandwidths of ±0.5% aroundthe 9.5% threshold, thus avoiding the problem of sorting around the 10% threshold.26A density test by McCrary (2008), Appendix Figure B.2, fails to reject the null hypothesis at the 5% level (one sidedp-value 0.093) that there is no discontinuity in the density of the running variable at the 9.5% threshold.422.4. The Fuzzy Regression Discontinuity Empirical StrategyFigure 2.5: Histogram of Credited ChangesNotes: Histogram of households’ credited changes during their initial conservation challenge. The sold red line is the 10%conservation target and the dashed line the 9.5% threshold for success. The increase in mass to the left of the verticalline demonstrates the potential for bunching at the 10% target.warm-glow effect in the initial months, unless they are cancelled out by an equal and opposite increasein program effects from the financial incentive.432.4. The Fuzzy Regression Discontinuity Empirical StrategyFigure 2.6: Density Test of the Running Variable - 10% TargetNotes: McCrary (2008) density test of the percent change in electricity use from a household’s initial conservationchallenge. The dark line is a smoothed local linear fit to the density of changes in electricity use, with 95% confidenceintervals indicated by the light grey line. Point estimates of the density are grey circles. The dashed red line is the 9.5%reduction threshold, and the sold line is the 10% reduction target.442.5. Fuzzy Regression Discontinuity Estimates2.5 Fuzzy Regression Discontinuity EstimatesThis section presents the fuzzy-RD estimates of the treatment effect of a second conservationchallenge. Across a wide variety of specifications and robustness checks I find a consistent patternwhere re-enrolling in a second conservation challenge causes a large additional reduction in electricityuse. These results are consistent with the event-study results and support that additional conservationchallenges cause additional reductions in electricity use, and that electricity use rebounds as householdsleave the program.Table 2.2 presents my preferred specification. Columns (3) through (7) show results estimated fordifferent bandwidths from ±7% to ±3% around the threshold of a -9.5% change in credited electricityuse.27,28 I restrict the estimation sample to households starting a second challenge within 12 monthsof completing their prior challenge.29 Panel (A) shows the first-stage results for the probability ofcontinuing to a second challenge, estimated from equation (2.1). For my preferred bandwidth of 5%I find that, conditional on failing the challenge, 53% of households continue to a second conservationchallenge. At the 9.5% threshold for success, households that just succeed in their initial conservationchallenge are 14.5% more likely to continue to an additional challenge than those which just failed. Thispattern repeats across various estimation window widths. Approximately 50% of households re-enrollin a second conservation challenge if they fail their initial challenge, while success in a challenge causesan additional 14% to 20% of households to re-enroll.30 Across bandwidths from ±7% to ±3% I find theF-statistic on the instrument decreases from 22 to 6.5. This indicates that the first-stage is reasonablystrong for larger bandwidths, but the small sample size becomes relevant as the bandwidth narrows.The large and significant estimate on the discontinuity, γˆ1, and the generally small and insignificantestimate on billed changes, γˆ4, shows that the significant correlation between billed changes in electricityuse and the probability of continuing, visible in Appendix Figure B.1, is a composition effect from theweather adjustment changing the probability of success near the threshold.Table 2.2 panel (B) reports the OLS and second-stage instrumental variable estimates of equation(2.2). Specification (1) is the OLS result for all households. (1) shows that re-enrolling in an additionalchallenge is associated with a 1.6% decline in post-challenge electricity use, relative to households thatdo not re-enroll. Specification (2) is the OLS results for households within ±5% of the threshold. Thisfinds that, for households at the 9.5% threshold, ending participation is associated with a rebound of1.5% and re-enrolling with a reduction of 2.4%. Specifications (3) through (7) show the IV estimatesfor different estimation bandwidths. These estimates find a consistent pattern where, for householdsthat comply with the instrument, continuing to a second conservation challenge causes a reduction inelectricity use. For my preferred bandwidth of 5%, I estimate that continuing to a second conservationchallenge causes a 23% reduction in electricity use (βˆ1 = −0.231). This is a large effect. By definition,27I present estimates using a range of bandwidths and a uniform weighting instead of kernel estimates. See Imbensand Lemieux (2007) for a discussion on the practical similarities of varying the bandwidth to using different kernels. Ifind results are robust across different bandwidths to using a triangular kernel.28Plots of the First Stage and Reduced Form are presented in Table B.4 in the Appendix.29Results are robust to other restrictions on the gap length between challenges. Table B.3 in the Appendix presentsone such robustness check using a gap length of 6 months.30A weak instruments test by Moreira (2003) rejects (p-value 0.013, 5% bandwidth) that the binary indicator forSuccess (γ1) is a weak instrument.452.5. Fuzzy Regression Discontinuity Estimatesthe treatment effect is the change in electricity use for complier households relative to what they wouldhave had, had they not re-enrolled. An instrumental variables estimation strategy cannot identify thelevel of electricity use, in the absence of continuing, for these compliers. As a result, the treatmenteffect does not separately identify a potential rebound in electricity use among those that leave theprogram from additional reductions in electricity use beyond those achieved in the first conservationchallenge.31 Given the average reduction of 9.1% during the first challenge for households within the±5% bandwidth, and the target of an additional 10% conservation, the estimated treatment effect islikely comprised of both a significant rebound in electricity use among complier households that endparticipation and a large additional reduction among complier households that re-enroll in anotherchallenge.32Specifications (3) through (7) show that the magnitude of the treatment effect of a second challengeis sensitive to the estimation window width. Increasing the estimation bandwidth trades off decreasedvariance from a larger sample size against increased potential bias from misspecification (Lee andLemieux, 2010). The concern with a large bandwidth is that households farther from the thresholdmay differ from those close to the threshold. This is less of a concern in this context due to the largeweather adjustment. As Figure 2.1 demonstrates, households with the same billed changes in electricityuse receive a large shock to their credited changes. Households receiving significantly different signalson their credited changes in use will, unknown to the households, have exerted the same effort andcaused the same physical reductions in electricity use. This randomizes households by their actualeffort - as measured by billed changes correctly adjusted for weather - across credited changes andaround the discontinuity.This randomization by billed changes is also important as post-challenge changes in electricityuse are correlated with changes during the challenge. For example, households that experienced anunusually warm winter and decreased their use, but made no other changes, would be expected torebound the following year to their use conditional on the expected number of heating degree days.While the credited changes, βˆ2, and billed changes, βˆ4, are either only marginally significant at a 10%level or not significant, the negative sign on the point estimates is consistent with the expected patternof households that have larger increases in an initial challenge having a larger post-challenge reduction,and households with larger initial challenge reductions having larger post-challenge rebounds in use.As discussed previously, an identifying assumption of a fuzzy RD estimation strategy is that house-holds just on either side of the discontinuity are as good as randomly assigned. Evidence that thisassumption does not hold would be if the IV estimates were sensitive to the inclusion of additionalcovariates. Table 2.3 shows IV estimates controlling for detailed household characteristics and changesin heating degree days. I control for the percent change in heating degree days between both the pre-program and first conservation challenge years (HDD0,1) and between the first conservation challenge31β0 cannot be interpreted as the average electricity use, conditional on other covariates, for complier households inthe absence of a conservation challenge. For example, in the simplest instrumental variable setup of a constant and asingle endogenous variable, βˆ0 ≡ y¯ − βˆ1 · x¯.32In comparing the OLS and fuzzy-RD estimates in Table 2.2 panel (B), it is important to note that the OLS estimatesare for all households within the estimation window while the fuzzy-RDD is a LATE for compliers. As a result, thedifference in estimates may be partially due to compliers being responsive to the incentive as estimated, with always-taker’s and never-taker’s electricity conservation remaining largely unresponsive to the financial reward incentive.462.5. Fuzzy Regression Discontinuity EstimatesTable 2.2: Fuzzy Regression Discontinuity Estimates of a Second Challenge(1) (2) (3) (4) (5) (6) (7)PanelA− First StageDependent variable: Continue to a Second Challenge CiWindow ±7% ±6% ±5% ±4% ±3%γ1: Success Ind. 0.202∗∗∗ 0.190∗∗∗ 0.145∗∗∗ 0.137∗∗ 0.173∗∗(0.0432) (0.0468) (0.0516) (0.0573) (0.0677)γ2: Cred.Reduc. -0.532 -1.391 -2.937∗∗ -1.290 2.090(0.778) (0.971) (1.244) (1.760) (2.765)γ3 : Success× 1.166 2.491∗ 2.565 -0.778 -3.973Cred.Reduc. (1.104) (1.383) (1.809) (2.447) (3.906)γ4 :BilledReduc. -0.300 -0.368 -0.0474 -0.282 -0.511(0.324) (0.344) (0.366) (0.404) (0.491)γ0 :Constant 0.487∗∗∗ 0.508∗∗∗ 0.530∗∗∗ 0.510∗∗∗ 0.475∗∗∗(0.0303) (0.0330) (0.0364) (0.0409) (0.0479)F-statistic 21.95 16.41 7.882 5.668 6.485PanelB− SecondStageDependent variable: Percent change in post-challenge electricity useOLS Instrumental Variable EstimatesWindow ±5% ±7% ±6% ±5% ±4% ±3%β1 :Re-Enroll -0.0160∗∗∗ -0.0242∗∗∗ -0.125∗∗ -0.178∗∗ -0.231∗∗ -0.323∗∗ -0.183∗(0.00422) (0.00683) (0.0605) (0.0738) (0.116) (0.164) (0.111)β2: Cred.Reduc. -0.171 -0.412∗ -0.643∗ -1.185∗ -1.108 0.785(0.245) (0.241) (0.354) (0.654) (0.828) (0.654)β3 : Success× 0.431 0.303 0.375 0.867 -0.229 -1.732Cred.Reduc. (0.439) (0.310) (0.426) (0.624) (0.985) (1.229)β4 :BilledReduc. -0.0858 -0.0461 -0.113 -0.101 -0.216 -0.222(0.0990) (0.0917) (0.103) (0.121) (0.168) (0.161)β0 :Constant -0.00773∗∗∗ 0.0146∗ 0.0712∗∗ 0.103∗∗ 0.138∗∗ 0.184∗ 0.0944(0.00289) (0.00773) (0.0356) (0.0447) (0.0698) (0.0950) (0.0625)N 5432 1475 2050 1763 1475 1196 888Notes: This table reports fuzzy-RD estimates corresponding to equations (2.1) and (2.2). Estimation sample isrestricted to households that either start their next challenge within 12 months or do not undertake an additionalchallenge. Estimation window is restricted to ± the listed percent around the 9.5% threshold in credited changes.Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1.472.5. Fuzzy Regression Discontinuity Estimatesand post-challenge year (HDD1,2). Increases in heating degree days during the post-challenge periodare positively correlated with post-challenge changes in electricity use. This is consistent with colderweather increasing the demand for electricity. The inclusion of these additional covariates has onlya small effect on the estimated effect of a second conservation challenge and supports the identifyingassumption that households are as good as randomly assigned at the discontinuity.A potential concern with the weather adjustment is if households with the same credited changesdiffer substantially in billed changes in the vicinity of the discontinuity. If billed reductions affect thepost-program outcomes, for example if households were to exhibit a strong reversion to the mean,then outliers in the weather adjustment could cause a violation of the good-as-randomly assigned as-sumption. Evidence that this is not a problem is gained by further restricting the estimation sampleto households that had billed changes within ±5% of 9.5% in billed reductions. This excludes thosehouseholds receiving large weather adjustments to their billed electricity use, in addition to the estima-tion bandwidth in credited reductions. Estimates, Table 2.4, are robust to this restriction. A potentialconcern with RD estimates is that the using observations away from the threshold increases the risk ofbiased estimates (Calonico et al., 2014). In Table 2.5 and Appendix Table B.2 I present bias-correctedestimates using 1st and 2nd order polynomial fits and the method of Calonico et al. (2014). Specifi-cation (8) presents the optimal bandwidth, 9%, determined using the variance-bias tradeoff method ofCalonico et al. (2014). Bias-corrected estimates lose significance for small bandwidths in the 1st orderestimates, and in all bandwidths narrower than 9% for 2nd order estimates. However, in all cases thepoint estimates stay a consistent sign and large magnitude. This suggests that while the magnitudeof point estimates vary, the causal effect of an additional conservation challenge is a large additionalreduction in electricity use for complier households — those households whose decision to re-enroll inTeam Power Smart is affected by their success or failure in their prior conservation challenge.482.5. Fuzzy Regression Discontinuity EstimatesTable 2.3: Fuzzy Regression Discontinuity Estimates: Additional Covariates(1) (2) (3) (4) (5) (6) (7)PanelA− First StageDependent variable: Continue to a Second Challenge CiWindow ±7% ±6% ±5% ±4% ±3%γ1: Success Ind. 0.202∗∗∗ 0.188∗∗∗ 0.143∗∗∗ 0.137∗∗ 0.169∗∗(0.0432) (0.0467) (0.0515) (0.0572) (0.0675)γ2: Cred.Reduc. -0.484 -1.335 -2.834∗∗ -0.981 2.186(0.800) (0.995) (1.268) (1.781) (2.774)γ3 : Success× 1.130 2.467∗ 2.524 -0.979 -3.635Cred.Reduc. (1.108) (1.385) (1.807) (2.437) (3.892)γ4 :BilledReduc. -0.329 -0.417 -0.169 -0.475 -0.870(0.358) (0.381) (0.403) (0.439) (0.539)HDD1,2 0.0867 -0.0662 0.142 -0.128 -0.145(0.360) (0.386) (0.398) (0.429) (0.482)HDD0,1 -0.0805 0.0703 -0.00803 0.301 0.591(0.351) (0.375) (0.384) (0.410) (0.463)γ0 :Constant 0.462∗∗∗ 0.476∗∗∗ 0.505∗∗∗ 0.483∗∗∗ 0.468∗∗∗(0.0342) (0.0372) (0.0407) (0.0456) (0.0531)F-statistic 21.82 16.27 7.736 5.757 6.266PanelB− SecondStageDependent variable: Percent change in post-challenge electricity useOLS Instrumental Variable EstimatesWindow ±5% ±7% ±6% ±5% ±4% ±3%β1 :Re-Enroll -0.0159∗∗∗ -0.0241∗∗∗ -0.119∗∗ -0.168∗∗ -0.214∗ -0.306∗ -0.176(0.00421) (0.00683) (0.0600) (0.0726) (0.113) (0.157) (0.112)β2: Cred.Reduc. 0.352∗∗∗ 0.348∗∗∗ 0.310∗∗∗ 0.297∗∗ 0.376∗∗∗ 0.255 0.299∗(0.0748) (0.111) (0.103) (0.120) (0.137) (0.177) (0.166)β3 : Success× -0.105 -0.113 -0.142 -0.113 -0.122 0.0475 0.0459Cred.Reduc. (0.0698) (0.102) (0.0964) (0.114) (0.130) (0.173) (0.167)β4 :BilledReduc. -0.0507 -0.323 -0.510 -0.962 -0.853 0.906(0.250) (0.245) (0.354) (0.630) (0.772) (0.646)HDD1,2 0.432 0.320 0.368 0.826 -0.239 -1.543(0.438) (0.308) (0.421) (0.601) (0.956) (1.207)HDD0,1 -0.216∗∗ -0.142 -0.222∗ -0.249∗ -0.418∗∗ -0.442∗∗(0.108) (0.103) (0.114) (0.130) (0.185) (0.183)β0 :Constant 0.00460 0.0302∗∗∗ 0.0782∗∗ 0.105∗∗ 0.138∗∗ 0.185∗∗ 0.109∗(0.00447) (0.00977) (0.0342) (0.0421) (0.0656) (0.0872) (0.0626)N 5432 1475 2050 1763 1475 1196 888Notes: This table reports fuzzy-RD estimates corresponding to equations (2.1) and (2.2). All specifications includebuilding type and heating category fixed effects. HDD0,1 and HDD1,2 are, respectively, the percent change in heatingdegree days from the pre-program year to the initial challenge, and initial challenge to the post-program year. Estimationsample restricted to households that either start their next challenge within 12 months or do not undertake an additionalchallenge. Estimation window is restricted to ± the listed percent around the 9.5% threshold in credited changes.Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1.492.5. Fuzzy Regression Discontinuity EstimatesTable 2.4: Fuzzy Regression Discontinuity Estimates: Restricted Billing(1) (2) (3) (4) (5) (6) (7)PanelA− First StageDependent variable: Continue to a Second Challenge CiWindow ±7% ±6% ±5% ±4% ±3%γ1: Success Ind. 0.185∗∗∗ 0.181∗∗∗ 0.121∗∗ 0.121∗∗ 0.172∗∗(0.0485) (0.0516) (0.0561) (0.0614) (0.0721)γ2: Cred.Reduc. 0.124 -0.0825 -2.105 -1.072 3.004(1.016) (1.205) (1.476) (2.003) (3.073)γ3 : Success× -0.697 -0.292 0.0330 -1.981 -5.156Cred.Reduc. (1.412) (1.679) (2.104) (2.740) (4.291)γ4 :BilledReduc. 0.177 0.0615 0.215 0.283 -0.163(0.612) (0.625) (0.643) (0.691) (0.762)γ0 :Constant 0.475∗∗∗ 0.482∗∗∗ 0.515∗∗∗ 0.500∗∗∗ 0.458∗∗∗(0.0349) (0.0371) (0.0401) (0.0444) (0.0511)F-stat 14.57 12.34 4.649 3.889 5.665PanelB− SecondStageDependent variable: Percent change in post-challenge electricity useOLS Instrumental Variable EstimatesWindow ±5% ±7% ±6% ±5% ±4% ±3%β1 :Re-Enroll -0.0160∗∗∗ -0.0239∗∗∗ -0.171∗∗ -0.191∗∗ -0.269∗ -0.307 -0.118(0.00422) (0.00769) (0.0782) (0.0848) (0.159) (0.188) (0.103)β2: Cred.Reduc. -0.282 -0.510∗ -0.638∗ -1.240∗ -1.118 0.953(0.282) (0.308) (0.355) (0.733) (0.876) (0.631)β3 : Success× 0.385 -0.153 -0.00562 0.319 -0.386 -1.527Cred.Reduc. (0.505) (0.441) (0.487) (0.719) (1.132) (1.204)β4 :BilledReduc. 0.192 0.283 0.203 0.238 0.252 0.0407(0.172) (0.190) (0.194) (0.238) (0.279) (0.212)β0 :Constant -0.00773∗∗∗ 0.00903 0.0886∗∗ 0.102∗∗ 0.150 0.166 0.0524(0.00289) (0.00817) (0.0448) (0.0490) (0.0916) (0.106) (0.0564)N 5432 1147 1394 1291 1147 982 763Notes: This table reports fuzzy-RD estimates corresponding to equations (2.1) and (2.2). Sample restricted to householdswith billed changes within ±5% of the 9.5% conservation target along with restricting households to those within thelisted estimation window around the 9.5% threshold in credited reductions. Estimation sample restricted to householdsthat either start their next challenge within 12 months or do not undertake an additional challenge. Estimation windowis restricted to ± the listed percent around the 9.5% threshold in credited changes.502.6. Cost EffectivenessTable 2.5: 1st Order Bias-Corrected Fuzzy Regression Discontinuity Estimates(1) (2) (3) (4) (5) (6) (7) (8)Conventional -0.187∗ -0.236∗∗ -0.261∗∗ -0.239∗∗ -0.201∗∗ -0.173∗∗ -0.164∗∗ -0.164∗∗(0.104) (0.118) (0.128) (0.108) (0.0858) (0.0727) (0.0668) (0.0669)Bias-corrected -0.281∗∗∗ -0.176 -0.194 -0.265∗∗ -0.299∗∗∗ -0.293∗∗∗ -0.257∗∗∗ -0.189∗∗∗(0.104) (0.118) (0.128) (0.108) (0.0858) (0.0727) (0.0668) (0.0669)Robust -0.281∗ -0.176 -0.194 -0.265∗ -0.299∗∗ -0.293∗∗∗ -0.257∗∗∗ -0.189∗∗(0.157) (0.177) (0.188) (0.156) (0.122) (0.103) (0.0936) (0.0763)Observations 888 1196 1475 1763 2050 2296 2543 2538Order Poly. (p) 1 1 1 1 1 1 1 1Order Bias (q) 2 2 2 2 2 2 2 2BW Poly. (h) 3% 4% 5% 6% 7% 8% 9% 9%BW Bias (b) 3% 4% 5% 6% 7% 8% 9% 17%F-Conv. 6.8 7 7.1 9.2 12.9 16.5 19.4 19.3F-Bias 6.8 11.2 12.9 10.4 8.9 9.4 12.1 17.7F-Robust 3.1 4.9 5.5 4.5 3.9 4.1 5.3 13.5Notes: This table reports fuzzy-RD estimates using the method of (Calonico et al., 2014). All specifications use 1st orderlocal polynomial regressions using a triangular kernel and restricted to households that either start their next challengewithin 12 months or do not undertake an additional challenge. Specifications (1) through (7) are for bandwidths BWPoly. (h) around the threshold. Specification (8) determines the optimal polynomial and bias-correction bandwidthsto be 9% and 17%, respectively. Conventional, bias-corrected, and bias-corrected and robust F-stats on the 1st stageinstrument respectively denoted by F-Conv., F-Bias, and F-Robust. The bias correction is 2nd order, local polynomial.Standard errors in parentheses. Conventional and Bias-corrected have conventional standard errors, Robust estimatesuse robust standard errors. *** p<0.01, ** p<0.05, * p< Cost EffectivenessThe Team Power Smart program is designed to produce electricity generation capacity savings andreduce the expected future increase in demand for electricity. A full cost-benefit analysis of the TPSprogram is beyond the scope of this work. Instead, I provide a lower bound on the cost of avoidedelectricity generation caused by this financial reward program. I estimate a lower bound for two reasons.First, because the costs of administering and advertising the Team Power Smart reward program areconfidential to BC Hydro, I consider only the cost of the $75 rebates rewarded to households, and leaveaside the costs of administering the program.33 Second, I make the assumption that the estimatedelectricity conservation from the event-study model, Figure 1.6, are treatment effects; any overestimateof the true treatment effect will bias upward the cost of avoided generation. This is a reasonableassumption given the findings of Sections 1.3.1 and 2.1. From the estimated electricity conservation andthe average electricity use among participants, Table 1.1, I find that the average aggregate reductionin electricity use over the first six years after an initial challenge is 2.7 MWh per household. Thisis the average across all households and accounts for their decisions whether to re-enroll after eachchallenge. Taking into account households’ average success in their conservation challenges, and thenumber continuing to additional challenges, the average aggregate rebate payment over the six years33Because the program is administered online, variable costs excluding the rebate are likely to be negligible. Programfixed costs may not be insignificant relative to the cost of the rewarded rebates. One full time equivalent employeecompensated at $70,000 per year for managing the program would add approximately $6 per challenge to the program.This is $20 per awarded rebate using the 30% success rate over the initial five challenges households undertake.512.7. Conclusionis $53 per household. This finds an average cost of avoided generation of $20/MWh. In comparison,participants paid an average retail price of $96/MWh in 2016, while a large hydroelectric dam underconstruction in the province is estimated to have a levelized cost of electricity of $34-$83/MWh (BritishColumbia Utilities Commission, 2017). This makes the Team Power Smart program a cost-effectiveway to reduce the demand for electricity in comparison to the cost of new generation.What is the cost of avoided carbon emissions due to this energy conservation program? It isimportant to note that this energy conservation program was not designed to principally reduce carbonemissions and the cost of avoided emissions is not particularly relevant to BC Hydro. British Columbiagenerates over 90% of its electricity from hydroelectric dams and has a low emissions intensity of9kgCO2e/MWh (BCH, 2016); $20 per avoided MWh is a cost of avoided greenhouse gas emissionsof $2,222/tCO2eq. However, BC Hydro engages in large cross-border trade in electricity with theUnited States, primarily California. Lower electricity use in British Columbia allows BC Hydro to sellrelatively low cost and low emissions power to California. Assuming all reductions in B.C. electricityuse reduces generation in California finds, using the 2017 California average emissions intensity (EPA,2017), a cost of emissions abatement of $71/tCO2. At the 2017 U.S. average emission intensity, thisfalls to $45/tCO2 (?). These abatement costs are within the range of commonly discussed estimatesof the SCC (?), and indicate that in some jurisdictions, repeated financial reward programs similar tothe one studied in this work may be cost effective from a social perspective. The results of Chapter1 and Chapter 2 show that the continued incentive of repeated financial reward is important formaintaining and causing additional reductions in electricity use. The continued incentive improves theprogram’s cost-effectiveness, compared to a program offering a single annual conservation challenge.This improved cost-effectiveness occurs for two reasons. First, the program administration fixed costsare spread across additional conservation challenges. Second, the repeated incentive causes additionalreductions, and keeps use from rebounding back close to pre-program levels.2.7 ConclusionIn this chapter, I analyze the re-enrollment of households in a program offering financial rewardsfor energy conservation. I first study households’ extensive margin decisions to re-enroll. I find thatin deciding whether to re-enroll, households are responsive to their success or failure in achieving theirconservation target, and yet, conditional on this success or failure, are notably unresponsive to theirdegree of electricity conservation. The decision to re-enroll also differs little across observable householdcharacteristics. These patterns suggest that households use heuristics in making participation decisions,rather than accounting for the incentive structure of the program or information on their degree ofconservation effort. I then exploit the discontinuous change in the probability of re-enrollment at thethreshold for success in a fuzzy regression discontinuity strategy; I estimate that, despite self-selectioninto continuing, re-enrollment causes additional reductions in electricity use. This chapters findingsimply it is important for repeated incentive programs to explicitly consider the process of self-selectioninto or out of re-enrollment. This is especially important when treatment effects fully dissipate afterthe incentive ends. Programs may be able to improve their cost effectiveness by encouraging re-enrollment, particularly when consumers fail to achieve their goal and self-select out of the program522.7. Conclusionas a result. One way to address this could be to offer tiered incentives, such as offering an alternativechallenge only to consumers that missed their target and are likely to self-select out of the program.Such an alternative incentive could be either transparently offered at the outset of participation, orrevealed only to consumers that have not re-enrolled after some time period to target those likelyto be ending participation. The responsiveness of households to their success or failure also opensup the possibility of modifying the reward structure to exploit this sensitivity; for example, by usingunexpected consolation prizes instead of an all-or-nothing reward.The use of information is central to how we model the decisions of agents across many questionswithin economics, from how tax rates affect labour market responses to voting behavior. The use ofheuristics may be ubiquitous in these decisions. Heuristics could result from rational inattention andallow households to avoid the cognitive and time costs of considering complex incentives, or alterna-tively they could result from households responding to incentives and information based on modelsof behaviour beyond standard neoclassical models of decisions. Disentangling the ways in which con-sumers use information is an important avenue for future research. It is particularly important tothe design of complex price schedules that are increasingly facilitated by the spread of smart meters,distributed electricity generation, and electricity storage.A further direction for inquiry are the consequences of repeating interventions. Combined together,chapter 1 and chapter 2 showed how interventions that do not cause persistent effects can still producecost-effective long-run changes by being repeatedly offered. These findings also suggest that consumersrespond to each discrete reward in isolation, and do not consider the dynamic consequences of theireffort on the future incentive structure. This raises the questions of whether this is a feature of theannual time scales of this program, or is a common feature of consumer responses to discrete rewards,and how consumers would respond as the time between potential rewards was reduced towards thelimit of a continuous incentive.53Chapter 3The Choice of Transportation Mode InInternational Trade3.1 IntroductionAll international trade of physical products requires a method of transportation. Transportation modesdiffer in many ways. Air freight is substantially faster but more expensive than sea freight. Fast de-livery times are particularly important for perishable products, to industries utilizing just-in-timemanufacturing, and in assisting firms meet unexpected demand shocks or recover from supply chaininterruptions. Geographic constraints affect access to markets, with planes able to deliver directly tothe interior of continents while ships are limited to navigable waters and accessible ports. Infrastruc-ture improvements and technological changes vary between transport modes, causing different impactsacross countries and industries depending on the modes they rely upon. In addition, transportationmodes have very different environmental impacts. For example, airplanes generate on the order of 100times the carbon emissions of shipping the same good the same distance by sea, while the high sulfurbunker fuels used by ships are responsible for 15%–30% of global NOx emissions (Corbett et al., 2007;Cristea et al., 2012). Understanding how these factors affect trade, evaluating policies like Pigoviantaxes or infrastructure investments, and exploiting variation in mode-specific factors like distance allrequire a model of trade differentiated by the mode of transport. Critical to this is the degree ofsubstitution between, and choice of, transport modes.In this chapter, I develop a general model of the choice of transport mode in international trade.I use this model to show how several extant trade models incorporating mode choice start from dif-ferent theoretical motivations, yet produce closely similar reduced form equations for bilateral tradedifferentiated by transport mode. I then show that this reduced form equation—which is commonacross several trade models—imposes strong and possibly unrealistic restrictions on substitution pat-terns across modes and countries. Importantly, all these models share a common assumption of apositive cross-elasticity for the share of imports carried by separate transport modes with respectto their trade costs. This positive cross-elasticity has been used to argue that transport modes aresubstitutes, but—as I will demonstrate—this is in fact insufficient to define transport modes to besubstitutes. Instead, I show that the condition under which separate transport modes within bilateraltrade are complements or substitutes depends on the magnitudes of this mode-share elasticity anda conventional trade elasticity. Prior modeling approaches that have estimated or assumed positivecross-elasticities—and have concluded that modes are substitutes—are in fact imposing modes to becomplements, while other models are imposing modes to be substitutes. This assumption can substan-543.1. Introductiontially affect counterfactual trade patterns. As a result, these models are particularly sensitive to thechoice of substitution elasticities and can poorly approximate the policies and trade patterns they aredesigned to analyze: those involving mode-specific changes in freight costs.Improving on these limitations motivates the empirical contributions of this chapter. I first usedetailed data on U.S. imports arriving by air and ocean transport to undertake estimates of the substi-tutability of transport modes within international trade. By exploiting idiosyncratic changes in freightrates to estimate reduced form own- and cross-price elasticities for mode-specific imports, I find thatwhile higher freight costs reduce imports, little of this reduction substitutes to the alternative transportmode within bilateral trade. Instead, the evidence found implies a small or zero cross elasticity of de-mand for imports typically carried by air, and a larger and negative cross elasticity—complements—forimports typically carried by sea. These estimates demonstrate that the way multiple transportationmodes have been modeled to date does not accurately approximate real substitution patterns. It thussuggests future work should return to the drawing board of modeling multiple modes of transporta-tion within international trade, and must further empirically establish the substitution patterns acrossmodes and countries that need to be approximated. I then reconsider the previously made observationthat a substantial share of imports arrives by both transport modes. I find evidence that this overlapin products arriving by both modes reflects unobserved heterogeneity in product quality and thereforemay not—as has been argued previously—be evidence of a large potential for substitution betweentransport modes. In addition, I find that unobserved quality is a particularly important, and largelyunrecognized, determinant of the choice of transport mode across countries.A variety of work has considered international trade differentiated by the method of transport; ofparticular importance are models of Lux (2011), Hummels and Schaur (2013), and Shapiro (2016).These models start from different theoretical motivations, and their models have been used to considerdifferent policies and aspects of mode-specific trade. As a result, the close similarities between thesemodels are not immediately obvious. The first contribution of this chapter is to develop a generalizedmodel of mode choice in international trade—generalized in the sense that the reduced form equationsfor bilateral trade derived and estimated by Lux (2011), Hummels and Schaur (2013), and Shapiro(2016) can all all be viewed as special cases of this generalized model. This demonstrates how thesemodels are closely connected and that they share common restrictions on trade patterns. In particular,whether they implicitly model transport modes as substitutes or complements depends on the values oftwo key elasticities—the elasticity of trade shares and mode shares.34 This “generalized” model is notan attempt to build a new microfounded model of endogenous mode choice or demonstrate alternativereduced form equations for bilateral trade. In particular, the goal of this model is not to accommodatedifferent theories of how importers choose a transport mode—such as the theoretical origin of transportmodes being complements vs. substitutes—or accommodate some important features of the data, suchas unobserved product heterogeneity. Instead, the assumptions underlying this generalized model areintentionally chosen to show the similarity between the prior models of Lux (2011), Hummels andSchaur (2013), and Shapiro (2016), their shared strengths and weaknesses in modeling substitutionpatterns across countries and methods of transport, and demonstrate how the elasticities of mode34Trade shares refers to standard bilateral trade shares and mode shares are the value share within bilateral tradecarried by a specific transport mode. Both are defined in Section 3.2.553.1. Introductionshares and trade shares jointly determine whether modes are complements or substitutes.Lux (2011) extends the work of Eaton and Kortum (2002) to incorporate multiple transportationmodes and endogenous mode choice in a general equilibrium trade model. Lux (2011) uses this modelto estimate a mode share elasticity that implicitly treats transport modes as highly substitutable. Asa result of this high substitutability between modes, Lux (2011) concludes that reductions in mode-specific trade have relatively little impact on welfare. In this chapter, I contribute contrary empiricalestimates that find modes are not highly substitutable. In addition, I show how a low substitutabilitybetween transport modes is inconsistent with restrictions on across-country substitution patterns thatare implicit in Lux (2011) and similar models. Closely related to the work by Lux (2011) and thischapter is a paper by Shapiro (2016), who builds an Armington trade model differentiated by transportmode to consider welfare impacts of regulating carbon emissions from international transportation. Asdiscussed in Shapiro (2016), shipping a product by air releases approximately 103 times the emissionsper tonne-km as shipping the same product the same distance by sea.35 While not considered by Shapiro(2016), this substantially larger emissions intensity for air is further exacerbated by the additionalradiative forcing of contrails and ozone formation—a tonne of CO2 released by an airplane contributes1.2–2.7 times the warming impact of a tonne of CO2 released at sea level (Grassl and Brockhagen, 2007).These differences in radiative forcing and carbon emission intensities make the choice of transport modeparticularly critical to the direct climate change impacts of international transportation. I show thatthe model of Shapiro (2016) has close analytic similarities to that of Lux (2011), however Shapiro (2016)does not estimate the substitutability across modes. Instead, Shapiro (2016) assumes parameter valuesfor his model that, as I will show, implicitly impose air and ocean to be complements; this assumptionhas a substantial effect on estimated changes in trade flows, carbon emissions, and policy findings.How substitutable are air and ocean transport? The magnitude of substitutability and how tomodel it depends on what determines mode choice. Several important and inter-related determinantsof mode choice have been considered previously in the literature. A particularly important one isdifferences in delivery time between air and sea transport. Without a value on time, importers wouldalmost always choose the typically cheaper option of ocean freight. Hummels and Schaur (2013) modelthis trade off between time and cost in mode choice to estimate a value of time: they find “each dayin transit is equivalent to an ad-valorem tariff of 0.6 to 2.1 percent.” In this work, I show that theequation estimated by Hummels and Schaur (2013) is equivalent to that of Lux (2011). Hummels andSchaur (2013) exploit cross-sectional variation in freight rates across U.S. coasts while using the samedata and estimating equation, and they estimate an elasticity of substitution that implies that air andocean are complements. This directly, though not obviously, contradicts the estimates of Lux (2011)and supports the assumption of complements made implicitly by Shapiro (2016). While I note that thispaper does not attempt to model a microfounded reason why transport modes may be complements orsubstitutes, one potential source of complementarity could be fixed costs in supply chains. For example,consider firms that pay a fixed cost per country to source imports. A shock to a single mode’s transportcosts may, on the margin, induce a firm to pay the fixed cost for an alternative country—from which itthen sources imports by both air and sea transport. Similarly, firms may wish to source intermediate35This point was also previously discussed by Cristea et al. (2012).563.1. Introductioninputs used in Leontief type production from the same or similar suppliers to ensure compatibility.If they rely on different transport modes for different products, a single mode cost shock may inducethem to import products carried by multiple modes from a different exporting country.It has been previously observed that many products within detailed product category-trade route-years arrive by both air and ocean transport (Hummels and Schaur, 2010; Lux, 2011; Hummels andSchaur, 2013). As these authors note, the same products arriving by both air and ocean transport implya greater potential substitution across modes compared to if different modes were used exclusively fordifferent products. In this paper, I document a substantial heterogeneity in unit values which impliesthat, even within detailed product categories, air and ocean transport modes may be specializing indifferent varieties of a product. This reduces the potential for substitution between transport modes.In addition, as freight charges are predominantly determined on a per weight basis, iceberg trade costsfall as the unit value of a product rises (Hummels and Skiba, 2004). This makes the ad-valorem pricepremium paid for air transport fall as unit values rise. The importance of unit values to mode choice hasbeen previously considered by Harrigan (2010), who builds a model of comparative advantage betweentransport modes based on product weight and shipping distance. He tests and confirms two modelpredictions: the U.S. imports heavier products from nearby countries and light products from distantcountries, and products imported from distant locations have higher unit values. The findings of thischapter support the observation by Harrigan (2010) that the importance of distance to mode choicemay be highly non-linear, and that a comparative advantage in high quality products by countrieswith high productivity may be particularly important to the choice of transport mode. As a result,these comparisons across modes within a country suggest a potentially new way to study unobservedquality differences within products across countries (Schott, 2004; Hallak and Schott, 2011; Hummelsand Klenow, 2005). In a separate paper to their work on time as a trade barrier in Hummels andSchaur (2013), Hummels and Schaur (2010) show how fast delivery by air, compared to slow butcheap ocean shipping, can be used to hedge uncertainty in demand and prices.36 I add to both ofthese papers by contributing evidence that differences in distance between countries, and therefore indelivery times, are a relatively unimportant determinant of the choice of mode. In contrast, I showthat unobserved product quality—as proxied by unit values within the most detailed product categoryavailable, HS10—is highly correlated with the choice of transport mode across countries. This largelyunrecognized factor of unobserved quality may be more important in determining the choice of modethan the variation in distance between countries and across U.S. coasts that has been previouslyexploited for identification, for example by Harrigan (2010) and Hummels and Schaur (2013).The remainder of this chapter is organized as follows. Section 3.2 derives a model of mode-specificbilateral trade and discusses implications of the model. Section 3.3 shows the similarities betweenthis model and existing models that incorporate mode choice. I present reduced form estimates of theelasticity of substitution across modes in Section 3.4. In Section 3.5 I discuss how unobserved productquality can explain much of the variation in mode choice across countries and within detailed product36An additional literature considers the value of time in delivery without explicitly differentiating across transportmodes. In particular, Harrigan and Venables (2006) consider time as a factor in agglomeration of stages of productionand Evans and Harrigan (2016) consider how different valuations for fast delivery determine the distance from whichgoods are imported.573.2. A Model of Endogenous Transportation Mode Choicecategories. I conclude in Section A Model of Endogenous Transportation Mode ChoiceIn this section I develop a simple trade model incorporating endogenous mode choice, which I refer toas the nested CES model.37 After deriving the nested CES model, Subsection 3.2.1 shows how thismodel predicts trade flows to change in response to a shock to trade costs. Subsection 3.2.2 exploresthe implications of this model for substitution patterns across countries and transport modes, includingthe definition and conditions under which modes are modeled as complements or substitutes.The primary advantage of this nested CES model is that it produces an intuitive and generalmodel of mode-specific trade. This model does not, and is not intended to, produce any new insightsinto theoretical mechanisms for substitution across transport modes, nor a reason for why transportmodes may be complements or substitutes. As I show in Section 3.3, this general nested CES modelyields the mode-specific trade patterns derived in Lux (2011), Hummels and Schaur (2013), and Shapiro(2016), and the estimating equations of Lux (2011) and Hummels and Schaur (2013). By transparentlyclarifying the relationships between these models, the nested CES model demonstrates that, althoughthey have been derived from different theoretical assumptions and to answer different questions, thesemodels are closely related and share strengths and weaknesses in approximating mode-specific tradeflows.Consider a representative consumer with CES preferences over a composite bundle Qw of productvariety w delivered by mode m, and with elasticity of substitution η > 1 across varieties,38U =[∑w(Qw)η−1η] ηη−1(3.1)Within the bundle Qw the consumer has CES preferences over physical goods qmw delivered by modem with elasticity of substitution ρ > 1 across modes,Qw =[2∑m=1λmw (qmw )ρ−1ρ] ρρ−1(3.2)λmw is a price-equivalent preference shifter that captures preferences over different modes, in partic-ular shipping time, and models delivery time as a form of perceived quality in the same manner asHallak (2006) and Hummels and Schaur (2013). The representative consumer of importing country nmaximizes utility subject to their budget constraint of total expenditure Xn39,37CES refers here to constant elasticity of substitution.38The bundle Qw includes both imports and domestically sourced varieties.39In this model I abstract away from a production function and factor markets and consider only the consumer demand.I hold expenditure Xn fixed. However, this is not only a partial equilibrium analysis; the model includes the indirecteffect of a change in trade costs through its impact on all other modes and countries via the price indexes. As Section3.3 will show, this yields the same equation for mode-specific trade as the general equilibrium models of Lux (2011) andShapiro (2016).583.2. A Model of Endogenous Transportation Mode Choice∑w∑mpmw qmw ≤ XnWith the Armington assumption that each country produces a differentiated variety w, the expen-diture share XmniXnby country n on imports from country i by mode m can be derived,XmniXn=(λmni)ρ(pmni)1−ρP 1−ρni︸ ︷︷ ︸γmni(PniPn)1−η︸ ︷︷ ︸pini(3.3)where price indexes for bilateral trade Pni from i and Pn for country n are given byP 1−ρni =∑m(λmni)ρ(pmni)1−ρP 1−ηn =∑iPni1−ηThe derivation is discussed in Appendix C.1.1 and follows Sillard and Wilner (2015).40 λmni isperceived quality across modes and which may differ across origin-destination, and pmni is the Cost-Insurance-Freight (CIF) unit price of quantity qmni.41 I assume that the Free-On-Board (FOB) price ciis independent of mode and there are iceberg trade costs τmni such that pmni = ciτmni .42Equation (3.3) gives the mode-specific bilateral trade shares conditional on unobserved preferencesλmni, origin prices ci, and iceberg trade costs τmni .43 Mode-specific bilateral expenditure Xmni can bedecomposed into a conventional bilateral trade share pini and, within that bilateral trade, a mode shareγmni, such that Xmni = Xnpiniγmni. The trade share pini is the share of value imported from country i tocountry n by both modes, and for this model is derived as44pini ≡ XniXn=(PniPn)1−η(3.5)Mode share γmni is defined as the share of value within bilateral imports Xni from country i to n that40An interpretation of this derivation is the consumer uses two-stage budgeting as in Sillard and Wilner (2015). Therepresentative consumer first chooses their optimal expenditure over variety w and then their optimal expenditure overmodes within a variety. The importance of this becomes apparent when considering the income and substitution effectinterpretation of the separable trade and mode shares derived here.41With a single transport mode, the trade shares of equation (3.3) reduces to a standard form for bilateral trade sharescommon to a wide variety of structural gravity models (Head and Mayer, 2015),pini ≡ XniXn=(PniPn)1−η=(λniρ1−ρ ciτni)1−η∑i Pni1−η (3.4)42In Section 3.4 I show the assumption that ci is independent of mode does not hold in the data. I maintain theassumption here to show the similarity to other models.43It is only necessary to specify a functional form for λmni for some estimates of ρ. This is discussed in Subsection follows from Appendix C.1.2.593.2. A Model of Endogenous Transportation Mode Choiceis shipped by mode m,γmni ≡XmniXni=λmniρ(pmni)1−ρP 1−ρni(3.6)3.2.1 Transport Cost Shocks and Trade ChangesHow trade changes due to trade cost shocks provides an intuitive interpretation for the elasticities ofsubstitution ρ and η. Consider changes in imports from country i by mode m, Xmni, due to a changein bilateral mode-specific trade costs τm′nj from exporting country j to importing country n by modem′,45∂lnXmni∂lnτm′nj=∂lnXn∂lnτm′nj+∂lnpini∂lnτm′nj︸ ︷︷ ︸Eqn. (3.8)+∂lnγmni∂lnτm′nj︸ ︷︷ ︸Eqn. (3.9)(3.7)Imports are valued CIF and the minor difference from using FOB values is discussed in AppendixC.1.3. Equation (3.7) is general. It includes both changes in trade costs within bilateral trade n − iby mode m (m = m′ and j = i) as well as changes in trade costs among alternative transport modesm 6= m′ and alternative origin countries j 6= i. I assume that total expenditure Xn, which includesexpenditure on domestic sourcing, is constant and therefore the first term of equation (3.7) is zero.Changes in imports Xmni due to changes in a trade cost has two components. The second term ofequation (3.7) is the change in trade shares,∂lnpini∂lnτm′nj=(1− η)(1− pini)γm′ni < 0 if i = j ∀ m,m′(1− η)(−pinj)γm′nj > 0 if i 6= j ∀ m,m′(3.8)The third term of equation (3.7) is the change in mode shares,∂lnγmni∂lnτm′nj=(1− ρ)(1− γm′ni ) < 0 if i = j and m = m′ (3.9a)(1− ρ)(−γm′nj ) > 0 if i = j and m 6= m′ (3.9b)0 if i 6= j ∀ m,m′ (3.9c)Combining, the total changes in expenditure from country i by mode m is∂lnXmni∂lnτm′nj=(1− η)(1− pini)γmni + (1− ρ)(1− γmni) if i = j and m = m′ (3.10a)(1− η)(1− pini)γm′ni + (1− ρ)(−γm′ni ) if i = j and m 6= m′ (3.10b)(1− η)(−pinj)γm′nj if i 6= j ∀ m,m′ (3.10c)Equation (3.10) shows how importsXmni involve a change in trade shares pini as trade redistributes toor from other origin countries than i, and within this bilateral trade a change in the share transported by45Derivation in Appendix C.1.2. Partial derivatives indicate that while all indirect effects of ∂lnτm′nj through othercountries and modes are accounted for, other trade costs are held fixed.603.2. A Model of Endogenous Transportation Mode Choicemode m, mode share γmni. Equations (3.8) and (3.9) provide a simple interpretation of the substitutionelasticities ρ and η. 1−η ≡ θ is the conventional trade elasticity common to a variety of gravity models(Head and Mayer, 2015).46 1− ρ is the elasticity of mode shares γmni to changes in transport costs τm′nj .Note that other factors that affect trade, like perceived quality for fast delivery, distance, or differencesin origin prices, are determinants of the observed trade and mode shares through equations (3.5) and(3.6).3.2.2 The Substitutability of Transport ModesThe previous section showed how changes in mode-specific bilateral trade shares, equation (3.3), canbe decomposed into changes in conventional trade shares and mode shares. While the analytic formof this decomposition is convenient, in this subsection I show this analytic form comes at a costof imposing potentially strong restrictions in how trade redistributes across countries and modes inresponse to a trade cost shock. Because equation (3.3) incorporates the mode-specific trade sharesof Lux (2011), Hummels and Schaur (2013), and Shapiro (2016), the restrictions discussed here alsoapply to their models.47 In other words, the restrictions on substitution patterns discussed here are notonly characteristic of the nested CES model but are a general characteristic of the class of models thatyield mode-specific trade flows in the form of equation (3.3). In addition, these restrictions are a directconsequence of the assumptions underlying these trade models. Alternative trade models, for examplea model with an alternative ordering of preferences over varieties and modes, produce a differentdecomposition of mode-specific bilateral trade and alternative sets of restrictions over counterfactualtrade patterns.Complements or SubstitutesThere are two ways to define the substitution across transportation modes. The models of Lux (2011)and Shapiro (2016) use one potential definition: the elasticity of mode shares to a change in tradecosts,∂lnγmni∂lnτm′ni≡Own− priceModeShareElasticity < 0 for m = m′Cross− priceModeShareElasticity > 0 for m 6= m′This form is intuitive. An increase in trade costs for mode m decreases the mode share for m,while an increase in trade costs for an alternative mode m′ causes a rise in the mode share for m.48However, defining transportation modes as substitutes if they have a positive cross elasticity in modeshares may be misleading.In contrast, consider the own and cross-price elasticities for the level of imports, Xmni.46The additional terms multiplying 1− η in equation (3.8) reflect the fact the change in trade shares is not isoelasticand capture the general equilibrium effect of freight cost changes on the price index. Similarly for 1−ρ in equation (3.9).47The restrictions are equivalent to the Independence of Irrelevant Alternatives (I.I.A.) property common, and wellknown, to nested discrete choice models. However, it may not be apparent that this is also an implicit property of manytrade models incorporating transportation mode choice.48This is the general form of the own and cross-price elasticities of mode shares to bilateral trade costs in the nestedCES model, equations (3.9a) and (3.9b).613.2. A Model of Endogenous Transportation Mode Choice∂lnXmni∂lnτm′ni=Own− price ImportElasticity if m = m′Cross− price ImportElasticity if m 6= m′ (3.11)The specific analytic form of these will depend on the particular model of mode-specific trade. Forthe nested CES model and equivalent models these have the form of equations (3.10a) and (3.10b).The own-price elasticity for changes in expenditure Xmni to a trade cost change to the same mode mwithin that bilateral trade route is unambiguously negative,49∂lnXmni∂lnτmni= (1− η)(1− pini)γmni︸ ︷︷ ︸(−)+ (1− ρ)(1− γmni)︸ ︷︷ ︸(−)This is intuitive: increases in freight costs for a transport mode decrease imports carried by thatsame mode. The sign of the cross-price elasticity for the level of imports arriving by mode m dependson two terms,∂lnXmni∂lnτm′ni= (1− η)(1− pini)γm′ni︸ ︷︷ ︸(−)+ (1− ρ)(−γm′ni )︸ ︷︷ ︸(+)(3.12)Imports carried by each mode are gross substitutes if this cross-price elasticity of equation (3.12) ispositive—imports by mode m rise in response to a rise in trade costs for the alternative mode m′—andgross complements if the cross-price elasticity is negative. The first term is the change in trade sharesand is strictly negative while the second term is the cross-elasticity of mode shares and is strictlypositive. The cross-price elasticity for this level of imports is positive, and modes are substitutes, if(1− pini) < (1− ρ)(1− η) (3.13)Note that, while expenditure here is the CIF value, the cross-price elasticity is the same whenexpressed in FOB values.50 Intuitively, complementarity arises when the decrease (increase) in totalimports through trade share changes is larger than the increase (decrease) in imports substituting frommode m to m′.51This highlights the important distinction between the elasticity of mode shares and the elasticityof substitution for the level of imports. An increase or decrease in the mode share of imports doesnot identify the changes in levels of constituent imports carried by each mode. A rise in the share ofimports carried by air can occur along with a decline in the level of imports arriving by air, as long asimports arriving by the alternative mode ocean fall faster. In this way, a positive elasticity of mode49I assume that η > 1 and ρ > 1.50A change in freight costs will change the value of imports that include those freight costs; products redistributingto other modes and countries will face those other country and mode freight costs and modes, which are unaffected inthis model, and therefore the percentage change in value will be the same for a cross-price elasticity whether measuredin CIF or FOB values. This is shown formally in Appendix (C.1.3).51This can be considered as an income and substitution effect. Complementarity arrises when the income effect ofreduced expenditure on imports within a bilateral trade route is larger than the substitution effect between modes withinthat bilateral trade.623.2. A Model of Endogenous Transportation Mode Choiceshares is consistent with the level of imports carried by air and ocean transport being either substitutesor complements.I stress that the potential for both substitutes and complements is not in itself a model downside.Does complementarity occur only for unreasonable values of the elasticities of substitution ρ and η,or only within the nested CES model of mode choice? In Section 3.3 I show that complementaritybetween modes can occur in several additional models of mode choice, and prior work has estimatedand assumed values for ρ and η such that air and ocean transport are treated as complements andsubstitutes.Independence of Trade and Mode ElasticitiesEquation (3.8) shows changes in trade shares are weighted by the share of bilateral trade subject tothe cost increase, γm′nj . Notably, these changes in trade shares are independent of the mode shareelasticity. An advantage of this independence—an assumption of these models—is it allows the tradeelasticity to be identified from mode-specific changes in freight costs, for example as in Shapiro (2016),without considering how trade redistributes across modes within bilateral trade. Is this independenceassumption realistic? Perhaps not. It is reasonable to expect that a shock to a single transport mode’strade costs would induce a smaller change to trade shares if imports are highly substitutable acrossmodes, compared to if modes have a low elasticity of substitution. For example, consider this modelframework and a region with a 50% air shares. A 1% increase in both this region’s air and ocean tradecosts would then cause the same reduction in trade shares as a 2% increase to a single mode’s tradecost. This rules out the situation where the 2% single-mode cost shock, compared to the 1%, primarilyinduces a substitution to the alternative mode with little reduction in trade shares.52Independence of Mode Shares to Costs in Alternative Trade RoutesA closely related restriction is that mode shares within a bilateral trade route are independent ofthe trade costs in alternative routes. This is shown by the elasticity of 0 in equation (3.9c).53 Theimportance of this restriction can be seen by considering hypothetical imports arriving from China tothe U.S. carried via air freight. What happens if there is a decline in air freight costs for imports to theU.S. from a different country, Japan? On the margin it is reasonable to expect this negative cost shockto induce products to switch from China to Japan to take advantage of the now-lower air freight cost.It is also reasonable for this reduction in trade from China be largest for products that are alreadytransported by air from China, compared to products that are already shipped by ocean from China.As a result, we would expect the share of products imported by air from China to fall due to thenegative shock to Japan’s air freight costs. This cannot happen in these models. Instead, in responseto trade cost shocks, imports redistribute across or from alternate trade routes proportional to thoseroutes’ initial mode and trade shares; whether these imports were previously transported by air or oceandoes not matter. A further and important implication of (3.9c) is that these models are particularly52This independence assumption may be particularly important to estimates of sectoral trade elasticities where boththe elasticity of substitution between products and level of mode shares are likely to vary across sectors.53This is the Independence of Irrelevant Alternatives (I.I.A.) property common to nested discrete choice models.633.3. Comparisons to Existing Models of Mode Choicepoor at approximating trade changes when there is little substitutability across modes. For example,under the condition that the cross-price elasticity within bilateral trade—equation (3.12)—was 0, anincrease to air freight costs from Japan would induce no substitution to imports by ocean from Japan.At the same time, the reduction in imports by air from Japan would redistribute across both air andocean among other countries with a larger redistribution to imports via ocean—not air—among othercountries.3.2.3 Estimating Equation for the Elasticity of Mode SharesIn addition to observed trade and mode shares, simulating counterfactuals with this model requiresestimates of the elasticities of substitution η and ρ. A wide variety of estimates for the trade elasticity,1−η, are available in the empirical trade literature. One approach to estimating the elasticity of modeshares ρ starts from taking the ratio of expenditures from equation (3.3) across modes within bilateraltrade,XaniXoni=XnpiniγaniXnpiniγoni=γaniγoni=λaniρ(pani)1−ρλoniρ(poni)1−ρwhere λmni is the perceived quality over delivery times and pmni and Xmni are measured CIF. Twofurther assumptions simplify the estimation. First, assume that λmni is constant over time and importprices are time-varying with iceberg trade costs, pmni,t = cmi,tτmni,t. Taking logs produces the following,ln(Xani,tXoni,t)= ρlnλaniλoni+ (1− ρ)cai,tcoi,t+ (1− ρ)τani,tτ oni,t+ ni,t (3.14)By choosing a parameterization of λmni and potentially additional fixed effects, equation 3.14 can beestimated. This is the general specification estimated by both Lux (2011) and Hummels and Schaur(2013), discussed below.3.3 Comparisons to Existing Models of Mode ChoiceThe implications for changes in trade discussed in Section 3.2 are not unique to the nested CES modelof endogenous mode choice. In this section, I show under what conditions the mode-specific bilateraltrade shares derived from the nested CES model—and the resulting counterfactual trade changes andrestrictions on substitution patterns—are equivalent to the models of Lux (2011), Hummels and Schaur(2013), and Shapiro (2016).Lux (2011) is, to the best of my knowledge, the only attempt to model endogenous mode choicewith an elasticity of substitution for mode shares that differs from the trade elasticity. Lux (2011)builds a general equilibrium Eaton and Kortum (2002) style model, incorporating multiple transportmodes within international trade. His model incorporates transport modes by extending the Frechetdistribution of productivity differences across varieties into a multi-dimensional distribution of variety-mode specific productivities. This allows Lux (2011) to derive equations for mode-specific trade shares,mode shares, and expenditure shares that are identical to those obtained from the nested CES model.643.3. Comparisons to Existing Models of Mode ChoiceThe difference, beyond the theoretical underpinnings of the model, is in the interpretation of thetrade and mode share elasticities. Whereas the nested CES model interprets ρ as the elasticity ofsubstitution over products delivered by different transport modes, Lux (2011) interprets ρ as a functionof the dispersion of productivity draws from the Frechet distribution combined with the correlationof productivity draws across transport modes. As a result of the equivalence of the equations formode-specific trade shares, the estimating equation for the elasticity of mode shares in Lux (2011) isequivalent to equation (3.14) of the nested CES model. Instead of specifying a form for λmni, Lux (2011)assumes it is time-invariant and estimates the mode share elasticity using first-differencing to controlfor the value of time in delivery and other time-invariant parameters. He finds a central estimate ofρ = 7.7.54 Lux (2011) does not estimate a trade elasticity. Instead, he uses θ = 4 from Simonovskaand Waugh (2014). As a result, Lux (2011) implicitly finds that equation (3.13) is satisfied, and airand ocean transportation are substitutes.It is important to contrast the estimate of ρ from Lux (2011) with that in Hummels and Schaur(2013). Hummels and Schaur (2013) do not consider different elasticities of substitution across modescompared to product varieties. The equivalence to the nested CES model results from imposing therestriction of a single elasticity of substitution across both varieties and modes, or ρ ≡ η.55 Hummelsand Schaur (2013) also derive an estimating equation for ρ from the ratio of imports by air and oceanwithin exporter-importer pairs. This is identical to that of the nested CES model, equation (3.14),when using the same parameterization for the value of delivery time as Hummels and Schaur (2013).Hummels and Schaur (2013) devote substantial time and care to estimating two key coefficients: thesubstitution elasticity across products and modes, and the coefficient on delivery time. The ratio ofthese estimated coefficients gives the value of time—the ad-valorem premium paid to reduce deliverytime by one day. In their preferred specifications, Hummels and Schaur (2013) estimate ρ ranges from1.5 to 3.3.56 This is substantially smaller than the central estimate of 7.7 from Lux (2011). The keydistinction between these estimates is that Hummels and Schaur (2013) exploit cross-sectional variationacross U.S. coasts, while Lux (2011) exploits the time dimension only.The difference in these estimates can be interpreted several ways. The first is to assume that thenested CES model (and, by extension that of Hummels and Schaur (2013)) is correctly specified suchthat ρ ≡ η. The estimates of Hummels and Schaur (2013) would then correspond to trade elasticitiesof θ = 0.5 to 2.3. This is smaller than commonly estimated (Head and Mayer, 2015). The assumptionthat ρ ≡ η would also imply that ocean and air freight are substitutes—albeit with a small cross-priceelasticity. Alternatively, in the more flexible case of potentially different elasticities of substitutionacross products and modes, ρ 6= η, the estimates of Hummels and Schaur (2013) are an estimate ofthe mode share elasticity only. For common trade elasticities on the order of ∼ 4, these estimates andequation (3.13) imply that air and ocean transport are complements. This contradicts the findings ofLux (2011). An important caveat to these estimates is in order. Identifying ρ from the ratio of airto ocean imports within a product category, as done by Lux (2011) and Hummels and Schaur (2013),54Where “mode share elasticity” here refers to the nested CES definition of ρ used in this chapter. Lux (2011) usesdifferent notation under which ρ is a rank correlation statistic.55See Appendix C.2.56Coast-differenced estimate from Tables 2 and 3. Note ρ in the notation of the nested CES model is called σ in thenotation of Hummels and Schaur (2013).653.3. Comparisons to Existing Models of Mode Choiceimplicitly assumes that similar products are being compared. Section 3.4 provides evidence that thisratio may compare substantially different varieties of products, calling into question what precisely isbeing identified through this estimation approach.The comparison of Shapiro (2016) to the nested CES model is less straight-forward because Shapiro(2016) does not have a model of endogenous mode choice. Instead, Shapiro (2016) constructs tradeshares and bilateral freight costs from mode-specific trade weighted by bilateral mode shares, thenholds mode shares fixed when calculating counterfactuals. Shapiro (2016) also undertakes a robustnesscheck for approximately endogenous mode shares by assuming a unit elasticity of mode shares to freightcosts. Shapiro (2016) finds that “[t]hese counterfactuals lead to extremely similar quantitative resultsto the main calculations, and provide one piece of evidence that endogenous mode share substitutionfor a given country pair and sector has limited impact on results.” As Shapiro (2016) notes, thisrobustness check is also not strictly speaking an endogenous mode choice, but instead a re-weightingof aggregate trade and freight costs by the new mode shares. This approach differs from the mode-specific trade shares of the nested CES model as the assumed mode share changes in Shapiro (2016)are not isoelastic. However, the central case considered by Shapiro (2016)—holding mode shares fixedin counterfactuals—corresponds to the nested CES model with fixed mode shares, or ρ = 1. Similarly,Shapiro (2016)’s assumption of a unit mode share elasticity is closely similar to the case of ρ = 2.25.57As a result, both the main policy analysis and the robustness check of a unit mode share elasticityconsidered by Shapiro (2016) impose that air and ocean are complements.Lastly, I note that the structural equations for trade shares of equation (3.5) and mode shares ofequation (3.6) can be derived from a discrete choice model. In particular, the equation of Hummelsand Schaur (2013) is equivalent to a multinomial logit discrete choice model while the model of Lux(2011) or a nested CES model allow more general substitution patterns and are equivalent to a nestedlogit discrete choice model with the lower nest defined across modes.3.3.1 The Importance of the Mode Share ElasticityA back-of-the-envelope comparison shows that the range of substitution elasticity ρ estimated andassumed in Section 3.3 quantitatively and qualitatively matters. In Table 3.1 I show changes in coun-terfactual trade and emissions from three representative scenarios: 1% increases in trade costs for airimports, for sea imports, and for both together. These scenarios apply the respective trade cost changesto a region responsible for 20% of U.S. imports, which approximates the European Union trade share.Counterfactual trade is calculated using the mode-specific trade shares of equation (3.3).58 I assumethat any trade redistributing to domestic sourcing generates no direct transportation emissions, andthat every dollar of trade that substitutes from ocean to air generates 50 times the emissions impact ofsea. I consider three scenarios for the mode share elasticity. ρ = 1 corresponds to the fixed mode sharesassumption of Shapiro (2016), ρ = 2 for the endogenous mode shares but complements assumption ofShapiro (2016), and ρ = 7 corresponding to the case of substitute transport modes in Lux (2011).57For the case of an own-price elasticity with air shares of 20%.58Using CEPII data for 2006 I find U.S. imports from home to be 75%. Including domestic expenditure makes 20%of U.S. imports a trade share of 5%. The % Change in Imports shows the change in total U.S. imports from all regionswhere total expenditure is held fixed and imports are displaced to domestic production.663.3. Comparisons to Existing Models of Mode ChoiceTable 3.1: Counterfactual Trade Changes - Complements and SubstitutesIncreases in trade costs of:1% Air, 1% Sea 1% Air 1% Seaρ = 1 ρ = 2 ρ = 7 ρ = 1 ρ = 2 ρ = 7 ρ = 1 ρ = 2 ρ = 7Cross-price elasticity (-) (-) (+) (-) (-) (+) (-) (-) (+)%4 E.U. Imports -3.80 -3.80 -3.80 -1.14 -1.14 -1.14 -2.66 -2.66 -2.66%4 E.U. Air Imports -3.80 -3.80 -3.80 -1.14 -1.84 -5.34 -2.66 -1.96 1.54%4 R.O.W. Air Imports 0.20 0.20 0.20 0.06 0.06 0.06 0.14 0.14 0.14%4 E.U. Emissions -3.80 -3.80 -3.80 -1.14 -1.80 -5.07 -2.66 -2.00 1.27%4 World Emissions -0.60 -0.60 -0.60 -0.18 -0.31 -0.97 -0.42 -0.29 0.37Emissions per $ trade 1.00 1.00 1.00 1.00 1.73 5.37 1.00 0.69 -0.87Notes: Counterfactual percentage changes in trade due to, respectively, 1% increases in both air and ocean trade, onlyair trade, and only ocean trade costs. These trade costs are applied to a region approximating the E.U. trade share inU.S. imports of 5%. The Rest of the World (R.O.W.) has a trade share of 20%. Air transport is assumed to generate50 times the emissions impact per tonne-km of ocean trade. Counterfactuals use η = 5 to match conventional tradeelasticities of ∼ −4. The Cross-price elasticity indicates whether air and ocean imports are complements or substitutes;(-) for complements and (+) for substitutes.In Table 3.1 the first pattern of note is that changes in imports from the E.U. (%4 E.U. Imports)do not depend on the elasticity of mode shares under any of the trade cost scenarios. This is theconsequence of the model assumption that the conventional trade elasticity is independent of the modeshare elasticity. As noted previously, this is a potentially strong assumption, but the implications ofthis are not considered here.The change in imports arriving by air from the E.U. is sensitive to the mode share elasticity. A 1%increase in air trade costs decreases E.U. imports arriving by air by 1.84% for complements (ρ = 2) and5.34% under substitutes (ρ = 7). In contrast, a unilateral 1% increase in ocean trade costs decreasesimports arriving by air by 1.96% under ρ = 2 and increases air imports by 1.54% under ρ = 7. Anypolicy analysis interested in trade volumes differentiated by mode would find not only a substantiallydifferent scale of effect but also potentially a different sign of effect, depending on the value of ρ used.In addition, differences in E.U. imports between the complements case of ρ = 2 and substitutes of ρ = 7are larger than the differences across the scenarios of air and sea cost increases. This sensitivity to themode share elasticity has important consequences for evaluating policies on carbon emissions. Bothchanges in the direct carbon emissions associated with imports from the E.U. (%4 E.U. Emissions) andin the direct emissions from all imports (%4 World Emissions) differ substantially depending on themode share elasticity.59 Under the complements case of fixed mode shares (ρ = 1), one would concludethat all three policies generate the same emissions reductions per dollar of lower trade. The policiesdiffer only in the scale of changes. In contrast, under ρ = 7, regulating ocean transport increases thedirect carbon emissions from trade while decreasing imports. This is likely welfare reducing.59Changes in %4 World Emissions are small in levels because this policy is applied to the 20% of imports arrivingfrom the E.U. region but are evaluated as percentage changes against all imports.673.3. Comparisons to Existing Models of Mode ChoiceTable 3.2: Counterfactual Trade Changes - No SubstitutionIncreases in trade costs of:1% Air, 1% Sea 1% Air 1% Seaρ = 4.8 NS ρ = 4.8 NS ρ = 4.8 NS%4 E.U. Imports -3.80 -3.80 -1.14 -1.14 -2.66 -2.66%4 E.U. Air Imports -3.80 -3.80 -3.80 -3.80 0 0%4 E.U. Sea Imports -3.80 -3.80 0 0 -3.80 -3.80%4 R.O.W. Air Imports 0.20 0.20 0.06 0.20 0.14 0%4 R.O.W. Sea Imports 0.20 0.20 0.06 0 0.14 0.20Cross-mode substitution 70 0 30 0%4 E.U. Emissions -3.80 -3.80 -3.63 -3.63 -0.17 -0.17%4 World Emissions -0.60 -0.60 -0.68 -0.57 0.08 -0.03GHG/$ trade 1.00 1.00 3.767 3.185 -0.186 0.064Notes: Counterfactual percentage changes in trade due to, respectively, 1% increases in both air and ocean trade, only airtrade, and only ocean trade costs. These trade costs are applied to a region approximating the E.U. trade share in U.S.imports of 5%. The Rest of the World (R.O.W.) has a trade share of 20%. Air transport is assumed to generate 50 timesthe emissions impact per tonne-km of ocean trade. Counterfactuals use η = 5 to match conventional trade elasticities of∼ −4. The counterfactual labeled NS assumes there is no substitution between transport modes both within and acrossbilateral trade.Independence of Mode Shares to Costs in Alternative Trade RoutesSection 3.2 discussed the independence of mode shares within a bilateral trade route from trade costsamong alternative trade routes. This imposes substitution across transport modes across trade routeseven in the case of no mode substitution within bilateral trade. Table 3.2 shows how this Independenceof Irrelevant Alternative assumption affects counterfactual trade patterns.The case ρ = 4.8 corresponds to zero substitution between transport modes within bilateral trade;this can be seen in the 0% change in imports by air [sea] from the E.U. under the 1% increase in ocean[air] trade costs. In contrast, both transport modes among the rest of the world have increases inimports (%4 R.O.W. Imports for Air and Sea.) Consider a different counterfactual that assumes allsubstitution is within-mode regardless of the trade route. This has no direct equivalent in the nestedCES model framework, and is equivalent to modeling trade by air and ocean as completely independenttrade with no general equilibrium connection between them. I denote this case in Table 3.2 by NS (NoSubstitution).Under a 1% increase in air trade costs, the nested CES model predicts that, among air importsredistributing to alternative origin countries (R.O.W. imports), 70% will substitute to imports arrivingvia ocean—despite the zero substitution between air and ocean within bilateral trade. Similarly, 30% ofthe ocean imports substituting away from the E.U. to the R.O.W. under the 1% increase in ocean tradecosts will substitute to air. This is why the nested CES model predicts an increase in global emissionsfrom regulating ocean trade even without bilateral mode substitution, where as a true within-moderedistribution of trade would decrease world emissions. This also highlights how evaluating policies ofmode-specific trade costs, particular for the direct environmental externalities of trade, can be criticallydependent on the elasticity of mode shares and the restrictions over substitution patterns implicit inthe model used.683.4. Estimates of the Elasticity of Substitution Between Modes3.4 Estimates of the Elasticity of Substitution Between ModesSections 3.2 and 3.3 demonstrated that prior models of the choice of transportation mode withininternational trade share close similarities in how they model counterfactual trade flows. This priorwork also leaves it unclear whether air and ocean transport should be modeled as complements orsubstitutes, and whether import substitution between transport modes is important to consider inpolicy design and analysis. Are air and ocean transport complements or substitutes? There are tworeasons why this key fact remains unclear, despite prior estimates of the mode share elasticity ρ. First,as Subsection 3.2.2 discussed, estimates of ρ alone do not pin down complements or substitutes. Thisrequires an estimate of η, which to date have been estimated from different data sets and with differentidentification strategies than ρ. This leaves the suitability of comparing these parameters uncertain,particularly given the large differences in estimates of ρ between Hummels and Schaur (2013) and Lux(2011). Second, identifying complements or substitutes using using equation (3.13) or estimating ρusing equation (3.14) both assume that this model framework for mode choice is correctly specified. Ifit is not, then comparing ρ and η in equation (3.13) may not be sufficiently informative. In addition,the error term of equation (3.14) is likely to include other important explanatory factors and be subjectto an omitted variable bias. This is, of course, a caveat that can be applied to any structural model.The cause for concern with this model is the potentially strong restrictions on substitution patternsdiscussed in Subsection 3.2.2. Because of these limitations, this section takes a different approachand I do not exploit variation in the ratio of imports carried by air and ocean transport. Instead, Idirectly test whether modes are complements or substitutes by estimating their reduced form own-price and cross-price elasticities. This estimation does not require the nested CES or associated modelsto be correctly specified, as does comparing η and ρ. The goal of this reduced form approach is toavoid estimates predicated upon a particular model being correct, and to understand the aggregatesubstitution patterns across countries and modes that a model of mode choice must reflect.3.4.1 Data - U.S. Imports of MerchandiseData suitable for studying mode choice is limited. Most publicly available customs data records importor export values, trade routes, and product categories, but not freight costs or the specific transportmode used. In addition, most industry data on freight costs is based on containers or aggregate weight,and does not observe the specific product being shipped. As a result, much work studying mode choiceuses the same U.S. Imports of Merchandise dataset used in this chapter. This dataset records monthlydata since 1990 on U.S. imports at an HS10-exporting country-importing district level, including theFree-on-Board value, weight, and freight costs all differentiated by air vs. ocean transport. HS10corresponds to ten digit Schedule B product codes for U.S. imports and exports.60 I exclude U.S.imports from Canada and Mexico, as I do not observe the method of transport and focus on importsarriving from overseas. I drop all imports of oil and natural gas and limit the panel to 1992-2007 toinclude complete years and exclude the Great Recession. Most results below are based on the dataaggregated across months to the year level. I use monthly data to construct a measure of weight per60The first 6 digits of this 10 digit code are the Harmonized System product code.693.4. Estimates of the Elasticity of Substitution Between Modesshipment, and aggregate to the six digit HS level in some estimations. Details on the data are availablein Appendix C. Reduced Form Elasticity EstimatesMy preferred specification for estimating the own-price and cross-price elasticities of imports to tradecosts is of the formlog Xmnipt = βmlog(fmnipt) + βm′ log(fm′nipt) + γni + δnt + αit + ηp + nipt (3.15)where Xmnipt is the FOB import value for HS6 product p by mode m exported from country i to U.S.import regions n in year t, fmnipt are per kilogram freight rates, γni, δnt, αit, and ηp are fixed effects atthe origin-destination, destination-year, origin-year, and HS6 product level. Coefficients βm and βm′are the own and cross-price elasticities of mode m and I estimate equation (3.15) separately for air andocean imports. I use FOB import values to avoid endogeneity arising from including freight chargesin the dependent variable, and use per kilogram freight rates — as opposed to ad-valorem — for thesame reason.61Identifying these own and cross-price elasticities has several challenges. Ideally, a natural experi-ment could be found that causes exogenous variation to a single mode’s freight rates.62 Lacking this,I exploit idiosyncratic origin-destination-time varying freight rates to identify the own and cross-priceelasticities.The first challenge to estimating equation (3.15) is endogeneity arising from omitted variable bi-ases. I address most sources of omitted variable bias by using origin-year, destination-year, and origin-destination fixed effects. These control for any potential confounding variables that vary at these levels.For example, increases in region-specific energy prices that affect the demand for imports or the priceof exports and are correlated with freight costs, economic booms, region-time varying labour costs,or mode-specific geography differences across routes are all controlled for through these flexible fixedeffects.63 Instead, I use any source of variation in freight costs that varies at the trade route-year-modelevel. For example, changes in fuel costs that differentially affect freight rates across modes and traderoutes is one source of identifying variation. This has close similarities to the identification strategiesin Shapiro (2016) and, to a lesser extent, Hummels and Schaur (2013). Shapiro (2016) uses a similarspecification to equation (3.15) to estimate sectoral trade elasticities. Shapiro (2016) also includesfreight costs for Australian imports, which gives him two destination countries. Lacking Australianfreight data, I exploit variation in destination regions within the United States; this is similar to the61βm and βm′ are own and cross-price elasticities to per kilogram freight rates. These can be expressed as approximateiceberg trade cost elasticities βτm, βτm = βm · (1+sm)sm + 1, where sm is the average freight charges divided by FOB value.62Several possible candidates have been considered and found unsuitable. The closure of the Suez Canal studied byFeyrer (2009) would be a good candidate but that era lacks mode-specific trade data. Open-Skies Agreements consideredin Micco and Serebrisky (2006) are another possible candidate. In attempting to replicate their results I find that OSA’shave a smaller and largely statistically insignificant impact on freight rates. As a result, I do not find OSA’s to be asuitable exogenous shock to freight rates sufficient for a first stage.63Shapiro (2016) considers changes in tariffs and finds they do not affect his estimates; I do not repeat that exercisehere.703.4. Estimates of the Elasticity of Substitution Between Modescountry-import district variation used by Hummels and Schaur (2013).Table 3.3 presents the results of estimating equation (3.15) separately for air imports (Panel A)and ocean imports (Panel B). Specification (1) finds own-price elasticities of the expected sign andmagnitudes. Expressed in ad-valorem terms, at the median weight-to-value ratio the estimates inSpecification (1) correspond to -2.9 for air and -7.1 for ocean. These are similar to trade elasticities inthe literature, for example -4.25 in Melitz and Redding (2013) and in -3.7 in Shapiro (2016). To myknowledge, estimates of trade elasticities have not been undertaken for different transportation modes.To estimate the cross-price elasticity, Specification (2) includes freight rates for imports arriving bythe alternative mode within the same 6-origin-destination-year. In Panel A, for air imports, I find asmall but statistically significant positive effect of ocean freight rates on air imports. This coefficient isan order of magnitude smaller than the own-price elasticity, and indicates little aggregate substitutionbetween modes. In Panel B, for imports arriving by ocean, I find the cross-price elasticity is againsmaller in magnitude than the own-price elasticity; however, I find a negative cross-elasticity. This isconsistent with air and ocean imports being complements—not substitutes. Specification (3) uses analternative set of origin country, destination region, and year fixed effects, and finds broadly similarresults. This set of fixed effects is not preferred, however, as it does not allow origin and destinationregions to have separate time trends. In Specification (4) I control for the value-to-weight ratio ofimports, as it may be directly affect import volumes and freight rates; this finds the same patternamong the own and cross-price elasticities. Specification (5) uses import weight instead of importvalue as the dependent variable. This finds the opposite sign, though a still small cross-elasticityfor imports arriving by air and a similar negative cross-price elasticity for imports arriving by ocean.Results are also robust to restricting the sample to different subsets of origin countries, destinationregions, and time periods (Appendix C.4).The second endogeneity challenge is simultaneity. While freight rates affect import volumes, it isalso likely that import volumes affect freight rates. The sign of this bias is undetermined. Increases inimports may lead to port congestion and increase freight rates, or a higher import demand may lead tohigher markups to freight rates under monopolistic competition (Hummels et al., 2009). Alternatively,rising imports may result in economies of scale that reduce freight rates. To address this source ofendogeneity, I first note the unit of observation is at the HS6-year-trade route level. These observationsare typically a small share of aggregate trade; as a result, they individually will have little impact ontotal freight volumes. I assume that, conditional on included fixed effects, including time fixed effectsto control for aggregate trade volumes, the volumes in individual HS6-year-trade routes have no effecton freight rates through aggregate import volumes.The “through aggregate import volumes” is important. A second source of simultaneity bias canarise if importers receive a discount on freight costs through bulk imports—a fact documented byHolmes and Singer (2018). This can occur independent of the contribution of an individual observationsexpenditure to aggregate trade. While bulk discounting may cause a negatively bias to βm, it will notaffect estimates of βm′ as this is the coefficient on freight rates for the alternative transport mode. Iaddress this potential bias in βm by constructing a proxy for freight rates fmni that is orthogonal to713.4. Estimates of the Elasticity of Substitution Between ModesTable 3.3: Own and Cross-Price Elasticities(1) (2) (3) (4) (5)Panel A : Imports by AirDependent variable: Log Air Value Log Air WeightLogAir Freight ($/kg) -0.353∗∗∗ -0.297∗∗∗ -0.297∗∗∗ -0.410∗∗∗ -0.774∗∗∗(0.00638) (0.00816) (0.0216) (0.0113) (0.0149)LogOceanFreight ($/kg) 0.0304∗∗∗ 0.0163∗∗∗ 0.0163∗∗∗ -0.0292∗∗∗(0.00528) (0.00578) (0.00508) (0.00568)LogAirValue/Weight 0.237∗∗∗(0.00893)Fixed Effects A A B A AN 4396852 1742710 1743484 1742710 1742710r2 0.323 0.375 0.344 0.382 0.317Panel B : Imports by OceanDependent variable: Log Ocean Value Log Ocean WeightLogAir Freight($/kg) -0.130∗∗∗ -0.125∗∗∗ -0.131∗∗∗ -0.136∗∗∗(0.00692) (0.0119) (0.00691) (0.00683)LogOceanFreight($/kg) -0.409∗∗∗ -0.420∗∗∗ -0.450∗∗∗ -0.501∗∗∗ -0.927∗∗∗(0.00689) (0.00833) (0.0167) (0.0101) (0.0104)LogOceanValue/Weight 0.159∗∗∗Fixed Effects A A B A AN 4396852 1742710 1743484 1742710 1742710r2 0.323 0.375 0.344 0.382 0.317Notes: This table reports estimates of equation (3.15) for air and ocean imports. Fixed Effects A include HS6, Origin-Destination, Origin-Year, Destination-Year. Fixed effects B include HS6, Origin, Destination, and Year. Standard errorsfor Fixed Effects A are clustered at the origin-destination level and at the origin country level for Fixed Effects B. ***p<0.01, ** p<0.05, * p<0.1.723.4. Estimates of the Elasticity of Substitution Between ModesTable 3.4: Own and Cross-Price Elasticities - Proxy Rates(1) (2) (3) (4) (5) (6)Dependent variable: Log Air Value Log Sea ValueAirRate (Proxy) -0.245∗∗∗ -0.261∗∗∗ -0.243∗∗∗(0.0168) (0.0214) (0.0380)SeaRate 0.00517 -0.0000403 -0.00863(0.00541) (0.00784) (0.0132)AirValue/Weight 0.0669∗∗∗(0.00973)AirRate -0.153∗∗∗ -0.144∗∗∗ -0.148∗∗∗(0.00713) (0.00992) (0.0194)SeaRate (Proxy) -0.304∗∗∗ -0.315∗∗∗ -0.419∗∗∗(0.0225) (0.0257) (0.0690)SeaValue/Weight -0.0933∗∗∗(0.0113)Fixed Effects A A B A A BN 1644286 163542 1644583 1656316 164758 1656622r2 0.367 0.392 0.336 0.324 0.351 0.291Notes: This table reports estimates of equation (3.15) for air and ocean imports. Air [Sea] Rate are log freight ratesper kg. Proxy Rates are the average freight rate within the same trade route and industry excluding that observationsfreight rates. Value/Weights are log value to weight ratios. Fixed Effects A include HS6, Origin-Destination, Origin-Year,Destination-Year. Fixed effects B include HS6, Origin, Destination, and Year. Standard errors for Fixed Effects A areclustered at the origin-destination level and at the origin country level for Fixed Effects B. *** p<0.01, ** p<0.05, *p<0.1.discounts for bulk shipping. For each observation I use the average of all other freight rates withinthe same industry (HS2 level), year, and trade route, excluding the specific HS6-trade route-yearobservation in calculating its own proxy freight rate. Estimates using these proxy freight rates are inTable 3.4. This finds a similar pattern of point estimates close to zero for the cross-price elasticity ofair imports, and a negative and statistically significant cross-prices elasticity for ocean imports.The cross-price elasticities estimated in Tables 3.3 and 3.4 show that air and ocean transport arenot in aggregate substitutes. The negative cross-prices may indicate that imports typically carried byair have little substitution with ocean trade, where as imports typically carried by ocean are to a degreeresponsive to air freight rates. This is consistent with complementarity across transport modes. Suchcomplementarity across transport modes could arise through complementarity in intermediate inputs.Based on their value-to-weight ratio and preferences over delivery time, some of these complementaryinputs may typically be imported by air and others by sea. Firms facing fixed costs in sourcingcomplementary inputs may then source the entire bundle of goods from a new origin in response toa rise in a single modes freight costs, instead of substituting imports across modes. Similarly, fixedcosts for setting up supply chains may lead firms to seek the same supplier for multiple items, orsuppliers located geographically close together, even if individual items are not complementary goods.Conditional on ocean freight rates, increases in air freight rates may then lead firms to source allinputs from an alternative origin. This could cause the complementarity observed across modes. Thesubstitutability of air and ocean transport will depend on the time frame in question. It is likely that733.5. Heterogenous Unit Values and Mode Choicein the short run of several months, air and ocean would exhibit little substitution due to pre-paidcontracts, the relatively long time required to ship by sea, and difficulty of redirecting multi-modalfreight that is already in transit. In the long run of many years to decades, supply chains and technologywill adapt, leading to a likely larger substitutability. The time scale of observations used in this section- annual - results in estimates corresponding to a mid-range scale of several years where infrastructureremains mostly fixed.3.5 Heterogenous Unit Values and Mode ChoiceThe lack of strong substitution between transport modes found above–and the finding of complemen-tarity–contradict the expectation of substitution implied by the overlap in products carried by bothmodes. As a result, the overlap noted by Hummels and Schaur (2010), Lux (2011), and Hummels andSchaur (2013) is important to reconsider. This overlap is also pertinent to the choice of transport modebecause, as I show below, it may result from unobserved heterogeneity in product quality—which inturn is highly correlated with the across-country share of import value transported by a specific mode.The overlap in products carried by both modes is demonstrated in Figure 3.1. This histogramshows the air value shares within detailed HS10-exporter-import district-year observations. Theseobservations are concentrated at air shares close to 0 and 1, and the overlap in imports is relativelyuniformly distributed among those products arriving by both modes. HS10-exporter-import district-year observations with both modes represent 19% of observations and 46% of total import value.However, many products may be predominantly moved by one mode while having small quantitiesshipped by the alternative mode, such as scientific ore specimens arriving by air when nearly all oreimports arrive by bulk ocean carriers. For HS10-exporter-import district-year observations with airvalue shares between 5% and 95%, the overlap between air and ocean transport falls to 13% of productsrepresenting 19% of value. 19% of value regularly carried by each mode within a trade route is not aninsignificant fraction of imports. Implicit in the association between imports within HS10-year-traderoutes arriving by both modes and potential substitution between modes is that, at the point of arrivalto the importer or consumer, products are in fact closely similar varieties that serve as substitutesin the hands of a consumer or importing firm. However, inspection of the product categories in theU.S. Imports of Merchandise data suggests there is scope for substantial heterogeneity in varieties ofproducts even within the most detailed HS10 product level recorded by customs.For example, HS code 8517.12.0000 corresponds to “Telephones for cellular networks or for otherwireless networks” (Census, 2018). This includes everything from cheap flip phones to expensive smartphones. Similarly, HS code 6110.11.0010 corresponds to Sweaters, pullovers, sweatshirts, waistcoats(vests), and similar articles knitted or crocheted: Of wool: Men’s or boys’. While this is a detaileddescription, men’s wool sweaters and sweatshirts vary widely in cost for a similar weight garment andmay serve different markets. If expensive sweaters tend to arrive by air and low cost sweatshirts byocean, then the arrival of imports across both modes within a HS10 code may not be indicative of a highdegree of potential substitutability across modes. Instead, it reflects the aggregation over heterogeneousproduct varieties. Heterogeneity in quality across varieties would manifest itself as variation in unitprices within detailed product categories. Unit prices are not observed. Instead, I use the ratio of743.5. Heterogenous Unit Values and Mode ChoiceFigure 3.1: Histogram of Air SharesNotes: Density of air value shares within HS10-origin country-importing customs district-year observations.753.5. Heterogenous Unit Values and Mode Choicefree-on-board value to weightV alueWeight=p ∗ qw ∗ q =pwwhere value is a product’s unit price in the origin country times quantity, and weight is a product’s unitweight w times quantity.64 This is a unit price where the unit is a kilogram of the product rather thana single item of unknown weight. Figure 3.2 plots the log of FOB value to weight ratios across HS10-year-trade route observations. Air shipping has substantially higher average FOB values per kilogramwith a median of $61/kg for air and $7.0/kg for sea. There is also substantial heterogeneity in valueto weight ratios within modes. However, this heterogeneity in part reflects product composition at theHS10 level. To control for product composition, I regress the log of value to weight on HS10 productαp and year γt fixed effects,65log value/weightnipt = αp + γt + niptThis controls for all value to weight variation that is due to observed product composition atthe HS10 level or aggregate changes over time. Figure 3.3 plots the histogram of residuals fromthis estimation. This shows air has a higher median value/weight while there remains substantialheterogeneity within detailed product categories.A limitation to this comparison is that value-to-weight ratios may reflect discounts from bulkpurchasing even within identical product varieties. Bulk purchasing, referring to the quantity purchasedby an individual firm from a particular supplier within some time period, is not observed but is likelyhigher among ocean imports. However, a proxy for bulk purchases can be constructed as the weight inkilograms per individual shipment listed on an individual customs declaration form. A limitation to thismeasure is it will not capture discounts from bulk purchases that are split across separate shipments.Data limitations require constructing the measure of bulk purchases at the most detailed observationlevel available, HS10-exporting country-month-importing district-unloading port. A measure of bulkpurchases can be constructed for 75% of import value.66 To control for bulk shipments in value toweight differences between modes, I estimate the following,log value/weightnipt = Mnipt +Mnipt ×WgtCardnipt + (1−Mnipt)×WgtCardnipt+ ηn + δi + γt + αp + nipt (3.16)where Mnipt is an indicator for an observation arriving by air transport, WgtCardnipt is the log ofweight per shipment, and remaining terms are origin country, import district, year, and HS10 product64Free-on-board value excludes shipping charges. The U.S. Customs Bureau on FOB values: “this value is generallydefined as the price actually paid or payable for merchandise when sold for exportation to the United States, excludingU.S. import duties, freight, insurance and other charges incurred in bringing the merchandise to the United States.”Census(1996)65This has close similarities to an estimate by Harrigan (2010), but where I explore differences across modes while heis interested in the effect of distance.66As high-value imports are less likely to be assigned to individual shipments this measure of bulk purchasing has aselection bias towards those products with lower total import value. Details are available in Appendix C.3.763.5. Heterogenous Unit Values and Mode ChoiceFigure 3.2: Log Value/Weight RatiosNotes: Log of value to weight ratios within HS10-year-origin country-import district observations.773.5. Heterogenous Unit Values and Mode ChoiceFigure 3.3: Log Value/Weight Ratio ResidualsNotes: Residual value to weight ratios within HS10-year-exporting country-import district observations after regressinglog value to weight ratios on HS10 and year fixed effects.783.5. Heterogenous Unit Values and Mode ChoiceTable 3.5: Differences in Value/Weight Across Modes(1) (2) (3) (4) (5)Dependent variable: Log Value per WeightAir 2.319∗∗∗ 2.087∗∗∗ 1.107∗∗∗ 1.078∗∗∗ 0.331∗∗∗(0.0699) (0.0685) (0.0460) (0.0599) (0.0433)OceanXShipmentWeight -0.361∗∗∗ -0.489∗∗∗(0.00883) (0.0186)AirXShipmentWeight -0.500∗∗∗ -0.482∗∗∗(0.0146) (0.0133)N 4155978 4155978 4154759 3642211 1048027r2 0.383 0.427 0.712 0.839 0.621Year     Country    District    HS10   Notes: Estimates of equation 3.16. Fixed effects for year, origin country, import district, and HS10 product are includedwhere indicated. Air is an indicator for the transport mode being air; ocean is the excluded reference category. Shipmentweight is the log of weight attributed to that modes shipment as declared on a customs import form. This table reports*** p<0.01, ** p<0.05, * p<0.1.fixed effects. Table 3.5 presents the estimates. Specifications (1) and (2) show that without controllingfor HS10 product composition air freight is on average over 209% more valuable per kilogram than seafreight. After controlling for HS10 product composition, specification (3) finds a 111% increase for airtransport. Specifications (4) and (5) control for bulk purchasing through the weight per shipment. Thisfinds that imports by both air and ocean have substantially lower unit values the larger the shipmentsize, consistent with discounts for bulk purchasing. In Specification (5) I limit the sample to individualshipment sizes between the 25th and 75th percentile of air shipment weight, 18 to 230 kilograms, tocompare shipment sizes across ocean and air that can easily be carried within a single airplane flightor shipping container.67 This estimate finds air shipments continue to have a 30% price premium.These differences in the value-to-weight ratio support that, while air and ocean transport specializein different products, there remains substantial heterogeneity in product varieties within ten digit HSproduct categories and across transport modes.683.5.1 Differences in Air Shares Across CountriesHow the share of imports carried by air within a bilateral trade route varies across countries suggeststhat unobserved product quality is important to the choice of mode, particularly in comparison to theimportance of distance. Figure 3.4 plots the average air value shares for all U.S. Imports arriving fromoverseas, and separately for imports from Asia and Europe. Despite the large growth in U.S. importsover this period, the aggregate air share has not changed substantially. To explore the persistentdifferences in air shares and the role of product composition, I focus on the top 15 Asian and European67230 kilograms is also the maximum weight allowed for 10 checked bags on Air Canada.68This point was partially noted by Harrigan (2010); “This great range of log unit values is suggestive of substan-tial heterogeneity even within narrowly-defined HS10 categories.” However, Harrigan (2010) does not note that thisheterogeneity differs systematically across transport modes.793.5. Heterogenous Unit Values and Mode ChoiceFigure 3.4: Trends in Air Value SharesNotes: Time trends in average annual air value shares. All Imports includes all countries in addition to European andAsian countries.countries by total exports to the U.S., along with U.S. import districts located on the East Coast andWest Coast of the United States. These coastal districts simplify the comparison between imports byair and ocean freight as ports and airports are located close together, and because the East Coast andWest Coast introduce a wedge in relative transit distance between air and ocean freight due to thenecessity for ships to transit the Panama Canal. The average distance by air from countries in Asiato the East Coast of the U.S. is 20% farther than to the West Coast, but is 79% farther by sea. Incontrast, for European countries the West Coast is on average 49% farther from the East Coast by airand 138% farther by sea.69Figure 3.5 plots the average air value shares within country-U.S. coast trade routes and orderscountries by their average air shares. Three patterns are of note. First, air shares differ greatly acrosscountries. For example, China has an average air share of 14% compared to the United Kingdom at62%. Second, average air shares within countries differ little between coasts of the U.S. despite thedifferences in distance. This suggests that differences in shipping time across coasts and countriesis a relatively unimportant determinant of air shares compared to an unobserved factor that variesacross countries and is correlated within countries. Third, consistent with Figure 3.4, countries with69Air distances are measured using Google Maps from countries’ capital cities to the major port in the U.S. district ofentry. Sea distances account for geography, such as the Panama canal, and are measured using Sea-distances.org fromthe largest port of export from a country to the largest port in the U.S. district of entry. Continent-Coast distances arethe trade value weighted averages across country to import district trade routes.803.5. Heterogenous Unit Values and Mode ChoiceFigure 3.5: Average Air Shares By CountryNotes: Air value shares averaged within country-coast trade routes. Countries are ordered by their average air shares,and coasts refer to the East Coast and West Coast of the United States. 95% confidence intervals on the mean air shareare shown.813.5. Heterogenous Unit Values and Mode ChoiceFigure 3.6: Average Residual Air Shares By CountryNotes: Residual air value shares averaged within country-coasts. Countries are ordered by their average air value sharesas in Figure 3.5. 95% confidence intervals on the mean of the residual air share are shown.high air shares are concentrated in Europe. Notable exceptions in Asia are Australia, Singapore, andNew Zealand. This is consistent with the correlation of per capita GDP with air shares noted by Lux(2011).However, this comparison of air shares does not control for product composition. To control forHS10 product composition, I regress air shares for HS10-exporter-district-year observations on HS10product and year fixed effects and predict the residuals. These residual air shares are orthogonal toany determinant of air shares that is common within 10-digit product categories. In Figure 3.6 I plotthe air share residual averaged within country-coast and with the same country order as Figure 3.5.Even after controlling for product composition at the HS10 level, the three patterns remain closelysimilar to the original patterns in Figure 3.5. While the range of average air shares across countries hascompressed slightly from 0.59 in Figure 3.5 to 0.44, average air shares still differ substantially acrosscountries compared to across coasts within a country.As previously discussed, heterogeneous product quality varies across transport modes and couldbe one such factor that is correlated within countries. To explore this, Figure 3.7 plots the residualair shares against the residual air value-to-weight ratios averaged within country-coast trade routes.A strong correlation is clear: after controlling for product composition, the air shares across countriesare highly correlated with residual unit values. Countries that produce high quality product varieties823.6. ConclusionFigure 3.7: Residual Air Shares and Value to Weight RatiosNotes: y-axis values Air Share Residual and x-axis value to weight residuals are the residuals orthogonal to year andHS10 fixed effects. Both are averaged within exporting country-U.S. coast.have a high value to weight ratio. With shipping costs being primarily per unit, rather than ad-valorem, air shipping is relatively less expensive compared to ocean shipping the higher the value ofthe product. This suggests that unobserved quality is a particularly important determinant of thechoice of transport mode that future models of mode choice must account for. While previous modelshave focused on distance, the lack of strong dependence on shipping distance suggests that estimatesrequiring a parameterization of distance or shipping time may be sensitive to the functional formchosen. In addition, a focus on distance and time as the key determinant misses the important factorof unobserved quality.3.6 ConclusionThis chapter shows how prior models that consider trade differentiated by the method of transportationimpose strong, and potentially unrealistic, restrictions on substitution patterns across modes and coun-tries. I show that existing models have treated bilateral trade by air and sea as both substitutes andcomplements, and that this has significant quantitative and qualitative consequences for counterfactualtrade patterns. This finding has broad applicability; the elasticity of substitution between modes isimportant in evaluating the impacts of any factor that differs across methods of transportation, in-cluding distance, freight costs, delivery times, and environmental impacts. Turning to the empiricalevidence, I exploit idiosyncratic variations in freight rates to estimate reduced form own-price and833.6. Conclusioncross-price elasticities of substitution for imports arriving by ocean and air transport. These estimatesfind little evidence for substitution between transport modes for products primarily carried by air, andsome evidence for complementarity between modes for imports typically carried by ocean transport. Ithen show that previous cross-sectional evidence which motivates the assumption of substitution acrossmodes, the overlap in products arriving by both modes, may instead reflect unobserved heterogene-ity in product quality. This unobserved quality is a particularly important, and so far unrecognized,determinant of the choice of transportation mode across countries.These results have important implications for future work on models of mode-specific trade, theimportance of product quality and distance, and for proposed policies addressing the direct environ-mental impacts of international trade. As this chapter showed, models of mode choice face a trade offbetween quantitatively accurate approximations of substitution patterns across countries and modes,and maintaining a tractable form that is consistent with the large theoretical and empirical literatureon international trade. It is important that future work further establish a set of empirical facts thatmust be approximated in models of endogenous mode choice. These empirical patterns are also impor-tant to understand before microfounded models are developed to explain aggregate complementaritybetween modes, or incorporate unobserved heterogeneity in product quality.Of particular importance are additional estimates of the elasticities of substitution between trans-port modes, both within bilateral trade and across countries. These estimates are necessary to establishhow many separate substitution elasticities are necessary, and what analytically convenient approxima-tions can be made. For example, the shared model framework considered in this chapter imposes thata single elasticity governs substitution between transport modes within bilateral trade, and bilateralmode-shares are independent of relative freight costs among other countries. An alternative frameworkcould impose that a single elasticity governs substitution across countries within a transport mode,and a country’s share of imports within each mode is independent of relative freight costs among al-ternative transport modes. This alternative substitution pattern may be a more accurate model foroverall substitution patterns, or for particular classes of products such as those with a low elasticity ofsubstitution across transport modes.Similarly, key determinants of mode choice–particularly unit values–need to be systematically ex-plored. Heterogeneity in unit values may matter in two ways. The first is different papers and regressionspecifications use observations aggregated to different product levels, in particular HS10, HS6, and HS2(industry). The implications, if any, of these aggregations on empirical work considering trade differ-entiated by mode is unknown. The second is that while prior work has exploited variation in distancefor identification and considered it as a source of comparative advantage, the importance of distanceto the choice of mode, relative to other determinants, is not well understood. This chapter suggeststhat differences in distance between U.S. coasts is not a particularly important factor, and documenteda strong correlation among air shares within European and Asian countries with product unit values.As a result, unobserved product quality is highly correlated with the choice of transport mode—andmay in turn be correlated with distance from the United States—potentially confounding estimatesexploiting variation in mode shares and distance. This has the potential to be a widespread problemsince most work to date considering separate transportation modes in international trade uses the same843.6. ConclusionU.S. Imports of Merchandise dataset used in this chapter.While a variety of regulations on the direct carbon emissions from international aviation and ship-ping sources have been proposed, these efforts have considered transport modes separately and do notconsider the potential interactions between them. This chapter’s findings that air and ocean transportare not aggregate substitutes—and the potential for them to be complements—has two important im-plications for such regulations. First, air and ocean not being substitutes indicates that there is nolow-cost opportunity to shift a substantial share of trade from air to ocean to reduce negative pollutionexternalities without reducing imports. The silver lining is this also indicates that carbon emissionsfrom international ocean shipping can be regulated largely without concern for inducing offsettingincreases through substitution to air transportation.85ConclusionThis dissertation studies topics in environmental economics and international trade: how householdsconserve energy in response to financial rewards, and the choice of transportation mode within inter-national trade.In Chapter 1, I examine households’ electricity use and their participation in a voluntary programoffering financial rewards in exchange for achieving energy conservation targets. I estimate households’short and long run intensive margin responses and find that while electricity use declines as householdsattempt to achieve their conservation target, it rebounds as they leave the program. This reboundsuggests households do not make persistent changes through new capital investments or habits. Im-portantly, I find no evidence that households respond strategically to the voluntary program designthrough their decisions when to begin participating.In Chapter 2, I use the same dataset to study households’ extensive margin decisions whether tocontinue participating in the energy conservation program. I find that the decision to re-enroll differslittle across household characteristics, yet is strongly and discontinuously predicted by their success inachieving the conservation target—and not the structure of the incentive. Exploiting this discontinuityin the probability of re-enrolling using a fuzzy regression discontinuity design, I estimate the causaleffect of re-enrolling. Consistent with the results of Chapter 1 I find that additional conservationchallenges cause lower electricity use. In addition, households’ sensitivity to their success—and notthe incentive structure—is consistent with using heuristics in making participation decisions instead ofresponding as a well informed agent making an optimal choice given the structure of the incentive.Chapter 3 considers the choice of transportation mode within international trade. This chapter findsthat international trade models incorporating a choice of mode have imposed potentially unrealisticrestrictions on possible substitution patterns across countries and modes. In particular, I show howmodels have implicitly imposed transport modes to be complements, while other models have implicitlyimposed modes to be substitutes. I then show that this has a substantial impact on counterfactualtrade patterns and policy recommendations for any mode-specific cost change. This chapter thencontributes two pieces of empirical evidence on the choice of mode. 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Journal of Applied Psychology 63 (1), 73–80.90Appendix AAppendix to Chapter 1A.1 Event Study Estimates: Robustness ChecksThis section presents several event-study robustness checks. Figure A.1 plots the event study estimatesof equation (1.1) estimated without non-participant control households. This estimation strategyidentifies the program effects by exploiting the variation in timing in when a household starts theirfirst conservation challenge. Households that start a challenge later in the panel serve as the controlpopulation for households that undertake a challenge earlier in the panel. Figure A.1 shows that theestimated pre-treatment trend is not due to diverging trends between participant and non-participanthouseholds. Confidence intervals are larger due to the lack of non-participant households for identifyingthe date fixed effects. Figure A.2 plots the estimated program effects including the full set of non-participant households. Figure A.3 plots estimated program effects using an alternate baseline periodof the third year prior to the initial conservation challenge.91A.1. Event Study Estimates: Robustness ChecksFigure A.1: Estimated Treatment Effects For Participant Households OnlyNotes: This figure plots estimates of βˆτ and 95% confidence intervals from specification (1.3) estimated for participanthouseholds only. Estimates βˆτ are ordered by event-time τ and point estimates in red denote the 12 months of the initialconservation challenge. The gap between -11 and -23 is the excluded reference period; βˆτ identifies the percent changein electricity use relative to the average use in this period. Point estimates are in Appendix Table D.1, specification (2).92A.1. Event Study Estimates: Robustness ChecksFigure A.2: Estimated Treatment Effects For All HouseholdsNotes: This figure plots estimates of βˆτ and 95% confidence intervals from specification (1.3) for the unbalanced setof participant and non-participant households. Estimates βˆτ are ordered by event-time τ . Point estimates in reddenote the 12 months of the initial conservation challenge (τ = [1..12]). The additional yearly variation in this figure,compared to Figure 1.6, arises due to the higher share of electric-heating households among the full set of non-participanthouseholds, compared to program participants. Electric heating households have higher seasonal variation than non-electric households which the common date fixed effects cannot fully absorb.93A.1. Event Study Estimates: Robustness ChecksFigure A.3: Estimated Treatment Effects For All Households — Alternate BaselineNotes: This figure plots estimates of βˆτ and 95% confidence intervals from specification (1.3) for all participant andnon-participant households. Estimates βˆτ are ordered by event-time τ . Point estimates in red denote the 12 months ofthe initial conservation challenge (τ = [1..12]). The pre-treatment period is denoted by the months prior to Start (τ ≤ 0).The visual gap in estimates between months τ = −24 and τ = −36 is the excluded reference period. βˆτ identify thepercent change in electricity use relative to the average electricity use within a household during this excluded referenceyear.94Appendix BAppendix to Chapter 2B.1 Selection Into a Second Conservation ChallengeFigure B.1 plots the probability of continuing to a second conservation challenge against the reductionsin billed electricity use from that household’s first challenge. Larger reductions in billed electricity useare associated with a greater likelihood of continuing to a subsequent challenge. Figure B.1 also showsthe fraction of households succeeding in their challenge. From this we can see some households withreductions greater than 9.5% do not pass their challenge, while other households with reductions lessthan 9.5% do pass. This occurs because success or failure in a challenge is evaluated from changes inweather-adjusted - not billed - electricity use.B.2 Continuity at the DiscontinuityFigure B.2 shows the McCrary (2008) density test at the 9.5% threshold. This test fails to reject thenull hypothesis of no sorting, supporting that if households are bunching in success, they are not doingso at the 9.5% threshold and instead only at the 10% target.In Figure B.3 I plot the average of four household observables across the 9.5% threshold. Thisvisually shows no sorting of households by observables around the discontinuity. Table B.1 shows theresults of a linear regression discontinuity model estimated for these four and two additional observablesat the threshold. This finds no statistically significant change in the density of observables and supportsidentifying assumption that households are not sorting around the discontinuity.The McCrary (2008) density test, Figure B.2, suggests that there may be an increased densityof households above the 10% conservation target. In a standard regression-discontinuity setup, thiscould indicate sorting around a threshold lead to concerns that the RD estimates may be biased byself-selection into success. However, the threshold for success in this fuzzy-RD setup is at a reduction of9.5% — not the 10% target. If households were precisely sorting around the 10% target it is reasonableto expect this to appear as a discontinuity in either, or both, of the probability of continuing and thepost-program outcome. Inspection of Figure B.4 indicates this is not happening; the only discontinuityoccurs at precisely the 9.5% threshold.B.3 Fuzzy-RD Robustness Checks95B.3. Fuzzy-RD Robustness ChecksFigure B.1: Probability of Continuing to a Second Challenge: Billed Electricity UseNotes: Billed changes are the percent change in billed electricity consumption from the pre-program year to the yearof the first conservation challenge. The -9.5% level is shown by the vertical dashed line - note this is not the thresholdfor success as success was defined from credited - not billed - changes. Point estimates in the top bottom panel are theaverage probability of continuing to a second conservation challenge within 0.75%-wide bins of billed changes from thefirst conservation challenge. The dashed line in the top panel shows separate 1st order polynomial fits to households withbilled changes above and below the indicated -9.5% threshold.The bottom panel shows the corresponding fraction who pass their initial reduction challenge (dark connected line) andsubsequent challenge (light grey scatter plot.) The dashed grey line in the bottom panel is a 3rd order kernel-weightedlocal polynomial fit to the fraction of households that pass their second conservation challenge.96B.3. Fuzzy-RD Robustness ChecksFigure B.2: Density Test of the Running Variable - 9.5% ThresholdNotes: McCrary (2008) density test of the percent change in electricity use from a household’s initial conservationchallenge. The dark line is a smoothed local linear fit to the density of changes in electricity use, with 95% confidenceintervals indicated by the light grey line. Point estimates of the density are grey circles. The dashed red line is the 9.5%reduction threshold, and the sold line is the 10% reduction target.97B.3. Fuzzy-RD Robustness ChecksFigure B.3: Continuity of Covariates at The DiscontinuityNotes: Averages of four example covariates in the vicinity of the discontinuity by 0.25% wide binds of credited changes.Electric Heating is the share of households with electric space heating. Floor Area is the average floor space of ahousehold. Pre-Challenge Use is the average electricity use in the year before a household begins its first challenge. ColdMonth Before Challenge Start is the average heating degree days in the last month prior to the initial challenge. This isa measure of the last weather shock prior to the initial participation decision. The x-axis shows reductions in crediteduse with the dashed red vertical line denoting the 9.5% threshold for success and the solid red vertical line denoting the10% conservation target.98B.3. Fuzzy-RD Robustness ChecksTable B.1: Discontinuity Tests of CovariatesDependent Variable: Window Size3 4 5 6 7Heating 0.089 0.036 0.022 0.004 0.037(0.076) (0.065) (0.058) (0.053) (0.049)Floor Area -168.672 -118.697 -110.062 -61.026 -27.826(129.915) (111.300) (99.744) (91.517) (85.809)Pre-Program kWh 1155.694 1126.179 673.470 71.468 198.537(853.864) (720.725) (663.070) (589.560) (552.341)Pre-Program HDD -23.74 -18.97 -6.499 -4.555 -2.678(23.32) (19.74) (17.53) (15.82) (14.67)Property Value -48.510 -30.153 5.379 34.891 54.255(68.793) (62.081) (54.773) (51.611) (47.112)Share SFD -0.065 -0.022 -0.042 -0.052 -0.012(0.078) (0.067) (0.060) (0.054) (0.050)Notes: The table shows regression discontinuity estimates of γ1 estimated using equation 2.1 for the listed dependentvariables. The lack of statistically significant differences in covariates at the discontinuity supports that treatment is asgood as randomly assigned at the discontinuity. Estimates included separate linear trends billed reductions and are notshown for conciseness. Standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 are listed for completeness butno coefficients are significant at a 10% level.Table B.2: 2nd Order Bias-Corrected Fuzzy Regression Discontinuity Estimates(1) (2) (3) (4) (5) (6) (7) (8)Conventional -0.281 -0.189 -0.211∗ -0.264∗ -0.319∗ -0.331∗ -0.281∗ -0.181∗∗(0.199) (0.125) (0.123) (0.156) (0.192) (0.193) (0.153) (0.0794)Bias-corrected -0.421∗∗ -0.315∗∗ -0.207∗ -0.149 -0.133 -0.216 -0.323∗∗ -0.196∗∗(0.199) (0.125) (0.123) (0.156) (0.192) (0.193) (0.153) (0.0794)Robust -0.421 -0.315∗ -0.207 -0.149 -0.133 -0.216 -0.323 -0.196∗∗(0.264) (0.168) (0.166) (0.210) (0.259) (0.257) (0.201) (0.0848)Observations 888 1196 1475 1763 2050 2296 2543 4160OrderPoly.(p) 2 2 2 2 2 2 2 2OrderBias(q) 3 3 3 3 3 3 3 3BWPoly.(h) 3% 4% 5% 6% 7% 8% 9% 18%BWBias(b) 3% 4% 5% 6% 7% 8% 9% 33%F-Conv. 3.1 4.9 5.5 4.5 3.9 4.1 5.3 14.8F-Bias 1.4 3.6 6 9.2 9.1 7.3 5.8 14.8F-Robust .8 2.1 3.4 5.1 5 4 3.2 13Notes: All specifications are a 2nd order polynomial estimated with a triangular kernel and restricted to householdsthat either start their next challenge within 12 months or do not undertake an additional challenge. Specifications (1)through (7) are for ± the listed bandwidths around the threshold. Specification (8) determines the optimal polynomialand bias-correction bandwidths to be 18% and 33%, respectively. Conventional, bias-corrected, and bias-corrected androbust F-stats on the 1st stage instrument respectively denoted by F-Conv., F-Bias, and F-Robust. Standard errors inparentheses. *** p<0.01, ** p<0.05, * p<0.1.99B.3. Fuzzy-RD Robustness ChecksFigure B.4: First Stage and Reduced Form Discontinuities(a) First Stage - ±5% Bandwidth (b) First Stage - ±9% Bandwidth(c) Reduced Form - ±5% Bandwidth (d) Reduced Form - ±9% BandwidthNotes: This figure plots the first stage and reduced form discontinuities for bandwidths of ±5% and ±9% around the9.5% reduction threshold in credited changes. Individual point estimates are the average of the outcome variable within0.25% width bins in credited changes.100B.3. Fuzzy-RD Robustness ChecksTable B.3: Fuzzy Regression Discontinuity Estimates: 6 Month Gap(1) (2) (3) (4) (5) (6) (7)PanelA− First StageDependent variable: Continue to a Second Challenge CiWindow ±7% ±6% ±5% ±4% ±3%γ1: Success 0.203∗∗∗ 0.195∗∗∗ 0.161∗∗∗ 0.163∗∗∗ 0.170∗∗Indicator (0.0468) (0.0505) (0.0556) (0.0622) (0.0727)γ2: Cred.Reduc. -0.775 -1.480 -2.573∗∗ -0.510 1.794(0.822) (1.016) (1.282) (1.818) (2.876)γ3 : Success× 1.854 3.156∗∗ 2.909 -0.527 -3.965Cred.Reduc. (1.204) (1.491) (1.959) (2.689) (4.183)γ4 :BilledReduc. -0.576∗ -0.678∗ -0.367 -0.649 -0.867∗(0.344) (0.367) (0.391) (0.433) (0.520)γ0 :Constant 0.435∗∗∗ 0.453∗∗∗ 0.466∗∗∗ 0.440∗∗∗ 0.419∗∗∗(0.0317) (0.0344) (0.0377) (0.0424) (0.0495)F-stat 18.79 14.85 8.374 6.872 5.452PanelB− SecondStageDependent variable: Percent change in post-challenge electricity useOLS Instrumental Variable EstimatesWindow ±5% ±7% ±6% ±5% ±4% ±3%β1 :Re-Enroll -0.0171∗∗∗ -0.0246∗∗∗ -0.143∗∗ -0.165∗∗ -0.190∗ -0.241∗ -0.162(0.00444) (0.00718) (0.0651) (0.0739) (0.102) (0.124) (0.114)β2: Cred.Reduc. -0.0829 -0.482∗ -0.580 -0.864 -0.607 0.940(0.255) (0.272) (0.363) (0.570) (0.642) (0.675)β3 : Success× 0.451 0.423 0.544 0.827 -0.126 -1.758Cred.Reduc. (0.456) (0.338) (0.446) (0.596) (0.905) (1.246)β4 :BilledReduc. -0.136 -0.120 -0.197∗ -0.198 -0.325∗∗ -0.333∗(0.105) (0.101) (0.112) (0.122) (0.162) (0.173)β0 :Constant -0.00773∗∗∗ 0.0145∗ 0.0747∗∗ 0.0879∗∗ 0.104∗ 0.124∗ 0.0731(0.00289) (0.00793) (0.0348) (0.0407) (0.0554) (0.0646) (0.0571)N 4810 1287 1779 1535 1287 1039 775Notes: This table reports fuzzy-RD estimates corresponding to equations (2.1) and (2.2). Estimation sample restricted tohouseholds that either start their next challenge within 6 months or do not undertake an additional challenge. Estimationwindow is restricted to ± the listed percent around the 9.5% threshold in credited changes. Standard errors in parentheses.*** p<0.01, ** p<0.05, * p<0.1.101B.3. Fuzzy-RD Robustness ChecksRobustness Checks - Log monthly electricity useAn alternative to defining the outcome in the fuzzy-RD approach as the post-program changes inelectricity use, equation (2.3), is to use log monthly electricity use. This has the benefit of not requiringaggregating to annual changes at the cost of a less transparent estimation. Using log monthly electricityuse finds similar estimates as using post-program changes from (2.3).The first stage relationship isCi = αi+γ0Dit,1+γ11{Ri ≤ R¯}×Dit,1+γ2Ri×Dit,1+γ31{Ri ≤ R¯}×Ri×Dit,1+γ4Bi×Dit,1+γ5Xi+ηit(B.1)where Ci is a binary indicator for whether a household continues to a second challenge, Ri arehouseholds’ credited changes in electricity use from the first challenge, Rd is the threshold for successin the challenge and is -9.5%, 1{Ri ≤ R¯} is the dummy variable for success in the initial challenge, Biare the billed changes from the initial challenge, and Xi is a vector of other controls. The instrumentexcluded from the second stage is 1{Ri ≤ R¯}. Dit,1 is an indicator for if household i in month twas participating in the second challenge. The estimation sample is restricted to only observationsfor households undertaking their first conservation challenge or in their post-program year of a secondchallenge or after exiting the program.The second-stage relationship isyit = λi + β0Dit,1 + β1Ci + β2Ri ×Dit,1 + β31{Ri ≤ R¯} × Ri ×Dit,1 + β4Bi ×Dit,1 + β5Xi + i(B.2)where yit is log monthly electricity use.102B.3. Fuzzy-RD Robustness ChecksTable B.4: Fuzzy Regression Discontinuity Estimates: Log Monthly Electricity Use and 12Month Gap(1) (2) (3) (4) (5) (6) (7)PanelA− First StageDependent variable: Continue to a Second Challenge CiWindow ±7% ±6% ±5% ±4% ±3%γ1: Successi 0.197∗∗∗ 0.185∗∗∗ 0.139∗∗∗ 0.138∗∗ 0.177∗∗∗(0.0431) (0.0467) (0.0515) (0.0574) (0.0679)γ0:Dit,1 0.473∗∗∗ 0.477∗∗∗ 0.504∗∗∗ 0.519∗∗∗ 0.503∗∗∗(0.0251) (0.0270) (0.0297) (0.0324) (0.0380)γ2:Ri ×Dit,1 -0.431 -0.721 -2.133∗∗ -1.961 0.285(0.629) (0.763) (0.968) (1.304) (2.052)γ3 : 1{Ri≥R¯} 2.268∗∗∗ 2.757∗∗∗ 1.936∗ 2.066 0.0676×Ri ×Dit,1 (0.687) (0.875) (1.133) (1.477) (2.315)γ4 :Bi ×Dit,1 -0.288 -0.357 -0.0474 -0.288 -0.527(0.323) (0.345) (0.367) (0.402) (0.488)F-stat 21.00 15.66 7.302 5.772 6.818PanelB− SecondStageDependent variable: Logmonthly electricity useOLS Instrumental Variable EstimatesWindow ±5% ±7% ±6% ±5% ±4% ±3%β1: Successi -0.0216∗∗∗ -0.0279∗∗∗ -0.144∗∗ -0.184∗∗ -0.229∗ -0.299∗ -0.146(0.00435) (0.00732) (0.0679) (0.0816) (0.127) (0.162) (0.109)β0:Dit,1 -0.0156∗∗∗ -0.00267 0.0647∗ 0.0880∗ 0.115 0.161∗ 0.0747(0.00302) (0.00539) (0.0388) (0.0465) (0.0731) (0.0953) (0.0648)β2:Ri ×Dit,1 -0.289 -0.437 -0.773 -1.233 0.00274(0.227) (0.295) (0.574) (0.808) (0.565)β3 : 1{Ri≥R¯} 0.689∗∗ 0.863∗∗ 1.414∗∗∗ 2.216∗∗∗ 2.418∗∗∗×Ri ×Dit,1 (0.278) (0.349) (0.435) (0.591) (0.814)β4 :Bi ×Dit,1 -0.136 -0.214∗ -0.214 -0.328∗ -0.367∗∗(0.108) (0.119) (0.135) (0.171) (0.173)N 130368 35400 49200 42312 35400 28704 21312Households 2050 1763 1475 1196 888Notes: Estimates using log monthly electricity use from Appendix section B.3. *** p<0.01, ** p<0.05, * p<0.1.103B.3. Fuzzy-RD Robustness ChecksTable B.5: Fuzzy Regression Discontinuity Estimates: Log Monthly Electricity Use and 6Month Gap(1) (2) (3) (4) (5) (6) (7)PanelA− First StageDependent variable: Continue to a Second Challenge CiWindow ±7% ±6% ±5% ±4% ±3%γ1: Successi 0.187∗∗∗ 0.176∗∗∗ 0.154∗∗∗ 0.134∗∗∗ 0.145∗∗∗(0.0391) (0.0411) (0.0426) (0.0470) (0.0523)γ0:Dit,1 0.420∗∗∗ 0.431∗∗∗ 0.440∗∗∗ 0.445∗∗∗ 0.439∗∗∗(0.0234) (0.0245) (0.0258) (0.0285) (0.0318)γ2:Ri ×Dit,1 -0.894∗∗ -1.047∗∗ -1.264∗∗∗ -1.817∗∗∗ -1.812∗∗∗(0.404) (0.438) (0.475) (0.577) (0.668)γ3 : 1{Ri≥Rd} 2.526∗∗∗ 2.557∗∗∗ 2.427∗∗∗ 2.961∗∗∗ 1.370×Ri ×Dit,1 (0.604) (0.736) (0.856) (1.008) (1.249)γ4 :Bi ×Dit,1 0.185 0.327 0.284 0.638 1.241(0.444) (0.514) (0.611) (0.771) (1.062)F-stat 22.82 18.25 13.01 8.174 7.657PanelB− SecondStageDependent variable: Logmonthly electricity useOLS Instrumental Variable EstimatesWindow ±5% ±7% ±6% ±5% ±4% ±3%β1: Successi -0.0223∗∗∗ -0.0281∗∗∗ -0.151∗∗ -0.178∗∗ -0.219∗∗ -0.286∗∗ -0.208∗(0.00462) (0.00768) (0.0618) (0.0723) (0.0920) (0.130) (0.115)β0:Dit,1 -0.0156∗∗∗ -0.00267 0.0569∗ 0.0700∗ 0.0884∗ 0.124∗ 0.0836(0.00302) (0.00539) (0.0316) (0.0373) (0.0474) (0.0663) (0.0584)β2:Ri ×Dit,1 -0.420∗∗ -0.558∗∗∗ -0.720∗∗∗ -0.998∗∗ -0.906∗∗(0.164) (0.202) (0.262) (0.425) (0.406)β3 : 1{Ri≥Rd} 0.394∗ 0.545∗∗ 0.748∗∗ 1.038∗∗ 1.233∗∗∗×Ri ×Dit,1 (0.228) (0.259) (0.309) (0.459) (0.328)β4 :Bi ×Dit,1 0.156 0.240 0.389∗ 0.291 0.645∗(0.136) (0.166) (0.213) (0.298) (0.374)N 115440 30888 44976 38496 32352 26112 19536Households 1874 1604 1348 1088 814Notes: Estimates using log monthly electricity use from Appendix section B.3. *** p<0.01, ** p<0.05, * p<0.1.104Appendix CAppendix to Chapter 3C.1 DerivationsC.1.1 Mode-specific expenditure from nested CES preferencesThe representative consumer has CES preferences over quantity Qw of product variety w delivered byeither mode,U =[∑w(Qw)η−1η] ηη−1(C.1)and preferences over aggregate quantity QwQw =[2∑m=1λmw (qmw )ρ−1ρ] ρρ−1(C.2)where qmw is the quantity delivered by mode m. Elasticity of substitution across varieties and acrossmodes are η > 1 and ρ > 1 and the consumer maximizes U subject to their budget constraint of totalexpenditure I,∑m∑wpmw qmw ≤ IThe solution to this optimization problem requires proving that expenditure is independent acrossvarieties w and has been proved in Strotz (1957) and is equivalent to Sillard and Wilner (2015). To seethe equivalence define Qm ≡ [∑i αimxρmim ]1ρm so that the maximization of Sillard and Wilner (2015) isU(x) = {∑mQρm} 1ρ . Transform notation from Sillard and Wilner (2015) to this chapter by105C.1. Derivationsm → wi → mαim → λmwρ → η − 1ηρm → ρ− 1ρxim → qmwσm → ρσ → ηwhich delivers the same optimization problem as this chapter,U(x) ={∑w(Qw)η−1η} ηη−1andQw ≡[∑mλmw (qmw )ρ−1ρ] ρρ−1Expenditure on variety w is given byXw =(∑m(λmw )ρ (pmw )1−ρ) 11−ρand final demand becomesqmw = R(λmwpmw)ρXρ−ηw∑wX1−ηw= R(λmwpmw)ρ (∑m (λmw )ρ (pmw )1−ρ) ρ−η1−ρ∑w(∑m (λmw )ρ (pmw )1−ρ) 1−η1−ρ= R(λmwpmw)ρ(Pw)1−ρ(PwP)1−η=Xnpmw(λmw )ρ(pmw )1−ρP 1−ρw(PwPn)1−η(C.3)The Armington assumption of a continuum of differentiated varieties produces the final country-106C.1. Derivationsmode specific expenditure.C.1.2 Elasticities of Trade and Mode SharesTrade and mode shares follow with algebra from their respective definitions. pini ≡ XniXn follows fromXni =∑mXmni=∑mXn(λmni)ρ(pmni)1−ρP 1−ρni(PniPn)1−η= Xn(PniPn)1−η 1P 1−ρni∑m(λmni)ρ(pmni)1−ρ (C.4)= Xn(PniPn)1−ηand mode shares follow from the definition and equation (3.3),γmni ≡XmniXni=λmniρ(pmni)1−ρP 1−ρniElasticitiesAssume a shock to the transport costs for imports from country j to n by mode m’, τm′nj . Changes CIFexpenditures can be decomposed from Xmni = Xnpiniγmni,∂lnXmni∂lnτm′nj=∂lnXn∂lnτm′nj+∂lnpini∂lnτm′nj︸ ︷︷ ︸(A)+∂lnγmni∂lnτm′nj︸ ︷︷ ︸(B)Term (A)Term (A) starts fromlnpini = (1− η)(lnPni)− lnP 1−ηnTaking derivatives of each term w.r.t. τm′nj , and starting with the first term:107C.1. Derivations(1− η)∂lnPni∂τm′nj= 0 if i 6= j, ∀ m,m′=(1− η)(1− ρ)∂lnP 1−ρni∂τm′nj=(1− η)(1− ρ)1P 1−ρni∂∂τm′nj∑m(λmni)ρ(pmni)1−ρ=(1− η)P 1−ρni(λm′nj )ρ(pm′nj )−ρcj=(1− η)P 1−ρni τm′nj(λm′nj )ρ(pm′nj )1−ρ= (1− η)γm′niτm′niif i = j, ∀ m,m′Solving for the second term,∂lnP 1−ηn∂τm′nj=1P 1−ηn∂P 1−ηn∂τm′nj=1P 1−ηn∂∂τm′nj∑iPni1−η =1P 1−ηn∂P 1−ηnj∂τm′nj=P 1−ηnjP 1−ηn∂lnP 1−ηnj∂τm′nj= pinj∂lnP 1−ηnj∂τm′njCombined with the result from the first term we have∂lnP 1−ηn∂τm′nj= (1− η)pinjγm′njτm′njTherefore,(A) =∂lnpini∂lnτm′nj=(1− η)(1− pini)γm′ni if i = j ∀ m,m′(1− η)(−pinj)γm′nj if i 6= j ∀ m,m′Term (B)Term (B) begins from γmni =λmniρ(pmni)1−ρP 1−ρniand the prior derivations for changes in the price indexes,∂lnγmni∂lnτm′nj=∂ln(λmniρ(pmni)1−ρ)∂lnτm′nj− ∂lnP1−ρni∂lnτm′nj= (1− ρ)(1− γm′ni ) if i = j and m = m′= (1− ρ)− (1− ρ)γm′ni if i = j and m = m′(B) =∂lnγmni∂lnτm′nj=(1− ρ)(1− γm′ni ) if i = j and m = m′(1− ρ)(−γm′nj ) if i = j and m 6= m′0 if i 6= j ∀ m,m′108C.1. DerivationsExpenditure changesCombining (A) and (B) and assuming aggregate expenditureXn is fixed gives the change in expenditurefrom a change in iceberg trade costs,∂lnXmni∂lnτm′nj=(1− η)(1− pini)γmni + (1− ρ)(1− γmni) if i = j and m = m′(1− η)(1− pini)γm′ni + (1− ρ)(−γm′ni ) if i = j and m 6= m′(1− η)(−pinj)γm′nj if i 6= j ∀ m,m′C.1.3 Difference between CIF and FOB valuesNote that Xmni is defined in CIF terms, Xmni = pmni · qmni, where pmni is the CIF price pmni = ci · τmni . As aresult, an increase in τmni will both change the quantity imported, qmni, and the value of the imports.∂lnXmni∂lnτm′nj=∂lnpmni∂lnτm′nj+∂lnqmni∂lnτm′nj=∂lnci∂lnτm′nj+∂lnτmni∂lnτm′nj+∂lnqmni∂lnτm′njAssume Free-on-Board origin prices are independent of changes in trade costs, ∂lnci∂lnτm′nj= 0,∂lnXmni∂lnτm′nj=∂lnτmni∂lnτm′nj+∂lnqmni∂lnτm′nj=1 +∂lnqmni∂lnτm′njif i = j and m = m′∂lnqmni∂lnτm′njif i 6= j or m 6= m′Consider FOB values,Xm,FOBni = ci ∗ qmni =pmniqmniτmni=Xm,CIFniτmniTherefore,∂lnXm,FOBni∂lnτm′nj=∂lnXm,CIFni∂lnτm′nj− ∂lnτmni∂lnτm′nj=∂lnXm,CIFni∂lnτm′nj− 1 if i = j and m = m′∂lnXm,CIFni∂lnτm′njif i 6= j or m 6= m′Importantly, this means that the cross elasticity - which determines substitutes or complements - isthe same whether imports are valued in CIF and FOB values. This is intuitive, since a change in freightcosts will only affect the value of imports that include those freight costs; products redistributing toother modes and countries will face those countries freight costs and modes, which are unaffected, andtherefore the percentage change in value will be the same whether measured in CIF or FOB values.109C.2. Comparison to Existing ModelsC.2 Comparison to Existing ModelsC.2.1 Lux (2011)The equivalence follows from equations (5)-(7) of Lux (2011). Let θ′ and ρ′ denote parameters fromLux (2011) and define the transformations − θ′1−ρ′ ≡ (1 − ρ), −θ′ ≡ (1 − η), and pmni ≡ T11−η′i ciτmni .Note the typo in Lux (2011) equation (6) which is missing a negative sign in the exponent 1−ρ′θ′ . Thisproduces the same reduced form equations for mode and trade shares as the nested CES model.C.2.2 Hummels and Schaur (2013)Equation (1) in Hummels and Schaur (2013) is equivalent to the nested CES model equation C.3under the assumptions ρ = η in the CES model, which then collapses to a single CES preferencesover product varieties and perceived quality from fast delivery, and using the same parameterizationover fast delivery used by Hummels and Schaur (2013). That is, variety w delivered by mode m isλmw = υmw exp(−τ ·daysmw ). See Hummels and Schaur (2013) for the definition of these terms. Similarly,equation (3.14) for the elasticity of substitution over modes is equivalent to equation (6) of Hummelsand Schaur (2013).ln(Xani,tXoni,t)= ρτ(daysow − 1) + (1− ρ)cai,tcoi,t− ρτani,tτ oni,t+ ρlnυaniυoni+ ni,tC.2.3 Shapiro (2016)Shapiro (2016) combines mode-specific carbon taxes in a weighted average to produce an equivalenttariff on aggregate trade. After counterfactual trade patterns are determined from the model, the tradeis projected back into mode shares based on the initial shares (his standard approach) or by assuminga unit mode elasticity in his endogenous mode shares robustness check. Consider a change in tradecosts like a carbon price applied to both air and ocean transport within a trade route, and assume thestandard form for trade and mode shares. Changes in imports by air are,dlnXani =∂lnXani∂lnτanidlnτani +∂lnXani∂lnτ onidlnτ oni= [(1− η)(1− pini)γani + (1− ρ)(1− γani)]dlnτani + [(1− η)(1− pini)γoni + (1− ρ)(−γoni)]dlnτ oni= (1− η)(1− pini)(γanidlnτani + γonidlnτ oni) + (1− ρ)γoni(dlnτani − dlnτ oni)= (1− η)(1− pini)dlnτwni + (1− ρ)γoni(dlnτani − dlnτ oni)where τwni is the mode-share weighted average change in trade cost. If we assume mode shares arefixed, then ρ = 1 and this is a similar change in expenditure shares from a weighted average carbon tax(dlnτwni) to that of Shapiro (2016). Alternatively, using a unit elasticity of mode shares to freight rates(equation 3.9) as assumed by Shapiro (2016) corresponds approximately to ρ = 2. The comparison110C.3. Dataisn’t exact as Shapiro (2016) doesn’t have a model of endogenous mode choice and assumes isoelasticmode shares instead of including the term γmni in the elasticity of mode shares.C.3 DataThe U.S. Imports of Merchandise monthly data is available from the United States Census Bureau.Within each individual monthly file I drop all observations that have missing data for shipping value,weight, or freight charges. Eight of the monthly files were corrupted and are missing from the dataset. Iinterpolate a missing month’s data using the average of the previous and subsequent months within themost detailed observation available; HS10, country, import district, and unloading district. I constructthe measure of import bulk using the variable CARDS_MO, which is defined as the “Number ofDetailed Records, Current Month.” This variable is available within an HS10-month-origin country-import district-unlading port observation and indicates the number of distinct shipments recordedby Customs Census (1996). However, the variable aggregates over both air and ocean imports. Toconstruct the number of separate air and ocean shipments, I first assign all observations with shipmentsvia a single mode the corresponding CARDS_MO value. For those observations with imports observedover both modes, I use those observations with CARDS_MO of 1 or 2 only. This allows me to uniquelyattribute the observed trade flow to shipments. Observations with greater than 2 shipments cannotdistinguish which mode has the greater number of shipments and I cannot generate a value for importbulk for these observations. This attribution succeeds for 75% of import value. For estimating the ownand cross-price elasticities I aggregate to the HS6 product level, and drop any observation with a perkilogram or ad-valorem freight rate below the 1st or above the 99th percentiles.C.4 Estimated ElasticitiesTables C.1 and C.2 show estimated own and cross-price elasticities for air and ocean imports restrictedto several subsets of observations, and which find results consistent with the main estimates.111C.4. Estimated ElasticitiesTable C.1: Estimated Elasticities: Air Imports(1) (2) (3) (4) (5) (6)Dependent variable: Log Air ValueAirRate (Proxy) -0.217∗∗∗ -0.219∗∗∗ -0.258∗∗∗ -0.287∗∗∗ -0.248∗∗∗ -0.235∗∗∗(0.0338) (0.0200) (0.0203) (0.0536) (0.0193) (0.0177)SeaRate -0.00226 0.00392 0.0128∗ 0.00853 -0.00746 0.0105∗(0.0101) (0.00502) (0.00710) (0.0119) (0.00692) (0.00584)N 741338 712073 880487 358252 781859 862020r2 0.399 0.409 0.370 0.402 0.362 0.388Subset E.U. E.A. East C. West C. < 2000 ≥ 2000Notes: This table reports estimates of equation (3.15) for air imports limited to subsets of observations. All specificationsinclude HS6, HS6, Origin-Destination, Origin-Year, and Destination-Year. Air [Sea] Rate are log freight rates per kg.Air Rate (Proxy) is the average freight rate within the same trade route and industry excluding that observations freightrates. Subset E.U. [E.A.] are imports arriving from European Union [East Asian] countries. East C. [West C.] are importsarriving from all countries to the East Coast [West Coast] import districts of the United States. <2000 and >2000 arerespectively restricted to the years 1992-1999 and 2000-2007. Standard errors are clustered at the origin-destination level.*** p<0.01, ** p<0.05, * p<0.1.Table C.2: Estimated Elasticities: Ocean Imports(1) (2) (3) (4) (5) (6)Dependent variable: Log Sea ValueAirRate -0.106∗∗∗ -0.159∗∗∗ -0.160∗∗∗ -0.152∗∗∗ -0.170∗∗∗ -0.139∗∗∗(0.00817) (0.00920) (0.0102) (0.00940) (0.00838) (0.00746)SeaRate (Proxy) -0.320∗∗∗ -0.191∗∗∗ -0.325∗∗∗ -0.312∗∗∗ -0.299∗∗∗ -0.305∗∗∗(0.0394) (0.0190) (0.0308) (0.0542) (0.0255) (0.0239)N 756517 705370 891302 362227 787419 868452r2 0.360 0.311 0.305 0.421 0.329 0.335Subset E.U. E.A. East C. West C. < 2000 > 2000Notes: This table reports estimates of equation (3.15) for ocean imports limited to subsets of observations. All specifica-tions include HS6, HS6, Origin-Destination, Origin-Year, and Destination-Year. Air [Sea] Rate are log freight rates perkg. Sea Rate (Proxy) is the average freight rate within the same trade route and industry excluding that observationsfreight rates. Subset E.U. [E.A.] are imports arriving from European Union [East Asian] countries. East C. [West C.] areimports arriving from all countries to the East Coast [West Coast] import districts of the United States. <2000 and >2000are respectively restricted to the years 1992-1999 and 2000-2007. Standard errors are clustered at the origin-destinationlevel. *** p<0.01, ** p<0.05, * p<0.1.112Appendix DAppendix to Chapter 1 (II): Table of AllEstimatesD.1 Event Study Estimates For All HouseholdsTable D.1: Event-Study Point EstimatesPre 0.020∗∗∗ 0.030∗∗∗(0.0051) (0.010)M-59 0.027∗∗∗ 0.034∗∗∗(0.0055) (0.0097)M-58 0.032∗∗∗ 0.038∗∗∗(0.0054) (0.0093)M-57 0.024∗∗∗ 0.030∗∗∗(0.0055) (0.0090)M-56 0.024∗∗∗ 0.030∗∗∗(0.0052) (0.0087)M-55 0.016∗∗∗ 0.021∗∗(0.0054) (0.0087)M-54 0.019∗∗∗ 0.024∗∗∗(0.0053) (0.0086)M-53 0.017∗∗∗ 0.021∗∗(0.0053) (0.0087)M-52 0.020∗∗∗ 0.024∗∗∗(0.0051) (0.0086)M-51 0.022∗∗∗ 0.026∗∗∗(0.0049) (0.0084)M-50 0.024∗∗∗ 0.028∗∗∗(0.0048) (0.0082)M-49 0.026∗∗∗ 0.030∗∗∗(0.0048) (0.0079)M-48 0.029∗∗∗ 0.033∗∗∗(0.0048) (0.0076)M-47 0.027∗∗∗ 0.030∗∗∗113D.1. Event Study Estimates For All Households(1) (2)All Households Participant HouseholdsDependent Variable: Ln monthly electricity use(0.0047) (0.0072)M-46 0.026∗∗∗ 0.030∗∗∗(0.0045) (0.0069)M-45 0.023∗∗∗ 0.026∗∗∗(0.0045) (0.0066)M-44 0.020∗∗∗ 0.023∗∗∗(0.0044) (0.0064)M-43 0.012∗∗∗ 0.015∗∗(0.0045) (0.0064)M-42 0.013∗∗∗ 0.015∗∗(0.0045) (0.0064)M-41 0.013∗∗∗ 0.015∗∗(0.0045) (0.0064)M-40 0.016∗∗∗ 0.018∗∗∗(0.0043) (0.0063)M-39 0.013∗∗∗ 0.015∗∗(0.0043) (0.0062)M-38 0.018∗∗∗ 0.020∗∗∗(0.0041) (0.0059)M-37 0.017∗∗∗ 0.019∗∗∗(0.0041) (0.0058)M-36 0.017∗∗∗ 0.018∗∗∗(0.0041) (0.0055)M-35 0.017∗∗∗ 0.018∗∗∗(0.0041) (0.0052)M-34 0.017∗∗∗ 0.018∗∗∗(0.0040) (0.0049)M-33 0.0091∗∗ 0.010∗∗(0.0039) (0.0047)M-32 0.0054 0.0063(0.0038) (0.0045)M-31 0.0040 0.0048(0.0039) (0.0045)M-30 0.0064∗ 0.0069(0.0037) (0.0043)M-29 0.0071∗∗ 0.0075∗114D.1. Event Study Estimates For All Households(1) (2)All Households Participant HouseholdsDependent Variable: Ln monthly electricity use(0.0035) (0.0042)M-28 0.0091∗∗∗ 0.0094∗∗(0.0035) (0.0041)M-27 0.0077∗∗ 0.0080∗∗(0.0033) (0.0039)M-26 0.0093∗∗∗ 0.0095∗∗(0.0032) (0.0037)M-25 0.0061∗ 0.0061∗(0.0031) (0.0036)M-24 0.0069∗∗ 0.0067∗∗(0.0030) (0.0033)M-11 0.0017 0.0013(0.0029) (0.0031)M-10 0.0024 0.0020(0.0029) (0.0033)M-9 0.0011 0.00046(0.0030) (0.0035)M-8 -0.0047 -0.0055(0.0031) (0.0037)M-7 -0.0031 -0.0041(0.0032) (0.0038)M-6 -0.0021 -0.0033(0.0031) (0.0038)M-5 -0.0034 -0.0046(0.0031) (0.0038)M-4 -0.0047 -0.0060(0.0032) (0.0039)M-3 -0.011∗∗∗ -0.012∗∗∗(0.0032) (0.0039)M-2 -0.0080∗∗ -0.0093∗∗(0.0032) (0.0040)M-1 -0.017∗∗∗ -0.018∗∗∗(0.0034) (0.0043)M0 -0.022∗∗∗ -0.023∗∗∗(0.0033) (0.0044)M1 -0.041∗∗∗ -0.042∗∗∗115D.1. Event Study Estimates For All Households(1) (2)All Households Participant HouseholdsDependent Variable: Ln monthly electricity use(0.0035) (0.0049)M2 -0.049∗∗∗ -0.051∗∗∗(0.0036) (0.0052)M3 -0.051∗∗∗ -0.053∗∗∗(0.0036) (0.0054)M4 -0.052∗∗∗ -0.054∗∗∗(0.0035) (0.0055)M5 -0.050∗∗∗ -0.052∗∗∗(0.0036) (0.0057)M6 -0.049∗∗∗ -0.051∗∗∗(0.0037) (0.0058)M7 -0.048∗∗∗ -0.050∗∗∗(0.0036) (0.0057)M8 -0.050∗∗∗ -0.052∗∗∗(0.0036) (0.0057)M9 -0.054∗∗∗ -0.056∗∗∗(0.0038) (0.0059)M10 -0.049∗∗∗ -0.051∗∗∗(0.0038) (0.0060)M11 -0.050∗∗∗ -0.052∗∗∗(0.0037) (0.0062)M12 -0.049∗∗∗ -0.051∗∗∗(0.0037) (0.0065)M13 -0.053∗∗∗ -0.055∗∗∗(0.0038) (0.0069)M14 -0.055∗∗∗ -0.057∗∗∗(0.0038) (0.0072)M15 -0.056∗∗∗ -0.058∗∗∗(0.0039) (0.0075)M16 -0.057∗∗∗ -0.059∗∗∗(0.0039) (0.0076)M17 -0.058∗∗∗ -0.060∗∗∗(0.0039) (0.0077)M18 -0.059∗∗∗ -0.061∗∗∗(0.0039) (0.0078)M19 -0.060∗∗∗ -0.063∗∗∗116D.1. Event Study Estimates For All Households(1) (2)All Households Participant HouseholdsDependent Variable: Ln monthly electricity use(0.0039) (0.0078)M20 -0.059∗∗∗ -0.061∗∗∗(0.0040) (0.0079)M21 -0.061∗∗∗ -0.063∗∗∗(0.0041) (0.0080)M22 -0.052∗∗∗ -0.055∗∗∗(0.0041) (0.0081)M23 -0.053∗∗∗ -0.056∗∗∗(0.0041) (0.0084)M24 -0.050∗∗∗ -0.053∗∗∗(0.0042) (0.0087)M25 -0.051∗∗∗ -0.054∗∗∗(0.0043) (0.0091)M26 -0.054∗∗∗ -0.057∗∗∗(0.0043) (0.0094)M27 -0.053∗∗∗ -0.056∗∗∗(0.0043) (0.0097)M28 -0.054∗∗∗ -0.057∗∗∗(0.0044) (0.0099)M29 -0.054∗∗∗ -0.057∗∗∗(0.0045) (0.010)M30 -0.054∗∗∗ -0.058∗∗∗(0.0045) (0.010)M31 -0.053∗∗∗ -0.056∗∗∗(0.0045) (0.010)M32 -0.051∗∗∗ -0.055∗∗∗(0.0045) (0.010)M33 -0.053∗∗∗ -0.056∗∗∗(0.0046) (0.010)M34 -0.048∗∗∗ -0.052∗∗∗(0.0047) (0.011)M35 -0.045∗∗∗ -0.049∗∗∗(0.0047) (0.011)M36 -0.038∗∗∗ -0.042∗∗∗(0.0047) (0.011)M37 -0.042∗∗∗ -0.046∗∗∗117D.1. Event Study Estimates For All Households(1) (2)All Households Participant HouseholdsDependent Variable: Ln monthly electricity use(0.0048) (0.011)M38 -0.048∗∗∗ -0.052∗∗∗(0.0048) (0.012)M39 -0.046∗∗∗ -0.049∗∗∗(0.0048) (0.012)M40 -0.045∗∗∗ -0.049∗∗∗(0.0049) (0.012)M41 -0.046∗∗∗ -0.049∗∗∗(0.0049) (0.012)M42 -0.049∗∗∗ -0.053∗∗∗(0.0050) (0.012)M43 -0.048∗∗∗ -0.052∗∗∗(0.0050) (0.012)M44 -0.048∗∗∗ -0.051∗∗∗(0.0051) (0.013)M45 -0.048∗∗∗ -0.051∗∗∗(0.0052) (0.013)M46 -0.043∗∗∗ -0.046∗∗∗(0.0052) (0.013)M47 -0.041∗∗∗ -0.044∗∗∗(0.0052) (0.013)M48 -0.037∗∗∗ -0.041∗∗∗(0.0052) (0.013)M49 -0.039∗∗∗ -0.042∗∗∗(0.0053) (0.014)M50 -0.043∗∗∗ -0.046∗∗∗(0.0053) (0.014)M51 -0.046∗∗∗ -0.048∗∗∗(0.0055) (0.014)M52 -0.046∗∗∗ -0.048∗∗∗(0.0054) (0.014)M53 -0.042∗∗∗ -0.044∗∗∗(0.0055) (0.015)M54 -0.045∗∗∗ -0.047∗∗∗(0.0056) (0.015)M55 -0.045∗∗∗ -0.048∗∗∗118D.1. Event Study Estimates For All Households(1) (2)All Households Participant HouseholdsDependent Variable: Ln monthly electricity use(0.0058) (0.015)M56 -0.043∗∗∗ -0.046∗∗∗(0.0057) (0.015)M57 -0.052∗∗∗ -0.055∗∗∗(0.0058) (0.015)M58 -0.044∗∗∗ -0.047∗∗∗(0.0059) (0.015)M59 -0.040∗∗∗ -0.043∗∗∗(0.0059) (0.015)M60 -0.036∗∗∗ -0.039∗∗(0.0059) (0.016)M61 -0.038∗∗∗ -0.040∗∗(0.0061) (0.016)M62 -0.039∗∗∗ -0.040∗∗(0.0061) (0.016)M63 -0.042∗∗∗ -0.044∗∗∗(0.0062) (0.017)M64 -0.047∗∗∗ -0.048∗∗∗(0.0062) (0.017)M65 -0.044∗∗∗ -0.045∗∗∗(0.0063) (0.017)M66 -0.044∗∗∗ -0.044∗∗(0.0063) (0.017)M67 -0.049∗∗∗ -0.050∗∗∗(0.0064) (0.017)M68 -0.050∗∗∗ -0.050∗∗∗(0.0065) (0.017)M69 -0.053∗∗∗ -0.054∗∗∗(0.0066) (0.017)M70 -0.051∗∗∗ -0.051∗∗∗(0.0066) (0.017)M71 -0.043∗∗∗ -0.043∗∗(0.0067) (0.018)M72 -0.041∗∗∗ -0.041∗∗(0.0068) (0.018)Observations 2243267 1065236119D.2. Event Study Estimates By Number of ChallengesAll specifications include individual and date fixed effects. Specification (1) estimated including both participant andnon-participant households. (2) estimated for participant households only. Standard errors are clustered at the householdlevel. *** p<0.01, ** p<0.05, * p<0.1 denote significance levels where 0 is defined as the second year pre-treatment andconsists of months M-12 to M-23.D.2 Event Study Estimates By Number of ChallengesTable D.2: Event-Study Estimates: Selection Into ChallengesPre 0.024∗∗∗ 0.020∗ 0.014 0.015 0.012 0.0088 0.015(0.0073) (0.011) (0.0090) (0.018) (0.0100) (0.016) (0.012)M-59 0.035∗∗∗ 0.037∗∗∗ 0.021∗∗ 0.039∗∗ 0.012 0.0034 0.017(0.0076) (0.011) (0.0097) (0.019) (0.011) (0.017) (0.014)M-58 0.037∗∗∗ 0.046∗∗∗ 0.019∗ 0.031 0.012 0.0091 0.013(0.0075) (0.011) (0.0098) (0.020) (0.011) (0.017) (0.014)M-57 0.028∗∗∗ 0.031∗∗∗ 0.015 0.033∗ 0.0053 0.017 -0.0014(0.0076) (0.011) (0.0099) (0.019) (0.011) (0.016) (0.015)M-56 0.029∗∗∗ 0.025∗∗ 0.019∗∗ 0.034∗ 0.011 0.020 0.0066(0.0071) (0.011) (0.0089) (0.018) (0.0100) (0.015) (0.013)M-55 0.021∗∗∗ 0.012 0.015 0.034∗ 0.0049 0.0035 0.0057(0.0074) (0.011) (0.0094) (0.019) (0.011) (0.016) (0.014)M-54 0.023∗∗∗ 0.016 0.017∗ 0.047∗∗∗ 0.0030 -0.0079 0.0087(0.0071) (0.010) (0.0093) (0.018) (0.011) (0.016) (0.014)M-53 0.022∗∗∗ 0.016 0.015 0.040∗∗ 0.0033 -0.0089 0.0096(0.0073) (0.011) (0.0094) (0.019) (0.011) (0.019) (0.013)M-52 0.029∗∗∗ 0.030∗∗∗ 0.017∗ 0.049∗∗∗ 0.0023 -0.0034 0.0051(0.0068) (0.010) (0.0089) (0.018) (0.0099) (0.017) (0.012)M-51 0.031∗∗∗ 0.033∗∗∗ 0.019∗∗ 0.054∗∗∗ 0.0031 -0.0022 0.0055(0.0064) (0.0097) (0.0081) (0.014) (0.0096) (0.016) (0.012)M-50 0.035∗∗∗ 0.039∗∗∗ 0.021∗∗∗ 0.057∗∗∗ 0.0046 -0.0036 0.0083(0.0062) (0.0095) (0.0080) (0.014) (0.0093) (0.017) (0.011)M-49 0.034∗∗∗ 0.042∗∗∗ 0.018∗∗ 0.039∗∗∗ 0.0076 0.0030 0.0096(0.0062) (0.0098) (0.0078) (0.015) (0.0091) (0.016) (0.011)M-48 0.035∗∗∗ 0.037∗∗∗ 0.023∗∗∗ 0.044∗∗∗ 0.012 0.015 0.010(0.0062) (0.0094) (0.0080) (0.016) (0.0091) (0.015) (0.011)M-47 0.025∗∗∗ 0.021∗∗ 0.018∗∗ 0.030∗ 0.010 0.012 0.0092(0.0064) (0.010) (0.0080) (0.016) (0.0090) (0.016) (0.010)M-46 0.024∗∗∗ 0.018∗ 0.018∗∗ 0.038∗∗ 0.0078 0.0046 0.0086(0.0060) (0.0092) (0.0078) (0.015) (0.0089) (0.016) (0.010)M-45 0.025∗∗∗ 0.021∗∗ 0.018∗∗ 0.047∗∗∗ 0.0042 0.012 -0.000069(0.0060) (0.0090) (0.0077) (0.015) (0.0090) (0.016) (0.011)120D.2. Event Study Estimates By Number of Challenges(1) (2) (3) (4) (5) (6) (7)All One Two+ Two Three+ Three Four+Dependent Variable: Ln monthly electricity useM-44 0.021∗∗∗ 0.021∗∗ 0.011 0.031∗∗ 0.0016 0.021 -0.0080(0.0058) (0.0086) (0.0076) (0.015) (0.0086) (0.015) (0.011)M-43 0.014∗∗ 0.0048 0.0100 0.031∗ -0.000074 0.0058 -0.0033(0.0059) (0.0089) (0.0078) (0.016) (0.0086) (0.015) (0.010)M-42 0.017∗∗∗ 0.0030 0.017∗∗ 0.042∗∗∗ 0.0052 0.020 -0.0021(0.0059) (0.0092) (0.0075) (0.014) (0.0088) (0.015) (0.011)M-41 0.017∗∗∗ 0.0065 0.015∗∗ 0.046∗∗∗ 0.00034 0.021 -0.0096(0.0058) (0.0092) (0.0074) (0.015) (0.0085) (0.015) (0.010)M-40 0.022∗∗∗ 0.019∗∗ 0.014∗∗ 0.044∗∗∗ 0.00029 0.012 -0.0055(0.0055) (0.0085) (0.0071) (0.014) (0.0081) (0.014) (0.0097)M-39 0.016∗∗∗ 0.019∗∗ 0.0052 0.025∗ -0.0046 0.0055 -0.0098(0.0056) (0.0087) (0.0073) (0.015) (0.0083) (0.014) (0.010)M-38 0.023∗∗∗ 0.024∗∗∗ 0.014∗∗ 0.036∗∗∗ 0.0029 0.0034 0.0021(0.0053) (0.0084) (0.0068) (0.014) (0.0077) (0.013) (0.0092)M-37 0.023∗∗∗ 0.025∗∗∗ 0.013∗ 0.036∗∗∗ 0.0028 -0.0070 0.0066(0.0054) (0.0082) (0.0071) (0.013) (0.0084) (0.016) (0.0097)M-36 0.019∗∗∗ 0.018∗∗ 0.012 0.029∗∗ 0.0026 -0.0033 0.0046(0.0054) (0.0082) (0.0071) (0.013) (0.0084) (0.015) (0.010)M-35 0.017∗∗∗ 0.021∗∗∗ 0.0072 0.014 0.0023 -0.0010 0.0032(0.0054) (0.0079) (0.0071) (0.013) (0.0084) (0.016) (0.0097)M-34 0.015∗∗∗ 0.015∗ 0.0070 0.014 0.0021 0.0040 0.00062(0.0053) (0.0082) (0.0068) (0.013) (0.0079) (0.013) (0.0097)M-33 0.0058 0.0088 -0.0029 0.0099 -0.0096 -0.0058 -0.012(0.0051) (0.0079) (0.0066) (0.013) (0.0076) (0.013) (0.0094)M-32 0.0014 0.0061 -0.0082 -0.0030 -0.012 0.00071 -0.018∗(0.0049) (0.0072) (0.0067) (0.014) (0.0075) (0.013) (0.0092)M-31 0.0014 -0.00049 -0.0027 0.0085 -0.0084 0.0037 -0.014(0.0051) (0.0074) (0.0070) (0.012) (0.0084) (0.012) (0.011)M-30 0.0049 0.0033 0.00085 0.0077 -0.0030 0.00041 -0.0051(0.0047) (0.0072) (0.0063) (0.012) (0.0072) (0.013) (0.0085)M-29 0.0061 0.0094 -0.0014 0.0057 -0.0053 -0.000065 -0.0082(0.0046) (0.0067) (0.0062) (0.013) (0.0070) (0.013) (0.0084)M-28 0.011∗∗ 0.016∗∗ 0.0017 0.014 -0.0040 0.0029 -0.0075(0.0044) (0.0065) (0.0059) (0.012) (0.0067) (0.012) (0.0082)M-27 0.0065 0.0081 0.0014 0.011 -0.0030 0.0028 -0.0060(0.0042) (0.0065) (0.0055) (0.010) (0.0064) (0.011) (0.0079)121D.2. Event Study Estimates By Number of Challenges(1) (2) (3) (4) (5) (6) (7)All One Two+ Two Three+ Three Four+Dependent Variable: Ln monthly electricity useM-26 0.0082∗∗ 0.013∗∗ 0.0011 0.0067 -0.0018 -0.0048 -0.0010(0.0041) (0.0064) (0.0053) (0.010) (0.0062) (0.011) (0.0075)M-25 0.0054 0.010∗ -0.0020 0.0032 -0.0048 -0.0079 -0.0038(0.0040) (0.0060) (0.0054) (0.010) (0.0064) (0.010) (0.0079)M-24 0.0060 0.0069 0.0025 0.0093 -0.00068 -0.0039 0.00053(0.0039) (0.0056) (0.0054) (0.010) (0.0063) (0.010) (0.0078)M-11 0.0045 0.0042 0.0063 0.012 0.0046 -0.00089 0.0069(0.0035) (0.0049) (0.0048) (0.0095) (0.0056) (0.010) (0.0067)M-10 0.0045 0.0031 0.0073 0.014 0.0050 0.0058 0.0047(0.0036) (0.0050) (0.0051) (0.0093) (0.0061) (0.0095) (0.0076)M-9 0.0011 0.00014 0.0036 0.0090 0.0017 0.0065 -0.00016(0.0037) (0.0052) (0.0053) (0.010) (0.0061) (0.011) (0.0074)M-8 -0.0048 -0.0086 0.00041 0.0058 -0.0014 0.0051 -0.0039(0.0040) (0.0058) (0.0055) (0.011) (0.0063) (0.011) (0.0078)M-7 -0.0013 -0.0018 0.00086 0.0027 0.00057 0.0047 -0.00081(0.0040) (0.0055) (0.0058) (0.012) (0.0066) (0.011) (0.0080)M-6 0.00059 0.0016 0.0012 -0.0083 0.0057 0.0100 0.0043(0.0040) (0.0054) (0.0059) (0.012) (0.0066) (0.011) (0.0081)M-5 0.00023 0.0021 0.00017 -0.0034 0.0022 0.0054 0.0012(0.0040) (0.0054) (0.0059) (0.012) (0.0068) (0.011) (0.0084)M-4 -0.0033 -0.0029 -0.0018 0.0055 -0.0044 -0.014 -0.000036(0.0040) (0.0056) (0.0056) (0.011) (0.0065) (0.012) (0.0077)M-3 -0.0087∗∗ -0.0054 -0.010∗ 0.0054 -0.016∗∗ -0.035∗∗∗ -0.0080(0.0041) (0.0057) (0.0058) (0.012) (0.0067) (0.013) (0.0077)M-2 -0.0039 0.0017 -0.0076 -0.0039 -0.0087 -0.025∗∗ -0.0021(0.0040) (0.0055) (0.0057) (0.011) (0.0064) (0.012) (0.0076)M-1 -0.012∗∗∗ -0.0010 -0.020∗∗∗ -0.028∗∗ -0.017∗∗ -0.038∗∗∗ -0.0080(0.0042) (0.0058) (0.0060) (0.011) (0.0072) (0.012) (0.0088)M0 -0.015∗∗∗ 0.0019 -0.029∗∗∗ -0.028∗∗∗ -0.029∗∗∗ -0.047∗∗∗ -0.021∗∗∗(0.0041) (0.0058) (0.0058) (0.011) (0.0067) (0.012) (0.0081)M1 -0.029∗∗∗ -0.0069 -0.049∗∗∗ -0.043∗∗∗ -0.051∗∗∗ -0.074∗∗∗ -0.042∗∗∗(0.0044) (0.0062) (0.0060) (0.011) (0.0069) (0.013) (0.0080)M2 -0.035∗∗∗ -0.012∗∗ -0.056∗∗∗ -0.047∗∗∗ -0.059∗∗∗ -0.077∗∗∗ -0.052∗∗∗(0.0043) (0.0061) (0.0059) (0.011) (0.0069) (0.012) (0.0082)M3 -0.039∗∗∗ -0.014∗∗ -0.062∗∗∗ -0.054∗∗∗ -0.064∗∗∗ -0.071∗∗∗ -0.062∗∗∗(0.0044) (0.0061) (0.0060) (0.011) (0.0072) (0.013) (0.0085)122D.2. Event Study Estimates By Number of Challenges(1) (2) (3) (4) (5) (6) (7)All One Two+ Two Three+ Three Four+Dependent Variable: Ln monthly electricity useM4 -0.043∗∗∗ -0.016∗∗∗ -0.067∗∗∗ -0.056∗∗∗ -0.071∗∗∗ -0.069∗∗∗ -0.072∗∗∗(0.0043) (0.0060) (0.0059) (0.010) (0.0070) (0.013) (0.0083)M5 -0.039∗∗∗ -0.012∗ -0.063∗∗∗ -0.052∗∗∗ -0.068∗∗∗ -0.070∗∗∗ -0.066∗∗∗(0.0045) (0.0061) (0.0063) (0.011) (0.0074) (0.013) (0.0088)M6 -0.037∗∗∗ -0.0100∗ -0.061∗∗∗ -0.064∗∗∗ -0.060∗∗∗ -0.073∗∗∗ -0.054∗∗∗(0.0046) (0.0060) (0.0067) (0.013) (0.0075) (0.015) (0.0086)M7 -0.035∗∗∗ -0.0056 -0.062∗∗∗ -0.059∗∗∗ -0.062∗∗∗ -0.071∗∗∗ -0.059∗∗∗(0.0045) (0.0062) (0.0062) (0.011) (0.0073) (0.013) (0.0086)M8 -0.038∗∗∗ -0.0043 -0.068∗∗∗ -0.060∗∗∗ -0.072∗∗∗ -0.079∗∗∗ -0.069∗∗∗(0.0045) (0.0064) (0.0061) (0.011) (0.0071) (0.013) (0.0084)M9 -0.045∗∗∗ -0.011∗ -0.077∗∗∗ -0.061∗∗∗ -0.083∗∗∗ -0.089∗∗∗ -0.081∗∗∗(0.0048) (0.0069) (0.0063) (0.012) (0.0073) (0.014) (0.0085)M10 -0.039∗∗∗ -0.0032 -0.073∗∗∗ -0.062∗∗∗ -0.077∗∗∗ -0.082∗∗∗ -0.075∗∗∗(0.0048) (0.0066) (0.0066) (0.013) (0.0076) (0.013) (0.0091)M11 -0.040∗∗∗ -0.0026 -0.074∗∗∗ -0.062∗∗∗ -0.079∗∗∗ -0.089∗∗∗ -0.075∗∗∗(0.0046) (0.0063) (0.0064) (0.012) (0.0075) (0.014) (0.0089)M12 -0.038∗∗∗ 0.00075 -0.073∗∗∗ -0.049∗∗∗ -0.083∗∗∗ -0.086∗∗∗ -0.082∗∗∗(0.0046) (0.0062) (0.0065) (0.012) (0.0075) (0.014) (0.0088)Gap 1 -0.053∗∗∗ 0 -0.076∗∗∗ -0.061∗∗∗ -0.081∗∗∗ -0.073∗∗∗ -0.084∗∗∗(0.0056) (.) (0.0062) (0.011) (0.0073) (0.013) (0.0087)M13 -0.050∗∗∗ -0.0084 -0.089∗∗∗ -0.059∗∗∗ -0.10∗∗∗ -0.094∗∗∗ -0.10∗∗∗(0.0048) (0.0065) (0.0066) (0.012) (0.0077) (0.014) (0.0090)M14 -0.053∗∗∗ -0.013∗∗ -0.090∗∗∗ -0.053∗∗∗ -0.11∗∗∗ -0.100∗∗∗ -0.11∗∗∗(0.0050) (0.0067) (0.0069) (0.014) (0.0079) (0.014) (0.0094)M15 -0.049∗∗∗ -0.0076 -0.088∗∗∗ -0.037∗∗∗ -0.11∗∗∗ -0.10∗∗∗ -0.11∗∗∗(0.0050) (0.0066) (0.0070) (0.013) (0.0082) (0.015) (0.0095)M16 -0.047∗∗∗ -0.0076 -0.085∗∗∗ -0.036∗∗∗ -0.11∗∗∗ -0.096∗∗∗ -0.11∗∗∗(0.0049) (0.0065) (0.0069) (0.013) (0.0080) (0.015) (0.0094)M17 -0.044∗∗∗ -0.0081 -0.077∗∗∗ -0.032∗∗ -0.097∗∗∗ -0.092∗∗∗ -0.099∗∗∗(0.0049) (0.0066) (0.0069) (0.013) (0.0078) (0.014) (0.0092)M18 -0.048∗∗∗ -0.013∗ -0.081∗∗∗ -0.043∗∗∗ -0.096∗∗∗ -0.089∗∗∗ -0.099∗∗∗(0.0050) (0.0067) (0.0071) (0.014) (0.0081) (0.014) (0.0096)M19 -0.049∗∗∗ -0.012∗ -0.083∗∗∗ -0.042∗∗∗ -0.10∗∗∗ -0.10∗∗∗ -0.10∗∗∗(0.0051) (0.0067) (0.0072) (0.013) (0.0084) (0.015) (0.0099)M20 -0.050∗∗∗ -0.012∗ -0.086∗∗∗ -0.046∗∗∗ -0.10∗∗∗ -0.10∗∗∗ -0.10∗∗∗(0.0051) (0.0069) (0.0070) (0.013) (0.0081) (0.015) (0.0096)123D.2. Event Study Estimates By Number of Challenges(1) (2) (3) (4) (5) (6) (7)All One Two+ Two Three+ Three Four+Dependent Variable: Ln monthly electricity useM21 -0.053∗∗∗ -0.011 -0.093∗∗∗ -0.060∗∗∗ -0.11∗∗∗ -0.095∗∗∗ -0.11∗∗∗(0.0052) (0.0068) (0.0073) (0.015) (0.0082) (0.014) (0.0098)M22 -0.043∗∗∗ 0.0025 -0.086∗∗∗ -0.055∗∗∗ -0.100∗∗∗ -0.088∗∗∗ -0.10∗∗∗(0.0052) (0.0067) (0.0073) (0.015) (0.0081) (0.015) (0.0096)M23 -0.044∗∗∗ -0.0013 -0.084∗∗∗ -0.038∗∗∗ -0.10∗∗∗ -0.090∗∗∗ -0.11∗∗∗(0.0052) (0.0068) (0.0073) (0.014) (0.0085) (0.015) (0.010)M24 -0.040∗∗∗ 0.0016 -0.080∗∗∗ -0.018 -0.11∗∗∗ -0.095∗∗∗ -0.11∗∗∗(0.0052) (0.0069) (0.0073) (0.013) (0.0085) (0.016) (0.0099)Gap 2 -0.062∗∗∗ 0 -0.085∗∗∗ 0 -0.099∗∗∗ -0.083∗∗∗ -0.11∗∗∗(0.0082) (.) (0.0088) (.) (0.0092) (0.017) (0.011)M25 -0.042∗∗∗ 0.00020 -0.083∗∗∗ -0.022∗ -0.11∗∗∗ -0.078∗∗∗ -0.12∗∗∗(0.0052) (0.0069) (0.0073) (0.013) (0.0085) (0.015) (0.010)M26 -0.045∗∗∗ -0.0016 -0.086∗∗∗ -0.020 -0.11∗∗∗ -0.088∗∗∗ -0.13∗∗∗(0.0052) (0.0068) (0.0074) (0.013) (0.0086) (0.015) (0.010)M27 -0.042∗∗∗ 0.00018 -0.082∗∗∗ -0.0093 -0.11∗∗∗ -0.081∗∗∗ -0.13∗∗∗(0.0053) (0.0069) (0.0074) (0.013) (0.0086) (0.014) (0.010)M28 -0.041∗∗∗ -0.00085 -0.080∗∗∗ -0.0071 -0.11∗∗∗ -0.073∗∗∗ -0.13∗∗∗(0.0053) (0.0069) (0.0074) (0.014) (0.0085) (0.015) (0.010)M29 -0.040∗∗∗ -0.000075 -0.078∗∗∗ -0.0094 -0.11∗∗∗ -0.074∗∗∗ -0.12∗∗∗(0.0054) (0.0071) (0.0076) (0.014) (0.0086) (0.015) (0.010)M30 -0.042∗∗∗ -0.0052 -0.078∗∗∗ -0.016 -0.10∗∗∗ -0.075∗∗∗ -0.12∗∗∗(0.0055) (0.0073) (0.0076) (0.014) (0.0087) (0.016) (0.010)M31 -0.044∗∗∗ -0.0029 -0.084∗∗∗ -0.016 -0.11∗∗∗ -0.076∗∗∗ -0.13∗∗∗(0.0056) (0.0072) (0.0079) (0.014) (0.0093) (0.017) (0.011)M32 -0.040∗∗∗ 0.0021 -0.082∗∗∗ -0.028∗∗ -0.11∗∗∗ -0.070∗∗∗ -0.12∗∗∗(0.0055) (0.0072) (0.0077) (0.014) (0.0091) (0.017) (0.011)M33 -0.042∗∗∗ 0.0020 -0.085∗∗∗ -0.034∗∗ -0.11∗∗∗ -0.058∗∗∗ -0.13∗∗∗(0.0057) (0.0075) (0.0078) (0.014) (0.0091) (0.017) (0.011)M34 -0.038∗∗∗ 0.0054 -0.082∗∗∗ -0.023 -0.11∗∗∗ -0.044∗∗∗ -0.13∗∗∗(0.0056) (0.0073) (0.0079) (0.014) (0.0091) (0.016) (0.011)M35 -0.036∗∗∗ 0.0090 -0.082∗∗∗ -0.012 -0.11∗∗∗ -0.051∗∗∗ -0.13∗∗∗(0.0056) (0.0072) (0.0079) (0.015) (0.0092) (0.017) (0.011)M36 -0.030∗∗∗ 0.018∗∗ -0.080∗∗∗ -0.0027 -0.11∗∗∗ -0.051∗∗∗ -0.13∗∗∗(0.0057) (0.0073) (0.0081) (0.014) (0.0095) (0.017) (0.011)Gap 3 -0.050∗∗∗ 0 -0.076∗∗∗ 0 -0.091∗∗∗ 0 -0.098∗∗∗(0.010) (.) (0.011) (.) (0.012) (.) (0.012)124D.2. Event Study Estimates By Number of Challenges(1) (2) (3) (4) (5) (6) (7)All One Two+ Two Three+ Three Four+Dependent Variable: Ln monthly electricity useM37 -0.034∗∗∗ 0.0092 -0.080∗∗∗ -0.0017 -0.11∗∗∗ -0.037∗∗ -0.14∗∗∗(0.0058) (0.0075) (0.0083) (0.014) (0.0097) (0.017) (0.011)M38 -0.038∗∗∗ 0.0060 -0.084∗∗∗ 0.0052 -0.12∗∗∗ -0.045∗∗∗ -0.15∗∗∗(0.0060) (0.0074) (0.0086) (0.015) (0.010) (0.017) (0.012)M39 -0.037∗∗∗ 0.0094 -0.086∗∗∗ -0.00075 -0.12∗∗∗ -0.047∗∗∗ -0.15∗∗∗(0.0059) (0.0074) (0.0084) (0.015) (0.0098) (0.016) (0.012)M40 -0.034∗∗∗ 0.0086 -0.079∗∗∗ 0.00053 -0.11∗∗∗ -0.053∗∗∗ -0.13∗∗∗(0.0060) (0.0075) (0.0086) (0.015) (0.010) (0.018) (0.012)M41 -0.033∗∗∗ 0.011 -0.080∗∗∗ -0.012 -0.11∗∗∗ -0.051∗∗∗ -0.13∗∗∗(0.0061) (0.0076) (0.0088) (0.016) (0.010) (0.018) (0.012)M42 -0.033∗∗∗ 0.0073 -0.077∗∗∗ -0.011 -0.11∗∗∗ -0.041∗∗ -0.13∗∗∗(0.0061) (0.0077) (0.0088) (0.015) (0.010) (0.019) (0.012)M43 -0.032∗∗∗ 0.0065 -0.074∗∗∗ -0.0091 -0.10∗∗∗ -0.038∗ -0.12∗∗∗(0.0061) (0.0077) (0.0088) (0.014) (0.011) (0.020) (0.012)M44 -0.031∗∗∗ 0.0100 -0.076∗∗∗ -0.015 -0.10∗∗∗ -0.031 -0.13∗∗∗(0.0062) (0.0077) (0.0090) (0.016) (0.011) (0.020) (0.012)M45 -0.030∗∗∗ 0.011 -0.076∗∗∗ -0.012 -0.11∗∗∗ -0.023 -0.13∗∗∗(0.0063) (0.0077) (0.0093) (0.016) (0.011) (0.020) (0.013)M46 -0.027∗∗∗ 0.015∗ -0.076∗∗∗ -0.017 -0.10∗∗∗ -0.024 -0.13∗∗∗(0.0063) (0.0079) (0.0092) (0.016) (0.011) (0.020) (0.013)M47 -0.028∗∗∗ 0.015∗ -0.078∗∗∗ -0.017 -0.11∗∗∗ -0.048∗∗ -0.12∗∗∗(0.0064) (0.0080) (0.0093) (0.017) (0.011) (0.021) (0.012)M48 -0.024∗∗∗ 0.018∗∗ -0.074∗∗∗ -0.0039 -0.11∗∗∗ -0.059∗∗ -0.12∗∗∗(0.0065) (0.0080) (0.0096) (0.016) (0.011) (0.024) (0.013)Gap 4 -0.050∗∗∗ 0 -0.080∗∗∗ 0 -0.097∗∗∗ 0 -0.11∗∗∗(0.015) (.) (0.016) (.) (0.016) (.) (0.017)M49 -0.029∗∗∗ 0.012 -0.077∗∗∗ -0.0028 -0.11∗∗∗ -0.068∗∗∗ -0.13∗∗∗(0.0065) (0.0080) (0.0094) (0.016) (0.011) (0.022) (0.013)M50 -0.028∗∗∗ 0.011 -0.076∗∗∗ -0.0069 -0.11∗∗∗ -0.061∗∗∗ -0.12∗∗∗(0.0066) (0.0082) (0.0097) (0.016) (0.011) (0.019) (0.013)M51 -0.024∗∗∗ 0.012 -0.069∗∗∗ 0.00069 -0.10∗∗∗ -0.059∗∗∗ -0.12∗∗∗(0.0067) (0.0083) (0.0097) (0.016) (0.012) (0.020) (0.014)M52 -0.025∗∗∗ 0.011 -0.072∗∗∗ -0.0011 -0.11∗∗∗ -0.057∗∗∗ -0.12∗∗∗(0.0067) (0.0083) (0.0098) (0.016) (0.012) (0.020) (0.014)M53 -0.025∗∗∗ 0.014 -0.076∗∗∗ -0.029 -0.100∗∗∗ -0.038∗ -0.12∗∗∗(0.0072) (0.0084) (0.011) (0.022) (0.013) (0.020) (0.015)125D.2. Event Study Estimates By Number of Challenges(1) (2) (3) (4) (5) (6) (7)All One Two+ Two Three+ Three Four+Dependent Variable: Ln monthly electricity useM54 -0.024∗∗∗ 0.016∗ -0.077∗∗∗ -0.022 -0.10∗∗∗ -0.055∗∗ -0.12∗∗∗(0.0070) (0.0083) (0.011) (0.017) (0.014) (0.027) (0.015)M55 -0.026∗∗∗ 0.017∗ -0.082∗∗∗ -0.027 -0.11∗∗∗ -0.029 -0.13∗∗∗(0.0071) (0.0085) (0.011) (0.018) (0.013) (0.023) (0.016)M56 -0.028∗∗∗ 0.014 -0.083∗∗∗ -0.032∗ -0.11∗∗∗ -0.022 -0.13∗∗∗(0.0073) (0.0088) (0.011) (0.019) (0.014) (0.025) (0.016)M57 -0.031∗∗∗ 0.0070 -0.082∗∗∗ -0.040∗∗ -0.10∗∗∗ -0.031 -0.13∗∗∗(0.0074) (0.0089) (0.012) (0.020) (0.014) (0.026) (0.016)M58 -0.029∗∗∗ 0.010 -0.083∗∗∗ -0.033∗ -0.11∗∗∗ -0.052 -0.13∗∗∗(0.0076) (0.0090) (0.012) (0.020) (0.015) (0.032) (0.016)M59 -0.032∗∗∗ 0.0085 -0.087∗∗∗ -0.025 -0.12∗∗∗ -0.065∗ -0.13∗∗∗(0.0075) (0.0088) (0.012) (0.019) (0.015) (0.038) (0.016)M60 -0.025∗∗∗ 0.017∗ -0.085∗∗∗ -0.013 -0.12∗∗∗ -0.079∗∗ -0.14∗∗∗(0.0076) (0.0089) (0.012) (0.019) (0.015) (0.038) (0.016)Gap 5 -0.050∗∗∗ 0 -0.083∗∗∗ 0 -0.10∗∗∗ 0 -0.11∗∗∗(0.018) (.) (0.019) (.) (0.019) (.) (0.020)M61 -0.023∗∗∗ 0.016∗ -0.077∗∗∗ 0.0083 -0.12∗∗∗ -0.046∗ -0.15∗∗∗(0.0076) (0.0091) (0.012) (0.019) (0.015) (0.027) (0.017)M62 -0.022∗∗∗ 0.016∗ -0.078∗∗∗ 0.0015 -0.12∗∗∗ -0.041 -0.14∗∗∗(0.0077) (0.0091) (0.012) (0.019) (0.015) (0.029) (0.017)M63 -0.024∗∗∗ 0.014 -0.079∗∗∗ 0.0042 -0.12∗∗∗ -0.032 -0.15∗∗∗(0.0077) (0.0092) (0.012) (0.019) (0.015) (0.028) (0.018)M64 -0.026∗∗∗ 0.011 -0.081∗∗∗ 0.0036 -0.13∗∗∗ -0.046 -0.15∗∗∗(0.0079) (0.0094) (0.013) (0.019) (0.016) (0.031) (0.018)M65 -0.024∗∗∗ 0.011 -0.077∗∗∗ 0.014 -0.13∗∗∗ -0.032 -0.16∗∗∗(0.0080) (0.0094) (0.013) (0.018) (0.016) (0.027) (0.019)M66 -0.021∗∗∗ 0.011 -0.068∗∗∗ -0.00079 -0.11∗∗∗ -0.021 -0.13∗∗∗(0.0080) (0.0094) (0.013) (0.019) (0.016) (0.028) (0.019)M67 -0.020∗∗ 0.0065 -0.057∗∗∗ 0.011 -0.093∗∗∗ -0.0025 -0.12∗∗∗(0.0082) (0.0098) (0.013) (0.019) (0.016) (0.027) (0.019)M68 -0.022∗∗∗ 0.0080 -0.066∗∗∗ 0.0019 -0.10∗∗∗ -0.017 -0.13∗∗∗(0.0082) (0.0097) (0.013) (0.019) (0.017) (0.032) (0.019)M69 -0.024∗∗∗ 0.0033 -0.062∗∗∗ -0.0059 -0.093∗∗∗ -0.028 -0.12∗∗∗(0.0086) (0.010) (0.014) (0.021) (0.018) (0.033) (0.020)M70 -0.024∗∗∗ 0.0064 -0.070∗∗∗ -0.020 -0.097∗∗∗ -0.057∗ -0.11∗∗∗(0.0085) (0.010) (0.014) (0.021) (0.018) (0.030) (0.021)126D.2. Event Study Estimates By Number of Challenges(1) (2) (3) (4) (5) (6) (7)All One Two+ Two Three+ Three Four+Dependent Variable: Ln monthly electricity useM71 -0.022∗∗∗ 0.012 -0.076∗∗∗ -0.0046 -0.12∗∗∗ -0.064∗∗ -0.14∗∗∗(0.0085) (0.0100) (0.014) (0.019) (0.019) (0.030) (0.023)M72 -0.027∗∗∗ 0.0089 -0.086∗∗∗ -0.016 -0.13∗∗∗ -0.079∗∗ -0.15∗∗∗(0.0085) (0.0100) (0.014) (0.019) (0.018) (0.034) (0.021)Post -0.020∗∗∗ 0.0072 -0.064∗∗∗ -0.0087 -0.10∗∗∗ -0.053∗ -0.12∗∗∗(0.0077) (0.0087) (0.013) (0.018) (0.017) (0.030) (0.019)Observations 1513669 1184992 1190510 958670 1093673 928673 1026833All specifications include individual and date fixed effects, participant and non-participant households, and are restrictedto participant households that begin their subsequent challenges within 12 months of finishing their previous challenge.In addition, specifications have the following restrictions: (1) has no further restrictions; (2) is households that undertakea single challenge only; (3) is households that undertake two or more challenges; (4) households that undertake two chal-lenges only; (5) households undertaking three or more challenges; (6) three challenges only; (7) Four or more challenges.Standard errors are clustered at the household level. *** p<0.01, ** p<0.05, * p<0.1 denote significance levels where 0is defined as the second year pre-treatment and consists of months M-12 to M-23.127


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