THE EFFECT OF REBATES ON THE SOLICITATION OF PRIVATE CONTRIBUTIONS TO FINANCE PUBLIC GOODS A Thesis Presented to the faculty of the Department of Economics California State University, Sacramento Submitted in partial satisfaction of the requirements for the degree of MASTER OF ARTS in Economics by Lucas Lee Krall FALL 2013 © 2013 Lucas Lee Krall ALL RIGHTS RESERVED ii THE EFFECT OF REBATES ON THE SOLICITATION OF PRIVATE CONTRIBUTIONS TO FINANCE PUBLIC GOODS A Thesis by Lucas Lee Krall Approved by: __________________________________, Committee Chair Jonathan Kaplan __________________________________, Second Reader Craig Gallet ____________________________ Date iii Student: Lucas Lee Krall I certify that this student has met the requirements for format contained in the University format manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for the thesis. __________________________, Graduate Coordinator ___________________ Kristin Kiesel Date Department of Economics iv Abstract of THE EFFECT OF REBATES ON THE SOLICITATION OF PRIVATE CONTRIBUTIONS TO FINANCE PUBLIC GOODS by Lucas Lee Krall California is currently in the midst of an ongoing water crisis. Agriculture in central California and urban centers in the southern parts of the state rely on the Sacramento-San Joaquin Delta to deliver water to them. However, the Delta as a water conveyance system is unsustainable given that the water supply is stochastic and shortages often occur. Additionally, the infrastructure’s inherent vulnerability to potential supply disruptions from natural disasters, such as earthquakes, is equally as alarming. If policy makers hope to mitigate this crisis and the impending collapse of California’s water supply system, they will first need to identify the next conveyance system or deal with the consequences of cutting off the flow of water to those south of the Delta. Then they will need to finance it. At a time when the condition of California’s fiscal house leaves much to be desired, alternative financing mechanisms utilizing private contributions for a new water conveyance system should be considered. This thesis evaluates alternative financing mechanisms for soliciting private contributions towards financing such a system in a laboratory setting. Reliability pricing v and endogenous sizing mechanisms are compared to fixed historical allocations of water resources in a private provisioning of a public threshold good game. The overall experiment simulates likely conditions that California will experience if such a project were attempted. The treatment groups and solicitation mechanisms in this study follow those in Kaplan et al. (2012). The treatment groups considered are Fixed Historical (FH), Fixed Reliability (FR), and Endogenous Reliability (ER). FH is based on a fixed sized system that allocates water based on historical allocations. FR takes this notion a step further by adding priority rights with increased benefits for subjects who contribute more money. ER creates an environment where reliability pricing with priority rights coexists with endogenous sizing of the project via subject contributions. This thesis, however, deviates from Kaplan et al. (2012) by considering how rebates may play a role in their results. In order to assess the impact that the proportional rebate policy in Kaplan et al. (2012) has on contributions, sessions without the rebate are conducted and compared by examining variations across the treatment groups. The underlying theory revolves around the notion that the inclusion of rebates are likely to affect how individuals contribute when mechanisms such as pricing and availability are uncertain. In addition to rebate effects, order effects in these data are also considered since subjects take part in two different treatments in which they may not sufficiency understand how to play the game until the second part. Subjects face two different treatments in a single session to control for systematic differences in individual vi characteristics. When these treatments are sufficiently complex, subject learning may lead to significant order effects. A preliminary descriptive analysis on experiment results revealed inconsistencies of subject contributing behaviors from one part to another. A more robust statistical analysis discovered that order has a statistically significant impact on contributing. This effect became more apparent when focusing on order within the more complicated reliability pricing treatments. Overall, these results indicate that subject learning outweighs gains from controlling for systematic differences among subjects. A statistical analysis of rebate effects revealed that rebates have a profound influence in reducing the deviation between subject WTP and contributions in the treatments with reliability pricing given that subjects tend to contribute more than their WTP when offered a rebate. Conversely, the influence of rebates in the FH treatment was not found to be statistically significant. This result is expected, as subjects in the FH treatment have no real incentive to contribute more than their WTP. Further, when the size of the system is determined endogenously, rebates are estimated to increase the size of the system upwards of two units. However, the inclusion of rebates does not seem to affect the probability of the system successfully being built in the fixed sized treatments. _______________________, Committee Chair Jonathan Kaplan _______________________ Date vii ACKNOWLEDGEMENTS Indeed, the pursuit of a timely completion of a master’s degree in economics can be a perilous undertaking. One riddled with frustration, expletives, and copious amounts of caffeine. However, as always, persistence is the key. Although I would certainly love to bask in all the glory of this journey, alas, I cannot. I had an amazing support system who I would like to thank. Foremost, I would like to begin by thanking my advisor Prof. Jonathan Kaplan for all his help during the course of this thesis and his guidance through the master’s program. He extended me the exhilarating opportunity to participate in conducting experimental economic research for both his study and mine. It was such an amazing experience to herd undergraduates into the computer lab and watch them peck away at their keyboards while data rolled in real-time. Prof. Kaplan was also extremely patient as he provided me with the vision and assistance that was necessary to complete the thesis process. Additionally, I would like to thank him and the Center for Watershed Sciences at UC Davis for funding the water experiments. Thanks also go to a number of professors at California State University, Sacramento. To Prof. Craig Gallet who served as my second reader as well as my microeconomics life coach: I will never forget at least some of your lessons or your good spirited nature when I sent you my empirical results hours before my defense. Further viii thanks are extended to Prof. Terri Sexton who is all too aware of what it means to advise some of my research. I am sure she can sympathize with Prof. Kaplan’s pains. But sincerely though, Prof. Sexton was such an enormous help during my undergraduate studies. To Prof. Pierre duVair: Thanks for all the great conversations about water policy and teaching me so much about cost-benefit analysis. I use those skills almost daily. Do not think that I forgot about you, Dr. Karen DeGannes! My sincere thanks go to you for giving me the amazing opportunity to continue my research professionally. It is such an immense feeling to be in on the ground floor of a bleeding edge analytical group in the utility sector during these times. I will carry the torch. Further thanks for taking a personal interest in my wellbeing as well as all your career advice that you share with me. I am more grateful than a few sentences could ever express! To my family: Special thanks go to my beautiful pregnant wife, Loring. Her endless support provided me with the motivation to actually complete my thesis before the impending collapse of California’s water supply system is averted (or realized). I could not have done it without you! Extra thanks for all the smiling and nodding whenever I rambled on about water policy and rebates. And, of course, thanks go to my mom and dad who were there every step of the way providing me with continuous love and encouragement to finish my journey. On a serious note, I graciously extend my thanks to you, reader. If you are reading this sentence after reading the other consecutive sentences in this section, then you have officially read two pages of my thesis. Thank you! ix TABLE OF CONTENTS Page Acknowledgements .......................................................................................................... viii List of Tables ................................................................................................................... xiii List of Figures .................................................................................................................. xiv 1. INTRODUCTION ..........................................................................................................1 1.1 Peripheral Canal ................................................................................................ 1 1.2 Alternative Long-Term Delta Water Exporting Strategies ............................... 4 1.2.1 Delta Fish Viability .................................................................................. 5 1.3 Water Supply and the Sustainability of California’s Economy ........................ 6 1.4 Potential Supply Disruptions of the Sacramento-San Joaquin Delta ................ 7 1.5 Costs of Building a Peripheral Canal ................................................................ 8 1.6 Alternative Financing Mechanisms .................................................................. 9 1.7 Summary of Major Findings and Conclusions ............................................... 10 1.8 Outline of Thesis Content ............................................................................... 12 2. LITERATURE REVIEW .............................................................................................13 2.1 Introduction ..................................................................................................... 13 2.2 The use of Private Provision of Threshold Public Good Experiments in Policy Making ................................................................................................. 14 2.3 Soliciting Contributions .................................................................................. 15 2.4 Reliability Pricing and Priority Rights ............................................................ 16 2.5 Endogenous and Fixed Sizing......................................................................... 17 x 2.6 Subject Expulsion Mechanisms in Public Good Games ................................. 18 2.7 Rebate Rules in Threshold Public Good Provision Games ............................ 19 2.8 Refunds in Threshold Public Good Provision Games .................................... 21 2.9 Summary ......................................................................................................... 22 3. EXPERIMENTAL DESIGN ........................................................................................24 3.1 Introduction ..................................................................................................... 24 3.2 General Setting................................................................................................ 25 3.3 Treatment Groups ........................................................................................... 26 3.3.1 Fixed Size Historical Allocation Treatment .......................................... 27 3.3.2 Fixed Size Reliability Pricing Treatment ............................................... 28 3.3.3 Endogenous Size Reliability Pricing Treatment .................................... 30 4. DATA DESCRIPTION ................................................................................................31 4.1 Introduction ..................................................................................................... 31 4.2 Survey Results ................................................................................................ 32 4.3 Preliminary Order Effect Investigation ........................................................... 41 4.4 Average Percentage Change of the Deviation between Maximum Willingness to Pay and Contributions............................................................. 51 4.5 Frequency of Success for Fixed Size Treatments ........................................... 61 4.6 Sizing of the Delivery System ........................................................................ 67 4.7 Summary ......................................................................................................... 69 5. EMPIRICAL ANALYSIS ............................................................................................70 xi 5.1 Introduction ..................................................................................................... 70 5.2 Empirical Models and Methodology .............................................................. 71 5.3 Order Effects ................................................................................................... 73 5.3.1 Order Effects on WTPCONT................................................................. 73 5.4 Rebate Effects ................................................................................................. 77 5.4.1 Rebate Effect on WTPCONT ................................................................ 77 5.4.2 Rebate Effects on Probability of Success .............................................. 81 5.4.3 Rebate Effects on SIZE .......................................................................... 85 5.5 Summary ......................................................................................................... 88 6. CONCLUSION .............................................................................................................90 Appendix A. Instructions for Fixed Historical Treatment .................................................94 Appendix B. Instructions for Fixed Reliability Treatment ................................................99 Appendix C. Instructions for Endogenous Reliability Treatment ...................................111 Appendix D. Fixed Reliability Payout Schedules............................................................123 Appendix E. Endogenous Reliability Payout Schedules .................................................128 Appendix F. Survey Questions Screenshot ......................................................................133 Appendix G. Empirical Results for Binding Effects .......................................................135 References ........................................................................................................................137 xii LIST OF TABLES Tables Page Table 3.1 FH Payout Schedule by Type ......................................................................... 27 Table 3.2 Endowment of Units by Type ......................................................................... 28 Table 3.3 Delivery Classes ............................................................................................. 29 Table 4-1 Summary Statistics of Subjects .......................................................................39 Table 4-2 Session t-scores for Systematic Demographic Differences .............................40 Table 5-1 Determinants of Order Effects on WTPCONT ...............................................76 Table 5-2 Determinants of Rebate Effects on WTPCONT .............................................80 Table 5-3 Determinants of Fixed Size Probability of Success ....................................... 84 Table 5-4 Determinants of Endogenous Sizing .............................................................. 86 Table A-1 Determinants of Binding Effects by Player Type ......................................... 136 xiii LIST OF FIGURES Figures Page Figure 4-1 Subjects by Declared Major .......................................................................... 35 Figure 4-2 Subjects by Class........................................................................................... 36 Figure 4-3 Age of Subjects ............................................................................................. 37 Figure 4-4 Subject Understanding of the Game ............................................................. 38 Figure 4-5 FH Player Type 1 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 43 Figure 4-6 FH Player Type 2 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 44 Figure 4-7 FH Player Type 3 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 45 Figure 4-8 FH Player Type 4 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 46 Figure 4-9 FR Player Type 1 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 47 Figure 4-10 FR Player Type 2 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 48 Figure 4-11 FR Player Type 3 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 49 xiv Figure 4-12 FR Player Type 4 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 ............................................................................................ 50 Figure 4-13 Player Type 1 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data ............................................................................................. 53 Figure 4-14 Player Type 2 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data ............................................................................................. 54 Figure 4-15 Player Type 3 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data ............................................................................................. 55 Figure 4-16 Player Type 4 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data ............................................................................................. 56 Figure 4-17 Player Type 1 Average Percent Change of WTP-Contribution Part 2 Data .............................................................................................................. 57 Figure 4-18 Player Type 2 Average Percent Change of WTP-Contribution Part 2 Data .............................................................................................................. 58 Figure 4-19 Player Type 3 Average Percent Change of WTP-Contribution Part 2 Data .............................................................................................................. 59 Figure 4-20 Player Type 4 Average Percent Change of WTP-Contribution Part 2 Data .............................................................................................................. 60 Figure 4-21 Frequency of Success for Fixed Size Treatments (Part 1 and 2 Data) ......... 63 Figure 4-22 Frequency of Success for Fixed Size Treatments (Only Part 2 Data).......... 64 xv Figure 4-23 Frequency of Success for Fixed Historical Treatment (with and without Rebates)........................................................................................................ 65 Figure 4-24 Frequency of Success for Fixed Reliability Treatment (with and without Rebate) ......................................................................................................... 66 Figure 4-25 Size of Delivery System for Endogenous Reliability Treatment (with and without Rebates) .......................................................................................... 68 xvi 1 Chapter 1 INTRODUCTION Currently, Californians are faced with a critical dilemma: finding a reliable water source. According to CALFED (2012), 23 million Californians, roughly two-thirds of California’s population, rely on the Sacramento-San Joaquin Delta to provide them with water. However, the existing water conveyance system is unsustainable given that the water supply is stochastic and shortages often occur. In brief, the water supply throughout the state is hindered given most of the rainfall occurs in the northern and eastern parts of California. CALFED (2013) believes shortages are especially problematic for the urban centers in southern parts of the state as well as to the arid Central Valley where most of California’s crops are grown. Further instability of California’s water conveyance system gravitates around physical risks associated with the infrastructure. Levees and other structural assets are susceptible to rising sea levels as well as damages caused by natural disasters, such as earthquakes. If particular levees were to collapse, the Delta would be flooded with copious amounts of salt water. The resulting damages could potentially cost the California economy billions of dollars and take years to reverse (Hanak et al. 2012). Additionally, because of Delta water exports, many habitats for local wildlife are being destroyed and various fish species are being driven towards extinction. Massive amounts of ecological restoration need to be undertaken to mitigate the impact from decades of pumping water out of the Delta. In spite of all these circumstances, exports from the Delta have been critical to the economic and social stability of California. Therefore, a 2 more efficient water transfer system is vital to the long-run health of California’s economy and citizens. To solve this problem, CALFED initiated the Water Supply Reliability Program to begin addressing the water supply issues in California (2013). One such solution that the Water Supply Reliability Program is arguing for is the construction of a peripheral canal. 1.1 Peripheral Canal The idea of building a peripheral canal is not new to California. According to Gwynn et al. (1983), Proposition 9 on the June 8, 1982 ballot proposed building a peripheral canal and other water infrastructure to supply water to southern California. However, many stakeholders were not sold on the idea of building the canal. Proposition 9 had fierce opposition from an array of interests. Northern California farmers were worried that the canal would divert too much water away from their farms and the reduction of water would lead to salinity issues (Gwynn et al. 1983). Large agricultural entities were concerned with provisions in Proposition 9 because the legislation placed limitations on development of rivers in the north to protect water quality. Environmentalists took issue with building the canal because they felt that its construction would have negative implications for the environment (Gwynn et al. 1983). Even some governmental agencies had problems with building the canal. For instance, Gwynn et al. (1983) mention that California Department of Fish and Game came out in opposition to the canal because it felt too much water would be diverted away and that the operation of the canal would be mismanaged. Ultimately, Proposition 9 failed to pass. 3 This, of course, came as a blow to the urban centers in Southern California, central valley farming, and the presumed overall long-run sustainability of the state. Although the construction of the peripheral canal was rejected in the 1980s, policy makers of today are attempting to revisit this concept given the impending crisis. One such advocate of building critical water infrastructure was previous California Governor Arnold Schwarzenegger. In 2006, under Gov. Schwarzenegger, California Proposition 84 passed which authorizes roughly $5.4 billion in general obligation bonds (Voter Information Guide 2006). The purpose of these bonds is to generate water quality and supply projects in California. Further, in 2008, Gov. Schwarzenegger proposed a $9.3 billion water bond, known as the Safe, Clean, and Reliable Drinking Water Supply Act, for a water supply infrastructure project (Saskal 2008). By 2009, California lawmakers passed an $11.1 billion water supply plan that included new dams, water cleanup, and ecological restoration (Associated Press 2009). However, in 2010, due to the looming budget crisis in California and fear that the water bond would not pass, Gov. Schwarzenegger pulled the measure from the November 2010 ballot and placed it on the 2012 ballot (McGreevy 2010). As it stands now, current California Gov. Jerry Brown took the initiative off the 2012 ballot and deferred its vote until 2014. Gov. Brown believes that the burden of financing California’s water supply infrastructure should not be placed entirely on tax money. Rather, Gov. Brown states, “The big water users will pay for having water reliability.” (York 2012). Gov. Brown is currently proposing a $23 billion project that would consist of constructing twin peripheral canals as well as conducting ecological 4 restoration in an attempt to mitigate the past and present burden on the Delta. According to Brown’s plan, $14 billion would go to constructing the canal system and $3-4 billion would go to ecological restoration (Boxall 2012). 1.2 Alternative Long-Term Delta Water Exporting Strategies According to Lund et al. (2008), a peripheral canal is not the only potential solution to California’s water crisis. Essentially, California has four choices about how to handle long-term Delta water exports: (1) Continue with the current policy of pumping water directly out of the Delta using the existing water infrastructure; (2) Build a peripheral canal; (3) Construct a dual conveyance facility; and (4) Stop exporting water out of the Delta. In essence, constructing a peripheral canal means that water would stop being exported directly out of the Delta. Instead, the canal would obtain water supplies upstream that would be transported around the Delta. The dual conveyance facility also contains a peripheral canal; however, water would continue to be exported directly out of the Delta as well. Lund et al. (2008) note each policy comes with advantages and disadvantages. Continuing the current policy is unsustainable. It may be cheaper in the present not to do anything, and given California’s fiscal problems, many policy makers might be tempted to go this route. However, eventually the existing Delta infrastructure will fail which would cost the California economy billions of dollars. Further, constructing a dual conveyance facility would still mean that the Delta levees require repairs at additional costs beyond building a peripheral canal. Environmental stability is also impacted 5 differently depending on the long-term Delta strategy. According to Lund et al. (2008), stopping all Delta water exports would have the most significant impact on the environment. However, this would come as a huge blow to the California economy given that more expensive alternatives would have to be considered (e.g. out of state water exports). Further ecological (dis)advantages, in terms of fish viability, from choosing a long-term Delta water export strategy are discussed below. 1.2.1 Delta Fish Viability The Delta is home to many different fish species, some of which are on the endangered species list (Lund et al. 2008). Key species of fish include: Delta smelt, Striped bass, Longfin smelt, and Sacramento River Salmon. Unfortunately, for the fish in the Delta, endangered and otherwise, the intakes for the water exports kill millions of fish every year (Weiser 2012). According to the California Sportsfishing Protection Alliance (CSPA) (2013) and Restore the Delta (RTD) (2013), 130 million fish have been salvaged at the Delta intake pumps between 2000 and 2011, many of which were killed in the process. However, estimates of actual fish losses are 5-10 times higher than the amount of salvaged fish (Larry Walker Associates 2010). Lund et al. (2008) also state that the endangered species of fish may also face some probability of extinction even if all water exports stopped. At any rate, Federal wildlife officials are not sitting idly by while the massive impact on the fish in the Delta continues. Weiser (2013) notes that according to Endangered Species Act rules, only 305 smelt are allowed to be killed at the water pumps 6 in the Delta per year. As of February 2013, 232 smelt had been killed. Consequently, the Federal wildlife officials are ordering that Delta water exports be reduced in an attempt to offset the impact on the smelt population. Unfortunately, these cuts may come later in the year when the water supply is critical for agriculture (Weiser 2013). Lund et al. (2008) also explain that different water exporting strategies will have varying effects on the fish viability in the Delta. Their study mentions that although it is difficult to quantify the ecological impacts of fish viability, a number of experts on the Delta were consulted during the analysis. Accordingly, ending all water exports would have the greatest positive ecological impact on the fish and the local habitats within the Delta. Next, a peripheral canal or dual conveyance facility would have similar and next best effects on fish viability. Lastly, continuing the current policy of only exporting water directly out of the Delta is estimated to have the worst impact on fish viability. 1.3 Water Supply and the Sustainability of California’s Economy The sustainability of California is impacted by the reliability of water supply. As mentioned previously, much of the California’s agricultural crops are located within its arid region and require a stable supply of water (CALFED 2013). These crops are crucial for California’s economy and local food supplies as well as supplies in regions where the crops are exported. Moreover, Hanak (2008) discusses the impact that limited water supplies and regulations have on residential construction. Essentially, the long-term availability of water in an area is critical for housing. If a particular area happens to have certain water regulations that protect homeowners from shortages by restricting their 7 supply, then it may be possible that new housing construction will be limited. As a result, the area will not grow. 1.4 Potential Supply Disruptions of the Sacramento-San Joaquin Delta Water exports from the Delta are also susceptible to supply disruptions. According to the U.S. Geological Survey (2007), California has a probability greater than 99% to have at least one major earthquake, exceeding 6.7 on the Richter scale, within the next thirty years. Focusing on Northern California, Field et al. (2007) predict that there is a 97% probability of an earthquake greater than or equal to 6.7 on the Richter scale and a 37% probability of an earthquake greater than or equal to 7.5 on the Richter scale in the next three decades. As such, the existing water infrastructure around the Delta is vulnerable to damages from earthquakes that may take years to reverse. According to Hanak et al. (2012), if particular levees collapse as a consequence of an earthquake, large amounts of salt water could potentially flood into the Delta and contaminate the water supply for up to two years. The costs of this failure are estimated to range from $8 billion to $16 billion. This range of costs is based on the season of the failure as well as the duration of time needed to restore water exports. Further, if this occurrence were to happen after a long drought, the economic costs would be even greater. Hanak et al. (2012) note this concept has received sparse attention and, as such, more research on finding solutions for the Delta is warranted. 8 1.5 Costs of Building a Peripheral Canal Two main cost-benefit analyses have emerged as key elements in aiding policy makers. The first analysis is by Lund et al. (2008). The second analysis is from the Bay Delta Conservation Plan (2013) The Bay Delta Conservation Plan was conducted by a group of local water agencies, environmental and conservation organizations, state and federal agencies, and other interests (Bay Delta Conservation Plan 2013). According to Lund et al. (2008), the estimated cost range of building a peripheral canal, for use in either a dual conveyance strategy or a standalone strategy, is $4.75 billion on the low end and $9.75 billion on the high end. Many assumptions, however, are considered within this range. They also note that if a dual conveyance strategy was implemented, then the costs of building a peripheral canal could vary. A smaller canal could be considered given that water will be exported from two places. As such, costs for building a peripheral canal could be lower. However, if a second canal was considered as part of this strategy, then costs would certainly rise. To further complicate matters, a dual conveyance strategy or a continued through-Delta pumping strategy would require additional repairs to the levees and other upgrades at a cost of nearly $10 billion. Lund et al. (2008) also considers rising sea levels and earthquakes. When these scenarios are considered, the dual conveyance strategy can result in costs that are almost twice as high as a peripheral canal strategy alone. Costs for repairing levees are not considered given that water exports directly out of the Delta would end. Lastly, Lund et al. (2008) assume that the dual conveyance strategy does not increase water quality costs as compared to a 9 standalone peripheral canal strategy. However, their study notes that these estimates probably underestimate costs, especially when considering rises in sea levels. According to the Bay Delta Conservation Plan (2012), the midpoint of the estimated cost range of building a peripheral canal is $12.7 billion. This amount is higher than the estimated upper end of the range ($9.75 billion) in the Lund et al. (2008) figure. In a separate study, Sunding (2011) estimates the cost of building the necessary water infrastructure will range from $7.5 billion to $12.5 billion. The upper range of the Sunding (2011) estimates is also below the midpoint estimate of the Bay Delta Conservation Plan (2012). In any case, it seems likely that the costs of constructing the water infrastructure will be upwards of $10 billion, if not higher. The Bay Delta Conservation Plan (2012) analysis also made a number of assumptions in their study. First off, their study considers high and low ranges of estimated costs in their itemization of the project. As noted, the differences within the ranges reflect varying assumptions. At times, the range of highs and lows were simply 10% in either direction of the estimated costs. Further, Lund et al. (2008) use a nominal discount rate of 4.375%. This discount rate was used because it is required by the U.S. Army Corps of Engineers and the U.S. Bureau of Reclamation when evaluating water projects like this one. 1.6 Alternative Financing Mechanisms If a conveyance system is built to mitigate the impending collapse of California’s water supply system, alternative financing mechanisms for a new water conveyance 10 system must be considered given California’s fiscal state. This thesis considers such mechanisms in a laboratory setting and attempts to more accurately reveal subject preferences and behavioral decisions. To do so, three treatment groups are considered: Fixed Historical (FH), Fixed Reliability (FR), and Endogenous Reliability (ER). FH is based on a fixed sized system that allocates water based on historical allocations. FR takes this notion a step further by adding priority rights for subjects who contribute more money to the construction of a water conveyance system. As such, subjects with a higher willingness to pay (WTP) should be able to outbid those with lower WTP values to accrue greater benefits by receiving a more reliable supply of water. ER creates an environment where reliability pricing with priority rights coexists with endogenous sizing of the project. The size of the project is determined by the sum of contributions and benefits are distributed according to ranked contributions. During the endogenous sizing process, however, lower ranked contributions can be discarded if higher thresholds are not met and smaller sized systems are considered. Theoretically, the ER treatment group should see the least amount of free-riding and the greatest price formation efficiency given that subjects have both an incentive to contribute more for greater reliability of benefits as well as for fear of being excluded from the system. 1.7 Summary of Major Findings and Conclusions Analysis in this thesis explicitly examines the influence of order and rebate effects on subject contributing behaviors. Order can potentially confound results from one part of an experiment to another given that subjects learn over time. As such, to control for 11 systematic individual characteristics, experiment sessions consisted of two parts (see for example Mitani and Flores (2009)). Conceivably, observations that occur in an earlier part of an experiment do not necessarily reflect actual contributing behavior. A preliminary descriptive analysis on experiment results revealed inconsistencies of subject contributing behaviors from one part to another. A more robust statistical analysis discovered that order has a statistically significant impact on contributing behavior given that the deviation between subject WTP and contributions is reduced in Part 2 relative to Part 1. This effect became more apparent when focusing on order within specific treatments. Overall, these results indicate that subjects are indeed learning and essentially Part 1 observations are not accurate portrayals of subject contributing behavior. Therefore, analysis estimating the influence of rebate effects only considers Part 2 observations. The effects of rebates are examined rigorously by using data collected by Kaplan et al. (2012). Results of a descriptive data analysis suggest that the different treatment groups were influenced by rebates. Observations in the FH treatment had an unexpected result given that no-rebate observations tended to have higher frequencies of success for building a fixed sized system than observations in which rebates were offered. The examination of the FR treatment, however, told a different story. In earlier periods, the observations that did not contain rebates tended to have higher frequencies of success. However, in the later periods both sets of observations, with and without rebates, converged to have 100% success rates. On the other hand, potential rebate effects were much more pronounced in the ER treatment. The sizes of the delivery system across all 12 the periods were consistently larger for observations that contained rebates. A more robust statistical analysis revealed that rebates have a profound influence in reducing the deviation between subject WTP and contributions in the treatments with reliability pricing given that subjects tend to contribute more than their WTP when offered a rebate. Conversely, the influence of rebates in the FH treatment was not found to be statistically significant. This result is expected, as subjects in the FH treatment have no real incentive to contribute more than their WTP. Further, when the size of the system is determined endogenously, rebates are estimated to increase the size of the system upwards of two units. However, the inclusion of rebates does not seem to affect the probability of the system successfully being built in the fixed sized treatments. 1.8 Outline of Thesis Content The following chapter of this thesis discusses the relevant academic literature as it pertains to threshold public good games in the context of rebates, refunds, soliciting contributions, reliability pricing, endogenous and fixed sizing, and subject expulsion mechanisms. Chapter 3 provides a description of the experiment design and discusses the conceptual framework of the treatment groups in this study. A descriptive analysis in Chapter 4is conducted on these data collected from subjects during the experiment. Demographics and systematic differences of subjects across sessions are explored as well. Chapter 5 discusses the model and methodology used for the statistical analysis of the experiment data and the results from the statistical analysis are presented. Lastly, Chapter 6 provides insights and concluding remarks. 13 Chapter 2 LITERATURE REVIEW 2.1 Introduction The analysis in this thesis relies heavily on the decision making of subjects within a laboratory setting. More specifically, the mechanisms impacting the solicitation of private contributions within a threshold public good experiment are considered key elements to the design of the treatments to be used in this thesis. Therefore, it is of utmost importance that these mechanisms in this type of setting are explored by probing the relevant academic literature. In this chapter, the impact of rebate and refund policies is considered. Reliability pricing and endogenous sizing of a threshold public good are explored as well as the solicitation of private contributions for the good. Lastly, mechanisms for subject expulsion due to uncooperativeness and free-riding are also discussed. This thesis adds to the literature by evaluating the impact that rebates have on subject contributions in a threshold public good provision experiment by conducting experimental sessions where subjects are not offered a rebate and incorporating data from sessions where they are. Further, this thesis also adds to the literature by considering incentives within an environment where self-sizing of threshold public goods and reliability pricing can potentially increase benefits while reducing free-ridership. 14 2.2 The use of Private Provision of Threshold Public Good Experiments in Policy Making In light of the shortcomings of the water infrastructure in California and the ongoing fiscal woes of the state, alternative mechanisms for financing a peripheral canal may be worth considering. In recent times, California has been faced with devastating budget deficits that have impacted all levels of state and local governments as well as the financing of new projects. As such, financing a water infrastructure project using private contributions should be explored. In a threshold public good experiment, one can test such financing mechanisms by creating treatment groups that are designed to solicit private contributions in order to reach a certain dollar amount, called a provision point. If the provision point is reached, then the proposed project will be built. If the contributions fall short, the project is abandoned and a refund policy for the contributions takes place. If, however, the sum of total subject contributions exceeds the provision point, then some sort of rebate policy takes effect. Further discussions of rebate and refund policies are found in the sections below. Bergstrom et al. (1986), however, note a particular caveat pertaining to the solicitation of private contributions towards public goods; pure public goods tend to be inefficiently allocated when relying solely on voluntary private contributions given that some agents may be tempted to free-ride. Since that time, considerable work has been done on the provision of public goods. In the following sections, this past literature will be reviewed allowing us to see the connections between the past literature and this thesis. 15 Foremost among these previous studies is Kaplan, Howitt, and Kroll (2012), which examines the effect of reliability pricing and endogenous sizing on the private provisioning of a threshold public good in a laboratory experiment. In their analysis, they considered solicitation mechanisms that contain a proportional rebate. Theoretically, these rebates are likely to affect how individuals contribute when concepts such as pricing and availability are uncertain. This thesis considers such incentives and examines the impact that rebates have on free-riding. Further discussion of these contribution altering mechanisms is provided below. 2.3 Soliciting Contributions Past research has explored the importance of conducting simultaneous solicitations versus sequential solicitations. A simultaneous solicitation mechanism is when all agents submit their bids at once, whereas in sequential solicitations, earlier bids are made public. Coats et al. (2009) argue that sequential solicitations can create coordination benefits that are not available during simultaneous ones. Further, sequential solicitations can also have higher rates of successful provision of the good when compared to simultaneous mechanisms. On the other hand, Bangoli and Mckee (1991) found that Pareto-efficient provision of the public good can indeed result using a simultaneous bidding mechanism when all agents are aware of everyone’s payouts. This study employs an iterative contribution mechanism as in Kaplan et al. (2012) that exploits the benefits of sequential bidding by allowing agents to play a repeated game for three periods. The third and last period of this game is binding and counts 16 toward the agents’ overall earnings. The first two periods provide feedback on total contributions and the solicitations are similar to how sequential bidding mechanisms might be. This third period game is then repeated four times, allowing subjects to learn how the game is played dynamically. 2.4 Reliability Pricing and Priority Rights When it comes to providing a stochastic public good (such as water supplied through a peripheral canal) in which some agents stand to derive greater benefits than others, reliability pricing may be a mechanism for financing such a project. Kaplan et al. (2012) explores this concept and builds on the notion of priority rights. In their study, Kaplan et al. (2012) created treatment groups for an experiment in which subject contributions are ranked and placed into reliability rate classes. Those with contributions in the highest rate class receive their input with greater frequency, thus allowing them to realize the maximum potential benefits when a canal is built. Those in lower rate classes receive fewer benefits from their share of the resource because they receive it less frequently. Ultimately, Kaplan et al. (2012) found that reliability pricing mechanisms outperform historical allocation mechanisms in financing a stochastic common property resource. Given that the literature in this area of research is sparse and limited, the results from Kaplan et al. (2012) could potentially play a big role in policy making for this type of project. The treatment groups in this study follow those in Kaplan et al. (2012), but also consider how rebates may play a role in their results. This thesis tests this notion by 17 conducting sessions without rebates and incorporating data from sessions in which subjects were offered rebates. 2.5 Endogenous and Fixed Sizing Endogenous sizing occurs when the sum of the agents’ contributions determine the size of the particular project to be provided. Each size has individual thresholds and if the highest threshold is not met, smaller sized systems are considered. In contrast, fixed sizing is when the size of the project is determined exogenously and is static. In the case of threshold public good experiments, if the provision point is not met, the project is not built. Rauchdobler et al. (2010) challenge the efficiency of an exogenous (fixed sized) threshold in a one-shot public good game by also allowing players to vote on the threshold in a referendum. They posit that creating an environment where the players endogenously determine the level of the threshold will reduce free-ridership whilst increasing formation efficiency via improved coordination. Their results suggest that introducing an endogenous threshold did not mitigate the inefficient provision of public goods. Subject voting patterns in their experiment have a tendency to generate more ambitious thresholds when determined endogenously compared to an imposed exogenous threshold. Subject contributions, however, typically did not meet the higher thresholds. Rauchdobler et al. (2010) attributed this possible occurrence to the one-shot nature of the game. In other words, subjects were not given the opportunity to learn as they would in a repeated game. The design of the treatment groups in this thesis will address this problem 18 by employing an iterative contribution mechanism in which subjects play a repeated game and are given time to learn. Kaplan et al. (2012) exploited endogenous and fixed sizing of public goods in their experimental design when analyzing financing mechanisms to build a water conveyance facility. The results of their study suggest that an endogenous self-sizing mechanism when used in combination with reliability pricing outperforms historical fixed sizing mechanisms consistently. This study will use a similar approach to those in the study by Kaplan et al. (2012) by utilizing the concepts of fixed and endogenous sizing mechanisms as well as priority rights. 2.6 Subject Expulsion Mechanisms in Public Good Games At some level, subjects in public good games are required to cooperate with one another. Even in the face of an un-cooperating free-riding participant, subjects must coordinate their efforts if they hope to derive benefits from the provision of a good. As unfortunate as this sounds, this occurrence happens all too often in a public good game setting (Bergstrom et al., 1986). One way to increase the cooperation of the members within a group is to employ a mechanism that effectively expels low contributing or uncooperative subjects. Cinyabuguma et al. (2003) test one such expulsion mechanism by allowing groups to simply vote out members. If half or more of the group votes to remove a particular member, the subject can no longer participate in the group’s contributions. The theoretical foundation of this mechanism is not so much the actual act of excluding 19 uncooperative group members, but the threat of doing so. Subjects have an incentive to pull their weight. Moreover, low contributing subjects were often given ample warning of a possible expulsion through votes earlier in the game which did yet contain a majority of the group. Therefore, subjects had time to adjust their contributions and avoid exclusion. Cinyabuguma et al. (2003) note that cooperation broke down after the threat was removed. Kaplan et al. (2012) have an expulsion mechanism built into their endogenous reliability treatment group. Although the mechanism does not allow for such blatant expulsion through voting as in the study by Cinyabuguma et al. (2003), subjects can effectively be left out of the provisioning of the good if their contributions are below the necessary threshold for determining the size of the system. If they are left out, then they receive no benefits. Kaplan et al. (2012) suggest that subjects will indeed contribute closer to their maximum willingness to pay in order to avoid being excluded. This thesis will also utilize the same expulsion mechanism as in Kaplan et al. (2012). 2.7 Rebate Rules in Threshold Public Good Provision Games In a threshold public good provision game, subjects contribute towards the provision point of some good. If, however, subject contributions exceed the threshold, then a rebate policy for the participants goes into effect. In theory, rebates can have a significant effect on subject contribution patterns given the profit maximizing nature of the game. 20 Marks and Croson (1998) investigate the impact that different forms of rebates have on contributions towards a threshold public good. One possible rebate policy, is simply giving no rebates at all. If the contributions exceed the provision point, the excess contributions are not returned to the contributors and they receive no additional benefits. Another type of rebate is a proportional one. Here, the excess contributions are returned to contributors based on their proportionate share of the overall contributions to the project. Marks and Croson (1998) also discuss a utilization rebate policy. Under this paradigm, excess contributions are used to provide a different, yet continuous, public good. Essentially, this policy is less harsh than the no rebate rule because, while no money is directly returned, a continuous public good is created that generates benefits. Marks and Croson (1998) found that under each type of rebate policy there are different sets of Pareto-efficient outcomes. The no rebate policy is Pareto-disimproving, the proportional rebate policy is Pareto-neutral, and the utilization policy is Paretoimproving. Additionally, they find no differences across the rebate policies in terms of the proportion of times that the public good is successfully provisioned. However, they do find that when subjects are offered a utilization rebate, total contributions are greater than under a proportional or no-rebate policy. Spencer et al. (2009) also evaluate rebate rules in providing a threshold private good. This time, however, additional rebate policies beyond the ones mentioned previously are used. In this experiment, winner-take-all rebates and random full rebates are utilized. The winner-take-all rebate mechanism distributes all excess contributions to one randomly chosen person by lottery. The winner-take-all rebate is further split into 21 two different subsequent rules. The first rule requires no contribution to be entered into the lottery and the second rule requires a contribution to be entered into the lottery. The random full rebate rule uses a lottery system too. Essentially, one person is chosen to receive a rebate on his or her full contribution and enjoy the benefits of the public good at no cost. Ultimately, Spencer et al. (2009) found that the winner-take-all rebates and the full rebates experienced a demand over-revelation. In essence, participants in the experiment were valuing not only the provision of the public good, but also the chance to win the lottery and receive a full rebate or all the excess contributions. On the other hand, the proportional rebate rule was found to achieve both aggregate and individual demand revelation. To add to this literature, this thesis evaluates the effectiveness of the proportionate rebate policy in reducing free-riding and in improving price-formation efficiency with the setting established by Kaplan et al. (2012) relative to a zero rebate policy. In order to assess the impact that the proportional rebate has on contributions, sessions without the rebate are conducted and statistically analyzed along with data collected from sessions in the study by Kaplan et al. (2012). 2.8 Refunds in Threshold Public Good Provision Games In a threshold public good game, refunds are simply the return policy of subject contributions if the provision point is not met. Refund policies can potentially have a significant impact on voluntary contributions. For instance, subjects may not necessarily want to contribute towards a good if they risk getting nothing in return. 22 Coats et al. (2009) test the impact that refund policies have on sequential and simultaneous contribution mechanisms. They posit that the order in which subjects make contributions and the refund policy offered can play a significant role in providing a public good efficiently. In their study, Coats et al. (2009) implemented a full refund rule and no refund rule. Results from their study suggest that providing a full refund in both simultaneous and sequential contribution mechanisms leads to higher success rates of reaching the provision point. They note, however, that sequential contributions tend to outperform simultaneous contributions regardless of the refund rule. In other words, the order in which contributions are solicited has a greater impact on voluntary contributions than a given refund policy. This thesis will employ a full refund rule in the treatment groups when the provision point is not met as well as an iterative contribution mechanism that is similar to sequential bidding. 2.9 Summary Data for this thesis are gathered from a private provision of a threshold public good game with treatment groups that follow the study by Kaplan et al. (2012). In their analysis, they considered the concepts of reliability pricing and endogenous sizing of the good. Further, their solicitation mechanisms include a proportion rebate rule. Theoretically, these rebates are likely to affect how individuals contribute when mechanisms such as pricing and availability are uncertain. This thesis considers such incentives and examines the impact of a proportional rebate rule on free-riding by conducting sessions without the rebate rule and statistically analyzing these data along 23 with the sessions conducted by Kaplan et al. (2012). Ultimately, the goal of this study is to aid policy makers in averting the impending doom of California’s water crisis by providing insights into ways of funding mitigation projects. 24 Chapter 3 EXPERIMENTAL DESIGN 3.1 Introduction The overall experimental design used in this thesis follows Kaplan et al. (2012). Sessions were held in a computer laboratory at California State University, Sacramento. Students in principles of economics classes were recruited as subjects to participate in the experiment. The software program z-Tree (Fishbacher 2007) was used to conduct the computer-based experiment. Subjects earned lab dollars (L) during the experiment, which were converted to US dollars at the end of the session and paid to them before they left. Subjects earned $25, on average. The average amount of time for each session was approximately one hour. A session consisted of two parts and participants were paid based on their performance in both parts. Moreover, Parts 1 and 2 of the session were different treatments. The parts were designed this way to control for systematic individualist characteristics (see, for example Mitani and Flores (2009)). Each part of the experiment was divided into four rounds with three contribution periods in each round, for a total of twelve periods. At the end of each period, subjects were provided a report on the outcome of the delivery system based on group performance. This allowed subjects to update their expectations about how the game was to be played as well as how others in their group played. The first two periods of a round were non-binding, allowing subjects to become familiar with the game and their group. This notion also simulates the repeated sealed bid 25 conditions assumed to be utilized if California were to finance a water infrastructure project. The third period of each round was binding and the results of this period counted towards subjects’ earnings. Subjects in each session were divided into groups of four with each group playing independently of the other groups. That is, each group played a unique game consisting of the same treatments during the session. Subjects within a group were assigned a different player type with varying levels of benefits and subsequent maximum willingness to pay (WTP) across player types. Player Types 1 and 2 represent highvalued agriculture and low-valued agriculture entities respectively, whereas player Types 3 and 4 represent medium sized and large-sized urban center entities respectively. Further, Type 3 and 4 players have a considerably higher WTP than Type 1 and 2 players as can be seen by the payout values reported in Table 3.1 for the fixed size historical treatment.1 3.2 General Setting At the beginning of each session, subjects were randomly seated in the computer lab and assigned to a group. Subjects received no information regarding the other three members of their group. Further, subjects were informed that their group shared the use of a generic good that provided each of them benefits. The problem the groups faced, however, was that no delivery system existed to deliver the good to them. Subjects were told that they would have to finance the construction of the delivery system for their 1 The payouts for the other treatments are of similar magnitude but vary depending on the size of the system built and the delivery rate class one finds his or her input located. 26 group to derive benefits from the good. They were told that they could individually contribute zero or more lab dollars to the construction of the delivery system. Subjects were each given packets containing instructions to playing the game, information on the cost of building the system, and their individual benefits and contribution limit (i.e. WTP). The individual benefits of each subject were not made public to the other members of the group, only the cost of building the system. Subjects were, however, informed that the benefits of each member of the group differed. After the two treatments, a questionnaire was administered to the subjects to test for any pre-existing systematic differences in the subjects across the sessions. 3.3 Treatment Groups The treatments used in this thesis are identical to three considered in Kaplan et al. (2012) so that the results for the study can be used to evaluate the effectiveness of reliability pricing and self-sizing at reducing free-riding and enhancing price formation efficiency.2 This study differs from Kaplan et al. (2012) in that it excludes rebates in order to uncover any variation amongst contributions between treatments with and without rebates.3 Instructions for each treatment can be found in Appendix A, B and C. The following sub-sections cover these treatment groups in more detail. 2 Kaplan et al. (2012) also evaluate a solicitation that has endogenous size of historical allocations. In the study by Kaplan et al. (2012), proportional rebates were provided to subjects if their combined contributions were more than the cost of building the system. 3 27 3.3.1 Fixed Size Historical Allocation Treatment In the fixed sized historical allocation treatment (FH), subjects play a traditional threshold public good game in which they make one contribution per period.4 Subjects in each group must have a combined amount of contributions totaling L4,452.5 or more per period for the system to be built. If contributions exceed L4,452.5, no rebate is provided and the excess contributions are discarded. Moreover, each of the player types derive different levels of fixed benefits if the system is built. Following the conceptual framework from Kaplan et al. (2012), the benefits of the player types were derived from the present discounted value of the stream of benefits following the building of such a system for entities of similar nature. If the system is built, each subject receives his or her fixed benefits. If, however, the total sum of contributions is less than L4,452.5, the system is not built, nobody receives any benefits, and the subjects receive a refund. The payout schedule for FH is as follows.5 Table 3.1 FH Payout Schedule by Type Player Type 1 2 3 4 Units L1,875 L1,200 L8,580 L22,950 Based on the conceptual framework and the zero rebate policy, it is expected that contributions will not exceed the cost of building the system. Since player Types 1 and 2 (high-valued agriculture and low-valued agriculture entities) have WTP values that are 4 5 Instructions for the Fixed Historical Treatment can be found in Appendix A. The payouts for the other treatments are more complicated and are presented in Appendix D and E. 28 lower than the cost of building the system, whereas player Types 3 and 4 (medium sized and large-sized urban center entities) have WTP values above it, we might expect to see the relative deviations between WTP and contributions greater for player Types 1 and 2. In other words, the agricultural users may be tempted to free-ride given that no real incentives exist for players to contribute more in this treatment. 3.3.2 Fixed Size Reliability Pricing Treatment In the fixed size reliability pricing treatment (FR), the size of the system is divided into thirteen units and allocated amongst the player types based on historical evidence (see Kaplan et al. 2012).6 The distribution of units across player type is shown in Table 3.2 and subjects are asked to contribute on each of their allocated units per period. Again, the cost for building the system is L4,452.5. If total contributions equal or exceed this amount the system is built but no rebate is available. Further, subjects are given a contribution limit in which the sum of their contributions towards their units cannot exceed. This limit reflects the subjects’ maximum willingness to pay (WTP). Table 3.2 Endowment of Units by Type Player Type 1 2 3 4 6 Units 3 5 2 3 Instructions for the Fixed Reliability treatment are presented in Appendix B. 29 At the end of each period the contributions are ranked and placed in their respective delivery rate classes as shown in Table 3.3. The four highest ranked contributions are placed into Class 1; the next two highest contributions (the 5th and 6th highest) are placed into Class 2; and the remaining 7 contributions are placed in Class 3. Correspondingly, the class that the units are located in determines the level of benefits they receive if the system is built (See Appendix D for the payouts by player type in this treatment). Class 1 has the highest benefits from the use of the input, whereas Class 3 has the lowest level of benefits. Table 3.3 Delivery Classes Class 1 2 3 Units 4 2 7 It is possible, however, for subjects to earn negative profits. If subjects contribute excessive amounts towards particular units that they believe will be placed into a higher class and end up having their units placed in a lower class, then they will not earn their expected benefits which can lead to negative profits. The overall framework of the class system reflects reliability pricing and priority rights; subjects who contribute more and have higher ranked contributions receive greater benefits from the system because they are implicitly receiving their inputs first and more frequently. In contrast to the FH treatment, we expect to see the contributions exceeding the cost of building the system as a result of the reliability pricing. 30 3.3.3 Endogenous Size Reliability Pricing Treatment The endogenous size reliability pricing treatment (ER) contains much of the same framework as the fixed size reliability pricing treatment. Subjects are allotted units depending on their player type as seen in Table 3.2 and contributions are ranked and placed into a class for derivation of benefits in the same manner as in Table 3.3.7 The ER treatment deviates from the FR treatment in that the size of the delivery system is determined endogenously by the amount of contributions. The maximum size of the system that can be built is thirteen units. At the end of each period, if the total amount of contributions does not amount to the cost of building a thirteen unit system, the lowest ranked contribution is discarded and a twelve unit system is considered. This continues until the system is built, if it is built at all. If a subject has his or her contribution discarded, then no benefits from that unit will be received. If the subject does not receive a unit because their contribution for that unit was too small to offset the cost of another unit in the delivery system, then they receive a refund for that portion of their overall contribution to building the system. In theory, subjects in this treatment will contribute closer to their WTP to build the system to take advantage of reliability pricing and for fear of being “left out” during the endogenous sizing process. Therefore, this treatment should see the least free-ridership and greatest price formation efficiency. 7 Instructions for the Endogenous Reliability treatment are presented in Appendix C and the payouts by player type are found in Appendix E. 31 Chapter 4 DATA DESCRIPTION 4.1 Introduction Subjects for the experiment were recruited in economics principle courses at California State University Sacramento in the fall of 2012. Different subjects participated in three separate experiment sessions. Upon completion of the sessions, students received compensation based on their performance and were asked to complete a survey. Section 4.2 discusses the survey results and the statistical tests that were conducted in exploration of systematic differences among the subjects across sessions. Accordingly, results largely show that there are no systematic differences. Subsequent analysis in Section 4.3 serves as a preliminary investigation into potential order effects within the sessions. Subjects are separated by player type and treatment to observe differences between Part1 and 2 data. Results in this section indicate that potential order effects may exist given inconsistencies discovered in subject contributing patterns. Section 4.4 characterizes the average percentage change of the deviation between subject WTP and contributions by player type, treatment, and across the periods. As discussed in the previous chapter, we would expect to see the ER and FR treatments outperforming the FH treatment. Although the results show this tendency at times, the performances of the treatments are not always clear. In fact, many observations are behaving quite unexpectedly. This phenomenon could be due to possible rebate effects and is explored in subsequent sections as well as the following chapter. Section 4.5 discusses the frequency of success for building the 32 fixed size delivery system in the FH and FR treatment groups. In this section, data from Part 1 and 2 are compared to data from Part 2 only to gain additional insight into potential order effects. Results again tend to suggest an order effect given that FH outperformed FR when examining data from both Part 1 and 2. When analyzing data strictly from Part 2, FR consistently outperformed FH in the majority of the periods. Further, an initial exploratory analysis of potential rebate effects occurs by comparing the frequency of success of the fixed sized treatments with observations containing rebates from the study by Kaplan et al. (2012). Results for the FH treatment tend to show that the observations without rebates tend to outperform ones where rebates were offered, especially in later periods. In the FR treatment, a noticeable convergence of the observations with and without rebates transpires in the later periods with both sets having an average 100% success rate of the system being built. Section 4.6 continues the exploratory analysis of possible rebate effects by comparing the sizing of the delivery system in the ER treatment with observations containing rebates again from Kaplan et al. (2012). By comparison, it is apparent that the sizing of the delivery system is consistently larger when subjects are offered a rebate. Lastly, Section 4.7 provides a summary of the analysis and then concludes with insights drawn from this exploration of the data. 4.2 Survey Results Upon completion of each experiment session, subjects were asked to complete a survey questionnaire.8 Figures 4-1, 4-2, 4-3, and 4-4 illustrate results from this survey. 8 A screenshot of the survey questions that subjects completed at the end of the experiment is presented in Appendix F. 33 Figure 4-1 shows the various majors declared by each subject, where the majority is pursuing a degree other than economics. Figure 4-2 illustrates the subjects’ year in school. Accordingly, 45 percent are freshmen and 71.43 percent of subjects are in their first two years of college. Figure 4-3 shows the age distribution of the test subjects. The mean age is 19.7 with a minimum age of 18 and a maximum age of 36. Figure 4-4 presents the subjects’ perception on when during the session they believe they understood the game. Roughly half of the subjects reported that they understood the game by the end of Part 1, whereas it took the rest until Part 2. These data may suggest a possible order effect when analyzing the results of the experiment. Table 4-1 provides the summary means by session for each of the survey questions. Across all the sessions, 52% of subjects were females and 48% were males. The gender distribution within the sessions, however, appears to be distributed less evenly. The percentage of females in Session 1 was only 25%, whereas in Sessions 2 and 3, the percentages were 65% and 60% respectively. Age of the subjects was roughly 1920 years old and this coincides with the average year (denoted by Year in Table 4-1) the students were in school (sophomore). Further, the results in Table 4-1 indicate that subjects, on average, completed less than two economics courses (denoted by Economics Classes in Table 4-1). Lastly, the results show that subjects, on average, did not understand the game until Part 2.9Again, this strongly suggests possible order effects. 9 In the survey, when subjects were asked when they perceived to understand the game, they were given the following options: 1=”Right away”, 2=”Early periods of the first part”, 3=”Towards the end of the first part”, 4=”Early periods of the second part”, 5=”Towards the end of the second part”, 6=”Never”. 34 Potential systematic differences between the sessions are explored. Statistical ttests are conducted for testing differences between means. Table 4-2 illustrates the results from the tests. Although the results largely show that there are no systematic differences between the students in the sessions, some systematic differences were found in gender. As discovered in Table 4-1, Session 1 had a relatively small proportion of females (25%). The author, however, feels that gender effects are not prevalent in this type of setting and the results of the experiment are not biased.10 10 Cadsby and Maynes (1998) tested for systematic differences between genders in a voluntary public goods provision experiment and found that neither male nor female contributions were more generous.In a separate public threshold goods experiment, Mitani and Flores (2009) found that there are no differences between genders in actual contributions. Figure 4-1 Subjects by Declared Major 35 Figure 4-2 Subjects by Class 36 Figure 4-3 Age of Subjects 37 Figure 4-4 Subject Understanding of the Game 38 39 Table 4-1 Summary Statistics of Subjects Means of Demographics Variable All Sessions Session 1 Session 2 Gender (1=female) 0.52 0.25 0.65 Age 19.68 20.06 20.05 Year (0=Freshman, 0.96 1.00 1.05 1=Sophomore, etc) Economics Classes 1.38 1.3125 1.65 Understanding 3.11 3.06 3.45 Observations 56 16 20 Session 3 0.60 19.00 0.85 1.15 2.80 20 40 Table 4-2 - Session t-scores for Systematic Demographic Differences t-scores Sessions 1&2 Sessions 1&3 Sessions 2&3 gender -2.56 -2.21 0.32 age 0.01 0.94 1.63 study 0.55 -1.24 -1.78 year -0.15 0.44 0.55 economics classes -1.05 0.63 1.65 Understanding -0.96 0.58 1.63 41 4.3 Preliminary Order Effect Investigation Essentially, subject learning over time may confound results. In this case, subjects played the game over two parts and previous results suggest that subjects largely did not understand the game until Part 2. Therefore, data from Part 1 of the experiment may not clearly reflect treatment effects. However, before arriving at that conclusion, an order effect investigation is warranted. To begin the preliminary order effects investigation, player types are separated by treatment and part.11 The average percentage change of the deviation between subject willingness to pay (WTP) and contributions was the variable of interest in this analysis. In general, if order effects did indeed exist, a clear separation between Part 1 and Part 2 would be observed. Further, the percentage change of the average deviation between subject WTP and contributions should be closer to 0% in FR in Part 2 relative to Part 1 given the incentive for subjects to contribute more. Since the FH treatment should theoretically see greater free-ridership, the percentage change of the average deviation between subject WTP and contributions should be closer to 100% in Part 2 relative to Part 1. If these occurrences in the FR and FH treatments are to be observed, this would be indicative of subject learning over time. Figures 4-5, 4-6, 4-7, and 4-8 illustrate the results for the FH treatment. For the most part, a clear separation between Part 1 and Part 2 exists across player types. However, the direction of the separations is somewhat confounded. The differences between Part 1 and 2 data for player Types 1 and 2 are behaving as expected (i.e. Part 2 11 Treatment group ER was not included in the preliminary order effects investigation given that only data from Part 2 existed. 42 observations are clearly separated from Part 1 and the averages percentage changes are closer to 100%). The observations for player Types 2 and 3, however, are not so clear. Player Type 2 has no clear separation between Parts 1 and 2. Further, the observations for player Type 3 are behaving quite unexpectedly. While a clear separation between the parts exists, the roles are reversed; Part 1 observations seem to be performing as expected for the ones in Part 2. Perhaps Type 2 players, on average, learned to play the game in Part 1 whereas it took Type 3 players until Part 2 to realize they were systematically paying too much because of confusion (i.e. order). Figures 4-9, 4-10, 4-11, and 4-12 present the results for the FR treatment across player types. Again, the results continue to be relatively unclear. No distinguishable differences between the parts amongst Types 1 and 3 players are readily apparent. Once more, perhaps these players were not confused, on average, and learned the game early. Observations for player Types 2 and 4, on the other hand, are behaving as expected; Part 2 data are tending to outperform Part 1, in terms of reducing the deviation between subject WTP and contributions. In any case, the results from this preliminary order effect investigation tend to show a separation between the observations found in Part 1 and 2 data. Although, the observations do not always behave as expected, much of the time they do. Therefore, a more rigorous statistical analysis for order effects will take place in the following chapter. Figure 4-5 FH Player Type 1 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 43 Figure 4-6 FH Player Type 2 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 44 Figure 4-7 FH Player Type 3 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 45 Figure 4-8 FH Player Type 4 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 46 Figure 4-9 FR Player Type 1 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 47 Figure 4-10 FR Player Type 2 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 48 Figure 4-11 FR Player Type 3 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 49 Figure 4-12 FR Player Type 4 Average Percentage Change of WTP-Contributions Part 1 vs. Part 2 50 51 4.4 Average Percentage Change of the Deviation between Maximum Willingness to Pay and Contributions Figures 4-13 through 4-16 illustrate the average percentage change of the deviation between each player type’s WTP and contribution over the periods in each treatment using Part 1 and 2 data, whereas Figures 4-17 through 4-20 only utilize Part 2 data. According to the grouping of the figures, not only can the treatments be analyzed relative to one another but also an extended look into possible order effects is given. In general, we should expect to see the ER and FR treatments outperforming the FH treatment, with the ER treatment being the best performer. This is due to the theoretical reduction in free-ridership given reliability pricing as well as the fear that players should have from being “left out” by having a lower ranked contribution tossed out in the ER treatment. Consequently, there is clearly an incentive to contribute more; thus, reducing the deviation between subject WTP and contributions. However, we see that is not consistently the case. For player Type 1, there is no discernable difference between the FR and ER treatments, even when considering both Part 1 and 2 data vs. only Part 2 data. Further, FR and ER tend to outperform FH as a whole, as expected. Therefore, it is conceivable that Type 1 players are not confused in Part 1. For Type 2 players, when considering data from both Part 1 and 2, there are no clear differences between the performances of the treatments. In other words, the results are muddled. When considering data only from Part 2, the ER treatment seems to slightly outperform FH, whereas the FR treatment has a consistently lower average percentage change of the deviation between subject WTP and contributions. Observations for player Type 3 continue to behave unexpectedly. The ER 52 treatment is tending to be the worst performer of the treatment groups, whereas no clear difference between the FR and FH treatments is observed. Lastly, Player Type 4 has a clear separation of the treatments with the reliability treatments consistently outperforming the FH treatment, in both data from Part 1 and 2 and data from Part 2 only. In general, we would expect to observe the reliability treatments outperforming FH with ER having the lowest average percentage change of the deviation between subject WTP and contributions. However, the results seem to lack clarity. One potential reason is the impact of subjects not being offered a rebate. Subjects may be more hesitant to contribute for fear of earning negative profits, especially those with low relative WTP given the payoffs they face. A deeper examination of possible rebate effects will follow as well as a more rigorous statistical approach in the next chapter. Figure 4-13 Player Type 1 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data 53 Figure 4-14 Player Type 2 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data 54 Figure 4-15 Player Type 3 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data 55 Figure 4-16 Player Type 4 Average Percent Change of WTP-Contribution Part 1 and Part 2 Data 56 Figure 4-17 Player Type 1 Average Percent Change of WTP-Contribution Part 2 Data 57 Figure 4-18 Player Type 2 Average Percent Change of WTP-Contribution Part 2 Data 58 Figure 4-19 Player Type 3 Average Percent Change of WTP-Contribution Part 2 Data 59 Figure 4-20 Player Type 4 Average Percent Change of WTP-Contribution Part 2 Data 60 61 4.5 Frequency of Success for Fixed Size Treatments Figure 4-21 illustrates the frequency of success for building the fixed sized delivery system with and without reliability pricing using data from both Part 1 and 2 whereas Figure 4-22 only utilizes data from Part 2. Again, this approach is used to gain additional insight into possible order effects. Clearly, the frequency of success is greater in both the FR and FH treatments when considering data only from Part 2 relative to the observations that include data from both Part 1 and 2. The frequency of success using data from Part 1 and 2 tends to be weak, especially for the FR treatment group given that FH is the better performer in the majority of the periods. Conversely, the observations using only Part 2 data tell a much different story. In the majority of periods, FR outperformed FH given that reliability pricing had a 100 percent frequency of success in 9 periods, three of which are binding periods. Again, these results tend to suggest a lack of understanding until Part 2. By using data containing observations with rebates from Kaplan et al. (2012), preliminary insight into potential rebate effects is possible.12 Figure 4-23 compares the frequency of success for FH treatments with and without rebates. At first glance, no clear rebate effect is apparent given that the frequencies of success are not noticeably greater when subjects are offered a rebate. To the contrary, FH observations where no rebate was offered tend to outperform observations where rebates were. This especially holds true in the later periods where FH observations with no rebates have four periods in which the frequency of success was 100%, two of which are binding periods. Figure 4-24 focuses 12 Only data from Part 2 is included in this analysis because Kaplan et al. (2012) had significant order effects as well. 62 on the frequency of success for the FR treatment with and without rebates. Again, no clear rebate effect is readily apparent. Observations with and without rebates tend to both have high frequencies of success with many periods having a 100% success rate. Further, it appears that there is a convergence in the last four periods where both have a 100% success rate, including the last two binding periods. Figure 4-21 Frequency of Success for Fixed Size Treatments (Part 1 and 2 Data) 63 Figure 4-22 Frequency of Success for Fixed Size Treatments (Only Part 2 Data) 64 Figure 4-23 Frequency of Success for Fixed Historical Treatment (with and without Rebates) 65 Figure 4-24 Frequency of Success for Fixed Reliability Treatment (with and without Rebate) 66 67 4.6 Sizing of the Delivery System Once more, using data collected from Kaplan et al. (2012), insight into possible rebate effects is granted.13 Figure 4-25 illustrates data on the size of the delivery system in the ER treatment with and without rebates. In earlier periods, the observations without rebates tend to show larger sizes of the delivery system. However, as the periods progress, sizing of the system began to shrink. Conversely, observations containing rebates tend to have much larger systems across all the periods. It is apparent from this comparison that rebates have a clear impact on the sizing of the delivery system. As such, a deeper statistical analysis will explore this impact more thoroughly in the following chapter. 13 Again, data from Part 2 only is in this analysis due to order effects found in Kaplan et al. (2012). Figure 4-25 Size of Delivery System for Endogenous Reliability Treatment (with and without Rebates) 68 69 4.7 Summary Over the course of this chapter, an exploratory descriptive analysis of possible session, treatment, order, and rebate effects in the experiment for this thesis took place. Survey results were quantified and illustrated as well as used to test for systematic differences amongst the subjects across sessions. Results largely show that there were no differences. Further preliminary examinations of the data reveal possible order effects. Clear separations of observations between Part 1 and 2 of the data were discovered much of the time. Further, by utilizing data collected in Kaplan et al. (2012), an investigation into possible rebate effects was possible. In the FH treatment, observations where subjects were not offered a rebate tended to unexpectedly outperform observations where subjects were. The examination of the FR treatment, however, told a different story. In earlier periods, the observations that did not contain rebates tended to have higher frequencies of success.14 However, in the later periods both sets of observations, with and without rebates, converged to have 100% success rates. On the other hand, potential rebate effects were much more pronounced in the ER treatment. The sizes of the delivery system across all the periods were consistently larger for observations that contained rebates. Overall, the results suggest that rebate and order effects are indeed present. Therefore, a much more robust statistical analysis will take place in the following chapter to estimate the true impacts of these effects. 14 Referencing Figure 4-24 due to probable order effects. 70 Chapter 5 EMPIRICAL ANALYSIS 5.1 Introduction The empirical analysis performed in this thesis examines possible rebate and order effects that potentially influence the decision making of subjects in the experiment conducted for this study. This analysis utilizes a series of generalized least squares (GLS) regressions to identify possible effects on the percentage change of the deviation between subject WTP and total contributions within a period as well as endogenous sizing of the systems and the probability of successfully building fixed size systems. This approach is possible given the strictly exogenous nature of the experimental data. Additionally, period fixed effects are incorporated into various models to control for any unobserved factors, such as subject learning over time. Pair-wise F-tests are performed to statistically test whether the estimated treatment effects differ across FH, FR, and ER as well as for joint significance. In the following sections, a robust statistical analysis identifying possible order and rebate effects is presented. Section 5.2 discusses the various dependent and control variables used in this analysis as well as statistical methods. In section 5.3, analysis of order effects is conducted to identify potential bias in observations from early parts of the experiment sessions. Section 5.4 examines rebate effects on the probability of a fixed sized system being built, the size of the system when determined endogenously, and the deviation between subject WTP and contributions in percentage terms (i.e. (WTP- 71 Contribution)/WTP). Lastly, Section 5.5 provides a summary of the results as well as concluding remarks. 5.2 Empirical Models and Methodology In order to estimate potential order, rebate, and treatment effects, a series of generalized least squares (GLS) regressions are performed with Prais-Winsten transformations, using robust heteroskedasticity and autocorrelation adjusted standard errors. This approach is possible given the strictly exogenous nature of these data gathered for the study (i.e. the present error is uncorrelated with past, present, and future realizations of the treatments). Additionally, treatment binary variables FH, FR, and ER are used in the models to estimate treatment effects as they apply. The intercept term in each regression was removed in order to allow for pair-wise treatment comparisons. Ftests provide statistical evidence on whether the estimated effects differ across FH, FR, and ER. The empirical models examining order and rebate effects evaluate whether these effects are common to all treatments or are more pronounced in some treatments relative to others by incorporating interaction terms between these effects and the treatment. Ftests on a set of joint hypotheses based on these effects and their interactions with treatments are also performed in the analysis. Additionally, period fixed effects are considered to control for any unobserved factors that might affect all subjects the same, such as learning how to play the game over consecutive periods. This differs from the 72 type of learning that we would expect to see in relation to order effects, where subjects are simply tying to learn the game itself. The dependent variables of interest denoted in the empirical models presented below by y1t, y2t, and y3t, are WTPCONT, BUILT and SIZE respectively at time t. WTPCONT is the deviation between subject WTP and contributions divided by WTP. SIZE is the size of the delivery system when determined endogenously and BUILT is the probability of successfully building the fixed sized system. The control variables used throughout the analysis include: Rebate, Part, Period, FH, FR, and ER. Rebate is a binary variable that has a value of 1 if rebates are offered in the observation. Part indicates if the observation occurred in Part 2 by assuming a value of 1, 0 for Part 1. FR, ER, and FH are binary variables for each of the treatments: Fixed Reliability (FR), Endogenous Reliability (ER), and Fixed Historical (FH). Lastly, Period is a combination of 11 binary variables that account for the 12 periods and as mentioned previously, control for unobserved factors, such as subject learning. These control variables are also used to create interaction variables, mentioned above. Further discussion of these interaction variables is provided below in the appropriate sections. This analysis also included an examination into binding effects to determine if subjects behaved differently in the binding periods (i.e. periods 3, 6, 9, and 12) relative to the other 8 periods. Table A-1 in Appendix G presents the findings of this analysis. The lack of binding effects leads to the ultimate exclusion of them in subsequent analysis on order and rebate effects. 73 5.3 Order Effects Experiment sessions consisted of two parts to control for systematic individualistic characteristics (see for example Mitani and Flores (2009)). Although, statistically testing for order effects is not theoretically relevant to the conceptual framework of the treatments groups or the associated hypothesis testing, order can potentially confound results. Statistical inferences drawn from data with order effects may be biased. In the previous chapter, an exploratory descriptive analysis discovered clear separations of the observations between Part 1 and 2 much of the time. Therefore, it is critical to test if order effects are present, and if they are, take action to mitigate its effect. 5.3.1 Order Effects on WTPCONT The models shown in Equations 5-1 through 5-4 estimate the influence of order effects on WTPCONT. The control variables in Equations 5-1 and 5-2 are Part, FR, and FH, with the latter containing period fixed effects.15 These first two models estimating the impact that Part has on WTPCONT will grant us an encompassing view of subject contributing behaviors across both parts. Equations 5-3 and 5-4 examine order effect by treatment by adding the interaction variables PartFR and PartFH, where each term has a value of 1 if the observation is in Part 2 of the specified treatment and 0 otherwise. 15 ER is not included because only data from Part 2 were collected for this treatment due to computer malfunctions and an inability to conduct additional sessions given a limited subject pool. 74 y1it = B1Partit + B2FRit + B3FHit + uit (5-1) y1it = B1Partit + B2FRit + B3FHit + B4Period_1it + … +B14Period_11it + uit (5-2) y1it = B1Partit + B2FRit + B3FHit + B4PartFRit+B5PartFHit + uit (5-3) y1it= B1Partit + B2FRit + B3FHit + B4Period_1it + … +B14Period_11it + B15PartFRit + B16PartFHit + uit (5-4) Given results of the preliminary order effect investigation that took place in the previous chapter, it is entirely possible that order effects are present. The exploratory descriptive data analysis revealed inconsistent subject contributing behavior across Part 1 and Part 2. Therefore, it is reasonable to suspect that this effect will be statistically significant in a more robust analysis. As such, the regression results from Equations 5-1 and 5-2 should indicate that Part will have a significant impact on reducing WTPCONT as subjects learn the game. Further, the inclusion of PartFR and PartFH in Equations 5-3 and 5-4 should also have a statistically significant negative impact on WTPCONT. Pairwise F-tests on the treatments should reveal if the effects differ across treatments and if period fixed effects are joinly significant. Table 5-1 presents the regression results from Equations 5-1 through 5-4. In Equations 5-1 and 5-2, we notice that Part is estimated to reduce WTPCONT by roughly 9.8, even when controlling for period fixed effects. In other words, on average, the deviation between subject WTP and contributions is reduced by 9.8% in Part 2 of the experiment relative to Part 1. Thus, we see the gap between WTP and contributions shrinking. This result is statistically significant at the 1% significance level and is 75 presumably because the subjects typically understand the game by Part 2. We also see that FH has a higher average deviation than FR, which is theoretically understandable given the persistance of free-riding found in FH. Further, pair-wise comparison between the effects of FH and FR shows a difference between these treatments, in general, at the 1% significance level. When controlling for period fixed effects in Equation 5-2, these results do not change in a meaningful way. The results in Table 5-1 for Equations 5-3 and 5-4 continue to reveal the impact of order on subject contributing behavior. In these equations, PartFR and PartFH are added to test the impact that order has on these specific treatments. Here we see that PartFR has a statistically significant impact on reducing WTPCONT by roughly 16.5%. PartFH, on the other hand, was not shown to be statistically different from zero. Not surprising, this result suggests that order potentially has a greater effect on more complicated games. Pair-wise comparison of the coefficients of FH and FR reveal that there are no differences between the treatment effects in Part 1; however, further F-tests reveal statistically significant differences between these effects in Part 2. Again, period fixed effects were shown to be jointly significant in Equation 5-4, but the results do not change in a meaningful way. Overall, these results indicate that subjects are indeed learning and essentially Part 1 observations are not accurate portrayals of subject contributing behavior. Therefore, future analysis only considers Part 2 observations. Table 5-1 – Determinants of Order Effects on WTPCONT 76 77 5.4 Rebate Effects Much of the conceptual foundation of this thesis relies heavily on rebate effects. Rebates should have significant impact on contributing behavior due to the profit maximizing nature of the game. When offered a rebate, subjects can contribute more than their willingness to pay and still receive positive profits. If rebates are excluded from the equation, subjects may be more hesitant to contribute in excess for fear of lesser or even negative profits. Therefore, the inclusion of rebates should incentivize subjects to contribute more; thus reducing WTPCONT and increasing the probability of success and price formation efficiency. The following sections tests this notion by incorporating observations from Kaplan et al. (2012) in which subjects were offered a proportional rebate. 5.4.1 Rebate Effect on WTPCONT Equations 5-5 through 5-8 estimate the influence of rebates on subject contributing behavior. Equations 5-5 and 5-6 estimate overarching effects of rebates with Equation 5-6 accounting for period fixed effects. Equations 5-7 and 5-8 add the interaction terms RebateFR, RebateFH, and RebateER to test if rebate effects are more pronounced in some treatments relative to others. These interactions are binary variables that have a value of 1 if the observation is in the specified treatment where a rebate is offered, 0 otherwise. Equation 5-8 accounts for period fixed effects. 78 y1it = B1Rebateit + B2FRit + B3FHit + B4ERit + uit y1it = B1Rebateit + B2FRit + B3FHit + B4ERit + B5Period_1it (5-5) (5-6) +…+B15Period_11it + uit y1it = B1FRit + B2FHit + B3ERit + B4Rebate*FRit + B5Rebate*ERit (5-7) +B6Rebate*FHit+ uit y1it= B1FRit + B2FHit + B3ERit + B4Period_1it +…+B14Period_11it + (5-8) + B15Rebate*FRit + B16Rebate*ERit + B17Rebate*FHit + uit In Equations 5-5 and 5-6, Rebate should have a negative impact on WTPCONT given that subjects could contribute more than their maximum willingness to pay and still be able to see positive profits. In other words, there is a stronger incentive to finance the system. Further, the interactive terms RebateFR and RebateER in Equations 5-7 and 5-8 should have a negative impact on WTPCONT given that subjects have both a rebate and a higher incentive to contribute more to gain reliability. Moreover, RebateFH is not surmised to have a very profound impact on WTPCONT given the overall lack of incentives for subjects to contribute more in FH whether they are offered a rebate or not. Also, following each regression, pair-wise F-tests are performed to test whether treatment effects differ as well as for the joint significance of the period fixed effects. Table 5-2 presents the results of Equations 5-5 through 5-8. In Equations 5-5 and 5-6, we observe that Rebate has a strong predicted effect on WTPCONT by reducing it roughly 100%. These results are significant at the 1% significance level and are possible because subjects have the ability to contribute more than their WTP when rebates are available. Once again, the FH treatment is observed to have a higher average deviation 79 than the other treatments. However, we also notice that the coefficient on ER is insignificant. This result is desired given that we would expect the deviation between WTP and contributions to be zero given the incentives to contribute more in the ER treatment. When examining the F-tests we see that, in general, there are differences between all of the treatment effects. Fixed effects in Equation 5-6 were not found to be significant and they were not in Equation 5-8 either. The results for the model in Equation 5-7 continue to tell the story about the impact of rebates on subject contributing behavior in each of the treatments. Interaction variables RebateFR, RebateFH, and RebateER are added to the equations to capture the influence of rebates across treatment groups. In Equation 5-7, RebateER reduces WTPCONT by 202% and RebateFR reduces it by 73%, both at the 1% significance level. These results indicate that subjects are taking advantage of the ability to contribute more than their WTP when rebates are offered. Further, this is what we would expect to see given that subjects want reliability, plus they also face the risk of having their contributions excluded in the ER treatment during the endogenous sizing process. On the other hand, RebateFH is not estimated to be statistically different from zero. This result is expected, as subjects in the FH treatment have no real incentive to contribute more than their WTP. F-tests reveal that there are differences between all of the treatment effects when rebates are offered. Ultimately, we see that rebates allow differentiation in the treatments and they do indeed affect subject contributing behaviors. In essence, we are observing that subjects tend to contribute more than their WTP in the reliability pricing treatments when rebates are offered. Table 5-2 – Determinants of Rebate Effects on WTPCONT 80 81 5.4.2 Rebate Effects on Probability of Success The inclusion of rebates is likely to impact whether the fixed sized delivery systems are ultimately built given the profit maximizing nature of the game. As mentioned in previous sections, subjects may be more willing to contribute money if they know that some portion of the excess contributions is returned to them, opposed to just being discarded. As such, given the probable reduction of the deviation between WTP and contributions, it is fair to assume that the probability of the system being built is increased as a result. The descriptive results from Figures 4-23 and 4-24 in the previous chapter illustrate the frequency of success for fixed sized systems with and without rebates. Accordingly, in Figure 4-23 we observe no clear trend in the frequency of success for the FH treatment beyond a few sporadic periods where the no-rebate observations had an average 100% success rate. Further, in Figure 4-24 we saw that for the FR treatment, no-rebate observations tended to outperform observations with rebates until the later periods where a convergence of the two mechanisms occurred. Consequently, a clear rebate effect might not be especially profound when estimating rebate effects within the treatments or perhaps even in general. Equations 5-9 and 5-10 estimate the overall effects of rebates on the probability of successfully building fixed sized systems, with Equation 5-10 controlling for period fixed effects. Equations 5-11 and 5-12 add the interaction terms RebateFH and RebateFR to allow for a more a specific look into the impact that rebates have on BUILT in the FH and FR treatments with the latter equation accounting for period fixed effects. 82 y2it = B1Rebateit + B2FHit + B3FRit + uit (5-9) y2it = B1Rebateit + B2FHit + B3FRit + B4Period_1it +…+B14Period_11it + uit (5-10) y2it = B1Rebateit + B2FHit + B3FRit + B4Rebate*FHit + B5Rebate*FRit + uit (5-11) y2it = B1Rebateit + B2FHit + B3FRit + B4Rebate*FHit + B5Rebate*FRit + (5-12) B6Period_1it +…+B16Period_11it + uit Table 5-4 illustrates estimation results for Equations 5-9 through 5-12. In Equations 5-9 and 5-10, Rebates are not estimated to be statistically significant. Results for Equation 5-9, however, did estimate statistically significant differences between FH and FR with the FR treatment having a 92% chance of building the system; whereas FH was estimated to have an 80% probability of success. These results were significant at the 1% level. When controlling for period fixed effects in Equation 5-10, the probability of the system being built in the FH and FR treatment dropped to 69% and 82% respectively. This result suggests that subjects are, on average, continuing to learn as they play game over consecutive periods. The results for Equations 5-11 and 5-12 continue to estimate a lack of importance of rebates. RebateFR and RebateFH are not estimated to be statistically significant in either equation. When controlling for period fixed effects in Equations 5-12, we again observe a reduction in chances of success for the system being. FH drops from a 78% chance to a 68% chance and FR drops from 94% to 83%. Although the F-tests reveal differences between the treatments, rebates ultimately are not estimated to affect the success rates of the fixed sized systems being built. However, we would expect this result 83 for the FH treatment given that rebates still do not produce a strong enough incentive for subjects to contribute more than their WTP. Table 5-3 – Determinants of Fixed Size Probability of Success 84 85 5.4.3 Rebate Effects on SIZE When size of the delivery system is determined endogenously, rebates are likely to have a statistically significant impact. Once more, subjects conceivably have more of an incentive to finance the delivery system. Moreover, when it comes to endogenous sizing in the ER treatment, subjects are also mindful about the consequences of freeriding and becoming excluded from the system. Yet, it is still possible to fear negative returns. Recalling Figure 4-25 from the previous chapter, we observed that the sizing of the delivery system tended to be larger the majority of the time across all the periods with observations containing rebates. Therefore, it is very likely that the inclusion of Rebate will have an estimated coefficient that increases the size of the system when rebates are available. Equations 5-13 and 5-14 estimate this impact by explicitly focusing on Rebate, while the latter equation controls for period fixed effects. y3it = B1Rebateit +B2ERit+ uit (5-13) y3it = B1Rebateit + B2ERit+ B3Period_1it +…+B13Period_11it + uit (5-14) Table 5-5 illustrates the results from estimating Equations 5-13 and 5-14. Here we observe that Rebate has a predicted statistically significant positive impact on SIZE. Rebate has an estimated coefficient of 1.8 in both equations; thus indicating that systems are upwards of two units larger, on average, when rebates are available. These results support the theory that rebates influence subject contributing behavior. F-test also estimates statistical significance of the period fixed effects, which indicates further evidence of subjects learning over time. 86 Table 5-4 – Determinants of Endogenous Sizing Equation 5-13 Equation 5-14 Rebate 1.750* (0.638) 1.799* (0.669) Intercept 10.482* (0.638) 12.200* (0.430) 0.882 0.244 108 0.731 0.280 108 - 0.019** SIZE Adjusted R2 Correlation Coefficient RHO Observations p-values for F-tests Prob>F:I.periods_*= 0 Notes: Robust Standard Errors Reported in Parentheses. *, **, and *** indicate significance at the 1%, 5%, and 10% level, respectively. 88 5.5 Summary Over the course of this chapter, a rigorous analysis was conducted to identify the influence of order and rebate effects. According to the results, order had a statistically significant influence on contributing behavior given that the deviation between subject WTP and contributions was reduced by 9.8% in Part 2 of the experiment relative to Part 1. When examining the impact of order specifically in the FR treatment, the deviation between subject WTP and contributions is estimated to be reduced in Part 2 when compared to Part 1. Order effects in the FH treatment, on the other hand, are not found to be statistically significant; thus, suggesting that order plays a bigger role in more complex treatments. Overall, these results suggest that subjects are indeed learning and that essentially Part 1 observations do not accurately reveal subject contributing behaviors. Therefore, future analysis only considers data obtained in Part 2 of the experiment. Rebates are found to have a general effect on reducing the deviation between subject WTP and contributions by 100%. This is possible because subjects have the ability to contribute more than their WTP when rebates are offered. Further, the coefficient of ER is estimated to be insignificant. This result is desired given that we want the deviation between subject WTP and contributions to be zero. Subjects have both the incentive of greater benefits from increased reliability as well as the fear of being excluded from the system if lower ranked contributions are discarded. F-tests for treatment effects reveal that, in general, there are differences between all of the treatments. 89 An analysis of rebate effects across treatments reveals that rebates have a profound influence on subject contributing behavior when reliability pricing is offered given that subjects tend to contribute significantly more than their WTP. Conversely, rebates in the FH treatment were not found to be statistically significant. This result is expected given that rebates still do not provide enough incentive for subjects to contribute more than the WTP in this treatment. Nevertheless, F-tests reveal statistically significant differences in treatment effects across all the treatments when rebates are offered. Ultimately, we observe that rebates allow for differentiation in the treatments and they do indeed affect subject contributing behavior. When examining how treatments affect the probability of successfully building the fixed sized system, results indicate that the systems in the FR treatment have higher success rates than in the FH treatment. Additionally, results suggest that rebates are insignificant in general and within the treatment groups. Although F-tests reveal differences between the treatments, the inclusion of rebates does not seem to affect the probability of the system ultimately being built. However, this result is expected for the FH treatment given that rebates still do not produce a strong enough incentive for subjects to contribute more than their WTP. When the size of the system is determined endogenously, rebates are estimated to increase the size of the system upwards of two units. These results support the theory that rebates influence subject contributing behavior. F-test also estimates statistical significance of the period fixed effects, which indicates further evidence of subject learning over time. 90 Chapter 6 CONCLUSION California is currently in the midst of an ongoing water crisis. Agriculture in central California and urban centers in the southern parts of the state rely on the Sacramento-San Joaquin Delta to deliver water to them. However, the Delta as a water conveyance system is unsustainable given that the water supply is stochastic and shortages often occur. Further, the infrastructure’s inherent vulnerability to rising sea levels as well as to potential supply disruptions from natural disasters, such as earthquakes, is equally as alarming. If particular levees were damaged, large amounts of salt water could potentially flood into the Delta and cost California’s economy billions of dollars (Hanak et al. 2012). To make matters worse, local wildlife habitats are being destroyed and particular fish species in the Delta are being driven towards extinction because of water exports. If policy makers hope to mitigate this crisis and the impending collapse of California’s water supply system, they will first need to identify the next conveyance system or deal with the consequences of cutting off the flow of water to those south of the Delta. Then they will need to shift their focus to financing it. At a time when the condition of California’s fiscal house leaves much to be desired, alternative financing mechanisms utilizing private contributions for a new water conveyance system should be considered. This thesis evaluates alternative financing mechanisms for soliciting private contributions towards financing such a system in a laboratory setting. Reliability pricing 91 and endogenous sizing mechanisms are compared to fixed historical allocations of water resources in a private provisioning of a public threshold good game. The overall experiment simulates likely conditions that California will experience if such a project were attempted. The treatment groups and solicitation mechanisms in this study follow those in Kaplan et al. (2012), but also consider how rebates may play a role in their results. In order to assess the impact that the proportional rebate policy in Kaplan et al. (2012) has on contributions, sessions without the rebate are conducted and statistically compared by examining variations in contributions amongst the FH, FR, and ER treatment groups. The underlying theory revolves around the notion that the inclusion of rebates are likely to affect how individuals contribute when mechanisms such as pricing and availability are uncertain. In addition to rebate effects, order effects in these data are also considered since subjects take part in two different treatments in which they may not sufficiency understand how to play the game until the second part. The results from a preliminary order effects investigation suggest that subjects largely did not understand the game until Part 2. As such, a rigorous statistical analysis of order effects was conducted. According to the results, order has a statistically significant impact on contributing behavior given that the deviation between subject WTP and contributions is reduced in Part 2 relative to Part 1. The influence of order effects became more apparent when examining it across treatments. Results indicate that order effects in the FR treatment lead to an even greater reduction in the deviation between subject WTP and contribution. On the other hand, order effects were not significant in the FH 92 treatment, suggesting that order plays a greater role in games that are more complex. To mitigate the influence of order effects, only observations from Part 2 of the experiment sessions are considered in the empirical analysis of rebate effects. Initial observation of the data obtained in the experiments revealed possible rebate effects occurring within each of the treatment groups. According to the results for the FH treatment, no-rebate observations tended to unexpectedly have higher frequencies of success for building a fixed sized system than observations in which rebates were offered. The examination of the FR treatment, however, told a different story. In earlier periods, the no-rebate observations tended to have higher frequencies of success. However, in the later periods both sets of observations, with and without rebates, converged to have 100% success rates. On the other hand, potential rebate effects were much more pronounced in the ER treatment. The sizes of the delivery system across all the periods were consistently larger for observations that contained rebates. A more robust statistical analysis on rebates revealed that they generally influence contributing behavior by reducing the deviation between subject WTP and contributions by 100%. This is possible because subjects tend to contribute more than their WTP when rebates are offered. When examining the effects of rebates specifically within the different treatments, ER and FR are estimated to have even smaller deviations between subject WTP and contributions when rebates are offered. Conversely, rebates were not estimated to be statistically significant in the FH treatment. This result is unsurprising given that rebates still do not provide enough incentive for subjects to contribute more than their WTP in this treatment. When the size of the system is determined 93 endogenously, rebates are estimated to increase the size of the system upwards of two units. However, the inclusion of rebates does not seem to affect the probability of the system ultimately being built in the fixed sized treatments. This result coincides with study by Marks and Croson (1997) which suggests that the rate of successfully provisioning a public good with private contributions is not influenced by rebate policies. Future analysis of such financing mechanisms may include more information to each subject on the benefits of other subjects in their group. As suggested by Bangoli and Mckee (1997), this may illicit greater Pareto efficiency. Different rebate rules may also be explored. Perhaps a Pareto-improving utilization rebate rule similar to the one proposed by Marks and Croson (1998) might reveal greater reductions in the deviation between subject maximum willingness to pay and contributions. According to the results of their study, subject contributions under a utilization rebate policy tend to be greater than under proportional or no-rebate policies. As such, if the goal were to simply maximize contributions, this would be a relevant avenue to explore in future analysis. In any case, this study adds to the literature by considering incentives within an environment where self-sizing of threshold public goods and reliability pricing can potentially increase benefits while reducing free-ridership. Perhaps policy makers will one day consider such financing mechanisms and avert the impending collapse of California’s water supply system. 94 APPENDIX A. Instructions for Fixed Historical Treatment 95 (Fixed Historical Treatment – Player Type 1) Part II General Setting This part of the experiment works in nearly the same way as Part 1, except now you only have one unit of the good and you make only one contribution. Furthermore, there is no longer a queue. As such, if the system is built you receive a single amount of benefits. Benefits from using the Good The benefit you receive from your unit when the system is built is equal to £1,875 Please do not share this information with anyone else. Cost of Delivery Systems The total cost of building the delivery system is still£4,452.5 Submitting Your Contribution The contribution screen is slightly different from the one used in Part I. The interim and final reports differ slightly too. The screen shown at the front of the room shows the screen you will see when making your contribution. In the middle of the screen is where you enter your contribution. Once you enter a number click the OK button so the computer can recognize your entry. Once everyone has clicked OK or 30 seconds have expired the period will end. The screen now shown at the front of the room shows the interim report, including whether the system would be built or not, what your benefits would be, what you decided to contribute, and what your earnings would be. Once you are done reading the information on the screen, please click the OK button. Once everyone has clicked OK or 30 seconds have past the next period will begin. Once again, the final report provides similar information except it will count toward your overall earnings. Remember, the first 2 periods of each round are non-binding. The 3rd and last period of each round counts toward your overall earnings. Are there any questions? We will begin this part of the experiment now. Once it has concluded we will calculate you total earnings, convert them to $US and pay them to you before you leave. 96 (Fixed Historical Treatment – Player Type 2) Part II General Setting This part of the experiment works in nearly the same way as Part 1, except now you only have one unit of the good and you make only one contribution. Furthermore, there is no longer a queue. As such, if the system is built you receive a single amount of benefits. Benefits from using the Good The benefit you receive from your unit when the system is built is equal to £1,200 Please do not share this information with anyone else. Cost of Delivery Systems The total cost of building the delivery system is still£4,452.5 Submitting Your Contribution The contribution screen is slightly different from the one used in Part I. The interim and final reports differ slightly too. The screen shown at the front of the room shows the screen you will see when making your contribution. In the middle of the screen is where you enter your contribution. Once you enter a number click the OK button so the computer can recognize your entry. Once everyone has clicked OK or 30 seconds have expired the period will end. The screen now shown at the front of the room shows the interim report, including whether the system would be built or not, what your benefits would be, what you decided to contribute, and what your earnings would be. Once you are done reading the information on the screen, please click the OK button. Once everyone has clicked OK or 30 seconds have past the next period will begin. Once again, the final report provides similar information except it will count toward your overall earnings. Remember, the first 2 periods of each round are non-binding. The 3rd and last period of each round counts toward your overall earnings. Are there any questions? We will begin this part of the experiment now. Once it has concluded we will calculate you total earnings, convert them to $US and pay them to you before you leave. 97 (Fixed Historical Treatment – Player Type 3) Part II General Setting This part of the experiment works in nearly the same way as Part 1, except now you only have one unit of the good and you make only one contribution. Furthermore, there is no longer a queue. As such, if the system is built you receive a single amount of benefits. Benefits from using the Good The benefit you receive from your unit when the system is built is equal to £8,580 Please do not share this information with anyone else. Cost of Delivery Systems The total cost of building the delivery system is still£4,452.5 Submitting Your Contribution The contribution screen is slightly different from the one used in Part I. The interim and final reports differ slightly too. The screen shown at the front of the room shows the screen you will see when making your contribution. In the middle of the screen is where you enter your contribution. Once you enter a number click the OK button so the computer can recognize your entry. Once everyone has clicked OK or 30 seconds have expired the period will end. The screen now shown at the front of the room shows the interim report, including whether the system would be built or not, what your benefits would be, what you decided to contribute, and what your earnings would be. Once you are done reading the information on the screen, please click the OK button. Once everyone has clicked OK or 30 seconds have past the next period will begin. Once again, the final report provides similar information except it will count toward your overall earnings. Remember, the first 2 periods of each round are non-binding. The 3rd and last period of each round counts toward your overall earnings. Are there any questions? We will begin this part of the experiment now. Once it has concluded we will calculate you total earnings, convert them to $US and pay them to you before you leave. 98 (Fixed Historical Treatment – Player Type 4) Part II General Setting This part of the experiment works in nearly the same way as Part 1, except now you only have one unit of the good and you make only one contribution. Furthermore, there is no longer a queue. As such, if the system is built you receive a single amount of benefits. Benefits from using the Good The benefit you receive from your unit when the system is built is equal to £22,950 Please do not share this information with anyone else. Cost of Delivery Systems The total cost of building the delivery system is still£4,452.5 Submitting Your Contribution The contribution screen is slightly different from the one used in Part I. The interim and final reports differ slightly too. The screen shown at the front of the room shows the screen you will see when making your contribution. In the middle of the screen is where you enter your contribution. Once you enter a number click the OK button so the computer can recognize your entry. Once everyone has clicked OK or 30 seconds have expired the period will end. The screen now shown at the front of the room shows the interim report, including whether the system would be built or not, what your benefits would be, what you decided to contribute, and what your earnings would be. Once you are done reading the information on the screen, please click the OK button. Once everyone has clicked OK or 30 seconds have past the next period will begin. Once again, the final report provides similar information except it will count toward your overall earnings. Remember, the first 2 periods of each round are non-binding. The 3rd and last period of each round counts toward your overall earnings. Are there any questions? We will begin this part of the experiment now. Once it has concluded we will calculate you total earnings, convert them to $US and pay them to you before you leave. 99 APPENDIX B. Instructions for Fixed Reliability Treatment 100 Instructions (Type 1 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £700 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In this part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods, each lasting 30 seconds. The first 2 periods of a round are non-binding and will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report containing information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round, showing you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 101 Individual 1 2 3 4 Units 3 5 2 3 You will play as Individual 1.During the experiment you will be making contributions for each unit separately. That is, each contribution corresponds to a single unit. Your number of contributions will be limited to the number of units you are allocated. That is, if you have 3 units you can make at most 3 contributions. System Size and Cost In the actual experiment you will contribute toward building a system that can deliver 13 units. This is sufficient for everyone to receive their units. The total cost of building the delivery system is £4,452.5. 102 Instructions (Type 2 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £700 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In this part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods, each lasting 30 seconds. The first 2 periods of a round are non-binding and will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report containing information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round, showing you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 103 Individual 1 2 3 4 Units 3 5 2 3 You will play as Individual 2.During the experiment you will be making contributions for each unit separately. That is, each contribution corresponds to a single unit. Your number of contributions will be limited to the number of units you are allocated. That is, if you have 3 units you can make at most 3 contributions. System Size and Cost In the actual experiment you will contribute toward building a system that can deliver 13 units. This is sufficient for everyone to receive their units. The total cost of building the delivery system is £4,452.5. 104 Instructions (Type 3 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £3400 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In this part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods, each lasting 30 seconds. The first 2 periods of a round are non-binding and will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report containing information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round, showing you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 105 Individual 1 2 3 4 Units 3 5 2 3 You will play as Individual 3.During the experiment you will be making contributions for each unit separately. That is, each contribution corresponds to a single unit. Your number of contributions will be limited to the number of units you are allocated. That is, if you have 3 units you can make at most 3 contributions. System Size and Cost In the actual experiment you will contribute toward building a system that can deliver 13 units. This is sufficient for everyone to receive their units. The total cost of building the delivery system is £4,452.5. 106 Instructions (Type 4 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £4000 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In this part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods, each lasting 30 seconds. The first 2 periods of a round are non-binding and will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report containing information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round, showing you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 107 Individual 1 2 3 4 Units 3 5 2 3 You will play as Individual 4.During the experiment you will be making contributions for each unit separately. That is, each contribution corresponds to a single unit. Your number of contributions will be limited to the number of units you are allocated. That is, if you have 3 units you can make at most 3 contributions. System Size and Cost In the actual experiment you will contribute toward building a system that can deliver 13 units. This is sufficient for everyone to receive their units. The total cost of building the delivery system is £4,452.5. Distributing Units without Contributions If the system is built, you will receive your units, regardless of whether your contribute £0, £1, or more for each unit. Delivery Queue The benefit you receive from obtaining those units in the system depends on where in a delivery queue your units are placed. If your units are in the front of the queue you receive your units first and receive higher benefits when those units are delivered to you. The further back in the queue your units are located the lower will be your benefits from them. The queue is divided into three classes. Class 1 is at the front of the queue, Class 2 is in the middle of the queue, and Class 3 is at the back of the queue. The following table shows you how many units are available in each delivery class. Class 1 2 3 Units 4 2 7 Your contributions for your units will be ranked among the contributions made by the other 3 people in your group and then allocated to the different classes such that the four highest ranked contributions in your group are in Class 1, the next two highest ranked contributions (the 5th and 6th highest) are in Class 2, and the remaining are in Class 3. In the event that more than one contribution is made at the same level by different players, then the contributions entered sooner will be ranked higher. If two or more contributions are entered simultaneously, then their relative rankings will be randomly assigned. 108 Again, the contributions you submit during the 3rd and last period in each round is binding and determines where you rank among all other contributions, where in the delivery queue your units are located, and ultimately your benefits for that round. Calculating your Earnings If your units are not delivered because the system could not be built due to insufficient funds, then you will not be assessed a contribution charge and you will have earned 0 lab dollars since you did not receive those units of the good. If the delivery system is built at the end of each round, your earnings will be calculated as follows. Earnings = benefits – contribution You earnings in each round will be added together at the end of the experiment and paid to you in cash. Determining Benefits We will now go over a few examples so you can see how to determine your benefits from the units you receive in the different classes. For these examples we will use the table below which is similar to the benefit table you will use during the experiment. Unit 1 2 3 Class 1 80 64 48 Class 2 60 48 36 Class 3 40 32 24 Example 1: At the end of a round, you have 3 deliverable units distributed across the classes as follows: Units 1 and 2 are located in Class 1, and Unit 3 is in Class 2. The benefits you will receive if the system is built are £80 + £64 = £144 for Units 1 and 2 in Class 1, and £36 for Unit 3 in Class 2for a total of £180. Here is another example. Example 2: At the end of another round, you have 3 deliverable units distributed as follows: Unit 1 is in Class 2 and Units 2, and 3 are in Class 3. The benefits you will receive if the system is built are £60 for Unit 1, in Class 2, and £32 + £24 = £56 for the Units 2, and 3 in Class 3, for a total of £116. Note: You receive the greatest benefit for a unit when it is in Class 1 and the lowest benefit when it is in Class 3. 109 Now locate the BLUE SHEET of paper in your folder. It shows you the benefits you will receive for each unit in each delivery class in the actual experiment if the system is built. Please take a moment to familiarize yourself with the information on the BLUE SHEET of paper. Do not share this information with anyone else. It is important that you are the only one who knows what your earnings will be if a large enough system is built. Submitting Your Contribution You will be submitting your contribution on the computer screen in front of you. The screenshot shown on the screen in the front of the room is identical to the screen you will see once the experiment begins. In the upper right hand corner is a clock that counts down from 30 seconds. Each period will last for 30 seconds. In the middle of the top of the screen you will see the period and the round. You will also see if the period is not binding or binding. Remember the 3rd and final period of a round is binding and counts toward you overall earnings. In the middle of the screen is where you will enter your contributions for your units. Suppose you have 3 units and want to contribute £100 for your first unit,£100 for your second unit, and £80 for your third. To enter these numbers click on the box next to the word Your Contribution. Enter £100 in the box and then press the OK button. Do the same for the second unit, and so on. If you do not click the OK button after each contribution, then your contribution will not be recognized by the computer. If your contribution is not recognized by the computer you will not receive any benefits for that unit if the system is built nor charged for a contribution. When contributing you will be limited in how much you can contribute overall toward the building on the delivery system. You will see this limit at the top of your blue sheet of paper. No one contribution or the total of all contributions may exceed this limit. If you wish to contribute to building the delivery system, then the smallest contribution you can make is £0. After that, you will be able to submit contributions in £0.5 increments. Furthermore, it is possible for you to receive negative earnings. For example, if your units are not located in Class 1, but you make your contributions assuming they are, then you will not receive your highest possible benefits from the use of that good. As such, if your contribution exceeds the benefits you do end up receiving, then this will result in negative earnings. If at the end of the session you have zero or negative earnings, you will still be paid your show-up fee. Once 30seconds have expired or everyone has entered their contributions by clicking their OK button the period will end. Each period begins with a new set of contributions 110 so if you do not like how much you contributed in one period; you will be able to change them in subsequent periods. PLEASE TAKE ANOTHER SECOND TO FAMILARIZE YOURSELF WITH THE BENEFIT TABLE ON THE BLUE SHEET OF PAPER. ALSO RECALL THAT THE COST OF BUILDING THE DELIVERY SYSTEM IS £4,452.5. The screenshot shown on the screen in the front of the room will appear after each of the first two periods of each round. This screen shows the interim report, which provides information for each class and the period. In each class you see the number of units that could be delivered in each class, your units in each class, the lowest contribution in each class, each of your contributions, its rank, and corresponding delivery class, whether the system would be built or not, what your total number of units across all classes would be, what your benefits would be, what your total contribution would be, and what your earnings would be if the system were to be built. Once you are done reading the information on the screen, please click the OK button. As before, once everyone has clicked OK or 30 seconds have passed the next period will begin. At the end of each round a similar profit display screen will appear as above, but this time the information shown will count toward your final payment. REMEMBER: THE BLUE SHEET OF PAPER SHOWS YOU HOW MUCH YOU WILL EARN FOR UNITS IN DIFFERENT DELIVERY CLASSES. DO NOT SHARE THIS INFORMATION. Are there any questions? We will begin this part of the experiment now. Once it has concluded we will go over the instructions for Part II. 111 APPENDIX C. Instructions for Endogenous Reliability Treatment 112 Instructions (Type 1 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £700 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In each part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods. Each period will last 30 seconds. The first 2 periods of a round are non-binding. In other words, your earnings in these non-binding periods will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report. This report contains information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round that shows you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 113 Individual Units 1 3 2 5 3 2 4 3 You are Individual 1 114 Instructions (Type 2 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £700 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In each part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods. Each period will last 30 seconds. The first 2 periods of a round are non-binding. In other words, your earnings in these non-binding periods will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report. This report contains information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round that shows you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 115 Individual Units 1 3 2 5 3 2 4 3 You are Individual 2 116 Instructions (Type 3 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £3400 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In each part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods. Each period will last 30 seconds. The first 2 periods of a round are non-binding. In other words, your earnings in these non-binding periods will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report. This report contains information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round that shows you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 117 Individual Units 1 3 2 5 3 2 4 3 You are Individual 3 118 Instructions (Type 4 players) Welcome You are about to participate in an experiment. If you follow these instructions carefully and make good decisions you can earn cash, which will be paid to you at the end of the session. The experiment will consist of two independent parts. Your earnings from each part will be added together to determine your overall earnings for the experiment. Your overall earnings in this experiment will be in “Lab dollars.” At the end of the experiment, Lab dollars (£) will be converted into US dollars, at the exchange rate of: $1US = £4000 During the entire experiment, communication of any kind is strictly prohibited. Communication between participants will lead to your exclusion from the experiment and the forfeit of all monetary earnings. Please raise your hand if you have any questions; a member of the research team will come to you and answer your questions privately. Part I General Setting You and 3 other individuals in the lab are in your group. Your group shares the use of a generic good. You receive benefits from the use of this good. A problem exists however. No delivery system currently exists to transport the good to you and everyone else in your group. You are being asked to contribute to the financing of this system. In each part of the experiment there will be 4 rounds in which you will be asked to contribute. Each round will have 3 periods. Each period will last 30 seconds. The first 2 periods of a round are non-binding. In other words, your earnings in these non-binding periods will not count toward your earnings in a round or in your overall earnings. Only your contributions in the third and last period of a round will be binding and count toward your earnings. After each of the first 2 periods of a round you will be given an interim report. This report contains information on your decisions and the outcomes given everybody’s decisions. After the last period of a round you will be given a final report for that round that shows you the results from that round including your earnings in lab dollars. Distribution of the Good Each of you is given a pre-determined number of units of the good. The table below shows you each individual’s number of units of the good. You each use these units in different ways and thus derive different levels of benefit from their use. 119 Individual Units 1 3 2 5 3 2 4 3 You are Individual 4 120 During the experiment you will be making contributions for each unit separately. That is, each contribution corresponds to a single unit. If you have 3 units you need to make 3 contributions. If you have 5 units you need to make 5 contributions. Determining the System Size The amount of lab dollars you will earn depends on the size of the system built. The size of the delivery system will be determined by the total contributions. The largest possible size is a 13 unit system. This is large enough for everyone in your group to get their units of the good. If the contributions added together meet or exceed the cost of building a 13 unit delivery system, it is built and everyone receives their benefits from each of their units. If the cost of a 13 unit system exceeds the contributions, then the computer ranks your contributions along with those from the other 3 individuals in your group, discards the lowest ranked contribution, and considers a system that is one unit smaller. If the cost of building a 12 unit system exceeds the contributions, then the computer discards the lowest ranked contribution among the remaining 12 contributions and considers a system that is one unit smaller, and so on. If a unit is discarded it is not delivered and you do not receive any benefits from its use. Determining Benefits The benefit you receive from your units also depends on where they are ranked among all contributions in your group and whether the system that is built is large enough to deliver your units. The four highest ranked contributions in your group are in Class 1, the next two highest ranked contributions (the 5th and 6th highest) are in Class 2, and the remaining seven units are in Class 3. If your units are in Class 1 you receive the highest benefits when those units are delivered to you. The lower the class the lower will be the benefits. The following table shows you how many units are available in each delivery class. Class Units 1 4 2 2 3 7 In the event that more than one contribution is made at the same level by different players, then the contributions entered sooner will be ranked higher. If two or more contributions are entered simultaneously, then their relative rankings will be randomly determined. Examples We will now go over a few examples so you can see how to determine your benefits from the units you receive in the different classes. For these examples we will use the table below which is similar to the benefit table you will use during the experiment. 121 Unit 1 2 3 Class 1 80 64 48 Class 2 60 48 36 Class 3 40 32 24 Example 1: At the end of a round, you have 3 deliverable units distributed across the classes as follows: Units 1 and 2 are located in Class 1, and Unit 3 is in Class 2. The benefits you will receive are £80 + £64 = £144 for Units 1 and 2 in Class 1, and £36 for Unit 3 in Class 2 for a total of £180. Example 2: At the end of another round, you have 3 deliverable units distributed as follows: Unit 1 is in Class 2 and Units 2, and 3 are in Class 3. The benefits you will receive are £60 for Unit 1, in Class B, and £32 + £24 = £56 for the Units 2, and 3 in Class 3, for a total of £116. Note: You receive the greatest benefit for a unit when it is in Class 1 and the lowest benefit when it is in Class 3. Now locate the PINK SHEET of paper in your folder. It shows you the benefits you will receive for each unit in each delivery class in the actual experiment if a system is built to deliver it to you. Note the benefit table on this sheet shows you the benefits you receive in each class for each unit you have. Do not share this information with anyone else. It is important that you are the only one who knows what your earnings will be if a large enough system is built. The cost for systems of different sizes is also on this sheet. Please take a moment to familiarize yourself with the information on the PINK SHEET of paper. Calculating your Earnings If a delivery system is built at the end of a round, your earnings will be calculated as follows. Earnings = benefits – contribution. You earnings in each round will be added together at the end of the experiment and paid to you in cash. Submitting Your Contribution The screenshot shown on the screen in the front of the room is identical to the screen you will see once the experiment begins. In the upper right hand corner is the clock that counts down from 30 seconds. In the middle of the top of the screen you will see the period and the round. You will also see if the period is not binding or binding. 122 In the middle of the screen is where you will enter your contributions for your units. To receive benefits for each unit you must enter an amount for each unit. Suppose you have 3 units and want to contribute £100 for your first unit,£100 for your second unit, and £80 for your third. To enter these numbers click on the box next to the word Your Contribution. Enter £100 and click the OK button. Repeat for the other entries. If you do not click the OK button your contribution will not be recognized by the computer and you will not receive benefits for the unit. If you wish to contribute to building the delivery system, then the smallest contribution you can make is £0. After that, you will be able to submit contributions in £0.5 increments. Also, you may not submit a contribution in excess of your benefits. This would suggest that you earn negative earnings. Distributing Units without Contributions If a system is built, then every unit in that system is delivered, regardless of whether someone contributes £0, £1, or more for a deliverable unit. PLEASE TAKE ANOTHER SECOND TO FAMILARIZE YOURSELF WITH THE BENEFIT TABLE ON THE PINK SHEET OF PAPER. The screenshot on the screen at the front of the room shows you the interim report used in this part of the experiment. In each class section you see the potential number of units that could be delivered given contributions, your quantity of units that would be delivered, your total contribution for units, and the lowest contribution in that class. In the middle of the screen you see information about the period. You see the total size of the system that would be built, what your total number of units across all classes would be, what your benefits would be, and what your earnings would be given the size of the system that is built. Below that you see each of your contributions, its rank, and corresponding delivery class. Once you are done reading the information on the report screen, please click the OK button. Once everyone has clicked OK or 30 seconds have passed the next period will begin. 123 APPENDIX D. Fixed Reliability Payout Schedules 124 Type 1 Players– FR Treatment Contribution Limit 1500 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 600 450 300 2 500 375 250 3 400 300 200 125 Type 2 Players– FR Treatment Contribution Limit 978 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 352 264 176 2 272 204 136 3 192 144 96 4 112 84 56 5 32 24 16 126 Type 3 Players– FR Treatment Contribution Limit 6864 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 4560 3420 2280 2 2304 1728 1152 127 Type 4 Players– FR Treatment Contribution Limit 18360 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 10440 7830 5220 2 6120 4590 3060 3 1800 1350 900 128 APPENDIX E. Endogenous Reliability Payout Schedules 129 Type 1 Players– ER Treatment Contribution Limit 1500 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 600 450 300 2 500 375 250 3 400 300 200 Cost of Delivery System of Different Sizes Size Cost Size Cost Size Cost 1 642.5 6 3105.0 11 4317.5 2 1235.0 7 3447.5 12 4410.0 3 1777.5 8 3740.0 13 4452.5 4 2270.0 9 3982.5 5 2712.5 10 4175.0 130 Type 2 Players – ER Treatment Contribution Limit 978 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 352 264 176 2 272 204 136 3 192 144 96 4 112 84 56 5 32 24 16 Cost of Delivery System of Different Sizes Size Cost Size Cost Size Cost 1 642.5 6 3105.0 11 4317.5 2 1235.0 7 3447.5 12 4410.0 3 1777.5 8 3740.0 13 4452.5 4 2270.0 9 3982.5 5 2712.5 10 4175.0 131 Type 3 Players– ER Treatment Contribution Limit 6864 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 4560 3420 2280 2 2304 1728 1152 Cost of Delivery System of Different Sizes Size Cost Size Cost Size Cost 1 642.5 6 3105.0 11 4317.5 2 1235.0 7 3447.5 12 4410.0 3 1777.5 8 3740.0 13 4452.5 4 2270.0 9 3982.5 5 2712.5 10 4175.0 132 Type 4 Players– ER Treatment Contribution Limit 18360 Benefit from Delivery Systems of Different Sizes Unit Class 1 Class 2 Class 3 1 10440 7830 5220 2 6120 4590 3060 3 1800 1350 900 Cost of Delivery System of Different Sizes Size Cost Size Cost Size Cost 1 642.5 6 3105.0 11 4317.5 2 1235.0 7 3447.5 12 4410.0 3 1777.5 8 3740.0 13 4452.5 4 2270.0 9 3982.5 5 2712.5 10 4175.0 133 APPENDIX F. 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