THREE ESSAYS ON THE INCENTIVE STRUCTURE OF ENERGY CONSERVATION PROGRAMS

Three Essays on the Incentive Structure of Energy Conservation Programs

Lang. In this manuscript, I address the question of whether strategic behavior by consumers could result in the erosion of energy savings in a demand response program. Understanding how the strategic behavior of consumers affects the net benefits from a demand response program has policy implications because of the increasing importance that demand response has come to play in utility load and reliability management during peak times. Using data from a large field experiment in California in 2007, we test the hypothesis that under a technology program, consumers' strategic behavior results in outcomes that are opposite what is obtainable under a program with price incentive or based of behavior. Chapter II is also an empirical study which explores how the preferences of consumers for large and heavy vehicles imposes costs on society in the form of external costs of accident. This chapter looks at how fleet changes in weight distribution due to corporate average fuel economy and consumer demand for heavier vehicles results in fatalities. It is important to understand how consumer behavior affects the accident rates so that one can obtain unbiased estimates of accident costs that go into benefit-cost analysis of the impact of regulations in automobiles. Chapter three addresses how unobserved heterogeneity and sorting affect the estimates of the consumer willingness to pay for reduction in future gasoline costs. This tradeoff is important to policy makers and manufactures because it could help explain why manufacturers fail to adopt technologies for which the fuel savings far outweigh the costs. The remainder of the abstract provides a more detailed outlines of the three essays.
Chapter 1 explores strategic behavior by consumers in demand response programs.
The chapter looks at how the confluences of consumer strategic behavior, technology and price incentives in demand response lead to conflicting outcomes. Demand response has become an important tool for utilities to manage load during peak periods. While the effects of demand response programs on peak load reductions are well studied and intuitive, assessments typically fail to recognize the potential for offpeak behavioral responses that may mitigate the total benefits of the program. Using smart meter consumption data on residential air conditioning units enrolled in a direct load control program, this paper examines changes in consumption prior to and after curtailment events. The manuscript rigorously estimates both peak and off peak changes in consumption to better understand net benefits of DR programs. We examine Pacific Gas and Electric's (PG&E) SmartAC program, which is designed to reduce peak cooling load by directly controlling air conditioning units of participants.
Usually, program evaluation uses the availability of a control group to obtain unbiased estimates of program impacts. However, we do not have the luxury of a control group in our data. Instead we estimate unit-specific non-linear consumption models and then compare load on event days to predicted load. Importantly, we use data from the summer 2007 training period from a stratified random sample of 294 participating AC units. In contrast to subsequent summers and normal DR designs, during the training period curtailment days were called for many different temperature levels, not just the hottest days. This aspect means we are not predicting out of sample, and we can have greater confidence in our econometric evidence. Our methodology is validated by a falsification test in which we find no changes in consumption during peak or off-peak times on non-curtailment days that match the temperature and timing profile of actual curtailment days.
Several key results emerge from this analysis. First, we confirm that the SmartAC program, like other DR and DLC programs, reduces peak load during event days. In this case, peak consumption was reduced 19% on average. However, we also find substantial increases in consumption in the hours preceding and the hours following an event by 8% and 7% respectively. Essentially, load is being displaced from peak to off-peak times. These behavioral changes mitigate the monetary benefits of the program by 41%.
Chapter II addresses the question of how much accident risks would change if consumers who purchase larger, heavier vehicles of the existing fleet where to behave strategically given regulatory constraints imposed by corporate average fuel economy.
The paper estimates both the risk of dying given a crash and the crash frequencies of different vehicles in the fleet. We use a unique data set that combines data from fatality analysis reporting system (FARS) and NASS 1 General Estimates Systems. The estimation strategy used corrects for selection bias due to moral hazard problems. The two equations are estimated simultaneously using simulated maximum likelihood without the need for exclusion restrictions (Green 2003(Green , 2007. This approach allows us to obtain estimates that are causal.
One of the main issues that have been left unanswered in earlier works is the existence of Peltzman-type moral hazard problems and endogeneity of vehicle choice. In the presence of Peltzman-type moral hazard problems, drivers in heavier vehicles will find it advantageous to change their behavior in ways that have opposite effect to regulations. From a public policy perspective if increasing the weight of a vehicle increases the probability of its being involved in collisions, then we might be interested in more than the impact of heavier vehicles conditional on a crash occurring. We find that increasing the weight of any vehicle increases the probability of it being the heavier vehicle in a collision and the probability of it being involved in a fatal accident. The external costs translate to about 38 cents/gallon of gasoline.
Chapter III explores how individual unobserved heterogeneity in tastes could lead to different customers sorting into different classes of fuel efficient vehicles and therefore affect estimates of consumer's ability to tradeoff vehicle costs and discounted future gasoline costs. The research question is important for several reasons. First, it is interesting from a theoretical basis if consumers make this trade off optimally. Many theoretical models in economics make the fundamental assumption that consumers equally weigh current and future events when making decisions today.
However, plenty empirical and laboratory evidence conclude the contrary. Second, Regulatory Impact Analyses (RIA) of regulations on energy efficiency standards usually find that the benefits of these programs are in many times larger than the costs, with the fuel savings over the life of the vehicle accounting for the majority of the benefits. However, if fuel savings are large relative to costs, then the question is why are manufacturers not incorporating these technologies in their product offerings? Therefore understanding energy paradox is critical for evaluating the standards and regulations so that policy makers can identify baseline for assessment in cost-benefit analyses.
In this paper, we contribute to the literature on Energy Paradox in Fuel Economy by providing empirical evidence that unobserved consumer heterogeneity could result in different consumers sorting into different classes of fuel efficient cars which results in consumers undervaluing fuel economy. Unlike existing literature in this topic, this paper accounts for sorting bias due unobserved heterogeneity by using a random coefficient logit with error components (Train and Winston 2007). We pair the random coefficient discrete choice model with a supply side model in which firms compete in Bertrand Nash fashion where price depends on elasticity of demand and marginal costs. With the random utility model, we can allow taste to vary across consumers. We treat the discounted operating costs and vehicle costs as random variables.
We find that a substantial portion of upper the 95% of households in our sample correctly value fuel economy (61%) as they are willing to pay $0.99 to reduce obtain a $1.00 discounted future gasoline costs over the lifetime of the vehicle. And 29% of the upper 95% overvalue fuel economy as they are willing to pay $1.57. These results are in contrast to those reported elsewhere by Alcott and Wozny (2009) but support results from the simulation study by Bento et al 2012 who find that not accounting for sorting bias and consumer heterogeneity could lead to a conclusion that consumers undervalue fuel economy.
viii ACKNOWLEDGMENTS I must acknowledge several individuals who taught, advised, and supported me in different ways in the last four years. Professor Jim Opaluch has been an outstanding advisor during this period. His thoughtfulness, insights and careful consideration have helped me through the graduate program, especially the dissertation process. I cannot express how grateful I am in words alone. I am eternally grateful for the opportunity that he has provided me.
I would like to express my sincere gratitude to Professor Corey Lang for his guidance and willingness to be part of my dissertation committee and involve me in some of his research. I learnt a great deal from working with Corey, and I am the better for it today. That I am able to complete my dissertation process, owes a lot him.
I have learned so much from Professor Hiro Uchida. I am really grateful for his insights and ideas as well as willingness to discuss research ideas. I gained a lot of economic intuition discussing with Hiro, and I am profoundly grateful for that. I am also grateful to Emi Uchida for all the help and guidance during my graduate program.
xiii LIST OF TABLES MANUSCRIPT 1: The Mitigating Effect of Strategic Behavior on the Net Benefits of a Direct Load Control Program

INTRODUCTION
The dissertation explores the potential effectiveness of government energy efficiency programs and regulations from both the producer and consumer perspectives. The last three decades has seen the deployment of various energy conservation policies as part of governments' energy policies. These energy efficiency programs are driven in part by the desire to reduce energy consumption, lower greenhouse gas (GHG) emissions in order to mitigate the impacts of climate change, reduce criteria air pollutants, and to provide affordable energy services. While it is widely acknowledged that there is still a large potential for energy and greenhouse gas savings, the design of effective policies to realize these potentials is challenging. For example, estimates from the International Energy Association (IEA 2001) suggests that over 34% of the expected carbon emissions under a scenario limiting the long term concentration of greenhouse gases could be obtained solely from direct end use efficiency measures alone.
However, achieving this target presupposes that individuals will invest in energy efficiency measures and firms will invest in innovations to commercialize energy efficient technologies.
Consumer decision making and/or behavior involving energy consumption and investment in energy efficiency projects have attracted increased scrutiny recently.
Policy design and evaluation have increasingly incorporated consumer behavioral responses to policy interventions. Given the inter-relationship between consumer behavior, energy and climate policy, it stands to reason that if consumers can be nudged to change their behavior and reduce their energy consumption or be more responsive to demand for weather induced changes in energy supply, we could 2 significantly reduce the cost of compliance to several policies. However, the general consensus is that consumers are generally not good optimizers with respect to the costs and benefits of energy conservation. Consumers generally place different life-cycle value on investments in energy efficiency than manufacturers and policymakers.
Behavioral economics offers insights and different perspectives regarding how consumers value energy efficiency products or regard energy conservation efforts.
Behavioral economics concepts, supported by anecdotal evidence from experimental economics suggests a set of reasons other than costs and benefits of why consumers are not good optimizers: consumers do not consider energy efficiency issues to be priority (work, family, healthcare, education and other family related matters are more important than energy efficiency; households exhibit preference and perceptual invariance in consumer choice situations; energy efficiency decision scenarios are complicated, with multiple options and difficult mathematical calculations; and people simply tend to procrastinate a lot (Kahneman andTversky. 1979, Dhar andGlazer1996;Abadie and Gay. 2006;Allcott andMullainathan 2010, DellaVigna 2009). Also households show significant differences in behavior which can affect energy consumption, suggesting that intervention strategies to promote sustainable behaviors should result in significant energy savings in the future.
If the foregoing is true, then we need to answer the following important questions: 1. As consumers invest in energy efficiency projects, they will obtain economics savings over the life of such projects, an important question is how consumers will utilize the economic savings over the lifetime of their investment from an energy efficient appliance?
3 2. What is the impact of strategic behavior by agents on the overall impact of energy conservation programs?
3. If changes in consumers' consumption patterns occur, producers are likely to adjust their production functions and what will be the effect on the overall social welfare?
4. Are the incentives in some energy policies such that they incentivize agents to behave in ways that are in conflict with the goals of regulations? Are these incentives such that could lead to unintended consequences? We use a falsification test in which we find no changes in consumption during peak or off-peak times on non-curtailment days that match the temperature and timing profile of actual curtailment days to validate our results. First, we confirm that the SmartAC program, like other DR and DLC programs, reduces peak load during event days. In this case, peak consumption was reduced 19% on average. However, we also find substantial increases in consumption in the hours preceding and the hours following an event by 8% and 7% respectively. Essentially, load is being displaced from peak to off-peak times. These behavioral changes mitigate the monetary benefits of the program by 41%.
In the second manuscript, we also explore how the interaction of consumer behavior and energy policy could result in unintended consequences by looking at how consumers' choices of vehicle weight could result in increased fatalities under regulatory constraints. In this manuscript, , we estimate the external costs of vehicle weight in traffic accidents using a random sample of police reported accidents by 5 estimating the number of fatally or seriously injured occupants in two vehicle crashes.
Our main challenge is that unobserved driver and occupant attributes could induce risky drivers to cluster around higher vehicles, and also cause them to switch across models as they re-optimize according to the conflicting incentives placed by gasoline and safety policies. This is because, there are interrelated human factors, which are not easily quantifiable, but are however related to vehicle weight and fatality/injury risk.
We use an estimation strategy that is robust enough to correct for such biases. The estimation strategy is semiparametric and based around baseline gamma density function. The estimation strategy is able to account for unobserved driver heterogeneity. Unlike earlier studies (Jacobsen 2013; Anderson and Auffhammer 2013) our unique data set and methodology allows us to adjust for the fact that heavier vehicles are involved in more fatal accidents than lighter vehicles ensuring that the coefficients of weight are causal. We find that it is vehicle weight dispersion rather than the absolute weight of vehicles involved in multiple vehicle crashes that is the key factor determining injury severity. In a two-vehicle crash involving a lighter vehicle and a heavier vehicle, the external costs imposed on the lighter vehicle increases with weight of the heavier vehicle and decreases with own weight.
Specifically, we find that increasing the weight of the heavier vehicle over the lighter vehicle by 1000 pounds increases the expected number of fatalities in the lighter vehicle by about 39%. Second, increasing the weight of any vehicle increases the probability of it being the heavier vehicle and increases the probability to be the heavier vehicle in a collision and the probability of it being involved in a fatal accident. The external costs translate to about 34 cents/gallon of gasoline.
6 Finally, we combine these empirical results with a theoretical framework develop simple tests to show that selection bias due to drivers of heavier vehicles involvement in more fatal/serious injury accidents. The paper contributes to two lines of literature.
First is the rich set of literature on individual choice of activity on self protection and averting behavior. The second area is the literature on the protective and aggressive effects of vehicle weight on occupant safety (NRC 2002;Peltzman 1975 This dissertation is divided into three main parts. The first part, this section provides a general introduction to the whole body of work. The second section is composed of three different chapters, with each chapter containing a different manuscript. The last section provides a general conclusion and tries to tie all the manuscript together.

Introduction
Many electricity utilities are challenged to meet demand during peak 2 consumption, usually during summer afternoons. Further, peak demand has been increasing at an average annual growth rate of 0.8% over the last 10 years (NERC 2013), heightening the need for solutions. Importing capacity from other areas and firing peak generators are two costly solutions; these can increase the cost of generation by $29.2-80/MWh. (EIA 2013). Alternatively, demand response (DR) programs offer the possibility of no or low cost reductions in peak load, and utilities and increasingly implementing these programs. While DR programs come in several forms, they are generically classed into two groups. Programs with price incentives-Time of Use (TOU), Critical Peak Pricing (CPP), Real Time Pricing (RTP) and Peak Time Pricing (PTR); and technology only programs with no price incentive-direct load control (DLC) programs in which the utility can control usage of appliances for a few hours per day during critical event days.
In general, all these programs seek to reduce peak load 3 by changing consumption prices or offering incentives to consumers. Impact evaluations have demonstrated large benefits of DR programs (e.g., Herter 2007, Faruiqui and George 2002, Crew et al. 1995, Matsukawa 2001, Binswanger 2001, Berkout et al. 2000, Gillingham et al. 2013, and comparison of load reduction during event hours show that DLC programs are more effective than programs with time-varying price structures (Wolak 2011, Newsham et al 2010. However most of these assessments tend to only examine benefits in terms of peak reductions, thereby ignoring behavioral responses that could be happening in technology only and potentially overestimating the total benefits. Although behavioral responses in programs with time-varying price incentives have been looked at in terms of load shifting, the closely related concept of precooling and snapback (two types of behavioral responses in technology only) less so (Newsham et al 2010, Jessoe and Rapson 2014, Wolak 2011. The purpose of this paper is to rigorously estimate both peak and off peak changes in consumption to better understand net benefits of DLC programs with no price incentive or behavioral aspect. We examine Pacific Gas and Electric's (PG&E) SmartAC program, which is designed to reduce peak cooling load by directly controlling air conditioning units of participants.
We use data from a stratified random sample of 294 participating AC units.
Because there is no data for a control group, we estimate unit-specific non-linear consumption models and then compare load on event days to predicted load. Importantly, we use data from the summer 2007 training period. In contrast to subsequent summers and normal DR designs, during the training period curtailment days were called for many different temperature levels, not just the hottest days. This aspect means we are not predicting out of sample, and we can have greater confidence in our econometric evidence. Our methodology is validated by a falsification test in which we find no changes in consumption during peak or off-peak times on noncurtailment days that match the temperature and timing profile of actual curtailment days.
Several key results emerge from our analysis. First, we confirm that the SmartAC program, like other DR and DLC programs, reduces peak load during event days. In this case, peak consumption was reduced 19% on average. However, we also find substantial increases in consumption in the hours preceding and the hours following an event by 8% and 7% respectively. Essentially, load is being displaced from peak to off-peak times. These behavioral changes mitigate the monetary benefits of the program by 41%.
The main contribution of this paper is to show DR energy policies can lead to unintended consequences. We contribute to the emerging body of work on the perverse incentives in energy policies (e.g., Fowlie 2009, Davis and Kahn 2010, Goulder and Stavins 2011. Particularly relevant to this paper are works by Holladay et al. (2013), and Jessoe and Rapson (2014). Holladay et al. (2013) examine changes in energy production when media outlets relay emergency calls from utilities for electricity reduction during off-peak hours on curtailment days. They estimate that behavioral responses lead to an increase in generation cost of about $43.70/MWh to $61.70/MWh in the late morning and early evening on emergency days. We estimate a smaller increase in generation cost, around $21/MWh, but the results largely corroborate each other. In contrast, to Jessoe and Rapson (2014) who examine the added benefit of load reduction during peak hours on non-event days due to learning, we look at behavioral responses on curtailment days in non-event hours in a technology only program.

13
Background on the SmartAC Program PG&E's SmartAC program is a DLC program designed to reduce participating households cooling load during peak load times. The program works by directly controlling air conditioning during peak hours on designated curtailment days.
Curtailment events can only occur between the hours of 11 am to 7 pm from May 1 to October 31 and only for a total of six hours per day and for no more than 100 hours per cooling season. Before and after each event, the customer has complete control over their AC unit(s).
Typically, curtailment days are called when system load is expected to be burdensome, usually the hottest days of the year. The California Independent System Operator (ISO) may declare a system emergency when an electric-resource generation facility reaches or exceeds a certain heat rate (usually heat rates of 15,000 British thermal units per kW).However, PG&E can also call events to test the devices and for other discretionary reasons such as transmission or distribution system overload. The Appendix gives a more detailed description of the process of initiating a control event.
In contrast to the normal objective of the program, summer 2007 was a training period, and curtailment days were called on days with a variety of temperatures, not just the hottest days of the year. The inclusion of typical summer temperature days is important because it allows the utility to test the operational performance of the control devices.
The SmartAC Program uses paging signals to reduce cooling load of enrolled air conditioning units during times of peak system demand. The control devices are either programmable communicating thermostats (PCTs) and/or direct load control adaptive switches (switches). Both technologies receive signals through a paging 14 device but differ by how they lower air conditioning load. Unlike the adaptive switch control devices, the thermostats provide additional functionality to participants.
Demand reduction during curtailment events are achieved by either adjusting thermostat temperature set points or limiting the duty cycles of switches in the units.
The PCTs implement load reduction by increasing the cooling set point temperature on the thermostat controls when an event signal is received. Increasing the PCT set point ensures that temperature increases are equitably distributed across the population irrespective of house, occupant temperature preference and air conditioner attributes.
The switches on the other hand, reduce air conditioner load by directly controlling how the unit's compressor operates. 4 The SmartAC program was structured such that 70% of the program participants had control switches and 30% smart thermostats.
Customers with either device can only opt out of an event by either calling a toll-free number or accessing the program website 5 . There were two schedules by which load was reduced for those households with PCTs, and PG&E alternated between them. The first schedule set thermostats back one degree every other hour, resulting in a maximum setback of three degrees in each 6 hour curtailment event. The second schedule set thermostats back one degree every hour for the first four hours of the event and then held constant. This last strategy was done in an attempt to evenly spread the load reduction resulting in a gradual temperature decline as against the steep temperature from the first strategy. 4 Switches generally control air conditioner load by limiting the compressor run-time or duty cycle to a maximum over a period. When activated on curtailment days, the switches use adaptive algorithm to reduce air conditioner load to a percentage of the load on -learning days‖. The -learning days‖ are days with similar characteristics as potential curtailment days and are chosen by the program administrator. The observed duty cycle on these learning days provides an estimate of expected duty cycle on a curtailment day. 5 While participants had the option to opt of the program, this option was never exercised by the households (KEMA 2008).
For units with adaptive switches, load reduction during curtailment event was achieved by limiting compressor duty-cycle to a maximum amount in the curtailment period.
Using information from focus groups and similar program evaluation surveys in other locations, participants were recruited into the SmartAC program through direct mail campaigns. Participants into the SmartAC program were first enlisted in the spring of 2007 in San Joaquin County. However this has been expanded to include all service areas covered by the utility. As at the beginning of July 2007 when the first curtailment event was called, the program had enrolled over 2,857. The 297 households sampled for this evaluation, are located in the city of Stockton and it's surrounding areas (San Joaquin County). And as of August 2007, which was the system peak, there were 8,193 participants in the program, which was almost composed exclusively of residential customers with less than 1% commercial customers. The program has subsequently grown in popularity to such an extent that by January 2008, there were 26,000 households enrolled in the program with an additional 22,000 waiting to be supplied control technology. All program participants received a one-off incentive payment of $25 in return for up to 100 hours/year of load control. In addition, participants in the program evaluation group were given a maximum payment of $110, based on the number of questionnaires answered in a survey conducted at the completion of the program's first year. Also, participants in the PCT group were given the thermostats free, with a market value of $200 (KEMA, 2008).The goal of the program is to enroll a sufficient number of participants to achieve load reduction of 305 MW with over 95% coming from residential accounts.

Methodology
We develop a methodology that estimates air conditioner load usage as a function of weather control (temperature and humidity) and time of day, parameterizing each unit separately. Then we use these predictions to compare actual usage on curtailment days to expected usage. While there are several methods for estimating baseline consumption patterns and load comparisons, we use a regression-based baseline modeling approach. The wide scale adoption of smart grid meters and availability of high-resolution, hourly or 15-minute energy consumption data has contributed a great deal to improvements in regression-based baseline models (Armel et al. 2013;Newsham et al. 2011;Santin and Itard 2010;Santin et al. 2009). Mathieu et al. (2011 find that the regression-based baseline model performs better than most models used in evaluating demand response programs. Given that the regressions coefficients are from a least squares estimator, Mittelhammer et al. (2000) show that coefficients from these models should be unbiased and consistent as long as we have controlled for all the relevant predictor variables (Newsham et al 2011). In addition, the regression based model allows for customer-specific response estimates to be used separately for decision making or easily averaged to any degree of aggregation.
We model each air conditioner's baseline electric load as a function of time of the day, relative humidity, cooling degree days, heat index and a 631 index. By estimating parameters for each unit, we better capture unique occupant cooling preferences and differences in physical properties of residences. We use 15-minute-interval fixed effects, which captures the pattern of usage of each unit. Cooling degree days enters into the model as a 2-breakpoint demand function. 6 The first breakpoint is the unit's base or reference temperature, which marks the temperature above which air conditioning is used. The second breakpoint represents the temperatures point above which the air conditioner runs at 100% duty cycle. This specification allows for three different regimes of sensitivity to temperature changes. The heat index is a function of relative humidity and temperature and gives an idea how hot it given the relative humidity and actual air temperature. We use an equation that reproduces NOAA's heat index chart to estimate the heat index for all participating units. The 631 index is a weighted average of temperature and is estimated as 60% of a given day, 30% of prior day and 10% of two days prior average temperature readings (CAISO 2013) 7 .
Specifically, we estimate the baseline model using only non-curtailment days for each unit as follows: breakpoints, respectively. R ih is unit i's relative humidity at hour h, X ih is heat index for unit i at hour h and Y i is the 631 temperature index for unit i. The breakpoints are defined as follows: One drawback to using the regression-based approach is that out-of-sample predictions could perform poorly due to the parameterization. Regression-based baseline models assume that the functional relationship between load and weather (cooling degree-days) is the same on curtailment days as on the non-curtailment days (KEMA 2008). There are two reasons to be optimistic that this is not a large problem in our case. First, our empirical approach allows for non-linearity in the load-weather relationship, which should enable the upper tail of the distribution to be modeled better. Second, as explained in more detail in the next section, curtailment days were not temperature outliers, and so our out-of-sample weather has strong statistical overlap with the in-sample days.
From the parameters of the baseline models determined with non-curtailment days, we then predict demand on curtailment days. The difference between actual consumption and predicted consumption is the key statistic for determining the effect of the program for both hours during the event and hours before and after the event.

Data
This section details the multiple sources of data used for the analysis. The main dataset is the 15 minute interval consumption data covering the period June 12 through October 31, 2007.We additionally use weather data to model consumption and data on the marginal cost of generating 1MWh in the wholesale market to monetize the benefits of changes in consumption on curtailment days.

Electric Load Data
As part of the SmartAC program load impact assessment, air conditioner load loggers were installed on a sample of 352 participating units. These units were contained in a stratified random sample of 297 (146 PCTs and 151 switches) program participants from a population 2,917. 9 The sample was stratified by type of device (PCT or switch), total number of cooling tons from all units (less than four tons, four tons or more), and multiple units (yes or no). The sample design, and stratification as well as design sample sizes, and installed sample sizes are presented in Table A1 in the Appendix. We removed one unit for having an anomalously high load of 253 kW (over 10 times larger than the mean load) and four units for having 0 kW consumption throughout the study period. 53 units were dropped because of missing data, which left us with a final sample of 254 participants and 294 loggers. Figure A5 in the online appendix is a density plot of load with the dashed vertical lines representing the quartile positions. About fifty percent of the participating units' rated KW loads were less than 20KW with the lowest unit having a rated load of 2.8KW and the maximum unit with rated KW load of 35KW.
Electricity consumption for the participating units were recorded by the data loggers in 15-minute ampere readings, which recorded the average instantaneous amp 9 Some participants had more than one unit. 20 reading for each minute during that period. The amperage was converted to kW using the voltage levels measured at the units. The average instantaneous readings were then converted to kWh by summing each participating unit's KW consumption over the four 15 minute interval readings within that hour. We discarded data on weekends and holidays, as curtailment days are only called on normal weekdays. In total, we had over 3.9 million observations at the 15-minute-unit level. The mean KW consumption was 0.26KW with a standard deviation of 0.85, while the maximum KW value was 7.66.

Temperature Data
Daily average temperatures were obtained from the NOAA data web site. 10 While we do not know the location of each sample unit, PG&E mapped each unit to the nearest weather station and we use this to match each sample unit with weather data.
Figure2 is a plot of the density of the average daily temperature data used in the analysis with vertical lines representing the average daily temperature at which curtailment events were called. Due to the experimental nature of this program in 2007, many curtailment days were called for average heat days when peak load reductions were unlikely needed. Calling curtailment events on days with mild temperature is important because it ensures that our out-of-sample predictions will have strong statistical overlap with the in-sample days. In addition, it allows program administrators to obtain data on the performance of the technologies over the whole period of the cooling season and get a good performance of the technologies on learning days.

Marginal Cost of Generating Electricity
In order to monetize the net savings from the SmartAC program, we obtained data on the marginal cost of generating 1MWh of electricity from California ISO website. 11 We use the locational marginal pricing (LMP) at Stockton, CA. We believe that the conditions existing in 2007 in the California ISO (CAISO) means that the price data we use are indicative of both the relative scarcity and abundance of the product and the sensitivity of the demand to variations in price. The CAISO market uses balancing energy market in allocating energy to match load less than 10 minutes ahead forecasting scenarios. This market has two important features, namely an hourly, paidas-bid market that is conducted at the intertie points with neighboring control areas, and a five-minute, single price auction market for internal generators. Prices for the balancing energy market are settled at a market determined price that is set by the most expensive energy dispatched by the system in any given interval using a uniform price auction. The LMP reflects the energy value at a specific location at a specific time, fluctuating with time of day, and can surge significantly with extreme temperature and other unpredictable events. The LMP data we use is hourly. During peak load hours on curtailment days, the mean price is $100/MWh, with a maximum of $230/MWh and a minimum of $60/MWh. During off-peak times, the mean LMP value is $58/MWh. In addition, the coefficient estimates on the breakpoint parameters were highly statistically significant. 88.4% were significant at the 0.1% level, and the remaining were significant at either 5% or 10% level. In contrast, when the models are estimated with uniform base temperature values of 65°F and 72°F for the first and second breakpoints, respectively, slightly less than 65% of the coefficient estimates were significant at the 10% level. Thus, our grid search method and 15-minute fixed effects substantially improves model fit.

Changes in consumption on curtailment days
In Figure 4, we plot a single unit's load profile for a typical curtailment day and non curtailment on the same axes. The dark, solid lines represent actual load profile while the red, dashed lines are for predicted load on a typical curtailment day. The Figure shows a trough in between two peaks. The two peaks represent precooling and snapback loads, while the trough represents load reduction during peak period. Next, we quantify these figures. Table 1 presents the results of our analysis of estimated change in consumption before, during and after a curtailment event on a curtailment day. Results are presented for each of the 13 curtailment days as well as an overall mean. The values in parenthesis represent standard errors computed by dividing the standard deviation obtained from a t-test of the difference in means between predicted and observed load with the square root of the number of observations. All values are significant at the 1% level except for the amount of precooling on July 17, which is negative and not significant. Therefore, the value for July 17 might just be random noise.

24
The first two columns give the date and average daily temperature of each curtailment day. During the curtailment event, the results indicate that the average sample AC unit reduced load between 0.020 kWh/h to 0.754KWh/h, with an average reduction of 0.410 kWh across all curtailment days. (We normalize kWh reductions by per hour because the length of curtailment varies between four and six hours). These estimates are consistent with prior studies that have estimated the load impact of demand response programs and found values ranging from 0KWh/h to 0.75KWh/h (KEMA 2007). Taken together, these figures imply that participating residents are consuming between 25-35% more in the hours immediately before and after a curtailment event than they would ordinarily have consumed. These results quantify behavior taken by households to maintain comfort during curtailment days. Table 1 indicates that households behave strategically to pre-cool their homes before curtailment. We wanted to further investigate if the amount of pre-cooling increased over time, suggesting that customers were learning how to best pre-cool their homes to cope with curtailment. If there is a pattern of learning, then the later days in the summer will be more indicative of the amount of pre-cooling to expect as this program and others like it mature.

Learning over time
First, a comparison of the amount of precooling on the curtailment days that occur early in the summer reveals that that pre-cooling is increasing over time. Second, customers precool their homes more in the late, hotter summer days than curtailment days with lower temperature. This last fact implies that there exists a positive correlation between the amount of precooling and temperature. This make sense because one would more pre-cooling will be needed to maintain comfort levels. This last fact presents challenges in trying to identify the evidence of learning from temperature effects.
To help us decipher whether the larger precooling amount in later, hotter summer days are due to learning by customers, and not a reflection of those days having higher temperatures, we undertake additional analysis. First, we look at amount of precooling in late hot summers days that are non-curtailment but occurring after two consecutive curtailment days. And then compare this to the amount of precooling occurring in noncurtailment days following consecutive curtailment days in July. Second, we also look at the load shape a day before curtailment and a day after curtailment. However, given the limited number of curtailment days in our sample, these two approaches could not 26 conclusively reveal additional information about whether or not households learn to precool their homes over the course of the program 14 .
The direction and size of precooling and rebound we find are in line with figures reported elsewhere from experiments about using building thermal mass to reduce peak cooling load (Xu 2006, Xu et al 2004 ). However, unlike Jessoe and Rapson (2014) who found that households learn to conserve energy beyond the conservation periods during peak hours under demand response programs with price incentives and behavioral intervention; our results show that whatever learning (if it does occur) that occurs under a direct load control program without price incentives is in the opposite direction: households learn to erase gains made during peak periods through precooling of their homes given comfort constraints. The two conflicting results provide an insight into how consumers' behavior responds to non-monetary intervention such as technology and a monetary intervention.

Heterogeneity by technology and load
We are also interested in how curtailment affects units with different installed technologies (PCT vs. switch) and units with different loads. In addition, we examined whether conditional on temperature, the curtailment days that occur on dates later in the summer have positive coefficients which could indicate some evidence of learning. We estimated a regression similar to equation 1, but using all days (both curtailment and noncurtailment days) and including variables to account for curtailment event and number of prior curtailment days in the summer experienced by households. The results of such regressions are presented in the online appendix in Table 7. We see a positive coefficient for the interaction terms of hours prior to curtailment period and the number of consecutive prior curtailment events experienced. This is just an additional indication that learning could be occurring and should be explored additionally if one has additional data.
show the same general pattern of decreases in consumption during the event and increases in consumption before and after the event for both groups. However, the changes for the PCT group are larger in every stagemore reductions during the event and more pre-cooling and snapback. One possible explanation for the heterogeneous change in consumption between the PCT units relative to those with adaptive switches could be related to how the two technologies effect load reduction during curtailment days. Another reason could be that the larger changes in consumption by thermostat compared to the adaptive switches is a reflection of the higher variation in thermostat load compared to switches.

Falsification test
In order to alleviate concerns that the estimated changes in consumption during event days were a spurious result, we conducted a falsification test with proxy days treated as curtailment days. To implement this, we sought a match for each curtailment day that had the same average temperature, was within two days of the curtailment day, and was not a curtailment day itself. Matches meeting these criteria were found for eight of 13 curtailment days. Our definition of proxy days uses only non-holiday weekdays, and accounts for daily maximum and minimum temperature. We also attempted to define proxy days using humidity; however it was difficult matching on several covariates. We then re-estimated our baseline model excluding both the true curtailment days and the proxy days, and then calculated the difference between actual and expected consumption for the proxy days. The results, shown in Table 3, suggest no evidence of systematic increases or decreases in consumption during any of the three periods (before, during, and after the event). Magnitudes in all three columns tend to be smaller than the numbers in Table 1 and flip sign from day to day.
In addition, we relaxed the criteria for selecting the proxy days and used all noncurtailment days as proxy. Doing this allows us to relax the temperature control and possibly account for humidity. We performed a Monte Carlo exercise, first excluding each non-curtailment day and then estimate the model and predicting demand for that proxy day. We did this for each non-curtailment day in the sample (including weekends and public holidays) and plotted the average observed load and predicted load. The results are presented in Figure 7. These results validate our methodology and results.

Calculating peak load savings and net savings
We now examine the complete effect of the SmartAC program and the mitigating effect that pre-cooling and snapback have on total benefits. Column G presents the cost of conservation, which is calculated as the marginal cost of generating the extra electricity needed to meet the increased off-peak demand due to conservation during peak times. The values indicate that reductions during peak times cost the utilities an additional $21.07/MWh on average, with values ranging from $5.40/MWh to $43.41/MWh. Of course, this is cheaper than the cost of generation during peak times, so the net benefit is still positive. But it is important to know that the cost is not zero. These estimates are similar though smaller to those of 16 The values in column A were obtained by averaging hourly savings during the curtailment period for all units. Those in column B were obtained by first multiplying the hourly cost of generating 1MWh with the change in consumption at that hour, and thereafter computing the average value. In the next column, C, we add the precooling and snapback values to the change in consumption during the curtailment period. Finally, the values in column D were obtained by summing the product the change in consumption in each hour with the marginal cost of generating 1MWh during each hour. 17 The discrepancy between percentage reductions is due to the higher generation costs during peak times. Holladay et al. (2013), who estimate conservations costs ranging from $43.70/MWh to $61.70/MWh.
Despite the large reductions in net benefits from pre-cooling and snapback, the program still offers substantial benefits. Projecting the net savings onto the entire 8,193 customers enrolled in the program leads to an estimated $194,000 in utility bill savings. Further, the hotter days in the latter part of the summer yield the largest monetary savings, due both to larger kWh reductions and higher marginal prices. This result suggests that per-unit savings are likely to be larger for summers in which curtailment occurs mostly on very hot days.

Estimates of Environmental Impacts
We use the load reduction estimates from the program to estimate the overall environmental impacts of the programs. We make simplifying assumptions that increased consumption increases in the period before and after curtailment occurs when natural gas is at the margin and the consumption reductions during the curtailment period occur when coal is the margin. While these assumptions may be very simplistic, they ensure that whatever environmental impact we attribute to the program are lower bounds. In addition, it does reflect what is obtainable since natural gas is the non-base load source in the Western Interconnection area. We use the hourly marginal emissions intensities from Graff-Zivin, Kotchen and Mansur (2012) to multiply the changes in consumption to estimate the environmental impacts.
The result from the analysis is presented in columns C and F of Table 4. In Column C, we report the values of reduced emission due to load curtailment attributable to the program. Column C reports estimates of emissions reduction due to avoided or displaced generation from coal of about 0.78 metric tons of CO 2 e per unit during the curtailment period. Finally, in Column F, we report net environmental effects by aggregating across the periods: precooling, curtailment and snapback periods. The program results in a net reduction of pollution even after accounting for increased emissions due to behavioral response by households of 0.42 metric tons of CO 2 e per unit. Given the high intra-day volatility in the marginal fuel, the emissions reductions we attribute to the program are lower abound.

Program with Price Incentives
Programs with price incentives achieve peak load reduction by encouraging either the elimination of on-peak energy consumption activities or shifting of such activities to other periods through economic incentives. The economic incentives are usually in the form differential pricing in residential electricity rate structure based on time of delivery of electricity. That is, utilities encourage behavioral modifications by charging higher prices during periods of high system-wide demand and lower prices in other periods. Alternatively, utilities could compensate households for every kWh reduced during periods of high system-wide demand. These programs come in various 32 forms. While programs with price incentives have been effective at reducing peak load, their relative effectiveness depends largely on how the price incentives are structured. Generally, CPP programs seems to be very effective at reducing peak loads, whereas TOU less so (Newsham et al 2010). Two main reasons have been proffered to account for the higher on-peak load reduction of CPP programs compared to TOU programs: price and frequency of occurrence. The intuition is that in the absence of enabling technologies, households are more apt to respond to a CPP program given the small number of events that are called over each summer. However, under the TOU pricing, households have to change their behavior daily, which could be cumbersome. In addition, CPP programs have been shown to reduce energy during peak periods on non-event days, implying that behaviors formed on event days can be transferred to non-event days (Newsham et al 2010, Faruqui andSergici 2008).
PTR programs are less effective at reducing peak load than CPP programs even though they are similar (e.g., Newsham et al 2010). However, unlike CPP programs, PTR programs are designed to provide rebates on bills for reduction in peak load. This result is in line with evidence from Psychology which found that people respond more to -sticks‖ than -carrots‖ (Kahneman and Tversky 1984). This also suggests that behavior-based programs might make price-based policies more effective by making people more aware of potential savings

Behavior Based Programs
A basic tenet of behavior change is providing consumers with regular feedback on their energy consumption to take action and achieve greater levels of energy Allcott and Rogers use large data sets from a series of programs by OPOWER to study how providing households' feedback information on their energy consumptions induces conservation behavior. They find that such behavioral programs result in about 1.1 to 2.8% reduction in energy consumption relative to baselines.
Jessoe and Rapson 2014 use a field experiment to study the additional impact of highfrequency information about households' residential electricity usage on the price elasticity of demand in addition to household's response to price incentives. They find that households that were not provided information reduce peak demand by about 2-6% in response to price incentives alone. Additionally, they find that households that were provided with the high frequency information on price are more likely to reduce peak load by 8-22% over and above the amount due to price incentives alone.

Technology Only Programs
Technology only programs are designed to reduce peak load through the use of equipment to modify the operation of appliances during peak period (Newsham 2010, CAISO 2013, Faruqui and Wood 2008 Our findings indicate technology only programs result in larger load reductions during the curtailment periods. This is because technology only programs provide fewer margins for adjustment (Newsham et al 2010). This result is expected from an automated system because technology provides opportunity for participating households to choose their preferred mode of response once during the program lifetime and not be bothered to remember when curtailment events are due. However, if we account for precooling and rebound, the net savings are comparable to load reduction from other programs with price incentives.
Although, we find that the result of customers' behavioral response and the interaction of technology under a non-monetary intervention results in the diminution of conservation gains, the fact that customers may learn to precool their homes at higher temperatures could also provide policy benefits. First, the fact that households precool their homes under a DLC only program is an indication that residential households may be averse to relinquishing complete control of their air conditioners to utilities during summer peak times. Perhaps giving consumers back some type of control during curtailment hours could be one way of improving the performance as it could provide additional avenues for adjustment. Second, the evidence of precooling suggests that utilities should bundle some sort of time-varying price incentive into DLC program to make them more efficient.
Taken together, our results suggests a hybrid policy program that incorporate some form of automation and time-varying price structure with behavioral aspects will perform better and reduce the most amount of peak load while still maintaining consumer comfort. 35

Conclusion
Deregulation has greatly impacted the ability for the electricity industry in the US to make profit. Specifically, additional generation capacity is no longer guaranteed a rate of return. Because of the costliness of new capacity and the growing pressure peak demand places on the system, there has been increasing implementation of demand response programs as away to curb peak load. DR can also be applied for energy conservation in general. Recent literature has quantified the benefits of DR by measuring the amount of load reduced during peak periods, and the impacts are substantial. However, little work has been done to quantify the impact of behavioral responses to such programs. This paper seeks to contribute to that gap in the literature by examining the strategic response of participants in one such DLC demand response program and how that response may undermine its effectiveness.
Our results suggest that program participants increase consumption before and after event hours relative to the counterfactual. These results are intuitive, but are also of critical importance as DR policies move forward and the need to understand net benefits and forecast demand grows. For example, the SmartAC program, now in its seventh year, has over 100,000 enrolled customers. To be clear, the results still support DR and DLC programs as an effective way to curb peak demand; but, the true conservation cost is not zero.  Notes: The values in columns 3,4, and 5 were computed by averaging the difference between the predicted mean hourly demand and observed demand on curtailment days. The baseline model was estimated using hourly observations on non-curtailment days alone. Impacts are calculated for each 15minute interval. The curtailment day loads are estimates is the same for each 15-minute interval in the hour. The impacts are calculated separately for each observed 15-minute average. The average precooling and rebound values were computed by averaging the differences between the observed and predicted cooling loads in the three hours prior to and after the curtailment event respectively. Standard errors are in parenthesis. The standard errors were computed by dividing the standard deviation obtained from a t-test of the difference in means between predicted and observed loads with the number of observations. 44   This appendix provides results that supplement, but are not critical to the analysis in the main paper.  Figure A3 is a density plot of change in consumption from a Monte Carlo exercise in which we use each non-curtailment day as a proxy event day. We then estimate our model without that day, predict the consumption for that proxy event day and compute the change in consumption between the observed and predicted loads.
We repeat for these for all non curtailment days and plot the density in A3.   Figure A6 is a plot of deviation (the difference between predicted and observed loads) one day before and one day after curtailment event. Figure A7 is a plot of (the difference between predicted and observed loads) Table 1-A is the hourly change in consumption on all curtailment days studied.
The values were computed by subtracting the 15 minute observed load from the 15 minute estimated load. While the baseline model was estimated using hourly observations, the change in consumption was however calculated for each 15-minute interval. The estimated cooling load is the same for each 15-minute interval within each hour. All colored values are significant except on July 12.

Typical Curtailment Event Initiation and Process
Typical process for a control event involves the following steps:  The evaluators decide what day and time period should be used for the curtailment event based on the weather forecast, and the mix of curtailment and non-curtailment days that were already experienced.
 If the evaluators call the curtailment event, they alternate the two smart thermostat subgroups within the special monitoring group that received the population treatment and the alternative treatment. If the event is called by PG&E --i.e., the curtailment applies to all SmartAC participants and not just those in the special monitoring group --then the entire special monitoring group received the population treatment.
 The day prior to the curtailment event, the evaluators submit these instructions to the PG&E SmartAC Program staff who then relay them to Cannon Technologies which manages the Yukon system that allows the curtailment events to be initiated.
 Third party technology solution provider writes a computer program that will implement the control instructions requested by the evaluators. These programs are tested.
 PG&E's Transmission and Operations staff receive the evaluator instructions and initiate the curtailment events.

Description of Curtailment Events Involving the SmartAC Monitoring Group (SMG)
During the period June 07-October 07, PG&E initiated 13 curtailment events affecting Program participants from the SMG. Of these 13 events, all the program 50 participants were exposed to two of the curtailment events compared to the 13 that the SMG was exposed to: one in July 2007 and     Notes: The values in columns 3,4, and 5 were computed by averaging the difference between the predicted mean hourly demand and observed demand on curtailment days. The baseline model was estimated using hourly observations on non-curtailment days alone. Impacts are calculated for each 15-minute interval. The curtailment day loads are estimates is the same for each 15-minute interval in the hour. The impacts are calculated separately for each observed 15-minute average. The average precooling and rebound values were computed by averaging the differences between the observed and predicted cooling loads in the three hours prior to and after the curtailment event respectively.  Notes: *,**,***-Stars indicate significance effect at 0.10,0.05 and 0.01 levels respectively. The dependent variable is the average 15-minute interval cooling demand (kW) with the same explanatory variables as those used in the main specification. However, the regressions were estimated using GLS estimator and Huber-White robust standard error. The estimates presented here from an aggregate model.

Introduction
In a bid to promote efficiency improvements and reduce competitive impacts across the vehicle fleet, the corporate average fuel economy standards ( This strategy helps avoid a host of selection issues, since it allows weight to vary holding all other attributes of the vehicle fixed. Kahane (2003) also finds estimates in the order of -30% to 70% for the protective effect of increasing vehicle weight and cautions that his estimates for the heavier vehicles may be biased due to driver selection.
However, an important potential weakness in these approaches is the existence of Peltzman-type moral hazard problems and endogeneity of vehicle choice. In the presence of Peltzman-type moral hazard problems, drivers in heavier vehicles will find it advantageous to change their behavior in ways that have opposite effect (Pederson 2003, Peltzman 197, Risa 1992, 1994. The change in their risk behavior results in their being involved in more fatal crashes 20 . Given these, it is more likely that estimates of the causal effect of weight in literature are biased. In contrast, it is also possible that safety conscious drivers may buy heavier vehicles and drive more cautiously. Which of these effects dominates is an empirical question. There are two challenges with correcting for selection on moral hazard issues. The first issue is whether the incentive effect occurs at all. The second issue is whether the effect is large enough to completely offset the reduction in the probability of injury such that the number of injuries increases as the vehicle fleet becomes heavier and safer. Also from a public policy perspective if increasing the weight of a vehicle increases the probability of its being involved in collisions, then we might be interested in more than the impact of heavier vehicles conditional on a crash occurring.
We make three main contributions in this paper. First, we provide empirical The rest of the paper is organized as follows. The next section describes the theoretical framework. Section III presents the data, while section IV describes the specification. Section V presents the results. Section VI performs policy experiments, while section VII concludes.

Theoretical Background
The theoretical framework is an extension of the standard law and economics of the choice of care model that accounts for a policy variable (Liao and White 2004;Shavell 1979Shavell , 1982Cummins et al 2001). Road transport is generally recognized to be characterized by several externalities -accident, air pollution, congestion and other externalities (Parry et al 2004, Elvik 1994, Newberry 1988. The severity of an accident is influenced by speed and rate by traffic density. The effects of these two factors tend to work in opposite directions, as increased traffic levels are often associated with a reduction in average speed. The external effects arise anywhere the risk faced by one driver depends on the actions of other drivers. The externality arises from the fact that even a careful driver could be injured in an accident that is caused by another driver who was careless. On the other hand, the actions of the careful driver will lead to reduction of risks imposed on others. Defining externality as above makes it easy to express accident externality as a function of the dimension of behavioral choice that is faced by the agent. Generally, when externalities are present, equilibrium behavior is inefficient and the overall level of actions taken by society to prevent accidents will be inadequate. We assume that accidents are bilateral, drivers maximize expected utility with initial wealth w i , are risk averse with respect to effort, and dislike effort or care (e i ).
). There are two states of the world-the loss state with probability  and the no-loss state with probability   1 . The utility function is written as The utility is twice differentiable. These priori assumptions about the functions are quite common with models of traffic safety. First it is assumed that utility is increasing and strictly concave function in wealth and that the drivers' marginal utility is strictly decreasing in her effort to be careful. Where u w >0, u e <0, ee u <0 and u ww < 0 22 . The accident losses are assumed to be non-stochastic and consist of economic losses represented by l, (medical bills, lost earnings, general damages). There are other losses such as pain and suffering that are not fully covered and are represented by g.
Insurance is available at actuarially fair premiums and drivers are assumed to be fully insured. Hence the premium is given as Increasing own vehicle weight reduces injuries in this struck vehicle, but at the same time increases probability of injuries in other vehicles. Given the above assumptions, driver i maximizes the expected utility given below: with respect to weight of car, m 23 , where p m is the price per unit weight of car ,m.
The first order condition with respect to m gives the optimal choice of weight for each driver.
The sum in brackets is the marginal benefit of additional unit of expenditure on weight. The last term is the marginal cost of incurring an additional expenditure on weight. The above FOC shows that an increase in weight will result in lower injury risk reflected in the lower losses. A risk adverse driver who maximizes utility will choose the optimal vehicle weight (or other attribute) such that the marginal benefit of having that extra weight just equals the increased cost of weight. This benefit could be in the form of extra protection from an accident and the cost includes things like additional expenditure on gasoline. If individual drivers choose m to maximize utility, EU (m, e, w, l), the sufficient condition for optimality is 23 Another physical factor affecting injury likelihood is vehicle size, specifically the distance from the front of a vehicle to its occupant compartment. The longer this is, the lower the forces on the occupants, provided vehicle designers take advantage of the extra length. In theory the lighter weights of smaller cars could be offset by increasing the sizes of their front ends, keeping weight down by using materials like aluminum, plastic, or titanium. But this typically doesn't occur because such materials cost so much. lower the driver's optimal effort level leading to higher accident rates. This is an example of the rebound effect discussed in literature (Sorrel 2007). In effect, an increase in weight could lead to an increase in accident frequency given that the higher weight offers more protection. Anderson and Auffhammer (2013) argues that other than the behavioral response, the physical features of heavier vehicles could also induce them to be involved in more collisions.

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General results from partial equilibrium suggest that the behavior represented by the above FOC is inefficient. To fix ideas, compare this to a social optimum case in which there are two types of drivers i and j. The first order condition leads to a situation in which the driver i chooses the level of policy variable that is higher than the social optimum such that her injury risk decreases and that of the second car increases. The degree of concavity of u (w) and the convexity of the loss functions ensures existence of interior solutions. The FOC for this is shown below: If the risk is not fully internalized, the market will produce too large of the last part of equation in brackets. For each choice of m j , there is a socially optimal choice m i *(m j ) and vice versa. The overall social optimum will occur where the equations cross each other and we will have a Nash equilibrium such that m i >m* i and m j >m* j .
Without regulation of the fleet, the optimal action of i vehicle is to impose more risk on j and j's best action is to take more averting behavior. The Nash equilibrium could lead to too much risky behavior by one driver and subsequently more precautions being taken by other drivers at the social optimum. Whether or not this produces less risk than the social optimum is an econometric question. Also, rather than being symmetric, the nature of the resulting externality is asymmetric. Generally, the situation is such that we have one person (m i ) imposing the risks and another taking averting behavior (m j ). The asymmetric nature of the equilibrium is significant in that, we can regulate the actions of m i alone to restore the social optimum (Avery et al

2001).
To obtain a tractable form for the estimation equation, we make the following additional assumptions and simplifications. We can represent the external costs part of the accident as where α is the cost per unit of accident (statistical value of life or statistical value of injury), and F ij is the number of fatalities or serious injuries in the struck vehicle in a crash with vehicle j. F ij is attributable to several causal factors which we will discuss later. We will also make assumptions about the general form of F ij , the distribution of fatality or injury states. If X denote the causal factors determining F ij , then we have where f(x) is some regression function of the causal factors.

Data
The  Closely related to the vehicle miles travelled data is the number of registered vehicles by vehicle type at the state level and the public road length by state in miles. These were also obtained from highway statistics series of the Department of Transportation.

Demographic Characteristics
Additional information on state level demographic characteristics like per capita alcohol consumption, unemployment rate, population data, and investment on road covering the period 2008 to 2012 were also obtained from several sources. The Bureau.

Econometric Model
The number of fatally or seriously injured occupants, F ij , in the struck vehicle is a count variable and nonnegative. Therefore we are inclined to use count models for our estimation. However, we are faced with two main challenges. First crash severity, a function of the weight of the two vehicles and their relative velocities at the point of impact is not observed. It reflects the influence of the mass of both vehicles and the behavior of both drivers 27 . And there are several interrelated human factors, which are not easily quantifiable, but are however related to vehicle weight and crash severity. In effect, unobserved factors related to weight and crash severity may be correlated with the error terms thereby introducing endogeneity. Second, from the derived external cost of accident section 2, one obtains that drivers of heavier vehicles are induced to drive more dangerously given that it is now less costly for drivers to be in an accident.
Drivers will expend fewer resources to avoid being in an accident, and thus the number of accidents will increase. This is the well known moral hazard effect discussed by Peltzman (1975). Selection on moral hazard implies that drivers of heavier vehicles are more likely to be involved in more fatal accidents in which occupants of other vehicle are killed or seriously injured. In effect, drivers of heavier vehicles could be induced to drive more dangerously because of several factors that 80 are not clear 28 . If drivers of heavier vehicles in our sample are on average more likely to be involved in more severe crashes, then selection bias would be a problem.
To account for unobserved driver effects, while also correcting for possible selection on moral hazard, we use a two-step procedure similar to that developed by Terza Nelsusan (1994). In the first stage, we estimate the probability of being involved in an accident. These estimates are then plugged into the second stage negative binomial regression estimates of the injury severity equation.

The selection model is
where Ф is a standard normal distribution function. But we do not require it to be normal. Acc ist is number of crashes in state s by vehicle type i at time t 29 , vmt is the vehicle miles travelled, l ts 30 is the traffic density at time t in state s, X its represents all other covariates such as weight of the vehicles, per capita alcohol consumption, share of population using seat belts, several variables representing population distribution, rural and urban speed restrictions, measures for weather variables (number of days with snowfall greater than 1and 5 inch, number of days with temperature lower than 0 o F, number of days with precipitation greater than 5 inches), control for census division, and investment in road network.
28 It is also possible that safety conscious drivers could pick heavier vehicles because they are safer, in part explaining the reduction in fatality or injury rates of such vehicles. 29 It can also represent 1 if the vehicle was involved in a fatal crash and 0 otherwise, which is the well known Probit selection model. We tried both specifications and the results are similar. 30 The traffic density is defined as the ratio of VMT over length of public road.

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We specify the number of fatalities or serious injuries in each vehicle as a function of the driver characteristics, the characteristics of the two vehicles, the environment in which the accident took place, and other covariates of interest. The model is: The dependent (F ij ) variable is the number of occupant injuries or fatalities in the struck vehicle. m 1 , m 2 denote the curb weight of the struck and striking vehicles respectively, Restraint is a dummy indicating whether the driver of the struck vehicle properly used a seat belt and Airbag is also a dummy indicating whether a driver-side air bag was deployed, SPDL denotes the speed limit on the accident location. Others include all other independent variables like location of accident (rural or urban road), dummies indicating if the driver is a male and greater than 65 years, dummy for gender of the driver, dummy if the driver is less than 21, dummies for if alcohol and drug was involved. A series of three indicator variables is used to capture the impact of crash configuration on the injury risk, year and state effects. ε i, the unobserved heterogeneity, is normally distributed with mean zero and standard deviation ζ; and in our framework this includes distance from a hospital, mental state of the driver that day, did the driver surfer heart condition, etc. Given the presence of the unobserved heterogeneity in equation 7b, Green (1998Green ( , 2008 and Cameron and Trivedi (1990, 1998, 2005 show that the right hand side of equation 7b is Negative Binomial (NB) distributed.
Writing the models in this form allows us to operationalize the selection problem through the correlation of the ε and μ error terms. The unobservables, ε and μ are assumed jointly normally distributed, i.e.
Where 2   and 2   are the variances of the ε and μ respectively, ρ is the correlation between the error terms. Conditional on selection, the dependent variable is unlikely to be either Poisson or NB distributed which would allow estimation through usual methods. Drawing on the results of Terza (1995Terza ( , 1998 and Green 2008, the likelihood function for the full model is equivalent to the joint density function for the observed data. The full set of parameters (ζ ε ζ μ β, γ and ρ) can be estimated through a single step simultaneously using full information maximum likelihood (FIML) or simulated maximum likelihood (SML) procedures without the need for exclusion restrictions (Ripham et al 2003, Green 2008. We proceed by forming the loglikelihood from the joint density of the selection model (6a) and injury severity (6b) as Following Green (1997, the log-likelihood function is estimated with the use of a SML.

Model Performance
As a way of evaluating the preference of the selection model over the simple Poisson or NB specifications, we first estimated both models and then conduct hypothesis tests based on the estimated correlation parameter, ρ, as well as a likelihood ratio test. Tables 2 and 4 present the regression estimates for the models without selection and with selection respectively. The results suggest that there appears to be selection effects in the estimates, as shown by different coefficients in the conditional model. A Wald test for the existence of selection effect against a null hypothesis that the correlation coefficient is zero, i.e. H 0 : ρ=0 is rejected. The Wald test produces a test statistic of (−100.024)2 = 50.012 (with a p value of 0.000), which is larger than the critical value of 1.96 for a standard normal, leading to the rejection of the null hypothesis. A likelihood ratio test was computed as the difference between the log-likelihood for the full model with selection and log-likelihood for the model without selection effect (when ρ equals zero This value leads us to reject the simple Poisson or NB model while accepting the bivariate model that allows significant correlations across the two dimensions of the vehicle safety. The test statistics confirm the high statistical significance of the structural parameters ζ ε,, ζ μ and ρ. The negative sign on the correlation coefficient indicates that the latent factors which decrease the severity of injury in two vehicle crashes increase the probability of being involved in an accident, a situation that is consistent with the selection bias. The model with correlated counts is deemed the most appropriate one to use in this situation and is the basis for the policy simulations in a later section. Further, we also investigated the fit for the data generating process for the two count variables. Figures 1A and 1B show that the NB model is a better fit for the data generating processes. Figure 1A represents the mean-variance relationship for the accident frequency model while Figure 1B is the variance relationship for the severity model. The Poisson and Negative Binomial (NB) models both do a good job of predicting fatal accidents at low mean values. However, the Poisson model does not do a good job at mean values above 0.2 compared to the NB model. Figure 2 is plot of predicted probability of being involved in a fatal accident at different weight classes.
The figure suggests that as the weight increases, the probability of being involved in a fatal accident increases. The following sections discuss the results from the first stage and the second stages as well as policy simulations. Table 3 (Anderson 2008, White 2004, and Gayer 2004. Table 4  reduces the expected number of fatalities in the struck vehicle by a mere 21.8%. These results, though similar to those obtained by Anderson and Auffhammer (2013) and Jacobsen (2013), with the results from the control function and SML approaches being larger. The first column results are similar to those obtained by Anderson and Auffhammer (2013) Table 4 reports the results from second stage regression estimates as well as the regression without selection for comparison. The results reported are for only SML approach. The dependent variable in this case is the number of seriously injured occupants in the struck vehicle. Similarly we conduct Wald and likelihood ratio tests for the presence of selection effects and we reject the null hypothesis null hypothesis that ρ equals zero. Based on these tests, there does appear to be selection problem and the coefficients do change somewhat in the conditional model.

Serious Injury in Two-Vehicle collisions
The predicted sign for the struck vehicles are negative again since increasing the weight of the struck vehicle will reduce the incidence of serious injuries in the vehicle. Similarly, the sign of weight for the striking vehicle is positive. Increasing the 87 weight of the striking by a 1000 pound will lead to an increase in the expected number of seriously injured occupants by a statistically significant factor of 1.23. This is equivalent to a 23% increase in the expected number of serious injuries in the struck vehicle. While increasing the weight of the struck vehicle will decrease the expected number of occupant injuries by 0.84 with a t-value of 8.28. This is equivalent to a decrease in the expected number of seriously injured occupants by about 18%. Table 5 presents the results of alternative specification in which we replace the weight of the two vehicles with a new explanatory variable that depicts difference in weights. The difference in weights is defined as ratio of weight of the struck vehicle to that of the striking vehicle. The coefficient of the ratio of weights is more difficult to interpret. The coefficient is negative and significant at the 1% level. The coefficient of mass ratio is -1. 460 with a t value of 7.87.

Moral Hazard and Falsification Tests
We will discuss the moral hazard issues and falsification (Keuzenkamp and Magnus 1995;Buck and Lady 2005) together because the issue of identification of the parameters is strongly linked to the assemblage of data and the hypothesis to be tested: existence or absence of moral hazard. We employ a largely qualitative procedure to test for existence of moral hazard presented by the econometric model. The emphasis here is placed less on the quantitative measure, but rather on the sign partials of the risk factor (weight) in the two equations. This approach allows the hypothesis to be falsified regardless of identification. The approach to estimation of the model parameters provide us with a unique opportunity to in-principle test for behavioral 88 adaptation does take place. The intuition behind the test is that if weight has opposite signed partials in the two equations (probability of accident and probability of injury given and accident), it is reasonable to infer that behavioral adaptation will take place.
Since weight reduces the probability of occupant injuries, then if behavioral adaptation occurs, then the accident frequency will increase. Therefore, the differently signed partial effects of weight of the struck vehicle in the two stages of the estimation procedure (probability of accident and probability of occupant injury given that an accident has occurred) is a manifestation of moral hazard effects.
This reasoning is in line with Fridstrom 1999 andPeltzman 1975, who hypothesized that whenever an accident risk factor has differently signed partial effects in the accident frequency and occupant injury severity equations, that risk factor is subject to risk compensation. These two tests provide weak support for our selection on moral hazard hypothesis.
Next we discuss results of the falsification tests. If drivers of heavier vehicles dot not involve in more fatal accidents, then one should not see any additional effect of increased weight on injuries and fatalities on motorcyclists, bicyclist and pedestrian.
If we do find a statistically significant coefficient, then this is an indication that drivers do indulge in Peltzman type behavioral response, by exposing non occupants of vehicles to higher risk. To do this, we estimate another model for crashes between a vehicle and pedestrian, bicyclist and compare the coefficients. The results for the model are reported in Table 7. The coefficient of increasing the weight of vehicle is highly significant with a t-value of 10.23

Policy Simulations
The conceptual framework and econometric specification is able to predict qualitatively and quantitatively how the weight of a vehicle affects the fatalities and injuries in two vehicle crashes. Using the estimates from the model, one can simulate the responsiveness to a policy change that results in the change in weight distribution of the fleet. That is we can estimate the net effects of the safety gains to occupants of the heavier vehicle and safety losses that the increased weight imposes on the occupants of the struck vehicle. The model allows us to simulate how individual risks changes if they switch from driving a heavier vehicle to a lighter vehicle. For example, if a policy creates the incentives for households to switch to a heavier vehicle then weighted average risk of the heavier drivers will change because their probability of being involved in accidents would change to that of the heavier drivers. The intuition being that factors such age and number of people in a household can interact with vehicle choices.

Expected Externality Cost
The econometric results suggest that the expected accident cost is affected by both the probability of being the heavier vehicle in a collision and the expected weight  billion related injuries (statistical value of serious injury used is $577,500 34 ). The total externalities due to serious injury and death are $50.38 billion. These results are presented in Table 8.

External Costs due to Gasoline
We have estimated that the expected external cost of accident imposed on lighter vehicles is about $44.6 billion. The heavier vehicles also consume more fuel due to their larger weights. If we take the 2008 model year vehicle, a 500 pound increase in fleet weight is about 10.35%. Klier (2010) finds that the elasticity of fuel economy with respect to weight is about 0.67, translating to 6.93% lower fuel economy estimates in these vehicles. And given the long run fuel economy estimates for VMT of about -0.25, the effect on heavier vehicles is about 6.45% increases in gasoline consumption. We also assume 2008 model year fuel economy of 23.9, annual VMT of 15,000 miles, the annual fuel consumption of 628 gallons, average 2008 gasoline price of $2.5, a social cost of carbon of $20/ton, annual emissions per gallon of gasoline of 8,887gCO 2 /gallon. The additional costs due to increased gasoline consumption and emissions are $1.14 billion and $0.1 billion respectively for the whole US fleet. 32 http://www.dot.gov/sites/dot.gov/files/docs/VSL%20Guidance_2013.pdf 33 From data on US fleet trend, there has been a 500 pound increase US fleet over the same period to 2005. 34 The statistical value of serious injury is obtained by multiplying the Fraction of VSL for a serious injury (0.105)

Policy Approaches to External Accident Costs
Several policy approaches have been implemented to reduce the accident costs.
One approach is to tax drivers based on odometer readings, or through some other technological systems that are attached to vehicles. An optimal policy would involve per mile fees that differ on the basis of driver risk and vehicle attributes. Some other policies could also be gasoline tax, etc.

Vehicle miles traveled (VMT) fees
A VMT or per mile fee charges drivers based on the distance they drive.
Unlike the gasoline tax, the vmt fee is a true usage based fee because a driver is charged on actual use of the roadway. VMT fees generate more and stable revenue than a gasoline tax because under a gasoline tax, more fuel efficient vehicles will consume less gas for every distance covered than less fuel efficient vehicles. Under VMT fees, technology improvements might not affect the distribution of fleet weight or improve fleet fuel economy because it charges all vehicles the same flat rate. The fees could be uniform or differentiated based on vehicle class. A uniform vmt charge scheme is not efficient because it tends to levy too low a charge on vehicles with high external costs ( leads in low welfare gains) and levy too high a charge on vehicles with low external costs (high welfare gains). One way to overcome this is to design a differentiated vmt fee.
Under a differentiated mileage charge, a per-mile charge based on vehicle type is levied on each vehicle class. The resulting effects of charge in mileage is a function of own price-effect and cross-price effect from increases in other vehicle classes. The potential welfare gains from a differential mileage charge is lower than a gasoline tax because some of the reduced demand from one vehicle class will be offset from the 93 increased demand from another class (Parry 2003). Preliminary evidence from mileage fee initiatives in the United States and other countries recommend several ways to gather mileage data and charge fees. Significant privacy-related concerns from the public and cost challenges have been raised in applying mileage fees to passenger vehicles. Other challenges include how drives can contest charges, substantial start-up and administrative costs.

Gasoline Tax
The government can also impose a per unit tax on the amount of gasoline consumed by drivers. The intuition is that increased price will reduce the amount of driving which in turn leads to aggregate reduction in external costs. How external costs changes with improvements in fuel economy due to improved technology is not well understood. For example, downweighting could improve fuel economy but may make occupants less safe; although drivers might internalize this risk when making purchase decisions.
Cost of administration of a gasoline tax is very low compared to mileage based charge or fee. However, the costs associated with a gasoline tax are higher than an equivalently scaled mileage tax because of the larger substitutions effect from the gasoline tax. These costs are represented by reductions in consumer surplus under the aggregate demand curve for gasoline. Also, under the gasoline tax system, the permile charge differs across vehicles in proportion to their mpg ratings. Because of the positive correlation between gasoline per mile (from weight mpg relationship) and external costs of accidents, we expect gasoline tax reduce more external costs than an equivalently scaled uniform vmt fee system (Parry 2003).

Weight Based Tax through a "Pay at the Pump" Tax
Since the externality costs vary based on the weight/type of the vehicle, one way to internalize the externality is through a differentiated weight based tax. The tax could be levied ex ante or ex post as a liability. One approach for implementing the weight based tax ex ante could be through increased premium on liability insurance. Since several states require drivers to obtain liability insurance, it would be easy to increase the existing premiums to account for weight difference. Because insurance already charge higher premiums for riskier drivers, it would be possible to charge heavier vehicles more because they are more likely to be involved in more accidents and impose more risks on others. This weight based premium could be implemented in such a way that it interacts with factors such as driving record through a multiplicative factor as opposed to a fixed dollar increase related to weight. Charging heavier vehicles higher premiums based on their weight could encourage drivers of such vehicles to adjust their risk levels. The downside to the weight based tax is that some states allow drivers to carry no insurance at all and others to only carry up to $10,000 coverage (with most common coverage amount being $25,000). Given the existence of such limited liability insurance contracts, there are few incentives for insurance companies to set higher insurance premiums for heavier vehicles. Another issue is the large percentage of uninsured drivers in some states 35 .
In place of gasoline taxes, or fixed mileage charges, drivers could be charged a -Pay at the Pump‖ tax that accounts for both the weight of the vehicle and fuel consumption.
The -Pay at the Pump‖ tax (Khazoom1997) involves bundling the additional insurance 35 As much as 30% of uninsured drivers exist in some states (White 2004) 95 premium with gasoline purchases. -Pay at the Pump‖ levies a surcharge that reflects the externality per mile for each driver. Adding the surcharge will increase the gasoline price, which in turn may lead to some reduction in travel demand based on elasticity of driving to gasoline price changes. The -Pay at the Pump‖ policy ensures that the VMT will equal the optimal level and remove the distortions in resource allocation. Because the marginal cost facing the driver incorporates the full marginal exposure to risk. The -Pay at the Pump‖ surcharge that internalizes the total externality amounts to 34 c/gallons ($46.13 Billion/137.5 billion gallons of gasoline).
The advantages of the -Pay at the Pump‖ tax are that it ultimately reduces the externality cost by removing uninsured motorists from the road. In addition, in the short term it provides incentives for drivers to switch to more efficient vehicles because the resulting increase in gasoline price due to the surcharge induces driver to switch to more fuel efficient vehicles will pay less than her marginal exposure risks.
The converse is true for a low fuel efficient vehicle. Over time, the increase gasoline price (arising from surcharge) induces a demand for newer, lighter, more efficient vehicles by owners of heavier less efficient vehicles.

Conclusion
Following the introduction of weight indexed fuel efficiency standards which have resulted in an increase in the weight of the vehicle fleet; this study examines the effect on societal safety of consumers demand for heavier vehicles. We present empirical estimates of the effect of vehicle heavier fleet on accident costs that adequately accounts for selection bias due to moral hazard issues. We capture unobserved driver behavior as correlated outcomes between the two dimensions of 96 vehicle safety. We find that increasing the weight of heavier vehicles increases the expected of occupant fatalities by 50-64% while decreasing expected number of fatalities by 21-26%. Based on our estimates, we find that not accounting for selection bias due to moral hazard problems results in estimates of the effect of weight externality that are downwardly biased by as much as 14%.
We first develop a theoretical framework model of individual driver choice for vehicle weight and risk aversion behavior that leads to Nash equilibrium with a predominantly heavier fleet. Then we employ data on fatal and non-fatal injuries to estimate the external costs of additional weight in two vehicle crashes. Though difficult to estimate empirically, we apply an estimator with a lognormally distributed random effect for bivariate count processes to account for selection bias due to moral hazard. In addition, we use two different testing schemes to confirm the existence of selection bias due to moral hazard problems.
First, we find that increasing the weight of a vehicle will increase the probability being involved in an accident. This is because, increasing the weight of a vehicle will increase the probability of it being the heavier vehicle in an accident, offering better protection, so the driver will reduce care level 36 . We also find that factors which reduce the probability of having severe injuries in two vehicle crashes induce them to be involved in more collisions weakly confirming the presence of These values have serious policy implications. In theory, an efficient fleet could be achieved through a carefully calibrated tax based on careful cost-benefit analysis. However, such a tax policy may pose practical problems of implementation in terms of public acceptance and monitoring. Given that the societal costs of traffic accidents vary by weight, we also find that implementing a weight based tax such as a -Pay as You Pump‖ surcharge of the 38c/gallon could fully internalize the costs. A policy such as the proposed one will also lead to the adoption of more fuel efficient vehicles over time and reduction in the weight of the fleet. Notes: Figure 1A and 1B above are plots of variance against mean for two different models with exactly the same covariates. The figure was plotted by first creating 20 groups based on Poisson and negative binomial model and then computing the mean and variance for each group, and then finally plotting the mean-variance relationship.   Notes: a The full sample contains observations that have information on the injury outcome of drivers' involved in crashes between 2008 and 2012 and the vehicle was manufactured on or after 1980. b The regression sample contains observations from the full sample that does not have a missing value for any of the independent variables.  Notes: Heteroskedasticity-Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Figures and Tables
The stars indicate the level of significance. The dependent variable is an indicator variable equal to one if the vehicle was involved in an accident in which there was serious injury or fatality. a. The value reported is the difference between the coefficient of natural log of 100 Million vehicle miles travelled per state and that of traffic density.

Introduction
In the last few decades, the U.S. government has introduced several taxes and subsidies on the purchase of new vehicles that depend on the performance of vehicle fuel economy. The main driver for taxation of fuel economy is to correct externalities that result from fuel consumption. Cost-benefits analyses of these regulations require precise estimates of the consumer marginal willingness to pay (MWTP) for reduced discounted future fuel costs . While the literature on how consumer value fuel economy is well established (Dreyfus andViscusi 1995, Hausman 1979 Busse . In a differentiated product market such as automobiles, we expect that consumers with similar preferences for certain attributes will make similar choices if they have similar preferences and face similar constraints. In terms of fuel economy, consumers with high MWTP for discounted future gasoline costs will sort into fuel efficient vehicles while those with low MWTP will sort into inefficient vehicles. This sorting bias has implications for the ability of econometric models to recover the value of fuel economy and other attributes.
However, the sorting process also reveals information about consumer heterogeneity that can be used to evaluate how consumers value fuel economy.
In this paper, we contribute to the literature on Energy Paradox 38 by providing empirical evidence that unobserved consumer heterogeneity could result in different consumers sorting into different vehicle types. This implies that the coefficient on fuel economy also reflects values on other attributes that are associated with fuel economy.
Unlike existing literature in this topic, this paper accounts for sorting bias due to unobserved heterogeneity by using an -equilibrium sorting‖ 39 model that uses a mixture of distributions to characterize unobserved and observed heterogeneity among households (Train and Winston 2007). The -equilibrium sorting‖ model uses the properties of market equilibria, as well as information on the behavior of economic agents, to infer structural parameters that characterize agent heterogeneity. We pair the random coefficient discrete choice model with a supply side model in which firms compete in Bertrand Nash fashion with differentiated products; where price depends on both the elasticity of demand and costs of production. With the random utility model, we allow annual vehicle miles travelled, time preferences and expectations of gasoline prices to vary across consumers. We treat the discounted operating costs and vehicle costs as random variables. This allows us to obtain a distribution of households' preferences for fuel economy across the population. 38 Energy Paradox is defined as the disconnect between net present value estimates of energy conserving cost savings and what consumers actually pay on energy conservation (Metcalf andHasset 1999, Jaffe et al 2001). 39 The paper uses a straight forward extension of the framework used by Bayer and Timmins (2003) to examine sorting in consumer choice of vehicle type.
Recent works on how consumers value fuel economy tend to use monthly within vehicle variation over time in gasoline prices to identify consumer tradeoffs between fuel costs and vehicle costs. The question is that in the presence of sorting bias due to observed and unobserved consumer heterogeneity, whether this is an accurate way to identify tradeoffs between vehicle costs and fuel economy.
Additionally, firms respond to gasoline prices in the short term by adjusting vehicle costs to match sales. A key aspect of this is that prices are negotiated by dealers, and will depend upon inventories. For example, if gas guzzlers are not selling, dealers will offer price discounts. When demand is high for vehicles with high mileage, discounts are lower, and dealers could charge a premium over the retail price. The consumer heterogeneity we find is substantial and significant. The heterogeneity arises from huge differences in the amount of miles travelled by consumers and heterogeneity in expectation of gasoline prices and time preferences.
We find that a substantial portion (61%) of upper the 95% of households in our sample correctly value fuel economy as they are willing to pay $0.99 to reduce obtain a $1.00 discounted future gasoline costs over the lifetime of the vehicle. Another group, those with environmentally driven preference pays significantly more than $1 per dollar gas savings and uses their vehicles frugally (about 28% of the upper 95% overvalue fuel economy as they are willing to pay an average of $1.57). The lower 5% of our sample are willing to pay only $0.50 for a $1 reduction in future fuel costs.
These results are in contrast to those reported elsewhere by Alcott and Wozny (2009) but support results from the simulation study by Bento et al 2012 who find that not accounting for sorting bias and consumer heterogeneity could lead to a conclusion that consumers undervalue fuel economy. In that light, our results might not necessarily imply that consumers overvalue/undervalue fuel economy, but can be interpreted as being heterogeneous in their valuation of fuel economy.
How consumers weigh temporal effects of future fuel costs have important policy implications. This is because the nature of the temporal weighting helps in determining if market failure exists and also helps indicate whether policy prescriptions that affect initial vehicle costs such as gas guzzlers tax will reduce fuel consumption at lower costs than gasoline tax. In addition, results from such -equilibrium sorting‖ models can be used to develop theoretically consistent predictions for the welfare implications of future policy changes on fuel economy and gasoline taxes.
In the last few decades, the literature on how to estimate consumer's qualityadjusted prices of automobiles have grown. Most of the literature in this area has mostly involved the relationship between fuel economy and fuel price and pricevehicle safety tradeoffs. However, the fuel economy-price tradeoff has received the most attention (Hausman 1979, Mannering and Winston 1985, Zauberman 2003, Greene 2010. And it is this part of the literature that this paper contributes. Estimates of how much consumers are willing to pay to reduce fuel costs vary greatly (Greene 2010 Bento et al (2012), this work is an 120 empirical study rather than a simulation and such provides empirical evidence of the effect of consumer heterogeneity in estimates of the consumer trade-off of fuel economy and vehicle costs.
This paper is structured as follows. Section two discusses the equilibrium model composed of a demand side and supply side model. Section three, present the data used for the analysis. Section Four discusses the identification and estimation strategy as well as the challenges in estimating the specification. This is followed by the results and discussion and finally, we conclude in section six.

Methodology and Conceptual Framework
The model is consistent with a structural model of equilibrium of a heterogeneous product competition. The approach is based on earlier models by Goldberg (1995) and Amil Petrin (2002), but with significant differences. The method aggregates individual preferences into market level demand system, and combines assumptions on cost functions and pricing behavior to generate equilibrium prices and quantities. The estimation strategy is divided into two different steps. In the first step, the paper estimates household-level demand functions and then aggregates these individual functions to construct estimated firm demand curves. In the second step, we use the estimated demand curves to solve firms' first order conditions under the assumptions of Bertrand -Nash competition. The demand side of the model is based on a random utility function of consumer vehicle choice following Berry, Levinsohn and Pakes (1995;henceforth, BLP). The demand specification is paired with a supply side. Household i maximize utility ijt U from choosing vehicle j or not (the outside good) in each choice occasions t=1,….T. The household's joint utility from quantity and vehicle type j is additive and can be expressed with a random indirect utility given by:

Consumer Preferences for fuel economy
where α i , β i and γ i are individual specific taste parameters. p j is transaction price for vehicle j. We allow preferences over price to vary with income so that α i represents the individual specific marginal utility of income. Specifying vehicle price this way (with income) ensures that the indirect utility function from which we obtain the demand for discrete alternatives satisfy Roy's Identity. This implies that within any household vehicle ownership level, the marginal rate of substitution between gasoline costs and vehicle costs is income independent (Mannering and Winston 1985). x j , is the vector of observed vehicle attributes interacted with demographic variables (includes product intercept term). A random variable (ζ ν i ) is included to account for correlation in unobserved utility over the choice alternatives (Brownstone and Train 1999). 43 By specifying the x ij appropriately, you can construct any pattern of covariance across alternatives. G ijt is the expected future fuel cost over the vehicle lifetime is represented by: where T is the vehicle expected lifetime for model j, r is household specific discount rate, g t+s is the expected gasoline price at time t+s, m ij,t+s is the annual vehicle miles However, oil price futures have been known to be very poor predictors of future price changes in crude markets (Hamilton 2009(Hamilton , 1983Menzie andCoibion 2013). Sawhill (2008) and Khan (1986) both fit ARIMA models to retail gasoline prices to obtain consumers expectations of future gasoline price.
Vehicle price is affected by omitted variable bias for several reasons (Train 2003) and as such the term does not have a zero mean. For example, the econometrician may have information on fuel efficiency, weight, length, horsepower, color, etc, but may not have information on other attributes such as prestige, style, comfort, etc. These attributes affect price. The existence of the unobserved attributes implies that vehicles sort into groups or market segments, and that models within each segment compete more closely with one another than with models belonging to other market segments. This causes the price, to be correlated with the unobserved attributes, . One method to overcome this endogeneity is to move into the component of the utility that is observed by introducing an alternative specific constant for each product j (Petrin and Train 2006, Train 2009, BLP 1995. However, due to the difficulty of estimating the contraction required for the BLP approach and the fact that some vehicle models could have zero shares because the model is not offered for sale in some periods; this research will adopt the control function approach to deal with potential endogeneity of vehicle price(Kim and Petrin 2010, Klein andVella 2010). 45 The probability that household i choose alternative j on choice occasion t, conditional on the model structural parameters is given by Averaging P ij over the N consumers in the sample (Train and Winston 2007), we can obtain the market share for each product. We then express the market share for each product as:

Supply Model and Equilibrium Prices
This section develops the supply side of the model in which vehicle manufacturers set prices to maximize profits, given price of its competitors. Vehicles are differentiated, that is two very similar vehicles from different manufacturers will be priced differently. The supply side is similar to the supply side model of BLP (1995) and Train (2003). The intuition behind the supply side model is that given the aggregated demand curves and market shares, one can solve for the product specific  Wealthier households (as measured by total yearly expenditures) also possess larger 48 Among the wide range of household demographic information the survey contains includes size of household, age of household members, sex, employment status, type of residence, whether or not the household is located in a rural or urban area, education level, household income 49 However, Goldberg (1998)  The information on automobiles includes the make, model, vintage and purchase price of each car, financing, disposal of old vehicles, and a large set of vehicle characteristics. Most importantly, the CEX includes the mileage of each car owned by the household during each quarter. I will supplement these datasets with data on vehicle characteristics from EPA fuel economy test data and Automotive News Market Data Book. The former provides information on fuel economy measured in miles per gallon 50 . While the latter includes information on size, performance, and standard options of various models. Data on annual observations of certain microeconomic and macroeconomic variables also included as well as gasoline prices.
Summary statics of the attributes of the estimation model is provided in Table 2 Finally, we also collect information on interest rates on new and old car loans from the Federal Reserve and Consumer Price Index for all goods from the Bureau of Labor Statistics.

Discounted Future Gasoline Price Expectations
Gasoline prices are generally difficult to predict. When consumers make vehicle purchase decisions, how they form expectations for future gasoline prices is not well known. The most common assumption past works have made is that consumers treat the gasoline price process as a random walk, with any price shock considered permanent with subsequent adjustments in demand (Biesebroeck and leuven 2010) . However if the price shocks decay rapidly, then estimated elasticity will be biased because price shock will have less of an effect on demand and measured price elasticities will be lower.
Consistent with prior literature, we will make the assumption that current gasoline prices are best predictors of the expected future gasoline prices, i.e. gasoline prices are follow a random walk process with time trend. Support for the random walk hypothesis comes from Anderson et al (2012) who concluded that the random walk 130 process is a good reflection of consumer expectations of future gasoline prices.
Additional support is provided by the result of a dickey fuller test in which we fail to reject the null hypothesis that average monthly gasoline prices exhibits a unit root.  Another important assumption we make in constructing consumer expectations of future gasoline costs is related to consumer demand for annual vehicle mileage conditional on buying a new vehicle. We assume that consumer demand for annual vehicle miles travelled is heterogeneous and varies with gasoline price. While the short run elasticity of vehicle usage with respect to gasoline is low -0.15 (Hughes et al 2008, Gillingham 2011; in the long run, the average elasticity values hover around -0.7. That is a 10 percent rise in gasoline prices will reduce driving by about 7 percent through people switching to cars with better mileage and driving less. Most of the existing literature recognizes that consumers show significant variation in their demand for annual mileage and we incorporate the consumers' heterogeneity for fuel mileage by using customer specific mileage reported in consumer expenditure survey.

Incorporating Heterogeneity and Sorting
The wide variation in estimates of consumers' valuation of fuel economy suggests that heterogeneity is still an issue. Take for example, the role of unobserved individual heterogeneity. One such heterogeneity is consumer driving habits. Green drivers may buy more fuel efficient vehicles and use them sparingly (i.e there is positive correlation in vehicle choice draws across drivers), then estimates of the consumer MWTP for fuel economy will be unnecessarily too high. It is also possible that the correlation will be in the opposite direction. That is, heavy rivers will sort into more fuel efficient vehicles in order to reduce cost per mile of driving.
A second problem arises if there is unobserved heterogeneity in individuals expectations of gasoline prices. That is expectations might vary over consumers and time. For example, consumers might expect gasoline prices to rise (especially if purchase decisions are myopic), and choose to purchase more fuel efficient vehicles thus lowering cost per mile of driving. When prices are high and rising, it might be perfectly rational to expect future prices will be higher compared to expectations that are formed when prices are low and stable. If we use average expectations of the consumer to estimate consumer demand for fuel economy instead, that estimate will be biased.
A third problem arises when individual drivers have heterogeneous rates of time preferences. In particular, consumers who put less value in future costs (have 132 present biased preferences) will underweight gasoline costs relative capital costs. This is because gasoline costs occur in the future. Therefore, consumers that exhibit present bias preferences will sort into less fuel efficient vehicles, biasing downward estimates of consumer valuation of fuel economy. Although panel data and individual fixedeffects offer one solution to preference based sorting, other researchers have also used other methods. Our estimation approach allows us to account for the individual unobserved heterogeneity. We adopt the general form of heterogeneity-random parameter representation. However, we re-parameterize the , = + ′ + , = + ′ + mean estimates of the random parameters (vehicle capital costs and gasoline prices) to establish heterogeneity (Hensher and Green 2003). Where ′ + is the mean of the distribution, z i is a vector of consumer specific attributes, = 1, … . . , is simulated to find the values that maximize the simulated log likelihood (Green 2012).
The time-invariant error terms reflects habit-persistence. The presence of a standard deviation of the two parameters accommodates the presence of preference heterogeneity in the sampled population.

Econometric Model and Estimation Strategy
Our estimation approach is driven by several factors. First, is that the durable goods nature of automobiles implies that we have to account for both consumers' taste for fuel efficiency and intensity of utilization in estimating elasticity. Therefore, households make a two-step decision. They first choose the number and type of vehicles to own based on driving habits and expectations of future gasoline prices.

Identification
Our identification strategy is based on the fact that firms set prices on the basis of demand for their products and that of the competitors. The prices (transaction prices) are the result of negotiations with customers, and auto dealers will provide a higher discount on cars that are selling slowly. The observed prices contain information about price elasticities, which if correctly extracted can be used to estimate the demand parameters. Therefore, we need to look at pricing behavior that can arise in markets and show how the specification of this behavior can be combined with the demand estimation to identify consumer demand for fuel economy. The intuition is that auto firms also respond to fuel price changes in the short run by adjusting relative prices to match sales. And in the medium run, firms can tweak small design changes in months to improve fuel economy by orders of 0.
where x j is a vector of all of the observed exogenous variables that affect marginal cost and the elasticity, X j (·) is a parametric function of these variables, and u j is the unobserved deviations of price around this function (Train 2010, Kim andPetrin 2010). We can estimate the pricing equation and retain the residuals. This is done by constructing estimates of the expected price for each model conditional on all exogenous factors 51 .
Estimation proceeds in two steps. In the first step, we recover μ*, (the residuals from the pricing equation) by inverting the pricing function. The product specific unobserved factor, ξ, enters the reduced form pricing equation as an argument. The μ* incorporates information about the and unobserved component of the elasticity based mark-up (Train 2002). In the second step, having specified the pricing function, we then estimate conditional choice model treating the controls as additional regressors. What is left is the standard errors. We need to correct them using the approach in Newey and McFadden (1994).
Because we have very few observations on the same nameplate over time and moreover, vehicle attributes change, new models are added, some models are discontinued, we cannot condition on a full set of fixed effects. Rather, we place restrictions across the vehicles. The only restriction we place is that the parameters of the pricing function are the same across all products and years. 51 We assume that are not correlated.

Parameter Estimates of Demand Model
Point estimates and standard errors from the specifications are presented in Tables   4 and 5. Table 6 translates these results to elasticity estimates. The two variables of interest are capital cost of vehicle (α) and discounted annual operating costs (γ) 52 .
Given that there is no specific direction in existing literature for other variables to include; we include weight, horsepower, size (wheelbase and track width), drive train, dummies if vehicle is an SUV, minivan, full sized van or pickup truck, and indicators that reflect make of a given vehicle. The indicators capture extent of household preference for a particular make of vehicle. We also control for engine size, but the values are not reported because they are not of any particular interests for our purposes. The demographic variables enter through interactions with vehicle attributes. The parameters vector has a multivariate normal distribution. We divide the coefficient on price by the income of consumer to allow the elasticity to vary with income. This way, households with high income are less sensitive to prices than those with low income.
Column 1 of Table 4 reports the logit specification without accounting for heterogeneity or including information from firms pricing behavior. All other coefficients are statistically significant. The coefficient on price is negative as expected, but that on operating cost is positive which is counter intuitive. In Column 2, we report random coefficient logit model with heterogeneity but do not include information on firms pricing behavior nor account for price endogeneity. The coefficient of discounted annual operating costs switches signs. In addition, price and all other variables have the right signs and are statistically significant. The values are in line with estimates elsewhere 53 (Train and Winston 2003, Petrin 2002, Kim and Petrin 2010, Sawhill 2008, and BLP 1994. Column 3 of Table 4 is our preferred model. In addition to accounting for consumer heterogeneity and price endogeneity, this model also includes information in firms pricing behavior. We expect the price elasticity to be higher than the result from the random coefficient logit model (Train 2012, Kim andPetrin 2010). Correcting for endogeneity and sorting improves the elasticity of both the capital cost and gasoline costs significantly. The mean price coefficient is 3.581 and significant. The standard deviation of a normally distributed price coefficient is 0.54. 54 We recover mean price coefficient with respect to discounted operating costs of 6.78 55 with a t-value of 14.74.
We also find standard deviation of the normally distributed coefficient of discounted yearly operating costs of 2.085 which implies that 95% of the drivers have mean coefficients ranging from 2.69 to 10.87.
We also report ratios of the coefficients of the two variables of interest: , with a value of 1.88. A Wald test of the null hypothesis that the coefficients on price and discounted operating costs are equal is rejected at 5% level (W=26.48<χ 2 <3.65). We find that 95% of the consumers in our sample have values ranging from 0.99 to 1.88 This large spread signifies heterogeneity in consumer response to fuel economy. In this vein, we uncover three segments of discounted operating costs: 28% of the consumers significantly overvalue fuel economy while 61% less so or are rational.
That is 61% of consumers in our sample make vehicle purchase decisions based on financial considerations only. The rest, 11%, seems to underweight future gasoline costs when making decisions. We profile the segments in terms of their average demographic characteristics. On average, rational households are lager and tend to have above average income, have higher number of school age children, men older than 45 years.
These are in line with the predictions from Bento et al (2012) and the effect of sorting and heterogeneity on parameter coefficient estimates (Bayer et al 2011). These results reinforce their arguments that ignoring consumer heterogeneity leads to undervaluation of energy savings by consumers. This is because consumer heterogeneity results in sorting which results in downwards bias effect. These results are in contrast to Alcott and Wozny (2009) who finds that report that consumers undervalue fuel economy. Table 5 reports the results of the regression of log of marginal costs on the vehicle characteristics. All the regressors enter with significant coefficients and have the expected signs. That is, it costs more to improve the fuel efficiency of a vehicle, build a bigger car, add additional luxury and comfort, power and acceleration, as well as increase weight. Next, we turn to the main question of this research by looking at the implications of the estimates of accounting for pricing behavior of firms in consumer valuation of fuel economy. Table 6 presents estimates of several ratios of computed over a range of discount rates and vehicle lifetime values. These values can be interpreted as the consumer willingness to pay for reduced future discounted costs. Expressing the results in this form makes it easy and the interpretation is intuitive. However, these ratios can be easily translated into a form that allows the values to be comparable to results reported elsewhere. We achieve this by dividing the ratio by try different values for T 10, 15, 20 and 25. Also, we assume discount rates ranging from 5-9%. Most published work have used discount rates or either 6 or 7%. The values in Column 3 are comparable to those reported by Alcott and Wozny (2009) who used a discount rate of 6% for their base model.

Do Consumers Undervalue Fuel Economy
In Figure 3, we plot the distribution of WTP to reduce future operating costs of vehicles by households in our sample over different vehicle life times and interest rates. The last two columns of Table 6 report our results. We estimate that for every $1dollar saved in the future, consumers take no more than $0.99 into account. We find evidence of small overvaluation and not one instance of undervaluation. These results are in stark contrast to results reported by Helfand and Wolverton 2010; Greene 2010; Alcott and Wozny 2009. We find that accounting for heterogeneity and sorting by consumers, tends to remove any significant evidence of consumer undervaluation of future fuel savings. The last two rows present lower 5% and upper 95% distribution of consumer valuation of fuel economy. Though the lower 5% consumers only place 141 values of $0.51 of a dollar savings, it does not signify energy paradox by this population in the strict sense. This is because, there is a huge spread in the amount of annual mileage by consumers across the population and this leads to huge valuation in fuel economy. For example, if they drive a few standard deviations outside the mean, they might choose the appropriate vehicle. The major take away from this is that different drivers sort into different vehicles based on their taste and demographic attributes. Those consumers who place higher values on fuel economy will sort into more fuel efficient vehicles and those that place less value of future fuel savings sort into large vehicles. Any demand estimation strategy that does not account for heterogeneity in driving habits and taste preferences will probably arrive at the wrong conclusion.

Conclusions
How consumers value fuel economy is one of the most researched questions in to the automobile and energy sectors. The estimates are highly variable with some papers concluding that consumers grossly undervalue fuel economy, while others have reached the exact opposite situation. The high variability of the estimates signifies that probably, heterogeneity in consumer might play a role in reconciling the different results obtained. Despite the fact that individual unobservable heterogeneity and sorting have been found in consumer vehicle choice and driving behavior, their effect on estimates of consumer fuel economy valuation has not been presented empirically.
This paper presents such empirical evidence of the effect of individual unobserved heterogeneity and sorting in the estimates of fuel economy valuation by consumers.
We demonstrate that sorting and unobserved heterogeneity has the potential to bias 142 estimates of consumers' ability to optimally tradeoff capital and operating costs when making durable choice decisions.
To restate our findings, we find no evidence to support the argument that consumers systematically underweight the cost of future events in real market settings.
However, we find significant evidence that different consumers sort into different groups such that rational consumers accurately tradeoff future operating costs and vehicle prices. Conservatively, about 61% of the population is accurately do not underweighting or overweighting operating costs when purchasing new vehicles. This research has several limitations which provide a useful roadmap for future studies.
First, we do not include used vehicles in our model. There is no evidence that consumers value new vehicles and old vehicles in a similar version or that different consumers drive their vehicles over their useful life as developed in this paper. In fact, evidence from textbook market exists that forward and myopic consumers place different values on the resale price of durable goods. Ideally, the model could be extended to allow for dynamic vehicle replacement as well creating a fully dynamic framework. Second, the model developed in this paper makes strong assumptions about the functional form of the distribution of consumers in the population for ease of estimation. By restricting consumer taste parameters for price and operating costs to be normally distributed, we are necessarily ruling out more flexible distributions of consumer behavior which may be present in the population.

CONCLUSION
Policy makers have employed various policy instruments in an attempt to achieve at least two policy goals. One goal is to reduce peak demand, obviating the need for a large excess generating capacity which is rarely used. A second policy goal is to reduce overall electricity consumption, thereby conserving fossil fuels and reducing pollution. However, behavioral response interacts with these policies in a complex manner sometimes resulting in unintended consequences. Therefore an understanding of behavioral response is essential in designing effective energy conservation policies.
This dissertation provides answers to several questions related to unanticipated ways in which consumer behavior has affected the outcomes of energy policies. First, I provide evidence from a field experiment on a demand response program that investments in energy efficiency results in significant reduction of anticipated energy consumption while at the same time reducing resultant emissions. Such reductions offer utilities avenues for managing summer peak load without the necessity to build costly peaking power plants. However, due to strategic behavior and income substitution effects, households utilize these savings in different ways. I provide evidence of direct rebound and precooling effects that an in the order of 41% of saved energy, monetary and environmental benefits. While the DR program was designed to create a flatter load shape for the utility to help reduce operating needs and complexity during peak periods, the benefits of this program are in part offset by behavioral response by consumers through precooling and rebound. That is the program results in reducing peak load and emissions reduction, but not as much as one would predict 155 because of behavioral response. This implies that behavioral response needs to be taken into account if we are to have realistic forecasts of potential project outcomes. It also implies that policies might be more effective if they are designed to create incentives for behavioral response that are consistent with the goals of the policy, so that behavioral response reinforces the program. This is really the notion of incentive compatibility.
Second, due to the changes in consumers' consumption patterns that occur as result of strategic behavior, utilities incur additional production costs which are then passed through to consumers. The rebound and precooling results in an increase in energy supply services, with a corresponding increase in effective prices, the size of which depends on the underlying cost structure. Therefore utilities in response to increased load during off-peak periods call more expensive generation units to meet increased load. This results in an increase in the cost of conservation which may have negative effect on the overall social welfare.
Third, one of the key barriers to achieving energy efficiency is the so-called -energy paradox,‖ the idea that consumers undervalue cost savings from investments in energy efficiency. The undervaluation of future fuel costs in the automobile market is a great example for demonstrating such market failure. However, it has always been challenging to accurately quantify the degree of the undervaluation, if it exists.
Consumer heterogeneity and sorting are important factors that must be considered in order when quantifying the level of consumer undervaluation of investments in energy efficiency. If consumers tend to undervalue long-term cost savings associated with efficient equipment, then this will reduce the effectiveness of some policies relative to others (e.g., carbon tax versus gas guzzler tax). I find that accounting for sorting bias and consumer heterogeneity explains a large fraction of the purported myopia found in literature and conclude that myopic behavior may be a less significant problem; and also that it may be confined to a subset of the population.
Fourth, CAFE standards are designed to improve gas mileage. However, CAFE as structured is less stringent for larger vehicles therefore may be behind the explosion in the demand for light duty trucks (SUVs, Minivans, Pickup-trucks, etc).
This explosion in the light truck share of the automobile fleet has introduced -prisoner's dilemma‖ situation where drivers buy heavy vehicles for better selfprotection in collisions and increasing risks to occupants of other drivers. These externalities have serious policy implications. In theory, an efficient fleet could be achieved through a carefully calibrated tax based on careful cost-benefit analysis.
However, such a tax policy may pose practical problems of implementation in terms of public acceptance and monitoring. A policy such as the proposed one will also lead to the adoption of more fuel efficient vehicles over time and reduction in the weight of the fleet.
Finally, estimates of emissions reduction impacts of energy conservation programs show that they result in reducing emissions but as one might expect because behavioral response will at least in part offset potential emission reductions from efficiency-based policies. This suggests we can improve the performance policies by integrating incentive-based programs such as carbon taxes or other tools policies that 157 increase energy prices. This dissertation reviews these policies, and concludes that while these policies do contribute to their major objectives, the benefits are at least in part offset by unintended consequences due to behavioral response by consumers. The main take away from this dissertation is that an understanding of behavioral response is essential in designing effective policies.