Deterrence and Geographical Externalities in Auto Theft


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Deterrence and Geographical Externalities in Auto Theft

  1. 1. ∗ Deterrence and Geographical Externalities in Auto Theft Marco Gonzalez-Navarro Princeton University † December 20 2008 Abstract Knowledge of the extent of crime displacement is crucial for the design and implementation of crime prevention policies. Nevertheless, previous empirical evidence documenting displacement remains inconclusive. This paper is the first to document extensive interstate displacement in auto theft. I propose an intuitive model to analyze the effects in the stolen vehicle market of the introduction of an observable theft deterrence device. I then study the changes in theft risk that were generated by the introduction of Lojack, a highly effective stolen vehicle recovery device, into a number of new Ford car models in some Mexican states, but not others. I find that Lojack-equipped vehicles in Lojack coverage states experienced a 48% reduction in theft risk due to deterrence effects. In states neighboring those where Lojack was introduced, I find that the Lojack program generated an increase in theft risk of 77% in unprotected Ford models. This kind of externality is expected when there is a strong model-specific demand for stolen cars – such as an active stolen autoparts market. In Lojack states, I find a small and non-significant reduction in theft risk of unprotected car models which coincides with the introduction of the Lojack program. The Lojack program introduction coincides with an increase in the number of criminals charged for property theft in Lojack states. I find no displacement to other crime categories in either Lojack or Non Lojack states. Given that most criminal law enforcement is an attribute of state or local governments, the results of this paper suggest that prevention efforts targeting highly mobile crimes – like auto theft – should be coordinated among jurisdictions, rather than independently designed. JEL: K420, H230 ∗ I would like to thank Angus Deaton, Adriana Lleras-Muney, Sam Schulhofer-Wohl, Chris Paxson, Anne Case, Climent Quintana, Rodrigo Barros, and David Atkin for their help and advice in this research project. The data used here would not have been available without the help of Enrique Olmedo Salazar and Laura Espinoza from AMIS, Juan Moreno from Lojack, and Carlos S´nchez and Susana Pineda from Ford. I would also like to thank the a participants of the development lunch seminar and the Public Finance Working Group at Princeton University for their useful comments. Financial aid from the Woodrow Wilson Scholars, Princeton University, and the Center for Economic Policy Studies is gratefully acknowledged. Any errors contained in the paper are my own. † Economics Department, Fisher Hall, Princeton, NJ 08544. Email: 1
  2. 2. 1 Introduction Does fighting crime locally reduce overall crime, or merely displace it elsewhere? Crime prevention policies depend crucially on the substitutability of crime across space, time, victims, and crime categories. An extensive theoretical literature explores the implications of crime displacement for law enforcement (cf. Clarke and Harris (1992), Shavell (1991), Clotfelter (1977), Clotfelter (1978)). However, empirical evidence demonstrating substantial crime displacement is elusive (Hesseling (1994)). Many policymakers advocate that law enforcement focus on highly crime-prone areas. The argument for targeting places is presented in the “hot spots” literature (Sherman, Gartin, and Buerger (1989), Sherman and Weisburd (1995)): By focusing on locations with high levels of crime, overall criminal activity is reduced efficiently. This literature implicitly assumes that targeted activities are not highly mobile. Otherwise, a crackdown in one location is replaced by crimes in other locations. If so, police targeting of locations with high-mobility crime will tend to show large reductions in criminal activity in targeted locations, at a cost of increased criminal activity elsewhere. Crime that is highly mobile – either across time,1 space or other crime categories – must be dealt with comprehensively, with an emphasis on incapacitation. Crimes that are spatially mobile are es- pecially important for fiscal federalism. The literature on the distribution of responsibilities across government levels (cf. Tiebout (1961), and Donahue (1997)) argues that government-provided goods may be suboptimally supplied whenever these expenditures exert spatial externalities on surrounding jurisdictions. If spatial externalities are pervasive, it may be welfare improving to delegate the responsibility in question to a higher level of government, which can internalize the ex- ternality. The fact that most criminal law enforcement is performed by state and local governments suggests that a limited amount of spatial spillovers in crime must be present for law enforcement to be provided at optimal levels (See Newlon (2001)). This paper provides evidence that for auto theft, spillovers across state boundaries are substantial. Because this type of crime is highly mobile, a high level of coordination across jurisdictions is required. Auto theft is an extremely salient property crime: the value of the stolen goods is large and 1 For criminal displacement over time see Jacob, Lefgren, and Moretti (2005). 1
  3. 3. violence is often involved. In the case of Mexico, over 50% of auto thefts involve violence, and often murder (AMIS 2005). Auto theft can be understood as a conflict between vehicle owners, manufacturers, and authorities on one side – whose objective is to minimize thefts – and thieves and the black market in general on the other, who gain from the theft of automobiles. In this game, technological improvements arrive continuously and can upset the equilibrium number of vehicles being stolen. To shed light on the extent of auto theft displacement, I study the introduction in Mexico of one of the most ingenious technological innovations in crime reduction policies of recent decades: the Lojack stolen vehicle tracking technology. Lojack is a device that allows stolen vehicles to be located with a high success probability. In Mexico, Lojack was introduced through an exclusivity agreement between Ford Motor Company and the Lojack vehicle recovery company. The agreement consisted of installing Lojack exclusively in all new cars sold by Ford within a specific subset of vehicle models. The device was installed, free of charge, and the recovery service was paid for during one year in new Ford cars included in the program from participating states. The program was rolled out gradually, both on the intensive margin – with new Ford models entering the program at different moments in time – and the extensive one, with an expansion over time in the number of states where the program was implemented. The introduction of a car model into the Lojack program was accompanied by a sustained publicity campaign orchestrated by the the local Ford distributors in the local media. Common knowledge of which car models where equipped with Lojack made Lojack an observable theft deterrence device. I use variation over time in theft risk, at the state and car model level, to measure both the impact of Lojack in deterring auto theft for Lojack-equipped vehicles and the displacements in theft risk that this generated on non-Lojack protected vehicles. I propose an intuitive equilibrium model of deterrence and displacement in the stolen automobile market. The model makes differential predictions about the impact of the Ford Lojack program on the theft risk of non-protected vehicles depending on which model they are, and their location. The model consists of two adjacent states, referred to as the Lojack and the non-Lojack state. In each state there are two car models, the Lojack car model and the non-Lojack car model. The introduction of Lojack into the Lojack state-Lojack car model generates a reduction in thefts for the protected vehicle, due to a deterrence effect. The reduction in thefts in this market is displaced 2
  4. 4. to the non-Lojack model if demand for stolen vehicles is common across car models (ie. if different car models are good substitutes). On the other hand, if demand for stolen vehicles is model specific – for example due to an active trade in stolen autoparts – the externality becomes geographical: Theft risk increases for the Lojack model in the Non-Lojack state. The empirical evidence supports this last type of externality. My empirical analysis is the first to use a dataset compiled by the association of insurance companies of Mexico (AMIS). The dataset consists of individual reports of automobile thefts in the country, with information on the car model involved, the year of manufacture, the state and the date the in which the vehicle was stolen, for virtually all thefts of insured vehicles in Mexico. The fact that the data come from a developing country contributes to the growing literature of crime in developing countries. One of the innovations of this study is the use of such an extremely detailed source of crime data. Previous crime studies could not follow theft risk at the car model level, making it impossible to identify differential changes theft risk for protected and unprotected vehicles when a policy that affected only certain vehicles was introduced. It is also worth noting that using theft reports of insured vehicles is much less subject to lack of reporting than police crime reports. The empirical results show that Lojack was an extremely effective theft deterrence device, generating an estimated reduction in theft risk of 48% for vehicles participating in the Ford Lojack program. I also find that Lojack generated increased theft risk for vehicles in states neighboring those where Lojack was implemented. Lojack models in surrounding states experienced an increase of 77% in theft risk. Furthermore, in states distant to those where Lojack was introduced, I find no significant change in theft risk. In Lojack states, I find a small and non-significant reduction in theft risk of non-Lojack car models which coincides with the introduction of the Lojack program. This could be a result of two effects: a displacement effect, which would increase theft risk in this group, and an incapacitation effect, which would decrease theft risk. If thieves or chop shops work with both Lojack and non- Lojack models, the increase in the recovery of stolen Lojack-equipped vehicles could have generated an increase in the capture of criminals. This increased incapacitation of criminals may well have generated reductions in thefts of non-Lojack models too. The incapacitation hypothesis is supported by an increase in the number of criminals charged for property theft after the introduction of the 3
  5. 5. Lojack program. In an analysis of other crime categories, kidnapping and drug trafficking, I find no evidence of displacement due to the Lojack program, in either Lojack or Non-Lojack states. The results of the paper are of importance for the crime displacement literature. They show that observable deterrence devices are likely to generate displacements of crime (cf. Karmen (1981)). Finding that externalities take place across state borders suggests that for easily displaceable crimes in high value articles, such as auto theft, crime prevention policies should be highly coordinated among states or possibly have the attribution shifted to the Federal Government level. By showing that observable deterrence devices generate a substantial reallocation of theft risk, the paper provides a counterpoint to Ayres and Levitt (1998). In their paper, the same Lojack technology is sold in such a way that thieves are unable to distinguish between protected and unprotected vehicles. The unobservability of the technology generates starkly different results to those of the observable case. Auto theft is reduced for all vehicles in the geographical areas with Loajck coverage, because all cars have a positive probability of being equipped with Lojack. The rest of the paper is structured as follows: Section 2 describes the recovery technology and how it was implemented in Mexico. Section 3 provides an equilibrium model of the stolen vehicle market and the predicted effects of the introduction of a theft deterrence device. Section 4 describes the data used in the paper. The estimation strategy is discussed in Section 5, while Section 6 presents the empirical results. Section 7 concludes. 2 Technology and Intervention 2.1 Technology Lojack is an automobile recovery technology developed in the late 1980s in Massachusetts. After a successful expansion in its home country, Lojack had been introduced into over 30 countries by 2007.2 Lojack uses radio technology to recover stolen vehicles. The system consists of two main components: a radio-frequency transceiver in the protected vehicles and a grid of locality-specific tracking antennas. Every geographic location that is covered requires a combination of tracking devices in fixed locations, vehicles, or aircraft in order to provide the recovery service. The specific combination depends on the topography, road system, and other relevant factors of the locality. 2 4
  6. 6. Lojack has an extremely high recovery rate, with 90% of vehicles being recovered within 24 hours of the report (LoJack (2006)) and 95% eventually recovered (Romano (1991)).3 Its small size – similar to a deck of cards – allows it to be hidden in many possible places inside a car, making it hard to locate. The device has its own power source, meaning that it does not depend on the car’s battery to operate. Cars equipped with the device do not signal its presence with decals of any sort. The company sells recovery – not deterrence – services, and announcing the presence of Lojack in the vehicle may compromise the likelihood of recovery. Finally, it only emits the signal once it is activated remotely. The combination of these factors make it impossible to know from a visual exterior inspection if a car is equipped with Lojack. The Lojack radio transceiver remains dormant unless a theft occurs. If an owner realizes that the vehicle has been stolen, she calls Lojack and her specific device is remotely activated. Once the signal is active, any of the tracking devices can perceive it if the car is in close proximity. After a signal becomes visible for one of the trackers, mobile trackers can be sent to follow and find the stolen vehicle. The radio signal is perceptible to the tracking devices even if the vehicle is in a covered environment, like a warehouse, a building, or a container. Competing technologies based on GPS are mainly used for better logistics, not as recovery devices. GPS antennas are conspicuous, which makes them straightforward to deactivate by thieves. Furthermore, the GPS system is severely compromised if the vehicle is placed under a roof. 2.2 Intervention Installing a Lojack recovery system in a locality requires large fixed costs. These take the form of lengthy agreements with the local police, regulatory approvals, and the cost of installing the network of tracking equipment. The owners of the Lojack technology gave exclusive distribution rights to a Mexican company to introduce the system in Mexico. The patent holders would supply the equipment and the Mexican company would be in charge of the management of the system. For a startup company, the large setup costs, together with uncertain demand for the product made the enterprise extremely risky. The Mexican company decided to offer a major car builder an exclusive agreement to have Lojack installed in its cars. The vehicle recovery company would 3 The information on Lojack is based on discussions with company executives in Mexico and on information from their web page. 5
  7. 7. instantly gain a large customer, improving the short-term viability of the company, and the large car manufacturer would offer an exclusive benefit for its customers. Ford Motor Company of Mexico agreed to be the sole Lojack customer for a prearranged period. Ford Motors agreed to pay the Lojack company a fixed cost per unit installed. In exchange for the payment, the company provided the transceiver, installation costs, and one year of Lojack recovery services. After the first year, customers had the option of continuing the recovery service at an annual cost of around $100. The system was first introduced into the Ford Windstar in 2001 in the state of Jalisco. In 2002, the Lojack tracking system was introduced into three more states in Mexico (Morelos, Estado de Mexico, and Mexico City) with Ford Windstar being the first car model to get the device. Once the recovery system had been implemented, Ford distributors in the coverage states engaged in large publicity campaigns to inform the population which of their models were equipped with Lojack. Lojack was introduced into different car models from 2001 until 2006, year in which Ford dropped the exclusivity agreement. In total, 9 different Ford models came equipped with Lojack in the period I study (1999-2004). A list of the Lojack models, the states, and dates of introduction into the program can be found in Table 1. Once a Ford model was introduced into the Ford-Lojack program, it maintained its Lojack status throughout the period being analyzed. Like other major automobile manufacturers in Mexico, Ford and its distributors have an agree- ment to sell new vehicles for the same price nationally. The Ford Lojack program did not change this arrangement: customers in Lojack states paid the same price for a vehicle as customers in non-Lojack states. The company administrating Lojack was in charge of obtaining the permits and necessary regulatory approvals. Lojack managers decided to operate the tracking system jointly with the local police forces. The high degree of control over the tracking system – as opposed to simply handing it over to the police – was arguably the best option in an environment where police forces were not deemed sufficiently trustworthy to operate the system up to its full capabilities. However, local police cooperation was always necessary given that, in Mexico, taking possession of stolen property is an exclusive attribute of police forces. 6
  8. 8. 3 Theoretical Framework The objective of the model presented here is to obtain predictions about the effects the introduction of Lojack had on theft risk of vehicles, both for those protected by Lojack and those that were not. I explore the different externalities that are expected to arise with and without geographical integration in the stolen vehicle market and with a high or low substitutability between Lojack and non Lojack models. In order to make the exposition as simple as possible, I consider two contiguous states, one where Lojack is implemented (referred to as a Lojack state) and one where it is not (the Non- Lojack state). Similarly, I consider the case in which there are only two car models subject to being stolen, which I call the Lojack car model and the Non-Lojack car model. I analyze the effect of equipping with Lojack the Lojack model in the Lojack state. In the baseline model, I ignore thief mobility, and derive the implications of the Lojack program. In Appendix A, I introduce thief mobility and show that it generates larger effects in the same direction as those of the baseline model. Let Ns1m1 , Ns1m0 , Ns0m1 , Ns0m0 denote the number of thefts in each of these markets, where the subscript s1 refers to the Lojack state, m1 to the Lojack model, s0 to the Non Lojack state, and m0 to the Non Lojack model. Denote by Nij = S(Pij ) the supply of stolen vehicles in each of the markets, where Pij is the amount of money the thief obtains when he steals a vehicle.4 A standard assumption is that the number of vehicles stolen is increasing in the payoff, ie, the supply is upward sloping in each of these markets (S (·) > 0). This is due to the increasing marginal cost of stealing cars. Cars targeted first are those that are easier to steal: those parked on the street, as opposed to inside a garage. In each of the markets there is a demand for stolen cars denoted by D(Nij ). Demand for stolen vehicles is decreasing in the price. This is generated by the decreasing marginal benefit of each additional vehicle that is stolen. Stolen vehicles are used for many lucrative activities. A common use is to sell them in the used vehicle market with a false title to an unsuspecting buyer. Another use is the sale to people who knowingly buy ill-obtained vehicles for personal use because they have a low probability of being prosecuted. One example are rural landowners, who can buy stolen 4 There is no assumption of equality of the supply functions S(·) in the model. They are written in this way for simplicity of notation. 7
  9. 9. trucks for use mainly inside their farms, and have a low probability of being discovered by law enforcement officers. Stolen cars are also inputs to other crimes. For example, in kidnappings and bank robberies, vehicles used by criminals to perpetrate a crime are commonly abandoned a short distance from the crime scene. Those vehicles are usually found to have reports of theft. Finally, stolen vehicles can also be exported. There are reports of stolen vehicles being sold in countries with an active used vehicle import market, which is the case in many countries of Central America, South America and Africa. Stolen vehicles are also stolen to be to be stripped of their valuable parts, which are then sold in the used autoparts market. Law enforcers have an especially hard time determining the origin of used autoparts. Stolen parts are easily sold to junk yards, parts shops, and collision repair shops with a low probability of detection. A different source of demand for stolen vehicles is thefts for joyriding purposes by amateur thieves. This theft source is not insignificant. Mayhew, Clarke, and Elliot (1989) find that mo- torcycle theft decreased in Germany after a law passed that required motorcycle drivers to wear a helmet. The interpretation given to this finding is that joyrider thieves do not prepare for a theft, but rather take advantage of attractive theft opportunities to have a moment of fun. Once police in Germany began pulling over anyone driving a motorcycle without a helmet, theft for joyriding pur- poses became much more likely to end in criminal charges and was thus less attractive for joyrider thieves. Given that such thefts are unrelated to the monetary value of a stolen vehicle, they can be thought of as a constant in the demand functions of the model I propose. The negative sloping demand curves and the upward sloping supply curves define an equilibrium price and quantity in each of the markets. I now explore the deterrence and displacement effects of the introduction of Lojack into the stolen vehicle markets according to the geographical integration of markets and the type of demand for stolen vehicles. 3.1 The Case of No Displacement: Geographically Isolated Markets and Model Specific Demand for Stolen Cars A scenario in which demand for stolen vehicles is model-specific arises when stolen cars are stolen for the value of their parts in the black market. Geographic isolation refers to a situation of no trade in stolen vehicles across state lines. Because stealing a car protected by Lojack is more difficult to 8
  10. 10. successfully accomplish, I model it as a negative supply shock. Alternatively, the introduction of Lojack can also be thought to decrease demand for stolen Lojack-equipped vehicles, because the chop shops are also at risk of being discovered whenever they disassemble or distribute a Lojack- equipped car. The model in which both demand and supply falls generates the same qualitative predictions in terms of the amount of vehicles that are stolen. The only difference in terms of quantities is that larger effects are predicted when both supply and demand shift down. s Supply in the Lojack model-Lojack state market is given by Ns1m1 = S(Ps1m1 )−Lojack. Where Lojack is a dummy variable indicating that the model is equipped with Lojack. Demand is given d d s by Ps1m1 = D(Ns1m1 ). The market clearing condition equates demand to supply: Ns1m1 = Ns1m1 . This is a simple nonlinear model of three equations in three unknowns with the Lojack variable changing exogenously from 0 to 1. I linearize around the equilibrium without Lojack and then solve the system with linear algebra tools in Appendix A. The predictions of the model under geographically isolated markets and model specific demand for cars are: ∗ ∂Ns1m1 ∂Lojack <0 ⇒ Deterrence Effect ∗ ∂Ns1m0 ∂Lojack =0 ⇒ No Within State Externality ∗ ∂Ns0m1 ∂Lojack =0 ⇒ No Geographical Externality Within Model ∗ ∂Ns0m0 ∂Lojack =0 ⇒ No Geographical Externality Across Models Where the star represents the equilibrium value of the number of thefts in each market. The introduction of Lojack into the Lojack model-Lojack state market generates a reduction in the amount of stolen vehicles in that market, while the other three markets are unaffected by the program. In the case of no spillovers in crime, like this one, crime reduction policies focused on particular crime category or crime location are efficient, because reductions in crime are not simply displaced elsewhere. As long as there is no displacement, devices that make certain crime objectives less attractive for thieves should not be regulated. Under no displacement, expenditures on crime deterrence devices generate net reductions in crime and are socially efficient: only devices that are effective are bought, and they are bought in the efficient quantity. As I show next, this is not the case when some of the assumptions of the model are changed. 9
  11. 11. 3.2 Within State Displacement: Geographically Isolated Markets and Common Demand Across Car Models Under the assumption of no interstate trade in stolen vehicles, the introduction of Lojack has no effect in thefts of either model in the Non-Lojack state. However, when demand for stolen vehicles is common across car models within a state, introducing Lojack generates increased thefts for the Non-Lojack model. Let demand for stolen vehicles in the Lojack state be given by Ps1m0 = d d s Ps1m1 = D(Ns1m1 + Ns1m0 ). As before, Lojack makes stealing Lojack models more costly: Ns1m1 = d s d s S(Ps1m1 ) − Lojack. The market clearing conditions are now Ns1m1 = Ns1m1 and Ns1m0 = Ns1m0 . The model is solved in Appendix A, with the following predictions: ∗ ∂Ns1m1 ∂Lojack <0 ⇒ Deterrence Effect ∗ ∂Ns1m0 ∂Lojack >0 ⇒ Within State Negative Externality ∗ ∂Ns0m1 ∂Lojack =0 ⇒ No Spatial Externality Within Model ∗ ∂Ns0m0 ∂Lojack =0 ⇒ No Spatial Externality Across Model With geographically isolated markets, Lojack reduces thefts of Lojack equipped vehicles but in- creases thefts of Non Lojack protected vehicles in the same state. Under the assumptions of this model, there should be no impact of the introduction of Lojack in neighboring states. Displacement within the same geographical location may have implications for the social de- sirability of observable theft deterrence devices. With close substitutes for crime targets, theft deterrence devices shift theft risk from protected to unprotected vehicles. This is a negative ex- ternality imposed on those that are not protected by the device. Under similar disutility of theft across individuals, such devices reduce social welfare by creating expenditures that simply shift theft risk across individuals without reducing overall thefts. 3.3 Model-Specific Geographical Displacement: Geographically Integrated Mar- kets and Model Specific Demand for Stolen Cars When demand for stolen vehicles is model specific and markets are integrated across geographical lines, the introduction of Lojack generates increases in theft of the Lojack model in the neighboring state. This is transmitted through an increased demand for those models. The common demand d d for Lojack car models across states is given by Ps1m1 = Ps0m1 = D(Ns1m1 + Ns0m1 ). As before, 10
  12. 12. s Lojack reduces the supply of Lojack-equipped stolen vehicles Ns1m1 = S(Ps1m1 ) − Lojack. The model is solved in Appendix A, with the following predictions: ∗ ∂Ns1m1 ∂Lojack <0 ⇒ Deterrence Effect ∗ ∂Ns1m0 ∂Lojack =0 ⇒ No Within State Externality to Non Lojack Model ∗ ∂Ns0m1 ∂Lojack >0 ⇒ Model Specific Spatial Externality ∗ ∂Ns0m0 ∂Lojack =0 ⇒ No Spatial Externality to Non Lojack Model In this case, the model predicts spatial externalities. If crime is highly mobile across jurisdic- tions, local law enforcement generates spatial externalities in crime for neighboring jurisdictions. Crime that is mobile across jurisdictions can also be harder to tackle for law enforcement agencies that act independently. In terms of efficient decision-making, with spatial spillovers, law enforcement should be done at a higher level of government such that the externality is internal- ized (Donahue (1997)). At the very least, with spatial externalities, law enforcement should be coordinated across jurisdictions. 3.4 Geographically Integrated Markets and General Demand for Stolen Cars The final case I consider is one in which demand for stolen cars is common across car models and states. Demand is given by d d d d Ps1m1 = Ps1m0 = Ps0m1 = Ps0m0 = D(Ns1m1 + Ns1m0 + Ns0m1 + Ns0m0 ) When demand for stolen vehicles is common across models, and markets are geographically inte- grated, the introduction of Lojack generates negative spatial spillovers to both car models in the Non-Lojack state. Further, non-Lojack models in Lojack states also experience increases in theft. s As before, Lojack reduces the supply of Lojack equipped vehicles Ns1m1 = S(Ps1m1 ) − Lojack. The model is solved in Appendix A, with the following predictions: ∗ ∂Ns1m1 ∂Lojack <0 ⇒ Deterrence Effect ∗ ∂Ns1m0 ∂Lojack >0 ⇒ Within-State Externality to Non Lojack Model ∗ ∂Ns0m1 ∂Lojack >0 ⇒ Model Specific Spatial Externality ∗ ∂Ns0m0 ∂Lojack >0 ⇒ Spatial Externality to Non Lojack Model 11
  13. 13. Under these conditions, the introduction of the Lojack program generates increases in theft risk in all other markets. When crime is displaced to all other markets as a reaction to efforts to reduce crime in one of them, more comprehensive crime reduction policies are called for. In this case, a stronger emphasis on incapacitation is desirable. The four cases of the model I oversaw give different predictions about the impact of Lojack introduction into the stolen vehicle market. The empirical analysis will show that the evidence favors the third case, in which crime is spatially displaced within car models. In concordance with the third case, I find insignificant changes in theft risk for the Non-Lojack models, in either state. 4 Data The data consist of detailed auto sales and theft reports at the Mexican state level. Because there is no country-wide auto theft database compiled by a government agency in Mexico, no longitudinal crime studies using Mexican data have been performed up to now. This paper is the first to use detailed auto theft data on Mexico from a a novel source, the internal reports generated by the Mexican Association of Insurance Companies (AMIS).5 AMIS is a non-profit organization funded by insurance companies that compiles industry-wide theft and accident rates. These statistics are then used by members of the association to price insurance contracts. AMIS associated companies have a market share of over 80% of the automobile insurance market. The database is generated continuously: when an insured vehicle is stolen, the owner calls his insurance company to file a report; as soon as the employee of the insurance company fills out the electronic report for the company’s use, a copy of it is automatically sent to the compiling system at AMIS. Under this system, if a stolen vehicle is recovered, the report of the robbery is still preserved. I use AMIS data on all countrywide theft cases reported from January 1999 to December 2004. For each event of theft reported to AMIS, I have information on the brand and model of the car, the date and state where the theft occurred, and the year the car was sold. The auto sales data were provided by the Mexican Association of the Automobile Industry (AMIA).6 AMIA is a non-profit organization formed by the major vehicle distributors and manu- 5 6 12
  14. 14. facturers in the country, which compiles detailed data on automobile sales. The series used here are annual dealership sales at the state level from 1999 to 2004. The data were available aggregated into various categories of brand and car type. For each brand, the vehicles were classified into categories: subcompacts, compacts, luxury cars, sports cars, SUVs, minivans, and trucks. I aggre- gated the AMIS theft data to match the AMIA sales data (annual state sales for each model group) and both datasets were then merged. The resulting groups of cars are shown in Table 2. Some of the groups consist of single models, while others contain various models. Throughout the paper, the terms model and model-group are used interchangeably to refer to the groupings of vehicles in Table 2. The econometric analysis uses variation in theft risk over time to identify the effect of Lojack. For that reason, the unit of observation should be car models whose theft risk can be followed throughout the analysis period. All theft cases of cars sold up to 1998 but stolen between 1999 and 2005 were not used as units of observation because of lack of data on the stock susceptible to being stolen: state level sales of vintages of car models sold before 1999. The second type of discarded observations was car models introduced into the national market after Lojack was implemented. For these vehicles, it is impossible to analyze theft risk before Lojack was introduced. Similarly, some models were discontinued before the Lojack intervention. For these models, there is no post-treatment data available to analyze theft behavior, so they are left out. After these deletions, I have data on car models for which information on theft risk is available before and after Lojack was implemented. In total, there are 69 model-groups for which I have up to 21 observations in each of 32 Mexican states. The panel is unbalanced with triangular matrix form: For each model and state, I have up to 6 annual theft observations for the 1999 vintage, 5 annual theft observations for the 2000 vintage, and so on, with only one theft observation for the 2004 vintage. However, the data do not consist of these 44,919 possible cases mainly because some car brands have no distribution channels in low population states. Additionally, some car models – especially sports cars and luxury cars – are not sold in some of the poorer states. The final dataset has a total of 26,213 observations. Summary statistics are presented in Table 3. Each cell in the dataset is defined by a quadruplet (state, model group, vintage, year) combi- nation with available data. Panel A of the table presents descriptive statistics for all observations. 13
  15. 15. The average vintage of cars has 632 vehicles, and in any given year 4.1 of those vehicles are stolen. This results in a mean annual theft rate of 6.5 cars per 1000 vehicles. The maximum number of thefts in any of the observation units was 1,502. The cars being studied are relatively new: they range from zero to five completed years on the road.7 The average car age is 1.6 years. Mean age is not three because, by construction, there are fewer observations of older cars: all cars are observed when they are new, but the only observations available for five year old cars are those that were made in 1999. Lojack is a dummy variable equal to one if the car was sold equipped with Lojack. Out of all the observation units, 0.4% had Lojack installed when they were new. Panel B provides descriptive statistics for vehicles equipped with Lojack when they were sold. Their mean age is smaller (0.44 years) than the whole group because Lojack was introduced in the latter part of the panel. Panels C and D partition the observations into Lojack and non-Lojack car models. Lojack model vintages are about a third the size of non-Lojack ones. This is due to the fact that Lojack models do not include any subcompact car models, which have the highest sales volumes. Panels E and F partition the observations into Lojack states and Non Lojack states. Lojack states have larger vintages, and correspondingly higher thefts than non-Lojack states. Their mean theft rate is also higher: 1.1% of vehicles are stolen in any given year in Lojack states versus only 0.2% in non-Lojack ones. A first caveat with this data is that it provides information about where the car was sold, but not where the car currently resides. Although the latter is preferred, if the probability that a car of a given model and year migrates from state j to state i is equal to the probability that a car of the same model and year migrates from state i to j, then the first variable is a noisy but unbiased measure of the number of cars in a state. However, one can imagine that some states are net exporters of cars to other states. This would induce a systematic error in the measure of cars exposed to theft, and is dealt with in the section on robustness checks. A second and more important caveat is that the data available are not total number of thefts, but rather total thefts of insured vehicles. The Robustness Checks section provides evidence that Lojack introduction did not have any effect on the rate at which Lojack models were being insured; this is important in identifying the effect of Lojack on theft risk for different vehicles. 7 Age is set to 0 if the vehicle is less than 12 months old, 1 if it is between 12 and 24 months old, etc. 14
  16. 16. 5 Estimation Strategy In the presence of spatial externalities, difference in difference estimation using observations from different geographical locations produces biased estimates of policy impact (cf. Miguel and Kremer (2004)). The basic challenge is that whenever treatment in one geographical location also has effects in control locations, the latter are no longer valid counterfactual observations. Furthermore, difference in difference estimation precludes estimation of externalities unless there is a set of observations subject to externalities and a set of observations that is not, where the latter can be treated as a control group. For these reasons, my baseline estimation identifies the impact of Lojack in each of the groups of interest from changes in theft risk coincidental with the introduction of the program. With this strategy, the control group consists of observations from before the onset of the Lojack program, instead of observations from other geographical locations. The dependent variable in the empirical analysis is the number of vehicles stolen in a (state, model group, vintage, year) cell; it is non-negative and integer-valued. A histogram of the theft variable is presented in Figure 1. As the figure makes clear, over 60% of the observations are zero. When the dependent variable is this type, OLS is problematic because the conditional mean function takes on negative values. I therefore use the canonical model for count data in my estimations – a Poisson regression model. The model presented in section 3 suggests four groups of vehicles in which the impact of Lojack should be assessed: (1) Lojack models in Lojack states, (2) Non-Lojack models in Lojack states, (3) Lojack models in non-Lojack states neighboring those where Lojack was introduced, and (4) Non-Lojack models in non-Lojack states neighboring those where Lojack was introduced. To estimate the deterrence effect of Lojack on Lojack equipped vehicles, I use observations of Lojack models in Lojack states to fit: 5 E[T hef tsijyt ] = (Sijy ) · exp γij + βj · t + βa · I[Age = a] + βLojack · Lojackijy (1) a=0 To estimate externalities to Non-Lojack models in Lojack states, I use observations of non-Lojack 15
  17. 17. models in Lojack states to fit: 5 E[T hef tsijyt ] = (Sijy )·exp γij + βj · t + βa · I[Age = a] + βAf terLojack · Af terLojackjt (2) a=0 Finally, to estimate externalities in non-Lojack states for Lojack and non-Lojack models, I estimate – for each group separately – the following equation in subsamples of increasing distance from Lojack states: 5 E[T hef tsijyt ] = (Sijy )·exp γij + βj · t + βa · I[Age = a] + βAf terLojack · Af terLojackjt (3) a=0 where the dependent variable T hef tsijyt is the number of vehicles stolen in a state, model group, vintage, and year combination. Sijy refers to the vintage size in a state-model-vintage combination, which is a proxy for the stock of cars susceptible to being stolen. I also include a fixed effect (γij ) for every combination of state and car model in the data. This incorporates the fact that theft risk varies according to location (state) and vehicle type (model group). A state specific time trend (βj · t) is also included. Vehicle-age dummies (I[Age = t − y]) capture the mean theft schedule according to the age of the car. Typically, newer cars are subject to higher theft risk. In equation (1), Lojackijy is a dummy variable indicating if the vehicle was equipped with Lojack when it was sold. The coefficient of interest, βLojack , is identified from a deviations (upward or downward) in theft risk of vintages sold with Lojack from what was predicted by the linear time trend estimated from vintages sold without Lojack. The four Lojack states are labeled in figure 2. Only data from Lojack models in Lojack states is used in the estimation of model (1). In equation (2), Af terLojackjt is a dummy variable equal to one if Lojack has been introduced into the state. βAf terLojack is identified in the same way as before, but is now interpreted as the magnitude of the within-state externality. Only non-Lojack model data from Lojack states is used in estimation of model (2). In equation (3), Af terLojackjt is a dummy variable indicating that the Lojack program has been introduced in the nearest Lojack state. The associated coefficient, βAf terLojack , is interpreted as the geographical externality that Lojack generated. Equation (3) is estimated separately for Lojack and non Lojack models on three different subsamples that vary according to their distance to the 16
  18. 18. nearest Lojack state. First are Lojack states contiguous to those where Lojack was implemented, referred to as First Ring states. Then the equation is estimated on the second ring of states around Lojack states – these are referred to as Second Ring states. The rest of states are referred to as Distant States and model (3) is estimated for those observations too. A map of these state groups can be found in figure 2. Including a state specific time trend is important because vehicles in the same state are subject to the same police and judiciary institutions, which generate different theft dynamics over time in each state. The descriptive statistics showed that there is much heterogeneity in theft risk depending on the model and the state. In such situations, one major worry is that estimated effects may simply be capturing cross-sectional differences in theft risk, particularly in cases such as this one in which the treatment was not randomly assigned. This concern is addressed by including a fixed effect (γij ) for every (state, car model) in the data. In other words, average differences in theft behavior across car models or states are not the source of identification of the coefficient of interest.8 Sijy allows for a meaningful comparison of theft risk given that the quantity of cars at risk varies by model, state and vintage. That is, given that different models have radically different market shares, any analysis of auto theft that seeks to distinguish between car models in the same geographic location must control for the quantity of cars at risk of theft.9 The exponential form of the conditional expectation, and the fact that the coefficient of interest, βLojack , is associated with a dummy variable, makes interpretation of the coefficient highly intuitive. The ratio of expected thefts conditional on having Lojack to expected thefts conditional on not having Lojack is: E[T hef tsijyt |xijyt , Lojackijyt = 1] = eβLojack E[T hef tsijyt |xijyt , Lojackijyt = 0] The estimated effect is independent of the values of the other regressors in xijyt . For this reason, alongside the Poisson regression coefficients I also report exponentiated coefficients-1, also known as incidence rate ratios (IRR-1). These are interpreted as percentage changes in theft risk due to 8 Standard errors are clustered at the state level (Bertrand, Duflo, and Mullainathan (2004)). Cameron, Gelbach, and Miller (2006) two-way clustered standard errors at the state and year level were also calculated, without changing the significance of the results. 9 In a Poisson regression, this is referred to as “controlling for exposure”. The exposure variable (Sijy ), is usually incorporated with a coefficient constrained to unity. This introduces the assumption that thefts are a function of the stock of cars and that this relationship is the same across all car models: a doubling of the stock accompanied by a doubling of thefts is interpreted as keeping theft risk constant. The results are robust to a relaxation of the coefficient restriction on Sijy . See the Robustness Checks section. 17
  19. 19. the Lojack program. The theoretical framework suggests that βLojack should be negative for vehicles equipped with Lojack. It also suggests that if demand for stolen vehicles is model specific and there is trade across state lines, Lojack models in neighboring states should experience increases in theft risk once Lojack is introduced in the nearest Lojack state: βAf terLojack would be positive in equation (3). The effect should be decreasing with distance from Lojack states. On the other hand, if demand for stolen vehicles is common across car models, increased theft risk for non-Lojack models in Lojack states would take the form a positive βAf terLojack coefficient in equation (2). An extensive literature has focused on the difficulty in measuring program effects when par- ticipation is voluntary (Heckman (1979)). This problem is not present in Ford’s Lojack program. Ford’s vehicles were sold for the same price nationally, regardless of whether the state was partici- pating in the Lojack program. This yields two benefits for this study. First, conditional on buying a Lojack model, participation in the program was not voluntary. Ford engaged in this program under the rationale that it would be able to sell more cars, albeit with a lower profit margin. Any effect of Lojack on sales is controlled for in the empirical analysis through the stock-of-cars expo- sure control. Second, the single national price, together with the locality-specific recovery service, means that there was practically no incentive for customers to buy their cars in a different state from where they lived. With equal prices, a customer in a Lojack state had no incentive to buy a car in a non-Lojack state. Similarly, a customer in a non-Lojack state had scant incentive to buy a Lojack-equipped car and drive it to a state that did not have the Lojack recovery service available. Before presenting the results, I should mention that Poisson models have standard errors that are too small if there is overdispersion in the data (conditional variance that is larger than the conditional mean). I present estimates of a model robust to overdispersion (the negative binomial) in the Robustness Checks section and show that the estimated standard errors are smaller than those of the Poisson model, which suggests that the Poisson model is adequate for the data. Further, in the tables, I also show the result of the overdispersion test suggested by Cameron and Trivedi (1998). If α < 1, overdispersion is modest and Poisson and Negative Binomial standard errors are of similar magnitude. However, under no (or modest) overdispersion, the Poisson model is preferred because it is robust to distributional misspecification of the dependent variable. The Negative Binomial model, on the other hand, generates inconsistent coefficients under distributional misspecification 18
  20. 20. in the dependent variable. 6 Results In Table 4 I present results for the impact of Lojack on theft risk of Lojack-equipped vehicles in Lojack states. The trend break identification strategy suggests that theft risk was reduced by 48% for vintages equipped with Lojack. This is an extremely large reduction in theft risk. For comparison, Di Tella and Schargrodsky (2004) find that stationing a police officer full time in a street block reduces theft risk by 75%. The theoretical model suggested that by making Lojack equipped vehicles more difficult to steal, thieves would reduce attempted thefts on this group of vehicles. The empirical evidence strongly corroborates this prediction. Regarding the Non-Lojack models in Lojack states group, I do not find a significant change in theft risk coincidental with the introduction of Lojack in the state. The estimated reduction of 5% in theft risk from Table 4 is not close to being significant. The theoretical model suggests that this result is due to a lack of common demand for stolen vehicles across car models. Another explanation is also possible. The incapacitation effects of Lojack work opposite to the displacement effects: If Lojack incapacitated criminals, and these were engaged in both types of vehicle thefts, this could have generated a reduction in thefts of the non-Lojack model. I show evidence below that indeed the number of criminals charged for property theft increased in Lojack states with the introduction of Lojack. Results from estimation of spatial externalities are presented in Table 5. In the set of states contiguous to those where Lojack was implemented, theft risk of Lojack models increased by 77% with the introduction of Lojack. Non-Lojack models, on the other hand, were not significantly affected. In the second ring of states around Lojack states, Lojack model thefts increased by 61% with the introduction of Lojack. Again, theft risk of non-Lojack models was not significantly affected. Finally, in all other states, referred to as “distant states”, introduction of Lojack in the nearest Lojack state was not associated to significant changes in theft risk for either the Lojack or the non-Lojack model groups. Taken together, the evidence suggests that Lojack was highly effective in reducing thefts of Lojack protected vehicles through a deterrence effect. Nevertheless, the reduction in thefts of 19
  21. 21. Lojack-protected models generated a negative spatial externality in Lojack models of nearby states. The estimations did not produce evidence of displacement across car models, either in the Lojack state or in nearby states. The reported effects in the previous tables are in terms of changes in theft risk. But Poisson regressions have the advantage that it is straightforward to obtain an estimate of the magnitude of the effect in terms of the number of cars stolen. The measure of interest is the difference in expected thefts with and without the Lojack program: (E[T hef tsijyt |xijyt , Lojackijyt = 1] − E[T hef tsijyt |xijyt , Lojackijyt = 0]) ij∈Λ where the sum is across all car models and states. Because of the conditional expectation’s form, the sum can be rewritten as the percent change in thefts attributable to Lojack multiplied by the pre-Lojack average annual thefts in the group:   (IRR − 1) ·  E[T hef tsijt | Lojackijyt = 0] (4) ij∈Λ This is simply a function of the Poisson coefficient and the size of the group of affected cars. The standard errors are obtained with the delta method. Table 6 presents the estimated impact in terms of vehicles stolen. For Lojack models in Lojack states, thefts are estimated to have gone from an average of 276 vehicles per year to 144 due to the Lojack protection. In the first ring of states around Lojack states, the mean number of Lojack models stolen went from 18.3 to 32.4 per year due to the Lojack externality. In the second ring of states around Lojack states the change was from 21.6 Lojack models to 35. All the other changes were not statistically different from zero. Although I have presented results of the impact of the Lojack program on the 4 groups of vehicles suggested by the empirical model, crime could have could have been displaced to other vehicle groups and other crimes. I am not able to analyze displacement to older vintages, because I do not have information of the number of older vehicles subject to theft. However, I can focus on Lojack models produced before Lojack was introduced. The expected direction of the spillover on this group is ambiguous. If a model vintage looks very similar in the years just before and just after it got Lojack, it may have been difficult for thieves to distinguish between those equipped with 20
  22. 22. Lojack from those that were not. Another reason for a positive externality is that some thieves may have been unsure about when the program started, in which case it would not be surprising to find a positive spillover effect of having Lojack installed in future versions of the model. However, if there is little confusion for thieves about which models had Lojack, and the cars are close substitutes, then one could find negative spillovers along this dimension, too. In other words, if auto thieves realize that Ford Windstars sold after 2000 have Lojack, do they increase or decrease the theft of close substitutes, like a Ford Windstar sold in 1999? I run a regression identical to equation (2) except that the Af ter Lojack regressor is one for Lojack models built before the model came equipped with Lojack, in years after Lojack was introduced in its newer versions. I use the subsample of observations consisting of old vintages of Lojack models in Lojack states. The result, shown in Table 7, is that the estimated impact is not different from zero, suggesting that there were no net externalities towards older versions of Lojack models. I now present evidence that suggests that the reduction in auto theft generated by Lojack was not displaced towards other types of crimes for which I have available data. I obtained a state level panel dataset from the Mexican national statistical agency (INEGI) with information on the number of criminals charged for different offenses. I analyze if the number of criminals charged (per 1000 adults) for kidnapping and drug trafficking offenses changed with the introduction of the Lojack program. Table 8 presents results from OLS difference in difference regressions of drug trafficking and kidnapping offenses in Lojack (and neighboring non-Lojack states). The results in the table show that there were no significant changes in crimes in either of these categories. This suggests that the reduction in vehicle thefts of Lojack models was not displaced towards these other crimes. The last panel in the table considers the number of criminals charged for theft (per 1000 adults) in the state. The table shows that in Lojack states, the number of criminals charged for theft (annual mean of 0.99 per thousand adults) increased by 0.30 coincidental with the introduction of Lojack. If this increase was caused by a larger number of automobile thieves being captured by the police, it may have had positive spillovers to Non-Lojack models in Lojack states. In Non-Lojack states, I find no significant change in the number of criminals charged for this crime category. The Ford Lojack program consisted of installing the Lojack tracking device in all participating 21
  23. 23. Ford models in Lojack states, and paying for the first year of recovery service. However, after the first year, continuation of the recovery service was conditional on a payment of around $100. 60% of Lojack equipped vehicles renovated their service after the first year, and 40% of the vintage did so after the second year. This is interesting because within the vintages of cars sold with the Lojack equipment, which vehicles had the recovery service after the first year was unknown to a casual observer. In a sense, Lojack had become an unobservable theft deterrence device within the older vintages of participating car models. The data allow me to estimate the impact of Lojack as the proportion of cars that effectively had the recovery service was declining. I subdivide the Lojack dummy into three categories: a dummy for Lojack equipped and age up to one year, Lojack equipped and age between one and two years, and Lojack equipped and age between two and more. I use the subsample of Lojack models in Lojack states. Table 9 reports the results of my estimation. At every age, the coefficients are very similar to the average effect estimated before. This suggests that the deterrence effect of Lojack was very similar in magnitude regardless of how old the vehicles were. Estimation of theft risk as the proportion of vehicles with Lojack recovery services went from 100% to 40% shows that the reduction in theft risk is very similar in magnitude regardless of the proportion with the recovery service. While it may be possible that auto thieves were not aware of the voluntary continuation of the service, another explanation is that the marginal impact of Lojack on theft deterrence is very high with a small proportion of vehicles protected, and decreases rapidly as the proportion of vehicles protected increases. Indeed, Ayres and Levitt’s (1998) study also finds evidence of a rapidly decreasing marginal impact of Lojack as the proportion of protected vehicles increases. The Ford Lojack program in Mexico was halted in 2006. Under severe cost cutting pressures, the auto maker decided to cancel the program. Ford executives had established the program with the objective of increasing sales of its vehicles. I provide evidence in Table 8 that although sales did increase measured by market share in category, the effect was rather small. I estimate that Lojack only generated an increase of 2.7% in market share within the model category. After the Ford deal collapsed, the Lojack-selling company started offering Lojack to anyone interested in having the recovery service, effectively ending the strategy of marketing to an exclusive set of cars. The company launched an aggressive publicity campaign and expanded their service to many other states and now offer coverage in all states. This way of selling Lojack should result in 22
  24. 24. generalized declines in theft rates, with large positive externalities and a positive net social benefit from the technology, as Ayres and Levitt (1998) have argued. The results presented in this section imply that selling Lojack to a discernible set of cars severely limits its potential positive spillovers. This finding may be useful in future scenarios to better inform policymakers about how to regulate and adopt new technology so as to maximize society’s welfare. 6.1 Robustness Checks 6.1.1 Data Limitations This section reviews the implications for the analysis of using insured vehicle theft data together with total stock of cars, instead of the insured vehicle stock of cars. The intuition of the problem this presents is relatively simple: the interpretation of the results is invalid if Lojack generated changes in the likelihood of a Lojack-equipped vehicle being insured. If buying a car with Lojack made owners less likely to buy insurance, then this would reduce the number of cars exposed to theft that are captured in the data, potentially influencing some of the results. The problem can be seen in terms of the estimated model. The data available, in which total stock of cars instead of the insured vehicle stock is used as the exposure variable, can be understood as a situation in which the true exposure variable is overblown by a factor larger than one. Assume that πij is the probability that a vehicle model i in state j is insured. Then the true stock of cars is Sijy = πij · Sijy , where S Obs refers to the stock of vehicles observable to the econometrician, T rue Obs while S T rue refers to the actual stock of insured cars on the road. Then, if the true model is 6 true E[T hef tsijyt |xijyt ] = (Sijy ) · exp γij + βj · t + βLojack · Lojackijyt + βa · I[Age = a] a=0 T rue Obs Substituting Sijy = πij · Sijy in the equation above yields 6 Obs E[T hef tsijyt |xijyt ] = (Sijy )·exp ln(πij ) + γij + βj · t + βLojack · Lojackijyt + βa · I[Age = a] a=0 ln(πij ) + γij is then absorbed by the model and state-specific fixed effect and the error in the exposure variable does not bias the results. The state-model fixed effect deals with another type of error in the exposure variable: migration rates of vehicles that are not netted out between states, 23
  25. 25. as long as they are stable throughout the panel. In conclusion, the specification used is robust to additive error in the exposure variable. However, a problem arises if there is temporal variation in πij which is correlated with the introduction of the Lojack program. Under such scenario, the coefficient of interest, (βLojack ) is not identified. For this reason, I now present evidence that: 1) Lojack-equipped vehicles were just as likely to be insured as non-Lojack-equipped vehicles; and 2) insurance likelihood of Lojack models evolved in an identical manner to non-Lojack models once Lojack was introduced. This allows me to conclude that Lojack introduction was uncorrelated with insurance coverage (πij ) probability, as required by the econometric model. First, note that the scope for this behavioral response would be severely limited by the fact that in the years after Lojack was introduced, around 70% of new vehicles were bought with financing loans, which require insurance coverage during the life of the loan. Cars bought through a loan are required to be insured because the financing company otherwise can lose the collateral that can be repossessed in case of an accident or theft. The insurance requirement for cars bought on credit was not relaxed because the car had Lojack. The data I use to measure the possible impact of Lojack introduction on insurance probability are the AMIS time series of the number of cars insured by year in the whole country for every car model. Since Lojack states command 40% of nationwide sales, a reduction in the insurance coverage of Lojack models would show up in the national insurance coverage rate for those models. I use national sales for the years 1999-2005 and the number of national insurance contracts, to construct a database that partitions the data into combinations of triplets (model group, vintage, year). I then generate the variable proportion insured which is defined as the number of vehicles insured divided by the stock of cars sold for every (model group, vintage, year) cell. I first use data for the years after the introduction of Lojack to regress the proportion insured on a dummy indicating whether the vehicle was sold with Lojack (Lojackij ), calendar year dummies (I[t = 1999], ..., I[t = 2005]) to capture time trends in national insurance coverage, and a set of age-of- car dummies (I[Age = 1], ..., I[Age = 6]) that flexibly capture average changes in the insurance probability as the car ages. The estimated equation in the first column of Table 11 is P roportion Insurediyt = β0 +βLojack ·Lojackiy +βage=t−y ·I[Age = t−y]+βyear=t I[Y ear = t]+uiyt 24
  26. 26. where i refers to the model group, y to the year the cars were sold, and t refers to the year of the observation. The coefficient of interest is βLojack . In the table, the Lojack coefficient is insignificant; this suggests that after Lojack was implemented, Lojack models were just as likely to be insured as non-Lojack models. Thus buying a car equipped with Lojack did not reduce the probability of the car being insured, as long as Lojack models were as likely to be insured as their counterparts before Lojack was introduced. The second regression addresses this issue by looking for differential changes over time in insurance coverage for Lojack models. The equation estimated in the second column of the table is P roportion Insurediyt = βi +βLojack ·Lojackiyt +βage=t−y ·I[Age = t−y]+βyear=t I[Y ear = t]+uiyt which differs from the previous regression in that it includes a model-specific intercept and uses data from all observations available: for the years 1999-2005. The insignificance of the coefficient in the table again suggests that Lojack models neither observed a decrease nor an increase in insurance likelihood, compared to other car models, once Lojack was introduced. The regressions lead me to conclude that Lojack did not induce a reduction in the probability of insuring vehicles for customers who bought Lojack-equipped cars. There may have been various reasons for this. People who bought the car with credit had no option of opting out of insuring their vehicle even if they wanted to. Another reason is that people value the services of insurance companies aside from theft coverage: insuring vehicle damage in case of accidents, medical expense insurance for vehicle occupants, and civil responsibility. A possible concern about the motivations determining which vehicles would be part of the Ford Lojack program is that the car models participating in the program could have been those for which theft rates were increasing before the program. If this were true, mean reversion could become a possible explanation for the reduction in theft risk of the Lojack-model, Lojack state group. To address this concern, I regress the annual change in theft rate10 on future Lojack program participation in columns 1 and 2 of Table 12. The results show that compared to both all car models, and all Ford models, Lojack participating vehicles did not experience different changes 10 Annual change in theft rate is a demeaned change in rate of theft, to account for differences across states and ages of vehicles. Change in theft rate defined as calendar year change in theft rate for a given car model, age and state combination. The mean of those changes is a weighted average across car models for a given age and state. 25
  27. 27. in theft risk before the Lojack program. The sign is insignificant and of opposite sign to what a mean reversion story would predict. 6.1.2 Specification Robustness Checks In this section I report the results of variants of the main regressions in order to verify their robustness. Table 13 reports results from the main specification in the first panel for comparability purposes. For space reasons, the table only reports the estimated percentage change in theft risk generated by Lojack in each group (IRR − 1). The second panel in the table, labeled “Difference in Difference” identifies the impact of Lojack using the set of Distant States as a control group. The justification for doing this is that the main specification results suggested that Lojack did not have a significant spillover effect on vehicles in distant states. The difference in difference identification strategy does not depend on breaks from a linear time trend to identify the impact of Lojack. Rather, it compares the evolution of theft risk between Lojack (or neighboring states) to distant states, under the assumption that Lojack did not generate any externalities in distant states and that time effects in theft risk were common across both groups. The results are very similar to those of the main specification, both in terms of signs and magnitudes. Instead of a 48% reduction in theft risk of the Lojack model-Lojack state group, the difference in difference identification strategy estimates a reduction of 42% in theft risk. Lojack models in the first ring around Lojack states experience an increase of 87% in theft risk as opposed to a 77% with the baseline strategy. Similarly, there are no significant impacts in non-Lojack models in any of the regressions. The only notable difference between these two estimations is that in the second ring of states around Lojack states, Lojack models are estimated to have suffered a 32% increase in theft risk (insignificant) versus a 61% increase (significant) in the baseline estimation. The third panel of the table, labeled “Negative Binomial”, replicates the main regressions using a Negative Binomial estimation procedure. Cameron and Trivedi (1998) warn that fitting a Poisson when there is overdispersion in the data generates standard errors that are too small. A Negative Binomial regression is adequate with overdispersed data, but its coefficient estimates are sensitive to misspecification of the data generating process, unlike the Poisson regression. Comparing the standard errors of both estimated models shows that those of the Negative 26
  28. 28. Binomial are in all cases smaller than those in the Poisson regression. The extremely small α’s found in the Poisson specification suggested that the standard errors in the Poisson and the Negative Binomial regression would not be very different. The size of the standard errors in the Negative Binomial estimation confirm this intuition. The estimated coefficients in the Binomial model are extremely close and of the same sign as those in the Poisson model. Given the robustness of the Poisson model to misspecification, and the small degree of overdispersion in the data, I take it as the preferred model. The fourth panel, labeled “Clusters of States” addresses the fact that the baseline estimations assume independence of error terms across states. This may not be a reasonable assumption if theft risk is spatially correlated across state lines. This is especially important because three of the Lojack states are contiguous. For the externality regressions, it is not difficult to imagine that Lojack states around a particular Lojack state may share common theft risk shocks. To address this concern, I place all contiguous Lojack states into a single cluster. For the externality regressions, I place all non-Lojack states surrounding a particular Lojack state into a single cluster. The panel shows that the results are robust to this redefinition of clusters. In the fifth panel, labeled “Inflated Thefts”, I use another approach to the problem of having only insured vehicle theft data. I inflate theft cases by the corresponding reciprocal of the national insurance rate for each (model group, vintage, year), so that if only half of the (national amount of) vehicles are insured, the observed theft cases are multiplied by two. This new dependent variable would adequately correct for the lack of information on insured vehicle stocks at the state level if national insurance rates were the same as state rates, and if theft risk were uncorrelated with insurance status. This is a crude correction, but in exchange it directly scales the dependent variable proportional to any national changes in insurance likelihood. With inflated thefts, the table shows that estimated impacts are larger than in the baseline specification, but so are the standard errors. In contrast to the main specification, however, the regression that uses inflated thefts displays negative externalities to non-Lojack vehicles in Lojack states, although the coefficient seems implausibly large. The last robustness check deals with an alternative explanation for the results. The theft- risk function used in the analysis assumes that there is a linear relationship between the stock of vehicles and the number of thefts, by constraining the coefficient on the stock of vehicles to enter 27
  29. 29. lineally in the regression. However, this might not be a good model of how theft actually works. For example, it may be that the demand for stolen vehicles is simply a target number of stolen cars, independent of the stock available (See Camerer, Babcock, Loewenstein, and Thaler (1997) for income targeting in the workplace). If this were the case, and Lojack generated an increase in sales of Lojack-equipped models, then my assumed specification would show a fall in theft risk, even though Lojack only generated an increase in sales. Any feature in a car that increased sales – like lower prices or more add-ons – would have the same effect as Lojack. This would make my interpretation about the effects of Lojack completely misleading. The main specification can be altered to accommodate this alternative hypothesis. This is done by eliminating the restriction that the stock variable have a coefficient equal to one. If the targeting hypothesis is true, then the stock coefficient would be smaller than one and the coefficient on Lojack would be sharply reduced (in absolute value). The panel labeled Unconstrained Exposure in the table reports the coefficients from this alternative specification, together with the coefficient on the exposure variable. The results are virtually unchanged from the main specification. Furthermore, the coefficient on the exposure variable does not seem to be consistently below or above one. In conclusion, the targeting hypothesis does not seem be supported in the data. Another exercise unreported for space reasons is to run the baseline regression sequentially deleting all of the observations for one of the car models. This would confirm that it is not one model that is driving the results. The coefficients are extremely similar to those of the baseline results. A final unreported robustness check addresses the concern that the data used is not a balanced panel. There is an increasing number of observations available for older vintages. I ran the regres- sions with a balanced panel, only using observations of every vintage when aged 0 and aged 1. The results are very similar to the baseline results, suggesting that the triangular form of the data is not something to be concerned about. 7 Conclusion Knowledge of the extent of crime displacement is extremely important in the design of effective crime prevention strategies. In spite of a firm theoretical grounding in the economics of crime 28
  30. 30. literature, crime displacement has proved difficult to document in previous empirical work. This paper used the introduction of the Lojack vehicle recovery technology to a discernible group of cars in Mexico to measure the extent of theft displacement from vehicles protected by an observable theft deterrence device to unprotected vehicles. The proposed model of deterrence and displacement in auto theft provided differential predic- tions regarding the location of displacement according to the structure of the market for stolen vehicles. In all cases of the model, Lojack equipped vehicles were predicted to experience lower theft risk. The empirical evidence confirmed this prediction, with an estimated reduction in theft risk of 48% for Lojack protected cars. If demand for stolen cars is model specific – possibly due to an active trade in stolen autoparts – and if markets for stolen vehicles are integrated across state lines, the theory predicts negative spillovers to states surrounding those where Lojack was implemented, but limited to the same car models that in Lojack states got Lojack. The empirical evidence supported this prediction. Lojack models in states directly surrounding Lojack ones experienced an increase in theft risk of 77% after the introduction of Lojack in the nearest Lojack state. For the second ring of states surrounding those where Lojack was introduced, the corresponding increase in theft risk was of 61%. For more distant states, there was no significant change in theft risk coincidental with the introduction of Lojack in the nearest Lojack state. The fact that actions to reduce auto theft in one state generated negative externalities in contiguous states has important implications for crime prevention policies. An influential view advocated by Sherman, Gartin, and Buerger (1989) is that law enforcement officials should focus their efforts on “crime hot spots” defined as high crime locations and times. Whenever there is relatively little displacement of crime, the recommendation of targeted interventions is adequate. However, this paper suggests that whenever crime is mobile, a more comprehensive approach is warranted. The evidence presented here shows that auto theft is a high mobility crime which may not be adequately combatted in a spatially targeted manner. For high mobility crimes, interjuris- dictional coordination in crime prevention policies, or a shift in the level of government in charge of this function may be a more desirable course of action for achieving reductions in crime than having independent and local criminal law enforcement efforts. 29
  31. 31. References Ayres, I., and S. Levitt (1998): “Measuring Positive Externalities From Unobservable Victim Precaution: An Empirical Analysis of LoJack,” Quarterly Journal of Economics, 113(1), 43–77. Bertrand, M., E. Duflo, and S. Mullainathan (2004): “How Much Should We Trust Differences-in-Differences Estimates,” Quarterly Journal of Economics, 119(1). Camerer, C., L. Babcock, G. Loewenstein, and R. Thaler (1997): “Labor Supply of New York City Cabdrivers: One Day At A Time,” Quarterly Journal of Economics, 112(2), 407–441. Cameron, A. C., J. B. Gelbach, and D. L. Miller (2006): “Robust Inference with Multi-Way Clustering,” NBER Working Paper, (T0327). Cameron, A. C., and P. K. Trivedi (1998): Regression analysis of count data. Econometric Society Monographs, no. 30. Clarke, R. V., and P. M. Harris (1992): “Auto Theft and Its Prevention,” Crime and Justice, 16, 1–54. Clotfelter, C. T. (1977): “Public Services, Private Substitutes, and the Demand for Protection Against Crime,” American Economic Review, 67. (1978): “Private Security and the Public Safety,” Journal of Urban Economics. Di Tella, R., and E. Schargrodsky (2004): “Do Police Reduce Crime? Estimates Using the Allocation of Police Forces after a Terrorist Attack,” American Economic Review, 94(1). Donahue, J. D. (1997): “Tiebout? Or Not Tiebout? The Market Metaphor and America’s Devolution Debate,” Journal of Economic Perspectives, 11(4), 73–81. Heckman, J. (1979): “Sample Selection Bias as a Specification Error,” Econometrica, 47. Hesseling, R. (1994): Displacement: A Review of the Empirical Literaturein R. Clarke, ed. Crime Prevention Studies, III. Criminal Justice Press. Monsey, NY. Jacob, B., L. Lefgren, and E. Moretti (2005): “The Dynamics of Criminal Behavior: Evi- dence from Weather Shocks,” KSG Working Paper No. RWP05-003. 30
  32. 32. Karmen, A. (1981): “Auto Theft and Corporate Irresponsibility,” Contemporary Crises, 5, 63–81. LoJack (2006): “LoJack Recovery Statistics,” Electronic document: Date retrieved: September 14, 2006. Mayhew, P., R. V. Clarke, and D. Elliot (1989): “Motorcycle Theft, Helmet Legislation and Displacement,” Howard Journal of Criminal Justice, 28, 1–8. Miguel, E., and M. Kremer (2004): “Worms: Identifying Impacts on Education and Health in the Presence of Treatment Externalities,” Econometrica, 72(1), 159217. Newlon, E. (2001): “Spillover Crime and Jurisdictional Expenditure on Law Enforcement: a Municipal Level Analysis,” Mimeo. Romano, J. (1991): “Device to Track Stolen Cars Raises Questions,” New York Times, June 30. Shavell, S. (1991): “Individual Precautions to Prevent Theft: Private versus Socially Optimal Behavior,” International Review of Law and Economics, 11. Sherman, L. W., P. R. Gartin, and M. E. Buerger (1989): “Hot Spots of Predatory Crime: Routine Activities and the Criminology of Place,” Criminology, 27. Sherman, L. W., and D. Weisburd (1995): “General Deterrent Effects of Police Patrol in Crime ‘Hot Spots’: A Randomized, Controlled Trial,” Justice Quarterly, 12. Tiebout, C. (1961): An Economic Theory of Fiscal Decentralizationin National Bureau Commit- tee for Economic Research Public Finances: Needs, Sources and Utilization. Princeton University Press, Princeton. 31
  33. 33. 8 Figures and Tables Figure 1: Histogram of Thefts The unit of observation is the number of thefts in each model group, state, year made, and year stolen combination. Note: Graph truncated at 10 thefts for visibility purposes. The full distribution follows the same pattern. 32
  34. 34. Figure 2: Lojack States and Non-Lojack States 33
  35. 35. Table 1: States, Dates and Models where Lojack was Introduced LojackModels Jalisco Estado de Mexico Distrito Federal Morelos Ford Windstar 2001 2002 2002 2002 Ford Explorer 2003 2003 2003 2003 Ford Escape 2003 2003 2003 2003 Mercury Mystique 2003 2003 2003 2003 Ford Expedition 2003 2003 2003 2003 Ford Focus 2003 2003 2003 2003 Ford Excursion 2003 2003 2003 2003 Ford Grand Marquis 2003 2003 2003 2003 Mercury Sable 2003 2003 2003 2003 34
  36. 36. Table 2: Non-Lojack Models Brand Model Group Brand Model Group Audi A3, A4, A6, A8, TT Land Rover Freelander, RangeRover BMW X3, X5 Lincoln Town Car BMW S3, S5, S7, S8, Z4 Lincoln Navigator Chrysler Cherokee, Liberty, Durango Mercedes Benz ML, G Chrysler JeepWrangler Mercedes Benz A, C, E, S, SLK, CLK Chrysler Neon Nissan Pathfinder, Frontier, X-trail, X-terra Chrysler Voyager, Ram Wagon Nissan Maxima, InfinityQ30, InfinityQ45 Chrysler Stratus, Cirrus, Cruiser Nissan Sentra, Almera, Tsubame, Lucino Chrysler Atos Nissan Quest Chrysler Pickup, Chassis Nissan Altima Ford Lincoln LS, Thunderbird Nissan Tsuru, Platina Ford CrownVictoria Nissan Pickup, Chassis, Estacas Ford Fiesta, Ikon, Ka Nissan Urvan Ford Ranger, Courier Peugeot 405, 406, 407, 607 Ford 150, 250, 350, 450, 550 Peugeot 306, 307 Ford Econoline, ClubWagon Peugeot 206 Ford Mustang Renault Clio General Motors Blazer, Aztek, Trailblazer Renault Megane, Scenic General Motors Tracker Seat Ibiza, Cordoba General Motors Venture, CadillacEscalade, Express Seat Toledo General Motors Malibu, Grandam, Grandprix, Vectra, Tigra Seat Alhambra General Motors Cavalier, Sunfire, Astra, Chevy SW, Meriva, Zafira Seat Leon General Motors Chevy, Monza, Corsa, Matiz Volvo S40, V40/V50, S60/S70, V70, S80, C70 General Motors Corvette Volkswagen Jetta, Beetle, Golf, Cabrio, PointerSW General Motors 1500, 2500, 3500, Avalanche, Luv, ChevyPickup, S10 Volkswagen Combi, Eurovan Honda Civic Volkswagen Sharan Honda Odyssey Volkswagen Passat Honda Accord Volkswagen OldBeetle Jaguar XJ, X, S Volkswagen Derby, Pointer, Polo Land Rover Discovery Volkswagen Pointer, PointerVan 35
  37. 37. Table 3: Descriptive Statistics Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max Panel A: All Observations (N=26,213) Panel B: Lojack Equipped (N=118) Stock 632.1 1,785.3 1 32,940 Stock 605.7 679.3 5 2,725 Thefts in Year 4.16 28.2 0 1,502 Thefts in Year 4.5 7.9 0 37 Age Car when Stolen 1.6 1.4 0 5 Age Car when Stolen 0.44 0.6 0 3 Sold with Lojack 0.004 0.06 0 1 Sold with Lojack 1 0 1 1 Panel C: Lojack Models (N=5,364) Panel D: Non Lojack Models (N=20,849) Stock 237.2 483.5 1 7,704 Stock 733.7 1,974.1 1 32,940 Thefts in Year 1.3 6.1 0 125 Thefts in Year 4.8 31.4 0 1,502 36 Age Car when Stolen 1.6 1.4 0 5 Age Car when Stolen 1.6 1.4 0 5 Sold with Lojack 0.021 0.14 0 1 Sold with Lojack 0 0 0 0 Panel E: Lojack States (N=4,845) Panel F: Non Lojack States (N=21,368) Stock 1,715.2 3,752.8 1 32,940 Stock 386.5 625.4 1 8,328 Thefts in Year 18.9 63.3 0 1,502 Thefts in Year 0.82 2.2 0 61 Age Car when Stolen 1.6 1.4 0 5 Age Car when Stolen 1.6 1.4 0 5 Sold with Lojack 0.02 0.15 0 1 Sold with Lojack 0 0 0 0 An observation unit is a quadruplet defined by a (state, car model, vintage, year). Stock and Thefts are in car units. Stock refers to cumulative sales in the specified (state, car model, vintage) combination. Age of car is in terms of completed years since sale (0 if the car is up to 12 months old, etc.) The Sold with Lojack variable equals one if the car model was equipped with Lojack when the vehicle was sold. Lojack Models refers to the 9 Ford vehicle models that participated in the Lojack program at some point between 1999 and 2004 (Panel C). Lojack states are the 4 states where Lojack was implemented between 1999 and 2004 (Panel E). Lojack Equipped refers to vehicles that were equipped with Lojack when the vehicle was sold (Panel B).
  38. 38. Table 4: Impact of the Lojack Program in Lojack States Poisson Regression Dep. Var: Number of Thefts Lojack Models Non-Lojack Models Coeff. IRR − 1 Coeff. IRR − 1 Equipped with Lojack −0.64*** −0.48*** (0.10) (0.05) After Lojack −0.05 −0.05 (0.09) (0.09) Observations 966 3,879 α 0.10 0.08 Bootstrapped standard errors clustered at the state level in parentheses. Observations weighted by sales. The first regression uses data from Lojack models in Lojack states. The second regression uses data from Non-Lojack models in Lojack states. Af terLojack is dummy variable equal to one for years after Lojack was introduced into the state. Equipped with Lojack is a dummy variable equal to one for vintages that were sold equipped with Lojack. Other controls: Size of vintage at the state-model level, state- model fixed effect, state specific time trend, age dummies. The Coeff. column reports the coefficient from the poisson regression. The incidence rate ratio column (IRR − 1) reports the estimated coefficient in its exponentiated form minus 1. It is interpreted as the rela- tive change in theft risk generated by the Lojack program. α is the estimated conditional over(+)/underdispersion(−) in the dependent variable. * significant at 10%; ** significant at 5%; *** significant at 1% for the test H0 : β = 0. 37
  39. 39. Table 5: Impact of Lojack in Non-Lojack States Poisson Regression Dep. Var: Number of Thefts Lojack Models Non-Lojack Models Coeff. IRR − 1 Coeff. IRR − 1 First Ring Around Lojack States After Lojack 0.57* 0.77* 0.04 0.04 (0.34) (0.61) (0.07) (0.07) Observations 1,800 6,951 α 0.01 0.13 Second Ring Around Lojack States After Lojack 0.47* 0.61* 0.15 0.16 (0.61) (0.44) (0.13) (0.16) Observations 1,276 4,998 α 0.15 0.24 All Other Non Lojack States After Lojack 0.57 0.77 0.05 0.05 (0.37) (0.67) (0.10) (0.11) Observations 1,322 5,021 α 0.25 0.27 Bootstrapped standard errors clustered at the state level in parentheses. Observations weighted by sales. The regressions use data from Non Lojack states only. The top panel (First ring around Lojack states) uses data from Non Lojack states contiguous to Lojack ones, the middle panel (Second Ring Around Lojack States) uses data from Non Lojack states adjacent to the ones in the top panel, and the third panel (All Other Non Lojack States) uses data from the remainding Non- Lojack states. Af ter Lojack is a dummy variable equal to one for years after Lojack was introduced in the nearest Lojack state. Other controls: Size of vintage at the state-model level, state-model fixed effect, state specific time trend, age dummies. The Coeff. column reports the coefficient from the poisson regression. The incidence rate ratio column (IRR − 1) reports the estimated coefficient in its exponentiated form minus 1. It is interpreted as the relative change in theft risk generated by the Lojack program. α is the estimated conditional over(+)/underdispersion(−) in the dependent variable. * significant at 10%; ** significant at 5%; *** significant at 1% for the test H0 : β = 0. 38