Deterrence and Geographical Externalities in Auto Theft ∗

Marco Gonzalez-NavarroPrinceton University †

December 20 2008

Abstract

Knowledge of the extent of crime displacement is crucial for the design and implementation ofcrime prevention policies. Nevertheless, previous empirical evidence documenting displacementremains inconclusive. This paper is the first to document extensive interstate displacement inauto theft. I propose an intuitive model to analyze the effects in the stolen vehicle market ofthe introduction of an observable theft deterrence device. I then study the changes in theftrisk that were generated by the introduction of Lojack, a highly effective stolen vehicle recoverydevice, into a number of new Ford car models in some Mexican states, but not others. I findthat Lojack-equipped vehicles in Lojack coverage states experienced a 48% reduction in theftrisk due to deterrence effects. In states neighboring those where Lojack was introduced, I findthat 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-significantreduction in theft risk of unprotected car models which coincides with the introduction of theLojack program. The Lojack program introduction coincides with an increase in the numberof criminals charged for property theft in Lojack states. I find no displacement to other crimecategories in either Lojack or Non Lojack states. Given that most criminal law enforcement is anattribute of state or local governments, the results of this paper suggest that prevention effortstargeting 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 dataused here would not have been available without the help of Enrique Olmedo Salazar and Laura Espinoza fromAMIS, Juan Moreno from Lojack, and Carlos Sanchez and Susana Pineda from Ford. I would also like to thank theparticipants of the development lunch seminar and the Public Finance Working Group at Princeton University fortheir useful comments. Financial aid from the Woodrow Wilson Scholars, Princeton University, and the Center forEconomic Policy Studies is gratefully acknowledged. Any errors contained in the paper are my own.†Economics Department, Fisher Hall, Princeton, NJ 08544. Email: marcog@princeton.edu

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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 and1For criminal displacement over time see Jacob, Lefgren, and Moretti (2005).

1

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

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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

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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.2www.lojack.com

4

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 would3The information on Lojack is based on discussions with company executives in Mexico and on information from

their web page.

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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.

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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 stolen4There is no assumption of equality of the supply functions S(·) in the model. They are written in this way for

simplicity of notation.

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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

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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.

Supply in the Lojack model-Lojack state market is given by N ss1m1 = S(Ps1m1)−Lojack. Where

Lojack is a dummy variable indicating that the model is equipped with Lojack. Demand is given

by Ps1m1 = D(Nds1m1). The market clearing condition equates demand to supply: Nd

s1m1 = N ss1m1.

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:

∂N∗s1m1∂Lojack < 0 ⇒ Deterrence Effect∂N∗s1m0∂Lojack = 0 ⇒ No Within State Externality∂N∗s0m1∂Lojack = 0 ⇒ No Geographical Externality Within Model∂N∗s0m0∂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.

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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 =

Ps1m1 = D(Nds1m1 +Nd

s1m0). As before, Lojack makes stealing Lojack models more costly: N ss1m1 =

S(Ps1m1)− Lojack. The market clearing conditions are now Nds1m1 = N s

s1m1 and Nds1m0 = N s

s1m0.

The model is solved in Appendix A, with the following predictions:

∂N∗s1m1∂Lojack < 0 ⇒ Deterrence Effect∂N∗s1m0∂Lojack > 0 ⇒Within State Negative Externality∂N∗s0m1∂Lojack = 0 ⇒ No Spatial Externality Within Model∂N∗s0m0∂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

for Lojack car models across states is given by Ps1m1 = Ps0m1 = D(Nds1m1 + Nd

s0m1). As before,

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Lojack reduces the supply of Lojack-equipped stolen vehicles N ss1m1 = S(Ps1m1) − Lojack. The

model is solved in Appendix A, with the following predictions:

∂N∗s1m1∂Lojack < 0 ⇒ Deterrence Effect∂N∗s1m0∂Lojack = 0 ⇒ No Within State Externality to Non Lojack Model∂N∗s0m1∂Lojack > 0 ⇒ Model Specific Spatial Externality∂N∗s0m0∂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

Ps1m1 = Ps1m0 = Ps0m1 = Ps0m0 = D(Nds1m1 +Nd

s1m0 +Nds0m1 +Nd

s0m0)

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.

As before, Lojack reduces the supply of Lojack equipped vehicles N ss1m1 = S(Ps1m1)−Lojack. The

model is solved in Appendix A, with the following predictions:

∂N∗s1m1∂Lojack < 0 ⇒ Deterrence Effect∂N∗s1m0∂Lojack > 0 ⇒Within-State Externality to Non Lojack Model∂N∗s0m1∂Lojack > 0 ⇒ Model Specific Spatial Externality∂N∗s0m0∂Lojack > 0 ⇒ Spatial Externality to Non Lojack Model

11

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-5www.amis.org.mx6www.amia.com.mx

12

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

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.7Age 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

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:

E[Theftsijyt] = (Sijy) · exp

(γij + βj · t+

5∑a=0

βa · I[Age = a] + βLojack · Lojackijy

)(1)

To estimate externalities to Non-Lojack models in Lojack states, I use observations of non-Lojack

15

models in Lojack states to fit:

E[Theftsijyt] = (Sijy) ·exp

(γij + βj · t+

5∑a=0

βa · I[Age = a] + βAfterLojack ·AfterLojackjt

)(2)

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:

E[Theftsijyt] = (Sijy) ·exp

(γij + βj · t+

5∑a=0

βa · I[Age = a] + βAfterLojack ·AfterLojackjt

)(3)

where the dependent variable Theftsijyt 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), AfterLojackjt is a dummy variable equal to one if Lojack has been introduced

into the state. βAfterLojack 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), AfterLojackjt is a dummy variable indicating that the Lojack program has been

introduced in the nearest Lojack state. The associated coefficient, βAfterLojack, 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

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[Theftsijyt|xijyt, Lojackijyt = 1]E[Theftsijyt|xijyt, Lojackijyt = 0]

= eβLojack

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 to8Standard 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 changingthe significance of the results.

9In a Poisson regression, this is referred to as “controlling for exposure”. The exposure variable (Sijy), is usuallyincorporated with a coefficient constrained to unity. This introduces the assumption that thefts are a function ofthe stock of cars and that this relationship is the same across all car models: a doubling of the stock accompaniedby a doubling of thefts is interpreted as keeping theft risk constant. The results are robust to a relaxation of thecoefficient restriction on Sijy. See the Robustness Checks section.

17

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: βAfterLojack 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 βAfterLojack 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

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

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:

∑ij∈Λ

(E[Theftsijyt|xijyt, Lojackijyt = 1]− E[Theftsijyt|xijyt, Lojackijyt = 0])

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) ·

∑ij∈Λ

E[Theftsijt| Lojackijyt = 0]

(4)

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

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 After 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

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

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 STrueijy = πij · SObsijy , where SObs refers to the stock of vehicles observable to the econometrician,

while STrue refers to the actual stock of insured cars on the road. Then, if the true model is

E[Theftsijyt|xijyt] = (Strueijy ) · exp

(γij + βj · t+ βLojack · Lojackijyt +

6∑a=0

βa · I[Age = a]

)

Substituting STrueijy = πij · SObsijy in the equation above yields

E[Theftsijyt|xijyt] = (SObsijy )·exp

(ln(πij) + γij + βj · t+ βLojack · Lojackijyt +

6∑a=0

βa · I[Age = a]

)

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

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

Proportion Insurediyt = β0+βLojack ·Lojackiy+βage=t−y ·I[Age = t−y]+βyear=tI[Y ear = t]+uiyt

24

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

Proportion Insurediyt = βi+βLojack ·Lojackiyt+βage=t−y ·I[Age = t−y]+βyear=tI[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 changes10Annual 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 andstate combination. The mean of those changes is a weighted average across car models for a given age and state.

25

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

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

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

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

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

Karmen, A. (1981): “Auto Theft and Corporate Irresponsibility,” Contemporary Crises, 5, 63–81.

LoJack (2006): “LoJack Recovery Statistics,” Electronic document:

http://www.lojack.com/why/lojack-recovery-statistics.cfm. 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

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

Figure 2: Lojack States and Non-Lojack States

33

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

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

Tab

le3:

Des

crip

tive

Stat

isti

cs

Var

iabl

eM

ean

Std.

Dev

.M

inM

axV

aria

ble

Mea

nSt

d.D

ev.

Min

Max

Pan

elA

:A

llO

bser

vati

ons

(N=

26,2

13)

Pan

elB

:L

ojac

kE

quip

ped

(N=

118)

Stoc

k63

2.1

1,78

5.3

132

,940

Stoc

k60

5.7

679.

35

2,72

5T

heft

sin

Yea

r4.

1628

.20

1,50

2T

heft

sin

Yea

r4.

57.

90

37A

geC

arw

hen

Stol

en1.

61.

40

5A

geC

arw

hen

Stol

en0.

440.

60

3So

ldw

ith

Loj

ack

0.00

40.

060

1So

ldw

ith

Loj

ack

10

11

Pan

elC

:L

ojac

kM

odel

s(N

=5,

364)

Pan

elD

:N

onL

ojac

kM

odel

s(N

=20

,849

)

Stoc

k23

7.2

483.

51

7,70

4St

ock

733.

71,

974.

11

32,9

40T

heft

sin

Yea

r1.

36.

10

125

The

fts

inY

ear

4.8

31.4

01,

502

Age

Car

whe

nSt

olen

1.6

1.4

05

Age

Car

whe

nSt

olen

1.6

1.4

05

Sold

wit

hL

ojac

k0.

021

0.14

01

Sold

wit

hL

ojac

k0

00

0

Pan

elE

:L

ojac

kSt

ates

(N=

4,84

5)P

anel

F:

Non

Loj

ack

Stat

es(N

=21

,368

)

Stoc

k1,

715.

23,

752.

81

32,9

40St

ock

386.

562

5.4

18,

328

The

fts

inY

ear

18.9

63.3

01,

502

The

fts

inY

ear

0.82

2.2

061

Age

Car

whe

nSt

olen

1.6

1.4

05

Age

Car

whe

nSt

olen

1.6

1.4

05

Sold

wit

hL

ojac

k0.

020.

150

1So

ldw

ith

Loj

ack

00

00

An

obse

rvat

ion

unit

isa

quad

rupl

etde

fined

bya

(sta

te,c

arm

odel

,vin

tage

,yea

r).

Stoc

kan

dT

heft

sar

ein

car

unit

s.St

ock

refe

rsto

cum

ulat

ive

sale

sin

the

spec

ified

(sta

te,

car

mod

el,

vint

age)

com

bina

tion

.A

geof

car

isin

term

sof

com

plet

edye

ars

sinc

esa

le(0

ifth

eca

ris

upto

12m

onth

sol

d,et

c.)

The

Sold

wit

hL

ojac

kva

riab

leeq

uals

one

ifth

eca

rm

odel

was

equi

pped

wit

hL

ojac

kw

hen

the

vehi

cle

was

sold

.L

ojac

kM

odel

sre

fers

toth

e9

Ford

vehi

cle

mod

els

that

part

icip

ated

inth

eL

ojac

kpr

ogra

mat

som

epo

int

betw

een

1999

and

2004

(Pan

elC

).L

ojac

kst

ates

are

the

4st

ates

whe

reL

ojac

kw

asim

plem

ente

dbe

twee

n19

99an

d20

04(P

anel

E).

Loj

ack

Equ

ippe

dre

fers

tove

hicl

esth

atw

ere

equi

pped

wit

hL

ojac

kw

hen

the

vehi

cle

was

sold

(Pan

elB

).

36

Table 4: Impact of the Lojack Program in Lojack States

Poisson RegressionDep. Var: Number of Thefts

Lojack Models Non-Lojack ModelsCoeff. 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 3,879α 0.10 0.08

Bootstrapped standard errors clustered at the state level in parentheses. Observationsweighted 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. AfterLojackis 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 soldequipped 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 thecoefficient from the poisson regression. The incidence rate ratio column (IRR− 1) reportsthe 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 conditionalover(+)/underdispersion(−) in the dependent variable.* significant at 10%; ** significant at 5%; *** significant at 1% for the test H0 : β = 0.

37

Table 5: Impact of Lojack in Non-Lojack States

Poisson RegressionDep. Var: Number of Thefts

Lojack Models Non-Lojack ModelsCoeff. IRR− 1 Coeff. IRR− 1

First Ring Around Lojack StatesAfter Lojack 0.57* 0.77* 0.04 0.04

(0.34) (0.61) (0.07) (0.07)Observations 1,800 6,951α 0.01 0.13

Second Ring Around Lojack StatesAfter Lojack 0.47* 0.61* 0.15 0.16

(0.61) (0.44) (0.13) (0.16)Observations 1,276 4,998α 0.15 0.24

All Other Non Lojack StatesAfter Lojack 0.57 0.77 0.05 0.05

(0.37) (0.67) (0.10) (0.11)Observations 1,322 5,021α 0.25 0.27

Bootstrapped standard errors clustered at the state level in parentheses. Observations weightedby sales. The regressions use data from Non Lojack states only. The top panel (First ring aroundLojack 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 thetop panel, and the third panel (All Other Non Lojack States) uses data from the remainding Non-Lojack states. After Lojack is a dummy variable equal to one for years after Lojack was introducedin the nearest Lojack state. Other controls: Size of vintage at the state-model level, state-modelfixed effect, state specific time trend, age dummies. The Coeff. column reports the coefficient fromthe poisson regression. The incidence rate ratio column (IRR−1) reports the estimated coefficientin its exponentiated form minus 1. It is interpreted as the relative change in theft risk generated bythe Lojack program. α is the estimated conditional over(+)/underdispersion(−) in the dependentvariable.* significant at 10%; ** significant at 5%; *** significant at 1% for the test H0 : β = 0.

38

Tab

le6:

Impa

ctof

the

Loj

ack

Pro

gram

inT

erm

sof

Stol

enV

ehic

les

Sta

tes

Loj

ack

Stat

esN

on-L

ojac

kSt

ates

1st

Rin

gA

roun

dL

ojac

kSt

ate

2nd

Rin

gA

roun

dL

ojac

kSt

ate

Dis

tant

Stat

esC

arM

od

elL

ojac

kN

onL

ojac

kL

ojac

kN

on-L

ojac

kL

ojac

kN

on-L

ojac

kL

ojac

kN

on-L

ojac

kP

re-P

rogr

amM

ean

Ann

ual

The

fts

276

4,85

418

.332

821

.821

1.6

20.3

265.

6

Effe

ctof

Loj

ack

−48

%**

*−

5%77

%*

4%61

%*

16%

77%

5%P

rogr

am(%Change)

(0.0

5)(0

.09)

(0.6

1)(0

.07)

(0.4

4)(0

.16)

(0.6

7)(0

.05)

Effe

ctin

Ter

ms

−13

2.4*

**−

242.

714

.1*

13.1

13.2

*33

.815

.613

.3of

Ann

ual

The

fts

(13.

8)(4

36.8

)(1

1.1)

(22.

9)(9

.5)

(33.

8)(1

3.6)

(13.

3)

Pre

-pro

gram

mea

nth

efts

are

the

aver

age

(ove

rti

me)

ofth

esu

mof

year

lyth

efts

inal

lsta

tes

inth

egr

oup

indi

cate

dby

the

colu

mn

head

erbe

fore

the

intr

oduc

tion

ofth

epr

ogra

m.

Effe

cts

ofL

ojac

kP

rogr

amar

eth

e(IRR−

1)fr

omm

ain

regr

essi

ons.

39

Table 7: Impact on Pre-Program Vintages of Lojack Modelsin Lojack States

Poisson RegressionDep. Var: Number of Thefts

Impact on Pre-Program Lojack Model VintagesCoeff. (IRR− 1)

After Lojack −0.11 −0.11(0.11) (0.09)

Observations 2,295α 0.1

Bootstrapped standard errors clustered at the state level in parentheses.Observations weighted by sales. Data from Lojack model vintages soldbefore the Lojack program. After Lojack is a dummy variable equal toone for years after Lojack introduced in newer vintages of the same carmodel in the state. Other controls: Size of vintage at the state-modellevel, state-model fixed effect, state specific time trend, age dummies. TheCoeff. column reports the coefficient from the poisson regression. Theincidence rate ratio column (IRR − 1) reports the estimated coefficient inits exponentiated form minus 1. It is interpreted as the relative change intheft risk generated by the Lojack program. α is the estimated conditionalover(+)/underdispersion(−) in the dependent variable.* significant at 10%; ** significant at 5%; *** significant at 1% for the testH0 : β = 0.

40

Table 8: Incapacitation and Displacement

OLS Estimation

Charged OffendersLojack State First Ring Second Ring

Dep. Var: Drug Trafficking Offense rateAfter Lojack 0.015

(0.03)Obs. 91R2 0.95After Lojack in Nearest LJstate −0.006 −0.03

(0.02) (0.03)Obs. 147 112R2 0.95 0.94Dep. Var: Kidnapping Offense rateAfter Lojack 0.008

(0.005)Obs. 75R2 0.53After Lojack in Nearest LJstate −0.002 0.005

(0.004) (0.003)Obs. 126 89R2 0.65 0.67Dep. Var: Theft rateAfter Lojack 0.30*

(0.14)Obs. 91R2 0.95After Lojack in Nearest LJstate 0.10 0.09

(0.06) (0.07)Obs. 147 112R2 0.96 0.97

OLS difference in difference estimation. Robust clustered standard errors at the state level.Dependent variables are charged offenders per 1000 adults in the state. Independent variablesare Lojack dummy (in the first column: Lojack introduced into states, in the second and thirdcolumns: Lojack introduced in nearest Lojack state), state fixed effect, and year fixed effect.Weights proportional to population size of the state. First Ring means contiguous to Lojackstates, Second Ring refers to the second ring of states around Lojack states. Control group aredistant states.

41

Table 9: Effect as Lojack-Equipped Vehicles Aged

Poisson RegressionDep. Var: Number of Thefts

Baseline Estimation Impact as Car AgesCoeff (IRR− 1) Coeff (IRR− 1)

Lojack Equipped −0.64*** −0.48***(0.10) (0.05)

Lojack equipped & Age=1 −0.75*** −0.53***(0.19) (0.09)

Lojack equipped & Age=2 −0.51*** −0.31***(0.10) (0.06)

Lojack equipped & Age=3 −0.86*** −0.58***(0.15) (0.06)

Observations 966 966α 0.100 0.102

Bootstrapped standard errors clustered at the state level in parentheses. Observations weightedby sales. The first column is the baseline estimation presented for comparison purposes. Thesecond column uses data from Lojack models in Lojack states. LojackEquipped&Age = k isa dummy variable equal to one if the car was sold with Lojack and is aged between (k− 1) · 12and k · 12 months old. Other controls: Size of vintage at the state-model level, state-modelfixed effect, state specific time trend, age dummies. The Coeff. column reports the coefficientfrom the poisson regression. The incidence rate ratio column (IRR− 1) reports the estimatedcoefficient in its exponentiated form minus 1. It is interpreted as the relative change in theft riskgenerated 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.

Table 10: Lojack Program Participation and Market ShareOLS Triple Difference EstimationDep. Var: Market Share in Category

Market Share in Category

Lojack Equipped 0.027***(0.009)

Obs. 4,701R2 0.85Full Year, State, Car Model interactions Y

OLS triple difference estimation of changes in market share withincategory. Regressors are year, state and car model main effects andinteractions. Robust standard errors in parenthesis. Control groupis the set of distant states.

42

Table 11: Effect of Lojack on Insurance Coverage

Dep. Var: Proportion of Cars Insured Nationally

(1) (2)

Lojack Equipped 0.0232 0.0362(0.2502) (0.2251)

Year Dummies YES YESAge of Car Dummies YES YESModel Group Dummies NO YESData used t ≥ 2003 t ∈ [1999, 2005]Observations 354 1510R2 0.04 0.07

Dependent variable is the proportion of cars in a (modelgroup, year made) combination that are insured nationallyin a given year, divided by the number of cars sold nationallyfor the same (model group, year made) duplet. The regres-sion in the first column uses data for 2003 on, when Lojackhad been implemented for most Lojack vehicles. The regres-sion in the second column has model specific fixed effects anduses all observations. Robust standard errors in parentheses.

* significant at 10%; ** significant at 5%; *** significant at

1%.

Table 12: Inclusion in Lojack Program and Pre-Program Theft Rates

Dep. Var: Indicator of Car Model Included in Lojack ProgramLogit Estimation

All models Ford Models

Regressor: Annual Change in Theft Rate −0.004 −0.0106(0.013) (0.024)

Observations 4,590 1,126

Each cell corresponds to a different regression. The dependent variable in allregressions is an indicator dummy for inclusion of the car model in the Lojackprogram. The header of the column refers to the data used. Only Lojack statedata used. Theft rates of Lojack models after Lojack introduced in the model areexcluded from regressions. Robust standard errors in parenthesis.

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.

43

Table 13: Robustness Checks

Dep. Var: Number of TheftsLojack States Non-Lojack States

First Ring Second Ring Distant States

LJM Non-LJM LJM Non-LJM LJM Non-LJM LJM Non-LJM(IRR − 1) (IRR − 1) (IRR − 1) (IRR − 1) (IRR − 1) (IRR − 1) (IRR − 1) (IRR − 1)

1) Main Specification

Lojack-Equipped −0.48***(0.05)

After Lojack −0.05 0.77* 0.04 0.61* 0.16 0.77 0.05(0.09) (0.61) (0.07) (0.44) (0.16) (0.67) (0.11)

2) Difference in

Difference1

Lojack-Equipped −0.42***(0.11)

After Lojack −0.14 0.87* 0.20 0.32 −0.03(0.17) (0.57) (0.20) (0.34) (0.16)

3) Negative Binomial

Lojack-Equipped −0.50***(0.05)

After Lojack −0.03 0.73 0.01 0.78** 0.17* 0.73** 0.10(0.07) (0.60) (0.07) (0.45) (0.11) (0.43) (0.10)

4) Clusters of States

Lojack-Equipped −0.48***(0.17)

After Lojack −0.05 0.77** 0.04 0.61* 0.16 0.77 0.05(0.07) (0.43) (0.10) (0.44) (0.16) (0.67) (0.11)

5) Inflated Thefts

Lojack-Equipped −0.73***(0.03)

After Lojack 1.33*** 1.90 0.34* 2.94* 1.01*** 0.61 −0.61(0.60) (2.18) (0.23) (3.00) (0.35) (1.22) (0.36)

6) Unconstrained

Exposure

Lojack-Equipped −0.30***(0.07)

After Lojack −0.05 0.76 0.04 0.68* 0.16 0.78 0.05(0.09) (0.61) (0.07) (0.46) (0.16) (0.70) (0.11)

Exposure Coefficient2 1.83*** 0.95*** 1.07*** 0.71*** 1.51*** 0.87*** 1.21*** 0.65***(0.14) (0.08) (0.10) (0.08) (0.31) (0.07) (0.15) (0.14)

Bootstrapped standard errors clustered at the state level in parentheses. Observations weighted by sales. AfterLojack is a dummy variableequal to one for years after Lojack was introduced into the state (in column 2) or the nearest Lojack state (in columns 3-8). Lojack Equippedis a dummy variable equal to one for vintages that were sold equipped with Lojack (column 1). Other controls (Except in Difference inDifference estimation): Size of vintage at the state-model level, state-model fixed effect, state specific time trend, age dummies. The incidencerate ratio column (IRR − 1) reports the estimated coefficient in its exponentiated form minus 1. It is interpreted as the relative change intheft risk generated by the Lojack program.

1 Difference in Difference estimation: Uses data from distant states as control group. Control variables: year dummies, state dummies, sizeof vintage at the state-model level (exposure), age dummies, Lojack dummy (in column 1 for Lojack equipped, in column 2 for years afterLojack introduced into state, in columns 3-8 for years after Lojack introduced into nearest Lojack state.)

2 Coefficient is reported, not (IRR− 1).* significant at 10%; ** significant at 5%; *** significant at 1% for the test H0 : β = 0.

44

Appendix A: Solving the Model

The signing of the impact of Lojack in terms of deterrence and externalities is accomplished by

linearizing the system of equations around an equilibrium without Lojack. I then study the effect of

the introduction of Lojack in all markets by obtaining the derivatives of the (endogenous) variables

with respect to Lojack introduction (the exogenous variable) using the implicit function theorem

of linear algebra. I show the procedure in more detail for the first case, and show the solution of

the other three cases more succinctly. For space reasons, the impact of thief mobility is only shown

for the case of mobility of thieves across state lines for the third case of the model, in which model

specific demand and geographically integrated markets across state lines are analized.

The Case of No Displacement: Geographically Isolated Markets and Model Spe-

cific Demand for Stolen Cars

Supply in the Lojack model-Lojack state market is given by N ss1m1 = S(Ps1m1) − Lojack. Where

Lojack is a dummy variable indicating whether the model is equipped with Lojack. Demand is given

by Ps1m1 = D(Nds1m1). The market clearing condition equates demand to supply: Nd

s1m1 = N ss1m1.

This is a nonlinear model of three equations in three unknowns with the Lojack variable changing

exogenously from 0 to 1. Under the assumptions of this case, there is no effect of Lojack in the

other markets for stolen vehicles. The equations that determine the equilibrium price and stolen

quantity are:

Supply N ss1m1 = S(Ps1m1)− Lojack

Demand Ps1m1 = D(Nds1m1)

Supply=Demand Nds1m1 = N s

s1m1

Linearization around the non-Lojack equilibrium gives: 1 −D′(N∗s1m1)

S′(P ∗s1m1) −1

dPs1m1

dNs1m1

=

0

dLojack

Multiplying by the inverse matrix gives the impact of Lojack on the equilibrium variables:

∂N∗s1m1

∂Lojack=

1D′(N∗s1m1) · S′(P ∗s1m1)− 1

< 0

45

∂P ∗s1m1

∂Lojack=

−D′(N∗s1m1)D′(N∗s1m1) · S′(P ∗s1m1)− 1

> 0

Lojack generates a reduction in the equilibrium number of thefts attempted on Lojack equipped

vehicles and increases the equilibrium price paid for each vehicle. Considering that I do not have

data on prices of stolen vehicles for my empirical analysis, I will not report price predictions in

what follows, and will report predictions only on the quantity of vehicles that are stolen in each

market. In this simple case, it is easy to see that modeling Lojack as also reducing demand for

Lojack equipped vehicles would have generated a stronger effect in terms of theft reduction of

Lojack equipped vehicles.

Within State Displacement: Geographically Isolated Markets and Common De-

mand Across Car Models

When demand for stolen vehicles is common across car models and there is no interstate trade

in stolen cars, introducing Lojack generates as an externality increased thefts for the Non-Lojack

model in the Lojack state. Let demand for stolen vehicles in the Lojack state be given by Ps1m0 =

Ps1m1 = D(Nds1m1 + Nd

s1m0) so that what determines the price of stolen vehicles is the aggregate

amount of vehicles stolen in the state. As before, Lojack makes stealing Lojack models more

costly: N ss1m1 = S(Ps1m1) − Lojack. The equations that determine the equilibrium price and

stolen quantity are:

Lojack model in the Lojack state market:

Supply N ss1m1 = S(Ps1m1)− Lojack

Demand Ps1m1 = D(Nds1m1 +Nd

s1m0)

Non-Lojack model in the Lojack state market:

Supply N ss1m0 = S(Ps1m0)

Demand Ps1m0 = D(Nds1m1 +Nd

s1m0)

The market clearing conditions are

Nds1m0 = N s

s1m0, Nds1m1 = N s

s1m1

Linearization around the non-Lojack equilibrium yields:

46

S′(P ∗s1m1) 0 −1 0

1 0 −D′(N∗s1m1 + N∗s1m0) −D′(N∗s1m1 + N∗s1m0)

0 −S′(P ∗s1m0) 0 1

0 1 −D′(N∗s1m1 + N∗s1m0) −D′(N∗s1m1 + N∗s1m0)

dPs1m1

dPs1m0

dNs1m1

dNs1m0

=

dLojack

0

0

0

So that multiplying by the inverse matrix of constants gives:

∂N∗s1m1∂Lojack = 1−S′(P ∗s1m0)D′(N∗s1m1+N∗s1m0)

D′(N∗s1m1+N∗s1m0)(S′(P ∗s1m1)+S′(P ∗s1m0))−1 < 0 ⇒ Deterrent Effect∂N∗s1m0∂Lojack = S′(P ∗s1m0)D′(N∗s1m1+N∗s1m0)

D′(N∗s1m1+N∗s1m0)(S′(P ∗s1m1)+S′(P ∗s1m0))−1 > 0 ⇒Within State Negative Externality∂N∗s0m1∂Lojack = 0 ⇒ No Spatial Externality Within Model∂N∗s0m0∂Lojack = 0 ⇒ No Spatial Externality Across Model

Model-Specific Geographical Displacement: Geographically Integrated Markets

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 a model specific demand for Lojack models. The common

demand for Lojack car models across states is given by Ps1m1 = Ps0m1 = D(Nds1m1 + Nd

s0m1). As

before, Lojack reduces the supply of Lojack-equipped stolen vehicles N ss1m1 = S(Ps1m1)− Lojack.

The equations that determine the equilibrium price and stolen quantity are:

Lojack model in the Lojack state

Supply N ss1m1 = S(Ps1m1)− Lojack

Demand Ps1m1 = D(Nds1m1 +Nd

s0m1)

Supply=Demand Nds1m1 = N s

s1m1

Lojack model in the Non-Lojack state

Supply N ss0m1 = S(Ps0m1)

Demand Ps0m1 = D(Nds1m1 +Nd

s0m1)

Supply=Demand Nds0m1 = N s

s0m1

Given that this case is very similar to that in the previous case, I omit presenting the linear system.

Solution is given by

47

∂N∗s1m1∂Lojack = 1−S′(P ∗s0m1)D′(N∗s1m1+N∗s0m1)

D′(N∗s1m1+N∗s0m1)(S′(P ∗s1m1)+S′(P ∗s0m1))−1 < 0 ⇒ Deterrent Effect∂N∗s1m0∂Lojack = 0 ⇒ No Within State Externality to Non Lojack Model

(A.1) ∂N∗s0m1∂Lojack = S′(P ∗s0m1)D′(N∗s1m1+N∗s0m1)

D′(N∗s1m1+N∗s0m1)(S′(P ∗s1m1)+S′(P ∗s0m1))−1 > 0 ⇒ Model Specific Spatial Externality∂N∗s0m0∂Lojack = 0 ⇒ No Spatial Externality to Non Lojack Model

For this case, I show the effect of thief mobility across state lines. Suppose that in response to

the Lojack program, thieves can move to the non-Lojack state, attracted by the higher net payoff

to stealing Lojack car models there. Thieves would have an incentive to move across state lines if

their skills are car model specific and relocation is not very costly. As shown below, thief mobility

exacerbates the reduction of thefts of Lojack models in Lojack states, and increases thefts of Lojack

models in the non-Lojack states.

The model with mobility incorporates a movement in the number of thieves operating in a

market in response to a difference in net payoff across the two markets. The demands for stolen

vehicles are as before:

Demand for Lojack model in the Lojack state:

Ps1m1 = D(Nds1m1 +Nd

s0m1)

Demand for Lojack model in the Non-Lojack state:

Demand Ps0m1 = D(Nds1m1 +Nd

s0m1)

The new element is the migration function of thieves in response to the state with the highest

payoff. Let M denote one can assume a linear response to the net payoff difference across the two

markets:

M = Ps0m1 − (Ps1m1 − Lojack)

The supply of thieves in each market is now affected by the amount of thieves migrating in response

to price differences:

Supply of Lojack model in the Lojack state:

Ns1m1 = (1−M)S(Ps1m1)− Lojack

Supply of Lojack model in the Non-Lojack state:

Ns0m1 = (1 +M)S(Ps0m1)

Linearizing this system as before and solving for the equilibrium changes in response to Lojackintroduction yields:

48

(A.2)∂N∗

s1m1∂Lojack

=

1− S′(P ∗s0m1)D′(N∗s1m1 +N∗s0m1)

D′(N∗s1m1 +N∗s0m1)(S′(P ∗s1m1) + S′(P ∗s0m1))− 1︸ ︷︷ ︸Substitution effect(−)

+S(P ∗s1m1)−D′(N∗s1m1 +N∗s0m1)[S′(P ∗s0m1)S(P ∗s1m1) + S′(P ∗s1m1)S(P ∗s0m1)]

D′(N∗s1m1 +N∗s0m1)(S′(P ∗s1m1) + S′(P ∗s0m1))− 1︸ ︷︷ ︸Outmigration effect(−)

< 0

Note that (A.2) is identical to (A.1) in its first component, and then has the additional effect of

outmigration in the second component, further reducing the number of thefts in the Lojack state.The effect of migration in the Non-Lojack state is correspondingly larger due to in-migration

of criminals:

∂N∗s0m1

∂Lojack=

S′(P ∗s0m1)D′(N∗s1m1 +N∗s0m1)

D′(N∗s1m1 +N∗s0m1)(S′(P ∗s1m1) + S′(P ∗s0m1))− 1︸ ︷︷ ︸Substitution effect(+)

+D′(N∗s1m1 +N∗s0m1)[S′(P ∗s0m1)S(P ∗s1m1) + S′(P ∗s1m1)S(P ∗s0m1)]− S(P ∗s0m1)

D′(N∗s1m1 +N∗s0m1)(S′(P ∗s1m1) + S′(P ∗s0m1))− 1︸ ︷︷ ︸Immigration effect(+)

> 0

Mobility could also work to generate within state migration in this case if vehicle stealing skills

are not model specific and geographical relocation is costly, because the mobility of thieves would

generate increased thefts of Non-Lojack models in Lojack states, even though demand for stolen

vehicles were model specific.

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

Ps1m1 = Ps1m0 = Ps0m1 = Ps0m0 = D(Nds1m1 +Nd

s1m0 +Nds0m1 +Nd

s0m0)

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.

As before, Lojack reduces the supply of Lojack equipped vehicles N ss1m1 = S(Ps1m1)−Lojack. The

equations that determine the equilibrium price and stolen quantity are:

49

Lojack model in the Lojack state

Supply N ss1m1 = S(Ps1m1)− Lojack

Demand Ps1m1 = D(Nds1m1 +Nd

s1m0 +Nds0m1 +Nd

s0m0)

Non-Lojack model in the Lojack state

Supply N ss1m0 = S(Ps1m0)

Demand Ps1m0 = D(Nds1m1 +Nd

s1m0 +Nds0m1 +Nd

s0m0)

Lojack model in the Non-Lojack state

Supply N ss0m1 = S(Ps0m1)

Demand Ps0m1 = D(Nds1m1 +Nd

s1m0 +Nds0m1 +Nd

s0m0)

Non-Lojack model in the Non-Lojack state

Supply N ss0m0 = S(Ps0m0)

Demand Ps0m0 = D(Nds1m1 +Nd

s1m0 +Nds0m1 +Nd

s0m0)

The market clearing conditions are now

Nds1m1 = N s

s1m1, Nds1m0 = N s

s1m0, Nds0m1 = N s

s0m1, and Nds0m0 = N s

s0m0

Linearization around the non-Lojack equilibrium yields:

S′(P ∗s1m1) 0 0 0 −1 0 0 0

1 0 0 0 −D′ −D′ −D′ −D′

0 S′(P ∗s1m0) 0 0 0 −1 0 0

0 1 0 0 −D′ −D′ −D′ −D′

0 0 S′(P ∗s0m1) 0 0 0 −1 0

0 0 1 0 −D′ −D′ −D′ −D′

0 0 0 S′(P ∗s0m0) 0 0 0 −1

0 0 0 1 −D′ −D′ −D′ −D′

dPs1m1

dPs1m0

dPs0m1

dPs0m0

dNs1m1

dNs1m0

dNs0m1

dNs0m0

=

dLojack

0

0

0

0

0

0

0

Where D′ is shorthand for D′(N∗s1m1 +N∗s1m0 +N∗s0m1 +N∗s0m0).

∂N∗s1m1∂Lojack = D′·[S′(P ∗s1m0)+S′(P ∗s0m1)+S′(P ∗s0m0)]−1

1−D′·[S′(P ∗s1m1)+S′(P ∗s1m0)+S′(P ∗s0m1)+S′(P ∗s0m0)] < 0 ⇒ Deterrent Effect∂N∗s1m0∂Lojack = −D′·S′(P ∗s1m0)

1−D′·[S′(P ∗s1m1)+S′(P ∗s1m0)+S′(P ∗s0m1)+S′(P ∗s0m0)] > 0 ⇒Within-State Externality to Non Lojack Model∂N∗s0m1∂Lojack = −D′·S′(P ∗s0m1)

1−D′·[S′(P ∗s1m1)+S′(P ∗s1m0)+S′(P ∗s0m1)+S′(P ∗s0m0)] > 0 ⇒ Model Specific Spatial Externality∂N∗s0m0∂Lojack = −D′·S′(P ∗s0m0)

1−D′·[S′(P ∗s1m1)+S′(P ∗s1m0)+S′(P ∗s0m1)+S′(P ∗s0m0)] > 0 ⇒ Spatial Externality to Non Lojack Model

50