Deterrence and Geographical Externalities in Auto Theft
Deterrence and Geographical Externalities in Auto Theft
Princeton University †
December 20 2008
Knowledge of the extent of crime displacement is crucial for the design and implementation of
crime prevention policies. Nevertheless, previous empirical evidence documenting displacement
remains inconclusive. This paper is the ﬁrst to document extensive interstate displacement in
auto theft. I propose an intuitive model to analyze the eﬀects in the stolen vehicle market of
the introduction of an observable theft deterrence device. I then study the changes in theft
risk that were generated by the introduction of Lojack, a highly eﬀective stolen vehicle recovery
device, into a number of new Ford car models in some Mexican states, but not others. I ﬁnd
that Lojack-equipped vehicles in Lojack coverage states experienced a 48% reduction in theft
risk due to deterrence eﬀects. In states neighboring those where Lojack was introduced, I ﬁnd
that the Lojack program generated an increase in theft risk of 77% in unprotected Ford models.
This kind of externality is expected when there is a strong model-speciﬁc demand for stolen cars
– such as an active stolen autoparts market. In Lojack states, I ﬁnd a small and non-signiﬁcant
reduction in theft risk of unprotected car models which coincides with the introduction of the
Lojack program. The Lojack program introduction coincides with an increase in the number
of criminals charged for property theft in Lojack states. I ﬁnd no displacement to other crime
categories in either Lojack or Non Lojack states. Given that most criminal law enforcement is an
attribute of state or local governments, the results of this paper suggest that prevention eﬀorts
targeting highly mobile crimes – like auto theft – should be coordinated among jurisdictions,
rather than independently designed.
JEL: K420, H230
I would like to thank Angus Deaton, Adriana Lleras-Muney, Sam Schulhofer-Wohl, Chris Paxson, Anne Case,
Climent Quintana, Rodrigo Barros, and David Atkin for their help and advice in this research project. The data
used here would not have been available without the help of Enrique Olmedo Salazar and Laura Espinoza from
AMIS, Juan Moreno from Lojack, and Carlos S´nchez and Susana Pineda from Ford. I would also like to thank the
participants of the development lunch seminar and the Public Finance Working Group at Princeton University for
their useful comments. Financial aid from the Woodrow Wilson Scholars, Princeton University, and the Center for
Economic Policy Studies is gratefully acknowledged. Any errors contained in the paper are my own.
Economics Department, Fisher Hall, Princeton, NJ 08544. Email: email@example.com
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
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
Crime that is highly mobile – either across time,1 space or other crime categories – must be dealt
with comprehensively, with an emphasis on incapacitation. Crimes that are spatially mobile are es-
pecially important for ﬁscal federalism. The literature on the distribution of responsibilities across
government levels (cf. Tiebout (1961), and Donahue (1997)) argues that government-provided
goods may be suboptimally supplied whenever these expenditures exert spatial externalities on
surrounding jurisdictions. If spatial externalities are pervasive, it may be welfare improving to
delegate the responsibility in question to a higher level of government, which can internalize the ex-
ternality. The fact that most criminal law enforcement is performed by state and local governments
suggests that a limited amount of spatial spillovers in crime must be present for law enforcement
to be provided at optimal levels (See Newlon (2001)). This paper provides evidence that for auto
theft, spillovers across state boundaries are substantial. Because this type of crime is highly mobile,
a high level of coordination across jurisdictions is required.
Auto theft is an extremely salient property crime: the value of the stolen goods is large and
For criminal displacement over time see Jacob, Lefgren, and Moretti (2005).
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
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
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
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
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
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
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.
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.
Installing a Lojack recovery system in a locality requires large ﬁxed costs. These take the form
of lengthy agreements with the local police, regulatory approvals, and the cost of installing the
network of tracking equipment. The owners of the Lojack technology gave exclusive distribution
rights to a Mexican company to introduce the system in Mexico. The patent holders would supply
the equipment and the Mexican company would be in charge of the management of the system.
For a startup company, the large setup costs, together with uncertain demand for the product
made the enterprise extremely risky. The Mexican company decided to oﬀer a major car builder
an exclusive agreement to have Lojack installed in its cars. The vehicle recovery company would
The information on Lojack is based on discussions with company executives in Mexico and on information from
their web page.
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
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.
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
Let Ns1m1 , Ns1m0 , Ns0m1 , Ns0m0 denote the number of thefts in each of these markets, where
the subscript s1 refers to the Lojack state, m1 to the Lojack model, s0 to the Non Lojack state,
and m0 to the Non Lojack model. Denote by Nij = S(Pij ) the supply of stolen vehicles in each
of the markets, where Pij is the amount of money the thief obtains when he steals a vehicle.4 A
standard assumption is that the number of vehicles stolen is increasing in the payoﬀ, ie, the supply
is upward sloping in each of these markets (S (·) > 0). This is due to the increasing marginal cost
of stealing cars. Cars targeted ﬁrst are those that are easier to steal: those parked on the street,
as opposed to inside a garage.
In each of the markets there is a demand for stolen cars denoted by D(Nij ). Demand for stolen
vehicles is decreasing in the price. This is generated by the decreasing marginal beneﬁt of each
additional vehicle that is stolen. Stolen vehicles are used for many lucrative activities. A common
use is to sell them in the used vehicle market with a false title to an unsuspecting buyer. Another
use is the sale to people who knowingly buy ill-obtained vehicles for personal use because they
have a low probability of being prosecuted. One example are rural landowners, who can buy stolen
There is no assumption of equality of the supply functions S(·) in the model. They are written in this way for
simplicity of notation.
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
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 Ns1m1 = S(Ps1m1 )−Lojack. Where
Lojack is a dummy variable indicating that the model is equipped with Lojack. Demand is given
d d s
by Ps1m1 = D(Ns1m1 ). The market clearing condition equates demand to supply: Ns1m1 = Ns1m1 .
This is a simple nonlinear model of three equations in three unknowns with the Lojack variable
changing exogenously from 0 to 1. I linearize around the equilibrium without Lojack and then
solve the system with linear algebra tools in Appendix A. The predictions of the model under
geographically isolated markets and model speciﬁc demand for cars are:
∂Lojack <0 ⇒ Deterrence Eﬀect
∂Lojack =0 ⇒ No Within State Externality
∂Lojack =0 ⇒ No Geographical Externality Within Model
∂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
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.
3.2 Within State Displacement: Geographically Isolated Markets and Common
Demand Across Car Models
Under the assumption of no interstate trade in stolen vehicles, the introduction of Lojack has no
eﬀect in thefts of either model in the Non-Lojack state. However, when demand for stolen vehicles
is common across car models within a state, introducing Lojack generates increased thefts for
the Non-Lojack model. Let demand for stolen vehicles in the Lojack state be given by Ps1m0 =
d d s
Ps1m1 = D(Ns1m1 + Ns1m0 ). As before, Lojack makes stealing Lojack models more costly: Ns1m1 =
d s d s
S(Ps1m1 ) − Lojack. The market clearing conditions are now Ns1m1 = Ns1m1 and Ns1m0 = Ns1m0 .
The model is solved in Appendix A, with the following predictions:
∂Lojack <0 ⇒ Deterrence Eﬀect
∂Lojack >0 ⇒ Within State Negative Externality
∂Lojack =0 ⇒ No Spatial Externality Within Model
∂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(Ns1m1 + Ns0m1 ). As before,
Lojack reduces the supply of Lojack-equipped stolen vehicles Ns1m1 = S(Ps1m1 ) − Lojack. The
model is solved in Appendix A, with the following predictions:
∂Lojack <0 ⇒ Deterrence Eﬀect
∂Lojack =0 ⇒ No Within State Externality to Non Lojack Model
∂Lojack >0 ⇒ Model Speciﬁc Spatial Externality
∂Lojack =0 ⇒ No Spatial Externality to Non Lojack Model
In this case, the model predicts spatial externalities. If crime is highly mobile across jurisdic-
tions, local law enforcement generates spatial externalities in crime for neighboring jurisdictions.
Crime that is mobile across jurisdictions can also be harder to tackle for law enforcement
agencies that act independently. In terms of eﬃcient decision-making, with spatial spillovers, law
enforcement should be done at a higher level of government such that the externality is internal-
ized (Donahue (1997)). At the very least, with spatial externalities, law enforcement should be
coordinated across jurisdictions.
3.4 Geographically Integrated Markets and General Demand for Stolen Cars
The ﬁnal case I consider is one in which demand for stolen cars is common across car models and
states. Demand is given by
d d d d
Ps1m1 = Ps1m0 = Ps0m1 = Ps0m0 = D(Ns1m1 + Ns1m0 + Ns0m1 + Ns0m0 )
When demand for stolen vehicles is common across models, and markets are geographically inte-
grated, the introduction of Lojack generates negative spatial spillovers to both car models in the
Non-Lojack state. Further, non-Lojack models in Lojack states also experience increases in theft.
As before, Lojack reduces the supply of Lojack equipped vehicles Ns1m1 = S(Ps1m1 ) − Lojack. The
model is solved in Appendix A, with the following predictions:
∂Lojack <0 ⇒ Deterrence Eﬀect
∂Lojack >0 ⇒ Within-State Externality to Non Lojack Model
∂Lojack >0 ⇒ Model Speciﬁc Spatial Externality
∂Lojack >0 ⇒ Spatial Externality to Non Lojack Model
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.
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-
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
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
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.
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.
Age is set to 0 if the vehicle is less than 12 months old, 1 if it is between 12 and 24 months old, etc.
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[T hef tsijyt ] = (Sijy ) · exp γij + βj · t + βa · I[Age = a] + βLojack · Lojackijy (1)
To estimate externalities to Non-Lojack models in Lojack states, I use observations of non-Lojack
models in Lojack states to ﬁt:
E[T hef tsijyt ] = (Sijy )·exp γij + βj · t + βa · I[Age = a] + βAf terLojack · Af terLojackjt (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
E[T hef tsijyt ] = (Sijy )·exp γij + βj · t + βa · I[Age = a] + βAf terLojack · Af terLojackjt (3)
where the dependent variable T hef tsijyt is the number of vehicles stolen in a state, model group,
vintage, and year combination. Sijy refers to the vintage size in a state-model-vintage combination,
which is a proxy for the stock of cars susceptible to being stolen. I also include a ﬁxed eﬀect (γij )
for every combination of state and car model in the data. This incorporates the fact that theft risk
varies according to location (state) and vehicle type (model group). A state speciﬁc time trend
(βj · t) is also included. Vehicle-age dummies (I[Age = t − y]) capture the mean theft schedule
according to the age of the car. Typically, newer cars are subject to higher theft risk.
In equation (1), Lojackijy is a dummy variable indicating if the vehicle was equipped with
Lojack when it was sold. The coeﬃcient of interest, βLojack , is identiﬁed from a deviations (upward
or downward) in theft risk of vintages sold with Lojack from what was predicted by the linear time
trend estimated from vintages sold without Lojack. The four Lojack states are labeled in ﬁgure 2.
Only data from Lojack models in Lojack states is used in the estimation of model (1).
In equation (2), Af terLojackjt is a dummy variable equal to one if Lojack has been introduced
into the state. βAf terLojack is identiﬁed in the same way as before, but is now interpreted as the
magnitude of the within-state externality. Only non-Lojack model data from Lojack states is used
in estimation of model (2).
In equation (3), Af terLojackjt is a dummy variable indicating that the Lojack program has been
introduced in the nearest Lojack state. The associated coeﬃcient, βAf terLojack , is interpreted as
the geographical externality that Lojack generated. Equation (3) is estimated separately for Lojack
and non Lojack models on three diﬀerent subsamples that vary according to their distance to the
nearest Lojack state. First are Lojack states contiguous to those where Lojack was implemented,
referred to as First Ring states. Then the equation is estimated on the second ring of states around
Lojack states – these are referred to as Second Ring states. The rest of states are referred to as
Distant States and model (3) is estimated for those observations too. A map of these state groups
can be found in ﬁgure 2.
Including a state speciﬁc time trend is important because vehicles in the same state are subject to
the same police and judiciary institutions, which generate diﬀerent theft dynamics over time in each
state. The descriptive statistics showed that there is much heterogeneity in theft risk depending on
the model and the state. In such situations, one major worry is that estimated eﬀects may simply
be capturing cross-sectional diﬀerences in theft risk, particularly in cases such as this one in which
the treatment was not randomly assigned. This concern is addressed by including a ﬁxed eﬀect
(γij ) for every (state, car model) in the data. In other words, average diﬀerences in theft behavior
across car models or states are not the source of identiﬁcation of the coeﬃcient of interest.8
Sijy allows for a meaningful comparison of theft risk given that the quantity of cars at risk
varies by model, state and vintage. That is, given that diﬀerent models have radically diﬀerent
market shares, any analysis of auto theft that seeks to distinguish between car models in the same
geographic location must control for the quantity of cars at risk of theft.9
The exponential form of the conditional expectation, and the fact that the coeﬃcient of interest,
βLojack , is associated with a dummy variable, makes interpretation of the coeﬃcient highly intuitive.
The ratio of expected thefts conditional on having Lojack to expected thefts conditional on not
having Lojack is:
E[T hef tsijyt |xijyt , Lojackijyt = 1]
E[T hef tsijyt |xijyt , Lojackijyt = 0]
The estimated eﬀect is independent of the values of the other regressors in xijyt . For this reason,
alongside the Poisson regression coeﬃcients I also report exponentiated coeﬃcients-1, also known
as incidence rate ratios (IRR-1). These are interpreted as percentage changes in theft risk due to
Standard errors are clustered at the state level (Bertrand, Duﬂo, and Mullainathan (2004)). Cameron, Gelbach,
and Miller (2006) two-way clustered standard errors at the state and year level were also calculated, without changing
the signiﬁcance of the results.
In a Poisson regression, this is referred to as “controlling for exposure”. The exposure variable (Sijy ), is usually
incorporated with a coeﬃcient constrained to unity. This introduces the assumption that thefts are a function of
the stock of cars and that this relationship is the same across all car models: a doubling of the stock accompanied
by a doubling of thefts is interpreted as keeping theft risk constant. The results are robust to a relaxation of the
coeﬃcient restriction on Sijy . See the Robustness Checks section.
the Lojack program.
The theoretical framework suggests that βLojack should be negative for vehicles equipped with
Lojack. It also suggests that if demand for stolen vehicles is model speciﬁc and there is trade across
state lines, Lojack models in neighboring states should experience increases in theft risk once Lojack
is introduced in the nearest Lojack state: βAf terLojack would be positive in equation (3). The eﬀect
should be decreasing with distance from Lojack states. On the other hand, if demand for stolen
vehicles is common across car models, increased theft risk for non-Lojack models in Lojack states
would take the form a positive βAf terLojack coeﬃcient in equation (2).
An extensive literature has focused on the diﬃculty in measuring program eﬀects when par-
ticipation is voluntary (Heckman (1979)). This problem is not present in Ford’s Lojack program.
Ford’s vehicles were sold for the same price nationally, regardless of whether the state was partici-
pating in the Lojack program. This yields two beneﬁts for this study. First, conditional on buying
a Lojack model, participation in the program was not voluntary. Ford engaged in this program
under the rationale that it would be able to sell more cars, albeit with a lower proﬁt margin. Any
eﬀect of Lojack on sales is controlled for in the empirical analysis through the stock-of-cars expo-
sure control. Second, the single national price, together with the locality-speciﬁc recovery service,
means that there was practically no incentive for customers to buy their cars in a diﬀerent state
from where they lived. With equal prices, a customer in a Lojack state had no incentive to buy a
car in a non-Lojack state. Similarly, a customer in a non-Lojack state had scant incentive to buy a
Lojack-equipped car and drive it to a state that did not have the Lojack recovery service available.
Before presenting the results, I should mention that Poisson models have standard errors that
are too small if there is overdispersion in the data (conditional variance that is larger than the
conditional mean). I present estimates of a model robust to overdispersion (the negative binomial)
in the Robustness Checks section and show that the estimated standard errors are smaller than those
of the Poisson model, which suggests that the Poisson model is adequate for the data. Further, in
the tables, I also show the result of the overdispersion test suggested by Cameron and Trivedi (1998).
If α < 1, overdispersion is modest and Poisson and Negative Binomial standard errors are of similar
magnitude. However, under no (or modest) overdispersion, the Poisson model is preferred because
it is robust to distributional misspeciﬁcation of the dependent variable. The Negative Binomial
model, on the other hand, generates inconsistent coeﬃcients under distributional misspeciﬁcation
in the dependent variable.
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
Lojack-protected models generated a negative spatial externality in Lojack models of nearby states.
The estimations did not produce evidence of displacement across car models, either in the Lojack
state or in nearby states.
The reported eﬀects in the previous tables are in terms of changes in theft risk. But Poisson
regressions have the advantage that it is straightforward to obtain an estimate of the magnitude
of the eﬀect in terms of the number of cars stolen. The measure of interest is the diﬀerence in
expected thefts with and without the Lojack program:
(E[T hef tsijyt |xijyt , Lojackijyt = 1] − E[T hef tsijyt |xijyt , Lojackijyt = 0])
where the sum is across all car models and states. Because of the conditional expectation’s form,
the sum can be rewritten as the percent change in thefts attributable to Lojack multiplied by the
pre-Lojack average annual thefts in the group:
(IRR − 1) · E[T hef tsijt | Lojackijyt = 0] (4)
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
Lojack from those that were not. Another reason for a positive externality is that some thieves may
have been unsure about when the program started, in which case it would not be surprising to ﬁnd a
positive spillover eﬀect of having Lojack installed in future versions of the model. However, if there
is little confusion for thieves about which models had Lojack, and the cars are close substitutes,
then one could ﬁnd negative spillovers along this dimension, too. In other words, if auto thieves
realize that Ford Windstars sold after 2000 have Lojack, do they increase or decrease the theft of
close substitutes, like a Ford Windstar sold in 1999?
I run a regression identical to equation (2) except that the Af ter Lojack regressor is one
for Lojack models built before the model came equipped with Lojack, in years after Lojack was
introduced in its newer versions. I use the subsample of observations consisting of old vintages of
Lojack models in Lojack states. The result, shown in Table 7, is that the estimated impact is not
diﬀerent from zero, suggesting that there were no net externalities towards older versions of Lojack
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
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
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
generalized declines in theft rates, with large positive externalities and a positive net social beneﬁt
from the technology, as Ayres and Levitt (1998) have argued.
The results presented in this section imply that selling Lojack to a discernible set of cars severely
limits its potential positive spillovers. This ﬁnding may be useful in future scenarios to better inform
policymakers about how to regulate and adopt new technology so as to maximize society’s welfare.
6.1 Robustness Checks
6.1.1 Data Limitations
This section reviews the implications for the analysis of using insured vehicle theft data together
with total stock of cars, instead of the insured vehicle stock of cars. The intuition of the problem
this presents is relatively simple: the interpretation of the results is invalid if Lojack generated
changes in the likelihood of a Lojack-equipped vehicle being insured. If buying a car with Lojack
made owners less likely to buy insurance, then this would reduce the number of cars exposed to
theft that are captured in the data, potentially inﬂuencing some of the results.
The problem can be seen in terms of the estimated model. The data available, in which total
stock of cars instead of the insured vehicle stock is used as the exposure variable, can be understood
as a situation in which the true exposure variable is overblown by a factor larger than one. Assume
that πij is the probability that a vehicle model i in state j is insured. Then the true stock of cars
is Sijy = πij · Sijy , where S Obs refers to the stock of vehicles observable to the econometrician,
T rue Obs
while S T rue refers to the actual stock of insured cars on the road. Then, if the true model is
E[T hef tsijyt |xijyt ] = (Sijy ) · exp γij + βj · t + βLojack · Lojackijyt + βa · I[Age = a]
T rue Obs
Substituting Sijy = πij · Sijy in the equation above yields
E[T hef tsijyt |xijyt ] = (Sijy )·exp ln(πij ) + γij + βj · t + βLojack · Lojackijyt + 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,
as long as they are stable throughout the panel. In conclusion, the speciﬁcation used is robust to
additive error in the exposure variable. However, a problem arises if there is temporal variation
in πij which is correlated with the introduction of the Lojack program. Under such scenario, the
coeﬃcient of interest, (βLojack ) is not identiﬁed. For this reason, I now present evidence that: 1)
Lojack-equipped vehicles were just as likely to be insured as non-Lojack-equipped vehicles; and 2)
insurance likelihood of Lojack models evolved in an identical manner to non-Lojack models once
Lojack was introduced. This allows me to conclude that Lojack introduction was uncorrelated with
insurance coverage (πij ) probability, as required by the econometric model.
First, note that the scope for this behavioral response would be severely limited by the fact that
in the years after Lojack was introduced, around 70% of new vehicles were bought with ﬁnancing
loans, which require insurance coverage during the life of the loan. Cars bought through a loan are
required to be insured because the ﬁnancing company otherwise can lose the collateral that can be
repossessed in case of an accident or theft. The insurance requirement for cars bought on credit
was not relaxed because the car had Lojack.
The data I use to measure the possible impact of Lojack introduction on insurance probability
are the AMIS time series of the number of cars insured by year in the whole country for every
car model. Since Lojack states command 40% of nationwide sales, a reduction in the insurance
coverage of Lojack models would show up in the national insurance coverage rate for those models.
I use national sales for the years 1999-2005 and the number of national insurance contracts, to
construct a database that partitions the data into combinations of triplets (model group, vintage,
year). I then generate the variable proportion insured which is deﬁned as the number of vehicles
insured divided by the stock of cars sold for every (model group, vintage, year) cell. I ﬁrst use
data for the years after the introduction of Lojack to regress the proportion insured on a dummy
indicating whether the vehicle was sold with Lojack (Lojackij ), calendar year dummies (I[t =
1999], ..., I[t = 2005]) to capture time trends in national insurance coverage, and a set of age-of-
car dummies (I[Age = 1], ..., I[Age = 6]) that ﬂexibly capture average changes in the insurance
probability as the car ages. The estimated equation in the ﬁrst column of Table 11 is
P roportion Insurediyt = β0 +βLojack ·Lojackiy +βage=t−y ·I[Age = t−y]+βyear=t I[Y ear = t]+uiyt
where i refers to the model group, y to the year the cars were sold, and t refers to the year of the
observation. The coeﬃcient of interest is βLojack . In the table, the Lojack coeﬃcient is insigniﬁcant;
this suggests that after Lojack was implemented, Lojack models were just as likely to be insured
as non-Lojack models. Thus buying a car equipped with Lojack did not reduce the probability of
the car being insured, as long as Lojack models were as likely to be insured as their counterparts
before Lojack was introduced. The second regression addresses this issue by looking for diﬀerential
changes over time in insurance coverage for Lojack models.
The equation estimated in the second column of the table is
P roportion Insurediyt = βi +βLojack ·Lojackiyt +βage=t−y ·I[Age = t−y]+βyear=t I[Y ear = t]+uiyt
which diﬀers from the previous regression in that it includes a model-speciﬁc intercept and uses
data from all observations available: for the years 1999-2005. The insigniﬁcance of the coeﬃcient in
the table again suggests that Lojack models neither observed a decrease nor an increase in insurance
likelihood, compared to other car models, once Lojack was introduced.
The regressions lead me to conclude that Lojack did not induce a reduction in the probability
of insuring vehicles for customers who bought Lojack-equipped cars. There may have been various
reasons for this. People who bought the car with credit had no option of opting out of insuring
their vehicle even if they wanted to. Another reason is that people value the services of insurance
companies aside from theft coverage: insuring vehicle damage in case of accidents, medical expense
insurance for vehicle occupants, and civil responsibility.
A possible concern about the motivations determining which vehicles would be part of the
Ford Lojack program is that the car models participating in the program could have been those
for which theft rates were increasing before the program. If this were true, mean reversion could
become a possible explanation for the reduction in theft risk of the Lojack-model, Lojack state
group. To address this concern, I regress the annual change in theft rate10 on future Lojack
program participation in columns 1 and 2 of Table 12. The results show that compared to both all
car models, and all Ford models, Lojack participating vehicles did not experience diﬀerent changes
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.
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
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
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
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
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.
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
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.
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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.
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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.
Figure 2: Lojack States and Non-Lojack States
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
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
Table 3: Descriptive Statistics
Variable Mean Std. Dev. Min Max Variable Mean Std. Dev. Min Max
Panel A: All Observations (N=26,213) Panel B: Lojack Equipped (N=118)
Stock 632.1 1,785.3 1 32,940 Stock 605.7 679.3 5 2,725
Thefts in Year 4.16 28.2 0 1,502 Thefts in Year 4.5 7.9 0 37
Age Car when Stolen 1.6 1.4 0 5 Age Car when Stolen 0.44 0.6 0 3
Sold with Lojack 0.004 0.06 0 1 Sold with Lojack 1 0 1 1
Panel C: Lojack Models (N=5,364) Panel D: Non Lojack Models (N=20,849)
Stock 237.2 483.5 1 7,704 Stock 733.7 1,974.1 1 32,940
Thefts in Year 1.3 6.1 0 125 Thefts in Year 4.8 31.4 0 1,502
Age Car when Stolen 1.6 1.4 0 5 Age Car when Stolen 1.6 1.4 0 5
Sold with Lojack 0.021 0.14 0 1 Sold with Lojack 0 0 0 0
Panel E: Lojack States (N=4,845) Panel F: Non Lojack States (N=21,368)
Stock 1,715.2 3,752.8 1 32,940 Stock 386.5 625.4 1 8,328
Thefts in Year 18.9 63.3 0 1,502 Thefts in Year 0.82 2.2 0 61
Age Car when Stolen 1.6 1.4 0 5 Age Car when Stolen 1.6 1.4 0 5
Sold with Lojack 0.02 0.15 0 1 Sold with Lojack 0 0 0 0
An observation unit is a quadruplet deﬁned by a (state, car model, vintage, year). Stock and Thefts are in car units. Stock refers to
cumulative sales in the speciﬁed (state, car model, vintage) combination. Age of car is in terms of completed years since sale (0 if
the car is up to 12 months old, etc.) The Sold with Lojack variable equals one if the car model was equipped with Lojack when the
vehicle was sold. Lojack Models refers to the 9 Ford vehicle models that participated in the Lojack program at some point between
1999 and 2004 (Panel C). Lojack states are the 4 states where Lojack was implemented between 1999 and 2004 (Panel E). Lojack
Equipped refers to vehicles that were equipped with Lojack when the vehicle was sold (Panel B).
Table 4: Impact of the Lojack Program in Lojack States
Dep. Var: Number of Thefts
Lojack Models Non-Lojack Models
Coeﬀ. IRR − 1 Coeﬀ. IRR − 1
Equipped with Lojack −0.64*** −0.48***
After Lojack −0.05 −0.05
Observations 966 3,879
α 0.10 0.08
Bootstrapped standard errors clustered at the state level in parentheses. Observations
weighted by sales. The ﬁrst regression uses data from Lojack models in Lojack states.
The second regression uses data from Non-Lojack models in Lojack states. Af terLojack
is dummy variable equal to one for years after Lojack was introduced into the state.
Equipped with Lojack is a dummy variable equal to one for vintages that were sold
equipped with Lojack. Other controls: Size of vintage at the state-model level, state-
model ﬁxed eﬀect, state speciﬁc time trend, age dummies. The Coeﬀ. column reports the
coeﬃcient from the poisson regression. The incidence rate ratio column (IRR − 1) reports
the estimated coeﬃcient in its exponentiated form minus 1. It is interpreted as the rela-
tive change in theft risk generated by the Lojack program. α is the estimated conditional
over(+)/underdispersion(−) in the dependent variable.
* signiﬁcant at 10%; ** signiﬁcant at 5%; *** signiﬁcant at 1% for the test H0 : β = 0.
Table 5: Impact of Lojack in Non-Lojack States
Dep. Var: Number of Thefts
Lojack Models Non-Lojack Models
Coeﬀ. IRR − 1 Coeﬀ. IRR − 1
First Ring Around Lojack States
After Lojack 0.57* 0.77* 0.04 0.04
(0.34) (0.61) (0.07) (0.07)
Observations 1,800 6,951
α 0.01 0.13
Second Ring Around Lojack States
After Lojack 0.47* 0.61* 0.15 0.16
(0.61) (0.44) (0.13) (0.16)
Observations 1,276 4,998
α 0.15 0.24
All Other Non Lojack States
After Lojack 0.57 0.77 0.05 0.05
(0.37) (0.67) (0.10) (0.11)
Observations 1,322 5,021
α 0.25 0.27
Bootstrapped standard errors clustered at the state level in parentheses. Observations weighted
by sales. The regressions use data from Non Lojack states only. The top panel (First ring around
Lojack states) uses data from Non Lojack states contiguous to Lojack ones, the middle panel
(Second Ring Around Lojack States) uses data from Non Lojack states adjacent to the ones in the
top panel, and the third panel (All Other Non Lojack States) uses data from the remainding Non-
Lojack states. Af ter Lojack is a dummy variable equal to one for years after Lojack was introduced
in the nearest Lojack state. Other controls: Size of vintage at the state-model level, state-model
ﬁxed eﬀect, state speciﬁc time trend, age dummies. The Coeﬀ. column reports the coeﬃcient from
the poisson regression. The incidence rate ratio column (IRR − 1) reports the estimated coeﬃcient
in its exponentiated form minus 1. It is interpreted as the relative change in theft risk generated by
the Lojack program. α is the estimated conditional over(+)/underdispersion(−) in the dependent
* signiﬁcant at 10%; ** signiﬁcant at 5%; *** signiﬁcant at 1% for the test H0 : β = 0.