Economics of property crime rate in Punjab.
Jabbar, Shahzad Mahmood ; Mohsin, Hasan M.
This study intends to ascertain the impact of socio-economic,
demographic and deterrent variables and the effect of technical criminal
know-how and past criminal experience on property crime rate. The
property crime equation comprises of the following independent
variables: population density, unemployment rate, literacy rate, police
strength and number of police proclaimed offenders in a society. The
property crime equation has been estimated by using a time-series data
set for Punjab from 1978 to 2012. We have applied Johansen cointegration
approach to test the long run relationship among the variables.
Empirical findings suggest that police strength has a deterrent effect
while past criminal experience enhances property crime rate in Punjab.
The study finds population density has a significant positive
relationship while education has a significant negative relationship
with property crime rate. Further we also find a negative relationship
between unemployment and property crime which is supported by the
concept of 'consensus of doubt' in the discipline of crime and
economics.
JEL Classification: D6
1. INTRODUCTION
"People respond to incentives" is a universal truth that
allows us to claim that people participate in criminal sector for their
own social, psychological or economic incentives. Current study has
focused on property crime rate that comprises of those types of offences
that intentionally and deliberately attempt to or actually cause loss of
property. A higher property crime rate discourages commercial activity
which in turn distorts the process of economic growth. The social
scientists particularly economists seem keen to identify the potential
determinants of property crime that can be helpful for policy-makers in
order to restore peace and stability. Becker (1968) introduced the crime
and economics discipline by designating criminals and law enforcement
agencies as rational individuals. Following in his footsteps economists
from all around the world are contributing to investigate those
potential factors which can affect the magnitude of crime rate in
different societies.
Unfortunately there is a growing concern about higher crime rate in
Pakistan but economics of crime have received a little attention in the
country. All available studies, which review this newly emerging
discipline have a common characteristic of using a country level data of
socio-economic variables in explaining their effect on crime rate.
The crime rate, however, seems sensitive to the geographical
boundaries of countries. The sizable literature uses states, provinces,
and even the districts level data to gain insights into this serious
issue. Thus it seems better to observe the effect of various
socioeconomic and demographic factors on crime rate at sub-national
level in Pakistan because there is lot of variation in most of the core
socio-economic and demographic aggregates across regions. We use the
sub-national data to estimate the crime rate equation in order to avoid
the overstatement or understatement of the effects of various
socioeconomic, demographic and deterrent variables. The current study
has selected Punjab as a case study due to higher property crime rate
there and its major role in Pakistan's economy. Moreover, we have
focused on the property crime rate only because it is more responsive to
socio-economic, demographic and law enforcement conditions of a society
[Becsi (1998)].
The higher incidence of property crimes in Punjab has ressulted in
a state of insecurity, frustration and mental unrest that spells out a
dire need to deal with the situation. Our empirical investigation
focuses on those factors which can significantly affect the property
crime rate but have been least focused in most of the empirical attempts
available at country level literature of crime and economics. First, a
deterrent variable labelled as police strength to check its deterrent
effect on property crime rate has been included in the current study.
Secondly, an explanatory variable population of police proclaimed
absconders (1) has been incorporated in economic model of property crime
to capture the effect of technical criminal know-how and past criminal
experience on property crime rate. Finally population density;
unemployment and education have been used as control variables to see
their impact on property crime rate.
For this purpose we have applied Johenson Cointegration approach to
a time series data set for Punjab from 1978-2012. The study finds a
significant negative impact of increasing police strength and education
on property crime rate. The increase in the number of police proclaimed
offenders and population density have a significant positive impact on
property crimes. In view of these findings, we believe current study
will not only be helpful in proposing sound policy recommendations
regarding property crime prevention but will also make useful
contribution to the existing literature of crime and economics.
The study has been arranged as follows: we review the literature in
Section 2. The theoretical framework is presented in Section 3. In
Section 4 there is a debate on methodology used in empirical estimation
along with the sources of data used. Empirical findings have been stated
in Section 5 and finally concluding remarks along with policy
recommendations are presented in Section 6.
2. LITERATURE REVIEW
Study of crime remained a subject of interest in each society
during different eras. When father of economics Smith (1776) talked
about the accumulation of wealth by people he also discussed the
motivation of people towards crime and demand of people for the
protection from crime. Paley (1785) reported the role of deterrent
variables in changing the magnitude of crime rate in different
societies. However, there was the father of utilitarianism Bentham
(1879), who introduced calculus while determining the criminal behaviour
and optimal level of law enforcement by crime prevention authorities.
Fleisher (1966), Tullock (1967), Rottenberg (1968), Becker (1968),
Stiggler (1974), Landes and Posner (1975) have contributed a lot to
reconnect economists with Crime and Economics Discipline [Ehlrich
(1996)].
If we talk about the recent theoretical foundations of crime and
economics, then we will have to go back to the contributions of Becker
(1968) who led the foundations of theoretical model of criminal
behaviour. He was of the view that every criminal is an economic agent
as he commits crime only, when there is an expectation of increase in
his utility. He also discussed the optimal structure of institutions
that are responsible for crime prevention in some state by arguing that
these institutions should be designed so that they should suffer minimum
cost during crime prevention. In this regard along with Stigler (1968)
he preferred private enforcement of law rather than public enforcement
of law.
Landes and Posner (1975) criticised the above mentioned idea of
Becker of turning the most likely and an ideal public enforcement of law
into private enforcement of law. They were of the view that private
enforcement has severe drawbacks as there can be possibility of under
enforcement or over enforcement. However they favour the private
enforcement of law only in civil offenses as these can be detected with
an ease and can be punished at zero cost.
Friedman (1984) defended the idea of private enforcement of law by
Becker and Stigler (1968) with the help of an historical example of
Ireland where private enforcement of law prevailed for three hundred
years not only in civil offences but also in most severe criminal
offences like murder etc. during the Anglo-Saxon period. Friedman
concluded that private enforcement is not as effective in offences under
criminal law as it is in offences under civil law but these
inefficiencies can easily be eliminated by making some minor changes in
some of the formal and informal institutions that play vital role in
crime prevention.
Friedman (1995) presented a new idea of turning the criminal law
into civil law in support of the above mentioned Becker's idea
about optimal enforcement of law. He argued that punishment for the
crime prevention either in terms of imprisonment or execution is not
optimal and turning of criminal law into civil law can enable a country
to punish offenders in terms of monetary fines. In this way net cost of
crime prevention will be zero and there will be lesser burden on
taxpayers.
The above mentioned debate about the rationality of criminals and
efficient law enforcement by a state is the main theme of modern crime
and economics discipline. Since a criminal activity involves
multi-disciplines but the current study will concentrate only on those
national and international studies which are related to identifying
socioeconomic, demographic and deterrent variables of crime rate.
Gillani, et al. (2009) have empirically investigated the effect of
unemployment, inflation and poverty on crime rate of Pakistan by using a
time series data from 1975-2007. They applied Johenson cointegration
approach to conclude that unemployment rate, poverty and inflation are
granger cause of crime in Pakistan. After that Jalil (2010) investigated
the link between urbanisation and crime rate in Pakistan using a time
series data set during 1964-2008. He also used Johenson cointegration
approach in this empirical investigation and reported that a lack of
planning regarding the expansion of urban areas increase crime rate
while literacy rate and unemployment have a significant and negative
impact on crime rate of the country.
All these studies had a little focus on deterrent variables in
economic model of crime. Jabbar and Mohsin (2014) highlighted the
measuring error problem and lack of deterrent variables in the economic
modal of crime at country level literature. Using a time series data set
for Punjab during 1978-2013, he applied Johenson cointegration approach
and proved that police strength, high conviction rate and a higher
literacy rate in a society have a significantly negative impact on
murder crime rate while the impact of unemployment on violent crime is
ambiguous.
In the large part of international literature the effect of various
socioeconomic variables particularly the effect of unemployment on crime
rate is ambiguous [Chiricos (1987)]. We will also discuss a few studies
of crime and economics at sub-national level. Chiricos (1987) has also
explored the unemployment crime relationship while other researchers
like Coack and Wilson (1985) found insignificant and weak relationship
between unemployment and crime rate. After a thorough research he
concludes that we can get a weak and even an insignificant relationship
between crime and unemployment if we use a time-series data or if we use
the data of U.S economy for unemployment through the 1970s. He concluded
that cross sectional studies better explain the relationship between
unemployment and crime rate as compared to the time series analysis.
Imroho, et al. (2006) examined the effect of various economic,
socio and demographic variables on the crime rate across different
countries of the world with the help of a cross-sectional analysis. They
selected at least one country from each of the continents of the world
and they selected 1980 in USA as a benchmark year. They checked the
effect of unemployment rate, fraction of low human capital individuals
in an economy, income inequality, age categories, and the probability of
apprehension along with duration of jail sentence on property crime. To
check the effect of above said variables on property crime rate they
used overlapping generation model to allow individuals to participate in
either legitimate market activities or in illegal activities. In their
final findings amazingly 79 percent people involved in property crime
were not found unemployed but they were under employed. Moreover their
model also predicted that 18 years of age or younger were 76 percent of
the total criminals who participated in property crimes. Furthermore
46.1 percent people who were involved in property crimes did not have a
high school diploma. Moreover they concluded that small differences in
probabilities of apprehension and income inequality can generate a
significantly large difference in the crime rates in similar
environments.
Gumus (2004) investigated the effects of deterrent, socio-economic,
and demographic variables on crime rate of 75 large US cities by using a
cross sectional data. He concluded that per capita income and poverty
are the root causes of crime in large US cities while the unemployment
was statistically significant only in 1/8 of empirical equations used in
this study.
Omotor (2009) used inflation, income, literacy rate, and
unemployment rate to investigate their role in crime nexus of Nigeria.
By using ECM and co-integration approach, he tested the relationship
between crime rate and above said socio-economic variables to conclude
that unemployment has a positive relationship with crime rate while a
low literacy rate and high population of Nigeria were not found the root
causes of stimulating crime rate in Nigeria.
New developments are taking place in the crime and economics
literature and providing new insights related to crime and its
determinants. Current study also intends to bring forward some of the
important causes of property crime rate in Punjab [Pakistan],
3. THEORETICAL FRAMEWORK AND EMPIRICAL PROCEDURE
In social sciences criminal behaviour can be discussed by different
theories, however an economist has his own ideas to examine it. An
economist always believes that people are rational and they respond to
incentives so they treat criminals as economic agents as they
participate in offences related to theft and snatching to enhance their
utility. It can be argued that the choice between committing and not
committing some criminal activity depends on the net-payoff
([[phi].sub.i]) of some criminal activity. Decision of participation in
an illegitimate activity ([P.sub.i]) by criminals is decreasing function
of expected cost ([C.sub.i])and increasing function of gain ([G.sub.i])
from criminal activity that can be described as under;
[P.sub.i] = f ([C.sub.i], [G.sub.i]) ... ... ... ... ... ... (1)
[C.sub.i] = f ([c.sub.i], [wl.sub.i], [p.sub.i], [f.sub.i]) ... ...
... ... ... ... (2)
[G.sub.i] = f ([L.sub.i]) ... ... ... ... ... ... (3)
Where, [C.sub.i] is total cost faced while committing a crime and
furthermore [c.sub.i] can be described as direct cost i.e. time spend in
planning and committing of a crime, efforts of self-defense, (2)
[wl.sub.i] denotes foregone market wages in case of arrest or
conviction, [p.sub.i] stands for probability of arrest or conviction and
[f.sub.i] represents the fines or other penalties in term of
imprisonment. While in the above stated Equation (3), [G.sub.i] is gross
gain and [L.sub.i] is something gained (loot) as a result of criminal
activity. Thus net pay off (3) [[phi].sub.i] can be defined as the
difference of gross gain and total cost i.e.
([[phi].sub.i] = [G.sub.i] - [C.sub.i] (4)
Or
[[phi].sub.i] = [L.sub.i] - [c.sub.i] - [wl.sub.i] - [p.sub.i]
[f.sub.i] (5)
It can be claimed that a criminal activity takes place if and only
if;
[[phi].sub.i] > 0
It is important to note that we consider the expected gains as
economic incentives because theft and snatching are more responsive to
socio-economic and law enforcement variables. The above discussion is
core of economic model of crime used in the current study. After studing
Buonnano, el al. (2008); Cherry, et al. (2002); Becsi (1999) and Jalil,
et al. (2010) we have formulated the following economic model of crime;
Crime = f (Population, Unemployment, Education, Police Strength,
Police Absconders)
The above stated function contains those types of socio-economic,
demographic and deterrent variables, which correspond to the theoretical
framework of the current study.
The current study will use a demographic variable in the form of
population density that can be the representative of urbanisation
because property crimes are often considered as an urban phenomenon
[Gumus (2004)]. The next variable used in our modal is unemployment,
which is one of the most controversial variables of crime analysis,
however it is likely to be correlated with crime in one or another way.
Third variable, education can affect the decision of committing some
crime as it increases the expected legitimate earnings. The next
variable included in our modal is a deterrent variable labelled as
police strength, which is expected to be negatively correlated with
property crime rate of a society. The last variable included in our
modal is the number of police proclaimed absconders in a society about
which it can be argued that in case of a low opportunity cost of
committing some crime police proclaimed absconders prefer to commit
property crimes for their material wellbeing.
The above discussion enables us to specify the following empirical
equation to estimate,
[PC.sub.t] = [alpha] + [[beta].sub.1] [P0P.sub.t] +
[[beta].sub.2]UR + + [[beta].sub.3] [LR.sub.t] +
[[beta].sub.4][PS.sub.t] + [[beta].sub.5] [PP0's.sub.t] + [e.sub.t]
... (6)
Property crime ([PC.sub.t]) is a dependent variable along with the
independent variables, [POP.sub.t] stands for population density,
[UR.sub.t] represents the unemployment rate, [LR.sub.i] stands for the
literacy rate, [PS.sub.t] exhibits the police strength and
[PPO's.sub.t] stands for the police proclaimed absconders in Punjab
during some t year. We will estimate Equation (6) by using suitable
econometric technique to get empirical findings of the study.
Since we have a time series data set so we will use the standard
practice of checking the data to see if it is stationary or
non-stationary by using unit root test. If unit root test (4) discloses
that all the variables are stationary at level then study will follow
the simple OLS technique. If all the variables are non-stationary at
level then study will follow the ARDL approach, finally if all the
variables will be stationary at level 1 then the study will follow the
Johenson maximum likelihood approach to find the long-run relationship
among the dependent and independent variables.
4. DATA, VARIABLE CONSTRUCTION AND ECONOMETRIC ISSUES
A data set related to Punjab during 1978-2012 has been used for
empirical investigations. In this regard a few missing values (5)
related to unemployment and literacy rate were obtained by calculating
averages and using compound interest formula [Jalil (2010)].
4.1. Descriptive Statistics
Table 2 given below narrates the descriptive statistics for the
variables used in this study. It becomes clear that in last 34 years,
average value of Property Crime (PC) per 1000 persons is 0.59. Magnitude
of coefficient of variation depicts that unemployment rate has least
variation ranging from 5.5 to 8.6 and population density and PC/1000 are
more volatile variables. Except the average value of proclaimed
offenders which lies above the middle of data, averages of the rest of
the variables in data lie almost in the centre of the data which shows
that data is almost equally spread around its mean values.
4.2. Estimation Procedure
Our purposed ADF test indicates that all the variables used in this
study are stationary at (1=1), therefore, we apply Johenson
Cointegration Approach to the following set of equations:
[PC.sub.t] = [alpha] + [[beta].sub.1][PD.sub.t] +
[[beta].sub.2][UR.sub.t] + + [[beta].sub.3] [LR.sub.t] + [[beta].sub.4]
[PS.sub.t] + [[beta].sub.5] PPO's + [[epsilon].sub.t]
5. EMPIRICAL RESULTS
Our purposed ADF test indicates that all the variables used in this
study are stationary (1=1), therefore, Johenson Cointegration Approach
is used for estimation purposes.
5.1. Results of Johansen Cointegration Techniques Trace test
indicates four cointegration equations while maximum eigen value test
indicates 2 cointegration equations at 5 percent level of significance
in property crime modal. Thus the variables of under discussion modal
have long run relationship with each other. The null hypothesis stating
that there are zero cointegration vectors is rejected.
The results of the estimated model are presented below.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
5.2. Interpretation and Discussion of the Results
Empirical findings indicate that there is a significantly positive
relationship between population density and property crime which is
consistent with the findings of Bechdolt Jr. (1975), O'Brien, et
al. (1980) and Regoeczi (2003) who also found a positive relationship
between property crimes and population density. Consistency of result
with the literature of crime and economics allow us to claim that
population density is one of the major determinants of property crime in
Punjab.
The logic of this result is quite simple that an increase in
population density decreases the probability of arrest, which leads to a
lower cost for offenders, that motivates them towards property crime. It
can also be argued that population density
increases the number of criminals and crime targets and decreases
protection of crime targets, which results in a positive relationship
between property crime rate and increase in population density.
Secondly, we have found a negative and significant relationship
between unemployment and property crime which is consistent with the
empirical findings of Entorf and Spengler (2000) who have reported
negative estimates for some of the theft crimes. Cantor and Land (1985)
also argued that unemployment could have both a positive and negative
impact on crime rates. Imrohoroglu (2001) concluded that about 79
percent of the people engaging in criminal activities are employed thus
it can be argued that rise in property crimes is not only related to
illiterate, unemployed and the poor class of a society but rich,
educated, employed and underemployed people can also boost these types
of crimes particularly in societies like Punjab.
Consensus of doubt in crime and economics discipline provides some
technical reasons of such a negative relationship between unemployment
and property crime. In this regard they state that most often unreliable
figures of crime and unemployment data are available because official
rates of unemployment considerably understate the true numbers of people
who are without work. Similarly crime prevention authorities often
understate or overstate the true number of registered crimes for their
own incentives. The above mentioned discussion reveals that a general
belief of positive relationship between unemployment and crime is not
necessarily proved true in each study [Orsagh and Witte (1981)].
Thirdly, there is a negative and significant relationship between
literacy and property crime rate, which is consistent with the empirical
findings of Buonanno (2003), Lochner and Moretti (2001), Usher (1997),
Lochner (2007) and Jalil, et al. (2010). The economic rationale behind
this empirical finding is that a literate person is relatively more risk
averse and forward-looking, which produces a negative association of
education with illicit behaviour.
Moreover, current study yields a significantly negative
relationship between property crime and per capita police men available
to society, which is similar to the findings of Sjoquist (2012), Baltagi
(2006), Vollaard (2005), Berkeley, et al. (2012), Kelaher and Sarafidis
(2011). It can be argued that an increase in per capita police men
available to society increases the probability of arrest that leads to a
higher expected cost of crime. It is well known that police
effectiveness regarding detection and prevention of crime in Punjab
depends upon the geographically focused police practices along with the
hot-spots policing. As property crimes are often considered as an urban
phenomenon, the presence of free media and influential personalities in
these areas compel crime prevention authorities to deter property crimes
first. Crime prevention authorities try to depute their most efficient
employees to deter the property crime for the sake of departmental
reputation and for some of the other job related incentives. Thus this
result is not only consistent with the international literature but also
quite logical and corresponds to the current culture of most of the
institutions of the province.
Finally, current study has reported a significantly positive
relationship between property crime and increase in number of police
proclaimed offenders in a society. It explicitly means that if number of
police proclaimed absconders increase in some society then obviously
there will be an increase in property crime rate of that society. This
result is quite logical and dynamics of this result need some
discussion. When police department declares a person as an absconder
then termination of such a person from legitimate labour market is not
amazing because a person of such repute is not accepted as a labourer by
any person or organisation. Furthermore, fear of arrest, imprisonment
and monetary penalties do not allow him to join legitimate labour market
for legal earnings. Then it becomes inevitable for such a person to
commit crime of theft and snatching for his survival. The above
reasoning supports a positive and significant impact of population of
proclaimed offenders on property crime rate as a police proclaimed
offender has a lower opportunity cost of committing a crime.
It is also very important to note that these persons have not only
a low opportunity cost of committing property crime but an adequate
criminal know how from their past criminal experiences helps them a lot.
All these factors support our positive and significant relationship
between number of police proclaimed absconders and property crime rate
[Buonnano (2008); Fajnzylber, et al. (2002); Sah (1991)].
CONCLUDING REMARKS
The main objective of the study was to identify the impact of
socioeconomic, demographic and deterrent variables on property crime
rate of Punjab empirically. For this purpose a time series data set from
1978-2012 was used. Johenson cointegration approach has been applied to
test the existence of long run relationships among the variables.
A positive and significant relationship of population density with
property crime is first empirical finding of the study, which leads us
to believe that population density is the main determinant of crime in
Punjab. Although unemployment depicts a negative relationship with
property crime. It may be due to the technicalities of data or empirical
procedure that study has adopted.
Third major finding of our study is that education plays a vital
role to control property crime rate in Punjab as literacy rate has a
negative and significant relationship with property crime. The empirical
results have proved that there is a deterrent effect of police strength
on property crime rate and finally an increase in number of police
proclaimed offenders in a society has a positive and significant effect
on property crime rate.
Policy Implications
The study brings forth some important policy recommendations
regarding crime prevention in Punjab. Authorities should concentrate on
controlling population growth rate in Punjab to make the province less
dense and there should be effective planning particularly in urban areas
regarding infrastructure. Developing new housing colonies near populated
areas can be an effective measure to minimise the effect of increasing
population densities on property crime rate. Promoting education level
can be a valid remedial measure to minimise the criminal behaviour. The
state should create not only more job opportunities but also improve the
real wages of prevailing jobs, otherwise education without jobs can be a
curse as awareness and technicalities of educated individuals can
promote white collar crimes. Finally, enhancing the police strength by
new recruitments, providing them a better training, better
transportation, better tools of communications and advance weapons can
be an effective measure in detection and prevention of crime in Punjab.
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(1) Police proclaimed absconders are the persons that have
committed crime but crime prevention authorities are still unable to
arrest these persons. A lot of police reports consider it as a vital
reason of high property crime rate.
(2) Efforts made to avoid penalties, arrest, imprisonments or
monetary fines etc.
(3) The net pay-off ([[phi].sub.i]) can also be stated as expected
utility of committing some crime by a criminal.
(4) Study follows the Augmented Dicky Fuller test [ADF] to check if
the data is stationary or not.
(5) We found missing values for those years in which labour force
survey had not been published.
Shahzad Mahmood Jabbar <
[email protected]> is MPhil
(Economics) student at the Pakistan Institute of Development Economics,
Islamabad. Hasan M. Mohsin <
[email protected]> is Head,
Department of Econometrics and Statistics at the Pakistan Institute of
Development Economics, Islamabad.
Table 1
Nature of Explanatory Variables their Brief Definitions
and their Data Sources
Property Crime Depicts Criminal Various Issues of
Behaviour/It has been Punjab Development
taken as sum of dacoity Statistics. Various
and burglary including Issues of Annual Crime
motor vehicle Report, DIG Police
snatching, motor (Crime). Punjab.
vehicle theft, cattle
theft, all other theft.
Population Demographic/Population Various Issues of
Density of Punjab in per square Punjab Development
miles during some Statistics.
specific year.
Unemployment Economic/Number of Various Issues of
Rate persons who are Labour Force Survey.
unemployed out of the
Total Labour force in
Punjab.
Literacy Rate Socio-economic/A person Various Issues of
is said to be literate Labour Force Survey.
who can read and write
his/her name.
Police Strength Deterrent/The number of Various Issues of
police employees Annual Administration
available to thousand Report. AIG Police
members of Punjab in (Establishment),
some particular year. Punjab.
Number of Police Depicts Criminal Various Issues of
Proclaimed Behaviour/number of Annual Crime Report,
Offender police proclaimed AIG Police (Crime),
absconders present in Punjab.
society to 1000 member
of Punjab.
Table 2
Descriptive Statistics
Coefficient
Variables Mean S.D. Min. Max. of Variation
PC per 1000 Persons 0.590 0.201 0.300 1.098 34.08
Population Density 337.96 78.46 215.18 470.8 23.21
Unemployment Rate 6.971 1.024 5.464 8.606 14.69
Literacy Rate 45.424 9.59 31.25 60.6 21.11
Police Strength 1.326 0.302 0.838 1.911 22.83
Proc. Offenders 0.21 0.23 0.022 0.88 110
Table 3
Results of the Unit Root Test
Only Trend and
Variable Intercept Intercept Conclusion
PC
Level -0.325323 -3.806383
1st Difference -6.227111 -6.218713 I(1)
Population Density
Level 0.966131 -1.798407
1st Difference -8.325482 -8.626124 I(1)
Unemployment
Level -2.757306 -2.898596
1st Difference -5.029617 -4.974713 I(1)
Literacy Rate
Level 0.062647 -3.277343
1st Difference -6.390288 -6.275866 I(1)
Police Strength
Level -0.002685 -2.030985
1st Difference -4.144891 -4.067436 I(1)
Proclaimed Offenders
Level -2.831661 -0.584165
1st Difference -3.867865 -4.872781 I(1)
Table 4
Cointegration Rank Test (Trace) [Property Crime]
Hypothesised Trace 0.05
No. of CE(s) Eigen Value Statistic Critical Value Prob. **
None * 0.97 239.69 103.84 0.00
At most 1 * 0.86 122.36 76.97 0.00
At most 2 * 0.53 60.19 54.08 0.01
At most 3 * 0.49 36.01 35.19 0.04
At most 4 0.25 14.33 20.26 0.27
At most 5 0.15 5.05 9.16 0.28
Table 5
Cointegration Rank Test (Maximum Eigenvalue) [Property Crime]
Hypothesised Eigen Max-Eigen 0.05
No. of CE(s) Value Statistic Critical Value Prob. **
None * 0.97 117.33 40.96 0.00
At most I * 0.86 62.16 34.81 0.00
At most 2 0.53 24.18 28.59 0.16
At most 3 0.49 21.68 22.29 0.06
At most 4 0.25 9.27 15.89 0.40
At most 5 0.15 5.06 9.16 0.28
