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An evaluation of a multiyear gun buy-back
programme: re-examining the impact on
violent crimes
Scott W. Phillips‡, Dae-Young Kim†and James J. Sobol†
‡(Corresponding author) SUNY Buffalo State, 1300 Elmwood Ave, Buffalo, NY 14222, USA.
Tel: +1 716 878 3154; ;email: phillisw@buffalostate.edu
†SUNY Buffalo State, Buffalo, New York, USA
Submitted 15 October 2013, accepted 11 November 2013
Keywords: gun buy-backs, police, violence-prevention programmes
Scott W. Phillips
is an associate professor in the
Criminal Justice Department at SUNY Buffalo
State. His research interests include police
officer decision-making and organisational
influences on officer’s behaviour. His work has
been published in Journal of Criminal Justice,
Criminal Justice Policy Review, International
Journal of Police Science and Management and
Police Practice and Research.
Dae-Young Kim
is an assistant professor in the
Criminal Justice Department at SUNY Buffalo
State. His current research interests include the
political economy of crime and punishment, pol-
icy analysis and programme evaluation, and
evaluating problem-based learning. His work has
appeared in journals such as Criminal Justice
and Behavior and Prison Journal.
James J. Sobol
is an associate professor in the
Criminal Justice Department at SUNY Buffalo
State. His research includes empirical assess-
ments of police behaviour and police attitudes.
His research has appeared in Justice Quarterly,
Crime and Delinquency, Journal of Criminal Jus-
tice and Criminal Justice Policy Review. His
recent research relates to understanding how
police organisations respond to contemporary
challenges and identifying ways to improve their
effectiveness.
A
BSTRACT
The purpose of this study is to examine gun buy-
backs as a policy response to gun-related crime. It
improves upon past studies by examining a city
that has used multiple gun buy-backs as a
standard crime prevention approach, allowing the
multiple intervention points to be assessed. Fur-
ther, the study examined crime data over a longer
period and included a comparison group of sim-
ilar crime trends without a gun. Total crime,
homicide, robbery and assault data spanning
several years are subject to an interrupted time-
series analysis. Non-gun crimes served as control
variables. Examining the first two intervention
dates indicated that the gun buy-back programme
had no impact on reducing crimes. Specifically,
the gun buy-back programme in the study loca-
tion reduced gun homicide levels, but results failed
to reach statistical significance. When the third
intervention date was examined, the gun buy-
back programme resulted in a significant decrease
in gun robbery levels, controlling for non-gun
robbery levels and unemployment rates.
The results for gun robbery suggest that gun
buy-back programmes may take years to affect
crime numbers, although future research is
warranted.
INTRODUCTION
The criminal justice system’s actions in both
preventing and responding to crime often
fluctuate as crime patterns and public
opinion change. Policy-makers oftentimes
implement crime-reduction strategies
despite lack of evidence of their success. An
International Journal of Police Science & Management Volume 15 Number 3
Page 246
International Journal of Police
Science and Management,
Vol. 15 No. 3, 2013, pp. 246–261.
DOI: 10.1350/ijps.2013.15.3.315
example of a standard police organisational
response to the problem of violent crime is
a gun buy-back programme. Such pro-
grammes are typically sponsored by local
government and work under the notion
that violent crime will decrease when the
number of guns in circulation is reduced
(Braga, 2004; Eck, 1995). Gun buy-back
programmes are often called for when there
is a ‘high-profile’ incident that makes
national headlines and captures the public’s
attention.1
Prior research has demonstrated a lack of
success in gun buy-back programmes
(Baker & McPhedran, 2007; Callahan,
Rivara, & Koepsell, 1994; Lee & Suardi,
2010; Rosenfeld, 1995). The failure of gun
buy-back to reduce violent crime may
result from its flawed premise as a crime-
reduction programme. For example, most
surrendered firearms are unworkable or are
easily replaced, and it is unlikely that a gun
turned in would be used in a crime (Levitt,
2004; Wellford, Pepper, & Petrie; 2004).
However, one study has reported a statistical
reduction in firearm deaths in locations
where more weapons were surrendered in a
buy-back programme (Leigh & Neill,
2010). The lack of consensus in the research
suggests that additional research into gun
buy-back programmes is warranted prior to
closing the books on the issue.
The purpose of this study is to examine a
gun buy-back programme in a way that fills
knowledge gaps that exist in past evalu-
ations. First, most gun buy-back studies
used short time frames to examine their
impact on crime (Cook, Moore, & Braga,
2000). The current study used violent crime
data spanning 7 years, and homicide data
spanning 11 years. Second, no other study
has examined buy-back efforts that used
multiple buy-back programmes over time.
The City of Buffalo, New York used gun
buy-back programmes in five of six years,
between 2007 and 2012. Finally, gun buy-
back evaluations often lack a comparison
group of trends in similar crimes without a
gun, such as robberies (Sherman et al.,
n.d.). This study employed such comparison
groups. Accordingly, we are able to provide
a more robust examination of the gun buy-
back intervention and discern the extent to
which the programme has an impact on
violent crime. We begin with a brief review
of the conceptual and methodological issues
surrounding the study of gun buy-back
programmes before turning to our specific
methods and findings from the Buffalo, NY
gun buy-back intervention.
LITERATURE REVIEW
Kohn (2005–2006) suggested that policy-
makers ‘have often fixated on gun control as
a solution to gun crime’ (p. 270). Gun
control strategies were highlighted as con-
tributing to the reduction in crime in New
York City in the 1990s. In New York City,
officers used arrests and field stops to ques-
tion suspects about guns (Manning, 2001).
The primary intent of a gun buy-back
programme is to reduce gun use in violent
crime (Braga, 2004; Callahan et al., 1994;
Kennedy, Piehl, & Braga, 1995; Mullen,
2001). Gun buy-back programmes are
founded on the logic that more guns in a
community contribute to higher levels of
violence, and ‘buying back’ firearms will
reduce their use in crime (Eck, 1995; Sher-
man, 2001; Sherman et al., n.d.).
Gun buy-back programmes have been
used intermittently in many cities across the
USA since 1991 (Sherman, 2001), and in
1996 as a national programme in Australia
(Lee & Suardi, 2010). Although not all gun
buy-back programmes are identical, at their
core, they provide financial compensation
to people who voluntarily surrender their
firearms (Callahan et al., 1994; Kleck, 1995;
Rosenfeld, 1995). Further, anyone who
surrenders a gun does so with ‘no questions
asked’ (Rosenfeld, 1995, p. 4). These pro-
grammes are now a fairly common method
Phillips, Kim and Sobol
Page 247
for dealing with gun violence in cities all
across the USA (Goering, 2010).
Policy makers justify gun buy-back pro-
grammes for several reasons. First, the pro-
gramme assumes that the surrendered guns
are weapons commonly used in violent
crimes, by individuals who are typically
engaged in criminal offending. Second, that
surrendered guns are in good working order
and are of the calibre typically used in
crimes. The research evidence does not
support either assumption (Kennedy et al.,
1995; Wellford et al., 2004). A gun buy-
back programme in Milwaukee did not
recover the type of guns that were used in
homicides and robberies (Kuhn et al.,
2002). A Sacramento gun buy-back pro-
gramme received mostly small calibre
weapons, and roughly one-quarter of the
guns turned in were not in working order
(Romero, Wintemute, & Vernick 1998). A
gun buy-back programme in Seattle found
that 17 per cent of the guns that were
surrendered were not operational; those
that were operational were not reliable
(Callahan et al., 1994). That is, the gun may
work, but may easily jam because parts are
worn or rusty. Finally, the guns surrendered
to buy-back programmes are often older.
Kuhn et al. (2002) found 14 per cent of the
weapons surrendered were manufactured by
companies that had been out of business for
more than 10 years. There is also evidence
that diminishes the assumption that the
guns available on the street are necessarily
the most dangerous guns. A study in Boston
(Kennedy, Piehl, & Braga, 1996) found that
64.4 per cent of the weapons recovered
from street-level arrests were small calibre
weapons (.38 calibre or smaller). Indeed,
almost one-third of the weapons recovered
in Boston were either .22 or .25 calibre, and
almost three-quarters of the weapons were
old (ie, ‘pre-1968’) firearms (Kennedy et al.,
1995).
Empirical examinations of gun buy-back
programmes have demonstrated little suc-
cess in reducing gun violence in the USA.
Rosenfeld (1995) studied two gun buy-
back programmes in St. Louis (1991 and
1994), and found no reduction in the num-
ber of gun homicides or assaults relative to
the same crimes committed without guns.
Callahan et al. (1994) examined a buy-back
programme in Seattle and found no reduc-
tion in the number of firearms-related
deaths or crimes. In 1997, Australia passed
the National Firearms Agreement (NFA),
which mandated that the government buy
back certain types of firearms from civilians.
Over 650,000 firearms, roughly one-fifth of
Australia’s firearms stock, were destroyed
(Leigh & Neill, 2010). Because of the
extent of the buy-back programme in Aus-
tralia, evaluations of the programme are
substantively different from those in the
USA. Still, studies of the Australian gun
buy-back programme produced conflicting
findings. Baker and McPhedran (2007) use
a straightforward interrupted time-series
analysis to examine the impact of the NFA,
but reported no relationship between homi-
cide and suicide patterns and the gun buy-
back programme. Lee and Suardi (2010)
argued that there is likely to be a ‘lagged’
impact of the NFA. Thus, rather than use
the date of the NFA as an intervention,
they used a ‘structural break test’ as part of
their time-series analysis. They reported no
significant impact of the NFA on homicides
and suicides. When Neill and Leigh (2008)
re-examined the data using a longer time
frame, they reported that the gun buy-back
programme significantly reduced firearm
homicides and suicides. In addition, their
2010 evaluation, which included a geo-
graphical variable, indicated a statistically
significant drop in homicides and suicides
in those states with higher firearm buy-back
rates (Leigh & Neill, 2010).
An evaluation of a multiyear gun buy-back programme
Page 248
CURRENT STUDY
Gun buy-back programmes have been part
of the police response to violent crime for
over 20 years. Cities in the USA continue
to use the programme in response to high-
profile incidents, such as the shooting in
Newtown, CT, despite a lack of evidence
that the programme will succeed in reduc-
ing violent crime.2These programmes have
gained legitimacy as a policy for dealing
with violent crime, having been used in
several large (eg, Boston, Chicago, Los
Angeles, Miami, San Francisco, Washing-
ton, DC) and moderate-size cities (eg,
Cleveland, Detroit, Louisville, Tampa, and
St. Louis) (Goering, 2010). The pro-
grammes appear to be ‘a logical and sensible
policy that helps to placate the public’s
fears’ (Lee & Suardi, 2010, p. 76). Studies of
gun buy-back programmes in the USA
indicate an ineffective policy, yet some
evidence from Australia seems to suggest
further analysis.
The present study examined the impact
of the City of Buffalo’s gun buy-back pro-
gramme. The unique nature of Buffalo’s
programme is that it has been used in five of
the past six years (between 2007 and 2012).
The buy-back programme in Buffalo,
therefore, is not simply a response to a
tragic or high-profile incident, but is part of
the city’s ongoing crime-reduction efforts.
In addition, this study included comparison
groups of similar crime trends without a
gun, such as robberies. Comparison groups
are commonly lacking in prior evaluations
of gun buy-back programmes (Sherman et
al., n.d.). The hypothesis of this research is
fairly simple: if a gun buy-back programme
is employed, violent crime will decrease.
Methods
Study location
The data for this study were provided by
the Erie County Crime Analysis Center and
contain crime reported in Buffalo, NY.
Buffalo is a mid-sized city located in the
northeastern USA with a population over
250,000 and is located in a metropolitan
statistical area of over 1 million. According
to US Census Bureau estimates, 50 per cent
of the city’s population is white, 38 per cent
is African American and 10 per cent is
Hispanic. The median age of the city
population is 34 (US Census Bureau, 2010).
The police department has over 750 sworn
officers. Approximately two-thirds of the
officers are white, 24 per cent are African
American and 8.3 per cent are listed as
‘other’. Seventy-seven per cent of the
officers are male.
Between 2007 and 2012, Buffalo held a
gun buy-back programme each year,
excluding 2010.3Pre-paid bank cards were
given to anyone who surrendered a firearm.
The value of the bank cards ranged from
$10 for non-working guns to $100 for
assault weapons. Funding for the gun buy-
back programme was made available from
assets forfeited in criminal cases. The buy-
back programme was promoted with sup-
port from a national advertising company
that designed signs and provided billboards
in different parts of the city, and posted on
bus shelters. There are typically six or seven
buy-back locations in the city, all situated at
neighbourhood churches. Since 2007, the
programme has collected more than 3,000
guns. Unfortunately, because the city’s buy-
back programme follows a ‘no questions
asked’ policy, there are no data available
regarding who surrendered a weapon or
why they gave it to the buy-back pro-
gramme. Nor is there any information on
the quality of guns surrendered.4
Data
The data file included all ‘robbery’ and
‘assault’ incidents from 1 January 2006 to 30
November 2012, and all homicide cases
from 2001 to 2012. The unit of analysis is
monthly crime. The number of observa-
tions (83 for non-homicide crimes and 144
Phillips, Kim and Sobol
Page 249
for homicides) was higher than the mini-
mum number of time points (50) required
for interrupted time-series analyses (Sayrs,
1989). The files included characteristics of
the crime (eg, gun, strong-arm robbery),
date and time of incident, street address and
type of location (eg, residence, business,
street). As discussed below, ‘all crimes’ were
analysed, and then the crime types were
divided for individual analysis to examine
the impact of the gun buy-back
programme.
Four dependent variables were of pri-
mary interest: total gun crime, gun homi-
cide, gun robbery and gun assault. They are
presented as the number of incidents per
month. Because of the lack of monthly
population data available at the local level,
this study used crime-level data. Many
interrupted time-series studies using city-
level data have used crime ‘counts’ as a
measure of outcomes rather than crime
‘rates’ (Britt, Kleck, & Bordua, 1996;
O’Carroll et al., 1991; Loftin & McDowall,
1984; Loftin, McDowall, Wiersema, &
Cottey, 1991).
The independent variable for this study is
the gun buy-back intervention, which is
defined as a dummy variable that indicates
the absence of the state prior to the event
(coded as 0) and the presence of the state
during and after the event (coded as 1). In
an interrupted time-series design, pre-
intervention series plays a role as a control
series (McDowall, Loftin, & Wiersema,
1996). Further, this study used non-gun
crimes in the intervention area as a control
variable to rule out some historical effects
(see Loftin & McDowall, 1984; Loftin et al.,
1991; McDowall, Loftin, & Wiersema,
1992). For this study, non-gun crimes can
be used as an appropriate control series. As
seen in the Appendix (Figure A1), for
example, non-gun crimes have similar over-
all trends to gun crimes. The correlation
coefficient between total gun and non-gun
crime series is 0.41 (p< 0.01) in levels and
0.37 (p< 0.01) in first differences. Our
assumption is that both crimes are deter-
mined by a similar set of causes and thus
their trends would be same if there were no
gun buy-back events (see Britt et al., 1996).
In addition, monthly unemployment rates
were included as a control variable because
both theory and past research posit an
association with criminal behaviour (see
Chiricos, 1987). Crime rates increase or
decrease as unemployment rates change
because unemployment deprives an indi-
vidual of means for quality living and social
capital to establish a law-abiding lifestyle.
Figure 1 illustrates the change in the level
of gun-related crimes over time for the
research city from January 2006 to Novem-
ber 2012. The vertical lines represent the
intervention dates. Although all the figures
fluctuated substantially over time, regardless
of the intervention, there were some
declining trends in all the series. In addi-
tion, the pre-intervention means are slightly
higher than post-intervention means (see
Table 1). Therefore, it is important to stat-
istically test whether such decreases in all
the series are attributable to the gun buy-
back programme.
Analytical strategy
This study uses interrupted time-series
analysis to examine the impact of gun buy-
back programmes on gun-related crimes.
Two basic steps are employed in this analysis
(for a more comprehensive and detailed
discussion for interrupted time-series ana-
lysis, see McCleary, Hay, Meidinger, &
McDowall, 1980; McDowall, McCleary,
Meidinger, & Hay, 1980). The first step
entails the identification and estimation of
an autoregressive integrated moving average
(ARIMA) noise model that represents the
underlying stochastic process generating the
time series. Examination of the autocorrela-
tion function (AFC) and partial auto-
correlation function (PACF) indicates
substantial seasonal variance in some of the
An evaluation of a multiyear gun buy-back programme
Page 250
time series. To remove the seasonal cycle
from the series, seasonal differencing tech-
niques have generally been used in prior
research, but were not used in this study
due to the loss of 12 of the whole 17
pre-intervention observations. This pre-
intervention time-series segment would be
obviously too short a period to permit
model specifications for the intervention
assessment. Before estimating models, sea-
sonal fluctuations in the data were adjusted
using the ratio to moving average (multi-
plicative) technique, which is available in
Eviews (the program used for data analysis:
http:// www.eviews.com/home.html) as an
ad hoc solution to prevent the loss of obser-
vations. Table 2 indicates which series are
seasonally adjusted.
Using the augmented Dickey–Fuller
(ADF) and Phillips–Perron (PP) tests, this
study formally tested for unit roots in the
time series to determine whether a variable
Table 1: Pre- and post-intervention means, 2006-2012 (intervention — June 2007)
Variable Pre-intervention mean
(17 observations)
Post-intervention mean
(66 observations)
Change in level
Total gun crime 94.41 85.88 –8.53
Gun homicide 1.47 0.79 –0.68
Gun robbery 52.24 49.45 –2.79
Gun assault 40.71 35.64 –5.07
Figure 1
Trends in gun-related
crimes in Buffalo,
2006–2012
Phillips, Kim and Sobol
Page 251
is non-stationary (Cromwell, Labys, &
Terraza, 1994; Koèenda & Èerny, 2007). As
seen in Table 2, all of the dependent vari-
ables are stationary and do not need to be
differenced. In addition, this study exam-
ined the patterns of serial correlation in the
ACF and PACF, and identified the follow-
ing ARIMIA models: ARIMA (1,0,0) for
the seasonally adjusted total gun crime,
ARIMA (0,0,0) for the gun homicide,
ARIMA (0,0,0) for the seasonally adjusted
gun robbery, and ARIMA (3,0,1) for the
seasonally adjusted gun assault. However,
there is conflicting evidence about the non-
stationary property of the both seasonally
adjusted total ‘nongun crime_sa’ and ‘non-
gun assault_sa’ series between ADF and PP
tests. The PP tests suggest that they are
stationary, whereas the ADF tests represent
otherwise. For a more conservative analysis,
they are first differenced to be stationary for
statistical analyses.
The second step in an interrupted time-
series analysis involves developing a full
impact assessment by adding an interven-
tion component to the noise model. There
are two methodological issues of signifi-
cance in this study. The first pertains to the
specification of the intervention point. It is
important to consider when the legal and
social policy might actually begin to exert
an impact on the variable under investiga-
tion (Britt et al., 1996). There have been
five gun buy-back event dates since 2007.
This study used the programme’s first event
date — June 2007 — as the intervention
point. This study also considers the second
event data (September 2008) as an alter-
native intervention time under the assump-
tion that it may take several years until the
buy-back programme gains publicity and
awareness and finally becomes fully effective
after the initial event date. All intervention
dates may be considered because each of the
intervention events respectively and/or
accumulatively resulted in a reduction in
crime. It should be noted, however, that
using multiple intervention points and
selecting the most significant estimate as the
intervention date would lead to an increase
in a Type I error rate because ‘at least one
Table 2: Results for unit root tests of the time series, 2006–2012
ADF PP
Model/crime type Intercept Trend and intercept Intercept Trend and intercept
Dependent variable
Total gun crime_sa –6.60** –7.42** –6.73** –7.55**
Gun homicide –7.11** –7.10** –7.09** –7.06**
Gun robbery_sa –7.25** –7.71** –7.20** –7.69**
Gun assault_sa –7.77** –8.51** –8.49** –9.10**
Control variable
Total non-gun crime_sa –2.39 –2.34 –5.79** –5.93**
Non-gun homicide –7.47** –8.03** –7.57** –8.04**
Non-gun robbery_sa –6.01** –6.33** –6.09** –6.46**
Non-gun assault_sa –2.16 –2.14 –6.14** –6.12**
Unemployment_sa –1.02 –1.07 –1.09 –1.41
Notes:
Figures for ADF and PP tests represent t-statistics.
**Significant at α= 0.01.
sa indicates the seasonally adjusted series.
An evaluation of a multiyear gun buy-back programme
Page 252
significant’ result can be expected by
chance alone (see McDowall et al., 1996).
The second issue concerns the specifica-
tion of the impact model. There are three
typical impact patterns differing in terms of
onset and duration: an abrupt–permanent
change, a gradual–permanent change and
an abrupt–temporary change (McCleary et
al., 1980). First, an abrupt–permanent
change is estimated by a zero-order transfer
function (ω0It), and the full impact assess-
ment model is written as Yt = ω0It + Nt.
Second, a gradual–permanent change is
implied by a first-order transfer function
(ω0/(1 – δ1B)*It) and the full impact
assessment model is defined as Yt = ω0/(1 –
δ1B)*It + Nt. Third, an abrupt–temporary
change is estimated by applying the first-
order transfer function to a differenced
intervention series (ω0/(1 – δ1B)*(1 –
B)It), and the full impact assessment model
is Yt = ω0/(1 – δ1B)*(1 – B)It + Nt. One
of these impact patterns should be identi-
fied based on theory, prior studies and an
understanding of the legal policy (Britt et
al., 1996; McDowall et al., 1996).
The implications of the impact model for
this study are relatively clear. The abrupt
and temporary impact hypothesis might be
more plausible in consideration of what it is
indicated in Figure 1. In general, the crime
time series decreased after the interventions
had returned to their pre-intervention levels
a few months later. The gun buy-back pro-
gramme may have an abrupt decreasing
impact on crimes when the programme
gained publicity in earnest, right after the
interventions. However, the impact may last
for only few months because it is implaus-
ible to expect that several buy-back events
eliminate gun availability on the streets and,
in turn, gun-related crimes. This study
began with testing the abrupt, temporary
intervention hypothesis, but also considered
other rival impact hypotheses for
comparison.
Findings
Analysis of all gun-related crimes
Table 3 presents the results for testing for an
abrupt and temporary impact of the gun
buy-back programme with the first inter-
vention date (June 2007). None of the
estimates of the intervention (ω0) reaches
statistical significance. The gun buy-back
programme had no impact on reducing
crimes. Although the gradual impact para-
meters (δ) in some of the models are statist-
ically significant at the 0.01 level, it is not
meaningful to interpret because the abrupt
impact parameters (ω0) are insignificant.
Diagnostic checks of the residuals for all the
models indicate no serial correlation, so all
the models are acceptable.
Table 4 presents the test results when the
second intervention date (September 2008)
was used as an alternative intervention
point. There is conflicting evidence regard-
ing the effectiveness of the gun buy-back
programme in these analyses. First, the gun
buy-back programme has a statistically sig-
nificant impact on gun robbery levels at the
0.10 level, but its effect is positive. In other
words, the gun buy-back programme resul-
ted in a significant increase in the level of
gun robbery. Second, the gun buy-back
programme has a significant impact on
reducing gun homicide at the 0.10 level but
fails to reach conventional levels of statistical
significance (α= 0.05). For all the models,
diagnostic checks of residuals show no serial
correlation. This study conducted additional
(unreported) analyses using the third inter-
vention date (August 2009) and found out-
come estimates quite similar in terms of
both magnitude and direction to those
found in the models with the second inter-
vention date.
Finally, this study considered other
impact models such as a gradual and perma-
nent impact and an abrupt and permanent
model, each using three intervention dates.
When the third intervention date and an
Phillips, Kim and Sobol
Page 253
abrupt and permanent model were
employed, the gun buy-back programme
resulted in a significant decrease in gun
robbery at the 0.05 level, controlling for
non-gun robbery levels and unemployment
rates. There are several possible explana-
tions. First, given the preponderance of
insignificant results in most of the statistical
models, using various combinations of both
multiple intervention points and impact
hypotheses might possibly generate this sig-
nificant result by chance alone. Second, the
gun buy-back programme might begin to
have a significant impact on reducing gun
robbery levels as publicity about the gun
buy-back programmes began in earnest
after the third intervention date. As seen in
Figure 1, there was an overall downward
trend in the level of gun robbery after the
third intervention, but the impact was only
temporary and lasted about for one year.
Finally, there are no further significant esti-
mate of the intervention at the level of .05.
These results are not reported in this study
due to page limitations.
Analysis of gun homicide
In the previous analyses, crime data are only
available back to 2006. Because the inter-
rupted time-series design is sensitive to the
length of data used in the study (Britt et al.,
1996; McDowall et al., 1980), substantive
outcomes would be otherwise if a few
dozen more pre-intervention observations
were available. This study was able to add
five years of homicide data and extended
the period covered from 2001 to 2012. As
Table 3: Model for an abrupt, temporary impact of the gun buy-back programme on
gun crime levels, 2006–2012 (intervention date — June 2007)
Total gun crime_sa Gun homicide Gun robbery_sa Gun assault_sa
ARIMA (1,0,0) (0,0,0) (0,0,0) (3,0,1)b
A 40.07** 2.78** 37.80** 3.23**
ω022.82 –0.25 20.73 –0.97
∆0.53** 0.23* –0.22* –0.90**
ϕ1–0.33* –––0.40**
ϕ2––––
ϕ3–––
θ1––––0.57**
Controlsa
Non-gun crime series 0.05 –0.14 0.02 0.19**
D (Unemploy_sa) 2.15 0.20 5.07 –0.15
B-G LM test –
F-values, Prob. 0.14 0.13 0.21 0.11
Obs*R2, Prob. 0.12 0.12 0.19 0.09
Qstatistics NA NA NA NA
Notes:
Significant at *α= 0.05; **α= 0.01.
aBased on the results drawn from unit root tests and the patterns of serial correlation in the ACF and PACF, all the control
variables except non-gun homicide were seasonally adjusted and/or first differenced.
bFor the analysis of gun assault_sa, ϕ2and ϕ3were dropped from the full intervention model because of their lack of
significance.
NA indicates no evidence of autocorrelation.
sa indicates the seasonally adjusted series.
An evaluation of a multiyear gun buy-back programme
Page 254
seen in Figure 2, gun homicide series fluc-
tuated substantially over the past decade in
Buffalo. Gun homicide levels during the
post-intervention period are slightly lower
than those in the pre-intervention counter-
part. Becuase of the lack of data availability,
Table 4: Model for an abrupt, temporary impact of the gun buy-back programme on
gun crime levels, 2006–2012 (intervention date — September 2008)
Total gun crime_sa Gun homicide Gun robbery_sa Gun assault_sa
ARIMA (1,0,0) (0,0,0) (0,0,0) (3,0,1)c
A 42.66** 2.87** 37.40** 3.34a
ω016.56 –3.55a18.52a1.82
∆0.50** 0.23* 0.23* 0.90**
ϕ1–0.28a–––0.40**
ϕ2––––
ϕ3––––
θ1––––0.56**
Controlsb
Non-gun crime series 0.05 –0.19 0.02 0.18**
D (Unemploy_sa) 2.60 0.16 5.65 –0.39
B-G LM test –
F-values, Prob. 0.12 0.23 0.78 0.12
Obs*R2, Prob. 0.10 0.20 0.77 0.10
Qstatistics NA NA NA NA
Notes:
Significant at *α= 0.05; **α= 0.01; aα= 0.1.
bBased on the results drawn from unit root tests and the patterns of serial correlation in the ACF and PACF, all the control
variables except non-gun homicide were seasonally adjusted and/or first differenced.
cFor the analysis of gun assault_sa, ϕ2and ϕ3were dropped from the full intervention model because of their lack of
significance.
NA indicates no evidence of autocorrelations.
sa indicates the seasonally adjusted series.
Figure 2
Trends in gun homicides
in Buffalo, 2001–2012
Phillips, Kim and Sobol
Page 255
no further analyses with the extended data
were conducted for other crime types.
As shown in Table 5, both gun and non-
gun homicide time series are stationary and
have a white-noise process. Seasonally
adjusted unemployment rates are non-
stationary and were thus first differenced for
further analyses. Based on the patterns of
serial correlation in the ACF and PACF, this
study identified an ARIMA (0,0,0) model
for the gun homicide series.
Table 6 presents the results for testing for
all the impact models of the gun buy-back
programme on gun homicides with the first
intervention date. There are no significant
estimates of impact parameters for all the
impact models. However, as seen in Table 7,
this study conducted additional analyses
using an alternative intervention time. The
intervention estimate for an abrupt and
temporary model is statistically significant,
but its effect is positive. So contrary to
Table 5: Results for unit root tests of the time series, 2001–2012
ADF PP
Model/crime type Intercept Intercept and trend Intercept Intercept and trend
Gun homicide –11.09** –11.05** –11.10** –11.06**
Non-gun homicide –11.74** –12.69** –11.82** –12.69**
Unemployment_sa –0.89 –1.44 –1.06 –1.71
Notes:
Figures for ADF and PP tests represent t-statistics.
** Significant at á=0.01.
sa indicates the seasonally adjusted series.
Table 6: Model for all impact hypotheses of the gun buy-back programme on gun
homicide levels, 2001–2012 (intervention date — June 2007)
Intervention impact Abrupt, temporary Gradual, permanent Abrupt, permanent
ARIMA (0,0,0) (0,0,0) (0,0,0)
A 3.10** 3.16** 3.40**
ω0–1.41 –0.09 –0.11
∆0.06 0.07 –
Controls
Non-gun homicide 0.07 0.30 0.03
D (Unemploy_sa) 0.16 0.14 0.19
B-G LM test
F-values, Prob. 0.89 0.80 0.67
Obs*R2, Prob. 0.88 0.79 0.65
Qstatistics NA NA NA
Notes:
** Significant at α= 0.01.
NA indicates no evidence of autocorrelation.
sa indicates the seasonally adjusted series.
An evaluation of a multiyear gun buy-back programme
Page 256
programme expectations, there were
increases in gun homicide levels after the
gun buy-back events. All the models in
both tables indicate no serial correlation of
residuals.
Overall, a wide range of model specifica-
tions were employed to evaluate the impact
of the gun buy-back programme. This study
considered multiple intervention points and
also three different types of intervention
models associated with a distinct pattern of
impact. In sum, these exhaustive model
estimations, using a range of designs, failed
to provide robust evidence that the gun
buy-back policy in Buffalo did significantly
lower post-intervention gun-related
crimes.
DISCUSSION AND CONCLUSION
This study set out to examine a public
policy that has, in the past, shown very little
impact on reducing violent crime in the
USA. For this study, data were made avail-
able that allowed a longer time frame for
analysis, as well as comparisons between
gun and non-gun crimes. Further, the pro-
gramme in Buffalo had been employed over
a period of several years. These features
were typically absent in past examinations
of gun buy-back programmes. Despite the
data and methodological improvements, the
results of this study are largely consistent
with extant empirical evidence showing
little support for the effectiveness of gun
buy-backs on violent crime. Before a thor-
ough discussion of the findings is offered, a
review of study limitations is warranted.
First, as a strong quasi-experimental
design (McDowall et al., 1996), interrupted
time-series analysis has been widely used for
testing policy impact, but is generally
viewed as suffering from internal validity
threats, especially history (Cook & Camp-
bell, 1979). The best way to deal with this
issue is to use one or more control series in
comparable areas that were not exposed to
the intervention. This is not the case for this
study due to the lack of data availability.
Nonetheless, the present study included
two control variables that both theory and
Table 7: Model for all impact hypotheses of the gun buy-back programme on gun
homicide levels, 2001–2012 (intervention date — September 2008)
Intervention impact Abrupt, temporary Gradual, permanent Abrupt, permanent
ARIMA (0,0,0) (0,0,0) (0,0,0)
A 3.16** 3.10** 3.33
ω07.68** 0.01 0.02
∆0.02 0.07 –
Controls
Non-gun homicide 0.09 0.04 0.04
D (Unemploy_sa) 0.13 0.12 0.17
B-G LM test
F-values, Prob. 0.66 0.81 0.66
Obs*R2, Prob. 0.65 0.80 0.65
Qstatistics NA NA NA
Notes:
** Significant at α= 0.01.
NA indicates no evidence of autocorrelation.
sa indicates the seasonally adjusted series.
Phillips, Kim and Sobol
Page 257
past research suggest may be associated with
violent crime: non-gun crimes and unem-
ployment rates. Another limitation involves
the difficulty in generalising findings for
other locations because the current study
area is not randomly chosen to implement
the gun buy-back programme. In addition,
there were no data available regarding the
quality of the weapons surrendered. Despite
these limitations, research concerning the
effectiveness of gun control policies has
again become very important; especially in
light of renewed attention gun violence has
received.
Past research examining this programme
was not extensive and, for the most part, has
become stagnant. It may be that researchers
ignored continued examination of the
policy because all prior studies found it
ineffective. The reduction that was found in
gun robberies took several years to materi-
alise. Thus, studies of a gun buy-back pro-
gramme may require longer time frames
before some level of success is achieved
(Neill & Leigh, 2008).
Because the findings of this study are in
line with most other evaluations in the
USA, it is important to consider the reason
that police agencies and political leaders
continue to rely on buy-back programmes
as a crime-reduction strategy. Given the
empirical evidence, police agencies may use
gun buy-back programmes not with the
expectation of reducing violent crime, but
to satisfy the public’s expectations. When
serious crime problems occur, mayors and
police chiefs are under pressure from their
constituents to ‘do something dramatic and
effective’ about the violence (Lawton,
Taylor, & Luongo, 2005, p. 428). Gun buy-
back programmes are a rational and work-
able policy to reduce the public’s fear (Lee
& Suardi, 2010). In addition, these pro-
grammes are defensible by saying ‘that
“every gun bought back is a potential life
saved”’ (Sherman, 2001, p. 19).
Gun buy-back programmes appear to
satisfy a local administrator’s need for instant
solutions to a problem, despite a lack of
evidence demonstrating effectiveness as a
violence reduction strategy.5These are not
the only remedies that are enacted. The
federal government is calling for a renewal
of the 1994 assault weapons ban, and the
state of New York enacted new legislation
that, among other things, expanded the
definition of ‘assault weapons,’ which were
then made illegal. The lack of empirical
evidence to support these types of public
policies implies that they are intended as
symbolic responses to a problem. If we are
to have a meaningful impact on crime, we
must enact policies that are based on
empirical evidence and not emotion.
Recycling these types of firearm policies to
assuage the public’s concerns about violent
crime may be considered rational, but they
are an ineffective response on the part of
local policymakers.
N
OTES
1. Within two weeks of the shooting at
Sandy Hook Elementary School in
Newtown, Connecticut in December
2012, gun buy-back programmes occur-
red in Bridgeport, CT, and in Los
Angeles, Oakland and San Francisco,
CA (http://www.cnn.com/2012/12/30
/justice/connecticut-bridgeport-gun-buy
back/).
2. A simple ‘Google’ search using the term
‘gun buyback program’ conducted on 27
January 2013 found 13 internet news
articles dating back one month reporting
the use or planned use of a gun buy-
back programme in the USA. The pro-
gramme was used, or planned, in very
diverse jurisdictions. Some locations
were large, such as Los Angeles, Miami
and Seattle, or small, such as Goshen,
NY (pop. 13,000) and Basking Ridge,
NJ (pop. 21,000). Other locations
An evaluation of a multiyear gun buy-back programme
Page 258
included Trenton, NJ (pop. 85,000) and
San Mateo, CA (pop. 97,000). The art-
icles stated the buy-back programmes
were justified because of the Newtown,
CT shooting on 19 December 2012.
3. The dates of the buy-back programme,
and the number of weapons surren-
dered, were: 18 August 2012 (745 fire-
arms); 14 May 2011 (639); 15 August
2009 (711); 27 September 2008 (723); 2
June 2007 (878).
4. Some limited audit information from
2007 and 2012 is available from the City
Comptroller’s Office regarding the type
of firearms surrendered. The breakdown
is as follows. In 2007, 31.7 per cent non-
working, 27.4 long guns, 39.6 handguns
and 1.1 assault weapons. In 2008, 32.5
per cent non-working, 30.9 long guns,
36.3 handguns and 0.6 assault weapons.
In 2009, 28.4 per cent non-working,
32.3 long guns, 38.6 handguns and 0.5
assault weapons. In 2011, 37.4 per cent
non-working, 27.8 rifles, 34.2 handguns
and 0.4 assault weapons. In 2012, 39.4
per cent non-working, 25.9 long guns,
33.9 handguns and 0.6 assault weapons.
The overall average for surrendered
weapons was 33.8 per cent non-
working, 28.7 long guns, 36.7 handguns
and 0.7 assault weapons.
5. Among the more notable shootings
drawing national attention include:
Columbine High School (April 1999),
Virginia Polytechnic Institute (Virginia
Tech, April 2007), Congress woman
Gabrielle Giffords in Tucson, AZ (Jan-
uary 2011), Aurora, CO (July 2012) and
Newtown, CT (December, 2012).
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APPENDIX
Figure A1
Trends in gun and non-
gun assault crimes,
2006–2012, in
standardised Z-scores
Phillips, Kim and Sobol
Page 261
