This is a preliminary draft so all errors are entirely my own. Please do not cite or quote without the author’s permission.

1. A FAREWELL TO FIREARMS?
Guns and Murders Through the Looking Glass of Cost-Benefit Analysis
Huy Q. Dang ∗
December 17, 2013
Abstract
The U.S. Supreme Court’s reconsideration, some even say revamping, of its
decades-long stance on the Second Amendment’s scope in District of Columbia v.
Heller in 2008 had engendered both cheers and jeers from Americans of different
political persuasion. As the 2012 mass shootings in Colorado and Connecticut
amply attested, no consensus about guns had ever really emerged and solidified at
the national level. The aim of this paper is twofold. First, we want to investigate
the relationship between domestic murders and domestic firearm production in the
United States. Second, we want to monetize the impact of regulating the firearm
industry. We find a statistically significant, though negligible impact of firearm
production on murder. From a cost-benefit perspective, we conclude that
regulating the firearm industry is a sensible policy.
∗
M.A. Candidate, Department of Economics, San Jose State University, One Washington Square, San Jose,
California, USA, 95192. Email: Jeffersonhuy@hotmail.com. This is a draft so all errors are entirely my own. Please
do not cite or quote without the author’s permission.

2. INTRODUCTION
In 2002 Clark Neily, a civil rights lawyer in Arlington, Virginia, decided to challenge the
constitutionality of gun control laws in the United States. For nearly sixty-five years, the
prevailing Second Amendment jurisprudence had maintained that gun ownership was not a right
so absolute and sacrosanct that it was beyond the regulatory reach of the federal government. 1
Undeterred, Neily and pro-gun advocates sued the District of Columbia in 2003 over the city’s
1975 gun law, the most encompassingly restrictive in the nation at that time. Supported by the
National Rifle Association (NRA), the case reached the United States Supreme Court for
arbitration in March 2008. Then, on June 23, 2008, in a narrow 5-4 split, the high Court voted to
invalidate the District of Columbia’s draconian gun ban as an infringement of Second
Amendment individual right to bear arms. According to one legal scholar, District of Columbia
v. Heller, as the case is known, illustrates that although there is “no national consensus against
handgun ownership[,]…[t]he need for laws to keep guns out of the hands of dangerous people
and to reduce gun violence is...part of the national consensus about guns.” (Winkler, 2012, p.
298)
Five years later, that supposed national consensus about guns remained elusive,
incoherently articulated, even after the country experienced two of the worst mass shootings in
its history. The first occurred in July 2012 at a theater in Aurora, Colorado; the second five
months later at Sandy Hook Elementary School in Newtown, Connecticut that left 26 people
1
In United States v. Miller (1939) the U.S. Supreme Court affirmed the constitutionality of a provision of the
National Firearm Act (NFA), enacted by Congress in 1934 in response to the St. Valentine’s Day Massacre in gangridden Chicago in 1929, regulating the interstate transportation of unregistered short-barreled shotguns, or any
unregistered firearms with a barrel less than 18 inches. Today, historians and legal scholars are divided over this
restrictive reading of the Second Amendment, whose scope has remained vexingly difficult to delineate, even with
the best historical and textual evidence available. Whether the Second Amendment enshrines a narrow collective
right applicable only to state-managed militia, or whether it confers a fundamental individual right to all private
citizens has remained an enduring source of interpretative controversy among academics and constitutional analysts.
See Rakove, Jack. “Words, Deeds, and Guns: Arming America and the Second Amendment.” William and Mary
Quarterly. 59.1 (2002): 205-10.
2.

3. dead, 20 of whom were school children. Although shaken by these twin tragedies, both sides in
the gun control debate continue to disagree – sometimes passionately and acrimoniously– over
the role of guns in American national life. While liberals are busy crafting their guns-are-theproblem narrative, conservatives are hard at work weaving a different narrative, one that places
primary responsibility on the shooters, not on the instruments of shooting. 2
The aim of this paper is twofold. First, we want to investigate the relationship between
murders and firearm prevalence in the United States. While much of the public discourse on gunrelated crimes tends to focus on the sale of magazine as a measure of gun ownership (Lott 2003),
we choose to focus on a different proxy: the annual domestic production output of firearms per
state. Employing cross-sectional data method, we test the hypothesis of whether an increase in
domestically produced firearms leads to an increase in domestic murders. To minimize omitted
variable bias in our study, we include such state-level variables as personal income per capita,
police density, and unemployment rate.
Second, we want to monetize the impact of regulating the firearm industry. Although
current scholarship has, for the most part, been fruitful in illuminating the complex relationship
between gun ownership and murder, as well as the associated monetary cost borne at the
individual and societal level, there has been, surprisingly, little effort to provide a more unified
policy framework in which to argue for gun control. The present study attempts, partially, to fill
that gap. The contribution we are making in this paper is unique in at least two related respects.
The first is we estimate a demand curve that reflects people’s willingness to pay (WTP) for a
2
On December 21, 2012, a week after the Newtown massacre, NRA Executive Vice President Wayne LaPierre
appeared at a televised press conference during which he made the now-infamous statement, “The only thing that
stops a bad guy with a gun is a good guy with a gun.” The implication is that the answer to future mass shootings is
more guns, not less.
3.

4. certain percentage reduction of murder. The second is we show why it makes sense, from a costbenefit perspective, to regulate the domestic production of firearm.
The paper is divided into three sections. Section 1 summarizes the relevant literature on
guns and crimes in the United States. In section 2 we discuss our data and methodology. Finally,
in section 3 we present our findings.
LITERATURE REVIEW
Studies on violent crimes in the United States typically fall into three broad, but related
areas – poverty, education, and firearm prevalence. The first uses unemployment rate to proxy
for poverty, and to estimate its causal effect on crime rate. The second uses education level,
proxied by the number of years of formal schooling attained, to estimate the cost of crime
incurred by individuals and by society. The third asks what impact the ubiquity of gun ownership
has on the reduction of crime. Finally, we discuss how the application of cost-benefit analysis
fits into the literature.
Social scientists have long observed that higher unemployment rates tend to be associated
with more crimes (Chiricos, 1987). However, it is not always clear which determines which, or
whether this relationship can be neatly decomposed into its dependent and independent parts. A
recent attempt to address this causality conundrum is Calvo-Armengol and Zenou (2003). While
agreeing with empirical studies that found crime and unemployment reciprocally feed on and
reinforce each other without running through a causal one-way street, they suggest that crime
causes unemployment through the mechanism of social networking. Within any social network,
information transmission is limited. Generally, criminals only network with other criminals, and
that creates a failure of matching job information with job seekers, thereby causing
unemployment to increase. Therefore, the authors contend, “to reduce unemployment in…areas
4.

5. [with high crime rate],” the aim of policymakers should be to “ameliorate information about jobs
(so that workers rely less on their social networks)” (p. 183).
Costs of crime can be classified as individual and social. At the individual level, Lochner
(2004) found that people with more years of education are less likely to commit crimes. An
increase in human capital levels through more years of education leads to a simultaneous
increase in the benefit, e.g., higher market wage rate, and in the cost—the time expended from
planning and committing a crime, as well as the foregone income and the loss of productivity
and quality of life from being incarcerated. At the social level, Lochner and Moretti (2004)
estimated the annual net social benefit to society from an increase of 1% in high school
completion rate among men between the ages of 20-60 to be $1.4 billion.
The efficacy of gun control and the impact of gun prevalence on violent crimes in the
United States have received much scholarly attention over the years, but the findings remain
inconclusive and controversial. Kwon et al. (1997) offered a useful study of this relationship.
Applying multivariate statistical analysis, they concluded that gun control laws had little impact
on firearm-related deaths. Notably, John Lott (1998) studied the dual impact of population
density and gun-control laws on murder rates. He found that more densely populous states with
laws permitting citizens to carry concealed handgun have statistically significant lower murder
rates than less densely populous states without such laws. Later scholars, however, have
criticized this so-called “more gun, less crimes” hypothesis. Ayres and Donohue (2003), for
instance, have faulted Lott’s methodology, concluding that his “statistical evidence that these
[concealed handgun] laws have reduced crime is limited, sporadic, and extraordinarily fragile”
(p.1201).
5.

6. More recently, public economists have begun looking at gun crimes through a costbenefit prism, yielding interesting conclusions with policy implication. Matt DeLisi et al. (2010)
estimated the total monetary cost per murder to be at least $17.25 million. In a closely related
study, Cook and Ludwig (2011) provided a cost argument for gun regulation. They argued for a
gun license fee commensurate with “the social costs of the additional homicides that appear to be
generated by widespread gun prevalence” (p. 389). Valuating these costs at around $1 million
per gun-shot injury for each assault, Cook and Ludwig estimated the optimal license fee to be
$600 per household.
DATA and METHODOLOGY
The relevant data are from 2009. We have chosen 2009 as our year of interest for two
reasons. First, the most recent national census was conducted in 2010. It offers a comprehensive
and detailed snapshot of American social, economic and demographic landscape between 2008
and 2010. Second, 2009 was immediately preceded by a landmark Supreme Court ruling that
effectively delimited the contour of gun control laws throughout the nation. Therefore, the
impact on gun manufacturing should be significant.
The data came from two main sources. The first is the U.S. Census Bureau (USCB),
which provides data for each state’s personal income per capita, police density, and reported
murders. The second is the DOJ’s Bureau of Alcohol, Tobacco, Firearms and Explosives (ATF),
which publishes an annual list of all legally and domestically operated firearm manufacturers
who are required by federal law to disclose their yearly output by type and by quantity. Using
ordinary least squares (OLS), we estimate a model of the following log-log specification
lnMURDER =β lnGUNS2 SLS + β lnUNEMP + β lnINCPC + β lnPOL + ε
β +
0
1
2
3
4
6.

7. The left-hand side is the dependent variable (the reported number of murders); and the
right-hand side consists of four independent variables, plus the error term ε and the constant
intercept β 0 . ln GUNS 2 SLS is an instrument. By implementing instrumental variables estimation,
we can preempt a potentially serious criticism against the internal validity of the model –
simultaneous or reversed causality bias: Does an increase in the domestic production of firearms
lead to an increase in domestic murders? Or does an increase in domestic murders lead to an
increase in people’s demand for firearms (presumably, for self-protection), which leads to more
firearms being produced? To control for this potential causality problem, we let
π0
ln GUNS 2 SLS = + π 1GOP + π 2 ln POP + π 3 ln AVCRM + GEO + υ ,
Eq.(1)
where
π 0 = constant
GOP = partisanship
POP 3 = population density, roughly 100,000 residents per square mile.
AVCRM = average reported violent crimes (murder, forcible rape, and robbery) per state
between 2007-08
GEO = geography
υ = random error
To obtain estimates for GOP and GEO , we followed a two-step approach. In the first
step, we compared the U.S. presidential electoral maps for 2004 and 2008 4, and we assigned an
3
Geographer Harm de Blij has criticized the use of arithmetic population density, writing “this statistic is not very
meaningful…Take the case of Pakistan: when tens of millions of people cluster in river basins and valleys and
almost nobody lives in deserts and high mountains, what does 227 people per square kilometer (783 per sq mi)
really mean? Not much…” (p. 414 from de Blij, Harm J. and Peter O. Muller. Geography: Realms, Regions, and
Concepts. 14th ed. New Jersey: John Wiley & Sons, 2010). We disagree. We think that population density is
meaningful because it accounts for “clustering” effect. For example, firearm producers are unlikely to locate their
manufacturing facility in places with low population density, where labor is scattered and thinly spread out. When
labor is scarce, wage increases. It makes more economic sense for producers to locate their manufacturing operation
in areas where population is more spatially clustered because that would mean more labor and lower wage. For this
reason, we expect states with high population density to have more firearms produced than states with low
population density.
7.

8. 1 to
0 if
indicator variable Ι 2004 = a state that voted Republican in 2004 and Ι 2004 = it voted
1 to
Democrat. Similarly we assigned another indicator variable Ι 2008 = a state that voted
0 if
Republican in 2008 and Ι 2008 = Democrat. We argue that states that voted Republican in both
presidential elections are more partisanly conservative – and therefore more hostile to gun
control– than states that voted Democrat either once or twice in the same elections. We expect
“Red States” to have more firearm production than other states, all else being equal. Hence,
GOP = I 2004 × I 2008 × ln GUNS2004
Eq.(2)
In the second step, we looked at firearm production regionally. The Bureau of Economic
Analysis divides the U.S. into eight geographic regions – New England (NE), Mideast (ME),
Great Lakes (GL), Plains (PLN), Southeast (SE), Southwest (SW), Rocky Mountain (RM), and
1
Far West (FW). For each state we assigned an indicator variable Ι R = if it belonged to region
0
R and Ι R = if otherwise. For instance, since California belongs to the Far West and Michigan
1 (or
0)
0
1)
is part of the Great Lakes we assign Ι FW = Ι GL = to California and Ι FW =(or Ι GL = to
Michigan. We expect that states belonging to one geographic region are more culturally
homogeneous than states belonging to another geographic region. Selecting only regions in
which a majority of the states went Democratic in both the 2004 and 2008 presidential elections,
we set
4
The U.S. presidential elections in 2004 and 2008 are unique in that single-issue voters made a difference in the
outcome. In 2004 nearly all the pre-election polls showed a statistical dead heat between the Republican incumbent
George W. Bush and his Democratic challenger John F. Kerry of Massachusetts. Several weeks before the
November election, the issue of gay marriage took on national significance when President Bush, in a strategic
campaign move, proposed a constitutional ban on same-sex marriage. Seen as a cynical ploy by the Kerry campaign,
the GOP-backed amendment failed to pass (as expected), but it did much to bolster Bush’s standing among so-called
“value voters,” primarily Christian social conservatives, who eventually helped tip the election to the Republican
president. On the other hand, in 2008 the issue that dominated the election was the economy. Several states that had
voted Republican in 2004 voted Democrat in 2008. This suggests that the states that continued to vote Republican in
2008 are tethered to the GOP for reasons other than economics.
8.

9. GEO = π 4 I NE ln GUNS 2004 + π 5 I ME ln GUNS 2004 + π 6 I GL ln GUNS2004 + π 7 I FW ln GUNS2004
Eq.(3)
Eq. (2) and Eq. (3) assume that political partisanship and cultural attitude toward guns
are captured by the relationship between the number of firearms produced in each state in 2004
and in 2009. That is, if New York produced more firearms than the Nebraska in 2004, we expect
the same pattern to hold in 2009. We have included ln AVCRM in Eq. (1) to account for
possible reversed causation. If this year’s firearm production depends on last year’s total reported
violent crimes – murders, rape, and robbery–then our model’s one-way-causality assumption is
problematic.
Table 1: Variable Definitions
Variables
MURDER
UNEMP
AVCRM
POP
GUNS
INCPC
POL
Definition
Reported murders
Uninsured unemployment
Average violent crimes, 2008-09
Population density
Firearm output
Personal income per capita
Police density
Source
USCB
USCB
USCB
USCB
ATF
USBEA
BJS
Sources: (1) U.S. Census Bureau (accessed 9/05/2013); Crime Rates by State, 2008 and 2009, and by Type, 2009;
<http://www.census.gov/compendia/statab/cats/law_enforcement_courts_prisons/crimes_and_crime_rates.html>
(2) U.S. Bureau of Economic Analysis; Per Capita Personal Income by State, 1990 to 2012; using Bureau of
Business & Economic Research (accessed 10/30/2013); <http://bber.unm.edu/econ/us-pci.htm>
(3) Bureau of Alcohol, Tobacco, Firearms and Explosives (accessed 9/07/213). Annual Firearms Manufacturers and
Export Report. < http://www.atf.gov/statistics/index.html > (4) Bureau of Justice Statistics (accessed 9/08/2013);
generated by Brian Reaves; < http://www.bjs.gov/content/pub/pdf/csllea08.pdf >
Our dataset has 47 observations representing 47 states in the Union. Since the firearm
data for North Dakota, Rhode Island, Hawaii, and the District of Columbia 5 for 2009 are
unavailable, we have decided to exclude them. Table 1 provides the variable names and their
5
Technically, the District of Columbia is not a state, although there has been clamoring for statehood in the past.
Neither does it have congressional representation as states do (it does, however, have three votes in the Electoral
College). Still, it exercises and retains jurisdictional sovereignty, under which the 1975 enactment of the gun ban
that was challenged in Heller was justified.
9.

10. definition. INCPC represents personal income per person, measured in 2005 dollars and ranged
from $30,013 to $52,900, with a mean of $37,586.21. POLICE is a density variable,
representing the number of fulltime law-enforcement agents per 100,000 residents. It is a proxy
for how gun-restrictive each state is. 6
Also important is UNEMP —a measure of economic dislocation proxied by the number of
unemployed people without unemployment benefits. Finally, GUNS is an aggregation, chiefly, of
four specific types of firearms—pistols, revolvers, rifles, and shotguns. In 2009 there were 5.6
million firearms manufactured in the United States. Of these, pistols accounted for 33.6% of the
total output; revolvers accounted for 9.8%, rifles 40.5%, and shotguns 13.5% (see Figure 1). For
summary statistics of all the variables discussed, see table 2 below.
Figure 1: 2009 U.S. Production of Firearms by Types
2500000
2000000
1500000
1000000
500000
0
Pistols
Revolvers
Rifles
Shotguns
Others
Source: Bureau of Alcohol, Tobacco, Firearms and Explosives (accessed 9/07/213)
6
Granted, using police density per state as a proxy for gun control is not perfect, but we argue that states with high
murder rates tend to have high police density, all else being equal, in order to provide additional protection to an
unarmed populace. If residents are legally armed—that is, if there are no laws regulating the acquisition or purchase
of firearms for self-protection by law-abiding citizens—then we would expect the size of police protection service
relative to the civilian population to be small, since an armed citizenry can be considered a substitute for statefunded police force. See Levy, Leonard W. Origins of the Bill of Rights (New Haven: Yale University Press, 1999).
10.

11. Table 2: Summary Statistics
Variable
Obs
Mean Std. Dev.
ln MURDER
47 5.105706 1.258105
lnUNEMP
47 11.99056 1.113078
2 SLS
ln GUNS
43 9.790698 1.980526
ln INCPC
47 10.52473 .1386048
ln POL
47 5.858835 0.2035572
Min
2.197225
9.863238
5.085875
10.30939
5.493062
Max
8.422882
14.53951
14.71224
10.87616
6.343881
Sources: (1) U.S. Census Bureau (accessed 9/05/2013); Crime Rates by State, 2008 and 2009, and by Type, 2009;
<http://www.census.gov/compendia/statab/cats/law_enforcement_courts_prisons/crimes_and_crime_rates.html>
(2) U.S. Bureau of Economic Analysis; Per Capita Personal Income by State, 1990 to 2012; using Bureau of
Business & Economic Research (accessed 10/30/2013); <http://bber.unm.edu/econ/us-pci.htm>
(3) Bureau of Alcohol, Tobacco, Firearms and Explosives (accessed 9/07/213). Annual Firearms Manufacturers and
Export Report. < http://www.atf.gov/statistics/index.html > (4) Bureau of Justice Statistics (accessed 9/08/2013);
generated by Brian Reaves; < http://www.bjs.gov/content/pub/pdf/csllea08.pdf >
RESULTS
This section has two parts. The first part is the statistical analysis. Here we will analyze,
interpret and discuss the estimates that our model produces, and how well the model explains the
data. The second and more crucial part is the cost-benefit analysis (CBA).
A.
Statistical Analysis
Table 3 contains the regression results. Of the six independent variables in the model,
only ln GUNS IV and lnUNEMP are statistically significant at the 10% and 5% level,
respectively. For historical reasons, it has become standard practice to adopt 5% significance
level as the cutoff point for rejection in hypothesis testing. However, we reject this convention as
arbitrary and restrictive, and instead we adopt the more liberal 10% significance level as our
rejection threshold. 7
7
According to Ronald A. Fisher , “In choosing the grounds upon which a general hypothesis should be rejected, the
experimenter will rightly consider all points on which, in light of current knowledge, the hypothesis may be
imperfectly accurate, and will select tests, so far as possible, sensitive to these possible faults rather than to others.”
(p. 47 from Fisher, Ronald A. Statistical Methods and Scientific Inference. New York: Hafner Publishing Company,
1956)
11.

12. Table 3: Regression Results
VARIABLES
lnUNEMP
ln GUNS 2 SLS
ln INCPC
ln POL
Constant
Observations
R-squared
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
ln MURDER
0.5985**
(0.235)
0.1502*
(0.085)
-1.6032
(0.999)
0.8375
(0.882)
8.689
(10.564)
43
0.4815
Although statistically significant, ln GUNS 2 SLS has a negligible impact on ln MURDER . A one
standard deviation decrease in the domestic output of firearms leads to only 0.3% decrease in
murders, all else being equal. To put it another way, a 100% decrease in ln GUNS 2 SLS reduces
murders by 15%, which is equivalent to the impact generated by a 25% decrease in
unemployment. Neither ln POL nor ln INCPC is statistically significant. Overall, the model
accounts for nearly 50% of the total variability.
Table 4 below presents the first-stage least squares estimates for ln GUNS 2 SLS
Table 4: First-Stage OLS Results for lnGUNS
VARIABLES
GOP
ln POP
ln GUNS IV
0.279**
(0.118)
0.841**
(0.321)
12.

13. I NE ⋅ ln GUNS2004
I ME ⋅ ln GUNS2004
I GL ⋅ ln GUNS2004
I FW ⋅ ln GUNS 2004
ln AVCRM
Constant
Observations
R-squared
F(7, 35)
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
0.361 ***
(0.109)
0.219 ***
(0.087)
0.158
(0.109)
0.245
(0.163)
0.346
(0.429)
0.722
(2.94)
47
0.5279
14.31
Since we have an F-statistic =14.31>10, ln GUNS 2 SLS is a relevant instrument. At the 10% level
GOP , I NE ⋅ ln GUNS2004 , I ME ⋅ ln GUNS2004 , and ln POP are statistically significant, and they are
positively correlated with firearm output as we have expected. It appears that Republican states
increase overall firearm production by 0.28%, and population density increases it by 0.84% for
every 1% increase. Interestingly, the impact of past average violent crimes, ln AVCRM , on
firearm production is not statistically significant, suggesting that reversed causation is unlikely.
Revealingly, unlike New England 8 and the Mideast, 9 the Far West 10 and the Great
Lakes 11 are not statistically significant in explaining firearm production. How do we explain this
regional difference? We can rule out partisanship because these regions have remained
8
Connecticut, Maine, Massachusetts, New Hampshire, Vermont
Delaware, Maryland, New Jersey, New York and Pennsylvania
10
Alaska, California, Nevada, Oregon, Washington
11
Illinois, Indiana, Michigan, Ohio, Wisconsin
9
13.

14. predominantly the electoral bastion of the Democratic Party in 2004 and 2008. We want to offer
a historical explanation for this puzzle: Since the states that make up today’s New England and
the Mideast were once part of the original thirteen British North American colonies that,
together, had fought a revolution (1775-1783) for independence, their cultural character was
chiseled by this bequeathed revolutionary ideology of popular armed resistance. Over time,
firearm ownership evolved into a powerful symbol and assumed a positive meaning for the
denizens of New England and the Mideast. On other hand, states that had joined the Union after
the Revolution – California, for example, was not formally annexed into the U.S. as a state until
1850– did not inherit the same legacy, and so their cultural traits were shaped by a different set
of historical experiences. Seen in this way, we can better understand the variation in regional
cultural attitude toward firearms.
B.
Cost-Benefit Analysis
In carrying out CBA, we rely on an important paper by Cohen et al. (2001). Surveying a
nationally representative sample of 1,300 U.S. residents, they found the price elasticity of
demand for reducing murders by 10% to be −0.16 , and the mean willingness to pay (WTP) was
$149. We will use the 2009 inflation-adjusted amount of $180.50 in our analysis . Using this
critical datum, we can estimate a willingness-to-pay demand curve. The derivations are provided
below.
Let us denote WTP = willingness to pay and R = reduction rate of murder . By
definition, the elasticity of demand is
e=
∆(WTP ) R
∂ (WTP ) R
=
= −0.16
∆R WTP
∂R WTP
(1)
Re-express (1) as
14.

15. ∂ (WTP )
∂R
= −0.16
WTP
R
And then solve for WTP
∫
∂ (WTP )
∂R
= = = R) + c , where c is a constant.
−0.16 ln(
ln(WTP ) −0.16 ∫
WTP
R
C
C⋅
⇒ WTP = R −0.16 = where C = ec is also a constant.
R 0.16
To solve for C , we set WTP = $180.5 and R 10% 0.10 so that
= =
=
$180.50
C
⇒ C $124.88
=
(0.1)0.16
Now we have
=
WTP f=
( R)
124.88
where R ≠ 0
R 0.16
(2)
Using the minimum amount of $12,046,090 that the public was willing to pay to prevent one
murder (DeLisi et al, 2010), 12 the total minimum public expenditure on the prevention of all
murders in 2009 is
$12, 046, 090
×18,590 ⋅ murders ≈ $224 ×109
per murder
(3)
In other words, the total minimum public willingness-to-pay to prevent 18,590 murders reported
in 2009 is about $224 billion. This is illustrated in the figure below.
12
This amount is in 2009 U.S. dollars. DeLisi et al. originally estimated it using 2008 U.S. dollars ($12,089,100).
15.

16. Willingness-to-Pay
400
300
Consumer Surplus
200
Payment for 100%R*
reduction of murder
100
$ 224 Billion
0
0.0
0.2
0.4
0.6
0.8
1.0
Reduction Rate
R*
Intuitively, if there is no reduction in murder rate, i.e., R = 0 , we would expect
WTP = 0. A reduction of one murder in 2009 represents a reduction rate of
=
R
1
= 5.38 ×10−5 , or 0.0054% . So WTP can be expressed as a step function:
18590
 124.88
if 5.38 ×10−5 ≤ R ≤ 1

0.16
WTP =  R
 0
if 0 ≤ R < 5.38 ×10−5

(4)
Defining consumer surplus ( CS ) as
CS = f ( R) =
=
∫
∫
124.88
dR − WTP × R
R 0.16
124.88
124.88
dR − 0.16 × R
0.16
R
R
[ from (4) ]
16.

17. =
∫
124.88
dR − 124.88 R 0.84
0.16
R
(5)
we can now introduce the following propositions for decision making with respect to gun
regulation policy.
|PROPOSITION 1:
If a policy can generate a murder reduction rate ℜ ∈ (0,1] such that the
consumer surplus CS > 0 , then the policy should be adopted for implementation.
Given a set of N policies, each policy Pi generates a reduction rate
|PROPOSITION 2:
ℜi ∈ (0,1] where i = 1, 2,..., N . If there exists a policy Pj that generates a reduction rate
N
ℜ j ∈  ℜi such that CS (ℜ j ) > CS (ℜk ) , where j ≠ k , then Pj is to be preferred over Pk , and
i=1
Pj should be adopted for implementation, all else being equal.
Suppose in 2009 the new President and his Democratic-controlled Congress wanted to
enact a sweeping nationwide ban on domestic firearm manufacturing. This would represent a
100% decrease in firearm output. The estimated impact on domestic murders in 2009 is
100% × 0.2215 ≈ 22.2% drop. Using (5) we can calculate the consumer surplus from a 22.2%
reduction of murder.
0.222
=
CS
∫
0
124.88
dR −124.88( R)0.84
0.16
R
= 148.67 R 0.84 |0.222 −124.88(.222)0.84 ≈ $6.72
0
Since CS $6.72 > 0 , the proposed total ban on firearm production in the U.S. is justified under
=
Proposition 1. Furthermore, if the choice is between a policy involving an absolute ban and a
policy involving a partial ban, we must adopt the former policy because it generates higher
consumer surplus (Proposition 2).
17.

18. Politically, this is easier said than done. Opposition to gun control has over the years
grown in size and influence. Even if the passage of the aforementioned gun ban is electorally
popular and congressionally feasible, it would have to pass constitutional muster with the
Supreme Court, the final arbiter of all executive and legislative acts within a tripartite system of
checks and balances. To get the Court to go along with the ban is no easy feat and would require
artful persuasion on the part of the government’s lawyers. In this paper, we are neither endorsing
such unprecedented wholesale restriction on firearm production, nor discouraging its regulation
by the government. The case we are making is that some form of regulation is a logical extension
of the cost-benefit analysis we have offered above.
CONCLUSION
The Supreme Court’s reconsideration, some even say revamping, of its decades-long
stance on the Second Amendment’s scope in District of Columbia v. Heller in 2008 had
engendered both cheers and jeers from Americans of different political persuasion. As the 2012
shooting massacres in Colorado and Connecticut amply attested, no consensus about guns had
ever really emerged and solidified at the national level. Politically fractured, Congress failed to
find common ground on the policy front. So divided were Republicans and Democrats on this
issue that gun-control legislations in 2013 had either stalled in committees or were formally
withdrawn due to filibuster or threats of filibuster from the opposing side. This paper attempts to
go beyond the politics and the strident rhetoric that have characterized much of the gun-control
debate in the public sphere and to offer empirical support for gun regulation. In this concluding
section, we want to briefly summarize what we did, to address potential criticisms of our
methodology, to discuss possible future research direction, and to offer some final thoughts on
the policy implication of our research.
18.

19. In this paper we have constructed a simple log-log model using OLS to address the
following hypothesis: Does an increase in the legal domestic production of firearms lead to an
increase in domestic murder? The answer, we found, is yes – there is a statistically significant
positive relationship between firearm production and murder. For every 10% increase in the
output of firearm, there is an estimated increase of 1.5% in murder, all else being equal. Next, we
turned to the policy question—Does firearm regulation make sense from a cost-benefit
perspective?—and we concluded that on the basis of society’s willingness to pay, the benefit
outweighed the cost with gun regulation.
The methodology we have adopted is, of course, not without shortcomings. In particular
we have come up with three shortcomings that any critical and fair-minded reader could point to
as a criticism. The first is the fact that our study is a cross-sectional data analysis, not a panel
data analysis. As such, it fails to capture the fixed state and time effects. The second is that
although the instrument ln GUNS 2 SLS is statistically relevant, we have not provided a good
theoretical argument for its exogeneity. And the third shortcoming is our decision to exclude
Hawaii, North Dakota, Rhode Island and the District of Columbia from the study, which could
cause omitted variable bias associated with missing data.
To address these shortcomings is a paper in itself, and therefore is beyond the scope of
this paper. We will leave this task to future researchers who are inclined to pursue it. However,
we concede that a cross-sectional study of a single country is far too narrow to gain much of an
insight into the not-so-simple relationship between gun prevalence and murder. A more
ambitious and, indeed, more informative study is one that looks at this relationship across
countries over time. Finding the necessary data, both in quality and quantity, for such a project is
immensely daunting, but is ultimately rewarding for anyone wishing to generate new knowledge.
19.

20. If there is one thing we hope we have achieved in this paper, it is to help elevate the
current national dialogue about gun control above the cacophony of opinion-driven talk radio
and 24-hour cable news and to ground it in a more empirical setting. Purely from a cost-benefit
standpoint, society is better off when domestic firearm production is regulated, all else being
equal. However, we recognize that it will take more than empirical argument to push for
meaningful regulation. We hope our paper will help nudge policymakers in that direction.
20.

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21.