# The effect of concealed handgun laws on crime: beyond the dummy variables

**ABSTRACT** So far 33 states have adopted right-to-carry concealed handgun laws. The advocates argue these laws have a deterrent effect on crime, while the opponents believe they facilitate crime by increasing gun availability. Although both sides assume that these laws affect behavior, no attempt has yet been made to model such effects using crime theory. Consequently, the empirical evidence on such effects lack a theoretical basis; for example, a highly publicized study by Lott and Mustard (1997) inappropriately models the effect of the law through a dummy variable (a binary-valued regressor). We extend the economic model of crime to formulate a theoretical basis for empirical examination of the issue. We show that using a dummy variable leads to misspecification, and use an alternative procedure to estimate the effect of concealed handgun laws in 1992 for states which had not yet adopted such laws. Our results show that the expected effect of the law on crime varies across the counties and states and depends on county-specific characteristics in a meaningful way. Such effects appear to be much smaller and more mixed than Lott and Mustard suggest, and are not crime-reducing in most cases.

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**ABSTRACT:**Does the death penalty save lives? A surge of recent interest in this question has yielded a series of papers purporting to show robust and precise estimates of a substantial deterrent effect of capital punishment. We assess the various approaches that have been used in this literature, testing the robustness of these inferences. Specifically, we start by assessing the time series evidence, comparing the history of executions and homicides in the United States and Canada, and within the United States, between executing and non-executing states. We analyze the effects of the judicial experiments provided by the Furman and Gregg decisions and assess the relationship between execution and homicide rates in state panel data since 1934. We then revisit the existing instrumental variables approaches and assess two recent state-specific execution moratoria. In each case we find that previous inferences of large deterrent effects based upon specific samples, functional forms, control variables, comparison groups, or IV strategies are extremely fragile and even small changes in specifications yield dramatically different results. The fundamental difficulty is that the death penalty - at least as it has been implemented in the United States - is applied so rarely that the number of homicides that it can plausibly have caused or deterred cannot be reliably disentangled from the large year-to-year changes in the homicide rate caused by other factors. As such, short samples and particular specifications may yield large but spurious correlations. We conclude that existing estimates appear to reflect a small and unrepresentative sample of the estimates that arise from alternative approaches. Sampling from the broader universe of plausible approaches suggests not just "reasonable doubt" about whether there is any deterrent effect of the death penalty, but profound uncertainty - even about its sign.Stanford Law Review 02/2006; · 4.32 Impact Factor - SourceAvailable from: psu.edu[Show abstract] [Hide abstract]

**ABSTRACT:**The interaction between offenders and potential victims has so far received relatively little attention in the literature on the economics of crime. The main objective of this paper is twofold: to extend the “market for offenses model” to deal with both “product” and “factor” markets, and to apply it to the case where guns are used for crime commission by offenders and for self-protection by potential victims. Our analysis offers new insights about the association between crime and guns and the limits it imposes on the efficacy of law enforcement and regulatory policies aimed to control both crime and guns.Journal of Policy Modeling 08/2010; 32(5):670-689. · 0.64 Impact Factor - SourceAvailable from: Paul H Rubin
##### Article: The Economics of the Bill of Rights

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**ABSTRACT:**We elucidate, connect, and synthesize the literature that employs economics to study the individual rights and freedoms protected by the constitutional amendments comprising the Bill of Rights, especially as they relate to crime. Economics is uniquely suited to studying decisions involving tradeoffs, and each of the amendments requires tradeoffs. Emphasizing these tradeoffs allows us to discuss the constitutional rights in terms of "more or less," as opposed to taking an absolutist approach. We find that the economic literature on the amendments of the Bill of Rights is vibrant and growing, and that viewing the amendments within the framework of economics is highly useful. Copyright 2008, Oxford University Press.American Law and Economics Review 01/2008; 10(1):1-60. · 1.14 Impact Factor

Page 1

International Review of Law and Economics 23 (2003) 199–216

The effect of concealed handgun laws on crime:

beyond the dummy variables

Paul H. Rubin∗, Hashem Dezhbakhsh

Department of Economics, Emory University, Atlanta, GA 30322-2240, USA

Abstract

Sofar33stateshaveadoptedright-to-carryconcealedhandgunlaws.Theadvocatesarguetheselaws

have a deterrent effect on crime, while the opponents believe they facilitate crime by increasing gun

availability.Althoughbothsidesassumethattheselawsaffectbehavior,noattempthasyetbeenmade

to model such effects using crime theory. Consequently, the empirical evidence on such effects lack a

theoretical basis; for example, a highly publicized study by Lott and Mustard (1997) inappropriately

models the effect of the law through a dummy variable (a binary-valued regressor). We extend the

economic model of crime to formulate a theoretical basis for empirical examination of the issue.

We show that using a dummy variable leads to misspecification, and use an alternative procedure to

estimate the effect of concealed handgun laws in 1992 for states which had not yet adopted such laws.

Our results show that the expected effect of the law on crime varies across the counties and states

and depends on county-specific characteristics in a meaningful way. Such effects appear to be much

smaller and more mixed than Lott and Mustard suggest, and are not crime-reducing in most cases.

© 2003 Elsevier Inc. All rights reserved.

Keywords: Concealed handgun laws; Crime; Dummy variables; Econometric specification

1. Introduction

The right-to-carry concealed handgun laws—“shall issue” laws—and their possible ef-

fects on crime have been the subject of extensive policy and academic debate as more states

adopt such laws.1From 1977 to 1992, 10 states passed such laws making it much easier to

obtain licenses to carry concealed handguns, and 15 states adopted this law between 1992

and 2001. These laws are at odds with the federal Brady Bill, which is restrictive of gun

∗Corresponding author. Tel.: +1-404-727-6365; fax: +1-404-727-4639.

E-mail addresses: prubin@emory.edu (P.H. Rubin), econhd@emory.edu (H. Dezhbakhsh).

1Henceforth, we refer to such provisions as “concealed handgun” laws. These laws are also referred to as “shall

issue” laws (laws mandating that authorities “shall issue” permits to carry concealed handguns).

0144-8188/$ – see front matter © 2003 Elsevier Inc. All rights reserved.

doi:10.1016/S0144-8188(03)00027-9

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P.H. Rubin, H. Dezhbakhsh/International Review of Law and Economics 23 (2003) 199–216

ownership, reflecting the conflict among various levels of government regarding the role

of handguns in violence. Such conflict also extends to academic circles. Some argue the

concealed handgun laws increase criminals’ access to guns through theft, overpowering

victims, or the black market. This leads to a civil arms race which can only increase crime

(Cook,1991;Cook&Leitzel,1996;Cook&Ludwig,1996;Hemenway,1997;Kellermann,

Westohal,Fischer,&Harvard,1995;Ludwig,1998;McDowall,Loftin,&Wiersema,1995).

We call this outcome the “facilitating effect” of concealed handgun laws. The supporters

of these laws dispute the facilitating effect, maintaining that the effect is opposite. They

argue that allowing citizens to carry firearms will increase criminals’ uncertainty regarding

an armed response, thus leading to less crime—the “deterrence effect” (Kleck & Patterson,

1993; Lott, 1998; Lott & Mustard, 1997; Polsby, 1994, 1995).

No study has formalized the above arguments theoretically. Such a theoretical basis is

necessary for any empirical investigation of the issue. In this paper we formalize these

arguments in the context of the economic model of crime. We demonstrate that the di-

rection and magnitude of any resulting change would depend on the parameters of the

criminal’s optimization function and the characteristics of the individual and his social

and economic setting. This means that any change in crime rate induced by concealed

handgun laws will depend on demographic, social, and economic specifities of the ob-

servation units (e.g. counties). Thus, these laws might lead to increases in crime in some

jurisdictions and decreases in others. For example, one would expect the effect of the law

on crime to be more pronounced in more populated counties, because authorities who

have discretion over issuing handgun-carrying permits in absence of a concealed hand-

gun law are the most restrictive in these counties. The largest changes in handgun den-

sity as the result of such laws are therefore expected in populated counties. Moreover,

since the law excludes juveniles from receiving gun-carrying permits, the deterrent ef-

fect is expected to be smaller in counties with a younger population. Other demographic

determinants of propensity to carry a concealed weapon may lead to similar differential

effects.

We empirically examine the effect of concealed handgun laws on crime drawing on the

aforementioned theoretical considerations. Accordingly, we allow the effect of the law on

crime to be a function of population characteristics in a given jurisdiction, so that we can

infer how various factors influence the magnitude of the change in crime resulting from

theselaws.Morespecifically,weprojectwhatthe1992crimerateforcountieswithoutsuch

alawwouldhavebeenifthecountyhadadoptedsuchalawby1992.Wethencomparethese

projections, which are a function of county characteristics, with actual crime data for each

county in 1992 to infer how the absence of the law has affected crime in these counties. We

also examine the relationship between these projected changes and county characteristics.2

Ignoring specific population characteristics when modeling the effect of the law leads

to model misspecification and invalid inference. For example, in a highly publicized study,

Lott and Mustard (1997) use a dummy variable to model the effect of the law as a shift in

2We use Lott and Mustard’s data which covers 3054 counties for the period 1977–1992 and includes series

on various categories of crime and arrest rates and economic, demographic, and political variables. The data set

allows us to exploit cross-county heterogeneities, while our theory-based empirical procedure allows us to make

state level inference about the potential effect of the law.

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201

the intercept of the linear crime equation they estimate.3The method is predicated on two

assumptions: (1) all behavioral (response) parameters of this equation (slope coefficients)

are fixed—unaffected by the law and (2) the effect of the law on crime is identical across

counties. We demonstrate that these assumptions can be rejected both on theoretical and

empirical grounds.4Our procedure is intended to overcome this shortcoming.

Theremainingsectionsareorganizedasfollows:Section2elaboratesonthestatedeffects

of the concealed handgun laws and extends the economic model of crime to examine such

effects. Section 3 discusses the estimation issues involved in measuring the effect of these

laws and the problems with using dummy variables for this purpose. This section also

presents an alternative estimation procedure that draws on the theoretical considerations

discussed in Section 2. Section 4 describes the data and presents and discusses the results.

Section 5 contains concluding remarks.

2. Concealed handgun laws and the economic model of crime

Thirty-three states have so far adopted concealed handgun laws.5These laws require that

permits to carry concealed handguns be granted to any adult applicant unless the individual

hasacriminalrecordorahistoryofseriousmentalillness.Priortoadoptingtheselaws,local

authorities had discretion in granting such permits on a case-by-case basis, and the most

populatedcountieswerethemostrestrictiveinissuingsuchpermits(Lott&Mustard,1997).

The supporters of concealed handgun laws argue that allowing law-abiding citizens to

carry concealed handguns increases the overall security by deterring attackers. Since the

firearmsareconcealed,predatorsdonotknowaprioriwhichpotentialvictimsorbystanders

might be armed. The armed citizens, therefore, not only enhance their own security but also

provide a positive externality for unarmed citizens. The resulting uncertainty increases the

criminal’s perceived failure probability, leading to a lower expected net benefit from a

criminal act and, therefore, to a lower crime rate.

The opponents argue that these laws are likely to increase the crime rate. For exam-

ple, Cook and Leitzel (1996) note that only a small percentage of felons and youths use

the primary market to acquire their handguns; the rest rely on friends, theft, or on street

transactions. Through these channels, concealed handgun laws may increase the number of

guns available to criminals. Criminals can also use their victims’ guns against them, when

victims are not able to use their guns effectively (Kellermann et al., 1995). Overall, these

authors believe that increased gun availability lowers the criminals’ cost of illegally obtain-

ing firearms, prompting their substitution for less lethal weapons in hostile confrontations.

This, in turn, leads to an increase in crime rates (Ludwig, 1998).

Both arguments imply that the net change in expected benefit from committing crime

is the causal link between concealed handgun laws and crime rates. The direction and

3Lott and Mustard report that passage of concealed handgun laws by a state causes a significant reduction in

violent as well as property crime rates (Lott and Mustard, Table 11). They attribute their results to a deterrent

effect.

4Ayres and Donohue (1999) and Zimring and Hawkins (1997) raise a similar concern about Lott’s work.

5States are adopting these laws at an increasing rate. Only 8 states had adopted such laws by 1986. By 1992,

another 10 states had adopted them, and since then 13 more states have joined the group.

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magnitude of such change depends on the relative strength of the hypothesized forces. In

the rest of this section we formalize these arguments, in the context of the economic model

of crime, to examine theoretically the effect of these laws. The analysis provides a basis for

empirical examination of the issue.

2.1. Modeling the effect of the law

We extend an economic model of crime to incorporate the effect of the gun laws. The

economicmodelsofcriminalbehavior—Becker(1968),BlockandHeineke(1975),Ehrlich

(1975), Fleisher (1966), and Sjoquist (1973)—are formulated within the framework of the

theory of choice under uncertainty. The basic model we consider assumes an optimizing

agentwhoallocatestimebetweenlegaland/orillegalactivitiesinsuchawayastomaximize

expectedutility.ThetimesallocatedtotheseactivitiesaredenotedbyTlandTi,respectively.

So, Tl+ Ti=¯T, where¯T is net of non-market activities (e.g. leisure).

To obtain the agent’s optimal supply of illegal (and legal) activities, we assume he max-

imizes the following expected von Newmann–Morgenstern utility function:

max

Ti

?

U[Tl,Ti,W0+ RTl+ (B − xP)C(Ti)] dF(x),

(1)

subject to Tl ≥ 0, Ti ≥ 0, and Tl+ Ti = ¯T. The third argument in the utility function

is wealth which includes the individual’s assets (net of expected current earnings) W0,

return on legal activities R (i.e. wage rate), number of criminal offenses C(Ti), benefit per

offense B, punishment (if arrested) per offense P, and a random variable x, representing the

stochastic failure (arrest) rate. The number of criminal offenses is assumed to increase with

the amount of time devoted to illegal activities—C?(Ti) > 0. The function F(x) denotes the

individual’s subjective probability distribution of x. Following Block and Heineke (1975),

we assume that random variable x can take any value in the interval [0, 1].6Also, note

that B, P, and other components of wealth incorporate pecuniary as well as non-pecuniary

(psychic) values.

We introduce concealed handgun laws through an index variable H defined on [0, 1]

interval, where H = 0 means no law (no concealed handgun-carrying) and a larger H value

indicates a more permissive handgun law. To incorporate the deterrent and the facilitating

effect of these laws, we allow some of the variables of the basic model to change with H.

The deterrent effect is captured by increasing the perceived probability of the failure rate x

as well as the possible punishment P. We model the probability change by augmenting the

failure rate to x + αH, where α is a shift parameter and the added term αH increases with

H in such a way that x + αH remains within the [0, 1] range. This increases the expected

failure rate in the presence of a concealed handgun law to E(x)+α. Moreover, the prospect

6This approach is more general than Becker, Ehrlich and Sjoquist’s approaches that assume x is either 1 or

0 and F(x) follows a Bernoulli distribution, and, therefore, encompasses those as special cases. Moreover, the

binary formulation assumes that the individual makes his allocative decision believing that he either succeeds in

all offenses he plans or fails them all. This is unrealistic because the individual may fail on all, none, or a fraction

of the attempted offenses; the formulation we adopt allows the individual to be confronted with a continuum of

failure possibilities.

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of an armed response from a civilian increases the possible punishment. We model this by

changing P to P(H), where P?(H) > 0.

The facilitating effect of the law manifests itself through an increase in the net benefit

per offense B, and an increase in the number of offenses committed under any given time

allocation C. Since B is net of any expense related to implementing a crime, the reduction

in the cost of acquiring handguns that results from these laws increases B. So, we change B

to B(H), where B?(H) > 0. Moreover, the substitution of handguns for less lethal weapons

increases the efficiency of the committed offenses. Accordingly, we change the offense

function to C(Ti, H), where CH= ∂C(·)/∂H > 0.

The wealth function obtained by incorporating the above effects of concealed handgun

laws is

W(x,H) = W0+ RTl+ [B(H) − (x + αH)P(H)]C(Ti,H).

And the individual’s optimization problem in the extended framework is given by

(2)

max

Ti

?

U[Tl,Ti,W0+ RTl+ (B(H) − (x + αH)P(H))C(Ti,H)] dF(x),

(3)

subject to Tl ≥ 0, Ti≥ 0, and Tl+ Ti=¯T. The first-order condition for maximization

requires that

A = E[Ui− Ul+ UW((B(H) − (x + αH)P(H))Ci(Ti,H) − R)] = 0,

where the first three terms denote the derivatives of U with respect to Ti, Tl, and W, re-

spectively, Cidenotes the derivative of C with respect to Ti, and Ui− Ulis referred to

as the individual’s preference for honesty. The second-order condition requires that ? =

∂A/∂Ti< 0.7

The effect of concealed handgun laws on the time allocated to criminal activities and the

number of crimes committed is analytically derived by differentiating Eq. (4). The effect

of a more permissive handgun law on Tiis

(4)

E

?∂Ti

∂H

?

= −1

?E

?

(UiW− UlW+ UWWG)D + UW∂G

∂H

?

,

(5)

where D is change in wealth resulting from a more permissive handgun law,8? is from

the second-order condition above, and G is the expression which is multiplied by UWin

Eq.(4).Sincetheratiooutsidethebracketispositivethesignofthederivativedependsonthe

expectationofthebracketedterm.Thistermcannotbesignedwithoutadetailedknowledge

of the individual’s preference structure and the magnitudes of D and G. However, Eq. (5)

7In the rest of this analysis we include both effects, although the effects can be isolated by setting either CH

and B?or a and P?equal to zero.

8For example, D = −[(αP +(x+α)P?)C(·)]+[B?C(·)+(B−(x+α)P)CH], where the first bracketed term

captures the deterrent effect and is negative and the second term captures the facilitating effect and is positive.

Note that B must exceed the expected punishment [E(x) + α]P for any offense to take place.

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clearlyindicatesthattheeffectofconcealedhandgunlawsoncriminalactivitiesdoesindeed

depend on several variables, some individual specific and others more general.9

Also, since the number of criminal offenses increases with Ti, the law has a similar effect

on the number of crimes:

E

?∂C(·)

∂H

?

= E

?

Ci∂Ti

∂H

?

+ E(CH),

(6)

where this effect cannot be signed either. Given the sign-ambiguity, the issue has to be

settled empirically. The above results, however, should influence the empirical examination

of the effect of the law, as will be discussed below.

2.2. Empirical implications

Eqs. (5) and (6) suggest that the effect of concealed handgun laws on the crime rate is

not fixed, because it depends on behavioral parameters as well as the exogenous variables

of the underlying model. This theoretical finding is also consistent with other observations

reported in the literature. Ludwig (1998), for example, argues that because juveniles are

not eligible to carry concealed weapons, any deterrent benefit from such laws will be lim-

ited to the non-juvenile population. Therefore, counties with a younger population may

not experience the full deterrent effect of these laws. Other demographic determinants of

the propensity to carry a concealed handgun, for example, age or gender, may also lead

to a similar differential effect. Moreover, the effect of the law on crime should be more

pronounced in the more populated counties, because authorities who have discretion over

issuing handgun-carrying permits in absence of a concealed handgun law are the most re-

strictive in using such discretion in populated counties. Finally, Black and Nagin’s (1998)

time-specific dummies also point to the variability of the effect of these laws.

Using the county as the basis for aggregation, behavioral Eqs. (5) and (6) can be written

in the following general form:

E

?∂C(·)

∂H

?

jt

= EK?W0,Rjt,Bjt,Pjt,αjtCjt(Ti),xjt,gjt(U),ηjt

where j and t denote county and time, K[·] is a general function, g(U) is a function denoting

higher derivatives of the utility function, and η is a portmanteau variable capturing higher

derivativesofthetermsintheaboveexpressionaswellasinfluenceswhichareunaccounted

for.

The heterogeneity indicated by the above equations implies that the effect of concealed

handgunlawsoncrimevariesacrosscounties.Moreover,thetestingprocedureshouldallow

the behavioral (response) parameters of the model to change. In fact, the effect may vary

with the age and gender composition of the population, population density, characteristics

of police, and economic conditions of the counties, among other things. Finally, variations

across counties within a state in terms of how easily permits were issued prior to adoption

?,

(7)

9These include, for example, the individual’s attitude toward risk UWW, the effect of increased wealth on his

preference for honesty UiW− UlW, his perceived failure rate, the perceived benefits and costs associated with

concealed handgun laws, and return on legal market activities.

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205

of concealed handgun laws provide additional justification for allowing the effect of these

laws to be heterogeneous across counties. For example, the most pronounced changes are

expectedincountieswiththemostrestrictivelicensingpracticepriortotheenactmentofthe

law. Ignoring such heterogeneity and assuming that E[∂C(·)/∂H]jtis a fixed quantity leads

to estimation bias due to imposing an incorrect restriction. We report empirical evidence to

support this point.

Also, note that a crime equation in implicit form can be derived from the first-order

condition, Eq. (4). The right hand side variables and parameters of this equation are the

same as the variables and parameters that appear on the right hand side of Eq. (7) which

captures the effect of the concealed handgun law on crime. We maintain the same parallel

betweenourcrimeequationandtheequationweproposeformeasuringtheeffectofthelaw.

3. Estimation methods and issues

3.1. Shortcomings of dummy variable approach

In regression analysis an intercept-shifting dummy variable is often used to estimate the

effectofaninstitutionalchange.Thestatisticalandconceptualramificationsofthispractice

isseldomexamined,particularlywhentheempiricalanalysisisnotpredicatedoneconomic

theory. To better motivate our procedure, which is intended to overcome the shortcomings

of this approach, we elaborate on this issue using Lott and Mustard’s (1997) study.10Lott

and Mustard use county level panel data to estimate several linear crime equations. The

dependentvariableineachequationisoneofseveralcrimerates—murder,rape,aggravated

assault, robbery, burglary, larceny, and auto theft. The regressors include the arrest rate

corresponding to that crime category, a host of economic and socio-demographic factors,

and a binary variable measuring the status of the concealed handgun law. This variable

equals 1 if a county has such a law in place in a given period and 0 otherwise. The other

regressors serve as control variables. The model they estimate is therefore

Cjt= α + γHjt+ βAjt+ δXjt+ εjt,

whereHisthebinaryvariable,Aisthearrestrate,Xincludestheeconomicanddemographic

variables and a set of time and county dummies (one for each sampling year or county), ε

is the regression error, and j and t denote counties and time periods, respectively.

Lott and Mustard’s inference about the effect of concealed handgun laws on various

categories of crime is based on the sign and statistical significance of the estimated coeffi-

cient of the binary variable—estimate of γ. A positive (negative) and significant estimate

suggests that concealed handgun provisions would increase (decrease) the crime rate. Note

that Lott and Mustard use γ in place of the expression in the right hand side of Eq. (7). This

expression clearly depends on county-specific exogenous variables as well as the behav-

ioral parameters of the model. Ignoring the heterogeneity of the effect of the law on various

(8)

10Lott and Mustard use the most comprehensive data set to examine this issue. There are several other useful

but smaller studies that examine the effect of gun availability on crime; See Kleck (1995) and Lott and Mustard

(1997) for a review.

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counties and parameterizing the effect as a fixed parameter γ leads to biased estimation.

The 2SLS estimate of γ reported by Lott and Mustard is negative, substantially large, and

significant for all crime categories, further supporting their deterrence hypothesis.11The

aforementioned bias can perhaps explain these unusually large negative estimates.12

3.2. Alternative approach

Following our theoretical results, we allow all behavioral parameters of the regression

model to change with the law, and thus allow the effect of the law on crime rates to be

heterogeneous across counties. The data will then show which of these parameters the law

indeed affects. We implement this parameter flexibility by first estimating two separate

crime equations, one for counties in states with a concealed handgun law and the other for

the remaining counties:

Cl,jt= αl+ βlAl,jt+ δlXl,jt+ εl,jt,

Cnl,jt= αnl+ βnlAnl,jt+ δnlXnl,jt+ εnl,jt,

where l and nl indicate the presence or the absence of the concealed handgun law, respec-

tively.Accordingly,thedatausedtoestimateEq.(9a)includeallcountiesthathaveadopted

aconcealedhandgunlawfortheperiodaftertheadoptionofthelaw.Theremainingdataare

used to estimate Eq. (9b); these include data for all counties that never adopted a concealed

handgun law during our sample period as well as data for the adopting counties over the

period before they adopt the law.

Wethenexaminewhetherthelawaffectstheresponseparametersbyusinganasymptotic

WaldtestofthenullhypothesisH0: Θl= ΘnlagainstthealternativeH0: Θl?= Θnl,where

Θ denotes (β, δ).13This hypothesis implies that the effect of the law on crime is a constant

parameter γ (or αl−αnl) which does not change across county or over time. This of course

is at odds with Eq. (7). A rejection of the null implies that the law affects the response

(slope) parameters of the model, thus rejecting a simple intercept change formulation such

as the one used by Lott and Mustard. As we report in the next section the above null is

rejected strongly in all cases, making it necessary to use a less restrictive procedure.

(9a)

(9b)

11The 2SLS that treats the arrest rate as an endogenous variable which is itself affected by the crime rate is the

appropriate method for estimating Eq. (8). In addition to 2SLS, Lott and Mustard use OLS method, which ignores

the simultaneity between crime and arrest, to project the expected reduction in the number of murders, rapes,

robberies, and aggravated assaults for 1992 through 1995 if those states without right-to-carry concealed handgun

provisions had adopted them in 1992. Much of the public attention that Lott and Mustard have received centers on

these OLS based projections and not the more appropriate 2SLS results; see, for example, the article by Richard

Morin, in The Washington Post, Sunday, 23 March 1997, page 5; also, see Black and Nagin (1998) and Ludwig

(1998) who criticize Lott and Mustard on methodological grounds. These authors all focus on the inappropriate

OLS results rather than the 2SLS results.

12Such specification bias also makes the coefficient estimates fragile with respect to small change in the model

such as inclusion or exclusion of various control variables. Bartley and Cohen (1998) use the method suggested

by Leamer and Herman (1983) to examine the range of estimates of the coefficient of the binary variable in

Lott–Mustard specification and find it to be quite wide in many cases.

13The Wald statistic is the quadratic form constructed on the estimate of the difference (Θl−Θnl). The statistic

is asymptotically distributed as a χ2variate with degrees of freedom equal to the number of parameters tested.

Godfrey (1988, chap. 4) and Lo and Newey (1985), see also Pesaran, Smith, and Yeo, 1985.

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We estimate, accordingly, the direction and extent of the change in crime rate that may

result from introducing the concealed handgun law. More specifically, we determine how

different the crime rate would have been during 1992 in the counties that did not have

the concealed handgun law in place, had they adopted the law by 1992. We obtain these

estimates, which are useful for policy purposes, simply by replacing the estimates of the

behavioral parameters in Eq. (9b) with those in Eq. (9a) and computing the resulting pre-

dicted values for the crime rate in 1992. For example, we estimateˆCj92= ˆ αl+ˆΘlZnl,j92,

where Znldenotes the regressors in Eq. (9b), Θ denotes (β, δ), 92 is year, and j is restricted

totheaforementionedgroupofcounties.Thesearesimplypredictedcrimeratesconditional

on adopting the concealed handgun law. The difference between the predicted and actual

crime rates measures the effect of concealed handgun laws on crime.

Weemphasizethatourinterestistoestimatetheexpected1992crimeratesconditionalon

the law being in place in a county that did not have it in 1992. Since the adoption of the law

changestheregressioncoefficients,wemustusethecoefficientsestimatedforthesubsample

ofcountieswithaconcealedhandgunlawwhenestimatingthisconditionalexpectation.The

conditional prediction so obtained is then compared with the county’s actual 1992 crime

rates to estimate the expected change resulting from adoption of the law. It is important to

note that in the above comparison, one should not use the county’s predicted crime rate

without the law in 1992, ˆ αnl+ˆΘnlZnl,j92, instead of the observed (actual) crime rate Cnl.

This is because the former does not have any information that is useful for our inference but

isnotcontainedinthecounty’sobserved1992crimerate.Therefore,ifweusedthepredicted

crime rate instead of the actual crime rate, we would just be adding extra noise (residual),

thus reducing the accuracy of the inference. Also, note that all the information relevant to

adopting the law is incorporated inˆΘlwhich is estimated using counties with the law.14

ToseehowourprocedurerelatestothetheoreticalEq.(7)andalsotoformallycontrastthis

procedure with the intercept-shifting dummy variable procedure, consider the following.

The latter procedure parameterizes the law-induced crime change as an intercept-shifting

parameter αl−αnl(or γ in Eq. (8)), implying the law does not affect any of the behavioral

parameters of the model. We, on the other hand, parameterize the change as

(αl+ ΘlZnl,92) − Cnl,j92,

which after substitution from (9b) and setting the random error ?nlequal to its expected

value which is zero yields

(αl− αnl) + (Θl− Θnl)Znl,92.

Note that the first term in the above expression is the intercept change, used, for example,

by Lott and Mustard, while the second term is our addition which varies with county

characteristics and is a function of model parameters. This expression is the empirical

14Lott (1998, p. 304) claims that our approach throws out useful information. In making this claim, he ignores

basic statistical concepts such as efficiency and sufficiency. Statistical inference involves extracting useful data

information by means of efficient and unbiased coefficient estimators and conditional predictors. And that is what

we do here. All the data pertaining to concealed handgun regimes (counties and time periods) are used to estimate

thecoefficientestimates,andtheseestimatesarethenusedalongwiththedatafornon-concealedhandgunregimes

to obtain conditional predictions.

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counterpart of the law-induced crime change given by Eq. (7). Also, note the similarities

between the parameters and variables in this expression and those in the crime Eqs. (9a)

and (9b). We documented a similar parallel between the theoretical counterparts of crime

and the change in crime.

We summarize the predictions we so obtain to generate an inference about the potential

influence of the law in each state which did not have a concealed handgun law in 1992.

The predictions are further analyzed to determine factors that influence their direction

or magnitude. This approach allows the effect of permissive handgun laws to vary with

population density, racial and gender characteristics, income, and so forth. At the same

time, it exploits the variation in the timing of these state laws to investigate their impact.

4. Data and results

4.1. Data

We use the data provided to us by Lott and Mustard. The data set covers 3054 counties

for the period 1977–1992. However, since several series are only reported for 1982 through

1992, the effective time span is shorter. The data set includes the FBI’s crime data for

murder, rape, aggravated assault, and robbery which comprise “violent crime” and auto

theft, burglary, and larceny which comprise “property crime”. The series also include the

corresponding arrest rate for these nine crime categories, population, population density,

real per capita personal income, real per capita unemployment insurance payments, real

per capita income maintenance payments, real per capita retirement payments per person

over 65 years of age, and population characteristics for 36 age and race segments (black,

white and other; male and female; and age divisions). The data set also includes state

level observations on police employment and payroll, percentage of votes received by the

Republican presidential candidate, and the percentage of each state’s population that are

members of the National Rifle Association.

The primary sources of data include FBI’s Uniform Crime Report (for crime and arrest

data),CramerandKopel,1995(forstateswithshallissuelaws),theBureauoftheCensus(for

demographicdata),CommerceDepartment’sRegionalEconomicsInformationSystemand

Statistical Abstract of the United States (for economic data), U.S. Department of Justice’s

ExpenditureandEmploymentDatafortheCriminalJusticeSystem(forpoliceemployment

and payroll), and National Rifle Association (for NRA membership data).15

WeusethepercentageofstatewidevotereceivedbytheRepublicanpresidentialcandidate

in the most recent election as a proxy for partisan influence on the process that we estimate.

Partisan influence is expected to capture any political pressure to adopt more permissive

gun legislations—a stand which is more popular with Republican candidates.

4.2. Results

FollowingEhrlich(1973),inallourestimationwetreatthearrestrate,A,asanendogenous

variable. A first stage equation then specifies arrest as a function of a set of independent

15See, also, Lott and Mustard’s (1997) data descriptions on pages 6, 7, 12–17, 42, 43, and 66–68.

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variables that include lagged crime rate, economic and demographic variables in the crime

equation, time and county-specific dummies, police employment and payroll, and a set of

variables to control for political influences. These latter variables include percentage of

votes received by the Republican presidential candidate, and the percentage of a states’

population that are members of the National Rifle Association.

We estimate Eqs. (9a) and (9b) along with the corresponding arrest equations via 2SLS,

allowingtheconcealedhandgunlawtoalsoshiftthecoefficientsofthearrestequationinthe

first stage of estimation; such shifts are incorporated in cases where the Wald test applied

to an arrest equation suggested such a change is warranted. This ensures the consistency of

the second stage estimates. In all our estimations, we correct the residuals from the second

stage least square to account for using predicted arrest rather than the actual arrest rate in

estimation of crime equation; see for example, Davidson and MacKinnon (1993, chap. 7).

As indicated earlier, our empirical strategy starts with testing whether the data sup-

ports modeling the effect of the law through an intercept-shifting dummy variable—the

hypothesis of no slope change due to the law. Using an asymptotic Wald test for all nine

categories of crimes, we find that this hypothesis is rejected strongly for all categories of

crime. The statistics for various crime equations are 131.2 (murder), 152.5 (rape), 395.3

(aggravated assault), 194.2 (robbery), 451.2 (burglary), 323.7 (larceny), 479.3 (auto theft);

all statistics have P-values which are close to zero. This suggests that there are signif-

icant changes in slope coefficients in all cases, so the assumption that all changes are

embedded in the intercept is invalid. The Lott–Mustard results are, therefore, biased by

misspecification.16

Similar results for the arrest equation, used in the first stage of the 2SLS estimation,

indicate the coefficients of these equations also change with the law. In fact, we incorporate

these changes when obtaining the predicted arrest rates. A comparison of our predicted

arrest rates to that of Lott and Mustard’s reveal the inaccuracy introduced by limiting the

changetotheinterceptterm.Forexample,dependingonthecrimecategory,themeansquare

error of Lott and Mustard’s predicted arrest rates is from 1.5 to 5.2 times larger than ours.

Their predicted arrest rates also include a large number of negative values; for example,

more than 19,000 of the 33,000 predicted arrest rates for auto theft are negative; the number

of negative arrest rates for aggravated assault and property crimes are, respectively, 9900

and 13,500.17

We use the two-stage procedure described earlier to estimate the hypothetical effect

on crime in each county in states that did not have a concealed handgun law in place if

such a law had been in effect in 1992. We examine these effects in two ways, both on a

county-by-county basis. First, we examine for each crime and for each county the predicted

effect of changing the law. Table 1 contains summary statistics derived from these county

level conditional predictions. Second, we examine the effect of county characteristics on

predicted change in crime rates for each aggregated crime category (violent, property).

Table 2 reports results of regressing these predictions on various county characteristics.

16We reported some of the empirical results in Dezhbakhsh and Rubin (1998).

17Obviously, any prediction has a range that may include undesirable values (e.g. negative estimates for a

positive-valued variable such as arrest rate). The problem here is that a large number of such values are obtained

by Lott and Mustard, which makes us suspect that their predicted arrest rates are biased downward.

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Table 1

The predicted effect of adopting concealed handgun laws on crimes in states without such laws in 1992

States without

such laws in 1992

(no. of counties)

No. of counties (population & crime as % of state population & crime) to experience

Murder Rape Robbery

Crime increase

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

Crime decrease

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

3 (2.1%, 15.8%)

0 (0%, 0%)

1 (0.2%, 7.5%)

3 (0.8%, 7.1%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (0.3%, 9.6%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (1.3%, 3.2%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

7 (0.4%, 9.4%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

Crime increase

0 (0%, 0%)

1 (3.0%, 0.2%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

5 (14.2%, 3.3%)

0 (0%, 0%)

1 (0.6%, 0.5%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

2 (1.6%, 1.4%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

2 (1.9%, 0.3%)

2 (2.6%, 0.4%)

0 (0%, 0%)

0 (0%, 0%)

1 (1.6%, 0.3%)

2 (10.9%, 8.1%)

0 (0%, 0%)

0 (0%, 0%)

1 (0.7%, 0.2%)

0 (0%, 0%)

Crime decrease

0 (0%, 0%)

0 (0%, 0%)

3 (1.7%, 8.0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (0.7%, 8.6%)

1 (0.1%, 2.2%)

9 (3.7%, 32.9%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

2 (3.7%, 4.3%)

0 (0%, 0%)

0 (0%, 0%%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (1.2%, 1.8%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

5 (5.2%, 13.8%)

8 (0.6%, 6.4%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

Crime increase

0 (0%, 0%)

1 (3.0%, 0.1%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (0.1%, 0.1%)

8 (18.1%, 5.7%)

1 (0.6%, 0.2%)

8 (4.8%, 4.2%)

1 (1.1%, 0.1%)

2 (14.7%, 8.6%)

0 (0%, 0%)

2 (1.0%, 0.2%)

1 (0.5%, 0.3%)

3 (1.8%, 1.4%)

0 (0%, 0%)

1 (3.2%, 6.3%)

0 (0%, 0%)

1 (3.2%, 0.4%)

0 (0%, 0%)

0 (0%, 0%)

5 (3.9%, 1.2%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

6 (12.7%, 17.3%)

2 (0.3%, 0.1%)

0 (0%, 0%)

2 (1.6%, 0.3%)

0 (0%, 0%)

Crime decrease

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (1.5%, 7.3%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (0.6%, 1.0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

1 (0.01%, 2.0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

Alaska∗(26)

Arizona∗(15)

Arkansas∗(75)

California (58)

Colorado (63)

Delaware (3)

Dist. of Col. (1)

Hawaii (5)

Illinois (102)

Iowa (99)

Kansas (105)

Kentucky∗(120)

Louisiana∗(64)

Maryland (24)

Massachusetts (14)

Michigan (83)

Minnesota (87)

Missouri (115)

Nebraska (93)

Nevada∗(17)

New Jersey (21)

New Mexico (33)

New York (62)

N. Carol.∗(100)

Ohio (88)

Oklahoma∗(77)

Rhode Island (5)

S. Carolina∗(46)

Tennessee∗(95)

Texas∗(254)

Utah∗(29)

Wisconsin (72)

Wyoming∗(23)

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211

Aggravated assaultBurglary Auto theft

Alaska∗(26)

Arizona∗(15)

Arkansas∗(75)

California (58)

Colorado (63)

Delaware (3)

Dist. of Col. (1)

Hawaii (5)

Illinois (102)

Iowa (99)

Kansas (105)

Kentucky∗(120)

Louisiana∗(64)

Maryland (24)

Massachusetts (14)

Michigan (83)

Minnesota (87)

Missouri (115)

Nebraska (93)

Nevada∗(17)

New Jersey (21)

New Mexico (33)

New York (62)

N. Carol.∗(100)

Ohio (88)

Oklahoma∗(77)

Rhode Island (5)

S. Carolina∗(46)

Tennessee∗(95)

Texas∗(254)

Utah∗(29)

Wisconsin (72)

Wyoming∗(23)

0 (0%, 0%)

1 (3.0%, 0.6%)

0 (0%, 0%)

0 (0%, 0%)

3 (5.7%, 2.0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

8 (5.3%, 2.8%)

8 (13.2%, 1.7%)

1 (0.3%, 0.3%)

0 (0%, 0%)

0 (0%, 0%)

1 (14.4%, 7.0%)

0 (0%, 0%)

0 (0%, 0%)

1 (0.2%, 0.2%)

4 (2.0%, 1.2%)

2 (0.6%, 0.8%)

0 (0%, 0%)

1 (3.2%, 5.0%)

1 (3.2%, 0.5%)

1 (3.9%, 0.8%)

2 (0.3%, 0.1%)

8 (7.3%, 4.4%)

2 (0.6%, 0.3%)

0 (0%, 0%)

0 (0%, 0%)

7 (13.2%, 7.8%)

3 (0.1%, 0.1%)

1 (0.6%, 0.2%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

(0%, 0%)

5 (7.5%, 6.2%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

2 (0.1%, 0.9%)

1 (0.4%, 2.0%)

0 (0%, 0%)

12 (6.4%, 8.2%)

1 (0.2%, 2.5%)

1 (1.5%, 4.4%)

0 (0%, 0%)

0 (0%, 0%)

2 (0.6%, 7.9%)

6 (4.7%, 11.2%)

3 (1.9%, 3.2%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

2 (0.4%, 4.2%)

0 (0%, 0%)

3 (2.0%, 9.6%)

1 (0.3%, 7.1%)

0 (0%, 0%)

0 (0%, 0%)

6 (9.4%, 13.8%)

17 (1.6%, 8.1%)

0 (0%, 0%)

2 (1.1%, 2.9%)

0 (0%, 0%)

0 (0%, 0%)

1 (3.0%, 1.0%)

2 (0.9%, 1.4%)

0 (0%, 0%)

9 (6.6%, 6.2%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

9 (1.8%, 2.6%)

23 (36.6%, 13.8%)

10 (2.0%, 3.1%)

50 (36.3%, 41.4%)

2 (1.3%, 0.9%)

3 (15.3%, 11.3%)

1 (0.1%, 6.6%)

0 (0%, 0%)

8 (2.1%, 3.3%)

18 (6.9%, 16.6%)

12 (3.6%, 11.6%)

0 (0%, 0%)

0 (0%, 0%)

2 (3.5%, 5.0%)

0 (0%, 0%)

2 (0.5%, 0.4%)

14 (9.0%, 10.1%)

0 (0%, 0%)

0 (0%, 0%)

10 (39.1%, 21.7%)

16 (16.1%, 12.6%)

13 (0.5%, 2.4%)

2 (0.9%, 3.2%)

0 (0%, 0%)

2 (2.7%, 3.2%)

0 (0%, 0%)

0 (0%, 0%)

8 (4.9%, 7.8%)

0 (0%, 0%)

3 (1.3%, 2.7%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

13 (5.1%, 11.8%)

4 (1.8%, 4.7%)

19 (24.6%, 16.8%)

6 (1.2%, 2.9%)

5 (6.4%, 8.5%)

2 (2.6%, 5.2%)

0 (0%, 0%)

1 (0.2%, 1.4%)

5 (1.2%, 4.6%)

8 (6.4%, 9.4%)

8 (5.2%, 8.0%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

3 (0.5%, 3.0%)

8 (4.0%, 5.0%)

2 (0.4%, 1.5%)

4 (0.6%, 3.2%)

0 (0%, 0%)

0 (0%, 0%)

3 (1.2%, 3.9%)

20 (1.0%, 5.9%)

4 (4.1%, 14.5%)

14 (9.0%, 17.6%)

1 (1.1%, 2.1%)

0 (0%, 0%)

2 (3.2%, 1.9%)

5 (2.3%, 0.8%)

0 (0%, 0%)

1 (0.1%, 0.8%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

15 (2.7%, 3.9%)

19 (33.8%, 12.4%)

16 (5.1%, 10.4%)

23 (9.0%, 13.2%)

4 (3.2%, 2.3%)

3 (15.3%, 12.3%)

1 (0.1%, 1.2%)

0 (0%, 0%)

3 (0.6%, 0.9%)

18 (6.1%, 7.4%)

12 (4.2%, 8.1%)

2 (0.7%, 5.4%)

0 (0%, 0%)

2 (6.5%, 4.4%)

0 (0%, 0%)

0 (0%, 0%)

9 (5.2%, 3.5%)

3 (0.9%, 1.6%)

0 (0%, 0%)

3 (9.6%, 7.6%)

15 (16.1%, 15.6%)

37 (2.2%, 7.2%)

2 (0.5%, 3.7%)

2 (0.9%, 0.1%)

4 (5.9%, 4.6%)

0 (0%, 0%)

0 (0%, 0%)

4 (2.2%, 4.0%)

1 (0.01%, 0.2%)

4 (5.4%, 4.9%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

6 (6.2%, 12.7%)

5 (2.4%, 6.9%)

15 (4.0%, 4.9%)

14 (4.7%, 6.9%)

4 (2.3%, 5.4%)

0 (0%, 0%)

0 (0%, 0%)

6 (1.0%, 4.2%)

12 (4.5%, 9.2%)

5 (4.8%, 3.5%)

6 (4.6%, 10.9%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

4 (3.4%, 2.2%)

5 (3.0%, 3.0%)

3 (1.7%, 2.9%)

1 (0.1%, 0.3%)

0 (0%, 0%)

0 (0%, 0%)

0 (0%, 0%)

24 (2.4%, 7.3%)

5 (5.6%, 12.8%)

16 (16.9%, 23.8%)

1 (1.1%, 3.5%)

Notes: The entries in each crime category are the number of counties in each states that would have experienced a statistically significant change in their 1992 crime rates,

had they adopted a concealed handgun law by 1992. The numbers in parentheses are the respective population of these counties as a percent of the state population and

their crime rates as a percent of the state total crimes in that category. In 1992 Philadelphia was the only county in Pennsylvania that was exempt from Pennsylvania’s

1989 concealed handgun law. Entries for Philadelphia, not reported, are all zero. An asterisk (∗) indicates that the state adopted a handgun law between 1992 and 1996.

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Table 2

Determinants of the magnitude of the change in crime induced by concealed handgun laws

Characteristics Violent crimesProperty crimes

Arrest rate

Police payroll

Population density

NRA membership

Income

Unemployment insurance

Retirement payment

Black males (10–29)

Black females (10–29)

Non-black males (10–29)

Non-black females (10–29)

Population over 65

+0.002765∗∗(0.00060)

−0.031942∗∗(0.00857)

−8.03e−07 (4.55E−06)

+0.000150∗∗(0.00003)

+0.000030∗∗(7.54E−06)

+0.000103 (0.00031)

−0.000016∗∗(3.49E−06)

−0.085921∗(0.05122)

+0.105542∗∗(0.04713)

+0.054673∗∗(0.01562)

−0.069583∗∗(0.02009)

−0.012907∗(0.00671)

0.276

+0.009427∗∗(0.00285)

−0.060959∗∗(0.01340)

+0.000028∗∗(8.51E−06)

−0.000250∗∗(0.00006)

+6.38E−06 (0.00001)

+0.000057 (0.00038)

+0.000022∗∗(9.84E−06)

+0.007725 (0.05856)

+0.071520 (0.05375)

−0.000593 (0.02344)

−0.053331∗(0.02962)

−0.016139∗(0.00897)

0.272

R2

Notes: Asymptotic heteroskedasticity-robust standard errors are in parentheses. (∗) and (∗∗) indicate significance

at the 10% and 5% levels, respectively.

The interpretation of Table 1 is as follows: In 1992, there were thirty-three states without

such laws, excluding Pennsylvania where Philadelphia county was given exemption from

the law passed in 1989. Consider, for example, murder in Texas. Since Texas is in our

sample, this indicates that in 1992 this state did not have a concealed handgun law in place,

although the asterisk (∗) indicates that it had adopted such a law by 1996. There are 254

counties in Texas as shown in (column 1). Had the concealed handgun law been in effect in

Texas in 1992, then in seven of those counties, which include 0.4% of the population in the

state and account for 9.4% of the state murders, murder rates would have decreased by a

statistically significant amount.18Thus, for counties in six states a concealed handgun law

would have reduced murder rates and for all counties in the other 27 states it would have

been ineffective. Overall, the results indicate a relatively small, and crime-reducing, effect

of concealed handgun laws on murder rates. Moreover, it appears that there would have

been little effect on rape with 21 states unaffected, 4 states with unambiguous increases,

and 2 states with unambiguous decreases.

The effect on robbery would have been an increase in crime for many states. For counties

in 13 states, there would have been an unambiguous increase in robbery; there would have

been mixed effects (increase in some counties and decrease in some) in counties in only

three states. The overall increase in robbery is not surprising. As discussed earlier, the

sum of the facilitating and deterrent effects determine how crime changes as the result of

these laws. For robbery, the facilitating effect is crime-inducing but the deterrent effect is

not necessarily crime-reducing. While some of the robberies such as street stick-ups are

deterrablebyconcealedhandguns,manypotentialrobberytargetssuchasbanksandvarious

shops already have armed protection. Concealed firearm laws, therefore, do not provide the

18Iftheactual1992crimerateforacountyfallsshortof(exceeds)theconfidenceintervalfortheprojectedcrime

rate conditional on the law being in place, then we infer that the law would have increased (decreased) the crime

rate for that county.

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lattergroupwithadditionaldeterrencebenefits.Thelowdeterrenceandtheapparentlylarge

crime-facilitating effect for robbers implies a net crime enhancing effect in this case.

For aggravated assault 11 states would have been unaffected, 7 states adversely affected,

and 4 states would have observed a drop in crime. The result for the remaining states is

mixed. For the three categories of property crime (only two reported in the table) the effect

would have been more mixed. Altogether there were 33 states containing 2074 counties

that did not have shall issue laws in 1992, so the largest percentage of counties predicted

to be affected in one direction by changing the law would have been the 15% of counties

predicted to experience an increase in larceny; all other predicted percentage changes in

any direction are less than 10%.

Wecanalsoderivepolicyimplicationsfromtheseexpostpredictionsforparticularstates

whichhadnotadoptedthelawby1996(stateswithoutanidentifyingasterisk(∗)).Maryland

would expect increases in robbery, assault, burglary, and auto theft, and so probably should

not adopt the law. Similarly New Mexico would expect small increases in robbery and all

three categories of property crime, and so also should not adopt the law. In Iowa, rape,

robbery, assault, burglary and auto theft would increase, if the law is adopted. On the other

hand, were Illinois to adopt a handgun law, then we would expect decreases in murder,

robbery, burglary, and auto theft, but an increase in assault. Kansas could expect reductions

in murder, rape, and burglary, and increases in auto theft and a small increase in assault.

Minnesota might also benefit from the law. For most other states that had not adopted the

law by 1996, effects would be small and mixed.

We next examine how various county characteristics affect the magnitude of the law-

induced changes in aggregate (violent and property) crimes. We do this by regressing the

predicted (law-induced) change in crime rates for each of the counties without the law

in 1992 on a set of demographic and economic variables for the county. The economic

variables, all measured per capita, are personal income, unemployment insurance, and

retirementpaymentsperpersonover65.Wealsoinclude(predicted)arrestrates,population

density, and demographic variables. Since most crime is committed by young males, we

include number of black and non-black males 10–29 years old, and similarly for females.

Weincludepersons65andover,whoareperhapsmorelikelytobevictimsthanperpetrators

ofcrimes.Finally,weincludepercapitameasuresofpolicepayrollandthenumberofNRA

membersinthestate.Inallcases,wemeasuretheeffectoftherelevantvariableonpredicted

changes in crime resulting from the existence of a concealed handgun law in the county.

Regression results are summarized in Table 2. A positive and significant coefficient

suggests that the characteristic is expected to have a positive influence on the change in

crime that results from right-to-carry concealed handgun laws; “positive” means that crime

increase will become larger (stronger facilitating effect) and crime decrease will become

smaller (weaker deterrence effect) when the characteristic takes a larger value. A negative

and significant coefficient suggests that the characteristic is expected to have a negative

influence on the change in crime that results from right-to-carry concealed handgun laws;

“negative” means that crime increases will become smaller (weaker facilitating effect) and

crimedecreasewillbecomelarger(strongerdeterrenceeffect)whenthecharacteristictakes

a larger value.

Forexample,thepositiveandstatisticallysignificantcoefficientofarrestratesuggestthat

concealed handgun laws have a stronger facilitating effect and a weaker deterrence effect in

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- Available from Paul H Rubin · Jun 5, 2014
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