Revisiting the Question More Guns, Less Crime? New Estimates Using Spatial Econometric Techniques

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1 Revisiting the Question Moe Guns, Less Cime? New Estimates Using Spatial Econometic Techniques Donald J. Lacombe Depatment of Agicultual and Resouce Economics and Economics Regional Reseach Institute West Viginia Univesity Mogantown, WV and Amanda Ross Depatment of Economics West Viginia Univesity Mogantown, WV Abstact In a highly debated pape, Lott and Mustad (1997) found that allowing citizens to cay concealed handguns educed cime. Since then, numeous eseaches have questioned the validity of the findings. In addition, ongoing wok has shown thee is an impotant spatial component to cime. In this pape, we use spatial econometic techniques to estimate the impact of adoption of concealed weapons laws by some states on cime ates acoss the U.S. We find thee ae spillove effects of concealed weapons laws and that spatial dependence plays an impotant ole when estimating the effect of these laws on cime. 1

2 I. Intoduction Gun contol is a hotly debated issue in the U.S. In addition to constitutionality aguments, thee ae questions egading the impact of guns on cime. Lott and Mustad (1997) found that allowing citizens to cay concealed handguns educed cime. Thei findings led to a debate amongst economists, with some suppoting the findings, while othes disputed the claims. Ayes and Donohue (2003) povide a summay of the eseach conducted on this issue. So fa, the eseach on gun laws has failed to account fo the spatial dimension of cime. Individuals ae mobile, so diffeences in policy may affect whee an individual commits a cime. We account fo this mobility by employing spatial econometic techniques and evisit the issue of how of a concealed weapon law impacts cime. A concealed weapons law allows an individual to cay a concealed handgun if he can demonstate a need to cay such a weapon. In some states, govenments have discetion ove issuing these pemits. Othe states have a shallissue law, which allow individuals to eceive a concealed weapon pemit unless specific and veifiable factos dictate othewise. States that have a shall-issue law ae what we efe to as states with a concealed weapon law o a ight-to-cay state. To test whethe thee is a spatial dependence of ight-to-cay laws on cime, we utilize a Spatial Dubin Panel Model (SDM). Ou esults indicate that spatial dependence is pesent, suggesting the pevious eseach that has not contolled fo the spatial elationships has poduced biased estimates. We find that concealed weapon laws educe the assault ate, consistent with the aguments of Lott and Mustad (1997) that the potential of an amed victim detes ciminals. Howeve, we find a positive effect fo all popety cimes, obbey, laceny, and moto vehicle theft (MVT). Ou findings also indicate that adoption of a shall-issue law has a positive spillove effect on neighboing states fo ape, obbey, laceny, MVT, and all popety cimes. Policy 2

3 makes should be cognizant of ou findings, as they suggest that anti-cime policies have spillove effects on adjacent states. II. Econometic Model and Data Econometic Model A family of elated spatial econometic models can be epesented by: N y w y x w x u u it ij jt it ij ijt i t it j1 j1 N w u it ij it it j1 N (1) whee i is an index fo the coss-sectional dimension (i.e. states), with i1,, N, and t is an index fo the time dimension, with t 1,, T. yit is an obsevation of the dependent vaiable at i and t, xit is an 1, K ow vecto of the explanatoy vaiables, and is a matching K,1 vecto of fixed but unknown paametes. The tems i and t epesent space- and time-peiod fixed effects. The additional tems ae what make the panel model a spatial econometic specification. The model may contain a spatially lagged dependent vaiable o a spatial autoegessive pocess in the eo tem. In addition, thee may be spatially weighted explanatoy vaiables in the model. An impotant aspect of any spatial econometic model is the spatial aangement of the units in the sample. In pactice, this is accomplished by specifying a spatial weights matix, W, which expesses fo each obsevation (ow) those locations (columns) that belong to its neighbohood set as nonzeo elements (Anselin & Bea, p. 243). The individual elements in the spatial weight matix, w ij, equal "1" if obsevations i and j ae "neighbos" and "0" othewise. 3

4 Nomally, a ow stochastic weight matix is used, which means that the ows of the spatial weight matix sum to unity. Depending on the context, both and measue the extent of the spatial autocoelation. Given (1), special cases can be obtained by esticting paametes. Fo example, setting 0 and 0, we obtain a model that exhibits spatial dependence only in the dependent vaiable. This model is the spatial autoegessive (SAR) model. The spatial eo model (SEM) aises when the estictions 0 and 0 ae in effect, ceating spatial dependence in the eo tem alone. Placing the estiction 0 esults in the spatial Dubin model (SDM). The SDM allows fo a spatially lagged dependent vaiable as well as spatially lagged independent vaiables. It is impotant to note that the inclusion of the Wy tem on the ight hand side of the above equation intoduces simultaneity bias and the use of OLS as an estimation stategy will poduce biased and inconsistent paamete estimates (Anselin 1988, pp ). Theefoe, maximum likelihood estimation is used to estimate the paametes in the SAR model. 1 The SEM is utilized when one believes that thee may be vaiables that ae omitted fom the model that ae spatially coelated but ae uncoelated with the included egessos. SEM can also be efficiently estimated via maximum likelihood. LeSage and Pace (2009) point out that SDM should be used when one believes thee ae omitted vaiables that ae spatially coelated with the included explanatoy vaiable. If these conditions hold, the SDM is the appopiate model. As indicated by (1), all thee of these models may include space- and time-fixed effects. In ou case, we have state- and yea-fixed effects. LeSage and Pace (2009) show that the maginal effect of a change in an explanatoy vaiable is calculated using the following fomula: 1 Details egading maximum likelihood estimation of spatial econometic models ae contained in Anselin (1988) and LeSage and Pace (2009). 4

5 y i y i x x i j S S W W ii ij (2) whee S W I W 1 W, i is the subscipt epesenting location i, j is the n subscipt denoting location j, epesents the th explanatoy vaiable, is the coefficient on the th explanatoy vaiable, and is the coefficient on the th spatially weighted explanatoy vaiable. The uppe quantity in equation (2) shows how a change in an explanatoy vaiable at location i affects the dependent vaiable at location i, known as the diect effect. The lowe quantity in equation (2) shows how a change in an explanatoy vaiable at location j affects the dependent vaiable at location i, whee i j. This is known as the indiect, o spillove effect. It should be noted that the quantity S W poduces a matix of effects estimates. LeSage and Pace (2009) ecommend that one calculate scala summaies of these measues to get an aveage effect. The aveage diect effect is the aveage of the diagonal elements of the S aveage indiect effect is the aveage of the off-diagonal elements of the S W matix, the W matix, and the aveage total effect is the sum of the two. Statistical infeence egading these effects estimates and how they ae calculated ae contained in LeSage and Pace (2009). In addition to the ight-to-cay law indicato and the state and yea fixed effects, we also include socio-economic contols to addess diffeences in the state population. We include contols fo the age, acial, and gende composition of the state. We also include contols fo the pe capita pesonal income in the state, pe capita unemployment insuance payments, and pe capita income maintenance. 5

6 Data We use the cime data ceated by Ayes and Donohue (2003) and use the indicato vaiables ceated by Lott and Mustad (1997) when detemining when a ight-to-cay law was passed. 2 One citicism of the Lott and Mustad esults is that the panel ends too ealy, and adding additional yeas causes the sign of the effect to flip. Fo this eason, and given the yeas of data that we have a balanced panel, we conside the impact of shall-cay laws on cime ates fom 1970 to Table 1 pesents the summay statistics of the cime vaiables. The fist column lists all the cime measues we use, including each of the index cimes mude, ape, obbey, aggavated assault, buglay, laceny, and MVT as well as violent and popety cime. Violent cime is the sum of mude, ape, obbey, and assault while popety cime is the sum of buglay, laceny, and MVT. III. Results Ou esults ae pesented in Table 2. Fo all specifications, we utilized the spatial Dubin model (SDM) with time and state fixed effects and a six neaest-neighbo spatial weight matix. The fist column epots the dependent vaiable, the type of cime which is measued as the log of the cime ate. Columns 2, 3, and 4 contain the aveage diect, indiect, and total effect fo the shallissue dummy vaiable. The final column is the value and statistical significance of the spatial autocoelation paamete,. We find that five cime categoies have a significant diect effect. Howeve, the sign of the effect diffes based on the cime. Robbey, all popety cimes, laceny, and MVT all have positive and significant aveage diect effects, meaning that states with a shall-issue law have 2 The Lott and Mustad data is not a balanced panel, and given the natue of the spatial weight matix, it is impotant that we have a balanced panel. 6

7 highe cime ates than states that do not. Shall-issue laws should affect those cimes with faceto-face inteaction, as the fea that the individual may have a concealed weapon will dete cime. Theefoe, a positive effect fo popety cimes is not counte to the aguments of Lott and Mustad (1997), as most popety cimes do not have a face-to-face inteaction. Howeve, the positive effect on obbey contasts the aguments of Lott and Mustad (1997). Thee is a negative diect effect on the assault ate, meaning states with a shall-cay law have a lowe assault ate. This finding is consistent with Lott and Mustad (1997) and suggests thee is some deteent effect of the policy. The aveage indiect effect measues spillove effects to adjacent states. Findings indicate a positive and significant spillove effect fo ape, obbey, all popety cimes, laceny, and MVT. This is not supising fo these types of cimes, especially MVT, as pevious wok has found these cimes ae especially mobile (Di Tella & Schagodsky, 2004; Daca et al., 2011; Klick & Tabaok, 2005). This esult futhe emphasizes that thee ae spillove effects when looking at the impact of policies on cime that pevious eseach has not popely measued. The final column of Table 2 is the paamete. This paamete measues the amount of spatial autocoelation in the dependent vaiable, which in this case ae the cime types. The esults indicate that many cime categoies exhibit negative spatial autocoelation, indicating a checkeboad patten in cime ates acoss states. The paamete fo many cime types is statistically significant, with the exception of all violent cimes, obbey, buglay, and MVT. IV. Conclusions Economists have debated the impact of gun contol laws on cime ates fo decades. One of the most contovesial papes on this topic, Lott & Mustad (1997), found that ight-to-cay laws 7

8 educe cime ates. Since that pape, numeous studies have both suppoted and efuted these findings. We evisit that question and ask if thee is a spatial dimension that the pevious liteatue has failed to contol fo. Ou findings suggest that thee is an impotant spatial dimension to the adoption of these laws that needs to be addessed. We also find that fo many cimes thee ae significant spillove effects, suggesting that adoption of these laws by the own state is associated with inceases in cime in adjacent states. This is an impotant contibution, as spillove effects in the cime liteatue ae likely to be pesent but ae undestudied. 8

9 Refeences Anselin, Luc. and Anil Bea (1998). Spatial Dependence in Linea Regession Models with an Intoduction to Spatial Econometics, in Ullah A and DEA Giles (Eds.), Handbook of Applied Economic Statistics. New Yok: Macel Dekke. Elhost, J. Paul (2010). Spatial Panel Data Models, in Fische M.M. and A. Getis (Eds.), Handbook of Applied Spatial Analysis. Belin: Spinge. Elhost, J.P. (2012). Matlab Softwae fo Spatial Panels. Intenational Regional Science Review, August 1, 2012, doi: / Di Tella, R., and E. Schagodsky, Do Police Reduce Cime? Estimates using the Allocation of Police Foces afte a Teoist Attack. The Ameican Economic Review, 94, Daca, M., S.J. Machin, and R. Witt, Panic in the Steets of London: Police, Cime, and the July 2005 Teoist Attacks. The Ameican Economic Review, 101, Klick, J. and A. Tabaok, Using Teo Alet Levels to Estimate the Effect of Police on Cime. Jounal of Law and Economics, 48, LeSage, James P. and R. Kelley Pace (2009). Intoduction to Spatial Econometics. Boca Raton: CRC Pess. Lott, John R., J. and David B. Mustad (1997). Cime, Deteence, and Right-to-Cay Concealed Handguns. Jounal of Legal Studies, 26(1),

10 Table 1: Summay Statistics Cime Rate Minimum Maximum Mean Violent Cime Mude Rape Robbey Assault Popety Cime Buglay Laceny Moto Vehicle Theft Notes: Violent cime is the sum of mude, ape, obbey, and assault. Popety cime is the sum of buglay, laceny, and MVT. 10

11 Table 2: Effect of Shall Cay Laws on Log Cime Rate Spatial Dependent Vaiable Diect Effect Indiect Effect Total Effect Autocoelation Paamete: ρ Violent Cime ( ) ( ) ( ) ( ) Mude ( ) ( ) ( ) ( )*** Rape ( ) ( )*** ( )** ( )*** Robbey ( )** ( )*** ( )*** ( ) Assault ( )** ( ) ( ) ( )*** Popety Cime ( )** ( )* ( )** ( )*** Buglay ( ) ( ) ( ) ( ) Laceny ( )*** ( )* ( )*** ( )*** Moto Vehicle Theft ( )*** ( )** ( )*** ( ) Notes: *** indicates statistical significance at the 1% level, ** indicates statistical significance at the 5% level, and * indicates statistical significance at the 10% level. Violent cime is the sum of mude, ape, obbey, and assault. Popety cime is the sum of buglay, laceny, and MVT. 11