INEQUALITY AND VIOLENT CRIME *

Transcription

1 INEQUALITY AND VIOLENT CRIME * Pablo Fajnzylber Daniel Lederman Norman Loayza Universiy of Minas Gerais The World Bank The World Bank Forhcoming in The Journal of Law and Economics Augus 2001 Absrac In his aricle we ake an empirical cross-counry perspecive o invesigae he robusness and causaliy of he link beween income inequaliy and crime raes. Firs, we sudy he correlaion beween he Gini index and, respecively, homicide and robbery raes along differen dimensions of he daa (wihin and beween counries). Second, we examine he inequaliy-crime link when oher poenial crime deerminans are conrolled for. Third, we conrol for he likely join endogeneiy of income inequaliy in order o isolae is exogenous impac on homicide and robbery raes. Fourh, we conrol for he measuremen error in crime raes by modelling i as boh unobserved counry-specific effecs and random noise. Lasly, we examine he robusness of he inequaliy-crime link o alernaive measures of inequaliy. The sample for esimaion consiss of panels of non-overlapping 5-year averages for 39 counries over in he case of homicides, and 37 counries over in he case of robberies. We use a variey of saisical echniques, from simple correlaions o regression analysis and from saic OLS o dynamic GMM esimaion. We find ha crime raes and inequaliy are posiively correlaed (wihin each counry and, paricularly, beween counries), and i appears ha his correlaion reflecs causaion from inequaliy o crime raes, even conrolling for oher crime deerminans. * We are graeful for commens and suggesions from Francois Bourguignon, Dane Conreras, Francisco Ferreira, Edward Glaeser, Sam Pelzman, Debraj Ray, Luis Servén, and an anonymous referee. N. Loayza worked a he research group of he Cenral Bank of Chile during he preparaion of he paper. This sudy was sponsored by he Lain American Regional Sudies Program, The World Bank. The opinions and conclusions expressed here are hose of he auhors and do no necessarily represen he views of he insiuions o which hey are affiliaed. 1

2 INEQUALITY AND VIOLENT CRIME I. Inroducion The relaionship beween income inequaliy and he incidence of crime has been an imporan subjec of sudy since he early sages of he economics lieraure on crime. According o Becker's (1968) analyical framework, crime raes depend on he risks and penalies associaed wih apprehension and also on he difference beween he poenial gains from crime and he associaed opporuniy cos. These ne gains have been represened heoreically by he wealh differences beween he rich and poor, as in Bourguignon (2000), or by he income differences among complex heerogeneous agens, as in Imrohoroglu, Merlo, and Ruper (2000). Similarly, in heir empirical work, Fleisher (1966), Ehrlich (1973), and more recenly Kelly (2000) have inerpreed measures of income inequaliy as indicaors of he disance beween he gains from crime and is opporuniy coss. The relaionship beween inequaliy and crime has also been he subjec of sociological heories on crime. Broadly speaking, hese have developed as inerpreaions of he observaion ha "wih a degree of consisency which is unusual in social sciences, lower-class people, and people living in lower-class areas, have higher official crime raes han oher groups" (Braihewaie 1979, 32). One of he leading sociological paradigms on crime, he heory of "relaive deprivaion," saes ha inequaliy breeds social ensions as he less well-off feel dispossessed when compared o wealhier people (see Sack 1984 for a criical view). The feeling of disadvanage and unfairness leads he poor o seek compensaion and saisfacion by all means, including commiing crimes agains boh poor and rich. I is difficul o disinguish empirically beween he economic and sociological explanaions for he observed correlaion beween inequaliy and crime. The observaion ha mos crimes are infliced by he poor on he poor does no necessarily imply ha he economic heory is invalid given ha he characerisics of vicims depend no only on heir relaive wealh bu also on he disribuion of securiy services across communiies and social classes. In fac, crime may be more prevalen in poor communiies because he disribuion of police services by he sae favors rich neighborhoods (Behrman and Craig 1987; Bourguignon 2000) or because poor people demand lower levels of securiy given ha i is a normal good (Pradhan and Ravallion 1998). Similarly, conrasing or consisen evidence on he effec of inequaliy on differen ypes of crime canno be used o conclusively rejec one heory in favor of he oher. For example, if income inequaliy leads 2

3 o higher hef and robbery raes bu no o higher homicide raes (as Kelly 2000 finds for he Unied Saes), he economic model could sill be valid given ha, firs, homicides are also commied for profi-seeking moives and, second, homicide daa are more reliable and produces more precise regression esimaes han propery crime daa. By he same oken, if income inequaliy leads o boh higher robbery and higher homicide raes (as we find in his cross-counry paper), we canno conclude ha he sociological model is incorrec because social deprivaion can have boh non-pecuniary and pecuniary manifesaions. A any rae, he objecive of his paper is no o disinguish beween various heories of he link beween inequaliy and crime; raher, we aemp o provide a se of sylized facs on his relaionship from a cross-counry perspecive. This iniial evidence could hen be used in furher, more analyically-oriened, research o discriminae among compeing heories. As he preceding remarks ry o convey, he correlaion beween income inequaliy and crime is a opic ha has inrigued social scieniss from various disciplines. Mos economic sudies on he deerminans of crime raes have used primarily microeconomic-level daa and focused mosly on he U.S. (see Wie 1980; Tauchen, Wie and Griesinger 1994; Grogger 1997; and Mocan and Rees 1999). In he 1990s he ineres on cross-counry sudies awakened, in par due o he appearance of inernaionally comparable daa ses on naional income and producion (Summers and Heson 1988), income inequaliy (Deininger and Squire 1996), and crime raes (Unied Naions Crime Surveys and World Healh Organizaion). In one of hese cross-counry sudies, Fajnzylber, Lederman, and Loayza (2001) find ha income inequaliy, measured by he Gini index, is an imporan facor driving violen crime raes across counries and over ime. Far from seling he issue, his resul opened a variey of quesions on he plausible ineracions beween crime raes, measures of income disribuion, and oher poenial deerminans of crime. Some of hese quesions refer o he robusness of he crime-inequaliy link o changes in he sample of counries, he daa dimension (ime-series or cross-counry), he mehod of esimaion, he measures of inequaliy and crime, and he ypes of conrol variables. Oher quesions pu in doub he direc effec of inequaliy on crime. For insance, Bourguignon (1998, 22) argues ha he significance of inequaliy as a deerminan of crime in a cross-secion of counries may be due o unobserved facors affecing simulaneously inequaliy and crime raher han o some causal relaionship beween hese wo variables. In his aricle we ake an empirical cross-counry perspecive o invesigae he robusness and causaliy of he link beween inequaliy and crime raes. Figures 1 and 2 plo he simple 3

4 correlaion beween he Gini index and, respecively, he homicide and robbery raes in a panel of cross-counry and ime-series observaions. In boh cases he correlaion is posiive and significan. In wha follows, we go behind his correlaion o assess issues of robusness and causaliy. We presen he sylized facs saring from he simples saisical exercises and moving gradually o a dynamic economeric model of he deerminans of crime raes. Firs, we sudy he correlaion beween he Gini index and, respecively, homicide and robbery raes along differen dimensions of he daa, namely, beween counries, wihin counries, and pooled cross-counry and ime-series. Second, along he same daa dimensions, we examine he link beween income inequaliy and homicide and robbery raes when oher poenial crime deerminans are conrolled for. These include he level of developmen (proxied by real GNP per capia), he average years of educaion of he adul populaion, he growh rae of GDP, and he level of urbanizaion. We also include he incidence of crime in he previous period as an addiional explanaory variable, hus making he crime model dynamic. Third, we conrol for he likely join endogeneiy of income inequaliy in order o isolae is exogenous impac on he wo ypes of crime under consideraion. Fourh, we conrol for he measuremen error in crime raes by modelling i as boh an unobserved counry-specific effec and random noise. We correc for join endogeneiy and measuremen error by applying an insrumenal-variable esimaor for panel daa. Fifh, using he same panel esimaor, we examine he robusness of he inequaliy-crime link o alernaive measures of inequaliy such as he raio of he income share of he poores o he riches quinile, an index of income polarizaion (calculaed following Eseban and Ray 1994), and an indicaor of educaional inequaliy (aken from De Gregorio and Lee 1998). Lasly, we es he robusness of his link o he inclusion of addiional variables ha may be driving boh inequaliy and crime, such as he populaion s ehno-linguisic fracionalizaion, he availabiliy of police in he counry, a Lain-America specific effec, and he share of young males in he naional populaion. As said above, his paper adops a comparaive cross-counry perspecive. Alhough here are well-known advanages o using micro-level daa for crime sudies, cross-naional comparaive research has he following advanage. Using counries as he unis of observaion o sudy he link beween inequaliy and crime is arguably appropriae because naional borders limi he mobiliy of poenial criminals more han neighborhood, ciy, or even provincial boundaries do. In his way, every (counry) observaion conains independenly all informaion on crime raes, inequaliy 4

5 measures, and oher crime deerminans, hus avoiding he need o accoun for cross-observaion effecs. The main conclusion of his aricle is ha an increase in income inequaliy has a significan and robus effec of raising crime raes. In addiion, he GDP growh rae has a significan crimereducing impac. Since he rae of growh and disribuion of income joinly deermine he rae of povery reducion, he wo aforemenioned resuls imply ha he rae of povery alleviaion has a crime-reducing effec. The res of he paper is organized as follows. Secion II presens he daa and basic sylized facs. Secion III inroduces he mehodology and presens he resuls from he GMM esimaions, including several robusness checks. Secion IV concludes. II. Daa and sylized facs This secion reviews he daa and presens he basic sylized facs concerning he relaionship beween violen crime raes and income inequaliy. Secion II.A presens he sample of observaions used in he various economeric exercises in he paper. Secions II.B and II.C review he qualiy and sources of daa for he dependen variable (crime raes) and he main explanaory variable (income inequaliy), respecively. Deailed definiions and sources of all variables used in he paper are presened in Appendix Table A1. Secion II.D examines he bivariae correlaions beween homicide and robbery raes and he Gini coefficien of income inequaliy. Finally, Secion II.E presens OLS esimaes of mulivariae regression for boh ypes of crime. A. Sample of observaions We work wih a pooled sample of cross-counry and ime-series observaions. The imeseries observaions consis of non-overlapping five-year averages spanning he period for homicides and for robberies. The pooled sample is unbalanced, wih a mos 6 (imeseries) periods per counry. All counries included in he samples have a leas wo consecuive fiveyear observaions. The sample for he homicide regressions conains 20 indusrialized counries; 10 counries from Lain America and he Caribbean; 4 from Easern and Cenral Europe; 4 from Eas Asia, Souh Asia, and he Pacific; and 1 from Africa. The sample for robberies conains 17 indusrialized counries; 5 counries from Lain America and he Caribbean; 4 from Easern and Cenral Europe; 10 from Eas Asia, Souh Asia, and he Pacific; and 1 from Africa. Appendix ables B1 and B2 show he summary saisics for, respecively, homicide and robbery raes for each counry in he sample. 5

6 B. Naional crime saisics We proxy for he incidence of violen crime in a counry by is rae of inenional homicide and robbery raes. These raes are aken wih respec o he counry s populaion; specifically, hey are he number of homicides/robberies per 100,000 people. Cross-counry sudies of crime have o face severe daa problems. Mos official crime daa are no comparable across counries given ha each counry suffers from is own degree of underreporing and defines cerain crimes in differen ways. Underreporing is worse in counries where he police and jusice sysems are no reliable, where he level of educaion is low, and perhaps where inequaliy is high. Counry-specific crime classificaions, arising from differen legal radiions and differen culural percepions of crime, also hinder cross-counry comparisons. The ype of crime ha suffers he leas from underreporing and idiosyncraic classificaion is homicide. I is also well documened ha he incidence of homicide is highly correlaed wih he incidence of oher violen crimes (see Fajnzylber, Lederman, and Loayza 2000). These reasons make he rae of homicides a good proxy for crime, especially of he violen sor. To accoun for likely non-lineariies in he relaion beween homicide raes and is deerminans, we use he homicide rae expressed in naural logarihms. The homicide daa we use come from he World Healh Organizaion (WHO), which in urn gahers daa from naional public healh records. In he WHO daa se, a homicide is defined as a deah purposefully infliced by anoher person, as deermined by an accredied public healh official. The oher major source of cross-counry homicide daa is he Unied Naions World Crime Survey, which collecs daa from naional police and jusice records. 1 In his paper we use he WHO daa se because of is larger ime coverage for he counries included. Couning wih sufficien ime coverage is essenial for he panel-daa economeric procedures we implemen (see Secion III below). To complemen he analysis on he homicide rae, we consider he robbery rae as a second proxy for he incidence of crime. Alhough daa on robberies is less reliable han homicide daa for cross-counry comparisons, i is likely o be more reliable han daa on lesser propery crimes such as hef. This is so because robberies are propery crimes perperaed wih he use or hrea of violence; consequenly, heir vicims have a double incenive o repor he crime, namely, he physical and psychological rauma caused by he use of violence and he loss of propery. Robbery s close connecion wih propery crimes, o which economic heory is more readily applicable, makes 1 See Fajnzylber, Lederman, and Loayza (1998) for a descripion of he Unied Naions Crime Survey saisics. 6

7 is sudy a good complemen o ha of homicide. The robbery daa we use come from he Unied Naions World Crime Survey. The robbery raes are also expressed in naural logs. C. Naional income inequaliy daa Mos of he empirical exercises presened below use he Gini coefficien as he proxy for income inequaliy. In a couple of insances, we also use he raio of he income share of he poores o he riches quinile of he populaion. In addiion, we use income quinile shares o consruc a measure of income polarizaion (see Appendix C for deails). Daa on he Gini coefficien and he income quinile shares come from he Deininger and Squire (1996) daabase. We only use wha hese auhors label high-qualiy daa, which hey idenify hrough he following hree crieria (p ). Firs, income and expendiure daa are obained only from household or individual surveys. In paricular, high-qualiy Gini index and income quinile shares are no based on esimaes generaed from naional accouns and assumpions abou he funcional form of he disribuion of income aken from oher counries. Second, he measures of inequaliy are derived only from naionally represenaive surveys. Thus, hese daa do no suffer from biases semming from esimaes based on subses of he populaion in any counry. Third, primary income and expendiure daa are based on comprehensive coverage of differen sources of income and ype of expendiure. Therefore, he high-qualiy inequaliy daa do no conain biases derived from he exclusion of non-moneary income. D. Bivariae correlaions Table 1 presens he bivariae correlaions beween boh crime raes and he Gini coefficien for hree dimensions of he daa, namely, pooled levels, pooled firs-differences, and counry averages. The firs se conains he correlaion esimaed for he pooled sample in levels, ha is, using boh he cross-counry and over-ime variaion of he variables. The second se presens he correlaions beween he firs differences of he crime raes and he firs differences of he Gini index. These correlaions, herefore, reflec only he over-ime relaionship beween crime raes and inequaliy, hus conrolling for any counry characerisics ha are fixed over ime, such as geographic locaion or culural heriage. The hird se shows he correlaions across counries only, based on he counry averages for he whole periods ( for homicides and for robberies). Consequenly, hese correlaions do no reflec he influence of counry characerisics ha change over ime. All correlaions of boh crime raes wih he Gini coefficien are posiive and saisically significan (he larges p-value is 0.12). The smalles, bu sill posiive, correlaions are hose esimaed using he daa in firs differences. While for he robbery rae here is no much 7

8 dispariy beween he correlaions esimaed for he hree daa dimensions, in he case of homicides he correlaion drops from 0.54 for he daa in pooled levels and 0.58 for counry averages o 0.26 for firs differences. This resul suggess ha almos half of he correlaion beween he Gini and homicide raes is due o counry characerisics ha are persisen over ime. Table 2 presens a second group of bivariae correlaions for wo cus of he cross-counry sample, namely wihin counries and wihin ime periods. The able conains he mean and he median of he correlaions beween each crime rae and he Gini index, obained using, respecively, all he observaions available for each counry ( wihin-counry ) and for each five-year period ( wihin-period ). In addiion, we repor he percenage of, respecively, counries and periods for which he correlaion beween crime raes and inequaliy is posiive. All he esimaed mean and median correlaions are posiive. In fac, for each of he five-year periods, he cross-counry correlaion of crime and inequaliy is posiive, while for abou 60% of he counries, he ime-series correlaion is also posiive. The fac ha for boh homicides and robberies he median wihincounry correlaion is higher han he mean indicaes ha here are some ouliers having negaive correlaions ha depress he average. An imporan problem for he inerpreaion of hese bivariae correlaions is ha he apparen posiive link beween crime raes and income inequaliy migh in fac be driven by oher variables ha are correlaed wih boh of hem. To address his issue, he following secion sudies he relaionship beween he Gini index and homicide and robbery raes, while conrolling for oher poenial correlaes of crime. E. Mulivariae regression analysis Based on previous micro- and macro-level crime sudies, we consider he following variables as he basic correlaes of homicide and robbery raes in addiion o inequaliy measures: 1) GNP per capia (in logs) as boh a measure of average naional income and a proxy for overall developmen (from Loayza e al. 1998). 2) The average number of schooling years of he adul populaion as a measure of average educaional aainmen (from Barro and Lee 1996). 3) The GDP growh rae o proxy for employmen and economic opporuniies in general (from Loayza e al. 1998). 4) The degree of urbanizaion of each counry, which is measured as he percenage of he populaion in he 8

9 counry ha lives in urban selemens (from World Bank daa). Appendix Table A1 conains a deailed descripion of he daa sources for hese and he oher variables used in his aricle. 2 The basic OLS mulivariae regression resuls are shown in Table 3. The homicide and robbery regressions were run on he same daa dimensions as in Table 1. The firs regression was esimaed using he pooled sample in levels; he second uses pooled firs differences, hus focusing on he wihin-counry variaion; and he hird regression uses counry averages o isolae he pure cross-counry dimension of he daa. The resuls indicae ha he Gini index mainains is posiive and significan correlaion wih boh crime raes. As expeced, he models esimaed in firsdifferences presen he lowes magniudes for he coefficien on he Gini index. When he crosscounry variaion is aken ino accoun, he coefficien on he Gini index increases from 0.02 o 0.06 in he case of homicides and from 0.04 o 0.11 in he case of robberies. Hence in boh cases, wohirds of he condiional correlaion beween crime raes and inequaliy seems o be due o counry characerisics ha do no change over ime. Of he addiional crime regressors, he mos imporan one seems o be he GDP growh rae. This variable appears consisenly wih a negaive sign, as expeced, for boh crimes. I is also saisically significan, alhough only marginally so in he robbery regression using counry averages. In conras, he oher crime regressors do no show a consisen sign or are no saisically significan in a leas half of he specificaions. The OLS esimaes jus discussed migh be biased for hree reasons. Firs, hese regressions do no ake ino accoun he possibiliy ha crime ends o persis over ime. Tha is, hey ignore ye anoher poenial deerminan of crime, which is he crime rae of he previous period. Second, hese esimaes migh be biased due o he possibiliy ha crime raes hemselves (our dependen variables) migh affec he righ-hand side variables. Third, i is very likely ha he crime raes are measured wih error, and his error migh be correlaed wih some of he explanaory variables, paricularly income inequaliy. The following secion examines alernaive specificaions ha include he lagged crime rae as an explanaory variable, accoun for cerain ypes of measuremen error, and allow for joinly endogenous explanaory variables. 2 Appendix Table B3, panel A, conains he marix of bivariae correlaions among he basic se of dependen and explanaory variables. Noe ha he Gini is indeed significanly correlaed wih log of income per capia (negaively), educaional aainmen of he adul populaion (negaively), and he GDP growh rae (posiively). 9

10 III. A Dynamic Empirical Model of Crime Raes A. Economeric Issues The evidence presened so far suggess ha, from a cross-counry perspecive, here is a robus correlaion beween he incidence of crimes and he exen of income inequaliy. However, here are several issues we mus confron in order o assure ha his correlaion is no he resul of esimaion biases. Firs, as menioned, he incidence of violen crime appears o have inerial properies (i.e., persisence) ha are noed in he heoreical lieraure and documened in he micro and macro empirical work (Glaeser, Sacerdoe, and Scheinkman 1996; Fajnzylber, Lederman, and Loayza 1998). To accoun for criminal ineria, we need o work wih a dynamic, lagged-dependen economeric model. The second issue we mus address is ha he relaionship beween violen crime raes and heir deerminans is ofen characerized by a wo-way causaliy. Failure o correc for he join endogeneiy of he explanaory variables would lead o inconsisen coefficiens, which depending on he sign of he reverse causaliy would render an over- or under-esimaion of heir effecs on violen crime raes. We address he problem of join endogeneiy by employing an insrumenalvariable procedure applied o dynamic models of panel daa. This is he Generalized-Mehod-of- Momens (GMM) esimaor ha uses he dynamic properies of he daa o generae proper insrumenal variables. The hird esimaion difficuly is ha despie our use of inenional homicide and robbery raes as he bes proxies for he incidence of violen crimes, i is likely ha measuremen error sill afflics our crime daa. Ignoring his problem migh also resul in biased esimaes especially because crime underreporing is no random measuremen error bu is srongly correlaed wih facors affecing crime raes such as inequaliy, educaion, he average level of income, and he rae of urbanizaion. Even if measuremen error were random, he coefficien esimaes would sill be biased given he dynamic naure of our model. To conrol for measuremen error, we model i as eiher random noise or a combinaion of an unobserved counry-specific effec and random noise. Economeric mehodology. We implemen a generalized-mehod-of-momens (GMM) esimaor applied o dynamic (lag-dependen-variable) models ha use panel daa. This mehod was developed in Arellano and Bond (1991) and Arellano and Bover (1995). I conrols for (weak) endogeneiy hrough he use of insrumenal variables consising of appropriaely lagged values of he explanaory variables. When he model does no include an unobserved counry-specific effec, he model is esimaed in levels, for boh he regression equaion and he se of insrumens. This is 10

11 called he GMM levels esimaor. When he model includes an unobserved counry-specific effec (resuling from ime invarian omied facors such as sysemaic measuremen error), he model is esimaed in boh differences and levels, joinly in a sysem. This is called he GMM sysem esimaor. For each esimaor, he correc specificaion of he regression equaion and is insrumens is esed hrough a Sargan-ype es and a serial-correlaion es. 3 Appendix D presens he economeric mehodology in deail. B. Basic Resuls Table 4 shows GMM esimaes for he basic se of deerminans of he homicide and he robbery raes, respecively in he lef- and righ-hand side panels. The firs wo columns of each panel presen he resuls obained for he model ha assumes no unobserved counry-specific effecs, esimaed using he GMM-levels esimaor. The difference beween he firs and he second column of each panel is relaed o he samples used in each case, which are resriced o, respecively, counries wih a leas wo and hree consecuive observaions. The hird column of each panel repors he resuls obained for he model ha allows unobserved counry-specific effecs, esimaed using he GMM-sysem esimaor. The sysem esimaor uses no only levels bu also differences of he variables and requires a leas hree consecuive observaions for each counry. Thus, resuls in he second and he hird columns of each panel are obained from he same samples bu are based on differen esimaors. In he basic levels specificaion for homicides, and using he larges possible sample (firs column), he lagged homicide rae, he level of income inequaliy, and he growh rae of GDP have significan coefficiens wih he expeced signs. The rae of urbanizaion also appears o be significanly associaed wih homicide raes bu unexpecedly, in a negaive way: counries wih a larger fracion of heir populaion in ciies would appear o have lower crime raes. Qualiaively similar resuls are obained wih he smaller sample used in column 2, alhough in his case he populaion s average income and educaional aainmen are significan, boh wih negaive signs. Regardless of he sample, boh he Sargan and he serial correlaion ess validae he resuls obained using he levels esimaor for homicides. 3 In boh ess he null hypohesis denoes correc specificaion. For he GMM-levels esimaor, serial correlaion of any order implies misspecificaion, while for he GMM-sysem esimaor, only second- and higher-order serial correlaion denoes misspecificaion (see Appendix D for deails). 11

12 error). 6 Third, he GDP growh rae has a significanly negaive effec on he homicide rae. Column 3 shows he resuls using he GMM-sysem esimaor. As in he case of he levels esimaor, boh he Sargan and he serial correlaion ess suppor he specificaion of he sysem esimaor. The main resuls are as follows. Firs, homicide raes show a sizeable degree of ineria. The coefficien on he lagged homicide rae is close o uniy (hough no as large as when counry-specific effecs are ignored). The size of his coefficien implies ha he half-life of a uni shock lass abou 17 years. 4 Second, income inequaliy, measured by he Gini index, has a posiive and significan effec on homicide raes. Using he corresponding coefficien esimae we can evaluae he crime-reducing effec of a decline in inequaliy in a given counry. If he Gini index falls permanenly by he wihincounry sandard deviaion in he sample (abou 2.4 percenage poins), he inenional homicide rae will decrease by 3.7 percen in he shor run and 20 percen in he long run. 5 If he Gini index were o fall by is cross-counry sandard deviaion, he decline in inequaliy would be much larger; however, a change in inequaliy by he magniude of cross-counry differences is implausibly large o be aained by a counry in a reasonable amoun of ime. I is noeworhy ha he esimaed coefficien on he Gini index is much larger wih he sysem esimaor han wih he levels esimaor, alhough hey are boh based on a common sample of 27 counries. I is possible ha he higher magniude obained wih he sysem esimaor is due o he fac ha his esimaor correcs for he posiive correlaion beween inequaliy and he degree of crime under-reporing (i.e., he measuremen According o our esimaes, he impac of a permanen one-percenage poin increase in he GDP growh rae is associaed wih a 4.3 percen fall in he homicide rae in he shor run and a 23 percen decline in he long run. Fourh, our measure of educaional aainmen remains negaive and significan bu he GNP per capia and he urbanizaion rae now lack saisical significance. The paern of significance (or lack hereof) of he basic explanaory variables is quie robus o all he 4 The half-life (HL) of a uni shock is obained as follows: HL=ln(0.5)/ln(α), where α is he esimaed auoregressive coefficien. According o column 3, Table 4, α= The wihin counry sandard deviaion is calculaed afer applying a wihin ransformaion o he Gini index, which amouns o subracing o each observaion he average value of ha variable for he corresponding counry and adding he global mean (based on all observaions in he sample). 6 This finding is ineresing because we expeced ha he magniude of he effec of he levels esimaor would be higher, because he analysis of he bivariae and condiional OLS correlaions showed ha a large porion of he correlaion beween he crime raes and he Gini were due o counry characerisics ha do no change over ime, and ha are los in he firs-differenced daa. 12

13 various empirical exercises of his paper. I is also similar o wha we found in our firs empirical cross-counry sudy on violen crime raes (see Fajnzylber, Lederman, and Loayza 2001). In he righ-hand-side panel of able 4, we repor analogous esimaes for he deerminans of robbery raes. For robberies, he resuls are qualiaively similar across samples and specificaions. In he case of he lagged dependen variable, he growh rae, and income inequaliy, he resuls for robberies are similar o hose for homicides. Indeed, here is evidence ha robberies are also subjec o a sizeable degree of ineria, alhough somewha smaller han in he case of homicides: he half life of he effecs of a permanen shock is beween 11 and 12 years, depending on he specificaion. The coefficiens on income inequaliy are also posiive and significan in all specificaions. Based on he resuls in column 6, a fall of one wihin-counry sandard deviaion in he Gini coefficien (abou 2.1 percen) leads o a 6.5-percen decline of he robbery rae in he shor run and a 23.2-percen decline in he long run. Similarly, a permanen one-percenage poin increase in he GDP growh rae produces an 11- and 45-percen fall of he robbery rae in he shor and long runs, respecively. As in he case of homicides, noe ha he magniude of he esimaed impac of he Gini index on robbery raes is larger for he sysem han for he levels esimaor (for equal samples, of course). As for he oher variables, heir signs and significance vary from homicides o robberies. The average income appears wih a negaive sign, bu is significan only for he smaller samples (columns 5 and 6). Educaional aainmen and urbanizaion are significan in all specificaions, boh wih a posiive sign. The laer resul was expeced, as robberies appear o be mosly an urban phenomenon. However, he finding ha robberies are posiively associaed wih educaion is puzzling. Regarding he GMM specificaion ess for he robbery models, all regressions are suppored by he Sargan es on he validiy of he insrumenal variables. However, in he levels regressions here is evidence ha he residuals suffer from firs-order serial correlaion, especially in he case of he larges sample of 37 counries. C. Alernaive measures of inequaliy This secion sudies he crime effec of alernaive measures of income inequaliy and hus checks he robusness of he resuls obained wih he Gini coefficien. The alernaive measures we consider are he raio of income of he riches o he poores quinile of he populaion, an index of income polarizaion, and he sandard deviaion of he educaional aainmen of he adul 13

14 populaion. 7 Given he fac ha he new variables lead o furher resricions in sample size, we choose o mainain our basic levels specificaion, which allows he larges possible sample in he conex of a dynamic model. The resuls are presened in Table 5. In columns 1 and 4 he raio of he income shares of he 1 s o he 5 h quinile is subsiued for he Gini coefficien in he basic regressions for homicides and robberies, respecively. The resuls are qualiaively analogous o hose repored in able 4. The new measure of income inequaliy is posiively and significanly associaed wih boh crime raes. A permanen fall of one wihin-counry sandard deviaion in he quinile raio (abou 1.3) leads o a 2-percen decline in he inenional homicide rae in he shor-run and a 16.2-percen fall in he long run. The corresponding impacs on he robbery rae are 4.7 and 21.5 percen, respecively in he shor and he long runs. In furher exercises (no presened in he ables), we examined he significance of he income levels of he poor and rich separaely. We found ha when he income of he poor was included by iself, is coefficien was no generally significan. When we included he incomes of boh he poor and he rich, neiher was saisically significan, which can be explained by he fac ha hey are highly correlaed wih each oher. These resuls conras wih he significan crime-inducing effec of he difference beween he income levels of he rich and poor (or more precisely he log of he raio of op o boom income quiniles of he populaion). Coupled wih he general lack of significance of per capia GNP in our crime regressions, he aforemenioned resuls indicae ha i is no he level of income wha maers for crime bu he income differences among he populaion. In columns 2 and 5, we subsiue an index of polarizaion for he Gini index. Some auhors argue ha a sociey s degree of polarizaion may be he cause of rebellions, civil wars, and social ension in general (Eseban and Ray 1994; Collier and Hoeffler 1998). Similar argumens can be applied o violen crime. The concep of polarizaion was formally inroduced by Eseban and Ray (1994). Though linked o sandard measures of income inequaliy, he polarizaion indicaors proposed by hese auhors do no only consider he disance beween he incomes of various groups bu also he degree of homogeneiy wihin hese groups. Thus, he social ension ha leads o violence and crime would be produced by he heerogeneiy of inernally srong groups. Following he principles proposed by Eseban and Ray, we consruced a polarizaion index from daa on naional income shares by quiniles (see Appendix C for deails). The resuls concerning polarizaion presened in Table 5 are similar o hose obained wih he oher inequaliy indicaors. The effec of 7 Appendix Table B3, panel B, shows he bivariae correlaions beween he Gini index and he hese hree alernaive indicaors of inequaliy. As expeced, hese correlaions are saisically significan and high in magniude, ranging from 14

15 polarizaion on crime appears o be posiive and significan for boh homicides and robberies, and he signs and significance of he oher core variables are mosly unchanged. As for he size of he polarizaion coefficien, a permanen reducion of one wihin-counry sandard deviaion (abou 7.6 percen) in his variable leads o a decline in he homicide and he robbery rae of, respecively, 3.8 and 3 percen in he shor run. In he long run, he corresponding reducions are 28.7 and 19.2 percen for he homicide and robbery raes. Columns 3 and 6 examine wheher he underlying inequaliy of educaional aainmen has he same impac on crime raes as he Gini index does. We measure he inequaliy of educaional aainmen as he sandard deviaion of schooling years in he adul populaion, as esimaed by De Gregorio and Lee (1998). The basic resuls discussed above remain essenially unalered. When we subsiue he measure of educaion inequaliy for he Gini index, he esimaed coefficien of his variable acquires he sign of he Gini index in he benchmark regression, bu appears significan only in he robbery regression. A fall of one wihin-counry sandard deviaion (abou 4 percen) in our measure of educaional inequaliy leads o a reducion in he robbery rae of 3.6 and 27.6 percen in he shor and long runs, respecively. D. Addiional Conrols This secion focuses on he poenial role played by addiional conrol variables in he crimeinducing effec of income inequaliy. 8 The regression resuls are presened in Table 6. Columns 1 and 5 show he resuls for he regression on he basic explanaory variables, wih he addiion of a measure of ehnic diversiy. This measure is he index of ehno-linguisic fracionalizaion employed by Mauro (1995) and Easerly and Levine (1997) in heir respecive cross-counry growh sudies. Our resuls indicae ha his index is significanly associaed wih higher homicide raes bu is link wih robberies is no significan (wih a negaive poin esimae). As o is quaniaive effec on homicides, an increase of one sandard deviaion (abou 4 percen) in ehno-linguisic fracionalizaion is associaed wih an increase in he homicide rae of 3.8 and 31.6 percen in he shor and long runs, respecively. Mos imporanly for our purposes, he Gini index keeps is sign, size, and significance in he homicide and robbery regressions even conrolling for ehnic diversiy as a crime deerminan o Appendix Table B3, panel C, conains he bivariae correlaions beween hese new conrol variables and he se of basic variables used in he paper. Of he addiional conrol variables, only he share of young males in he naional populaion exhibis a high and significan correlaion wih he Gini index. This variable is also posiively and significanly correlaed wih boh crime raes. 15

16 Columns 2 and 6 consider he possibiliy ha he crime-inducing effec of he Gini coefficien in fac reflecs an unequal disribuion of proecion from he police and he judicial sysem. We do his by adding he number of police per capia o he core explanaory variables. 9 This is an average measure for he whole populaion and may no represen egaliarian proecion by he police and he law. However, i is an appropriae conrol under he assumpion ha an unequal disribuion of proecion is more likely o occur when here is scarciy of police resources. Alhough for homicides he number of police per capia does presen he expeced negaive sign, for boh crimes his variable presens saisically insignifican coefficiens. Mos imporanly, he sign, size, and saisical significance of he Gini coefficien appear o be unalered by he inclusion of his proxy for police deerrence. In columns 3 and 7 we add a Lain American dummy o he basic explanaory variables. We do i o assess wheher he apparen effec of inequaliy on crime is merely driven by a regional effec, given ha counries in Lain America have among he highes indices of income inequaliy in he world and, in many cases, also very high crime raes. We find ha in fac he Lain American dummy has a posiive coefficien in he regressions for boh crimes, alhough i is saisically significan only in he case of robberies. Quaniaively, he resuls sugges ha in Lain America he rae of robberies is 35 percen higher han wha our basic model predics, given he economic characerisics of he counries in ha region. Mos imporanly for our purposes, he signs and significance of our basic explanaory variables, especially he Gini index, are no alered by he inclusion of he Lain American dummy. Finally, columns 4 and 8 repor resuls of regressions in which we inroduce he percenage of young males (aged 15 o 29 years) in he populaion as an addiional explanaory variable. I is well known ha he rae of crime paricipaion of individuals is highes a he iniial sages of adulhood, so ha one could expec counries wih large populaions in hose ages o have high crime raes. A he same ime, counries wih younger adul populaions may experience more income inequaliy, hrough a Kuznes-like effec. The inclusion of he proporion of young males as a deerminan of crime allows us o es wheher he inequaliy-crime link is driven by his demographic facor. Our resuls indicae ha afer conrolling for our basic crime deerminans, he share of young males in he populaion does no have a saisically significan effec on eiher 9 We average he available observaions of his variable for he period, and hen we use he average as a consan observaion for all five-year periods in he regression. We do his o increase he number of usable observaions per counry and, mos imporanly, o minimize he reverse causaion of his variable o over-ime changes in homicide raes (hough his does no solve he cross-counry dimension of reverse causaion). 16

17 homicide or robbery raes. In fac, for he former crime, he poin esimae of ha variable is acually negaive. As in previous robusness exercises, conrolling for he proporion of young males does no lead o any subsanial change in he esimaed effec of inequaliy on crime. E. Povery Alleviaion and Crime Alhough he main objecive of his aricle is o analyze he relaionship beween income inequaliy and crime, our empirical findings sugges ha here is also an imporan correlaion beween he incidence of crime and he rae of povery alleviaion. This relaionship exiss as a consequence of he join effecs of income inequaliy and economic growh on crime raes. The level of povery in a counry is measured as he percenage of he populaion ha receives income below a hreshold level, which is usually deermined by he necessary caloric inake and he local moneary cos of purchasing he corresponding food baske. Simply pu, he level of povery is joinly deermined by he naional income level and by he paern of disribuion of his income. When a reducion in income inequaliy is coupled wih a rise in economic growh, he rae of povery alleviaion improves. Through he several economeric exercises performed in he paper, we find ha he GDP growh rae and he Gini index are he mos robus and significan deerminans of boh homicide and robbery raes. Consequenly, hese resuls also indicae ha he rae of change of povery is also relaed o he incidence of crime. Tha is, when povery falls more rapidly, eiher because income growh rises or he disribuion of income improves, hen crimes raes end o fall. Esimaing he precise effec of povery reducion on violen crime and designing a sraegy for crime-reducing povery alleviaion remain imporan opics for fuure research. IV. Conclusions The main conclusion of he paper is ha income inequaliy, measured by he Gini index, has a significan and posiive effec on he incidence of crime. This resul is robus o changes in he crime rae used as he dependen variable (wheher homicide or robbery), he sample of counries and periods, alernaive measures of income inequaliy, he se of addiional variables explaining crime raes (conrol variables), and he mehod of economeric esimaion. In paricular, his resul persiss when using insrumenal-variable mehods ha ake advanage of he dynamic properies of our cross-counry and ime-series daa o conrol for boh measuremen error in crime daa and he join endogeneiy of he explanaory variables. 17

18 In he process of arriving a his conclusion, we found oher ineresing resuls. The following are some of hem. Firs, he incidence of violen crime has a high degree of ineria, which jusifies early inervenion o preven crime waves. Second, violen crime raes decrease when economic growh improves. Since violen crime is joinly deermined by he paern of income disribuion and by he rae of change of naional income, we can conclude ha faser povery reducion leads o a decline in naional crime raes. And hird, he mean level of income, he average educaional aainmen of he adul populaion, and he degree of urbanizaion in a counry are no relaed o crime raes in a significan, robus, or consisen way. The main objecive of his paper has been o characerize he relaionship beween inequaliy and crime from an empirical perspecive. We have aemped o provide a se of sylized facs on his relaionship: Crime raes and inequaliy are posiively correlaed (wihin each counry and, paricularly, beween counries), and i appears ha his correlaion reflecs causaion from inequaliy o crime raes, even conrolling for oher crime deerminans. If any, he conribuion of his paper is empirical. Analyically, however, his paper has wo imporan shorcomings. Firs, we have no provided a way o es or disinguish beween various heories on he incidence of crime. In paricular, our resuls are consisen wih boh economic and sociological paradigms. Alhough our resuls for robbery (a ypical propery crime) confirm hose for homicide (a personal crime wih a variey of moivaions), his canno be used o rejec he sociological paradigm in favor of he economic one. The reason is ha he saisfacion ha he relaively-deprived people in sociological models seek for can lead o boh pure manifesaions of violence and illici appropriaion of maerial goods. A more nuanced economeric exercise han wha we offer here is required o shed ligh on he relaive validiy of various heories on he inequaliy-crime link. The firs shorcoming of he paper leads o he second, which is ha we have no idenified he mechanisms hrough which worse inequaliy leads o more crime. Uncerainy abou hese mechanisms raises a variey of quesions wih imporan policy implicaions. For insance, should police and jusice proecion be redireced o he poores segmens of sociey? How imporan for crime prevenion are income-ransfer programs in imes of economic recession? To wha exen should public auhoriies be concerned wih income and ehnic polarizaion? Do policies ha promoe he paricipaion in communal organizaions and help develop social capial among he poor also reduce crime? Hopefully, his paper will help sir an ineres on hese and relaed quesions on he prevenion of crime and violence. 18

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21 Sack, Seven "Income Inequaliy and Propery Crime: A Cross-Naional Analysis of Relaive Deprivaion Theory." Criminology 22(2): Summers, Rober, and Alan Heson The Penn World Table (Mark 5): An Expanded Se of Inernaional Comparisons, The Quarerly Journal of Economics 106: Tauchen, Helen, Ann Dryden Wie, and Harrie Griesinger Criminal Deerrence: Revisiing he Issue wih a Birh Cohor. Review of Economics and Saisics 76: Wie, Ann Dryden Esimaing he Economic Model of Crime wih Individual Daa. Quarerly Journal of Economics 94:

22 Figure 1: Income Disribuion and Inenional Homicide Raes, (5-year-averages) 5 4 Sub-Saharan Africa Eas and Souh Asia Easern Europe Lain America 3 OECD Inenional Homicide Raes (logs) Y=-1.5 (-4.8) (7.8) X Gini Coefficien Sub-Saharan Africa Eas and Souh Asia Easern Europe Lain America OECD Figure 2: Income Disribuion and Robbery Raes, (5-year-averages) Y=1.3 (2.2) (3.3) X Robbery Raes (logs) Gini Coefficien 22

23 Table 1: Pairwise Correlaions beween he Gini Index and, respecively, Homicide and Robbery Raes (p-values in parenhesis below he corresponding correlaion. N is he number of observaions) Homicides Robberies Pooled Levels (0.00) (0.00) N=148 N=132 Pooled Firs Differences* (0.01) (0.05) N=106 N=94 Counry Averages (0.00) (0.12) N=39 N=37 Source: Auhors' calculaions using daa from WHO, Moraliy Saisics, UN, World Crime Surveys, and Deininger and Squire (1997), A New Daa Se Measuring Income Inequaliy. Crime raes expressed in naural logarihms. (*) Differences are obained from consecuive counry-period observaions. Three observaions are los for homicides (one for robberies), for counries for which we have non-consecuive daa. Table 2: Wihin-Counry and Wihin-Period Pairwise Correlaions beween he Gini Index and, respecively, Homicide and Robbery Raes (in logs) (N is he number of observaions) Homicides Robberies Wihin-Counry Wihin-Period Wihin-Counry Wihin-Period Mean Correlaion Median Correlaion Percenage of Po siive Correlaions (N=39) (N=6) (N=37) (N=5) Source: Auhors' calculaions using daa from WHO, Moraliy Saisics, UN, World Crime Surveys, and Deininger and Squire (1997), A New Daa Se Measuring Income Inequaliy. Crime raes expressed in naural logarihms. 23

24 Table 3: Basic Economic Model (OLS esimaion) Homicides Daa Source: World Healh Organizaion Moraliy Saisics (WHO) Robbery Daa Source: Unied Naions (UN) World Crime Surveys (-saisics are presened below heir corresponding coefficiens) Sample: Pooled Pooled Firs- Counry- Pooled Pooled Firs- Counry- Levels Differences Averages Levels Differences Averages Dependen Variable (in logs): Homicide Rae Homicide Rae Homicide Rae Robbery Rae Robbery Rae Robbery Rae [1] [2] [3] [4] [5] [6] Income Inequaliy (Gini Coefficien) Growh Rae (% Annual Change in Real GDP) Average Income (Log of GNP per capia in US $) Urbanizaion (% urban populaion) Educaional Aainmen (Avg. Yrs. of Educ., Aduls) Inercep Adjused R-Squared No. Counries No. Observaions Source: Auhors' calculaions. For deails on definiions and sources of variables, see Appendix Table A1. 24

25 Table 4: Basic Economic Model (GMM esimaion) Homicides Daa Source: World Healh Organizaion Moraliy Saisics (WHO) Robbery Daa Source: Unied Naions (UN) World Crime Surveys (-saisics are presened below heir corresponding coefficiens) Dependen Variable (in logs): Regression Specificaion: Levels Homicide Rae Levels (*) Levels and Levels Robbery Rae Levels (*) Levels and Differences Differences [1] [2] [3] [4] [5] [6] Lagged Dependen Variable Income Inequaliy (Gini Coefficien) Growh Rae (% Annual Change in Real GDP) Average Income (Log of GNP per capia in US $) Urbanizaion (% of Pop. In Urban Ceners) Educaional Aainmen (Avg. Yrs. Of Educ., Aduls) Inercep No. Counries No. Obs SPECIFICATION TESTS (P-Values): (a) Sargan Tes (b) Serial Correlaion : Firs-Order Second-Order Source: Auhors' calculaions. For deails on definiions and sources of variables, see Appendix Table A1. (*) The sample is resriced o he counries ha have a leas hree consecuive observaions. 25

26 Table 5: Alernaive Inequaliy Measures (GMM levels esimaion) Homicides Daa Source: World Healh Organizaion Moraliy Saisics (WHO) Robbery Daa Source: Unied Naions (UN) World Crime Surveys (-saisics are presened below heir corresponding coefficiens) Dependen Variable (in logs): Homicide Rae Robbery Rae [1] [2] [3] [4] [5] [6] Lagged Dependen Variable Growh Rae (% Annual Change in Real GDP) Average Income (Log of GNP per capia in US $) Urbanizaion (% of Pop. In Urban Ceners) Educaional Aainmen (Avg. Yrs. Of Educ., Aduls) Inercep Raio of he 1s o he 5h quinile Income Polarizaion (Log of Income Polarizaion Index) Educaional Inequaliy (Sandard Deviaion of Schooling Years) No. Counries No. Obs SPECIFICATION TESTS (P-Values): (a) Sargan Tes (b) Serial Correlaion : Firs-Order Second-Order Source: Auhors' calculaions. For deails on definiions and sources of variables, see Appendix Table A1. 26

27 Table 6: Addiional Conrol Variables (GMM levels esimaion) Homicides Daa Source: World Healh Organizaion Moraliy Saisics (WHO) Robbery Daa Source: Unied Naions (UN) World Crime Surveys (-saisics are presened below heir corresponding coefficiens) Dependen Variable (in logs): Homicide Rae Robbery Rae [1] [2] [3] [4] [5] [6] [7] [8] Lagged Dependen Variable Income Inequaliy (Gini Coefficien) Growh Rae (% Annual Change in Real GDP) Average Income (Log of GNP per capia in US $) Urbanizaion (% of Pop. In Urban Ceners) Educaional Aainmen (Avg. Yrs. Of Educ., Aduls) Inercep Ehno-Linguisic Fracionalizaion Police (per 100,000 populaion) Lain America (dummy variable) Young Male Populaion (15-29 years old as % of oal populaion) No. Counries No. Obs SPECIFICATION TESTS (P-Values): (a) Sargan Tes (b) Serial Correlaion : Firs-Order Second-Order Source: Auhors' calculaions. For deails on definiions and sources of variables, see Appendix Table A1. 27

28 Appendix A: Daa Definiions and Sources Inenional Homicide Rae Table A1: Descripion and Sources of he Variables Variable Descripion Source Number of deahs purposely infliced by anoher person, per 100,000 populaion. GNP Per Capia Gini Index Educaional Aainmen GDP Growh Gross Naional Produc expressed in consan 1987 US prices and convered o U.S. dollars on he basis of he noional exchange rae proposed by Loayza e al. (1998). Income-based gini coefficien. Consruced by adding 6.6 o expendiure-based indexes o make hem comparable o income-based indexes. Daa of high qualiy was used when available. Oherwise, an average of he available daa was used. Average years of Schooling of he Populaion over 15. Growh in he Gross Domesic Produc consruced as he logdifference of GDP a consan local 1987 marke prices. Consruced from moraliy daa from he World Healh Organizaion (WHO). Mos of his daa is available by FTP from he WHO server (WHO-HQ-STATS01.WHO.CH) in he direcory '\FTP\MORTALIT'. Addiional daa was exraced from he WHO publicaion World Healh Saisics Annual. The daa on populaion was aken from he World Bank s Inernaional Economic Deparmen daa base. Mos daa was aken from Loayza e al. (1998). For some counries he variable was consruced on he basis of he same mehodology using daa from he World Bank s Inernaional Economic Deparmen daa base Deininger and Squire (1996). The daa-se is available on he inerne from he World Bank s Server, a hp:// hweb/daases.hm. Barro and Lee (1996). The daa-se is available on he inerne from he World Bank s Server, a hp:// hweb/daases.hm. Loayza e al. (1998). Sandard Deviaion of Educaional Aainmen Sandard deviaion of he disribuion of educaion for he oal populaion over age 15. The populaion is disribued in seven caegories: no formal educaion, incomplee primary, complee primary, firs cycle of secondary, second cycle of secondary, incomplee higher, and complee higher. Each person is assumed o have an educaional aainmen of log(1+years of schooling). De Gregorio and Lee (1998). 28

29 Variable Descripion Source Measure ha wo randomly seleced people from a given counry will no belong o he same ehno-linguisic group (1960). Ehno-Linguisic Fracionalizaion Easerly and Levine (1997). The daa-se is available on he inerne from he World Bank s Server, a hp:// hweb/daases.hm. Police per 100,000 Young male populaion share Income of he Fifh Quinile relaive o he Firs Quinile Number of police personnel per 100,000 populaion. Male populaion years of age as a share of he oal populaion. Income of he populaion in he fifh quinile of he disribuion of income divided by he income of he firs quinile. Consruced from he Unied Naions World Crime Surveys of Crime Trends and Operaions of Criminal Jusice Sysems, various issues. The daa is available on he inerne a hp:// l#wcs123. World Bank daa. Same as above. 29

30 Appendix B: Summary Saisics Table B1. Summary Saisics, Homicide Raes (number of homicides per 100,000 populaion) Counry Obs. Mean Sd. Dev. Min. Max. Ausralia Belgium Brazil Bulgaria Canada Chile China Colombia Cosa Rica Denmark Dominica Finland France Germany Greece Hong Kong Hungary Ireland Ialy Japan Mauriius Mexico Neherlands New Zealand Norway Panama Peru Philippines Poland Romania Singapore Spain Sri Lanka Sweden Thailand Trinidad & Tobago Unied Kingdom Unied Saes Venezuela Source: Homicide daa from he World Healh Organizaion; populaion daa from he World Bank. 30

31 Table B2. Summary Saisics, Robbery Raes (number of robberies per 100,000 populaion) Counry Obs. Mean Sd. Dev. Min. Max. Ausralia Bangladesh Belgium Bulgaria Canada Chile China Denmark Finland Germany Greece Hong Kong Hungary India Indonesia Ialy Jamaica Japan Korea Malaysia Mauriius Neherlands New Zealand Norway Pakisan Peru Philippines Poland Romania Singapore Sri Lanka Sweden Thailand Trinidad Unied Kingdom Unied Saes Venezuela Source: Robbery daa from he Unied Naions World Crime Surveys; populaion daa from he World Bank. 31

32 Table B3: Bivariae Correlaions of Variables Included Simulaneously in Mulivariae Regressions (number of five-year-average observaions in parenheses) Log of Homicide Rae Log of Robbery Rae Gini Index Log of GNP per Capia Educaional Aainmen GDP Growh Urbanizaion A. Variables used in basic regressions Log of Homicide Rae 1.00 Log of Robbery Rae 0.46 (96) Gini Index 0.54 (148) Log of GNP per Capia (148) (132) 0.40 (132) (148) 1.00 Educaional Aainmen (148) GDP Growh -0.07* (148) Urbanizaion (148) 0.35 (132) (132) 0.51 (132) (148) 0.26 (148) (148) 0.64 (148) -0.15* (148) 0.68 (148) (148) 0.41 (148) * (148) 1.00 B. Alernaive indicaors of inequaliy used insead of he Gini index in GMM regressions Raio of Income Share of Fifh o Firs Quinile Log of Income Polarizaion Sd. Dev. of he log(1 + years of educaion) 0.61 (96) 0.53 (96) 0.31 (103) 0.31 (86) 0.35 (86) (91) 0.88 (96) 0.88 (96) 0.62 (103) (96) (96) (103) (96) (96) (103) 0.15* (96) 0.23 (96) 0.41 (103) (96) -0.12* (96) -0.07* (103) C. Addiional conrol variables used in GMM regressions Police per 100,000 Populaion -0.18* (97) 0.38 (92) 0.03* (97) 0.06* (97) -0.00* (97) Young Male ( years) Populaion as (106) (94) (106) (106) (106) Share of Toal Ehno-Linguisic 0.20* -0.12* -0.03* -0.07* 0.19* Fracion. in 1960 (96) (83) (96) (96) (96) Lain America Dummy (148) (132) (148) (148) (148) The * indicaes correlaions ha are NOT significan a he 5% level (97) 0.48 (106) 0.03* (96) -0.01* (148) 0.25 (97) -0.04* (106) -0.14* (96) -0.13* (148) 32

33 Appendix C: On he Empirical Implemenaion of Eseban and Ray s (1994) Measure of Polarizaion In his noe we briefly describe a possible empirical implemenaion of he measure of polarizaion proposed by Eseban and Ray (1994: 834) ER. More precisely, we propose an implemenaion of ER s equaion (3), exended o incorporae he possibiliy of idenificaion beween individuals belonging o differen income groups. We use daa on he percenages of oal income held by differen quiniles of he disribuion of income wihin a given counry. We hus consider a populaion ha is iniially subdivided in five groups (he quiniles). Since we do no have informaion on he degree of income heerogeneiy wihin each quinile, we assume ha hey are equally homogeneous and hus rea each quinile as having he same degree of idenificaion (as defined by ER). Following he suggesion conained in secion 4 of ER, we also permi idenificaion across income groups ha are sufficienly close (p. 846). We implemen his idea by assuming ha wo or more quiniles may group hemselves ino a new uni if heir incomes are sufficienly similar. As emphasized by ER, he definiion of he domain over which a sense of idenificaion prevails (p. 846) can no be specified a priori. Thus, we es wih differen values of he minimum logarihmic difference ( D ) ha gives rise o he merger of wo quiniles ino a new group. In our empirical exercise his minimum (percenage) disance is allowed o vary beween 10 and 100%. We also assume ha individuals ac as social climbers : when a given quinile is wihin he range of idenificaion wih boh a quinile wih higher income and a quinile wih lower income, he merger akes place firs beween he wo superior quiniles. Moreover, once wo (or more) quiniles have merged, he decision o form a larger group wih anoher quinile ress upon he quinile wih he highes income wihin he (pre-) exising grouping. Tha is, he new merger akes place only if he new candidae is wihin he range of idenificaion of he highes quinile wihin he previously exising group. In pracice, given our assumpions, here are 16 (or 2 o he 4 h power) possible srucures of groups, each formed by one or more quiniles: eiher he highes quinile merges wih he 4 h or no, eiher he 4 h quinile (wih or wihou he 5 h ) merges or no wih he hird, ec. On he basis of he Deininger and Squire inernaional daa se on income inequaliy, we apply a simple algorihm ha implemens our assumpions and deermines, for each counry and for each value of he parameer D, he ypes of groups ha are expeced o emerge. Once he srucure of groups in a given counry is defined, we calculae, for each year and counry, he value of a measure of polarizaion P, using a modified version of ER s equaion (3), which inends o reproduce he spiri of equaion (25) in his paper. Indeed, we assume ha he degree of idenificaion of a group depends posiively on is size and negaively on he log-difference beween he average income of he wo quiniles ha, wihin he group, are siuaed farhes away from each oher: 33

34 P( π, y) = ( i= 1 j= 1 1+ n n π i max y y i min i ) 1+ α π j y j y j where y i is he log of he average income of group i (formed by one or more quiniles), y max i is he average income of he highes quinile wihin group y min i is he average income of he lowes quinile wihin group and π i is wice he number of quiniles ha form group i (i s he number of deciles ha were merged o creae group i). Following he analysis in ER, we allow he parameer α o vary beween 1.0 and 1.6. Our preliminary exercises show ha he measure of polarizaion is increasing in D for sufficienly low values of his parameer, and hen becomes decreasing in D. The value of D afer which P sars o decrease wih D is, in urn, increasing in α. As expeced, he correlaion beween P and he Gini Index decreases wih he parameer α, and varies from 0.74 for α equal o 1, o 0.58 for α equal o

35 Appendix D: Dynamic-Panel GMM Mehodology i) Assuming no unobserved counry-specific effecs: momen condiions We use a dynamic model o explain he homicide and robbery raes. The basic model is given by, * * y α y 1 + β ' X + ξ = (D1) where y * is he rue crime (homicide or robbery) rae, X is he se of explanaory variables, and ξ is he unexplained residual. The subscrips i and denoe counry and ime period, respecively. Available crime daa suffers from measuremen error. For his secion, le us assume ha measuremen error is only sandard random noise (we relax his assumpion below). Then, y * = y +ν and ν is i. i.. (D2) d where y represens he measured crime rae. Subsiuing (D2) ino (D1): y = α y 1 + β ' X + ε where ε = ξ + ν αν 1 (D3) Equaion (D3) is our basic regression model. Esimaion via ordinary leas squares (OLS) would lead o inconsisen parameer esimaes because he explanaory variables are no independen wih respec o he error erm: y -1 is correlaed by consrucion wih ν -1, and X is poenially correlaed wih ξ. Consisen esimaion requires he use of insrumenal variables. Specifically, we use he Generalized-Mehod-of-Momens (GMM) esimaors developed for dynamic models of panel daa ha were inroduced by Holz-Eakin, Newey, and Rosen (1990), Arellano and Bond (1991), and Arellano and Bover (1995). Given ha for his secion we assume ha here is no counry-specific effec, we base our esimaes on he so-called levels GMM esimaor. The use of insrumens is required o deal wih boh he random noise measuremen error in he lagged dependen variable and he likely endogeneiy of he remaining explanaory variables, X, which may be affeced by crime raes (reverse causaion) and/or joinly caused by oher variables (simulaneiy). Insead of assuming sric exogeneiy of X (i.e., ha he explanaory variables be uncorrelaed wih he error erm a all leads and lags), we allow for a limied form of simulaneiy and reverse causaion. Specifically, we adop he more flexible assumpion of weak exogeneiy, according o which curren explanaory variables may be affeced by pas and curren realizaions of he dependen variable (he homicide or he robbery rae) bu no by is fuure innovaions. Under he assumpions ha (a) he error erm, ε, is no serially correlaed, and (b) he explanaory variables are weakly exogenous, he following momen condiions apply: E E [ y ] = 0 for s 2 i ε (D4), s [ X ] = 0 for s 1 i ε (D5), s 35

36 ii) Allowing and conrolling for unobserved counry-specific effecs: momen condiions Our second specificaion allows for he exisence of persisen counry-specific measuremen error. This alernaive model is given by, * * y α y 1 + β ' X + ηi + ξ = (D6) where y* is he rue crime rae, and η i is a counry-specific unobserved facor, which may be correlaed wih he explanaory variables. We now assume ha he mismeasuremen in crime raes is no only driven by random errors bu mos imporanly by specific and persisen characerisics of each counry. These characerisics can be relaed o he variables ha explain crime raes, such as he average level of income, educaional aainmen, and income inequaliy. Then, we model measuremen error as he sum of random noise and a counry-specific effec: y = y +ν + ψ (D7) * i where ν is i.i.d. and ψ is a counry-specific effec. Subsiuing (D7) ino (D6): where, y α y 1 + β ' X + µ i + ε = (D8) µ + = ηi + ( 1 α) ψ i and ε = ν αν 1 ξ Thus, he measuremen error in crime raes is subsumed ino boh he unobserved counryspecific effec and he ime-varying residual. Equaion (D8) is our second regression model. To esimae i we use he so-called sysem GMM esimaor, which joins in a single sysem he regression equaion in boh differences and levels, each wih is specific se of insrumenal variables. For ease of exposiion, we discuss each secion of he sysem separaely, alhough he acual esimaion is performed using he whole sysem joinly. Specifying he regression equaion in differences allows direc eliminaion of he counry-specific effec. Firs-differencing equaion (D8) yields, y y ( y y ) + β ( X X ) + ( ε ε ) = α (D9) ' 1 1 In addiion o he likely endogeneiy of he explanaory variables, X, and he random measuremen error of he lagged crime rae, he use of insrumens is here required o deal wih he correlaion which, by consrucion, is generaed beween he new error erm, (ε - ε -1 ), and he differenced lagged dependen variable, (y -1 - y -2 ). Once again, we adop he assumpion of weak exogeneiy, which ogeher wih he assumpion of no serial correlaion in he error erm yields he following momen condiions: E [ y ( ε )] = 0 for s 3 ε (D10) s 1 36

37 E [ X ( ε )] = 0 for s 2 ε (D11) s 1 The GMM esimaor simply based on he momen condiions in (D10) and (D11) is known as he differences esimaor. Alhough asympoically consisen, his esimaor has low asympoic precision and large biases in small samples, which leads o he need o complemen i wih he regression equaion in levels. 10 For he regression in levels, he counry-specific effec is no direcly eliminaed bu mus be conrolled for by he use of insrumenal variables. The appropriae insrumens for he regression in levels are he lagged differences of he corresponding variables if he following assumpion holds. Alhough here may be correlaion beween he levels of he righ-hand side variables and he counry-specific effec, here is no correlaion beween he differences of hese variables and he counry-specific effec. This assumpion resuls from he following saionariy propery, E [ y η ] = E[ y η ] and E [ X η ] = E[ X η ] + p i + q i + p i + q i for all p and q Therefore, he addiional momen condiions for he second par of he sysem (he regression in levels) are given by he following equaions: 11 E [( y y ) ( + ε )] = 0 for s 2 η (D12) s s 1 i = [( i, s i, s ) ( i i, )] E X X 1 η + ε = 0 for s=1 (D13) iii) Esimaion Using he momen condiions presened in equaions (D4) and (D5) and, alernaively, (D10) o (D12), and following Arellano and Bond (1991) and Arellano and Bover (1995), we employ a Generalized Mehod of Momens (GMM) procedure o generae consisen esimaes of he parameers of ineres and heir asympoic variance-covariance. These are given by he following formulas: 10 Alonso-Borrego and Arellano (1996) and Blundell and Bond (1998) show ha when he lagged dependen and he explanaory variables are persisen over ime, lagged levels of hese variables are weak insrumens for he regression equaion in differences. This weakness has repercussions on boh he asympoic and small-sample performance of he differences esimaor. As persisence increases, he asympoic variance of he coefficiens obained wih he differences esimaor rises (i.e., deerioraing is asympoic precision). Furhermore, Mone Carlo experimens show ha he weakness of he insrumens produces biased coefficiens in small samples. This is exacerbaed wih he variables overime persisence, he imporance of he counry-specific effec, and he smallness of he ime-series dimension. An addiional problem wih he simple differences esimaor relaes o measuremen error: Differencing may exacerbae he bias due o errors in variables by decreasing he signal-o-noise raio (Griliches and Hausman, 1986). Blundell and Bond (1997) sugges he use of Arellano and Bover s (1995) sysem esimaor ha reduces he poenial biases and imprecision associaed wih he radiional differences esimaor. 11 Given ha lagged levels are used as insrumens in he differences specificaion, only he mos recen difference is used as insrumen in he levels-specificaion. Oher lagged differences would resul in redundan momen condiions (Arellano and Bover 1995). 37

38 ˆ 1 X Z ˆ ( ' 1 1 θ = Ω Z' X ) X ' ZΩˆ Z' y (D14) ˆ) ˆ 1 1 AVAR( θ = ( X ' ZΩ Z' X ) (D15) where θ is he vecor of parameers of ineres (α, β), y is he dependen variable (sacked firs in differences and hen in levels in he case of he sysem esimaor), X is he explanaory-variable marix including he lagged dependen variable (y -1, X) (also sacked firs in differences and hen in levels for he sysem esimaor), Z is he marix of insrumens derived from he momen condiions, 12 and Ωˆ is a consisen esimae of he variance-covariance marix of he momen condiions. iv) Specificaion ess The consisency of he GMM esimaors depends on wheher lagged values of he explanaory variables are valid insrumens in he crime-rae regression. We address his issue by considering wo specificaion ess suggesed by Arellano and Bond (1991) and Arellano and Bover (1995). The firs is a Sargan es of over-idenifying resricions, which ess he overall validiy of he insrumens by analyzing he sample analog of he momen condiions used in he esimaion process. Failure o rejec he null hypohesis gives suppor o he model. The second es examines he null hypohesis ha he error erm ε is no serially correlaed. As in he case of he Sargan es, he model specificaion is suppored when he null of no serial correlaion is no rejeced. In our levels (basic) specificaion, we es wheher he error erm is firs-order serially correlaed. In our sysem (alernaive) specificaion we es wheher he differenced error erm (ha is, he residual of he regression in differences) is second-order serially correlaed. Firs-order serial correlaion of he differenced error erm is expeced even if he original error erm (in levels) is uncorrelaed, unless he laer follows a random walk. Second-order serial correlaion of he differenced residual indicaes ha he original error erm is serially correlaed and follows a moving average process a leas of order one. This would rejec he appropriaeness of he proposed insrumens (and would call for higher-order lags o be used as insrumens). 12 In pracice, Arellano and Bond (1991) sugges he following wo-sep procedure o obain consisen and efficien GMM esimaes. Firs, assume ha he residuals, ε, are independen and homoskedasic boh across counries and over ime. This assumpion corresponds o a specific weighing marix ha is used o produce firs-sep coefficien esimaes. Then, consruc a consisen esimae of he variance-covariance marix of he momen condiions wih he residuals obained in he firs sep, and use his marix o re-esimae he parameers of ineres (i.e. second-sep esimaes). Asympoically, he second-sep esimaes are superior o he firs-sep ones in so far as efficiency is concerned. 38