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The  Tradeoff:  Crime  vs.  Educa4on  Expenditures  in  the  Reduc4on  of  Crime  Rates  A  Dynamic  Panel  Regression  Analysis  using  GMM  By:  Allan  Ngei,  BriFany  Ward,  Shamier  SeFle,  Yisehak  Abraham,  Rebecca  Kerley  

Introduc4on  

Research  Ques4on  

Literature  Review  

Methodology  &  Empirical  Model  

The   nega4ve   rela4onship   between   public   expenditures   and   crime   rates   has   been   widely  speculated  within  academic  literature  and  the  poli4cal  arena.  The  prevailing  idea  that  a  more  educated  populous   is   less   likely   to  enter   jail–and   therefore  heighten  societal  produc4vity–is  alluring,   though   not   without   contest.   An   alterna4ve   school   of   thought   suggests   greater  expenditure   on   crime   preven4on   tac4cs   will   lead   to   greater   decreases   in   crime   rates.   This  project  explores  the  rates  at  which  the  marginal  u4lity  of  crime  rate  reduc4on  diminishes  for  each   type   of   expenditure.   Addi4onally,  we  will   seek   to   answer  which   variable   expenditure,  crime  or  educa4on,  appears  more  significant  in  its  aFempt  to  lower  total  crime  rates  as  well  as   its   effects   on   dis4nct   crimes   (i.e.   violent   and  property   crimes).  Our   results   show   that   an  increase  in  crime  expenditures  rela4ve  to  educa4on  will  decrease  crime  up  to  a  certain  point,  aXer  which  it  becomes  ineffec4ve  in  reducing  overall  crime  rates.  

Is  an  increase  in  crime  expenditures  rela1ve  to  educa1on  more  effec1ve  in  reducing  crime?       Hypotheses  1.  Both  crime  expenditure  and  educa4on  expenditure  exhibit  diminishing  marginal  u4lity  in  

terms  of  crime  reduc4on.    2.  Educa4on   expenditure’s   marginal   u4lity   diminishes   at   a   slower   rate   than   does   crime  

expenditure’s.    3.  Consequently,  aXer  a  certain  point,  further  Expenditure  on  crime  at  the  expense  of  

educa4on  will  yield  a  lower  reduc4on  of  crime  

Theore4cal  Model  

This   rela4onship   is   framed   in   terms   of   a   general   u4lity   curve,   where   u4lity   is   defined   as   crime  reduc4on,  assumed  as  some  func4on  of  the  inputs  crime  and  educa4on  expenditure.  

Crime  expenditure      

Education  expenditure    

Utility=crime  reduction    

    Total  Crime  Rate   Violent  Crime  Rate   Property  Crime  Rate       (1)   (2)   (3)   (4)   (5)   (6)  Regression  Specifica4on   Pooled   Fixed  Effects   Pooled   Fixed  Effects   Pooled   Fixed  Effects  Lagged  Dependent  Variable   0.825***   0.825***   0.895***   0.895***   0.842***   0.842***       (0.0436)   (0.0560)   (0.0512)   (0.0626)   (0.0422)   (0.0549)  Second  Lagged  Dependent  Variable   -­‐0.0821*   -­‐0.0821   -­‐0.0349   -­‐0.0349   -­‐0.0954**   -­‐0.0954*       (0.0423)   (0.0555)   (0.0459)   (0.0559)   (0.0406)   (0.0541)  Crime  Expenditure  Rela4ve  to  Educa4on  Expenditure   -­‐0.0325**   -­‐0.0325**   -­‐0.0575***   -­‐0.0575***   -­‐0.0256**   -­‐0.0256**       (0.0131)   (0.0127)   (0.0145)   (0.0127)   (0.0107)   (0.0120)  Crime-­‐Educa4on  Ra4o  Squared   0.00160***   0.00160***   0.00241***   0.00241***   0.00146***   0.00146***       (0.000533)   (0.000498)   (0.000600)   (0.000470)   (0.000495)   (0.000488)  Dropout  Rate   0.00303   0.00303   0.00397   0.00397   0.00119   0.00119       (0.00305)   (0.00362)   (0.00414)   (0.00344)   (0.00255)   (0.00287)  Dropout  Rate  Squared   -­‐7.02e-­‐05   -­‐7.02e-­‐05   -­‐9.49e-­‐05   -­‐9.49e-­‐05   -­‐3.17e-­‐05   -­‐3.17e-­‐05       (7.86e-­‐05)   (9.62e-­‐05)   (0.000104)   (8.74e-­‐05)   (6.87e-­‐05)   (8.11e-­‐05)  Median  Age   0.00601   0.00601   0.00479   0.00479   0.0114**   0.0114**       (0.00517)   (0.00521)   (0.00629)   (0.00844)   (0.00464)   (0.00478)  Median  Income  Logged   -­‐0.143**   -­‐0.143**   0.0193   0.0193   -­‐0.0844**   -­‐0.0844**       (0.0654)   (0.0627)   (0.0571)   (0.0662)   (0.0366)   (0.0406)  Unemployment  Rate   0.0187***   0.0187***   0.0135   0.0135*   0.0235***   0.0235***       (0.00520)   (0.00554)   (0.00828)   (0.00707)   (0.00501)   (0.00549)  Unemployment  Rate  Squared   -­‐0.00136***   -­‐0.00136***   -­‐0.00115**   -­‐0.00115**   -­‐0.00169***   -­‐0.00169***       (0.000355)   (0.000381)   (0.000544)   (0.000482)   (0.000329)   (0.000351)  Growth  in  GSP   0.0237   0.0237   0.118   0.118   -­‐0.0225   -­‐0.0225       (0.0702)   (0.0729)   (0.0867)   (0.0722)   (0.0641)   (0.0721)  Percent  Nonwhite   -­‐0.00428   -­‐0.00428   0.174*   0.174*   0.0596   0.0596       (0.0860)   (0.0799)   (0.0959)   (0.0980)   (0.0853)   (0.0744)  Percent  Male   2.063**   2.063*   2.892   2.892   3.273***   3.273***       (1.045)   (1.108)   (1.775)   (2.270)   (1.021)   (0.981)  Year   -­‐0.00675***       -­‐0.00160       -­‐0.0101***           (0.00213)       (0.00219)       (0.00155)      Trend       -­‐0.00675***       -­‐0.00160       -­‐0.0101***           (0.00212)       (0.00318)       (0.00153)  Constant   14.30***   0.789   1.444   -­‐1.789   19.55***   -­‐0.690       (3.498)   (1.149)   (3.845)   (1.406)   (2.772)   (0.773)                              Observa4ons   867   867   867   867   867   867  R-­‐squared   0.970   0.881   0.984   0.822   0.976   0.916  Number  of  State       51       51       51  

    Total  Crime  Rate   Violent  Crime  Rate   Property  Crime  Rate  

    (1)   (2)   (3)  Explanatory  Variables   GMM-­‐Diff   GMM-­‐Diff   GMM-­‐Diff                  Dependent  Lagged   0.787***   0.827***   0.851***       (0.0494)   (0.0548)   (0.0503)  Crime  Expenditure  Rela4ve  to  Educa4on  Expenditure   -­‐0.0474**   -­‐0.0948***   -­‐0.0279       (0.0189)   (0.0236)   (0.0195)  Crime-­‐Educa4on  Ra4o  Squared   0.00196***   0.00378***   0.00119       (0.000703)   (0.000874)   (0.000735)  Dropout  Rate   0.00220   0.00479   0.00293       (0.00453)   (0.00528)   (0.00488)  Dropout  Rate  Squared   -­‐4.91e-­‐05   -­‐0.000113   -­‐6.73e-­‐05       (0.000116)   (0.000129)   (0.000124)  Median  Age   -­‐0.0129*   -­‐0.00557   -­‐0.00713       (0.00662)   (0.0113)   (0.00552)  Median  Income  Logged   -­‐0.235**   -­‐0.0873   -­‐0.168**       (0.114)   (0.141)   (0.0734)  Unemployment  Rate   0.0199   0.0201*   0.0277***       (0.0129)   (0.0117)   (0.00955)  Unemployment  Rate  Squared   -­‐0.00153*   -­‐0.00156**   -­‐0.00224***       (0.000827)   (0.000745)   (0.000659)  Growth  in  GSP   0.00611   0.106   -­‐0.0488       (0.0905)   (0.113)   (0.0858)  Percent  Nonwhite   -­‐0.0476   0.328*   -­‐0.115       (0.112)   (0.168)   (0.161)  Percent  Male   0.855   2.072   -­‐0.0881       (1.569)   (2.882)   (1.565)                  Observa4ons   867   867   867  Number  of  State   51   51   51                  Specifica4on  tests  (p-­‐values)                    (a)  Hansen  Test   0.995   1.000   1.000        (b)  Serial  Correla4on                          First  Order   0.000   0.000   0.000              Second  Order   0.559   0.694   0.842  

The  literature  surrounding  the  economics  of  crime  begins  with  the  seminal  ar4cle  by  Becker  (1968),  which   uses   fundamental  microeconomic   theory   to   understand   the   reasons   why   individuals   take  part   in   illicit   ac4vi4es.  Within   the   literature   there   is   no   consensus   on   whether   or   not   crime   or  educa4on  expenditures  are  beFer  at  reducing  crime  rates.  The  ar4cle,  The  Effect  of  Educa.on  on  Crime:   Evidence   from   Prison   Inmates,   Arrests,   and   Self-­‐Reports   seeks   to   es4mate   the   effect   of  educa4on  on  par4cipa4on  in  criminal  ac4vity  by  analyzing  the  effect  of  schooling  on  incarcera4on  and  looking  at  the  effects  of  changes  in  state  compulsory  aFendance  laws.  The  paper’s  theore4cal  framework  highlights   that  an   individual's  wages  will   rise  as  a  result  of  educa4on,  which  will   raise  the  opportunity  cost  associated  with  criminal  ac4vi4es,  and  will  make  incarcera4on  more  costly  in  terms  of  lost  wages.  The  ar4cle,  Crime  Rates  and  Public  Police  Expenditures  looks  at  the  rela4onship  between  state  police  expenditures  to  crime  rates.  This  paper’s  theore4cal  model  takes  the  output  (crime  rate)  as  a  func4on  of  the  quan4ty  of  input  (number  of  police).    

2000  

4000  

6000  

8000  

10000  

12000  

14000  

7   12   17  

Crim

e  Ra

te  (p

er  100,000)  

Crime-­‐Educa1on  Expenditure  Ra1o  

Crime  Expenditures  Rela1ve  to  Educa1on  Expenditures  for  Top  10  Crime  States  

1900  

2400  

2900  

3400  

3900  

4400  

4900  

5400  

5900  

6400  

6900  

3.4   3.9   4.4   4.9   5.4   5.9  

Crim

e  Ra

te  (p

er    100,000)  

Crime-­‐Educa1on  Expenditure  Ra1o  

Crime  Expenditures  Rela1ve  to  Educa1on  Expenditures  for  BoGom  10  Crime  States  

Acknowledgements    American  Economic  Associa4on  Robert  Wood  Johnson  Founda4on    Dr.  Benjamin  Hansen    Teaching  Assistants:  Kris4na  Piorkowski  and  Samrat  Kunwar      Supervised  by  Dr.  Alok  Bohara  as  a  par4al  fulfillment  of  the  research  requirement  for  Econ  409:  Intermediate  Applied  Econometrics  (Department  of  Economics,  University  of  New  Mexico).    

Dynamic  Panel  Es1mates  Using  Generalized  Method  of  Moments  

Pooled  and  Fixed  Effects  Es1mates  

!

Becker,  G.  S.  (1986).  Crime  and  Punishment:  An  Economic  Approach.  Journal  of  Poli4cal  Economy,  76(2),  169-­‐217.  Greenwood,  Michael  J.  and  Walter  J.  Wadycki.  Crime  Rates  and  Public  Expenditure  for  Police  Protec4on:  Their  Interac4on,  Review  of  Social  Economy  Fajnzylber,  P.,  Lederman,  D.,  &  Loayza,  N.  (1998)  Determinants  of  crime  rates  in  La4n  America  and  the  world.  Marlow,  M  &  Shiers  A.  (2001).  Do  Crime-­‐Related  Expenditures  Crowd  out  Higher  Educa4on  Expenditures?  Public  Finance  Review,  369-­‐393.  Lochner  L.  Moreo,  The  Effect  of  Educa4on  on  Crime:  Evidence  from  Prison  Inmates,  Arrests,  and  Self-­‐Reports.  American  Economic  Review  155-­‐189.  Machin,  S.,  Marie  O.,  &  Vuiic,  S  (n.d).  The  Crime  Reducing  Effect  of  Educa4on.  The  Economic  Journal  463-­‐484.      

Discussion  &  Policy  Implica4ons  Wooldridge   and   Levin-­‐Lin-­‐Chu   tests   on   a   naïve   fixed   effects   model   indicated  autocorrela4on   and   a   unit-­‐root   problem   in   crime   rates.   Pooled   and   fixed   effects  regressions  using  lagged  values  of  the  dependent  variable  were  es4mated  to  adjust  for  autocorrela4on.  In  each  of  the  six  specifica4ons,  the  main  narra4ve  holds:  lagged  values  of  crime  rates  posi4vely  impact  current  crime  rates.  Furthermore  the  first  par4al  effect  of   the   rela4ve   crime-­‐expenditure   ra4o   is   nega4ve   and   the   second   par4al   is   posi4ve  across   all   six   specifica4ons.   This   convex   rela4onship   indicates   that,   ceteris   paribus,  spending  more  on  crime  rela4ve  to  educa4on  certainly  reduces  crime  rates,  but  only  to  some  level.      Deriving  efficient  es4mates  of  the  variables  of  interest  with  the  given  dataset  requires  a  dynamic  model   that  u4lizes  general  method  of  moments.  Both   the   lagged  dependent  variable   and   the   convexity   in   the   effect   of   rela4ve   crime   expenditure   on   crime   rates  narra4ves   hold   across   all   three   specifica4on   for   total   crime   rate,   violent   crime   and  property   crime   rate.   Through   the   Hansen   test,   we   fail   to   reject   exogeneity   of  instruments–furthering  our  lagged  dependent  narra4ve.      Inefficiency   of   state   governments   to   construct   impacrul   ra4os   of   expenditures   to  reduce  crime  rates  is  not  a  product  of  negligent  appropria4on  of  public  funds.  Current  crime   rates   are   highly   driven   by   past   crime   rates.   To   reduce   future   crime   rates,  governments   ought   to   focus  more   resources   on   impac4ng   the   crime   culture   in   their  respec4ve   states.   This   may   entail   more   investment   into   human   capital.  While   public  school   expenditures   take   a  while   to  make   a   direct   impact   on   crime   rates   (rela4ve   to  crime  expenditures)  it  may  be  well  worth  the  investment  in  the  long  run.  

References  

   Panel   data  was   collected   for   all   50   states   and   the   District   of   Columbia   from   1993-­‐2010,   from   the   Bureau   of   Jus4ce   Sta4s4cs   (BJS),   Census,   and  Na4onal  Center  for  Educa4on  Sta4s4cs  (NCES),  Federal  Bureau  of  Inves4ga4ons  (FBI),  and  the  Federal  Reserve  Bank  of  St.  Louis.  Crime  expenditures  are  defined  as  correc4ons,  judicial,  and  police  Expenditure.  Educa4on  expenditures  are  defined  as  K-­‐12  public  school  Expenditure.    

Data  Descrip4on  

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