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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).
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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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