An Explanation for the Curvilinear Relationship between Crime and Temperature

Transcription

1 Osaka Keidai Ronshu, Vol. 57 No. 2 July 2006 An Explanation for the Curvilinear Relationship between Crime and Temperature IIntroduction Yoshiko Hayashi* Abstract In this paper, we provide one explanation for the curvilinear relationship between crime and by using the maximizing utility theory for offenders. In our model we show the possibility that the relationship would be linear when the cost for captured is small enough, and would be curvilinear when the cost is large. Crime is one of the most challenging issues the world is facing today. Japan, in particular, has experienced a significant increase in the crime rate over the last decade 1. Crime would be the subject for relating not only to law, sociology and psychology, but also to economics. We call it the economics of crime 2. This particular topic has been studied since the seminal theoretical study by Becker 1968, which clarifies the offenders motivation based on a given expected utility function, and many studies focus on the behavior of property criminals, but some concentrate on violent crime based on economic theory 3. This is because analyzing property crime would be appropriate to think of as a subject in labor economics. Violent crime is also correlated with economic activities through the cost of crime. In addition, when we consider the cost of crime, we should also consider people who suffer from crime except direct victims ; such as the person who needs to pay a price to prevent crimes should be considered as a victim of crimes economically Cohen Moreover, as Lynch and Rasmussen 2001 indicates that the house price is significantly affected by the crime rate, crime has some influences on other economic factors as an external effect. Therefore, studying violent crime is also very useful for analyzing household behavior or consumption. In this paper, we focus on the relationship between crime and. There are several theories that suggest the negative linear relationship between and crime, such as simple negative affect model, which is that the warm s facilitates our tendency to move and hot s tend to stimulate violent emotion. Other than the negative affect model, Kelly 2000 suggests that the relationship between crime and would be explained by sociological theories called strain theory, and Field 1992 introduces * yhayashi@osaka-ue.ac.jp * This paper is dedicated to Professor Yoshihiko Seoka and I thank him for his helpful comments. Any remaining errors are of course mine. It was reported that we have some downward movement in Freeman 1999 surveys the economics of crime. See Lynch, Rasmussen and Moore 2001, Cohen 1990.

2 Osaka Keidai Ronshu, Vol. 57 No. 2 two psychological theories ; the first one is a direct psychological or physiological response in humans based on, and the second one is routine activities RA theory, which suggests the indirect effect of on crime through an effect of sociological social behavior. Among those studies, there is a controversy about the relationship. Anderson s consequent studies show the linear relationship between and crime, whereas Cohn and Rotton 1997, Rotton and Cohn 2000, and Cohn and Rotton 2005 show the inverted U-shaped curvilinear relationship there. For this contradiction, we will investigate an explanation for the relationship based on the maximizing utility theory. This paper is organized as follows: Section II shows some empirical evidence in Osaka. Section III introduces the theoretical model of the relationship between and crime, and section IV concludes the paper. IIEvidence in Osaka In this section, we will see the empirical evidence for the relationship between crime and in Osaka. Although weather shock is quite important factor for explaining crime, there are few studies in Japan to study the relationship. This is because frequent data, such as like the monthly data for prefectures of Japanese crime, are not published through markets, while the reputation of Japanese crime statistics is high among developed countries. For estimating our model, we use the numbers of murder and robbery and the total number of felonious offenses, which includes murder, robbery, arson, and rape. For and the length of daytime data we employ the monthly averages in Osaka. The estimation period is from January 1998 to December We source the crime data from HANZAI TOUKEI which is available at the information center of Osaka Prefecture Police. The weather data was taken from the Monthly Report of Japanese Meteorological Agency. Figure 1 shows the number of felonious crime in Osaka from January 1998 to December Figure 2 shows the estimated relationship between crime and by nonparametric regression and 95 confidence intervels. We use the Gaussian density function for the kernel function and the bandwidth is determined by least squares cross-validation 4. The confidence intervals use the WARPing method 5. From these figures, we can see the curvilinear relationships for total number of felonious offences in Osaka. When we look at the data of murder and robbery, robbery shows the curvilinear relationship, but murder does not. In the next section, we will show an explanation for the evidences. IIITheoretical model for violent crime According to Jacob et al. 2004, we illustrate the maximization problem for violent crime s Rice T, which has a relatively larger weight on variance reduction, shows the similar bandwidth but Shibata s selector, which has a larger weight on bias, shows smaller bandwidth for total number. See Hardle 1990.

3 An Explanation for the Curvilinear Relationship between Crime and Temperature Figure Felonious offences in Osaka Total number Murder Robbery

4 Osaka Keidai Ronshu, Vol. 57 No. 2 Figure Total number crime Murder crime Robbery crime

5 An Explanation for the Curvilinear Relationship between Crime and Temperature offenders. In each period an individual or offender chooses whether or not to commit a crime. His / her objective is to maximize the expected present value of spontaneous utility 6 under the restriction of cost for committing a crime as following. Where is the rate of violence in time t. We assume that is an increasing but a concave function of as follows: In equation 1, and represent the rates of s cost and other exogenous perunit cost of violence respectively and their total is positive. We also assume that is a decreasing function of shock because warm s facilitates offender s tendency to move or commit a crime and the marginal tendency would be smaller with higher. Thus we assume as following. Where is an adjustment parameter to be. We consider the length of daytime as one of the other costs because it can explain the probability of being captured. Thus, the cost should be correlated positively. Where daytime represents the length of daytime and includes the other costs except and the length of daytime. We assume that and the length of daytime are correlated positively as the following 7. Now we turn back to the maximization problem for offenders. The first order condition for crime is Thus, we could have the function for violence. Where. With our utility function, equation 6 becomes When other cost is relatively large, the case for the curvilinearrelationship would occur as follows. From the equations 2 8, the function of violence is obtained as follows. Figure 3a and 3b show the simulated examples for different. We use the parameters =3, =5, =1, =0.07, =0.5, and =0.03 respectively, and we assume that follows the normal distribution with 0 and 0.5 0, 0.5. The range for is 5, 30. Imai and Krishna 2004 suggests that the possibility of dynamics for criminal behavior. The equation should be described as. For convenience we take the formula in equation 5.

6 Osaka Keidai Ronshu, Vol. 57 No. 2 Figure a. violence Figure b violence We use the parameter as 0.2 for Fig. 3a, and 2 for Fig. 3b respectively. From these figures, as long as the relationship between the cost and the cost of captured is hyperbolic we can see the curvilinear relationship when the weight on cost of captured is large and the almost linear relationship when the weight is small for the same range of. The curvature in is or Thus, Violence is an increasing function in when and a decreasing function when

7 An Explanation for the Curvilinear Relationship between Crime and Temperature Therefore violence would be monotonically increasing as increase when other cost is small enough or does not correlate with. Consequently we can conclude that the relationship between crime and would be curvilinear when the cost of captured is large and would be monotonically increasing when the cost is small. Our result is consistent with both Anderson 1989 and Cohn and Rotton And Bushman et al. s 2005 result which shows the linear relationship by using a short interval data that is totally consistent with our results because the data excludes the effect of the length of daytime. IVConclusion There is a controversy about the relationship between crime and. Despite An derson s theory, which show the linear relationship between and crime, Cohn and Rotton 1997, Rotton and Cohn 2000 and Cohn and Rotton 2005 show the curvilinear relationship there. As Cohn s studies show the relationship is often curvilinear. For this problem, we provide an alternative explanation for the curvilinear relationship between crime and by using the maximizing utility theory. Our model could show that the relationship would be linear when the cost for captured is small enough, and would be curvilinear when the cost is excessively large. References Bushman, Brad, J., Wang, Morgan, C. and Anderson, Craig, A. 2005a, Is the Curve Relating Temperature to Aggression Linear or Curvilinear? Assaults and Temperature in Minneapolis Reexamines, Journal of Personality and Social Psychology, vol. 89, no. 1, pp Bushman, Brad, J., Wang, Morgan, C. and Anderson, Craig, A. 2005b, Is the Curve Relating Temperature to Aggression Linear or Curvilinear? A Response to Bell 2005 and to Cohn and Rotton 2005, Journal of Personality and Social Psychology, vol. 89, no. 1, pp Cohen, Mark A. 1990, A Note on the Cost of Crime to Victims, Urban Studies, Vol. 27, no. 1, pp Cohen, Jacqueline, Gorr, Wilpen, and Durso, Christopher, 2003, Estimation of Crime seasonality: A Cross-Sectional Extension to Time Series Classical Decomposition, The H. John Heinz working paper, Carnegie Mellon University. Cohn, Ellen, G. 1990, Weather and Crime, British Journal of Criminology, vol. 30, no. 1, pp Cohn, Ellen, G. and Rotton, James, 1997, Assault as a function of time and : A moderator-variable time-series analysis, Journal of Personality and Social Psychology, vol. 72, pp Fajnzylber, Pablo, Lederman, Daniel and Loayza, Norman, 2002, What causes violent crime? European Economic Review, vol. 46, pp Field, Simon, 1992, The effect of Temperature on Crime, British Journal of Criminology, vol. 32, no. 3, pp Jacob, Brian, Lefgren, Lars, and Moretti, Enrico, 2004, The Dynamics of Criminal Behavior: Evidence from weather shocks, NBER Working paper , Wolfgang, 1990, Smoothing Techniques with Implementation in S, Springer-Verlag Imai, Susumu and Krishna, Kala, 2004, Employment, Dynamic Deterrence and Crime,

8 Osaka Keidai Ronshu, Vol. 57 No. 2 International Economic Review, vol. 45, no. 3, pp Kelly, Morgan 2000, Inequality and Crime, The Review of Economics and Statistics, vol. 82 no. 4 pp Lynch, Allen K. and Rasmussen, David W. 2001, Measuring the Impact of Crime on House Prices, Applied Economics, vol. 33, no. 15, pp Rotton, James and Cohn, Ellen, G. 2000, Violence if a Curvilinear Function of Temperature in Dallas: A Replication, Journal of Personality and Social Psychology, vol. 78, no. 6, pp