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Optimal expenditures on police protection
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Socio-Economic Planning Sciences 39 (2005) 215–228
Optimal expenditures on police protection Hector Correa1,{ 3-N-27 Posvar Hall, University of Pittsburgh, Pittsburgh, PA 15260, USA Received 1 May 2002; received in revised form 1 September 2003; accepted 1 January 2004 Available online 24 May 2004
Abstract The object of this paper is to propose an approach for operationalizing Rubin’s (Minimizing Harm: a New Crime Policy for modern America, Westview Press, Boulder, CO, 1999) idea that minimizing harm is a solution to the crime policy conundrum. Harm is defined to be the total cost of damages due to crime plus the cost of police protection. Its minimization determines optimal expenditures for protection. This is an appropriate basis for specifying the optimal size of a police force, and provides a term of reference for actual policy decisions. Data for the states of the US are used to make the presentation more concrete and to clarify some of the problems that must be solved in actual applications of the method suggested. This does not eliminate the applicability of the approach to any other country or to the geo-political subdivisions within a country. The results obtained are of interest to policy makers dealing specifically with expenditures for police at local, regional or national levels or, more generally, with similar uses of public or private financial resources. r 2004 Elsevier Ltd. All rights reserved.
1. Introduction Rubin [1] suggests ‘‘minimizing harm as a solution to the crime policy conundrum’’. The object of this paper is to propose an approach to operationalize this idea. In it, harm is defined to be the total cost of damages due to crime plus the cost of police protection. Its minimization determines optimal expenditures for protection, an appropriate basis for specifying the optimal size of a police force. For comparison, a review of the methods currently available to estimate requirements for police personnel is presented in this Introduction.
1
Resource Professor, Growth Dynamics University Institute, Erasmus University, Rotterdam, The Netherlands. Deceased
{
0038-0121/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2004.01.002
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A necessarily incomplete review of the literature on police administration and management shows that only limited attention has been given to the optimum size of a police force and to the financial resources required. The mot commonly used forecasting methods are based on the assumption that the existing conditions are the most appropriate. Some examples of these methods are presented below. The Commission on Accreditation for Law Enforcement Agencies [2] suggests a method to estimate the number of patrol officers needed. It assumes a well-defined relationship between the number of complaints or incidents reported to a police department and the population of the community being served. This information is transformed into the amount of police time needed to deal with complaints, and to the number of officers needed to supply the time required. Omdorf [3] presents a numerical application of this method. The Commission’s approach could be improved by using, say, regression functions that include, as explanatory variables, the factors that influence the number of complaints and the time needed to attend to them. To a large extent, this is the method used when per capita expenditures per unit of time are expressed as functions of several of their determinants. A dated, but still useful, literature review of this method is presented by Hirsch [4]. Bahl et al. [5] extend the approaches just described. They specify and estimate a multiple function model that has as explained variables the number of police employees per thousand population, total compensation of police personnel per person in the community being served, and total crime per thousand population. Expanding on an observation made by Omdorf [3], the information on the demand for police services obtained using any of the methods mentioned above should be the basis for determining the number of supervisors and support personnel required in a police department. This idea is elaborated by Correa and Wakefield [6], who present a disaggregated demand-driven input– output model to analyze and forecast the personnel needed within a police department as determined by the number of officers providing services directly to the public. As a counterpart of their model, Ring and Dyson [7] suggest Markov chain models of the supply of police personnel. It is useful to emphasize that these methods simply extrapolate past experiences. They do not attempt to determine whether existing police resources are efficiently used. The claim made by Hudzik et al. [8], that manpower planning techniques like those outlined above are not consistently utilized to estimate requirements for police personnel, may still be valid today. On the other hand, Rubin [1] explicitly states that police resources influence crime and that both crime and the resources uses to combat it have costs. The minimization of harm caused by crime is the minimization of the total of these costs. For operationalization of Rubin’s [1] idea, a working definition of the harm caused by crime is presented in Section 2, and used as the basis for a simplified model. In Sections 3–7, this model is analyzed using data for the US for 1999. In the concluding section, possible improvements and extensions of the model and of its practical implementation are suggested.
2. A conceptual model for minimization of harm caused by crime As previously mentioned, harm caused by crime is defined here as equal to the total cost of damages due to crime plus cost of police protection. These two variables are related by the
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controversial hypothesis that police protection reduces the incidence of crime. As indicated by Eck and Maguire [9], and shown by Amove [10] and Brownfeld [11], some criminologists accept, while others reject, this hypothesis. On the other hand, the existence of police forces practically in every country in the world indicates that their protective value is generally recognized. Using this hypothesis as a point of departure, it is assumed that the incidence of crime approaches zero when expenditures on police protection increase without limit. This cannot be achieved, because police protection has costs. It follows that police protection should be increased only up to the point where the total costs of both crime and police protection are minimized. This, in agreement with the definition above, can be considered a simplified but operational formulation of Rubin’s [1] suggestion that the minimization of harm should be the basic objective of any crime reduction effort. An elementary mathematical formulation can be given to these ideas. Specifically, let: c ¼ f ðxÞ
ð1Þ
where c=cost of crime, x=cost of police protection, and f=convex function characterized with f ðxÞ-0 when x tends to infinity, f 0 ðxÞo0 f 00 ðxÞ > 0: Given (1), the total cost of crime and protection is t ¼ f ðxÞ þ x;
ð2Þ
where t=total harm due to crime, and all other symbols as previously defined. Function (2) provides the basis for minimization of the total cost of crime and protection. Elementary calculus shows that these conditions are: f 0 ðxÞ ¼ 1
ð3Þ
and f 00 ðxÞ > 0: The first-order condition can be used to specify the optimal value of x: The above analysis does not provide practical guidelines for the minimization harm caused by crime. This topic is studied in the remainder of this paper. In Section 3, a specific algebraic form to the cost of crime function (1) is assigned. Sections 4 and 5 deal with the empirical evaluation of the costs of crime and police protection. This information is used in Section 6 to estimate the parameters of the cost of crime. This, and the results above, are used in Section 7 to specify a ceteris paribus minimum of harm due to crime in the US.
3. Cost of crime function to be used in the empirical analysis For an operational formulation of the problem of minimization of harm, the following quasisigmoidal algebraic function is assigned to (1): c ¼ ao =ða1 þ a2 xÞ;
ð4Þ
where ai are positive parameters. While details are not presented here, it is easy to show that (4) satisfies the assumptions made in (1). The same is true for the use of (4) to operationalize the total function of harm due to crime in (2).
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Function (4) includes the assumption that crime reaches the maximum of a0 =a1 when x ¼ 0: The assumption that such a maximum exists may or may not be reasonable. Without any police protection, no existing law could be enforced and crime would be maximized. However, under the same conditions, society itself would cease to exist. Since there would be no authority specifying the actions that constitute crimes, there would be no crime. From the first-order conditions for the minimization of t obtained using (4), and ignoring negative solutions because they have no reasonable interpretation, the optimal expenditure in police protection (opt x) becomes: opt x ¼ ½Sqrtðao a2 Þ a1 =a2 :
ð5Þ
Using (5), it can be shown that opt x is an increasing function of ao ; a decreasing function of a1 ; and that it could be an increasing or decreasing function of a2 : Details of this analysis are not presented here. However, it should be observed that the first two conclusions are intuitively acceptable, while the third agrees with results reported by Cameron [12]. While helpful, the analysis presented has thus far not provided any practical insight for optimal allocations of resources to police protection. For this, it is necessary to obtain what Yunker [13] calls a functionally and parametrically explicit model with numerical values for the parameters of (4) from a specific society. Further, this information must be used to determine the optimal expenditures for police protection that, according to the model, should exist in society. If this is not the case, the reasons for any deviations between the actual and optimal values should be identified. Steps in this direction are completed in the remaining sections of the current paper.
4. Estimation of the costs of crime The estimation of the costs of crime presents several problems. To begin, a working definition of crime is needed. Criminologists, as indicated by Croall [14] and Keve [15], do not agree in this respect. No attempt will thus be made here to settle the controversy. In this paper, the Federal Bureau of Investigation (FBI) approach, which divides crime into violent crime and property crime, is used as a point of departure. A class of personal crimes, including murder, forcible rape, and aggravated assault, is extracted from the former, while the class of property crimes is extended to include robbery in addition to burglary, larceny-theft, and motor vehicle theft and robbery. The data presented by the US Census Bureau [16, Table 293] on crime rates and in [17, Table 20] on population by state are used to compute the number of crimes by type and state. Identification and measurement of the different events that can be considered crimes do not yet allow for the statistical analysis of (4). In addition, data limitations must be taken into account. This problem is analyzed in some detail by Berger et al. [18], Chaiken and Chaiken [19], Parks [20] and Tarver et al. [21] for the US, and by Coleman and Moynihan [22], Deadman et al. [23] and MacDonald [24] for England and Wales. For the presentation here, the question of how to combine the different types of crimes to obtain an aggregate index must be dealt with. In addition, the values of this composite index must be made comparable to those of costs of police protection. A reasonable way to deal with this issue is to assign monetary values to the various types of crime and the costs of protection.
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Klaus [25] uses information on average property loss measured in dollars for each of the property crime types defined above. This approach has the advantage of being based on objective, clearly verifiable data. On the other hand, it does not consider the negative impact that even property crimes have on the wellbeing of their victims. As a consequence, Klaus [25] sub-estimates the costs of property crimes. Unfortunately, there does not seem to be information available to correct this bias. Klaus’ [25] method, implemented with data from [16, Table 299] on the number of property crimes, is thus used here to compute per capita losses due to property crime by state. The problem encountered for the monetary evaluation of the costs of property crime are intensified when attempts are made to assign dollar values to the costs of violent crimes against persons, since these crimes affect the wellbeing of their victims even when they do not bring about any direct financial damages. Despite this, there are at least three approaches to assign monetary values to the costs of such crimes. The first is provided by legislation on the financial penalties assigned to different crimes, and on the compensation that the state should provide to victims. An interesting note on this topic is presented by Barret and Harrison [26], listing such penalties in medieval England. Current and detailed information on state compensation is provided by Villmow [27] and Parent et al. [28]. Secondly, there is the compensation to victims of accidents and crimes specified in judicial decisions. See, for instance, the Pennsylvania Bar Institute [29] and the Pennsylvania Trial Lawyers Association [30,31]. One handicap of these two approaches is that they depend on the subjective opinions of the legislators or judges to specify the compensations they consider appropriate. On the other hand, the methods based on principles of economic theory and described, for instance, by Drummond et al. [32], largely eliminate this subjectivity. A clear and critical summary of current research along these lines is given by Phelps [33], while more detailed analyses are made by Tengs et al. [34] and Viscusi [35]. Interestingly, similar methods are often used for policy decisions in such areas as environmental pollution as shown by Freeman [36]. The references mentioned above show that the first two approaches often assign larger monetary costs to personal crimes than does the last approach. The reason is that they better account for the pain and suffering these crimes cause. Despite this, the evaluations below are based on one of the methods in [32]. It is consistent with approaches used for costing the impact of property crimes; and further, the data needed for its application are more readily available. On this basis, the cost of murder in each state is defined as the present value of the income that the victim would have received in the remaining years of his/her life. In this regard, it is assumed that murder victims are rather young, that they would have had 40 more years of working life, but only be employed during half those years. Further, while employed, they would have received an income equal to that of the average worker, as estimated using the data from [17, Table 727], and that the discount rate is 5%. With this, an estimate of the cost per murder for each state is obtained. To evaluate the cost of forcible rape, it is arbitrarily assumed that the cost of damage to the victim is equal to 25% of the cost of murder. The average property loss suffered by victims of this type of crime is then added. In the case of aggravated assault, the assumptions used to evaluate damages generated by a rape are maintained, but no property loss is added because none is reported.
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Table 1 Estimated monetary losses generated by crime US $ 1966
United States Alabamaa Alaska Arizona Arkansasa California Colorado Connecticut Delaware Dist. Of Columb Florida Georgiaa Hawaiia Idahoa Illinois Indiana Iowaa Kansasa Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesotaa Mississippia
Property
Personal
Total loss
55.92 51.19 54.38 89.50 46.21 56.42 51.08 45.29 57.40 128.11 81.52 68.26 59.72 32.91 56.95 48.30 34.72 47.17 34.98 71.40 30.96 64.52 46.16 64.36 43.07 62.58
462.40 395.18 654.84 491.79 333.40 599.83 348.28 353.85 654.87 1902.86 676.29 461.13 206.12 222.32 662.96 315.41 243.14 330.35 239.88 572.66 114.72 609.18 625.45 569.17 252.87 260.69
518.32 446.37 709.23 581.30 379.61 656.25 399.36 399.14 712.27 2030.97 757.81 529.39 265.84 255.22 719.91 363.72 277.85 377.52 274.86 644.06 145.68 673.69 671.60 633.53 295.94 323.28
Missouri Montana Nebraskaa Nevada New Hampshire New Jersey New Mexico New York North Carolinaa North Dakota Ohioa Oklahomaa Oregona Pennsylvaniaa Rhode Islanda South Carolina South Dakota Tennessee Texas Utaha Vermont Virginiaa Washingtona West Virginia Wisconsina Wyominga
Property
Personal
Total loss
57.98 41.50 48.30 77.21 23.59 50.29 71.41 42.32 61.36 27.59 51.31 56.85 60.94 41.41 50.33 60.18 26.83 61.22 64.30 56.65 31.47 39.73 73.48 32.22 39.72 32.56
421.82 178.30 351.43 431.90 103.53 367.94 657.22 519.73 434.03 74.15 245.84 415.18 346.34 326.64 262.16 667.26 146.04 575.86 507.63 254.18 127.42 277.25 391.15 297.42 198.13 211.35
479.80 219.81 399.73 509.11 127.12 418.23 728.64 562.05 495.39 101.74 297.15 472.03 407.27 368.05 312.49 727.43 172.86 637.07 571.93 310.84 158.89 316.97 464.63 329.64 237.85 243.91
Sources: US Census Bureau [16, Table 299]. US Census Bureau [17, Table 727]. Computations described in Section 4. a Identifies states whose crime losses show a negative relationship with police expenditures.
It is now possible to compute the total cost of each class of personal crimes. This value can then be added to the cost of property crimes, whose evaluation is outlined above, obtaining an overall cost of crime per state (Table 1). Dividing this figure by the state’s population one obtains the cost of crime per capita.
5. Estimation of the costs of police protection State and local public expenditures on personnel, equipment, etc. for police protection are a useful point of departure for evaluation of the costs of this service, although these costs may under or overstate the extent of police protection. Understatement may occur, for example, when the
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value of the lives lost and injuries suffered by police officers, and the overall costs of private police forces, are not included in the evaluation. Public expenditures may overestimate police protection because, as indicated by Bayley [37] and Dantzker [38], they do not account for the use of police resources in non-criminal matters. This is the case despite the fact that police presence, even when attending to non-criminal matters, may deter crime. It is also likely that the distribution of personnel time among different police functions varies from community to community, and, as a consequence, from state to state. Thus, any relationship that may exist between expenditures to deterabstain crime and total police expenditures may be rather weak. These limitations aside, information on state and local public expenditures for police protection is used below as an index of the total cost of this service. Lindgren [39] summarized and analyzed this information for 1990. Its counterpart for 1999, elaborated from [16, Tables 438 and 440] is presented in Table 2.
Table 2 Estimated expenditures p/c for police protection US $ 1966
United States Alabamaa Alaska Arizona Arkansasa California Colorado Connecticut Delaware Dist. Of Columbia Florida Georgiaa Hawaiia Idahoa Illinois Indiana Iowa Kansasa Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesotaa Mississippia
State
Local
Total
28.64 20.37 83.87 29.30 25.87 28.12 17.26 39.00 80.90 0.00 22.50 21.31 4.22 27.96 25.81 30.12 26.14 17.33 31.81 40.48 34.32 40.80 61.05 26.76 22.19 20.59
158.82 119.91 183.87 169.11 98.78 218.37 169.13 155.70 118.04 545.28 199.13 119.54 171.31 115.81 195.58 89.69 104.91 140.54 75.74 137.92 87.79 146.95 151.42 142.23 144.47 103.65
187.46 140.27 267.74 198.41 124.66 246.49 186.39 194.70 198.94 545.28 221.63 140.86 175.53 143.77 221.39 119.80 131.06 157.87 107.55 178.41 122.11 187.74 212.47 169.00 166.67 124.23
Missouri Montana Nebraskaa Nevada New Hampshire New Jersey New Mexico New York North Carolinaa North Dakota Ohioa Oklahomaa Oregona Pennsylvaniaa Rhode Islanda South Carolina South Dakota Tennessee Texas Utaha Vermont Virginiaa Washingtona West Virginia Wisconsina Wyominga
State
Local
Total
24.32 28.31 27.61 26.53 28.31 36.60 40.23 23.14 41.43 20.50 18.03 9.23 35.28 62.70 32.29 44.78 24.56 20.79 15.91 32.39 40.40 27.50 24.84 23.24 18.86 37.50
127.29 88.34 91.24 208.40 110.74 205.21 143.10 261.14 114.89 80.44 154.04 109.59 144.75 106.80 149.34 97.27 87.31 129.65 131.46 126.76 65.66 127.31 132.04 55.34 171.43 147.92
151.61 116.65 118.85 234.94 139.05 241.80 183.33 284.28 156.32 100.95 172.07 118.82 180.04 169.50 181.63 142.05 111.87 150.44 147.38 159.15 106.06 154.81 156.88 78.58 190.29 185.42
Sources: US Census Bureau [16, Tables 438 and 440]. Computations described in Section 5. a Identifies states whose crime losses show a negative relationship with police expenditures.
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6. Estimation of the parameters of function (4) Before proceeding to estimate the parameters of function (4), some observations will be presented on the controversy mentioned in Section 3 that surrounds its conceptual basis: the hypothesis that increases in police expenditures decrease crime. Theoretical support for this hypothesis is provided by Gottfredson and Hirschi [40], Deadman and Pyle [41] and others. However, as observed by Deadman et al. [23], in some of the statistical analyses available the hypothesis is accepted while in others it is rejected. This is illustrated by Eck and Maguire [9], Cameron [12], O’Connor and Gilman [42], and Wilson [43] for the US, by Mehay and Shoup [44] for the US and Great Britain and by Bayley [37] for several other countries. An explanation of these contradictions is provided by Jones [45], who suggests that, because expenditures on protection decrease crime, increases in crime are likely to generate public demand to increase expenditures on protection, and this demand frequently is met by the government. Stahura and Huff [46] observe that increments in these expenditures also increase the capability of the police to know and report crime. As a consequence, data are likely to show a positive correlation between these two variables, particularly when crime is increasing. Another reason for such contradictory results is that many, perhaps most, causes of crime may not be related to expenditures on police protection, and vice versa. Causes of crime can be found in the characteristics of human beings and in those of their communities, as argued, for instance, by Coleman and Moynihan [22] for England and Wales, Berger et al. [18] and Gottfredson and Hirschi [40] for the US, and Tsushima [47] for Japan. As a consequence, crime may increase independently of the availability of police protection. Similarly, expenditures on police may be influenced, not only by changes in the demand for any of its functions, but also by the economic resources available in a community, and, as indicated by Levitt [48] and Roberts and Stalans [49], by political opportunism. From these observations, it follows that statistical analyses may show the existence or non-existence of a relationship between crime and expenditures on police protection, and in the former case, that the relationship could be positive or negative. Estimation of the parameters of (4), using data from Tables 1 and 2, is done using the simplified ad-hoc approach outlined below. A preliminary analysis of the data from all states showed a weak positive correlation between expenditures on police protection and cost of crime. It was thus decided to divide the states into two groups on the basis of whether they did or did not show the expected negative relationship between these two variables. The first group of 22 states showed this negative relationship, while the remaining 28 showed the opposite. An additional consideration is that (4) is not linear. Despite the possibility of using methods of regression analysis especially developed to deal with nonlinearities, the following more direct approach is used here. The average cost of crime in the first group, $356.41, is assigned to ao : It is then possible to compute ao =ci —where ci is the cost of crime net the cost of police protection for state i—and to use these quotients as the explained variable in a regression in which a1 þ a2 x appear linearly. Judge et al. [50], among others, state that since the data to be used to estimate the parameters of this linear function are divided into two groups, the appropriate method to estimate them is
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regression analysis with a dummy variable that simultaneously affect ai for i ¼ 1; 2: With this, the following results were obtained: ao =c ¼ 0:313 þ 0:005x for group 1; ð0:003Þ
ð6Þ
ao =c ¼ 2:67 0:009x for group2; ð0:000Þ
ð7Þ
and where the quantities in parentheses represent the corresponding levels of significance of a2 : R2 for the entire analysis is 0.40 with Fð3;46Þ ¼ 8:574; significant at the 0.000 level. Given the results in (6), the function for t in (2) becomes t ¼ ½356:41=ð0:313 þ 0:005xÞ þ x:
ð8Þ
7. Minimization of harm caused by crime Function (8) provides the basis for an empirical analysis of Rubin’s [1] suggestion that minimizing harm is a solution of the crime policy conundrum. Using (5), the optimal per capita police expenditure is opt x ¼ $206:58:
ð9Þ
Using this value in (8) and (4), the minimum of harm caused by crime, i.e., t; is opt t ¼ $477:83;
ð10Þ
and that of the direct cost of crime, c; is opt c ¼ $271:25:
ð11Þ
It is useful to note that the values in (9)–(11) are not sensitive to changes in the value of ao ; which was used as the basis for (6) and (7). Opt x and opt c; while obtained from the minimization of t; are not, in themselves, minimal values. The minima for these two variables are 0. It follows that observed values of x and c—to be denoted with obs x and obs c—can be greater, equal to, or less than the optimal results above. The different forms of the relationship between the observed and optimal values of x and c are analyzed below. In states having the combination obs coopt c and obs xoopt x, losses due to criminal activity and the expenditures on police protection are at lower levels than those considered optimal in the model. That is, a desirable result with respect to losses incurred is achieved at a cost below expectations. States in such a situation enjoy the benefits of a particularly efficient police force. On the other hand, the combination obs coopt c and obs x>opt x suggests that the observed low levels of crime are being obtained with larger than needed expenditures on police protection. The most obvious interpretation of the combination obs c>opt c and obs xoopt x is that expenditures on police protection are not sufficiently large. Finally, obs c>opt c and obs x>opt x imply that the police are inefficient.
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Table 3 States in classes defined by characteristics of the observed and optimal values of losses due to crime (c) and expenditures on police protection (x) obs xoopt x Quadrant 1
obs coopt c
obs x>opt x Quadrant 2 Hawaiia Idaho Maine Montana New Hampshire
North Dakota South Dakota Vermont Wisconsina Wyominga
Alabamaa Arizona Arkansasa Colorado Connecticut Delaware Georgiaa Indianaa Iowaa Kansasa Kentucky Louisiana Maryland Michigan Minnesotaa Mississippia
Missouri Nebraskaa New Mexico North Carolinaa Ohioa Oklahomaa Oregona Pennsylvaniaa Rhode Islanda South Carolina Tennessee Texas Utah Virginia Washington West Virginia
Quadrant 3
obs c>opt c
Quadrant 4 Alaska California Florida Illinois Massachusetts Nevada New Jersey New York
Source: Explained in Section 7. a Identifies states whose crime losses decrease when police expenditures increase. obs x and obs c denote observed values of x and c in Tables 1 and 2. opt x and opt c denote values computed with Eqs (9) and (11).
These four possible inequalities between observed and optimal values of c and x can be used to group the states into four classes as presented in Table 3. There it can be observed that (1) Only the 10 states in the first quadrant have low crime losses and expenditures for police protection; i.e. benefit from efficient police forces. (2) There are no states in the second quadrant, showing that none has excessive expenditures for police protection to achieve low crime rates. (3) Most states are in the third quadrant, characterized by large losses due to crime and low expenditures for police protection. Expenditures here are thus insufficient. (4) Results for the eight states in the fourth quadrant indicate that their expenditures for police protection are not being efficiently used. Importantly, despite model and data limitations, the results in Table 3 are in agreement with the conflicting opinions on crime and police protection in the US as described, for instance, by Amnesty International [51], Brewer et al. [52], Cothran [53], and Fitzgerald [54]. An interesting detail is that Amnesty International [55–57] has criticized in separate reports California, Illinois
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and New York, that is, states that, according to the classification in Table 3, do not use their expenditures in police protection efficiently.
8. Conclusions and suggestions for future research The current analysis shows the need for further study of the interdependence between police protection and crime. Such a study should, as observed in Section 7, explicitly consider not only the influence of protection on crime, but also the possibility that crime may increase the public demand for protection, and as a consequence, its supply. In Section 1 it was indicated that the main objective of this paper is the operationalization of Rubin’s [1] idea that the minimization of harm should be the basis of policies to combat crime. It can be argued that this objective has been achieved. However, this initial step can be extended in several directions. To describe the first possibility, it should be recalled that the cost of crime used in this paper is measured by the property losses due to property crime plus the value of human capital attributable to crimes against persons. It is intuitively appealing to add to these values estimates of the reduction in the quality of life of the victims. A method to evaluate this reduction and the results obtained with its application is presented by Cohen [58]. Data availability is the only reason why it may not be possible to integrate this extended measure of cost into the model used in this paper. Another possibility is to assume that both the amount of police protection available and the efficiency of its use influence crime. This would imply the integration of the analyses made by Golden [59] and Chaiken and Crabill [60], dealing with the efficient use of available resources for protection with the methods proposed here, in which those resources are optimally specified. The analysis made in this paper could also be improved by considering several factors that influence crime. Thus, in addition to expenditures on protection, those on incarceration, education, employment, social capital, etc. should also be considered. This extension would include in (4) the variables representing these expenditures. The parameters of the modified function obtained would have to be estimated, and the model obtained would have to be used to determine optimal levels for all the expenditures included. A fourth improvement could combine the three possibilities mentioned above. In it, attention would be paid to the extended definition of the costs of crime and to the efficient use of all expenditures for all the crime deterrents considered in the extended function (4) suggested above. Finally, it is useful to observe that the approach in this paper, as well as the suggested extensions, can be applied to other policy areas. These include fire protection, health, and the maintenance of government-owned infrastructure.
Acknowledgements I want to thank Professors Jack Karns and John Mendeloff of the University of Pittsburgh and the Commission on Accreditation for law Enforcement Agencies for their assistance in collecting the information used in this paper, Prof. Edward L. Rubin and unknown referees for suggestions
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for its improvement, and to Dr. Barnett R. Parker, Editor-in-Chief of SEPS for his support and suggestions for extensive revisions on several earlier versions of this paper.
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[23] Deadman D, Pudney S, Pyle D. Measurement error in economic models of crime. In: MacDonald Z, Pyle D, editors. Illicit activity: the economics of crime, drugs and tax fraud. Burlington, VT: Ashgate Publishing Co.; 2000. [24] MacDonald Z. The under-reporting of property crime. In: MacDonald Z, Pyle D, editors. Illicit activity: the economics of crime, drugs and tax fraud. Burlington, VT: Ashgate Publishing Co.; 1999. [25] Klaus PA. The costs of crime to victims. Crime data brief. Washington, DC: Bureau of Justice Statistics; 1994. [26] Barrett A, Harrison C. Crime and punishment in England: a sourcebook. Philadelphia, PA: UCL Press Ltd.; 1999. [27] Villmow B. Victim compensation in some western countries. In: Sessar K, Kerner HJ, editors. Developments in crime and crime control research: German studies on victims, offenders and the public. New York: Springer; 1991. p. 66–86. [28] Parent DG, Auerbach B, Carlson KE. Compensating crime victims: a summary of policies and practices. Washington, DC: US Dept. of Justice, Office of Justice Programs, National Institute of Justice; 1992. [29] Pennsylvania Bar Institute. Proving damages in personal injury, death cases. Harrisburgh, PA: Pennsylvania Bar Institute, 1989. [30] Pennsylvania Trial Lawyers Association. What’s it worth?: evaluating and settling personal injury claims. Philadelphia, PA: Pennsylvania Trial Lawyers Association, 1995. [31] Pennsylvania Trial Lawyers Association. What’s it worth?: evaluating and settling personal injury cases. Philadelphia, PA: Pennsylvania Trial Lawyers Association, 1996. [32] Drummond MF, O’Brien BO, Stoddart GL, Torrance GW. Methods for the economic evaluation of health care programs. New York: Oxford University Press; 1997. [33] Phelps CE. Health economics. New York: HarperCollins Publishers; 1992. [34] Tengs TO, Adams ME, Pliskin JS, Safran DG, Siegel JE, Weinstein MC, Graham JD. Five hundred life-saving interventions and their cost-effectiveness. Risk Analysis 1995;15(3):369–90. [35] Viscusi WK. Fatal tradeoffs: public and private responsibilities for risk. New York: Oxford University Press; 1992. [36] Freeman III AW. The measurement of environmental and resource values: theory and methods. Washington, DC: Resources for the Future Press; 2003. [37] Bayley DH. Police for the future. New York: Oxford University Press; 1994. [38] Dantzker ML. Understanding today’s police. Englewood Cliffs, NJ: Prentice-Hall; 1995. [39] Lindgren S. Justice Expenditure, Employment, 1990. Bureau of Justice Statistics Bulletin, 1992. [40] Gottfredson MR, Hirschi T. A general theory of crime. Stanford, CA: Stanford University Press; 1990. [41] Deadman D, Pyle D. Crime, deterrence and economic factors. In: MacDonald Z, Pyle D, editors. Illicit activity: the economics of crime, drugs and tax fraud. Burlington, VT: Ashgate Publishing Co.; 2000. p. 61–74. [42] O’Connor RJ, Gilman B. The police role in deterring crime. In: Cramer JA, editor. Preventing crime. Beverly Hills, CA: SAGE Publications; 1978. p. 75–108. [43] Wilson JQ. Do the police prevent crime? In: Snortum JR, Hadar I, editors. Criminal justice: allies and adversaries. Pacific Palisades, CA: Palisades Publishers; 1978. p. 36–47. [44] Mehay SL, Shoup DC. Models of police services for program analysis. In: Nagel SS, editor. Modeling the criminal justice system. Beverly Hills, CA: SAGE Publications; 1977. p. 111–26. [45] Jones ET. The impact of crime rate changes on police protection expenditures in America cities. In: Pogrebin MR, Regoli RM, editors. Police administrative issues: techniques and functions. Millwood, NY: National University Publications; 1986. p. 103–6. [46] Stahura JIM, Huff CR. Crime and police employment: a structural model. In: Petersen DM, editor. Police work: strategies and outcomes in law enforcement. Beverly Hills, CA: SAGE Publications; 1979. p. 79–95. [47] Tsushima M. Economic structure and crime: the case of Japan. Journal of Socio-Economics 1996;25(4):497–515. [48] Levitt SD. Hiring police and building prisons pays off. The American Enterprise 1995;6(3):46. [49] Roberts VJ, Stalans LJ. Public opinion, crime and criminal justice. Boulder, CO: Westview Press; 1997. [50] Judge GG, Griffiths WE, Hill RC, Lutkepohl H, Tsoung-Caho L. The theory and practice of econometrics. New York: Wiley; 1985. [51] Amnesty International. United States of America: rights for all. London: Amnesty International Publications, 1998.
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[52] Brewer JD, Guelke A, Hume I, Moxon-Browne E, Wilford R. The police, public order and the state: policing in Great Britain, Norther Ireland, the Irish Republic, the USA, Israel, South Africa and China, 2nd ed.. New York: St. Martin’s Press; 1996. [53] Cothran H, editor. Police brutality: opposing viewpoints. San Diego: Greenhaven Press. [54] Fitzgerald TJ. Police in society. New York: H.W. Wilson Co.; 2000. [55] Amnesty International. USA: Police brutality and excessive force in the New York City police department. Amnesty International Publications, New York, NY, 1996. [56] Amnesty International. USA: Torture, ill-treatment and excessive force by police in Los Angeles, California. Amnesty International Publications, New York, NY, 1992. [57] Amnesty International. USA: Allegations of ill-treatment in Marion Prison, Illinois. Amnesty International Publications, London, UK, 1987. [58] Cohen MA. The crime victim’s perspective in cost-benefit analysis: the importance of monetizing tangible and intangible crime costs. In: Welsh BC, Farrington DP, Sherman LW, editors. Costs and benefits of preventing crime. Boulder, CO: Westview Press; 2001. p. 23–50. [59] Golden JW. Productivity and performance evaluation. In: Doemer WG, Dantzker ML, editors. Contemporary police organization and management: issues and trends. Boston: Butterworth-Heinemann; 1999. [60] Chaiken JIM, Crabill T. Police Models. In: Chaiken JIM, Crabill T, Holliday L, Jaquette D, Lawless M, Quade E, editors. Criminal justice models: an overview. Washington DC: National Institute of Law Enforcement and Criminal Justice; 1976. p. 46–89. Hector Correa is Professor, University of Pittsburgh, PA, and he teaches in the Graduate School of Public and International Affairs, the Katz Graduate School of Business, the School of Education and the School of Information Science. His research has appeared in more than 125 refereed articles in De Economist, Educational Planning, Education Research Journal, Ekistics, Higher Education Management, Higher Education Policy, Journal of Peace Research, Journal of Policy Modeling, Management Science and Policy Analysis, Mathematical Social Sciences, Policy and Society, Scientia Paedagogica Experimentalis, and Socio-Economic Planning Sciences. He has also published or edited 11 books.
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Optimal expenditures on police protection Hector Correa1,{ 3-N-27 Posvar Hall, University of Pittsburgh, Pittsburgh, PA 15260, USA Received 1 May 2002; received in revised form 1 September 2003; accepted 1 January 2004 Available online 24 May 2004
Abstract The object of this paper is to propose an approach for operationalizing Rubin’s (Minimizing Harm: a New Crime Policy for modern America, Westview Press, Boulder, CO, 1999) idea that minimizing harm is a solution to the crime policy conundrum. Harm is defined to be the total cost of damages due to crime plus the cost of police protection. Its minimization determines optimal expenditures for protection. This is an appropriate basis for specifying the optimal size of a police force, and provides a term of reference for actual policy decisions. Data for the states of the US are used to make the presentation more concrete and to clarify some of the problems that must be solved in actual applications of the method suggested. This does not eliminate the applicability of the approach to any other country or to the geo-political subdivisions within a country. The results obtained are of interest to policy makers dealing specifically with expenditures for police at local, regional or national levels or, more generally, with similar uses of public or private financial resources. r 2004 Elsevier Ltd. All rights reserved.
1. Introduction Rubin [1] suggests ‘‘minimizing harm as a solution to the crime policy conundrum’’. The object of this paper is to propose an approach to operationalize this idea. In it, harm is defined to be the total cost of damages due to crime plus the cost of police protection. Its minimization determines optimal expenditures for protection, an appropriate basis for specifying the optimal size of a police force. For comparison, a review of the methods currently available to estimate requirements for police personnel is presented in this Introduction.
1
Resource Professor, Growth Dynamics University Institute, Erasmus University, Rotterdam, The Netherlands. Deceased
{
0038-0121/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.seps.2004.01.002
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A necessarily incomplete review of the literature on police administration and management shows that only limited attention has been given to the optimum size of a police force and to the financial resources required. The mot commonly used forecasting methods are based on the assumption that the existing conditions are the most appropriate. Some examples of these methods are presented below. The Commission on Accreditation for Law Enforcement Agencies [2] suggests a method to estimate the number of patrol officers needed. It assumes a well-defined relationship between the number of complaints or incidents reported to a police department and the population of the community being served. This information is transformed into the amount of police time needed to deal with complaints, and to the number of officers needed to supply the time required. Omdorf [3] presents a numerical application of this method. The Commission’s approach could be improved by using, say, regression functions that include, as explanatory variables, the factors that influence the number of complaints and the time needed to attend to them. To a large extent, this is the method used when per capita expenditures per unit of time are expressed as functions of several of their determinants. A dated, but still useful, literature review of this method is presented by Hirsch [4]. Bahl et al. [5] extend the approaches just described. They specify and estimate a multiple function model that has as explained variables the number of police employees per thousand population, total compensation of police personnel per person in the community being served, and total crime per thousand population. Expanding on an observation made by Omdorf [3], the information on the demand for police services obtained using any of the methods mentioned above should be the basis for determining the number of supervisors and support personnel required in a police department. This idea is elaborated by Correa and Wakefield [6], who present a disaggregated demand-driven input– output model to analyze and forecast the personnel needed within a police department as determined by the number of officers providing services directly to the public. As a counterpart of their model, Ring and Dyson [7] suggest Markov chain models of the supply of police personnel. It is useful to emphasize that these methods simply extrapolate past experiences. They do not attempt to determine whether existing police resources are efficiently used. The claim made by Hudzik et al. [8], that manpower planning techniques like those outlined above are not consistently utilized to estimate requirements for police personnel, may still be valid today. On the other hand, Rubin [1] explicitly states that police resources influence crime and that both crime and the resources uses to combat it have costs. The minimization of harm caused by crime is the minimization of the total of these costs. For operationalization of Rubin’s [1] idea, a working definition of the harm caused by crime is presented in Section 2, and used as the basis for a simplified model. In Sections 3–7, this model is analyzed using data for the US for 1999. In the concluding section, possible improvements and extensions of the model and of its practical implementation are suggested.
2. A conceptual model for minimization of harm caused by crime As previously mentioned, harm caused by crime is defined here as equal to the total cost of damages due to crime plus cost of police protection. These two variables are related by the
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controversial hypothesis that police protection reduces the incidence of crime. As indicated by Eck and Maguire [9], and shown by Amove [10] and Brownfeld [11], some criminologists accept, while others reject, this hypothesis. On the other hand, the existence of police forces practically in every country in the world indicates that their protective value is generally recognized. Using this hypothesis as a point of departure, it is assumed that the incidence of crime approaches zero when expenditures on police protection increase without limit. This cannot be achieved, because police protection has costs. It follows that police protection should be increased only up to the point where the total costs of both crime and police protection are minimized. This, in agreement with the definition above, can be considered a simplified but operational formulation of Rubin’s [1] suggestion that the minimization of harm should be the basic objective of any crime reduction effort. An elementary mathematical formulation can be given to these ideas. Specifically, let: c ¼ f ðxÞ
ð1Þ
where c=cost of crime, x=cost of police protection, and f=convex function characterized with f ðxÞ-0 when x tends to infinity, f 0 ðxÞo0 f 00 ðxÞ > 0: Given (1), the total cost of crime and protection is t ¼ f ðxÞ þ x;
ð2Þ
where t=total harm due to crime, and all other symbols as previously defined. Function (2) provides the basis for minimization of the total cost of crime and protection. Elementary calculus shows that these conditions are: f 0 ðxÞ ¼ 1
ð3Þ
and f 00 ðxÞ > 0: The first-order condition can be used to specify the optimal value of x: The above analysis does not provide practical guidelines for the minimization harm caused by crime. This topic is studied in the remainder of this paper. In Section 3, a specific algebraic form to the cost of crime function (1) is assigned. Sections 4 and 5 deal with the empirical evaluation of the costs of crime and police protection. This information is used in Section 6 to estimate the parameters of the cost of crime. This, and the results above, are used in Section 7 to specify a ceteris paribus minimum of harm due to crime in the US.
3. Cost of crime function to be used in the empirical analysis For an operational formulation of the problem of minimization of harm, the following quasisigmoidal algebraic function is assigned to (1): c ¼ ao =ða1 þ a2 xÞ;
ð4Þ
where ai are positive parameters. While details are not presented here, it is easy to show that (4) satisfies the assumptions made in (1). The same is true for the use of (4) to operationalize the total function of harm due to crime in (2).
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Function (4) includes the assumption that crime reaches the maximum of a0 =a1 when x ¼ 0: The assumption that such a maximum exists may or may not be reasonable. Without any police protection, no existing law could be enforced and crime would be maximized. However, under the same conditions, society itself would cease to exist. Since there would be no authority specifying the actions that constitute crimes, there would be no crime. From the first-order conditions for the minimization of t obtained using (4), and ignoring negative solutions because they have no reasonable interpretation, the optimal expenditure in police protection (opt x) becomes: opt x ¼ ½Sqrtðao a2 Þ a1 =a2 :
ð5Þ
Using (5), it can be shown that opt x is an increasing function of ao ; a decreasing function of a1 ; and that it could be an increasing or decreasing function of a2 : Details of this analysis are not presented here. However, it should be observed that the first two conclusions are intuitively acceptable, while the third agrees with results reported by Cameron [12]. While helpful, the analysis presented has thus far not provided any practical insight for optimal allocations of resources to police protection. For this, it is necessary to obtain what Yunker [13] calls a functionally and parametrically explicit model with numerical values for the parameters of (4) from a specific society. Further, this information must be used to determine the optimal expenditures for police protection that, according to the model, should exist in society. If this is not the case, the reasons for any deviations between the actual and optimal values should be identified. Steps in this direction are completed in the remaining sections of the current paper.
4. Estimation of the costs of crime The estimation of the costs of crime presents several problems. To begin, a working definition of crime is needed. Criminologists, as indicated by Croall [14] and Keve [15], do not agree in this respect. No attempt will thus be made here to settle the controversy. In this paper, the Federal Bureau of Investigation (FBI) approach, which divides crime into violent crime and property crime, is used as a point of departure. A class of personal crimes, including murder, forcible rape, and aggravated assault, is extracted from the former, while the class of property crimes is extended to include robbery in addition to burglary, larceny-theft, and motor vehicle theft and robbery. The data presented by the US Census Bureau [16, Table 293] on crime rates and in [17, Table 20] on population by state are used to compute the number of crimes by type and state. Identification and measurement of the different events that can be considered crimes do not yet allow for the statistical analysis of (4). In addition, data limitations must be taken into account. This problem is analyzed in some detail by Berger et al. [18], Chaiken and Chaiken [19], Parks [20] and Tarver et al. [21] for the US, and by Coleman and Moynihan [22], Deadman et al. [23] and MacDonald [24] for England and Wales. For the presentation here, the question of how to combine the different types of crimes to obtain an aggregate index must be dealt with. In addition, the values of this composite index must be made comparable to those of costs of police protection. A reasonable way to deal with this issue is to assign monetary values to the various types of crime and the costs of protection.
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Klaus [25] uses information on average property loss measured in dollars for each of the property crime types defined above. This approach has the advantage of being based on objective, clearly verifiable data. On the other hand, it does not consider the negative impact that even property crimes have on the wellbeing of their victims. As a consequence, Klaus [25] sub-estimates the costs of property crimes. Unfortunately, there does not seem to be information available to correct this bias. Klaus’ [25] method, implemented with data from [16, Table 299] on the number of property crimes, is thus used here to compute per capita losses due to property crime by state. The problem encountered for the monetary evaluation of the costs of property crime are intensified when attempts are made to assign dollar values to the costs of violent crimes against persons, since these crimes affect the wellbeing of their victims even when they do not bring about any direct financial damages. Despite this, there are at least three approaches to assign monetary values to the costs of such crimes. The first is provided by legislation on the financial penalties assigned to different crimes, and on the compensation that the state should provide to victims. An interesting note on this topic is presented by Barret and Harrison [26], listing such penalties in medieval England. Current and detailed information on state compensation is provided by Villmow [27] and Parent et al. [28]. Secondly, there is the compensation to victims of accidents and crimes specified in judicial decisions. See, for instance, the Pennsylvania Bar Institute [29] and the Pennsylvania Trial Lawyers Association [30,31]. One handicap of these two approaches is that they depend on the subjective opinions of the legislators or judges to specify the compensations they consider appropriate. On the other hand, the methods based on principles of economic theory and described, for instance, by Drummond et al. [32], largely eliminate this subjectivity. A clear and critical summary of current research along these lines is given by Phelps [33], while more detailed analyses are made by Tengs et al. [34] and Viscusi [35]. Interestingly, similar methods are often used for policy decisions in such areas as environmental pollution as shown by Freeman [36]. The references mentioned above show that the first two approaches often assign larger monetary costs to personal crimes than does the last approach. The reason is that they better account for the pain and suffering these crimes cause. Despite this, the evaluations below are based on one of the methods in [32]. It is consistent with approaches used for costing the impact of property crimes; and further, the data needed for its application are more readily available. On this basis, the cost of murder in each state is defined as the present value of the income that the victim would have received in the remaining years of his/her life. In this regard, it is assumed that murder victims are rather young, that they would have had 40 more years of working life, but only be employed during half those years. Further, while employed, they would have received an income equal to that of the average worker, as estimated using the data from [17, Table 727], and that the discount rate is 5%. With this, an estimate of the cost per murder for each state is obtained. To evaluate the cost of forcible rape, it is arbitrarily assumed that the cost of damage to the victim is equal to 25% of the cost of murder. The average property loss suffered by victims of this type of crime is then added. In the case of aggravated assault, the assumptions used to evaluate damages generated by a rape are maintained, but no property loss is added because none is reported.
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Table 1 Estimated monetary losses generated by crime US $ 1966
United States Alabamaa Alaska Arizona Arkansasa California Colorado Connecticut Delaware Dist. Of Columb Florida Georgiaa Hawaiia Idahoa Illinois Indiana Iowaa Kansasa Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesotaa Mississippia
Property
Personal
Total loss
55.92 51.19 54.38 89.50 46.21 56.42 51.08 45.29 57.40 128.11 81.52 68.26 59.72 32.91 56.95 48.30 34.72 47.17 34.98 71.40 30.96 64.52 46.16 64.36 43.07 62.58
462.40 395.18 654.84 491.79 333.40 599.83 348.28 353.85 654.87 1902.86 676.29 461.13 206.12 222.32 662.96 315.41 243.14 330.35 239.88 572.66 114.72 609.18 625.45 569.17 252.87 260.69
518.32 446.37 709.23 581.30 379.61 656.25 399.36 399.14 712.27 2030.97 757.81 529.39 265.84 255.22 719.91 363.72 277.85 377.52 274.86 644.06 145.68 673.69 671.60 633.53 295.94 323.28
Missouri Montana Nebraskaa Nevada New Hampshire New Jersey New Mexico New York North Carolinaa North Dakota Ohioa Oklahomaa Oregona Pennsylvaniaa Rhode Islanda South Carolina South Dakota Tennessee Texas Utaha Vermont Virginiaa Washingtona West Virginia Wisconsina Wyominga
Property
Personal
Total loss
57.98 41.50 48.30 77.21 23.59 50.29 71.41 42.32 61.36 27.59 51.31 56.85 60.94 41.41 50.33 60.18 26.83 61.22 64.30 56.65 31.47 39.73 73.48 32.22 39.72 32.56
421.82 178.30 351.43 431.90 103.53 367.94 657.22 519.73 434.03 74.15 245.84 415.18 346.34 326.64 262.16 667.26 146.04 575.86 507.63 254.18 127.42 277.25 391.15 297.42 198.13 211.35
479.80 219.81 399.73 509.11 127.12 418.23 728.64 562.05 495.39 101.74 297.15 472.03 407.27 368.05 312.49 727.43 172.86 637.07 571.93 310.84 158.89 316.97 464.63 329.64 237.85 243.91
Sources: US Census Bureau [16, Table 299]. US Census Bureau [17, Table 727]. Computations described in Section 4. a Identifies states whose crime losses show a negative relationship with police expenditures.
It is now possible to compute the total cost of each class of personal crimes. This value can then be added to the cost of property crimes, whose evaluation is outlined above, obtaining an overall cost of crime per state (Table 1). Dividing this figure by the state’s population one obtains the cost of crime per capita.
5. Estimation of the costs of police protection State and local public expenditures on personnel, equipment, etc. for police protection are a useful point of departure for evaluation of the costs of this service, although these costs may under or overstate the extent of police protection. Understatement may occur, for example, when the
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value of the lives lost and injuries suffered by police officers, and the overall costs of private police forces, are not included in the evaluation. Public expenditures may overestimate police protection because, as indicated by Bayley [37] and Dantzker [38], they do not account for the use of police resources in non-criminal matters. This is the case despite the fact that police presence, even when attending to non-criminal matters, may deter crime. It is also likely that the distribution of personnel time among different police functions varies from community to community, and, as a consequence, from state to state. Thus, any relationship that may exist between expenditures to deterabstain crime and total police expenditures may be rather weak. These limitations aside, information on state and local public expenditures for police protection is used below as an index of the total cost of this service. Lindgren [39] summarized and analyzed this information for 1990. Its counterpart for 1999, elaborated from [16, Tables 438 and 440] is presented in Table 2.
Table 2 Estimated expenditures p/c for police protection US $ 1966
United States Alabamaa Alaska Arizona Arkansasa California Colorado Connecticut Delaware Dist. Of Columbia Florida Georgiaa Hawaiia Idahoa Illinois Indiana Iowa Kansasa Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesotaa Mississippia
State
Local
Total
28.64 20.37 83.87 29.30 25.87 28.12 17.26 39.00 80.90 0.00 22.50 21.31 4.22 27.96 25.81 30.12 26.14 17.33 31.81 40.48 34.32 40.80 61.05 26.76 22.19 20.59
158.82 119.91 183.87 169.11 98.78 218.37 169.13 155.70 118.04 545.28 199.13 119.54 171.31 115.81 195.58 89.69 104.91 140.54 75.74 137.92 87.79 146.95 151.42 142.23 144.47 103.65
187.46 140.27 267.74 198.41 124.66 246.49 186.39 194.70 198.94 545.28 221.63 140.86 175.53 143.77 221.39 119.80 131.06 157.87 107.55 178.41 122.11 187.74 212.47 169.00 166.67 124.23
Missouri Montana Nebraskaa Nevada New Hampshire New Jersey New Mexico New York North Carolinaa North Dakota Ohioa Oklahomaa Oregona Pennsylvaniaa Rhode Islanda South Carolina South Dakota Tennessee Texas Utaha Vermont Virginiaa Washingtona West Virginia Wisconsina Wyominga
State
Local
Total
24.32 28.31 27.61 26.53 28.31 36.60 40.23 23.14 41.43 20.50 18.03 9.23 35.28 62.70 32.29 44.78 24.56 20.79 15.91 32.39 40.40 27.50 24.84 23.24 18.86 37.50
127.29 88.34 91.24 208.40 110.74 205.21 143.10 261.14 114.89 80.44 154.04 109.59 144.75 106.80 149.34 97.27 87.31 129.65 131.46 126.76 65.66 127.31 132.04 55.34 171.43 147.92
151.61 116.65 118.85 234.94 139.05 241.80 183.33 284.28 156.32 100.95 172.07 118.82 180.04 169.50 181.63 142.05 111.87 150.44 147.38 159.15 106.06 154.81 156.88 78.58 190.29 185.42
Sources: US Census Bureau [16, Tables 438 and 440]. Computations described in Section 5. a Identifies states whose crime losses show a negative relationship with police expenditures.
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6. Estimation of the parameters of function (4) Before proceeding to estimate the parameters of function (4), some observations will be presented on the controversy mentioned in Section 3 that surrounds its conceptual basis: the hypothesis that increases in police expenditures decrease crime. Theoretical support for this hypothesis is provided by Gottfredson and Hirschi [40], Deadman and Pyle [41] and others. However, as observed by Deadman et al. [23], in some of the statistical analyses available the hypothesis is accepted while in others it is rejected. This is illustrated by Eck and Maguire [9], Cameron [12], O’Connor and Gilman [42], and Wilson [43] for the US, by Mehay and Shoup [44] for the US and Great Britain and by Bayley [37] for several other countries. An explanation of these contradictions is provided by Jones [45], who suggests that, because expenditures on protection decrease crime, increases in crime are likely to generate public demand to increase expenditures on protection, and this demand frequently is met by the government. Stahura and Huff [46] observe that increments in these expenditures also increase the capability of the police to know and report crime. As a consequence, data are likely to show a positive correlation between these two variables, particularly when crime is increasing. Another reason for such contradictory results is that many, perhaps most, causes of crime may not be related to expenditures on police protection, and vice versa. Causes of crime can be found in the characteristics of human beings and in those of their communities, as argued, for instance, by Coleman and Moynihan [22] for England and Wales, Berger et al. [18] and Gottfredson and Hirschi [40] for the US, and Tsushima [47] for Japan. As a consequence, crime may increase independently of the availability of police protection. Similarly, expenditures on police may be influenced, not only by changes in the demand for any of its functions, but also by the economic resources available in a community, and, as indicated by Levitt [48] and Roberts and Stalans [49], by political opportunism. From these observations, it follows that statistical analyses may show the existence or non-existence of a relationship between crime and expenditures on police protection, and in the former case, that the relationship could be positive or negative. Estimation of the parameters of (4), using data from Tables 1 and 2, is done using the simplified ad-hoc approach outlined below. A preliminary analysis of the data from all states showed a weak positive correlation between expenditures on police protection and cost of crime. It was thus decided to divide the states into two groups on the basis of whether they did or did not show the expected negative relationship between these two variables. The first group of 22 states showed this negative relationship, while the remaining 28 showed the opposite. An additional consideration is that (4) is not linear. Despite the possibility of using methods of regression analysis especially developed to deal with nonlinearities, the following more direct approach is used here. The average cost of crime in the first group, $356.41, is assigned to ao : It is then possible to compute ao =ci —where ci is the cost of crime net the cost of police protection for state i—and to use these quotients as the explained variable in a regression in which a1 þ a2 x appear linearly. Judge et al. [50], among others, state that since the data to be used to estimate the parameters of this linear function are divided into two groups, the appropriate method to estimate them is
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regression analysis with a dummy variable that simultaneously affect ai for i ¼ 1; 2: With this, the following results were obtained: ao =c ¼ 0:313 þ 0:005x for group 1; ð0:003Þ
ð6Þ
ao =c ¼ 2:67 0:009x for group2; ð0:000Þ
ð7Þ
and where the quantities in parentheses represent the corresponding levels of significance of a2 : R2 for the entire analysis is 0.40 with Fð3;46Þ ¼ 8:574; significant at the 0.000 level. Given the results in (6), the function for t in (2) becomes t ¼ ½356:41=ð0:313 þ 0:005xÞ þ x:
ð8Þ
7. Minimization of harm caused by crime Function (8) provides the basis for an empirical analysis of Rubin’s [1] suggestion that minimizing harm is a solution of the crime policy conundrum. Using (5), the optimal per capita police expenditure is opt x ¼ $206:58:
ð9Þ
Using this value in (8) and (4), the minimum of harm caused by crime, i.e., t; is opt t ¼ $477:83;
ð10Þ
and that of the direct cost of crime, c; is opt c ¼ $271:25:
ð11Þ
It is useful to note that the values in (9)–(11) are not sensitive to changes in the value of ao ; which was used as the basis for (6) and (7). Opt x and opt c; while obtained from the minimization of t; are not, in themselves, minimal values. The minima for these two variables are 0. It follows that observed values of x and c—to be denoted with obs x and obs c—can be greater, equal to, or less than the optimal results above. The different forms of the relationship between the observed and optimal values of x and c are analyzed below. In states having the combination obs coopt c and obs xoopt x, losses due to criminal activity and the expenditures on police protection are at lower levels than those considered optimal in the model. That is, a desirable result with respect to losses incurred is achieved at a cost below expectations. States in such a situation enjoy the benefits of a particularly efficient police force. On the other hand, the combination obs coopt c and obs x>opt x suggests that the observed low levels of crime are being obtained with larger than needed expenditures on police protection. The most obvious interpretation of the combination obs c>opt c and obs xoopt x is that expenditures on police protection are not sufficiently large. Finally, obs c>opt c and obs x>opt x imply that the police are inefficient.
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Table 3 States in classes defined by characteristics of the observed and optimal values of losses due to crime (c) and expenditures on police protection (x) obs xoopt x Quadrant 1
obs coopt c
obs x>opt x Quadrant 2 Hawaiia Idaho Maine Montana New Hampshire
North Dakota South Dakota Vermont Wisconsina Wyominga
Alabamaa Arizona Arkansasa Colorado Connecticut Delaware Georgiaa Indianaa Iowaa Kansasa Kentucky Louisiana Maryland Michigan Minnesotaa Mississippia
Missouri Nebraskaa New Mexico North Carolinaa Ohioa Oklahomaa Oregona Pennsylvaniaa Rhode Islanda South Carolina Tennessee Texas Utah Virginia Washington West Virginia
Quadrant 3
obs c>opt c
Quadrant 4 Alaska California Florida Illinois Massachusetts Nevada New Jersey New York
Source: Explained in Section 7. a Identifies states whose crime losses decrease when police expenditures increase. obs x and obs c denote observed values of x and c in Tables 1 and 2. opt x and opt c denote values computed with Eqs (9) and (11).
These four possible inequalities between observed and optimal values of c and x can be used to group the states into four classes as presented in Table 3. There it can be observed that (1) Only the 10 states in the first quadrant have low crime losses and expenditures for police protection; i.e. benefit from efficient police forces. (2) There are no states in the second quadrant, showing that none has excessive expenditures for police protection to achieve low crime rates. (3) Most states are in the third quadrant, characterized by large losses due to crime and low expenditures for police protection. Expenditures here are thus insufficient. (4) Results for the eight states in the fourth quadrant indicate that their expenditures for police protection are not being efficiently used. Importantly, despite model and data limitations, the results in Table 3 are in agreement with the conflicting opinions on crime and police protection in the US as described, for instance, by Amnesty International [51], Brewer et al. [52], Cothran [53], and Fitzgerald [54]. An interesting detail is that Amnesty International [55–57] has criticized in separate reports California, Illinois
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and New York, that is, states that, according to the classification in Table 3, do not use their expenditures in police protection efficiently.
8. Conclusions and suggestions for future research The current analysis shows the need for further study of the interdependence between police protection and crime. Such a study should, as observed in Section 7, explicitly consider not only the influence of protection on crime, but also the possibility that crime may increase the public demand for protection, and as a consequence, its supply. In Section 1 it was indicated that the main objective of this paper is the operationalization of Rubin’s [1] idea that the minimization of harm should be the basis of policies to combat crime. It can be argued that this objective has been achieved. However, this initial step can be extended in several directions. To describe the first possibility, it should be recalled that the cost of crime used in this paper is measured by the property losses due to property crime plus the value of human capital attributable to crimes against persons. It is intuitively appealing to add to these values estimates of the reduction in the quality of life of the victims. A method to evaluate this reduction and the results obtained with its application is presented by Cohen [58]. Data availability is the only reason why it may not be possible to integrate this extended measure of cost into the model used in this paper. Another possibility is to assume that both the amount of police protection available and the efficiency of its use influence crime. This would imply the integration of the analyses made by Golden [59] and Chaiken and Crabill [60], dealing with the efficient use of available resources for protection with the methods proposed here, in which those resources are optimally specified. The analysis made in this paper could also be improved by considering several factors that influence crime. Thus, in addition to expenditures on protection, those on incarceration, education, employment, social capital, etc. should also be considered. This extension would include in (4) the variables representing these expenditures. The parameters of the modified function obtained would have to be estimated, and the model obtained would have to be used to determine optimal levels for all the expenditures included. A fourth improvement could combine the three possibilities mentioned above. In it, attention would be paid to the extended definition of the costs of crime and to the efficient use of all expenditures for all the crime deterrents considered in the extended function (4) suggested above. Finally, it is useful to observe that the approach in this paper, as well as the suggested extensions, can be applied to other policy areas. These include fire protection, health, and the maintenance of government-owned infrastructure.
Acknowledgements I want to thank Professors Jack Karns and John Mendeloff of the University of Pittsburgh and the Commission on Accreditation for law Enforcement Agencies for their assistance in collecting the information used in this paper, Prof. Edward L. Rubin and unknown referees for suggestions
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for its improvement, and to Dr. Barnett R. Parker, Editor-in-Chief of SEPS for his support and suggestions for extensive revisions on several earlier versions of this paper.
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[52] Brewer JD, Guelke A, Hume I, Moxon-Browne E, Wilford R. The police, public order and the state: policing in Great Britain, Norther Ireland, the Irish Republic, the USA, Israel, South Africa and China, 2nd ed.. New York: St. Martin’s Press; 1996. [53] Cothran H, editor. Police brutality: opposing viewpoints. San Diego: Greenhaven Press. [54] Fitzgerald TJ. Police in society. New York: H.W. Wilson Co.; 2000. [55] Amnesty International. USA: Police brutality and excessive force in the New York City police department. Amnesty International Publications, New York, NY, 1996. [56] Amnesty International. USA: Torture, ill-treatment and excessive force by police in Los Angeles, California. Amnesty International Publications, New York, NY, 1992. [57] Amnesty International. USA: Allegations of ill-treatment in Marion Prison, Illinois. Amnesty International Publications, London, UK, 1987. [58] Cohen MA. The crime victim’s perspective in cost-benefit analysis: the importance of monetizing tangible and intangible crime costs. In: Welsh BC, Farrington DP, Sherman LW, editors. Costs and benefits of preventing crime. Boulder, CO: Westview Press; 2001. p. 23–50. [59] Golden JW. Productivity and performance evaluation. In: Doemer WG, Dantzker ML, editors. Contemporary police organization and management: issues and trends. Boston: Butterworth-Heinemann; 1999. [60] Chaiken JIM, Crabill T. Police Models. In: Chaiken JIM, Crabill T, Holliday L, Jaquette D, Lawless M, Quade E, editors. Criminal justice models: an overview. Washington DC: National Institute of Law Enforcement and Criminal Justice; 1976. p. 46–89. Hector Correa is Professor, University of Pittsburgh, PA, and he teaches in the Graduate School of Public and International Affairs, the Katz Graduate School of Business, the School of Education and the School of Information Science. His research has appeared in more than 125 refereed articles in De Economist, Educational Planning, Education Research Journal, Ekistics, Higher Education Management, Higher Education Policy, Journal of Peace Research, Journal of Policy Modeling, Management Science and Policy Analysis, Mathematical Social Sciences, Policy and Society, Scientia Paedagogica Experimentalis, and Socio-Economic Planning Sciences. He has also published or edited 11 books.