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Urban Law Enforcement in Canada: An Empirical AnalysisAuthor(s): William J. Furlong and Stephen L. MehaySource: The Canadian Journal of Economics / Revue canadienne d'Economique, Vol. 14, No. 1(Feb., 1981), pp. 44-57Published by: Wiley on behalf of the Canadian Economics AssociationStable URL: http://www.jstor.org/stable/134839 .

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Urban law enforcement in Canada: an empirical analysis W I L L I A M J. F U R L O N G / Queen's University

S T E P H E N L. M E H A Y/ San Jose State University

Abstract. This paper examines the issue of crime deterrence as supplied by a single urban law enforcement agency. A simultaneous model consisting of the supply of offences, police production function, and police deployment function is specified and estimated.Account is also taken of crime spillovers among observations and the daily mobility patterns of the population. The deterrent impact of police output is confirmed, but the link between police inputs and the production of deterrence is found to be weak. Consideration of the population's mobility significantly reduces the effect on crime rates of socio-economic factors such as unemployment.

L'application de la loi dans une ville au Canada: une analyse empirique. Ce m6moire etudie les effets dissuasifs sur les criminels des activites d'un seul corps de police. Les auteurs elaborent un modele specifiant une fonction d'offre d'actes criminels, une fonction de production des services policiers et une fonction de deploiement du personnel policier, et puis ils calibrent leur modele. Les auteurs tiennent compte des effets de retomb6e d'un quartier a l'autre ainsi que des patterns journaliers de mobilite de la population a l'int6rieur de la communaut6 urbaine. Le m6moire vient confirmer l'effet dissuasif de l'activit6 policiere mais le lien entre le taux d'activit6 policiere et le niveau de dissuasion est faible. Une prise en compte de la mobilit6 de la population tend a r6duire de fagon consid6rable l'effet des facteurs socio-6conomiques comme le chomage sur le taux de criminalite.

INTRODUCTION

The purpose of this study is to examine empirically the existence and strength of the deterrent effects of urban police activities in a major Canadian metropolitan area. The hypothesis that criminal justice sanctions deter crime by altering the structure of incentives facing potential offenders was formulated initially by Becker (1968) and extended by Ehrlich (1973). The

Financial assistance provided by the solicitor-general of Canada is gratefully acknowledged. The authors would also like to acknowledge the helpful comments of Richard Arnott and members of the Queen's University Economics Workshop. An earlier version of this paper was presented at the Southern Economic Association meetings in Washington, D.C.

Canadian Journal of Economics/Revue canadienne d'Economique, XIV, No. 1 February/fevrier 1981. Printed in Canada/lmprime au Canada.

0008-4085 / 81 / 0000-0044 $01.50 ?) 1981 Canadian Economics Association



Urban law enforcement in Canada / 45

deterrent hypothesis has been examined extensively in previous econometric studies and, in general, the results have supported the predictions derived from the economic model of offender behaviour. Nonetheless, interpretation of the results of these studies has been clouded by numerous problems.1

A major problem in assessing the deterrent effect of the police is that the bulk of the econometric crime literature has used aggregated cross-sectional data for estimation purposes, often the state, county, or SMSA level for u.s. jurisdictions. The only Canadian crime deterrence studies (Avio and Clark, 1976, 1978) also used aggregated observations; provincial and Ontario census division, respectively. The level of aggregation in the data affects the accuracy of estimates of the effect of municipal police on crime2 and the implications for resource allocation at that level. Those studies which have used disaggregated data have produced conflicting results,3 and no such disaggregated studies of police deterrent effects have been conducted for Canadian cities.

This study extends and improves previous econometric analyses of crime deterrence in several ways. First, we employ a disaggregated data base composed of districts located within a single Canadian metropolitan area, Montreal. Second, our data reflect both the underlying pattern of resource deployment across districts (neighbourhoods) and the distribution of manpower between the two major crime deterrence police programs, patrol and investigation. The disaggregated data should enable us to establish the full deterrence link between alternative police deployment strategies and crime. It should also allow us to test a richer set of hypotheses concerning police resource allocation. Specifically, a three-equation simultaneous model is formulated to examine the impact of alternative manpower levels and deployment on clearance rates and the effect of the latter on property crime rates.

We augment and modify existing specifications of the crime deterrence model to incorporate additional factors and to sharpen the focus on the police. Because we are examining police services in a single metropolitan area, potential crime spillovers across neighbourhoods may bias empirical estimation of police deterrence effects. While previous cross-sectional studies have largely ignored the crime spillover problem,4 we explicitly integrate crime displacement effects into the model. A second source of bias in previous

1 For a survey and critical analysis of numerous econometric studies of crime see National Research Council (1978) and Taylor (1978).

2 Aggregated data will yield accurate results only if all micro units that comprise the aggregate react identically to changes in the variables; the estimated effect of local police will be an average of the true effects for all local units in the aggregate.

3 While a more direct deterrence link between the police and crime has been examined and supported by some previous studies (Thaler, 1977; Chapman, et al., 1975), it has also been either rejected or only weakly supported by numerous others (Pogue, 1975; Carr-Hill and Stern, 1973; Greenwood and Wadycki, 1973; Swimmer, 1974; Mathur, 1978).

4 The major exception is a study by Mehay (1977).



46 / William J. Furlong and Stephen L. Mehay

empirical estimates of deterrence is the omission of the effect of daily commutation patterns in metropolitan areas. In this study an alternative measure of district population, based on both daytime and night-time population, is used to adjust variables expressed in per capita terms.

EMPIRICAL MODEL AND DATA

The simultaneous system consists of offence supply, police output and manpower deployment equations. With a given level of resources, the chosen deployment strategy will affect police output, measured as clearances, in each district. Changes in the number of clearances in each district will alter crime rates which, in turn, will influence the police agency, either directly or indirectly through pressure from district residents, to revise the deployment of resources. Hence, the level of crime, police output, and geographic deployment of resources are assumed to be simultaneously determined. The model is estimated with data from the Montreal Urban Community (Muc).

The MUC Police Department is composed of thirty-nine police districts, or stations, thirty-eight of which comprise the sample observations for this study.5 We shall discuss each equation of the model in turn.

The supply of offences The individual decision to participate in illegal activities is assumed to depend on the expected utility of the net monetary gain where all relevant risk factors and potential rewards (monetary and psychic) are considered, including the opportunity cost of forgone legal earnings.6 The offence supply equations are specified to reflect the various economic risk and gain factors:

n cRj = Bo + BlcLCj + B2 In uNj + B3 In Yj + B4 In YGj

+ B5 In vLj + B6 In SLj + B7 DFj + el,(1) where

cR1j = rate of offences of type c in districtj,

CL,j = clearance rate for offence type c in districtj,

UNj = male unemployment rate inj,

Yj = average household income inj,

YGj = percentage of population male and aged fifteen to twenty-four inj,

VLj = median value of owner-occupied detached dwellings inj,

SLj = average sales per retail store inj,

DFj = crime spillover measure forj.

5 One district is omitted because it is devoted entirely to recreational use. 6 See Becker (1968) and Ehrlich (1973) for a full exposition of the basic model of individual

participation in criminal activities.




Separate offence supply equations are estimated for robbery (ROB), breaking and entering (BNE), and theft (THEFT). In addition, two unweighted crime indexes are used as dependent variables. The first is the unweighted sum of the above three property offences (PROP). The second index, MA, includes the violent crimes of homicide, rape, and assault in addition to the three property offences.7

The measure of police output is the clearance rate. An offence is classified as 'cleared' when sufficient evidence is available to identify and arrest suspects and to lay supportable charges, even though, as often happens, no arrest is made, owing to extenuating circumstances. Hence, clearances are composed of two separate types - crimes cleared by arrest and crimes cleared 'otherwise.' For robbery and breaking and entering the clearance rate is the ratio of crimes cleared by arrest to reported incidents. For theft, it was necessary to use total clearances to form the clearance rate, because of a lack of data.8

Because unemployment tends to reduce the opportunity cost of crime participation by individuals, the male unemployment rate (UN) is entered as an explanatory variable in the offence supply equations. Forgone legal income after capture and imprisonment is another opportunity cost associated with crime participation, accounted for by entering average household income (Y) in the crime equations. Since arrest data indicate an unduly high propensity towards crime by younger males, the proportion of the district's population composed of males aged fifteen to twenty-four is entered in the crime equations (YG).

Data on criminal earnings, either actual or expected, are of course difficult to obtain. We must rely on proxies to include the criminal's wage in the model. In an urban environment two classes of ciiminal targets appear important, commercial establishments and private citizens or their residences. Two proxy variables are included in the offence equations to reflect differential opportunities for monetary gain from crime across districts - the average sales per retail store in each district (SL) and median value of residences (vL).

It is assumed that the contents of commercial and residential units are the true targets of offenders and that the contents are proportional to the values of SL

and VL.9 In an intrametropolitan sample it is necesssary to represent both classes of criminal targets, because often one class or the other may be excluded from a district owing to zoning ordinances.

7 Misclassification of crimes often occurs and may introduce biases into the reported rates for individual crimes. Use of the two crime indexes may tend to cancel these misclassification effects. A second rationale for the crime indexes stems from the possibility for substitution among offences by offenders. Substitution effects may be falsely identified as deterrence if each individual crime is examined in isolation.

8 Nationwide, the proportion of non-arrest clearances for theft tends to be small, only about 8 per cent (Bell-Rowbotham and Boydell, 1972). Hence, actual differences between the clearance measures used for the three property crimes may be slight.

9 These variables encompass a wider spectrum of targets than variables used in previous studies. Avio and Clark (1976), for example, used the number of households with record- playing equipment.




One problem that arises in a study using observations of intracity areas is crime spillovers across district boundaries. To the extent that offenders are mobile, the socio-economic characteristics of a given district may be unrelated to the local crime pattern. Further, when the distribution of police manpower and therefore the risk of arrest is altered across districts, offenders may simply shift locations, presumably moving away from areas which have become relatively risky towards those that are safer. If so, it will be difficult to identify true police deterrence effects in a given district, since deterred crime may merely be crime that is exported to neighbouring districts.

Previous studies dealing with crime spillovers (Mehay, 1977; Avio and Clark, 1978) hypothesized that offenders respond to differentials in apprehension risk across jurisdictions. This specification is incomplete, since it omits a second important consideration in the criminal's selection of a target district: the potential pay off. The attractiveness of targets in district j is defined as Aj = (1 - CLPj) VSj, where the first term, 1 minus the clearance rate for all property offences, is the probability of success in j, and vs is the potential 'victim stock' inj, where VSj = SLj + VLj. I

Owing to transportation and information costs associated with committing offences in more distant locations, it is plausible to expect that spillovers will tend to decline with distance between any two districts i andj. Therefore, we confine the analysis of spillovers to contiguous districts. A contiguous area for each home districtj is identified as the set of police districts sharing common borders with]. The variable specified to account for the impact on crime rates in districtj of the differential attractiveness betweenj and its contiguous area i is: DFj = 2i=1NiAi INj - Ai, where Nj is the total number of districts adjacent to j. DF iS interpreted as the differential between average attractiveness of targets in the relevant contiguous area and attractiveness of targets inj. The hypothesized relationship between the absolute value of DF and the crime rate inj is negative; the larger DF, the more crime tends to 'spill out' ofj and into other areas.".

Police output equation The police clearance rate is assumed to be determined by the following factors:

CLej = a + a, In CPj + a2 In DNj + a3 In INj + a4 In PTj + e2j (2)

10 The summation of VL and SL in the construction of the victim stock will be warranted so long as the elasticities of crime with respect to each are approximately equal.

11 Because crime spillovers will depend on the distance between districts, the error structure of the supply of offences will be spatially autocorrelated. Cliff and Ord (1973) suggest that spatial autocorrelation be handled by a GLS procedure with the error terms weighted by an accessibility matrix. Arora and Brown (1977) argue that since accessibility is a system- atic influence, it should be included as an explanatory variable rather than in the disturbance terms. We follow the latter suggestion by including DF in the equation to capture crime spillovers and to purge the error structure of spatial autocorrelation.




where

cPj = police officers per 1,000 population in districtj,

DNj = population density inj,

INj = ratio of investigators to total manpower inj,

PTj = ratio of patrol manpower to total manpower inj.

Clearances will be affected not only by total police manpower in each district, but also by the distribution of manpower among various functions, given the level of total manpower. The ratio of detective-sergeants to total police manpower (IN) measures the independent impact of investigators on clearances, while the ratio of constables in patrol cars to total officers (PT) measures the impact of patrol activities in a district. 12 Population density (DN) reflects the influence of the physical environment on the ability of the police to produce clearances.

Police manpower equation In cross-sectional studies employing independent municipalities as observations, a manpower determinants equation can be interpreted as a conven- tional labour demand function, determined by wage rates, community income, tastes, etc. In this study, however, the observations are contained within a single police department and the dependent variable reflects the deployment of manpower across districts determined centrally by the police agency rather than by residents' demands for police services via, say, a median voter model (see Deacon, 1979).

Geographic distribution of police resources is a major decision facing police administrators and several alternative objective functions have been advanced to explain the determination of intracity deployment patterns.'3 Rather than construct a normative model of this decision based on a selected maximand, we utilize the determinants the police employ in explaining geographic deployment patterns: 14

ln cpj = do + d, ln MAj + d2 ln DNj + d3 ln sLj + d4 ln vLj

+ d5 ln Yj + d6 ln scj + e3j (3) where sc is calls for service in districtj.

12 Although the total level of manpower in a given district may be determined by district crime rates, the deployment of manpower by function will depend on more complex consid- erations, such as internal promotion and personnel policies. Thus, we treat the total level of manpower (cp) as endogenous to the system but the distribution of manpower by function (IN,PT) as exogenous.

13 For example, police resources could be deployed either to (1) minimize the overall city crime rate, (2) equalize crime rates in all districts, or (3) minimize the social cost of crime throughout the city, given heterogeneous crimes (Shoup, 1964). Each objective entails a unique distribution of manpower across districts.

14 These factors are described in Communaute Urbaine de Montreal, Service de Police (1974).




The two determinants stressed by the police are the overall crime rate (MA)

and calls for service (sc), the latter being a measure of the non-crime workload of the police.15 The assignment of manpower across districts will be negatively related to density (DN) if there are 'economies of density' in activities such as police patrol; it will be positively related if urban crowding reflects conditions which impose additional demands on police services, of all types. Manpower deployment patterns are also hypothesized to be positively related to the value of targets which must be protected by the police, SL and VL. Because publicly provided protection is a normal good, the income of district residents may still influence the level of manpower devoted to a district, ceteris paribus; residents' demands for police services within a city will be expressed via the same political process as the demands of residents of independent cities.

An abiding feature of metropolitan areas is the volume of daily trips by individuals for employment, shopping, and leisure. Commutation patterns may introduce biases to varibles adjusted by resident population. To illustrate, because a large portion of suburban residents commute to the central business district during the day, crime rates normalized by resident population will tend to understate the true suburban crime rate and overstate the true downtown crime rate. Utilizing information on daily trip patterns across Montreal police districts, an estimate has been made of each district's so-called 'dynamic' population, the sum of the average 'mobile' population and the resident population. The average 'mobile' population is the net number of persons entering and leaving a district each day, divided by two. This figure is added to a district's residential population to obtain the'dynamic' population16 (Communaute Urbaine de Montreal, Service de Police, 1974, 49). We use the 'dynamic' population to adjust all variables expressed in per capita terms, then the basic model is re-estimated with these variables and the results are compared with estimates using data normalized by resident population.

To summarize, the system is composed of equations (1), (2), and (3), the offence supply, clearance, and manpower deployment equations. The crime rate, clearance rate, and manpower levels are endogenous variables; all other variables are exogenous and used as instrumental variables in the reduced form regression equations. Since each equation is overidentified, the equations are estimated by two-stage least squares. The variables are specified as log linear and the estimated coefficients are interpreted as elasticities. 7

15 The proportion of calls that are crime-related appears to be small; one Montreal study found only 13 per cent of all calls to be crime-related (Evans, 1973).

16 Since the sign of any district's 'mobile' population depends upon the number of people entering the district relative to the number leaving, the district's 'dynamic' population could thus be greater than or less than its resident population.

17 However, for some observations CL and DF take on either zero or negative values and logarithms cannot be calculated.These variables are not specified as log-linear and the elasticities are calculated after first estimating the semi-log coefficients.



Urban law enforcement in Canada I 51

TABLE 1

Estimate of offence supply equations, resident population

In ROB In BNE In THEFT In PROP In MA

constant -3.86 5.95 -4.19 -0.25 0.86 (1.02) (2.25) (1.35) (0.12) (0.41)

CL -0.03 -0.07 -0.06 -0.04 -0.04 (2.86) (5.15) (1.84) (1.80) (2.26)

[-0.62] [-0.71] [-0.92] [-0.58] [-0.59]

In UN 1.92 2.31 2.65 2.01 2.03 (2.36) (4.77) (2.74) (3.06) (3.56)

In Y -1.84 1.26 2.25 1.33 1.27 (1.62) (1.98) (2.09) (1.62) (1.79)

In YG -1.07 -1.92 -2.38 -1.66 -1.71 (0.90) (2.80) (2.32) (2.12) (2.28)

In VL 1.24 -0.35 0.33 0.20 0.13 (2.30) (1.01) (0.94) (0.66) (0.43)

ln SL -0.11 -0.10 0.04 0.02 0.003 (2.33) (2.76) (1.32) (0.68) (0.10)

DF -0.002 -0.003 -0.002 -0.002 -0.002 (1.55) (4.99) (2.27) (3.14) (3.30)

R2 0.73 0.80 0.53 0.64 0.66

NOTES: Absolute t-values in parentheses. Figure in brackets for CL

variable is the estimated elasticity.

While socio-economic data from the 1971 Census coincide with the twenty- three suburban municipalities contained in the MUC, data for police districts within the city of Montreal were available only by census tract. Hence, it was necessary to align each of the 291 census tracts in Montreal with the relevant police district to obtain the socio-economic data for all districts.'8

EMPIRICAL RESULTS

Estimates of the offence supply equations normalized by resident population are presented in table 1 and by 'dynamic' population in table 2. The coefficients of the risk and gain variables - CL, SL, VL, DF - are similar in both tables. In contrast, the magnitude of the coefficients of the socio-ecomonic variables - UN, Y, YG - tend to be smaller when 'dynamic' population is used to normalize crime rates. Assuming that 'dynamic' population is a more accurate indicator of the actual population requiring protection in a district, this result suggests that previous studies may consistently overestimate the impact of community socio-economic characteristics on crime.

18 Data on crime, police manpower, and clearances are from the MUC Police annual report for 1973, while socioeconomic data are drawn from Statistics Canada, 1971 Census publications.




TABLE 2

Estimates of offence supply equations, dynamic population

ln ROB ln BNE ln THEFT ln PROP ln MA

constant -2.68 5.89 -1.88 0.83 1.88 (0.73) (2.13) (1.08) (0.62) (1.31)

CL -0.03 -0.06 -0.04 -0.04 -0.03 (2.82) (4.29) (2.67) (3.22) (2.98)

[-0.56] [-0.62] [-0.60] [-0.61] [-0.48]

InUN 1.46 1.57 1.53 1.47 1.29 (1.86) (3.08) (3.17) (3.71) (3.50)

In Y -1.82 0.86 1.51 1.20 0.90 (1.68) (1.29) (2.71) (2.41) (1.96)

In YG -0.79 -1.35 -1.55 -1.30 -1.16 (0.69) (1.88) (2.75) (2.71) (2.36)

In VL 1.03 -0.34 0.14 0.06 0.03 (2.00) (0.94) (0.68) (0.34) (0.14)

ln SL -0.10 -0.07 0.05 0.03 0.02 (2.09) (1.87) (2.57) (1.74) (1.00)

DF -0.001 -0.002 -0.001 -0.001 -0.001 (0.95) (3.04) (1.91) (2.50) (2.65)

R 2 0.69 0.68 0.58 0.68 0.67

NOTES: Absolute t-values in parentheses. Figure in brackets for CL

variable is estimated elasticity.

The sign of the clearance rate coefficent is negative in all crime categories and the associated t-values are generally high.'9 The risk of police arrest appears to produce a significant deterrent effect, even in the category of all major offences, which includes many violent crimes. The negative, and usually significant, sign ofthe coefficient for DF also suggests that offenders tend to search across districts for the highest expected net return. The small magnitude of the coefficient of DF, however, suggests that crime spillovers represent probably only a small proportion of crime in a given district, a result that corroborates the findings of Mehay (1977).

The unemployment rate is not only positively associated with all crimes but also has a sizeable elasticity. This result contrasts with previous studies (see for example, Ehrlich, 1973) including one for Canada (Avio and Clark, 1976,which were unable to obtain consistent relationships between unemployment and crime. In our results, the elasticity of crime with respect to the male unemployment rate is as much as three times the elasticity of crime with respect to the police clearance rate, indicating that property crime is considerably more responsive to economic conditions than to apprehension risk.

19 A particular level of confidence cannot be assigned based on the t-statistic, because two-stage least squares estimates are only asymptotically consistent. Nonetheless, values of 2.0 or greater indicate some degree of confidence.




In their second study, Avio and Clark (1978) did obtain a positive relationship between crime rates and unemployment. However, our estimate of the elasticity is considerably larger than any obtained by Avio and Clark. This difference might be explained by our restricting the definition of unemployment to males (who account for 85 per cent of all arrests) or by the different samples used. Avio and Clark used Ontario census divisions which includes rural areas where the pressures of unemployment may not be as great as in an urban environment.

Although we have concentrated on the role of the police in reducing crime, our results highlight the importance of other policies available to decision makers. A reduction in crime may well be an important secondary benefit of the many public programs aimed simply at reducing unemployment, espe- cially in urban areas. Certainly this effect warrants further attention for Canadian urban areas.

Income has a positive impact on all crimes except robbery. This result may be explained in two ways. First, income may be a proxy for criminal earnings as well as for the opportunity cost of crime. This argument was advanced by Sjoquist (1973) and Avio and Clark (1978), who encountered similar results. Alternatively, the positive sign may be due to the correlation between income and other explanatory variables in the equation; collinearity might also explain the three negative signs for the variables intended to capture the criminal wage, VL and SL. To examine this possibility, the offence equations were re-estimated excluding the income variable. The results, which are presented in the appendix, indicate that multicollinearity may have been present. The sign of VL becomes positive and the t-statistics for both VL and SL tend to improve.

The coefficient of the young males variable, YG, also consistently has a sign opposite of that expected. A similar variable used by Avio and Clark (1976) also revealed an inconsistent impact on provincial crime rates. Perhaps Canadian youth do not share the same propensity for crime as their counter- parts in the u.s., when other factors are held constant.

Two-stage least squares estimates of the police output equation are presented in table 3. The results using 'dynamic' and resident population are similar, so only the former are presented. Both total police manpower (cp) and the patrol ratio (Pr) have a positive impact on clearances for all crime types except robbery. However, robbery clearances do appear to respond to the ratio of investigators to total manpower. This result suggests simply that investigators are more likely to be assigned to the most serious offences, an interpretation that is supported by the negative relationship between investigators and theft, a less serious offence. The positive signs of density suggest that crimes in progress are more likely to be either witnessed or reported in denser areas so that arrest productivity is also higher in those areas.

Estimates of police (or criminal justice) effectiveness in previous studies have varied. Some studies do not even report these estimates (Avio and Clark, 1976), while others have used such aggregated data that the estimates




TABLE 3

Police output equation, dynamic population

CL CL CL CL CL

(ROB) (BNE) (THEFT) (PROP) (MA)

constant 94.49 17.73 -14.36 0.67 8.01 (2.08) (1.08) (0.75) (0.04) (0.50)

ln cp -11.17 6.41 4.91 4.41 5.23 (1.07) (1.70) (1.12) (1.26) (1.33)

[-0.54] [0.63] [0.32] [0.32] [0.33]

ln DN -7.86 0.11 4.22 2.30 2.06 (1.39) (0.05) (1.77) (1.21) (0.96)

[-0.38] [0.01] [0.27] [0.17] [0.13]

ln IN 7.99 0.93 -0.24 0.09 0.94 (1.65) (0.53) (0.12) (0.06) (0.52) [0.39] [0.09] [0.02] [0.01] [0.06]

ln PT -29.57 12.64 15.01 12.45 14.33 (1.26) (1.49) (1.52) (1.57) (1.61) [1.43] [1.24] [0.94] [0.90] [0.90]

R 2 0.17 0.30 0.10 0.11 0.14

NOTES: Absolute t-values in parentheses. Figures in brackets are estimated elasticities.

are rendered meaningless (Ehrlich, 1973). Others have found a weak or non-existent output effect of the police (Mathur, 1978; Swimmer, 1974; Pogue 1975).20 Direct comparisons with previous studies is hazardous because of different measures of police output and inputs. However, estimating police effectiveness has proved to be one of the weakest links in empirical studies of deterrence.

Unlike many previous studies, table 3 indicates a positive impact of district manpower levels on clearlances. Moreover, the disaggregated data permit greater confidence in estimates of police effectiveness. Substituting equation (2) into equation (1), the elasticity of crime with respect to police inputs E1 = B1a1 for total manpower and E2 = B1a4 for patrol manpower. Taking estimates of B1 from the total property crime equation (PROP) we find El = -0.18 and E2 = -0.50. Crime does respond to the addition of police manpower through its indirect effect on clearances. While the magnitude of the response is not large, it is significantly greater for patrol manpower than for all officers.

The following police deployment equation, using dynamic population, was

20 Several of these studies analysed the relationship between police spending and either police output or crime, under the assumption that spending levels reflect the risk of apprehension. This assumption may be unsupportable because spending levels may vary across cities for numerous reasons such as differences in input prices, output mix, and internal efficiency.




obtained (t-values in parentheses):

ln cP = -5.80 - 0.20 ln MA + 0.32 ln VL + 0.01 ln sL - 0.22 1n Y (3.35) (1.05) (1.30) (0.50) (0.72)

- 0. 14 In DN + 0.92 In sc, R 2 = 0.77. (2.37) (6.29)

Contrary to expectations, both the major crime rate (MA) and income (1Y) are negatively, although insignificantly, related to police presence. The stock of targets in a district, represented by VL and SL, have a positive impact on manpower deployment, although the t-statistics are low. Both density and calls for service have a statistically significant impact on police deployment. The negative coefficient of density suggests the existence of 'economies of density' such that denser areas require fewer officers to provide the same level of service as provided in less dense areas. The large elasticity of deployment with respect to calls for service suggests that the main criterion used by administrators in distributing resources is the relative workload per officer. Since it is unlikely that the distribution of calls by seriousness (i.e., crime calls, traffic calls, domestic disturbance calls, etc.) is equal across districts, administrators do not appear to weigh calls by their social losses but instead, treat them homogeneously. They may consider, for example, the amount of an officer's time required to deal with each. These hypotheses warrant further investigation.

CONCLUSIONS

In the only previous Canadian deterrence study, Avio and Clark found a 'weak or non-existent effect of incarceration coupled with a strong deterrent effect of apprehension/arrest' (1978, 15). However, their model did not connect the arrest variable directly with police inputs. Our results not only confirm the strength of the deterrent effect of the apprehension probability as measured by police clearances, but also demonstrate that the latter are a major output of police activities. The level of police manpower, the geographic deployment of manpower, and the distribution of manpower by function all appear to affect the ability of the police to generate arrests and clearances and to deter crime. However, our results do not clearly indicate which maximand guides the geographic deployment of manpower. But since unweighted calls for service are found to be the most influential factor determining deployment, minimizing the social cost of crime - an objective that frequently appears in the literature - does not appear to be the overriding concern of police distribution decisions.

Our findings indicate the presence of crime spillovers across intracity neighbourhoods, although the magnitude of such spillovers appears slight. Nonetheless, deterrence studies ignoring crime spillovers may obtain biased




estimates of police deterrence effects. Similarly, our study indicates that studies that normalize crime and other socioeconomic variables by resident population may overestimate the impact of important socio-economic determinants of crime.

The results in this paper suggest that the level for aggregation may be responsible in part for the weak or negative impact of the police found in earlier studies. The police deterrence process emerges most clearly in statistical investigations using data disaggregated to the level of the individual police department. Further, although our results suggest that simply adding manpower can be an effective deterrent policy, they also suggest that social policies aimed at reducing male unemployment may be equally, or more, effective in reducing urban crime.

APPENDIX TABLE

Re-estimated offence supply equations, dynamic population

In ROB In BNE In THEFT In PROP In MA

constant 0.25 3.55 -1.81 -0.39 0.63 (0.10) (1.68) (0.94) (0.29) (0.47)

CL -0.02 -0.05 -0.01 -0.02 -0.02 (2.26) (4.20) (1.03) (1.99) (2.18)

[-0.41] [-0.53] [-0.18] [-0.29] [-0.30]

In UN 2.63 0.97 0.30 0.57 0.63 (7.05) (4.60) (1.64) (3.92) (4.11)

In YG -2.03 -0.70 -0.39 -0.44 -0.47 (2.22) (1.35) (1.00) (1.27) (1.31)

In VL 0.32 0.07 0.42 0.41 0.33 (1.06) (0.37) (2.06) (3.03) (2.57)

In SL -0.11 -0.05 0.05 0.04 0.03 (2.50) (1.43) (2.34) (2.13) (1.52)

DF -0.001 -0.002 -0.001 -0.001 -0.001 (1.20) (2.86) (2.19) (2.61) (2.69)

R2 0.66 0.66 0.47 0.62 0.56

NOTES: Absolute t-values in parentheses. Figure in bracket for CL

variable is the estimated elasticity.

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