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Estimating deterrence effects: a public choice perspective on the economics of crime literature.

I. Introduction

Following Becker's path-breaking theoretical work on the economics of crime, a large econometric literature has developed to test his implications [3]. This literature typically focuses on a supply of offenses in which per capita crimes are related to the probability and severity of punishment for that type of crime, the expected income from the criminal activity, returns from alternative legal activities, and other socio-economic factors. However, the economic theory of crime also implies that the supply of offenses is determined simultaneously with community's demand for enforcement services [24; 25]. Theoretically, the crime rate depends on police deterrence efforts, police deterrence efforts depend upon the level of police resources, and the level of police resources depends on the crime rate. As a result, the "typical" econometric model employees data on reported crimes (Index I crimes) and a simultaneous equation estimating technique with at least two, and generally three (or more) equations in which police deterrence efforts are proxied by the probability of arrest [14].(1) A series of recent empirical studies of the economics of crime have broken with the simultaneous equation estimating technique, however. In particular, Layson [33] and Trumbull [52] both tested for exogeneity using Hausman's [31] test, confirmed it, and used OLS estimators, and Cover and Thistle [22] simply accepted Layson's findings and used OLS.(2) The purpose of the following presentation is to provide a theoretical explanation for why the econometrics of crime literature has not had sufficient data to adequately test for the deterrence hypothesis in a simultaneous equation model: that is, we explain why exogeneity was confirmed by Layson [33] and Trumbull [52].

Testing for exogeneity could be motivated by the poor performance of the simultaneous estimation techniques in the economics of crime literature which generally finds that the crime rate is responsive to incentives and that higher crime rates are associated with more police resources, but that the probability of arrest often does not appear to be negatively and significantly related to the level of police resources [13; 14; 15; 17; 24; 25; 26; 35; 43; 53].(3) However, we contend that the poor results usually arising with the probability of arrest equation reflects a theoretical issue which suggests that these models are misspecified because of the unavailability of data on the actual allocation of police resources.(4) The economics of crime literature has generally ignored the incentives of the police bureaucrats who have considerable discretion in allocating their resources among a wide array of activities. Consideration of such incentives make it clear that an increase in aggregate police resources does not necessarily lead to an increase in the probability of arrest for any of the reported crime categories. These incentives are examined in section II in order to illustrate that the assumed empirical relationship between the aggregate level of police resources and the probability of arrest is not actually likely to hold. Section III contains concluding remarks.

II. Police Bureaucracies and Their Incentives

Migue and Belanger [38] and Niskanen [41] proposed that bureaucratic managers seek discretion reflected by a budget with excess revenues over actual costs. These excess revenues are referred to as a "discretionary budget," "discretionary profit," "fiscal residuum," or "organizational slack" in the subsequent literature. The bureau manager cannot pursue discretion without constraint, of course, due to the monitoring and other controls imposed by the bureau's sponsor (e.g., legislature or city council overseeing the agency) [10; 41]. Uncertainty prevents perfect monitoring, however. This uncertainty arises at least in pan because for many bureaucracies output is not measurable and it cannot be objectively evaluated as in private sector markets. Furthermore, many bureaus have a number of different outputs, some of which are easily measurable, and some of which are not. When this is the case, a bureaucrat has incentives to produce the measurable output in quantities that correspond to the monitor's desires, while exploiting the uncertainty associated with unmeasurable outputs in order to gain discretionary budget [34].

Bureaucrats also have incentives to "educate" the sponsor regarding interest group demands which complement their own goals and to "propagate" their own agenda [4; 18]. In fact, given that they successfully obtain a discretionary budget, they can use part of it to cover lobbying costs [4]. Therefore, they should be relatively influential in the political arena. Furthermore, law enforcement bureaucrats are frequently called upon to provide "evidence" because of their "expertise" on crime matters, so they tend to be a primary source of the information for decision makers and other potential interest groups [28, 22]. With their acknowledged expertise, bureaucrats are obviously a source of information for sponsors, but they might be a source of misinformation as well. Thus, bureaucrats' power depends on the degree of uncertainty, which they themselves can expand by misinforming, or not informing at all on some issues, so the legislative monitor faces the dual problem of determining both what the bureau's output should be and how it should be produced, with the potential for self-interested bureaucrats misleading them on both counts.

The function of police in the minds of most citizens is to "fight crime." But how can we tell if they are doing a good job? The number of arrests is a natural measure of "effectiveness," as are response times, and these, along with reported levels of crime, tend to be the primary measures that police focus on in their lobbying efforts for expanded budgets [47, 156]. This in turn means that public police have incentives to produce fast response times and large arrest statistics relative to reported crime rates. Thus, incentives to watch or patrol in order to prevent crimes are relatively weak, and incentives to wait until crimes are committed in order to respond and make arrests are relatively strong. It is not surprising, therefore, that after an extensive study of police performance, Sherman [47, 149] concluded: "Instead of watching to prevent crime, motorized police patrol [is] a process of merely waiting to respond to crime." Indeed, Sherman's review of studies of police on duty concluded that about half of an officer's time is spent simply waiting for something to happen, and while police officials claim that this time is spent in preventative patrolling, systematic observation indicated that such time is largely occupied with conversations with other officers, personal errands, and sitting in parked cars on side streets [47, 151]. Few police officers aggressively "watch" when there are no calls to answer.

Given such a focus, additional police resources will not necessarily reduce reported crime rates directly. As Sherman [47, 149] lamented: "In general, as the level of crime prevention watching has declined, the level of crime has risen, and so has public dissatisfaction with public police." For instance, a study by the Police Foundation and the National Institute of Law Enforcement and Criminal Justice found that cutting response time by seconds or even minutes makes little difference in whether or not a criminal is apprehended [42]. The study measured the impact of police response time on the chances of intercepting a crime in progress and making an arrest. The difference in the probability was "nil" when comparing arrivals of between two minutes and twenty minutes. The main reason is that citizens take such a long time to report a crime that the criminal is gone long before the police arrive. The average victim of a crime where the victim and criminal confront each other delayed calling the police for fifty minutes. In other words, police manpower is allocated to focus on measurable outputs like arrests and response times while sacrificing the unmeasurable output of crime prevention.(5)

Arrest statistics, along with response times, may be the primary statistical indicator of police performance, but as mentioned above, they are not the only important statistic used in bargaining for larger police budgets. Indeed, as the economics of crime literature indicates, higher crime rates clearly are correlated with more police resources, supporting the assumption that taxpayers/voters demand more police services if crime rates are high. But in contrast to the assumptions of that literature, it does not follow that more police resources in aggregate lead to lower crime rates. After all, as Milakovich and Weis [37, 10] noted, police have a "vested interest" in keeping crime rates relatively high. If crime rates drop too much, then support for more police and larger budgets declines; and "like all bureaucracies, criminal justice agencies can hardly be expected to implement policies that would diminish their importance." Thus, if police do respond to such incentives, additional funding need not lead to a substantial decrease in reported crime rates, since high crime rates are clearly an important element in arguments for expanded criminal justice budgets. Seidman and Couzens [46, 457-93] suggest that police do respond, even by exaggerating the level of crime at times in order to gain increases in budgets.

Police can keep crime rates high while absorbing more resources and even while making more arrests, because they have been given many functions to perform beyond simply the prevention and/or solution of Index I crimes. Indeed, many more Index II (simple assault, narcotics, vandalism, vice, fraud, major traffic violations, etc.: all crimes except Index I offenses and minor traffic violations) arrests are made than Index I arrests. For instance, in 1987 117,029 Index I arrests were made in Florida, while 511,568 Index II arrests were made. Similar figures for Illinois were 117,322 and 521,894. Vice and narcotics functions of police appear to be particularly relevant to the issues under consideration here. As Blumberg [9, 184-85] emphasized, arrest statistics are often relatively easily expanded by pursuing vice and narcotics criminals, so "we have spent much of our limited resources . . . [to arrest] addicts, alcoholics, prostitutes, homosexuals, gamblers, and other petty offenders, simply because they are readily available and produce the desired statistical data that indicate 'production'." There were almost 69 thousand narcotics arrests in Florida in 1987, for example, and over 35 thousand in Illinois.(6)

The importance of crime statistics also tends to reinforce the lobbying incentives police face because of the role that arrest statistics play as an indicator of performance. In order to keep crime rates up and make growing numbers of arrests, for example, police have strong incentives to seek criminalization of increasing numbers of activities [4], and there is evidence that they are, in fact, very active in lobbying for increased criminalization [8]. Furthermore, they have incentives to allocate any increases in resources to the control of non-Index I crimes for which crime statistics are not kept, thereby holding Index I crime rates up while increasing arrest statistics.(7) Index II arrests (e.g., vice, narcotics), are measures of output too, after all, and they do not necessarily have a deterrent effect on Index I criminals. Indeed, under certain circumstances, police have incentives to reallocate existing resources to increase their efforts against non-Index I crimes. For instance, a substantial reallocated of police resources occurred during the 1984-89 period in order to fight a "War on Drugs." Presumably, this reallocation was a response to political demands, of course, but the fact is that police themselves were a primary source of such demands [2; 4; 7; 8], and a source of the information that fueled other supporting demands. Indeed, it is primarily as a result of information (much of which is inaccurate and/or unsubstantiated [7; 36, 311-24]) promulgated by police [2, 53], that it is now widely believed that drug crime is a primary cause of non-drug crime. If this is true, of course, a crime control policy that focuses on increasing drug arrests (and imprisonment of drug users) would reduce both drag crime and non-drug crime. However, the anticipated benefits of the drug war have not materialized.(8) In fact, Benson et al. [5], Benson and Rasmussen [6], and Sollars, Benson, and Rasmussen [48] all used county or jurisdiction level data from Florida and found that reallocating scarce police resources away from the control of property crime toward the control of drug crime significantly reduced the risks that property criminals faced. This reduction in deterrence led to a significant increase in property crime. Note the incentives that this creates. By reallocating police resources to make drug arrests, both arrests as a measure of output and crime rates as a measure of the "need" for more police resources rise, and police budgets rise accordingly.(9)

This public choice perspective does not suggest that either the assumption that crime rates affect the demand for police resources or that the probability of arrest affects the supply of offenses should be rejected. However, it does imply that the assumption that the aggregate level of police resources should necessarily affect the probability of arrest for Index I crimes is not appropriate. Indeed, the preceding presentation explains why Layson [33] and Trumbull [52] both confirmed exogeneity when they tested for it. Existing multi-equation empirical models of deterrence are based on data which are inadequate to the task. Empirical efforts to show that police produce deterrence effects require data that explicitly account for the resources that are allocated to the control of reported crime (i.e., Index I crime).

III. Conclusions

When empirical studies of public policy effectiveness fail to consider the incentives of the public employees who implement the policy, the researchers may misspecify their empirical model and come up with surprising results that cause them to question basic economic relationships. This is clearly the case in the economics of crime literature. The primary purpose of this presentation has been to explain why the typically assumed simultaneous equations model of the economics of crime literature often yields results that seem inconsistent with the deterrence hypothesis. This literature has generally ignored the incentives of police bureaucrats, the tremendous range of activities that they perform beyond the control of Index I (reported) crime, and the discretion that they have when it comes to allocating their resources. When these factors are considered it becomes clear that the typical production function assumption underlying the empirical models which employee simultaneous estimation procedures--that an increase in aggregate police resources necessarily leads to an increase in the probability of arrest for Index I criminals--is inappropriate for the data.(10) This is important because some critics reject the deterrence implications of a crime supply function, where the crime falls as the probability of arrest increases in a simultaneous equation model, simply because the probability of arrest is not also positively related to the level of aggregate police resources in another equation. Rejection of the deterrence implications is not justified, however, because aggregate police resources do not necessarily influence the probability of arrest.

1. The dependent variable in the "supply of offenses" equation is a crime rate, C[R.sub.i], for a particular type of crime, i. Some studies have used aggregate Index I crime rates (murder, manslaughter, rape, assault, robbery, burglary, larceny, and auto theft), while others have focused on specific crime categories (e.g., murder, property crimes). C[R.sub.i] depends on: (a) the expected income (E[I.sub.i]) from such crime in a community, adjusted for (b) the probability of arrest (P[A.sub.i]) in the community, and (c) the severity of punishment given arrest (S[P.sub.i]), as well as (d) the expected cost is the legal economic opportunities (OC) available in the community (and various control variables):

C[R.sub.i] = f(E[I.sub.i], P[A.sub.i], S[P.sub.i], OC,....).

The "production function" consists of two essential factors, the size of the police force (POL) and the overall level of crime in the jurisdiction (CR), as well as other control variables:

P[A.sub.i] = g(POL, CR,...).

The "demand for police services" depends on crime rates in the community (some disaggregation of the crime rate might be done to see if citizens consider violent crimes to be more serious than property crimes, for instance), the level of income or wealth (W), and other control variables:

POL = h(CR, W,...).

2. In addition, Corman, Joyce, and Lovitch [21] and Corman and Joyce [20] used Vector Autoregressive (VAR) Models. Interestingly, however, after determining the appropriate lag lengths, Corman, Joyce, and Lovitch and Corman and Joyce used OLS. Of course, this approach does not suffer from simultaneity bias, so the use of OLS does not mean that there is no simultaneity. Indeed, a VAR still retains the fundamental proposition that there is a structural relationship among the variables in the criminal justice system, so this approach is more of a methodological variant on the basic Becker-Ehrlich framework than a break from it. Similarly, Sollars, Benson, and Rasmussen [48] assumed a structural relationship in a property crime model, but lugged crime rates in the police resource equation and used non-property crime rates in the probability of arrest equation to represent the opportunity costs of property crime arrests, in order to justify a recursive model.

3. In addition, several simultaneous equations studies supported the deterrence hypothesis using the three equation model, but they did not report their production function equation results, suggesting that the equation did not perform well [19; 32; 40]--see Cameron [14] for additional references. Furthermore, several studies simply put some measure of police manpower directly into the supply of offenses equation rather than using an arrest rate, finding either no relationship or a positive relationship between police resources and crime rates [1; 12; 30; 50; 51]--again see Cameron [14] for additional references. The failure of measures of police manpower or budget to influence the crime rate directly, or indirectly through the probability of arrest, led Cameron [14, 308] to question the validity of the deterrence hypothesis.

4. This perspective also argues against the presumptive use of simultaneous estimation techniques, given the data usually used in the econometrics of crime literature.

5. Note that the econometrics of crime literature contains a considerable amount of support for the hypothesis that a higher probability of arrest for a particular crime deters that crime. The argument made here does not deny this empirical result, but rather, it suggests that waiting to arrest may not be the most effective way to deter crime.

6. Beyond that, a 1990 Bureau of Justice Statistics survey of state and local police departments found that police have responsibilities for many activities that may not produce any arrests: 96 percent were responsible for accident investigation, over half performed the community's telephone and radio emergency communications and dispatch services (e.g., 911 services), 43 percent had animal control duties, 33 percent did search and rescue, 18 percent had emergency medical services, 18 percent provided court security, 14 percent did civil defense, 10 percent civil process serving, and so on [44, 4]. A similar survey of sheriffs' departments noted that these agencies are even more likely to have non-law enforcement functions to perform [45].

7. Given the tremendous number of duties that police have and the fact that police resources are scarce, as long as observable and measurable outputs are produced in quantities that satisfy the oversight monitor (or rationally ignorant median voter), police bureaucrats should have considerable discretion in the allocation of bureau resources. Considerable evidence supports this expectation [49, 327-32; 54, 77-105]. With such discretion, police can choose which laws to enforce relatively strictly and which not to enforce [54, 4].

8. This is not surprising, since the academic literature has, for some time, suggested that the "drug causes Index I crime" argument is not valid--for reviews of this literature see Gottfredson and Hirschi [29], and Chaiken and Chaiken [16]. In fact, criminal activities generally precede drug use [27].

9. Police incentives to focus on the war on drugs were even stronger. Drug enforcement has become a major source of asset forfeitures, and under a federal statute in effect since 1984 (similar state laws also apply in many but not all states), asset seizures are returned to the police, significantly increasing police departments' discretionary budgets [7].

10. Other data problems include the general inability or failure to incorporate data on the private sector's contribution to crime control efforts and its affect on the level of crime [4; 14]. Furthermore, in the supply of offenses function, the proxy for the C[R.sub.i] (reported offenses in i/population), depends on the clearance rate (arrests for i/offenses in i) as the proxy for P[A.sub.i] in footnote 1, and P[A.sub.i] depends in turn on CR, including C[R.sub.i]. Some argue that the spurious correlation problem is insurmountable [11]. However, Myers [39] compared the deterrent effects using separate analyses on reported crime rates and crime rates corrected for under reporting, and concluded that "under reporting does not really matter." Craig [23] reported that the coefficient on the probability of arrest becomes more negative when actual crime is used rather than reported crime.


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Author:Rasmussen, David W.
Publication:Southern Economic Journal
Date:Jul 1, 1994
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