Unions and Police Productivity: An Econometric Investigation

Unions and Police Productivity: An Econometric Investigation

DENNIS BYRNE, HASHEM DEZHBAKHSH, and RANDALL KING*

We examine the effect of unionization on police productivity in large U.S. metropolitan areas. We define police output in the context of a production function model that draws also on the crime literature. We estimate the resulting model using a data set that includes published and unpublished government statistics as well as our own survey of police departments. Results suggest that the effect of unions on police productivity varies according to categories of police performance. In particular, if performance is stratified according to the severity of crimes, unions seem to have an insignificant effect on police productivity with respect to serious crimes. For minor crimes, unionization alters the parameters of police production function, leading to diminished productivity.

Introduction The economic effects of unions have been the subject of extensive re-

search and debate among economists. In particular, the productivity effect of unions has been a topic of interest to economists as well as business establishments. The existing literature on this topic largely deals with the private sector. Public-sector studies are few and their findings diverge considerably. For example, Allen (1986a, 1986b) reports the union effect

*The authors are affiliated, respectively, with the University of Akron, Emory University, and the University of Akron. Send inquiries to Hashem Dezhbakhsh, Department of Economics, Emory University, Atlanta, GA 30322-2240. We thank Daniel Levy for helpful comments, Ray Atkins for research assistance, the Federal Bureau of Investigation for providing us with city-specific crime and arrest data, major municipal police departments for responding to our survey, and the editor and three anonymous referees for valuable comments. The usual disclaimer applies.

I Addison and Hirsch (1989) and Freeman and Medoff (1984, chapter 11) provide valuable reviews of the private-sector union studies. This literature is replete with diverging views and unresolved issues.

INDUSTRIAL RELATIONS, Vol. 35, No. 4 (October 1996). 0 1996 Regents of the University of California Published by Blackwell Publishers, 238 Main Street, Cambridge, MA 02142, USA, and 108 Cowley

Road, Oxford.OX4 lJF, UK.

566

Unions and Police Productivity I 567

to be ambiguous for public school construction and insignificant for nursing home construction. Ehrenberg, Sherman, and Schwarz (1983) find the union effect to be insignificant in the case of public library services, and Noam (1983) reports a similar result for municipal building departments. Ebert and Stone (1987), on the other hand, report the effect of teacher’s unions on students’ performance to be positive and significant.

It is acknowledged that the dearth of public-sector union studies and their conflicting results warrant further examination of the issue.2 Furthermore, given that the public sector continues to grow despite its fiscal problems,” any examination of its productivity seems to be well justified. This is particularly true for police services, because public safety is an essential public service and safety expenditures comprise a sizable portion of all local governments’ budgets. Nonetheless, no attempt has yet been made to examine the union effect on police productivity. The neglect is probably because of the difficulties in conceptualizing and quantifying police ~ u t p u t . ~

In general, any empirical analysis of unionism and productivity faces two major challenges that must often be met with weak data. The first is to define operational measures of output and inputs. For many public services, this task is further complicated by the difficulties of conceptualizing output and productivity. The second challenge is to find a practical and justifiable set of control variables that account for productivity differentials that are neither union induced nor caused by a change in the level of inputs. The absence of rigorous theory detailing the production process for many public services makes it difficult to determine the corresponding control variables. These challenges have hindered studies on police unionism and productivity.

We examine the effect of unions on police productivity under the afore- mentioned measurement constraint. We use arrest-based output measures to examine, in a production function context, the effect of unions on the productivity of police departments in major U.S. metropolitan areas. Be- cause of data exigencies, we concentrate only on crime repression - or the punitive aspect of police services. Given that no data on police unionization were readily available: we conducted a survey of major municipal police departments and compiled a data set that also draws on published

2 See, for example, Ehrenberg, Sherman, and Schwarz (1983). Ehrenberg and Schwarz (1986), and

3 See Ehrenberg and Schwarz (1986) and Edwards and Field-Hendrey (1991) for related figures. 4 There are, however, a number of union-nonunion wage studies involving police departments, for

example, Ehrenberg (1980), Hall and Vanderporten (1977). and Bartel and Lewin (1981). Aggregate data on the number of unionized police departments in each state are available in

Census of Governments, but such data do not contain a breakdown at city level and therefore cannot be useful for our purpose.

Lewis (1990).

568 / DENNIS BYRNE, HASHEM DEZHBAKHSH, AND RANDALL KING

and unpublished government sources. The cross-section data cover 137 of the largest U.S. metropolitan areas. Individual municipal police departments are chosen as the unit of analysis.

The article is organized as follows. First, we derive the empirical model, discuss the measurement issues, and describe the data. Second, we report specification tests and estimation results and present our interpretations. Finally, we offer our concluding remarks.

Empirical Specification, Measurement Issues, and Data

Models and measurement. We adopt the production function approach commonly used in union productivity studies.6 This approach involves parameterizing a production function with a set of control variables, and making inference about the parameters of the assumed function.7 Follow- ing many union studies, we employ a variant of the Cobb-Douglas production function. For a typical unit the function is

Q = AK" LB,

where Q is output, K and L are capital and labor, a and p are parameters, and A includes a constant of proportionality and a control variable.s The Cobb-Douglas form is adopted for its simplicity and also to facilitate com- parison with earlier public-sector union studies (see, e.g., Ehrenberg, Sher- man, and Schwarz, 1983; Noam, 1983; Allen, 1986a, 1986b; and Edwards and Field-Hendrey, 1991).

Any reasonable measure of police output should reflect the functions that a police department performs. The U.S. Department of Justice identifies seven such functions: prevention of crime, repression of crime, apprehension of criminals, recovery of property, regulation of noncriminal activity, performance of miscellaneous services, and protection of constitutional guarantees (U.S. Department of Justice, 1982). These functions can be

Ehrenberg, Sherman, and Schwarz (1983) use another approach that involves estimation of a reduced form output equation assumed to be linear in its arguments.

We note that the limitations of the widely used production function tests have spawned some criticism of the procedure. For example, the critics argue that such tests fail to discriminate between marginal productivity differentials and uniodnonunion price (wage) differentials. In response, private- sector union studies have recently shifted attention from the union productivity issue to the union profitability issue. A similar trend has not been observed for public-sector studies, probably because profitability is not a stated objective of a public employer. Interested readers are referred to Hirsch (1991), Addison and Hirsch (1989). Reynolds (1986). and Mefford (1986).

Note that the assumption of constant returns to scale, imposed in earlier studies, is relaxed here by allowing a+P to differ from 1. This restriction will be tested in section 3. Other restrictions of the Cobb-Douglas form, namely unitary elasticity of substitution, homotheticity, and homogeneity, remain in place.


classified into two broad categories: one includes the first four functions that cover the traditional law enforcement role of police and the other includes the last three functions that relate to public service duties.

Data on some law enforcement aspects of police activities are available. The Federal Bureau of Investigation (FBI) surveys municipal police departments yearly and compiles data on the number of arrests and the crime index, with a detailed breakdown into twenty different categories (FBI, Crime in the United States, various issues). No usable data are collected, however, on the recovery of property; neither are there any data available on the public service activities of police departments. We therefore concentrate on law enforcement as the primary duty of police.

Furthermore, a distinction must be made between crime prevention and crime repression. Prevention refers to instances where crime is contem- plated but not committed, whereas repression implies that crime has oc- curred. Because the preventive effect of police services cannot be directly quantified, we confine our study to the repression of crime. Nonetheless, it may be argued that criminals' decision to commit a crime is affected by their perceived (or subjective) probability of being punished. This probability is proportional to the probability of arrest given that a crime is committed.9 Therefore, any measure of police performance involving repression of crime or apprehension of criminals is also a reasonable proxy for the preventive aspect of police services (see Schmidt and Witte, 1984, p. 197).

To make equation (1) applicable to police services, some modifications need to be made. In particular, A is decomposed into two multiplicative terms, the constant of proportionality A' and a control variable C. The production function is then expressed as

Q = A'CK" L?

In view of the earlier discussion of output, we define the number of arrests as an empirical measure of police output. The control variable C is the crime index for the municipality covered by a typical police department. This specification allows for interaction between crime and police output and also accommodates an important factual consideration. Given that arrest-based measures are used as police output, output must tend to zero disregarding the level of input utilization if no crime is committed. In our proposed specification, Q is allowed to change positively with crime and to approach zero in the limiting case of no crime. Entering crime as a multiplicative control variable satisfies this factual requirement.

9 See, for example, Block and Heineke (1975) and Witte (1980) for a choice-theoretic analysis of criminal behavior.

570 I DENNIS BYRNE, HASHEM DEZHBAKHSH, AND RANDALL KING

It is worth noting that this specification is equivalent to another specification wherein the number of arrests per crime, QlC, is defined as police output. The latter specification can be obtained by dividing both sides of equation (2) by C and defining an index of crime cleared by arrests, QlC, as police output in the resulting production function. An important advan- tage of equation (2) over this alternative formulation is that (2) allows crime to be treated as an endogenous variable that is influenced by the number of arrests.

With few exceptions, union productivity studies introduce the union effect as a shift parameter in a production-function-based regression. This is done by modifying equation (2) as follows:

Q = A’C(1 + yU)K“ Lp, (3) where U is a binary variable that equals one if the department is unionized and zero otherwise and y is the proportionate change in productivity resulting from unionization. We use the term unionization to mean that there is a formal written contract in effect in the police department. Although some officers may not join the union - there may be no union security clause in the contract - all officers are covered by the terms and provisions of the contract.

By dividing both sides of equation (3) by L, taking natural log, and adding an error term, we obtain

ln(Q / L ) = 1nA’ + yU + aln(K / L ) + (a + p - 1) 1nL + 1nC + E , (4)

where yUis the first-order Taylor series expansion of In(1 + yu> and E’S are independent and identically distributed (i.i.d.) errors with zero means. With labor defined as the number of patrol officers, the police productivity is measured by the number of arrests per patrol officer. Accordingly, a ceteris paribus increase in the number of arrests per officer is viewed as enhanced productivity. Note that because the crime index is used as a control variable in the production function equation, it is reasonable to interpret a larger number of arrests per officer, at a given level of input, as higher productivity.

The specification in equation (4) imposes the restriction that the production functions for unionized and nonunionized departments are identical except for a shift parameter. If such restriction is imposed incorrectly, the resulting estimates will be statistically biased. To avoid this problem, we use an alternative specification that allows all parameters of the production function to change according to the union status.lO This involves estimating two production functions, one for unionized and the other for

lo The tests reported in the section on model estimation support this specification in general.


nonunionized departments. The production functions have similar forms but differ in parameters. A rearrangement similar to the one used to derive equation (4) yields the equations:

ln(Q / L ) = InA,‘ + a,ln(K / L ) + (a, + 0, - 1)lnL + 1nC + E,, ( 5 )

and

ln(Q I L ) = lnA,’ + a,ln(K / L ) + (a, + p, - 1)lnL + 1nC + E,, (5’ )

where n and u indicate nonunion and union status, and E, and E, are i.i.d. error terms with zero mean.

Consistent estimation of equations ( 5 ) and (5’ ) by least squares requires the regressors to be exogenous-uncorrelated with the error term E (the orthogonality condition). A close examination of these equations, however, reveals that the crime index C does not satisfy this requirement, because the decision to commit crime is influenced by the criminals’ perceived (subjective) probability of getting arrested. Such probability is in turn affected by police productivity in arresting criminals. So C depends on Q/L, and QIL is a function of E , so C and E are correlated and a simultaneity problem is present.11 The problem can be resolved by specifying a crime equation and then either estimating the crime equation and equations ( 5 ) or (5 ’ ) simulta- neously, or substituting for crime from this equation into ( 5 ) or (5’) and estimating the resulting reduced form equations. The former approach is structural and the latter is reduced form; we use both approaches to examine the robustness of our findings.

To derive the reduced form, we first need to specify a crime equation. We rely on the economic literature on crime and particularly the results reported in Sjoquist (1973), Block and Heineke (1975), Witte (1980), Schmidt and Witte (1984), Good, Pirog-Good, and Sickles (1986), and Trumbull(l989) to specify a crime equation.’* Consider the following:

1nC = -8ln(Q I L ) + OX + 6, (6) where 6 is a positive parameter, QlL is police productivity defined by any of the measures of arrest per officer, 0 is a lxg parameter vector, X is a g

Other potential sources of simultaneity are K and L. The exogeneity of K and L can be tested using Hausman’s (1978) test for simultaneity. A significant test statistic indicates that the tested regressors are correlated with the error term and a simultaneity problem is therefore present. We performed this test but found no significant statistic at the 5 percent level. This suggests that capital and labor are both uncorrelated with the error terms, and we henceforth treat them as exogenous variables. This is consistent with Zax and Ichniowski’s (1988) findings that police staffing and capital expenditures are not affected by variables such as the union status of a department.

12 There has been some controversy concerning the use of aggregate versus micro level data in crime studies. Trumbull (1989) finds consistency between the results from the two types of data.


element vector of exogenous variables affecting crime, and 6 is a normal (0, a;) error term.13 The literature on the economic model of crime provides the basis for selecting the variables in X . We use seven such variables; they represent the socioeconomic and demographic characteristics affecting the crime rate. These variables are income, unemployment rate, age, percentage minority, population, population density, and a regional dummy. The first two variables, which represent economic characteristics, are median income of city residents and local unemployment rate. The remaining variables, which characterize social and demographic influ- ences, are the median age of city residents, percent of blacks and Hispanic residents, community population, population per square mile, and a binary variable that equals one if the community is in the southern region and zero otherwise. We use the dummy variable to control for the fact that southern states are traditionally less fertile ground for union activity than the rest of the nation because of the right to work laws. The descriptive statistics that we will discuss later support this point.

The functional form of equation (6) is specifically adopted to allow crime to be negatively affected by police productivity QlL. This specification which has a common place in the crime literature also accommodates explicit reduced form solutions to equations ( 5 ) and (5’) . We use the following union and nonunion versions of equation (6):

lnC,, = -6,,ln(Q / L ) + 0 , X + 6, (7)

and

where the parameters and variables are similar to those in equation (6) and u and n subscripts denote union and nonunion status of the police department in a metropolitan area. These crime equations can be used for structural and/or reduced form estimation.

The structural approach involves estimating equations ( 5 ) and (7) together and equations (5’ ) and (7’) together. The reduced form approach involves substituting for C from equation (7) into equation ( 5 ) and from equation (7’) into equation (5’ ) and then estimating the resulting reduced form equations which are

ln(Q / L ) = +(,,,, + +,,,,ln(K / L ) + +JnL + eX + u,, (8)

‘3 Note that this equation may be equivalently expressed as C = (Q/L)-’eeX’(, where the lognormal multiplicative error term e( is assumed to capture any approximation error resulting from this specification.


and

where 4,) = lnA’/(1+6), 4, = a/(l+S), +2 = ((u+p-1)/(1+6), the seven- element vector @* = 0/(1+6), and v’s are compound error terms. Note that because 6 is positive, each of the coefficients of KIL, and L has the same sign in equations (8) and (8’) as in production function equations ( 5 ) and (5’). The same is true for the coefficients of Xin equations (7) and (7’) and equations (8) and (8‘). This makes the interpretation of the coefficients of equations (8) and (8’) straightforward.

Data and survey. The cross-section data employed here are collected from a number of published and unpublished sources. Given that data on the union status of the municipal police departments were not available, we surveyed 192 police departments in the largest U.S. metropolitan areas, each with a population over 100,000 as of 1985. The questionnaire asked whether the department had a written union contract already in place (at the end of 1990), and if so, when the contract was initiated. We inquired specifically about a written contract because earlier studies suggest that a formal contract affects municipalities differently than a less formal arrangement. So we define a unionized department as one with a formal contract between the municipality and the police union. We received 137 responses-a response rate of over 71 percent. We compared two of the relevant characteristics of cities that responded to our survey to those that did not. Population and income differences between the two groups were statistically examined using Wilcoxon’s nonparametric two-sample rank test (see Randles and Wolfe, 1979, chapters 2 and 3 for a discussion of the test). This test is particularly chosen because of the nonnormality of population and income distributions. The test statistic, which has a standard normal distribution asymptotically, is significant for population data and insignificant for income data; the values are, respectively, 1.56 and -2.99. The rank statistic for population data suggests that the responding cities appear to be more populated than the nonresponding cities. This is not surprising because large city police departments are probably more image-conscious and thus more willing to make a public relations gesture by responding to inquiries. We did not perform similar tests for other variables because not much insight is expected to be gained from such an exercise.

The samples compiled for this study consist of 137 data points, except in cases of missing observations. The arrest data are extracted from unpublished material furnished to us by the FBI. The crime data are obtained from published sources compiled by the FBI (1983). The data on city

574 / DENNIS BYRNE, HASHEM DEZHBAKHSH, A N D RANDALL KING

budget, police budget, and city unemployment rate are collected from the Census of Governments (U.S. Department of Commerce, 1983). The data on demographic characteristics are taken from the City County Data Book (U.S. Department of Commerce, 1983). Data from both sources are available in similar five-year intervals.

The FBI classifies its arrest data as total arrests, arrests related to more serious crimes of murder, manslaughter, rape, robbery, assault, burglary, and car theft, and arrests related to all other, mostly minor, offenses. We use both arrest measures in our analysis. This allows us to inquire whether the effect of unionization on police performance varies with the severity of the related crimes. We refer to these as arrests related to serious crimes and arrests related to minor crimes.

As stated earlier, we use the number of patrol officers to measure labor.I4 Because of the absence of relevant data, no adjustment is made for labor quality. A direct measure of the capital stock of municipal police departments is not available. A reasonable proxy, however, may be constructed as follows. An examination of total police expenditure over the 1970s and 1980s reveals that most police departments allocate over 90 percent of their capital expenditures to the purchase of new equipment, with little spent to add or renovate the existing stock of buildings. More- over, purchase of vehicles is the major component of police expenditure on equipment. Consequently, the dollar value of vehicles in use by each police department seems to be a reasonable proxy for capital measure (see Reaves, 1988 for details). This measure is particularly appealing because output is measured in terms of the number of arrests, and vehicles are an important instrument for arresting criminals.

Model Estimation and Results Before presenting the main results, we discuss briefly the descriptive

statistics for variables of the model; these statistics are not reported for brevity. Considering first the socioeconomic and demographic characteristics, we observe that there is little difference between union and nonunion subsamples in terms of income and age of the residents. Unionized departments, however, are more likely to be in larger and more densely populated areas. Cities with unionized police departments on average have 23 percent larger population and 67 percent higher population density when compared to cities without a police union. Also, southern cities seem to have a disproportionately smaller share of the unionized police depart-

14 We also used total police manpower to measure labor but our findings remained essentially unchanged.


ments; unionization rate is 18 percent for the sample of southern cities but 65 percent for the entire sample.

Turning next to the input and output variables, unionized departments on average use more capital and labor than their nonunionized counterparts. The mean capital-labor ratio, however, is 2.4 percent smaller for unionized departments, but this difference is statistically insignificant. Moreover, the average crime frequency appears to be higher in cities with unionized police departments. Depending on the crime measure, the differential is 10.6 percent for serious crimes and 32.5 percent for minor crimes. There is very little difference in the average number of total arrests in the two subsamples. An examination of arrests stratified by the seriousness of the committed crime, however, presents a different picture. Arrests related to serious crimes have a 20.4 percent larger mean m the union subsample, whereas arrests related to minor crimes have a 3 percent larger mean in the nonunion subsample. We also observe that arrests related to serious crimes exceed serious crimes in all samples, probably as a result of cases where multiple arrests are made in relation to one crime.

Crime and arrest data are categorized according to the severity of the related crimes. This affords us the opportunity to use two measures of output: arrests related to serious crimes and arrests related to minor crimes, each in conjunction with the corresponding crime index. By using different output measures we can examine whether the effect of unions on police productivity is uniform across the two categories of crime.

We examine a number of relevant econometric issues before estimating the models. First, we must deal with sample selection bias that is the result of dividing the samples according to the union status (Heckman, 1979). The nonrandom division of the sample causes the regression errors to have a nonzero conditional mean, leading to inconsistent coefficient estimates. The problem can be resolved by augmenting each regression equation by a constructed regressor. The augmenting regressor in each equation is the corresponding estimate of the expected error term conditional on union status. The following procedure is used to construct the two augmenting regressors (see, e.g., Lee, 1978). A reduced form probit equation is speci- fied with union status U as the dependent variable and factors that affect unionization as the explanatory variables. In choosing these variables, we follow the standard practice by defining the unionization probability as a function of union-nonunion wage differential. We then substitute the wage differential, which is not directly observable for a given police department, with variables that may affect it. These variables include the exogenous variables of the model - for example, income, unemployment rate, age, population, and so on-and two dummy variables that characterize the


legal structure of collective bargaining. One dummy measures whether a bargaining law was in place in a department’s home state as of 1982 (the sample year), and the other measures whether a right-to-work law was in place in the state as of 1982.15 Collective bargaining legislation, such as right to strike, compulsory arbitration, and choice of procedure appear to have significant effects on wage and union status of public-sector employees (see, e.g., Freeman, 1986; Zax and Ichniowski, 1990; and Currie and McConnell, 1991).16

After estimating this probit equation, the fitted values, U s , are retrieved. The augmentipg variables, which are better known as selectivity variables, are -F(o) for the union equation and I-F(CI) for the nonunion equation, wheref(-) and F( . ) are, respectively, the density and distribution functions of a standard normal random variable. Finally, after these selectivity variables are added to the union and nonunion equations, the parameters are estimated using least squares method.I7 Because the usual least squares standard errors are biased, with unknown direction, we use adjusted standard errors derived in Greene (1981) to avoid invalid inference.Is

Second, we test the difference between parameters of union and nonunion regression equations. The relevant test is the asymptotic likelihood ratio (LR) test for parameter constancy (see, e.g., Godfrey, 1988, chapter 5) . In large samples, the test statistic has a chi-square distribution with degrees of freedom equal to the number of parameters tested. A significant statistic suggests that coefficients are different and the two samples should not be pooled. The LR statistic is computed from the reduced form equations (8) and (8’) which easily accommodate specification testing. The statistics are reported in the bottom of Table 1.

Resufts. Estimates of the reduced form equations, (8) and (87, are reported in Table l . I 9 The equations are estimated for the two output measures using the least squares method with selectivity adjustment. The estimated labor coefficient is insignificant in all cases, supporting the production function restriction a + p = The estimated coefficient of

f ( U ) f(0)

15 We collected the bargaining legislation data from PSRC (1982). As noted by Hirsch and Addison (1986, chapter 3), direct measures of membership and organizing

costs of unions are rarely available. These costs are affected by political climate and labor legislation. 17 See Heckman (1978) and Lee (1978) for selection bias in a simultaneous equation context and the

necessary corrective procedure. ‘8 See Heckman (1979) and Greene (1981) for theoretical details and LIMDEP User’s Manual,

Version 6.0, chapter 45 for computational details. We used LIMDEP software, Version 6.0, to carry out all computations.

l 9 Notice that only 128 observations are used instead of 137 because of missing data points. 3 We estimated the equations after enforcing this constraint (dropping labor), but the results

remained virtually unchanged in terms of the signs and significance of coefficients.


TABLE 1 REDUCED FORM ESTIMATES: EQUATIONS (8) AND (8’)

Dependent Variable- Arrest (serious crimes)ll Arrest (minor crimes)ll

Regressors1 Sample Sample Sample Sample Union Nonunion Union Nonunion

Intercept

KIL

L

Income

Unemployment Rate

Age

Percent Minority

Population

Population Density

Region

Selectivity Variable

Diagnostics Adjusted R2 Akaike Information Sample Size LR Statistic for Par. Constancy

3.240 (4.05)** 0.27 I

0.118

-0.0007

(3.49)**

(1.10)

(-0.20) 0.004

(0.37) -0.036

0.002 (0.45) 0.0002

(1.04) -0.0007 (0.04)

(-2.52)**

-0.079 (-3.17)** -0.143

(-1.36)

1.755 (1.85)* 0.235

(3.1 6)** 0.042

(0.40) 0.0006

(0.12) -0.021

(- 1.42) 0.014

(0.56) 0.003

(0.60) 0.0003

(0.82) -0.039

(-1.48) 0.002

0.198 (0.87)

(0.10)

0.302 0.369 0.139 0.775

15.779 82 46

3.725 (3.96)** 0.387

(4.26)** 0.156

(1.24) -0.0004

(-1.03) 0.0005

(0.04) -0.021

(- 1.26) 0.003

(0.67) 0.0004

0.012 (0.59)

-0.080 (-2.71)**

0.068

(2.25) * *

(0.55)

3.16 (1.96)* 0.052

(0.43) -0.139

(-0.81)

(0.55) 0.0005

-0.074 (-2.79)**

0.066 (1.57)

-0.009 (-0.99)

0.0001 (0.16)

-0.116

0.036

0.572 (1.57)

(-2.51)**

(1.10)

0.300 0.259 0.192 0.198

85.571** 82 46

Notes: Entries are obtained by applying the least-squares method with selectivity adjustment to equations (8) and (X‘). Asymptotic t-statistics are in parentheses, and * and ** indicate significance at the . I0 and .05 levels. respectively.

capital-labor ratio is significant in both the union and nonunion equations when the output is measured by arrests related to serious crimes, but for arrests related to minor crimes the estimated coefficient is significant only in union equation. The coefficient (Y is output elasticity with respect to capital; given the production function restriction cr + f3 = 1, a larger cr implies a smaller output elasticity with respect to labor, p. This result suggests that for minor offenses, unionization tends to enhance capital productivity and lower labor productivity. One possible explanation is the presence of union-negotiated contract clause that affects productivity. For example, our data show that unionized departments are located in larger


cities where crime is higher. Consequently, safety may be more of a con- cern to officers in these cities, so unions may negotiate a contract clause requiring that each officer have a partner while on patrol. Such a requirement can easily contribute to the above productivity effect. Indeed, the presence of similar provisions -for example, minimum aircraft crew size, maximum apprentice-journeymen ratio, and other forms of mandatory staffing-in union contracts is well documented (see, e.g., Addison and Hirsch, 1989).

Coefficients of several other variables tend to change with union status. Starting with demographic factors, the estimated coefficient of regional dummy for the South is negative and significant in the union samples but positive and insignificant in the nonunion samples. This variable is included to control for the regional differences discussed earlier. Coefficient estimates suggest that unionized police departments in the South have a smaller arrest productivity than their counterparts nationwide. A possible explanation for this effect is that southern states are less receptive to unions, so unions are less able in these states, than elsewhere, to negotiate a positive wage differential. Instead, they may resort to contract clauses that lead to a reduction in the total work performed by the department.*l

Estimates of the minority coefficient are positive and insignificant for both output measures in the union equations. A different pattern is observed in the nonunion equations, where the estimates are negative and insignificant for arrests related to minor crimes and positive and insignificant for arrests related to serious crimes. The similarity of the estimated signs for arrests related to serious crimes in the union and nonunion samples probably reflects the similarities between the way union and nonunion police departments investigate such crimes; however, we must exercise caution when drawing inference from an insignificant estimate.

Moreover, the estimate of population coefficient has a positive sign in all samples and for both output measures. The estimate is significant for union samples when output is measured in terms of arrests related to minor crimes. This implies that unionized police departments have a higher arrest productivity in larger cities, probably as the result of higher crime rates in these cities. The correlation between population and arrest per officer appears to be driven by the relationship between population and crime. This indirect relationship is more pronounced in the union equation because unionized departments are concentrated in larger cities.

Additional experiments, not reported here, show that eliminating the regional dummy leaves the signs of other coefficient estimates unchanged but reduces the explanatory power of the regression models.


Estimated coefficients of the economic variables (income and unemployment rate) have different signs in the union and nonunion samples. These estimates, however, are insignificant in all but two cases and do not reveal a consistent picture of the union effect.

We also note that the LR test for parameter constancy is significant for arrests related to minor crimes but insignificant for arrests related to serious crimes, suggesting that in the latter case the coefficients are similar for union and nonunion equations.22 An implication of this result is that unionization does not seem to affect police performance when investigat- ing serious crimes. The LR statistic is significant, however, for minor crimes, implying the presence of union productivity effect. In the next section, we estimate the resulting productivity differentials and suggest some possible explanations for the asymmetric effect of unions on the two arrest categories.

We also estimate structural equations ( 5 ) and (5’) jointly with crime equations (7) and (7’) in order to examine the robustness of our findings to alternative specification of the model.” The method of estimation is two stage least squares with selectivity adjustment. These results are not reported for economy of presentation but the highlights are as follows. Esti- mated coefficients for the input variables are remarkably similar to those reported for the reduced form models. Estimates of the labor coefficient are insignificant, supporting the a+p = 1 restriction. Estimates of KIL coefficient a are positive and significant in the union equation but insignificant in the nonunion equation when arrests related to minor crimes measure the output. This suggests a larger a (and thus a smaller p) for the union sample in this output category, implying a union-induced reduction in relative labor productivity which, as argued earlier, could be because of the contract clause regarding staffing of police cars. For serious crimes, in contrast, increased capital utilization has a positive effect on police productivity regardless of the union status. This finding accords well with our earlier results and the LR test for parameter constancy, suggesting that there is not much difference between union and nonunion departments when it comes to dealing with serious crimes. We also note that crime has a positive sign as expected in all samples and for all output definitions.

~

22 Given the result of this test, we also estimate the equation for serious crimes using the pooled sample. Results, which are not reported here for brevity, are similar to the corresponding results for union sample. Moreover, the estimated coefficient of the union dummy, which is included to isolate the union effect, turns out to be insignificant, suggesting no union effect on police productivity with respect to serious crimes.

23 Estimates of structural equations (5) and (5’) and crime equations (7) and (7’) are not reported here, but they are available from authors.

580 I DENNIS BYRNE, HASHEM DEZHBAKHSH, A N D RANDALL KING

Productivity differentials. Our results so far suggest that unions seem to have an insignificant effect on police productivity in the case of serious crimes and a significant effect in the case of minor crimes. To ascertain whether unionization has a positive or negative effect on police performance in the latter case, we estimate union-nonunion productivity differentials. We use the estimated coefficients of the structural equations (5) and (5') for this purpose so that we can also examine the effect of change in crime level on these differentials.

Each differential estimates the percentage difference in the expected output of otherwise identical union and nonunion police departments. We estimate these expected outputs using the estimated coefficients of equations (5) and ( 5 ' ) and common input and crime levels. By using common input and crime levels, we simulate a situation wherein union and nonunion departments face identical crime environments and utilize identical input quantities to fight crime. The input and crime levels are various percentiles of capital, labor, and crime averaged over union and nonunion samples. For example, we obtain the common 50th percentile (median) for capital by ordering the capital data for union and nonunion samples sepa- rately, obtaining the median capital for each sample, and averaging the two medians. We compute common labor and crime levels in a similar manner.

The differentials are computed for both measures of output (arrest types), with the corresponding crime data matching the arrest type. Esti- mates of the productivity differentials are reported in Table 2. Columns 1-

TABLE 2 UNION-NONUNION PRODUCTIVITY DIFFERENTIALS

Crime Percentile

Input Percentile (40th) Input Percentile (6f)th) Average Arrests Arrests Arrests Arrests Arrests Arrests

(serious crimes) (minor crimes) (serious crimes) (minor crimes) (serious crimes) (minor crimes)

20th -5.5% -40.5%* -4.9% - 32.6% * -4.8%"a -34.1 Yon a

40th - 0.6 YO -43.2%* 0.0% - 28.3 yo * 0 . 1 Y O " a -29.8%" a

50th 2.1% -41.3%* 3.3% -26.0%* 3.5%" a -27.5Yon a

60th 5.5% - 39.4 yo * 6.2% -23.6%* 6.4%" a -25.2%"' Average 3.8%"' -39.6Yon a 4.4Yon ' -24.7Yon a 4.6Yon a -26.3%"

Notes: Each differential is obtained by first estimating the difference between union and nonunion outputs from equations (S) and (S'). These differences are computed using the estimated coefficients of ( 5 ) and ( 5 ' ) and common input and crime levels (various percentiles of capital, labor. and crime). Each difference is then converted to a percent differential using 100 (2' - 1). where d is the raw difference. Also, note that average refers to average over IOth, 20th. .... and up to 90th percentiles. 'indicates significance at the .OS level and indicates that the standard error for the marked differential cannot be computed.


4 contain the differentials (for each arrest measure) computed based on the 40th and the 60th input percentiles. Columns 5 and 6 contain the average differentials that are obtained by averaging the differentials computed for all input percentiles (i.e., loth, 20th, e.., through 90th). Also, each row indicates what crime percentile is used to compute the corresponding differential. The last row, labeled average, reports differentials that are averaged over all crime percentiles (i-e., loth, 20th, - w e , through 90th). For example, a nonunion police department which is in the 60th percentile in terms of size (input) and faces a median crime level has a 26 percent less minor-arrest productivity than its unionized counterpart which utilizes identical input and faces a similar crime e n ~ i r o n m e n t . ~ ~

The reported differentials point to a negligible union effect for serious crimes and a sizable negative union effect for minor crimes. When the differentials are averaged, the negative effect is around 26 percent for the latter. We also note that an increase in crime percentile magnifies the union effect; the same is true for input percentile. This scale effect suggests that unionization in large departments and/or in large cities (with higher crime rates) may lead to a greater loss in productivity than in small departments and/or cities.

The most salient implication of these results is that the effect of police unions on arrest productivity varies with the output measure. Unions appear to have an asymmetric effect on police productivity -very little effect on productivity with respect to serious crimes but a negative and significant effect on productivity with respect to minor crimes. The overall effect is also negative. In the remaining part of this section we offer explanations for the observed asymmetric union effect.

The union productivity effect is usually considered to be a consequence of union activity. A written union contract codifies work rules and forces man- agement to allow employees to have input into setting work-related guide- lines. For example, because of safety concerns in large cities where most union departments are located, a union may negotiate a contract clause requiring two officers in each patrol car. Such contractual obligation limits departments from employing capital and labor in the most efficient way, thus adversely effecting productivity. In general, union contract provisions (grievance, sick leave, staffing requirements, wages, etc.) affect resource allocation decisions of both employees and employers, often leading to

*4 Note that the standard error for each differential determines whether or not the differential is statistically significant. The standard error for each average differential depends on the cross- differential covariances which cannot be computed. No inference is therefore made regarding the significance of the average differentials.

582 f DENNIS BYRNE, HASHEM DEZHBAKHSH, A N D RANDALL KING

efficiency loss. The adverse productivity effect of such provisions is more significant in the public sector where, in absence of product market competi- tion, there is little or no pressure to mitigate the efficiency loss (see, e.g., Addison and Hirsch, 1989). Finally, there may be institutional reasons for the observed productivity effect. Most of the unionized departments are located in large cities where prisons may be overcrowded. To help alleviate overcrowding in both the criminal justice and penal systems, police officers in these cities may have an incentive to limit arrests for relatively minor offenses. Also, police unions may give a higher priority to fighting serious crimes and thus direct more resources toward it. Solving serious crimes gives the department high visibility and helps the police gain public support for their public policy 0bjectives.~5 Both of these factors could explain, at least partially, the observed asymmetric effect of unionization on different categories of arrest productivity. However, more research is needed to gain further insight into the institutional mechanism through which police unions affect productivity.

Concluding Remarks This article examines the effects of unionism on police productivity,

Lack of an accepted and operational measure of police output has hindered research in this area. We use two arrest-based measures of police productivity in the context of a production function which includes crime index as a control variable. Our cross section data includes published and unpublished government statistics as well as our own survey of police departments.

Results suggest that unions do not affect various categories of police services uniformly. When output is stratified by the severity of crime, unions appear to have no significant effect on police productivity with respect to serious crimes, but they have a negative effect on productivity with respect to minor crimes. These findings are consistent across reduced form and structural models, indicating robustness to econometric specification.

In closing, we reiterate that the data limitations and measurement problems discussed in the article make it necessary to exercise caution when interpreting the reported results. The issue of police productivity, however, is important and merits attention, particularly in light of the fiscal and crime problems faced by many city governments.

2 j For example, police departments actively supported the 1994 Crime Bill that provides for increased police budgets and manpower. The presence of police unions probably facilitated such an orchestrated lobbying effort.


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Documents

Unions and Police Productivity: An Econometric Investigation