Managerial efficiency in local government: Implications on jurisdictional consolidation

Public ChOice 74: 221-231, 1992. © 1992 Kluwer Academic Publishers. Printed in the Netherlands.

Managerial efficiency in local government: Implications on jurisdictional consolidation* STEVEN C. DELLER EDWARD RUDNICKI Department of Agricultural and Resource Economics, University of Maine, Orono, ME 04469-0163 Accepted 5 February 1991

Abstract. Using data from Maine, estimates of size economies in the production of pubfic educa-

tion services are provided under the alternative assumptions of managerial efficiency and inefficiency. While size economies were identified under the traditional assumption of managerial efficiency, limited or no size economies were identified under the more general assumption of managerial inefficiency. These results question the validity of the traditional economies of size literature and the jurisdictional consolidation policy which follows from the traditional literature.

1. Introduction The decentralization of public responsibilities to lower levels of government over the past decade has renewed the debate over the operational efficiency of local governments. Arguments are made that the small size of operation for many local governments is inherently inefficient in an economic sense, hence costly (Chicoine and Walzer, 1985; Bish and Ostrom, 1972; and Bish, 1977). The natural policy conclusion which flows from these arguments is jurisdictional consolidation (Baumol and Schornhorst, 1983; and Mercier, 1983). The empirical evidence supporting the presence of size economies in the production of certain public goods and services appears to be well documented (Doeksen and Peterson, 1987; and Fox, 1980). This line of reasoning is perhaps most evident in the case of public education. In a review o f the literature examining the case of public education, Fox (1981) reported that the majority of the 34 studies included in his review identified the presence of size economies. These findings have been systematically translated into policy. Sokolow (1981) observed that in the 35 years between 1942 and * The authors wish to thank Michele Marra and an anonymous reviewer for helpful comments. Any errors are the sole property of the authors. Support for this research was provided by the Maine Agricultural Experiment Station, University of Maine, Orono. MAES external publication # 1537.

222 1977 the total number of school districts in the US declined from 108,000 to just over 15,000. The policy of consolidation on the premise of capturing size economies, however, ignores a central contention of the public choice school of thought. Specifically, public choice analysts view local government as aggregators of collective preferences on issues requiring public action (Chicoine and Walzer, 1985). Within this framework the degree of heterogeneity of the population living in the jurisdictional boundaries of the local government becomes a driving factor in determining the total public welfare achieved. It has been suggested by Tullock (1969) and later shown within the framework of club goods (Cornes and Sandler, 1986), that smaller governments (or clubs) composed of a more homogenous population are better suited to match levels of the public good with the preferences of the constituents. The policy of jurisdictional consolidation may introduce a sufficient degree of preference heterogeneity such that the preferences of some subgroups will no longer be met and total welfare may decrease. The issue addressed in this research centers on the consistency of the empirical evidence examining size economies. In particular, embedded in the empirical consolidation literature is the implicit assumption of managerial efficiency. The traditional empirical specification of these models assumes that all local officials are employing inputs into the production process in a cost-minimizing manner. If managerial inefficiencies are present, the validity of the traditional size economies literature may be questioned. In particular, managerial inefficiencies may be incorrectly attributed to size economies. In the extreme, no size economies are present, but rather managerial inefficiencies. The implication on policy is startling: simple consolidation to gain perceived size economies excludes the possibility of managerial inefficiencies. The research reported in this article examines the implication of managerial inefficiencies on size economies for the case of public education in Maine. The article is divided in six sections. The notion of managerial efficiency within a public setting is described in the second section. The theoretical framework and estimation methods are then described followed by a description of the empirical model and data. The empirical results are then discussed and the concluding section considers the study's policy implications.

2. Managerial efficiency in government Sokolow (1981) defines managerial capacity, or managerial efficiency, as the skills and experience needed to produce public goods and services in an economically efficient manner. Reid (1984 and 1986) observes that in many areas local government officials may not possess either the professional training or

223 experience to effectively allocate government resources in an economically efficient manner. Key functions such as budgeting, personnel management and evaluation may not be part of local functions or recognized as public functions. Coupled with the high rates of turnover amongst local officials, the ability of local public officials to use inputs into the production process in a costminimizing manner is questionable (Cigler, 1987; Reid and Sullivan, 1986). Particular concern has been expressed over the ability of the smallest of local governments to effectively perform functions (Deller and Nelson, 1991; Seroka, 1981 and 1990). Smaller local governments often lack the resources to attract trained professionals. Indeed, management decisions at many smaller governments are made by part-time officials who are often public-minded citizens. Given this pattern, it seems reasonable to expect the level of managerial inefficiency to be highest at these smaller levels of local government. The empirical literature examining managerial capacity in local government is, unfortunately, very limited. Indeed, Sullivan and Reid (1986) conclude that the notion of managerial capacity shortfalls (i.e., managerial inefficiencies) in the case of local governments is limited to logical speculation. There are, however, a small handful of empirical studies which do indicate the presence of managerial inefficiencies in local governments. In a study of rural road services in the Midwest, Deller and Nelson (1991) found that of the 446 townships studied, less than one percent were identified as managerially efficient. A consistent pattern identified by Deller and Nelson confirms the hypothesis concerning the relatively higher levels of inefficiency at the smallest levels of local government. Studies of managerial efficiency in the case of public education have tended to support the presence of inefficiencies. In a study of Missouri public schools, F~ire, Grosskopf and Weber (1989) reported that over half of the schools in their sample were identified as managerially inefficient. In a collection of studies of public schools in Texas, Bessent, Bessent and their colleagues (1980, 1982 and 1983) consistently identified the presence of managerial inefficiencies. These studies, however, focused on identifying general levels of efficiency and not patterns in efficiency. While these arguments have been used to suggest jurisdictional consolidation as a means of promoting professionalism (i.e., managerial capacity or efficiency) in local government, the implications of these arguments on the traditional economies of size literature has not been addressed. The intent of this research is to examine the role of managerial efficiency in the traditional test of economies of size.

224 3. A theoretical framework

To examine the implication of managerial inefficiencies on size economies, it is convenient to work within the theoretical framework of cost minimization. Such a framework is not only consistent with the size economies literature (i.e., long-run average cost curves) but also conforms to the Inman (1979) two-step decision making process (Deller and Nelson, 1991). In particular, the first step of the process corresponds to provisionary decisions (demand or public choice) while the second step refers to production related decisions. Given that most public officials operate in the second step, a reasonable criterion may be to produce the demanded level of the public good at the lowest possible cost.

3.1 The theoretical objective The assumed objective function facing public educators may be expressed: min x [ w ° ' x [ y° E V(x, se°[q°)}

(1)

where w ° represents a vector of strictly positive prices and x is a vector of inputs used in the eduction process. The problem outlined in eq. (1) represents a traditional cost-minimization problem given an output constraint. Output is assumed to be composed of two parts: y° (number of students, or school size) and q" (student performance). 1 Here, the second output, q° or student achievement, is assumed to be the minimal level of acceptable performance (demand determined). Note that from the school administrators perspective, both outputs are treated as parameters of the model. The production technology modeled in eq. (1), represented by the input requirement set V(.), is composed of two separate components: those within the control of the school administrator (x) and those beyond the control of the school administrator (se°). This specification of the educational production function is important because it recognizes the complexities of the educational production process. 2 Here, the vector of school inputs (x) is generally composed of teacher inputs, building facilities and school materials, whereas the vector of non-school inputs (se °) is generally composed of family and peer influences and innate ability. Note that the latter set of inputs is beyond the administrator's control and is deemed to be a parameter of the model. Further note that the input correspondence (V(.)) is conditional on the demanddetermined minimal level of student performance (q°). Solving the objective function outlined in eq. (I) yields the traditional cost function which may be expressed: C(y °, w °, q°, se').

(2)

225 This formulation of the cost function is consistent with traditional economic theory except for the presence of two additional parameters: quality and the set of inputs beyond the control of the administrator. This specification represents an improvement over most education cost models in that quality is implicitly held constant and non-school inputs are explicitly modeled (Fox). A vital assumption, however, in moving from the theoretical objective modeled in eq. (1) to the empirical model outlined in eq. (2) is the satisfaction of the necessary first order conditions. Few studies of size economies in the local public sector are clear to this point. In the terminology of the efficiency literature, managerial efficiency is implicitly assumed, or the first order conditions are satisfied. Given the notion of managerial ill-capacity and the limited empirical evidence, this assumption may not be justified in the case of local governments. A more general model of size economies in public services would explicitly allow for managerial inefficiency.

3.2 Estimation method The traditional estimation method use in studies of size economies assumes that any variation away from the cost curve (eq. (2)) is simply noise in the data and is captured by the least squares residual term. If managerial inefficiencies are present in the data, however, the least squares error term takes a slightly more complex form. Specifically, the error structure is composed of two parts: = v + u

(3)

where E is the total error of the cost model, v represents noise in the data and u represents additional costs due to managerial inefficiency or the costs associated with failure to satisfy the first order conditions. Aigner, Lovell and Schmidt (1977) suggest a maximum likelihood method which explicitly allows for an error structure of the form presented in eq. (3). Aigner et al. assume that the elements of v are iid as N(0, ~ ) and the elements of u are absolute values of variables which are iid as N(0, o2u)(or, u is iid as a half-normal) and all v's, u's and independent variables are independent of each other. The value of the likelihood function is then dependent on the frontier cost equation coefficients (fl) and two error-term-related measures 02 ( = o 2 + ~ ) and k ( = Ou/trv). By the specification of the likelihood function the difference between a cost function estimated by least squares and the frontier function can be statistically tested by computing the t-statistic for k. If k is statistically different from zero, there is sufficient evidence to suggest that managerial inefficiencies are present in the data. Therefore for this research, the central hypothesis focuses on (1)

226 the statistical difference between the ordinary least squares model and the frontier model and (2) the shape of the two cost curves in output (school size) space.

4. Empirical model The data used to test the influence of managerial inefficiencies on size economies is available for a sample public elementary schools in Maine. 3 A total of 147 observations from the years 1985 through 1989 were used in the estimations. A transformation of eq. (2) (i.e., an average cost function as opposed to a total cost function) is used for consistency with the traditional size economies literature. A parabolic relationship is assumed between average costs and enrollment while the remaining variables are assumed to be linear. The empirical model can be expressed as: AC = /~0 + BlY + ~2Y2 + ~n=l°tiWi + PlQ + P2SE + v + u

(4)

where Y is a measure of school size, W is a vector of input prices, Q is a measure of performance quality and SE is a measure of non-school inputs. The two error terms are defined in eq. (3). Average cost (AC) is computed by dividing total school expenditure by the measure of school size: average daily attendance (ADA). Using school size as the divisor to obtain average cost is consistent with the theoretical model presented in eq. (1) as well as the traditional economies of size literature. The selection of input prices were chosen for consistency with the literature. The price of teachers was broken into two groups: male teacher salaries (MSAL) and female teacher salaries (FSAL). This was done to reflect the substantial differences in the baseline salaries across the two groups. The price of administrative functions is proxied with school expenditures on administration per pupil (SCHAD). Finally, the price of building services is proxied by operations and maintenance expenditures per pupil (OPMAINT). Consistent with economic theory all prices are expected to be positively related with average cost. The measure of student performance (Q) is based on the cumulative threeyear (1986-1989) Maine Achievement Test scores (SCORE). 4 This measure implicitly assumes that current test scores are reflective of the level demanded by the local citizens. Under conditions of ceterisparibus, higher test scores require increased inputs, hence higher costs. Thus test scores are expected to be positively related to costs. Based on the review provided by Hanushek (1979 and 1986), parental educa-

227

Table 1. OLS and frontier results a Dependent variable: Total expenditures per pupil OLS SCORE COLL MSAL FSAL SCHAD OPMAINT ADA ADA2 Constant R2 Fstat )~

- 0.268

(0.566) 5.959 (4.435)* 0.006 (2.285)* 0.049 (5.127)* 0.728 (3.231 )* 1.881 (11.20)* - 0.083 (1.851)** 200 x 10 -7 (1.852)** - 108.68 (0.519) .7186 44.054* -

Frontier - 0.601 (1.504) 7.134 (5.571)* 0.007 (2.364)* 0.047 (4.495)* 0.765 (2.740)* 1.738 (11.60)* - 0.063 (1.345) 108 x 10-7 (0.785) - 159.37 (0.785) 2.182 (4.793)*

a Number in parentheses is the absolute value of the t-statistic. * Significant at .05 level, ** significant a t . 10 level. c a t i o n levels m a y p r o v i d e the best p r o x y o f n o n - s c h o o l inputs. F o r this s t u d y the p e r c e n t a g e o f p a r e n t s with a college d i p l o m a was used to c a p t u r e the role o f n o n - s c h o o l i n p u t s ( C O L L ) . U n d e r c o n d i t i o n s o f ceterisparibus, higher levels o f n o n - s c h o o l i n p u t s s h o u l d increase the m a r g i n a l p r o d u c t i v i t y o f school inp u t s t h u s exerting d o w n w a r d pressure o n costs. 5 O n the o t h e r h a n d , higher e d u c a t e d p a r e n t s m a y d e m a n d higher s t a n d a r d s (higher Q), thus p l a c i n g upw a r d p r e s s u r e o n costs. N o h y p o t h e s i s is p u t f o r t h in t e r m s o f the e s t i m a t e d coefficient a s s o c i a t e d w i t h this v a r i a b l e . 6

5. E m p i r i c a l r e s u l t s

T h e e m p i r i c a l estimates o f the a v e r a g e cost f u n c t i o n o u t l i n e d in eq. (4) are p r e s e n t e d in T a b l e 1. C o n s i d e r first t h e least squares e s t i m a t e s where m a n a g e r i al efficiency is i m p l i c i t l y a s s u m e d . A s e x p e c t e d , all prices a r e significant a n d positively r e l a t e d to a v e r a g e costs. T h e n o n - s c h o o l i n p u t m e a s u r e ( C O L L ) is

228 positive and significant. The quality variable (SCORE), however, is insignificant at either the .05 o r . 10 significance level and has a sign opposite than expected. This latter result is disappointing but is not inconsistent with the existing literature. Turning to the hypothesis of size economies in the presence of managerial efficiency, the least squares results suggest that a U-shaped average cost curve is present in the case of Maine public education. Given the optimal size of just over 2000 students and the rural nature of most public schools in Maine, these results suggest that cost savings may be realized through school consolidation. Under the assumption of managerial efficiency, the Maine data are consistent with prior expectations given the traditional economies of size literature. Turning to the empirical estimates under the more general assumption of managerial inefficiency, some interesting results are revealed. First, the estimated coefficients on the quality measure (SCORE), non-school input measure (COLL) and the input prices are consistent with the least squares estimates. Second, the constant term shifted downward reflecting both the enveloping effect of the frontier estimator and the lower costs associated with the frontier. Third, the system parameter, )~, is significantly different from zero at the .05 percent level. This result indicates that there is a statistically significant difference between the least squares estimate and the more general frontier estimate. Given the theoretical discussion, this result implies that additional costs due to managerial inefficiencies are present in the Maine data. By allowing for managerial inefficiency in the data, the policy conclusions related to size economies have been altered. Specifically, the size variables were not statistically different from zero indicating a flattening of the U-shaped average cost curve. Under the more general model where managerial inefficiencies are specifically modeled, no size economies were identified. Significant levels of managerial inefficiencies, however, were identified. Therefore, under the more general assumption of managerial shortfall (inefficiencies), the Maine data suggests that economies of size may not be present in the production of educational services. To lend additional insight into these results, the estimated coefficients for the least square and frontier models were used to estimate the difference between two sets of cost curves for each observation. The difference between the least squares and frontier curve is a proxy measure for the level of managerial inefficiency at each data point that is incorrectly attributed to economies of size. 7 If this difference is greater for smaller schools, then the notion that managerial inefficiencies may be incorrectly attributed to size economies is supported. At smaller levels of output higher levels of managerial inefficiency are attributed to noise, thus forcing the cost function to appear to be U-shaped. Regressing school size (ADA) on these computed differences indicates that smaller schools are more inefficient in a managerial sense (Table 2), thus the notion is supported.

229 Table 2. Cost curve comparisona

Dependent variable: Differences between LS and frontier estimates Constant ADA R2

Fstat

185.966 (81.346)* - 0.011 (5.433)* .1691 29.514

a Number in parentheses is the absolute value of the t-statistic. * Significant at 05. level.

6. Policy implications

The empirical results for Maine public schools indicate that under the restrictive assumption o f managerial efficiency size economies are identified, but under the more general assumption o f managerial inefficiency no evidence of size economies is found. In particular, smaller schools appear to exhibit higher levels of managerial inefficiency. The implication this result has on the size economies literature is profound. The results suggest that managerial inefficiencies, particularly at smaller levels o f operation, m a y be incorrectly attributed to size economies. This result casts doubts on the policy o f consolidation of rural schools into larger units. In short, the simple policy o f school consolidation to achieve size economies may be in error. In addition, the potential loss in total welfare f r o m aggregating preferences further compounds the argument against naively consolidating jurisdictions. Rather a policy o f additional training to enhance managerial capacity m a y achieve the desired expenditure reductions without the costs to welfare from consolidation. While this study does not disprove the presence o f size economies in the production o f local public services, it does cast serious doubt on the existing size economies literature. The implication these results have on policy is profound and warrants further empirical attention.

Notes

1. See Hanushek (1979 and 1986) and Fox (1981) for an excellent discussion of school output. 2. See Levin (1974), Hanushek (1979 and 1986) and Deller and Rudnicki (1990) for a detailed discussion of the educational production function literature. 3. Only schools with eighth grades were included in the analysis. Towns where eighth grades are part of the high school were removed to preserve student homogeneity. Multi-school districts were combined into a single unit due to data constraints.

230 4. The Maine Achievement Tests are taken annually by students in the 4th, 8th and 11th grades across the state. 5. Note that this argument explicitly assumes that the two types of inputs into the educational production process are non-separable. Given the interaction of parents with the school system, this seems a reasonable assumption. 6. Other studies have reported similar relationships (Walberg and Fowler, 1979). 7. A alternative method would be to compute Farrell type measures of efficiency where observed costs are compared to cost minimum.

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