Empirical estimates of economies of scale in the provision

Transcription

1 Economies of Scale in Property Tax Assessment Economies of Scale in Property Tax Assessment Abstract - We estimate the costs of performing property tax assessments using a translog cost function over a sample of 138 county-level assessment offices in Georgia. We find that there are substantial economies of scale. For example, computed at the sample means, a ten percent increase in the volume of assessments results in an increase of approximately three percent in total costs. The model considers both the number of parcels and the value of parcels as alternate measures of volume; both measures give similar results. We also estimate a two-product cost function, with residential and nonresidential property assessment as the different outputs. These results show no evidence of economies of scope, and calculated economies of scale are very close to the single output results. INTRODUCTION Empirical estimates of economies of scale in the provision of government services are useful in decisions regarding jurisdiction or service consolidations, and in decisions concerning the reassignment of functions to special districts. There is a substantial literature dating back to the early 1960s attempting to estimate the extent of economies of scale in the provision of government goods and services. One of the first studies, conducted by Hirsch (1965), investigated the effect of various factors on the cost of municipal refuse collection service. Other work related to the issue of economies of scale in the provision of public services includes Ahlbrandt (1973) and Duncombe and Yinger (1993) on fire services, Deller et al. (1988) on roads, Walzer (1972) and Gyimah-Brempong (1987) on police, Kitchen (1976) on refuse collection, DeBoer (1992) on public libraries, and Callan and Santerre (1990) on education. 1 Early studies of economies of scale for government services used functional forms that did not necessarily exhibit the theoretical properties associated with cost functions. Recent research, however, is based more heavily on the economic theory of cost minimization and takes greater care in specifying the empirical model. An example is Duncombe and Yinger (1993), who David L. Sjoquist & Mary Beth Walker investigate the existence of returns to scale in the provision of School of Policy fire protection, and allow costs to vary by the level of activity Studies, or output, service quality, the number of persons served, and Georgia State the number of functions performed (i.e., economies of scope). University, Atlanta GA Fox (1981) reviews the research on economies in education. 207

2 NATIONAL TAX JOURNAL This paper focuses on the economies of scale in the assessment of property for property tax purposes. There are several papers, including Sigafoos (1955), Cook (1974), Ohio Municipal League (1967), Wicks and Killworth (1967), Netzer (1966), and Advisory Commission on Intergovernmental Relations (1974), that provide jurisdictionspecific values of the cost, expressed as a percentage of revenue, of administering a tax. Only Wicks and Killworth and Netzer provide estimates specifically for property tax administration, which they estimate to be about 1.5 percent of revenue. 2 This paper explores the existence of economies of scale in the assessment of property for property tax purposes using data from assessment offices in Georgia. Our results suggest that considerable economies of scale exist in the assessment of property. For example, calculated at mean values of the independent variables, we find that the elasticity of total cost with respect to the volume of assessment is about 0.3. We calculate that consolidating all assessment offices with outputs below the median volume would reduce the total cost of assessing property for these smaller districts by over 20 percent. The rest of the paper is organized as follows. In the second section, the assessment process in Georgia is described, while the model to be estimated is developed in the third section. The fourth section presents the data, while the fifth section presents the empirical results. The final section presents the summary and conclusions. ASSESSMENT PROCESS The property tax assessment process in Georgia is highly decentralized. With the exception of public utilities, all assessments are done at the county level on an annual basis by appointed assessors. The county government pays the cost of property assessment. There is no requirement that counties conduct periodic mass appraisals, and only a handful of counties have adopted computer assisted mass appraisal (CAMA) systems. Nearly all property is assessed at 40 percent of fair market value; the principal exceptions are small farms, which are assessed at 35 percent of fair market value, and farm land that qualifies for conservation use, which is assessed on current use value. Appeals are initially heard by a threeperson appeals board that is appointed by the county tax assessor for that purpose. The state s involvement and oversight role is minimal. The state s Revenue Commissioner sets the minimum qualifications for tax assessors, but the state has little authority over how the tax assessor s office functions. The state does conduct a sales-assessment ratio study for each county, and can require counties whose assessments do not meet sales-assessment ratio standards for mean and distribution to correct assessment deficiencies within three years or face various penalties. Thus, it is reasonable to treat county assessment offices as independent agencies. The chief input into the production of property tax assessments is labor. Offices in Georgia hire assessors, appraisers, and mappers in addition to clerical staff. There are wide differences among the county offices both in the number of employees and the mix of types of labor. For example, the number of appraisers in a single office varies between 0 and 52. Some offices hire no mappers or assessors, while others hire as many as six. There is similar variation in the number of clerical workers. The production of property tax assessments also requires some capital beyond office space, primarily computers and appropriate software. The advent of the CAMA systems allows for the possibility of some substitutability between labor and capital, but as noted above, few counties have adopted this technology. 2 Sherwood-Call (1987) summarizes this line of research. 208

3 Economies of Scale in Property Tax Assessment THE MODEL 209 Based on these institutional facts, we now devise a formalized framework to consider the variation in production costs over the county offices. For property tax assessment, assessment office personnel, capital, and a parcel of property are combined to produce an appraisal of that parcel of property. It is not immediately obvious how to measure the output of appraisals. We consider the output as having two dimensions, a volume dimension and a quality dimension. The volume dimension is simply the number of appraisals conducted, which is identical to the number of parcels appraised. The quality of assessment refers to how closely the assessment tracks the fair market value of the property; the cost of assessment is expected to increase with the quality of the assessment. Thus, the cost of assessing a set of parcels is expected to increase as the number of parcels to be assessed increases and the quality of assessments increases. Suppose that a jurisdiction contains several types or classifications of property and that, within each classification, property is homogeneous. Let q ij represent the number of parcels of property type i located in jurisdiction j. Because each parcel is assessed each year, Σ i=1 m q ij represents the number of assessments made annually in the jth jurisdiction, where m is the number of different property classes. This formulation allows for the possibility that the production of assessments of different property types (residential versus industrial, for example) can be viewed as the production of multiple outputs. The cost of assessing all properties within a jurisdiction will, of course, depend on the levels of the q ij, denoted by the vector q; the quality or standard of assessments, denoted as s; and the prices of the factor inputs involved, denoted by the vector p. The cost of assessing property is also likely to be influenced by the factors outside the control of the assessment office. These environmental factors, denoted by the vector E, include such things as the geographic size of the assessment district. Thus, the cost function may be expressed as: C = c(q, p, s, E, ε, θ) where ε represents the unobservable random components that influence costs, and θ denotes the parameters of the cost function. The choice of functional form for the empirical model is limited by two factors. First, the available data set is small; there is complete information on only 138 assessment offices. Second, although two inputs contribute to the production of property tax assessments, labor and capital, we cannot obtain meaningful data on prices of capital across assessing districts. However, it is not unreasonable to assume, as we do, that the price of capital is the same throughout the state. Labor prices, on the other hand, show considerable variation across the sample due both to the different mixes of employees hired by the different offices and to geographic wage differentials. It is not unusual for wage rates to differ across the state; for example, mean earnings for rather specific occupational categories do differ across Georgia (Urban Study Institute, 1996). While the quality-adjusted wage rate might be expected to be the same throughout the state in the long run, wage rates may differ in the short run due to temporary inter-regional differences in supply and demand (Ihlanfeldt, 1988). In addition, wage differentials can result from differences in local fiscal conditions (Wallace, 1993) and in local amenities (Beeson, 1991); wage differences due to these factors may not disappear even in the long run. The data limitations mean that, for estimation purposes, we cannot follow the usual practice of estimating a subset of the input demand equations along with the

4 NATIONAL TAX JOURNAL cost function to increase degrees of freedom, and so improve efficiency. Together, these two limitations prohibit the use of some of the more recently developed flexible functional forms that require that a large number of parameters be estimated. 3 The function chosen is the multiproduct translog, which is somewhat more parsimonious than other flexible forms. (The Appendix contains the explicit form of the cost function and a discussion of the restrictions on the parameters.) The model as specified is multiproduct; that is, it allows for the possibility that costs will vary by the mix of properties to be assessed. In some cases, however, it is possible to aggregate multiple outputs into a single measure. If the data indicate that a single output measure is appropriate, then a much simpler version of the translog model can be used. Kim (1986) developed both necessary and sufficient conditions for the existence of a consistent output aggregate. The results of the test (which is discussed in the Appendix) imply that it is appropriate to combine the categories of parcels and treat all categories of property as an aggregate. Reduced to a single output, the log-cost function can be written as [1] ln C j = α 0 + α 1 ln p jl + α s ln s j + α q ln q j + α E ln (E j ) + 0.5δ 1 (ln p jl ) δ 2 (ln q j ) 2 + δ 3 (ln p jl )(ln q j ) + 0.5δ 4 (ln s j ) 2 + δ 5 (ln s j )(ln p jl ) + δ 6 (ln s j )(ln q j ) ln (E j ) Γ ln (E j ) + ln p jl λ p ln (E j ) + lnq j λ q ln (E j ) + ln s j λ s ln (E j ) + errors m where q j = Σ i=1 q ij represents the total number of assessments made in county j. Since capital costs are not directly included, equation 1 is a variable cost function. The estimated function will be consistent with the theoretical properties of cost functions and can provide evidence for either economies or diseconomies of scale. Our particular interest is in how cost varies with the volume of output, controlling for the other variables. The measure of economies to scale to output volume is based on equation 1, and is given by: ln C = ln q αq + δ ln q + δ ln p + λ ln (E) q This measure corresponds to what Duncombe and Yinger (1993) call technical returns to scale. The term ln C / ln q is the elasticity of cost with respect to q. If this term is less than one, then the percentage increase in total cost will be less then the percentage increase in q, which is the same as saying that average cost, i.e., cost per unit of q, falls as q increases. DATA The data come from several sources. First, data on the 1992 cost of assessing property were obtained from a survey of all 159 county assessing offices in Georgia. Completed and usable surveys were obtained from 138 assessment offices (12 offices did not return the survey and nine surveys had missing data). The survey information was used to measure the total cost of operating the assessment office (TCOST) and the annual wage rate (W). TCOST refers to actual operating cost less large nonrecurring expenses such as a mass reappraisal but does not include any implicit cost of capital. Annual wage was constructed by dividing the total wage bill by the number of employees. Part-time workers were weighted by the number of hours they worked. 3 See Diewert and Wales (1987) for a discussion of flexible functional forms with desirable properties. 210

5 Economies of Scale in Property Tax Assessment Second, two variables were alternatively used to measure q, the number of parcels (TNUM) and the assessed value (TVAL). The values of TNUM and TVAL, by property classification within each of the counties for 1992, were obtained from the state Department of Revenue. There are four categories of property identified: residential, commercial, industrial, and agricultural. As noted above, we determined that it is appropriate to combine these four property categories. (Utility property was excluded since it is assessed centrally.) While TNUM reflects our concept of volume of assessments, our model assumed that parcels were homogeneous. To allow for variations in the size of parcels we also use TVAL. Our observations encompass a substantial range of assessment office sizes. For example, the number of residential property varies across counties from a low of less than 1,000 parcels to more than 300,000. To measure differences in the quality of the assessment process, we used the inverse of the coefficient of dispersion of the sales-assessment ratios, denoted COD. 4 (Measures of the COD by property type were not available.) This is a standard descriptive measure of the quality of the assessment process (Gerau and Plourde, 1976). The coefficients of dispersion for 1992 were obtained from the state Department of Revenue. There are at least two possible measures of property assessment quality, the mean sales-assessment ratio and the coefficient of dispersion. While both capture some aspect of the quality of assessments, the coefficient of dispersion within each county is a superior measure. 5 A number of different variables were considered as environmental factors to control for differences in conditions across counties that could influence assessment costs, but would be beyond the assessment office s ability to control. We reviewed the literature on property tax assessment to help in identifying control variables. 6 However, the literature focuses on factors affecting the quality of assessment, not the cost of assessment, and hence is not directly relevant. Furthermore, given the number of available degrees of freedom, we needed to keep the number of control variables to a small number. We tested the percentage of the county s population classified as urban, URBAN; the population growth rate over the past decade, POPG; the population s education level as measured by the percent of the population with a high school degree or more, HS; and the area of the county measured in square miles, SQMI. Data for these variables were obtained from the 1990 Censuses of Population and Housing. We also computed the proportion of a county s property that is nonresidential, denoted NRES, using the property tax data from the Department of Revenue. The percentage of the population that is urban could affect the cost of assessment for at least two reasons. First, the greater density of urban areas should reduce travel time on the part of assessors. Second, a less urbanized area may have a larger share of its buildings that are unique, while in a more urbanized area, there will be more buildings that are similar to other buildings; i.e., in a rural area, each house may be very different, while in a city, there may be several houses that are very similar. The greater similarity will make assessment easier. It is also the case that property tax rates are higher in urbanized areas in Georgia, and studies of 4 Since larger values of the coefficient of dispersion imply lower quality assessment, we adopt the common convention and use the inverse of the coefficient. 5 We also estimated the model using the sales-assessment ratio in place of COD. The coefficient was positive as expected but not significant. The other parameters were essentially unaffected. 6 See Bowman and Mikesell (1990) for a review of these studies. 211

6 NATIONAL TAX JOURNAL assessment quality have found that higher property taxes will lead to greater assessment quality, likely as a result of increased appeals (Borland and Lile, 1980; Bowman and Butcher, 1986). Thus, the effect of URBAN on TCOST could be positive or negative. Counties that are growing are likely to have more property sales, thus making it easier to do comparative sales appraisals. (Studies of assessment quality find that more sales result in better assessment (Schroeder and Sjoquist, 1976)). On the other hand, growth will bring about new construction, and the cost of incorporating new parcels into the assessment process may add to the cost of assessment. Thus, the effect of POPG could be positive or negative. Education will reflect several factors since it is correlated with income, and hence housing value, and tastes for public services. The level of education may reflect a desire for higher quality public services, including higher quality assessments. This could result in an increase in the cost of assessment, although COD should measure this effect directly. On the other hand, education may reflect a demand for efficiency in the delivery of public services, or a more cooperative taxpayer, and thus be associated with lower costs. Higher valued housing, ceteris paribus, means higher property taxes, and hence a greater incentive to appeal property tax assessment. Thus, to the extent that education is positively related to housing value, education may lead to higher costs of assessment. Thus, the effect of HS could be positive or negative. The geographic size of the assessing jurisdiction will be related to the required travel time needed to assess all of the property. Thus, we expect that SQMI will be positively related to cost. To the extent that the type of property will affect assessment cost, the composition of the district will affect total cost. NRES is a measure of the composition of the tax base. Since we expect residential property to be less costly to assess, the expected sign on NRES is positive. EMPIRICAL RESULTS Summary statistics on all variables are presented in Table 1, and the regression results are presented in Tables 2 and 3. The regression in Table 2 uses the number of parcels (TNUM) to measure output, while the regression in Table 3 uses the total assessed value (TVAL). Due to the large number of parameters involved, it was not feasible to include a large number of environmental factors. Because there is no obvious way to choose a subset of the four environmental variables on theoretical grounds, we conducted a series of likelihood ratio tests to see which could be reasonably excluded. These tests suggest that the pair HS and SQMI are somewhat more effective than POPG and URBAN. 7 However, including the other set did not change the basic results. We also included NRES, the proportion of a county s property that is nonresidential, despite our test results that indicate that the different property types could be aggregated (Appendix). We believed a priori that nonresidential property is more costly to assess. Thus, we decided to include a control for variations in the property tax base across counties. Therefore, in our final models, the vector E includes three variables: HS, SQMI, and NRES. Our results indicate that although few of the individual parameters for these control variables are statistically significantly different from zero, as a group, these variables exert a strong impact on 7 There is a relatively small degree of collinearity among these variables; population growth is related to the education variable and the urban variable. 212

7 Economies of Scale in Property Tax Assessment Variable Name AGRCNT AGRVAL ($1,000 s) COD COMCNT COMVAL ($1,000 s) HS INDCNT INDVAL ($1,000 s) NRES RESCNT RESVAL ($1,000 s) SQMI TCOST ($) TOTN TOTPN W ($) Mean 2, , , , , , , , ,490 TABLE 1 DESCRIPTIVE STATISTICS Standard Deviation 1, , , , , , , , ,516.9 Minimum , , , ,153.6 Maximum 15, , ,520 4,898, , , ,530 6,251, ,483, ,977 Note: RESVAL and RESCNT refer to the value of residential properties and the number of residential parcels. AGRVAL and AGRCNT have the same definition for agricultural property, COMVAL and COMCNT for commercial property, and INDVAL and INDCNT for industrial property. TOTN and TOTPN refer to the numbers of fulltime and part-time workers, respectively. Parameter α 0 α 1 α q α s α e1 α e2 α e3 δ 1 δ 2 δ 3 δ 4 δ 5 δ 6 γ 11 γ 12 γ 13 γ 22 γ 23 γ 33 λ p1 λ p2 λ p3 λ s1 λ s2 λ s3 λ y1 λ y2 λ y3 TABLE 2 ESTIMATES FROM TRANSLOG COST FUNCTION USING PROPERTY COUNTS Variable (in Logs) INTERCEPT W TNUM COD HS SQMI NRES W 2 W TNUM TNUM 2 COD 2 W COD TNUM COD HS 2 HS SQMI HS NRES SQMI 2 SQMI NRES NRES 2 W HS W SQMI W NRES COD HS COD SQMI COD NRES TNUM HS TNUM SQMI TNUM NRES Log-of-likelihood function = Estimate Estimated Standard Error t-ratio

8 NATIONAL TAX JOURNAL Parameter α 0 α 1 α q α s α e1 α e2 α e3 δ 1 δ 2 δ 3 δ 4 δ 5 δ 6 γ 11 γ 12 γ 13 γ 22 γ 23 γ 33 λ p1 λ p2 λ p3 λ s1 λ s2 λ s3 λ y1 λ y2 λ y3 TABLE 3 ESTIMATES FROM TRANSLOG COST FUNCTION USING PROPERTY VALUES Variable (in Logs) INTERCEPT W TVAL COD HS SQMI NRES W 2 W TVAL TVAL 2 COD 2 W COD TVAL COD HS 2 HS SQMI HS NRES SQMI 2 SQMI NRES NRES 2 W HS W SQMI W NRES COD HS COD SQMI COD NRES TNUM HS TNUM SQMI TNUM NRES Log-of-likelihood function = Estimate Estimated Standard Error t-ratio total costs. 8 Rather than examine the individual coefficients for these variables, we compute the elasticities. These elasticities for E are given by: 3 = αek + Σ γ kj ln (E j ) ln E k j=1 + λ. pk ln p 1 + λ. qk ln q. We calculated the elasticities using the mean values of the variables and report them in Table 4. The values of the elasticities are similar for the estimates based on the two different measures of volume, number of parcels and value of property. The elasticity of total cost with respect to HS, the percent of the county completing high school, is positive and significant. As noted above, the expected sign was indeterminant. The positive coefficient is consistent with the argument that better educated communities will demand better government in general and better assessments in particular, resulting in greater expenditures. To some extent, this is also reflected in the positive correlation between HS and COD of The elasticity with respect to the composition of property, NRES, is negative but has a very large standard error. We expected that the elasticity with respect to NRES, the percent of property that is nonresidential, would be positive; i.e., nonresidential property would be harder to assess and hence the cost would be higher the larger the amount of nonresidential property. The insignificance of the elasticity reinforces our previous test results that the cost of assessing property does not 8 The equations were estimated using ordinary least squares. All standard errors were computed using a heteroskedasticity-consistent covariance matrix estimator. Brown and Walker s (1995) results indicate that cost functions with additive errors are conditionally heteroskedastic. 214

9 Economies of Scale in Property Tax Assessment TABLE 4 ESTIMATED ELASTICITIES (STANDARD ERRORS IN PARENTHESES) q = Counts q = Values = ln COD (0.096) = ln COD (0.092) ln HS = (0.427) ln HS = (0.427) ln SQMI = (0.104) ln SQMI = (0.106) ln NRES = (0.106) ln NRES = (0.116) = ln q (0.064) ln q = (0.055) depend upon the composition of the property tax base. We also redefined NRES to exclude agricultural property; the empirical results were essentially unchanged. The elasticity of total cost with respect to our measure of assessment quality, COD, is positive and significant at the ten percent level. In other words, attaining greater uniformity increases the cost of assessment. The magnitude of the coefficient indicates that a one standard deviation change in COD at the mean (a 45 percent change) would change costs by 6.8 percent. Finally, Table 4 presents the elasticities of cost with respect to output volume, i.e., / ln q. The two estimates are and for the regressions based on number of parcels and value of property, respectively. Both estimates are significantly less than one, meaning that there are substantial returns to scale in assessing property; a ten percent increase in the number of parcels will increase total cost by only 3.23 percent. To provide some perspective on these estimates, consider the calculations presented in Table 5. Using the mean values for the other independent variables and the parameter estimates reported in Table 2, we calculated the predicted total and average cost of assessing property for various levels of output volume. All of the values of output fall within the actual range of the number of parcels. Increasing the number of parcels from 30,000 to 50,000 reduces the cost per parcel from $5.73 to $4.29, while increasing the number of parcels from 100,000 to 200,000 reduces the cost per parcel from $3.08 to $2.39. (The existence of a minimum average cost from equation 1 depends upon the values of estimated parameters. Based on our estimated parameters, the average cost function does not reach a minimum for the range of quantities in the sample.) Table 6 illustrates how average cost increases with the quality of assessment, i.e., 10,000 15,000 30,000 50, , ,000 TABLE 5 PREDICTED TOTAL COSTS AND AVERAGE COSTS Number of Parcels Total Costs Average Costs $121, , , , , ,842 $

10 NATIONAL TAX JOURNAL TABLE 6 PREDICTED AVERAGE COST FOR DIFFERENT QUALITY LEVELS Quality a (COD) Average Cost $ a Recall that COD is the inverse of the coefficient of dispersion. The COD values are the quintile values. COD. As with the calculations in Table 5, the average costs in Table 6 are calculated using sample means of all variables other than COD and parameter estimates from Table 2. The COD values chosen are the quintile values from the sample data. Another way of considering the magnitude of the economies of scale is to calculate the effect on total cost from consolidating all of the assessing offices that have output volumes less than the sample median. To perform this calculation, we took the 68 counties with parcels less than the sample median. We then determined the total number of properties in these 68 smaller counties and divided this total by the median number of parcels. The result of this division is the number of assessing jurisdictions necessary to assess all of the parcels in these counties. We found that 39 offices, each assessing the median number of parcels, could cover the parcels currently being assessed by 68 offices. Using our estimated cost function from Table 2, we calculated the cost of assessing the median number of parcels, using the means of the other independent variable calculated only over the subsample of smaller counties. (The value of SQMI was calculated as the total area of the 68 offices divided by the 39 offices.) Our estimated cost of assessing all of these parcels is $5.82 million. The actual reported cost of assessing property in the 68 smaller counties is $7.4 million. Thus, the consolidation of the smaller counties would result in an estimated reduction in the costs of assessment of just over 20 percent. Consolidating assessment districts increases the output volume but also increases the area of the districts. Holding area constant, the consolidation would have reduced total cost by about 40 percent. Thus, half the gain from consolidating output volume is eliminated by the increase in the average area of the assessing district. Of course, these computations represent the maximum possible cost reduction for several reasons. Most importantly, we have assumed that consolidations were possible with no regard to geographical constraints. It is highly likely that a reasonable consolidation of property tax assessment offices would result in more offices than the 39 that we find necessary. Another important assumption in our calculation is the use of average values for the right-hand-side variables based on the subsample of 68 counties. Using the actual values for these variables for the combined offices may increase the predicted costs. We also considered the effect on cost from consolidating four small counties. 9 The actual cost per parcel for the four counties is $8.32, while the weighted average cost (nonconsolidated) predicted by our regression equations is $7.98. The predicted average costs for the consolidated office is $1.73. Consolidation would result in substantial savings. Two types of statistical evidence presented above suggested that it is appropriate to combine the different property types into a single aggregate measure of output. First, the test results reported in the Appendix indicated that we cannot reject the necessary conditions for a consistent aggregate output. Second, the estimated impact of the property mix variable, NRES, included in the single output cost function is very close to zero and is not statistically significant. Despite these 9 The counties and number of parcels are Dougherty (59,120), Lee (10,409), Mitchell (15,476), and Sumter (19,939). 216

11 Economies of Scale in Property Tax Assessment results, it is difficult to accept, given our priors, that the costs of assessing residential property are not substantially different from assessing commercial, industrial, and agricultural property. In order to explore this issue even more thoroughly, we also estimated a twooutput translog model that distinguishes between residential and nonresidential property using property counts (TNUM) as the output volume measures. The computed elasticities with respect to the environmental variables are nearly identical to the same measures for the single product translog using counts as the output measure (Table 4). Because the results are similar, we do not report the results of the two-output model. It is interesting to note that the value of the maximized log-likelihood function for the two-output model is 72.05, which is also very close to the single output value of (This suggests that the generalization of the model to two outputs adds very little to the results.) We also computed both the overall measure of economies of scale and the measure of economies of scope from these multiproduct model estimates. Using the basic results from Baumol, Panzar, and Willig (1988), we find that there are increasing returns to scale overall. Our value of for the elasticity of TCOST with respect to q for the two-output model is very close to the value for the singleoutput model using property counts. Economies of scope, defined as: 2 C q 1 q 2 measure the impact of changing one output on the marginal costs of producing another product. If this expression is negative, then the multiproduct production technology is less costly than single output production. The point estimate of scope economies for this model is positive, but the standard error is so large that no conclusion can be drawn. 217 CONCLUSIONS We have explored the existence of economies of scale in the assessment of property for property tax purposes. Using data from 138 county-level assessment offices in the state of Georgia, we estimated translog cost models using, alternatively, a single aggregate category of property and two categories of property. We estimated the model for both the number of parcels and the value of property assessed. These results are, to the best of our knowledge, the first to estimate economies of scale in assessing property. We find substantial economies of scale; at mean values of the variables, the elasticity of total cost with respect to the number of parcels is We estimate that consolidation of smaller assessment offices would reduce total costs in those offices by about 20 percent. Increasing the quality of assessment by ten percent increases the cost of assessment 1.5 percent. Our results are robust across models. The results suggest that states should consider allowing consolidation of small assessment offices. However, our results also suggest that beyond 100,000 parcels, the economies of scale have been pretty well exhausted. For point of reference, in Georgia, the ten counties that contain more than 100,000 parcels have populations from 150,000 to more than 500,000. Thus, while our results suggest that consolidating assessment offices could result in substantial savings in Georgia and other states with similar size districts, the same would not be true in states with large assessment districts. While the empirical results appear strong, they are the first such results. Thus, it would be desirable to estimate cost functions using data from other states. Likewise, data sets that allowed greater degrees of freedom, that allowed for variations in the price of capital, and that had more information on the wages of different types of employees would be desirable.

12 Acknowledgments The authors acknowledge assistance with the survey by Larry Griggers; the technical assistance of Edith Cash; and the helpful comments of Chris Bollinger, Loretta Mester, and three anonymous referees. The support of the Research Committee of the College of Business Administration is also acknowledged. REFERENCES Advisory Commission on Intergovernmental Relations. Local Revenue Diversification: Income, Sales Taxes and User Charges. Washington D.C.: ACIR, Ahlbrandt, Jr., Roger S. Efficiency in the Provision of Fire Services. Public Choice 16 (Fall, 1973): Baumol, William, John C. Panzar, and Robert Willig. Contestable Markets and the Theory of Industry Structure, second edition. New York: Harcourt Jovanovich Publishers, Beeson, Patricia E. Amenities and Regional Differences in Returns to Worker Characteristics. Journal of Urban Economies 30 No. 2 (September, 1991): Borland, Melvin, and Steven Lile. The Property Tax Rate and Assessment Uniformity. National Tax Journal 33 No. 1 (March, 1980): Bowman, John H., and William A. Butcher. Institutional Remedies and the Uniform Assessment of Property: An Update and Extension. National Tax Journal 39 No. 2 (June, 1986): Bowman, John H., and John L. Mikesell. Assessment Uniformity: The Standard and Its Attainment. Property Tax Journal 9 (1990): Brown, Bryan W., and Mary Beth Walker. Stochastic Specification in Random Production Models of Cost-Minimizing Firms. 218 NATIONAL TAX JOURNAL Journal of Econometrics 66 No. 1-2 (March/ April, 1995): Callan, Scott J., and Rexford E. Santerre. The Production Characteristics of Local Public Education: A Multiple Product and Input Analysis. Southern Economic Journal 57 No. 2 (October, 1990): Cook, John W. The Administration of the Earned Income Tax. Harrisburg, PA: Commonwealth of Pennsylvania, DeBoer, Larry. Economies of Scale and Input Substitution in Public Libraries. Journal of Urban Economics 32 No. 2 (September, 1992): Deller, Steven C., David L. Chicoine, and Norman Walzer. Economics of Size and Scope in Rural Low- Volume Roads. Review of Economics and Statistics 70 No. 3 (August, 1988): Diewert, William E., and Terrence J. Wales. Flexible Functional Forms and Global Curvature Conditions. Econometrica 55 No. 1 (January, 1987): Duncombe, William, and John Yinger. An Analysis of Returns to Scale in Public Production, with an Application to Fire Protection. Journal of Public Economics 52 No. 1 (August, 1993): Fox, William. Reviewing Economies of Size in Education. Journal of Education Finance 6 (1981): Gerau, Vincent J., and James L. Plourde. The Determinants of Uniform Property Tax Assessment. Assessor s Journal 11 (1976): Gyimah-Brempong, Kwabana. Economies of Scale in Municipal Police Departments: The Case of Florida. Review of Economics and Statistics 69 No. 2 (May, 1987): Hirsch, Werner. Cost Functions of an Urban Government Service: Refuse Collection. Review of Economics and Statistics 47 (1965): Ihlanfeldt, Keith R. Intrametropolitan Variation in Earnings and Labor Market Discrimination: An Econometric Analysis of the Atlanta Labor

13 Economies of Scale in Property Tax Assessment Market. Southern Economic Journal 55 No. 1 (July, 1988): Kim, Moshe. Banking Technology and the Existence of a Consistent Output Aggregate. Journal of Monetary Economics 18 No. 2 (September, 1986): Kitchen, Harry. A Statistical Estimation of an Operating Cost Function for Municipal Refuse Collection. Public Finance Quarterly 4 No. 1 (January, 1976): Netzer, Dick. Economics of the Property Tax. Washington, D.C.: The Brookings Institution, Ohio Municipal League. Statistics on Municipal Income Taxes in Ohio. Columbus: Ohio Municipal League, Schroeder, Larry D., and David L. Sjoquist. An Investigation of the Causes of Variations in Property Tax Assessments. Assessors Journal 11 (1976): Sherwood-Call, Carolyn. The Labor Tax as an Alternative Revenue Source. In Proceedings of the Seventy-Ninth Annual Conference on Taxation, Washington, D.C.: National Tax Association, Sigafoos, Robert Alan. The Municipal Income Tax: Its History and Problems. Chicago: Public Administration Service, Urban Study Institute. Adjusting State Education Funding for Geographic Cost Differences. Atlanta: Urban Study Institute, Inc., Wallace, Sally. The Effects of State Personal Income Tax Differentials on Wages. Regional Science and Urban Economics 23 No. 5 (November, 1993): Walzer, Norman. Economies of Scale and Municipal Police Services: The Illinois Experience. Review of Economics and Statistics 54 No. 4 (November, 1972): Wicks, John H., and Michael N. Killworth. Administrative and Compliance Costs of State and Local Taxes. National Tax Journal 20 No. 3 (September, 1967): Appendix The multi-product translog function is written as: [A.1] ln C = α 0 + α 1 ln p 1 + α s ln s + α ln q q + α ln E + 0.5δ ln (p 1 1 ) δ 2 ln (s) 2 E + δ 3 ln (s) ln(p 1 ) ln (q) B q ln (q) ln (E) Γ ln (E) + ln (q) λ q ln p 1 + ln (E) λ P ln p 1 + ln (E) λ s ln s + errors. λ P λ s The parameters to be estimated include the scalars α 0, α 1, α s, δ 1, δ 2, and δ 3 the m 1 vector α q, the g 1 vector α E (where g is the number of included environmental variables), the m m matrix B q, the g g matrix Γ, the m 1 vector λ q, and the g 1 vectors λ P and λ s. The parameters to capture possible interactions between quality of output, environmental variables, and outputs were restricted to zero due to the limited observations available. The restrictions implied by cost minimization reduce the number of parameters somewhat. In our case, with a single variable input, we cannot directly impose the restrictions of symmetry and linear homogeneity in factor prices. These restrictions require that the parameters on input prices sum to zero and that the parameter matrix of interaction effects between input prices be symmetric. Because the price of capital by assumption does not vary over the observations in our sample, its price and coefficients are subsumed into the model s constant term and the coefficient on the price of labor. To ensure that the quality of output and environmental factors do not violate the properties implied by the assumption of cost minimization, we must use additional parameter restrictions. For equation A.1, we must restrict g Σ k=1 λ kp + δ 3 = 0. The matrix Γ must be restricted to be symmetric in order to achieve identification. To determine whether a simpler version of the model can be used, our first task is to

14 NATIONAL TAX JOURNAL estimate the cost of equation A.1 to see whether these conditions are supported by this data set. Because the cost equation A.1 already sets the interactions between the output vector and the vector of environmental variables to zero, the sufficient conditions are simply λ q = 0. Using a likelihood ratio test, the data reject these restrictions with a test statistic value of (the five percent critical value for three degrees of freedom is 7.81). The necessary conditions, however, are not rejected. For this model, the null hypothesis for the necessary conditions is: H 0 : α 4 = ( α 1 α 2 α 3 ) λ q2 = λ q1. (α 2 / α 1 ) λ q3 = λ q1. (α 3 / α 1 ). Testing this against the alternative that at least one of the equalities does not hold, we find no statistical evidence against combining the output measures. The likelihood ratio test statistic, again with three degrees of freedom, is This result implies that it is appropriate to combine the volume output categories and treat all categories of property as an aggregate. 220