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The Competitive Structure of Urban School Districts in the United States

Sarah Battersby Department of Geography University of California, Santa Barbara, CA 93106

batts@geog.ucsb.edu

William A. Fischel (corresponding author)

Department of Economics Dartmouth College Hanover, NH 03755

bill.fischel@dartmouth.edu (603) 646-2940

Draft of September 2006.

§ Introduction and Overview

The Tiebout (1956) model assumes that households choose their community of residence in part by the quality of its public schools. For the model to operate efficiently, school districts should be numerous. In 1916, there were over 200,000 public school districts in the United States. By 2005, there were fewer than 15,000. Most observers regard this decline as evidence of diminished relevance of the Tiebout model (Kenny and Schmidt 1994). However, almost all of the reduction in school districts came from the consolidation of tiny, one-room-school districts in rural areas. The consolidation of school districts in the urbanized parts of metropolitan areas was only a small part of the decline. There are, however, real differences in the market-structure of school districts among regions of the country. This study offers a new measure of this structure.

Most studies of school district competitiveness focus on Metropolitan Statistical Areas (MSAs), which outside of New England include entire counties. The problem is that much of the land area of these counties is rural, so a count of MSA school districts includes many essentially rural districts whose enrollments are small but whose land area is large. We avoid this overcount by measuring school districts only within Urbanized Areas (UAs), whose geographic extent is determined by the density of population, not political boundaries. With this focus we can calculate the school district competitiveness of larger Urbanized Areas for the entire nation. Our primary measure of competitiveness is the fraction of UA land area that is occupied by the four largest districts. This gives us a measure of the district choices available to Tiebout-shoppers in the places where most people live.

Our chief finding is that a majority of the American urban population can choose among at least four school districts. Tiebout choice is a realistic option for most Americans. However, there is extraordinary variation in the extent of this choice. The most competitive regions are large Urbanized Areas in the Northeast and North-Central United States. They offer scores of realistic choices for mobile families. Smaller UAs are somewhat less competitive in this respect, but the most dramatic variation is by region. The South and the arid West have much less Tiebout choice. Both can be accounted for by scale economies of the past. In the arid West, rural densities were low, which necessitated larger areas to achieve graded schools. In the South, segregated schools were a diseconomy of scale that also required larger districts to achieve graded schools for whites and, later on, for blacks. These arguably oversize school districts persist because of the political and legal difficulties in breaking up school districts.

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§1. The Decline in School Districts Was Mostly Rural

The size of school districts in nineteenth-century America was determined primarily by the distance a child could be expected to walk. (Sources describing nineteenth-century districts are Fuller (1982: chap. 3) and Cuban (1984).) One-way walks of two miles were considered the acceptable maximum, so districts averaged about ten square miles. (A circle of radius 2 miles is 12.56 square miles, and geographic irregularities would round this down to about 10.) It is actually possible to get an approximation of the maximum number of rural school districts in the U.S. from this. If one assumes that about two-thirds of the area of the present 48 states was arable (and thus be subject to a rural school district), the total area would about to about 2 million square miles. Dividing this by 10 gives 200,000 school districts, which is close to the estimated number of school districts in 1900. (Accurate counts of school districts were difficult to come by because of their formerly fluid boundaries.)

Figure 1 on the following page illustrates the main cause of the decline in school districts in the twentieth century: the closing of the one-room school and transportation of rural students to consolidated districts. In 1938, there were about 120,000 school districts and about 120,000 one-room schools (these are more technically referred to as “one-teacher” schools, since they sometimes had more than a single room, but we will use the traditional term.) Such schools accounted for about 15 percent of elementary school enrollments (assuming 25 students per class in one-room schools at the time.) By 1972, there were essentially no one-room schools left, and the decline in the number of districts has likewise nearly ceased.

Almost all one-room schools were originally the only school in their district. The one-room school’s demise by consolidation is often lamented as being the product of coercion from state bureaucrats (Fuller 1982), but in fact most of these consolidations were voted upon by the residents of the district (Able 1923; Link 1986, p. 143). In this sense they were politically consensual. This does not mean personally consensual, since most votes required only a simple majority, though in most cases each district had to vote in favor for a consolidation to take place. But as corporate entities, the consolidation of school districts was no less voluntary than the consolidation of department stores, farms, or railroads.

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Figure 1 (Source: Nora Gordon 2002)

The reason that rural voters accepted consolidation was the now-unappreciated change in the

technology of education. Up to about 1900, the rural technology of education is almost perfectly illustrated by Figure 2. It shows how a one-room school operated. The four children are doing a “recitation” in a subject that they have been studying. The teacher, if she is good at her craft, is asking them to explain what they have learned, correcting their errors, and elaborating on the text they have studied. If she is less skilled or motivated, she is simply demanding that they recite from memory what they have been assigned to study. In either case, the students depicted in the background are, one hopes, studying the lessons their teacher has previously given them so that they can properly recite when their turn comes.

Note that the children in the foreground recitation group appear to be of different ages. This was common. The one-room school was “ungraded” in the modern sense of segregating children by age in separate classrooms. Age-grading was known and was often practiced in cities, where a sufficiently large number of students of various ages allowed school administrators to divide them into age-specific grades. But the walk-to school in the country did not have sufficient population density to do that. In addition, attendance in rural schools was often irregular, and the term of school itself was often irregular, its length often depending on the fiscal health of its district. The tutorial-recitation method was not fazed by this irregularity. In the picture in Figure 2, note that one child is considerably smaller and probably younger than the others. She is less

1938

1972

Total School Districts One-Room

Schools

1950

1960

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likely precocious than regular in her attendance. The three boys are apparently older. They may have attended school only when farm work was not pressing. They are thus placed in the same recitation group as the younger child, whose cumulative attendance and study of whatever subject they are being quizzed about is about the same as that of the boys.

Figure 2 A Nineteenth-Century One-Room School Recitation Group

from p. 70 of Edward Eggleston, The Circuit Rider (New York: Ford, 1874).

During the period 1870 to 1910, multi-room, age-graded schools gradually replaced the one-

room, ungraded schools. Several factors contributed to this. One was the relative growth of urban populations. Urbanization made age-grading the norm for public education by about 1910, even though the current degree of uniformity was not achieved in most rural schools until about 1940 (Angus et al. 1988). Another factor was the decline in the population-density of children in rural

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areas. This was caused by declining birth rates, economies of scale in farming that led to larger farm size, and in areas with marginal farming conditions, absolute declines in rural population.

These trends meant that the one-room rural school was becoming both excessively costly to operate and systematically obsolete. As rural enrollments declined, the one-room school could not lay off teachers, since a school had to have at least one. Thus there were still 50,000 one-room school districts in 1952, constituting more than two-thirds of all districts, but they enrolled less than five percent of public elementary school students. But even if the one-room schools struggled along for a while after 1910, their method of education was no longer the norm of the nation at large. This nonconformity made it unattractive to newcomers and burdensome for students who left for districts that were graded.

When all the nation was one-room schools, it did not matter much how good or what subjects were taught in a newcomer’s previous school. He simply brought his textbooks and showed the teacher how far he had gotten in various subjects. She would then place him in an appropriate recitation group, whose other students might be older or younger but had gone about as far in the textbook of that particular subject. In other words, the new student did not have to fit into any particular grade, and his arrival a month after the (typical) four-month term had a begun was not a matter of great inconvenience to the teacher or other students.

In a system where age-grading was the norm, however, all this irregularity was costly. A student coming from an ungraded school to a graded school might have mastered the equivalent of fifth grade reading, third-grade history, and fourth grade arithmetic. She would make a poor fit into a fully graded classroom. Just as importantly, a student moving from a graded school to an ungraded school would likely hurt her chances to go to high-school, which was becoming a national norm by the early twentieth century. High schools demanded that all students know more-or-less the same material upon entry, and ungraded one-room schools were highly variable in the subjects that teachers were able to teach.

Thus the decline in the number of school districts in Figure 1 implicitly tracks the realization by rural voters that their schools were becoming obsolete. This did not mean the education they got there was bad. In many ways it was a more humane way to learn, allowing students to progress at different rates in various subjects and tolerating the farm-family’s demand on children’s time far better than the graded schools could. Absent or slow students were never held back a grade, since there were none to be held back from. The ungraded rural school was like a well-functioning manual typewriter is today. For its owner, it may work as well as a word processing computer and be less aggravating when the power fails or the network goes down. But a typewriter does not fit easily into the system of electronic transmission of words, and so almost every user must switch to the computer-based system if she is to be able to function as a writer with a large, twenty-first century audience.

The reason for the digression into the technology of education and the politics of school consolidation is to set up the explanation for variations in the current size of school districts. Once a standard education became a systematic progression of children from grades 1 through 8 and eventually through grade 12, it became apparent that there were economies of scale in school districts. Under the old one-room technology, there was little reason for a school district to be very large. If population in a rural area grew so that another school was desirable, what normally happened was that a new district was established to govern the new school. Only if population growth were so large and compact that multiple grades could be formed would anything occur besides this amoeba-like division of districts and one-room schools. But after graded schools

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became the norm, and after road and vehicle improvements made transportation of students economically feasible (Ellsworth 1956), the optimal size of a school district radically changed.

As it became feasible to move children from farms to schools by horse-drawn wagons and later by motorized vehicles, the optimal rural school became a multiroom structure that served a larger area. Even if average class size was not changed, an eight-room graded school would now serve an area formerly served by eight one-room schools and (usually) eight independent districts. As high schools became the norm for education, the optimal district size was further enlarged, though many states initially established independent high-school districts into which a group of elementary districts funneled their graduates. Even in this latter case, though, it became important to coordinate the curriculum of the elementary districts so that their students would arrive in ninth grade with the same expected level and type of knowledge. This coordination required more supervision by nonteaching administrators, and this also became a scale economy that could be achieved by consolidation.

The contemporary economic and geographic prediction that this process should yield is that the land area of school districts should be smaller in rural areas with high population density. This will turn out to be a necessary but not sufficient condition for our explanation of why year-2000 Urbanized Areas with better growing conditions (as measured by average annual rainfall) should have more districts than urbanized areas with less favorable farming conditions. The other conditions that will be emphasized is the voluntary nature of consolidation and the near-impossibility of splitting up graded school districts once they have formed. Before getting to that, however, we have to develop a measure of urban school-district size and density that is consistent across the nation. America is no longer a rural nation, but its school districts are today the product of an educational transformation — the displacement of one-room schools by graded schools — that occurred in the early twentieth century.

§2. Measuring the Structure of School Districts in Urbanized Areas.

Until 1990, no national source produced comprehensive maps of school districts in all states. This made it difficult to provide geographic measures of the structure of school districts across states. Researchers in the Tiebout (1956) tradition who have been concerned with school district competition have invariably developed their own measures. Almost all of these measures have used the number of districts within a county or a Metropolitan Statistical Area (MSA or Consolidated MSA) as the unit of analysis (e.g., Alesina, Baqir, and Hoxby 2004). Counties are extremely useful in this regard because the entire country is blanketed by counties. There are no “dead spots” that are not subject to county government or the “county-equivalents” such as Louisiana Parishes, Alaska Boroughs, and Independent Cities of Virginia and a few other states. For comprehensiveness, counties are good.

Counties are less good for measuring school-district competitiveness because the urban population in almost all MSA counties occupies only a small fraction of the land area of the county. Nationwide, MSA and CMSA counties occupied about 24 percent of the 48-states’ land area, while the built-up Urbanized Areas within these MSAs occupied only about 2.4 percent of the 48-states’ territory. Since the vast majority of the population (about 80 percent) of MSAs is within their UAs, it follows that the population density of non-UA parts of MSAs is not much greater than most rural (non MSA) counties.

It is important to establish a consistent land-area base for comparing school districts because school district competition is largely spatial. This is because most parents want their children to

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live at home while they attend elementary and high school. Public schools no longer have to be within walking distance of homes because of the ubiquitous yellow school bus, but parents and children regard the time riding school buses as a cost. Long bus rides are also costly to the taxpayers and, for the most part, they do not offer useful time for school work or recreation for children.

It is important, however, not to conflate schools with school districts. Most urban school districts have numerous schools. As noted at the end of the last section, there are undoubtedly some degree of administrative scale economies in school districts. Multi-school districts can spread the costs of administration over more schools and taxpayers. The literature on district scale economies is not clear about the point at which scale economies cease. Most of the evidence comes from examining the consolidation of very small districts, and such evidence as there is about larger districts does not point to dramatic cost-saving from further consolidation.

The limiting factor on school district scale, however, is not administrative cost but political governance. Very large school districts are governed without much input from the voters, and research has suggested that very large districts respond more to teacher unions than to parental and voter concerns (Romer, Rosenthal, and Munley 1992; Rose and Sonstelie 2004). Voters are probably aware of this, and if they are not, there is ample opportunity for them to learn it during the special election that must precede most school district consolidations. Voter reluctance to consolidate districts most likely stems from their view that consolidation will reduce their role in governance, which would not offset the possible gains in scale economies of administration.

All of this is to argue that urban school districts will usually have more schools and more pupils than modern rural districts. Because of higher population density, the urban district can locate its schools closer to its students and also achieve administrative scale economies. Hence we would expect urban school districts to be smaller in land area than rural school districts. They can achieve the desired scale economies (balanced against governance diseconomies) over a smaller land area.

The smaller land area of urban school districts provides more districts for homebuyers to choose among. For any given job location in an Urbanized Area, there are usually several school districts within reasonable commuting distance. However, the rural parts of the MSA county are not realistic choices for most urban households. Hence we want a count of the choices of school districts that are located within Urbanized Areas, where most people live.

The basic statistic that we develop to do this is the percent of UA land area occupied by the largest school districts. (This method is the same that Fischel [1981] used to measure municipal competition.) This statistic is illustrated in Figure 3 below. There are three school districts, A, B, and C. The Urbanized Area is the heavy-lined rectangle, and the area of the UA is 10 square miles. The L-shaped District A occupies 5 square miles within the UA, so its contribution to the concentration ratio is 50 percent. The large square-shaped district B occupies 3 square miles, or 30 percent of the UA, and the smallest district, C, occupies 20 percent of the 10 square miles of the Urbanized Area.

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Figure 3 Schematic for Urbanized Area district concentration ratios, where the UA is bounded by the

heavy line. Numbers are square miles.

District C District B District A

2 of Dist. C

3 of Dist. B

5 of Dist. A

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To illustrate the process further, the calculations are applied to the Urbanized Area Portland,

Oregon, in the year 2000, in Table 1. (Portland is rank 28 in table 1.) The largest district in the UA is the central-city district, Portland. It occupies 18 percent of the UA. Only about half of the Portland School District is within the UA. Many “urban” districts include some rural (not-in-UA) area. The lightly-populated rural area of Portland School District 1J would not be counted in the 18 percent calculation. The second largest district within the UA is Beaverton, which occupies 11 percent of the Portland Urbanized Area. The third largest land area within the Portland UA is that of Vancouver, Washington, with 8 percent of the area. (Urbanized Areas can cross state lines, just as MSA boundaries do.)

The general measure of “competitiveness” that is adopted here is the “four-district concentration ratio.” This is the sum of the percentages within the UA of the four largest districts. For Portland, the four-district concentration ratio is 45 percent, which is about in the middle of the range of concentration ratios of the Urbanized Areas with populations over one million. The other 55 percent of the Portland UA is occupied by 24 other school districts or parts of those districts. Table 1: Four Largest School Districts within Portland, Oregon, Urbanized Area, and the percentage of the UA land area they occupy.

PORTLAND [OR] SCHOOL DIST. 1J 18% BEAVERTON SCHOOL DIST. 48J 11% VANCOUVER [WA] 8% NORTH CLACKAMAS SCHOOL DIST. 012 8% Four-District Concentration Ratio 45%

The number four is not by itself important as the sum of concentration ratios, but it is useful

for two reasons. One is that the four-firm concentration ratio is a common measure for industry concentration. Industries are not usually measured for spatial concentration (though the unit of space within which to count them can be critical), but there is a common norm among economists that a four-firm ratio of less than 40 percent is reasonably competitive, and above 80 percent is not competitive. The other use of the four-district ratio is that some previous studies suggest that the benefits of interdistrict competition kick in at four districts (Blair and Staley 1995; Zanzig 1997). Thus knowing something about the four largest districts gives some parameters for judging the competitiveness of school districts in an Urbanized Area and offers a reasonable basis for national comparisons. The relatively intuitive interpretation of the four-district concentration ratio is why we prefer the four-district ratio to the more sophisticated Herfindahl index of competition.

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§3. The Competitive Structure of Larger Urbanized Areas. The data presented in Table 2 are measures of the competitiveness of local school districts in

the U.S. Urbanized Areas that had a population of at least 500,000 in the 2000 Census. The seventy Urbanized Areas within this category are sorted by their 4-district concentration ratios, with the lowest concentration (most competitive structure) at the top. The first numerical column is the total number of school districts of any size that are within the Urbanized Area. Because school districts are listed as consisting of three types—elementary (typically Kindergarten through grade 8), high school (grades 9-12), and unified (K-12)—it is necessary to weight the various districts. The weighting we use is based simply on years of attendance, assuming kindergarten is counted as half a year. Thus a high school district is weighted is 4/12.5 (=32%) of a unified district, and elementary districts are weighted as 8.5/12.5 (=68%) of a unified district. In most places, one or more elementary schools feed into a single high-school district. Thus if there are two elementary districts that feed into one high school district, the combined elementary and high school districts count for 2 x 68% + 1 x 32% = 1.68 unified district rather than three districts. If Urbanized Area J has 10 unified districts and Urbanized Area K has 5 high school and 15 elementary school district, K is considered to be 18 percent more competitive, as its weighted unified-equivalent number of districts is 11.8. Just counting all districts would exaggerate the competitiveness of Urbanized Area K, which without the weighting would seem to have fifty percent more districts (15 instead of 11.8) than Urbanized Area J, which has 10 unified districts.

The second numerical column of Table 2 gives the four-district concentration ratio of the Urbanized Area, based on the weighted district counts and using the method described in the previous paragraphs. Thus the New York UA (ranked 2nd on the list) has a four-district concentration ratio of 13 percent, while the ratio of Los Angeles (ranked 24th) is 40.4 percent, indicating by our measure that Los Angeles has a less competitive structure than that of New York.

Two additional measures of competitiveness are in the next two columns. The third column shows the percent of the UA land area occupied by the largest single district, which is usually the central-city school district. This could be called the “one-district concentration ratio.” It is given because sometimes the largest district is much larger than the next three (as is the case in Los Angeles) and thus might be expected to exert even more monopoly power. (The Herfindahl Index, which squares the market share of each firm, incorporate this information.) The last column, “kids/district” is the UA population of children between ages 5 and 18 divided by the number of (weighted) districts. This gives a measure of the average district size according to potential student enrollment, though it must be kept in mind that children outside of the UA are not counted in any of these data.

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Table 2: Measures of School District Competition for the Seventy Largest Urbanized Areas (Bold denotes UAs in the South; italics denotes arid [<20 inches precipitation/year].)

UA (4-dist ratio rank #) Districts(wtd) 4-dist ratio 1-dist ratio kids/district

Boston, MA (1) 157.7 8.50% 2.70% 4,290 New York, NY (2) 417.9 13.00% 7.10% 7,575 Pittsburgh, PA (3) 86 17.10% 6.40% 3,366

Chicago, IL (4) 198.2 19.40% 10.60% 8,133 Philadelphia, PA (5) 152.7 19.70% 7.50% 6,632 Providence, RI (6) 49 22.30% 7.10% 4,206 Hartford, CT (7) 47.4 22.70% 5.90% 3,235 Detroit, MI (8) 85 23.00% 10.90% 8,898

Cleveland, OH (9) 58 25.40% 12.10% 5,732 Bridgeport, CT (10) 35.4 26.10% 7.30% 4,536 St. Louis, MO (11) 62.2 26.50% 7.40% 6,502 Seattle, WA (12) 37 27.00% 8.80% 12,856

Minneapolis, MN (13) 45 28.80% 11.70% 10,057 Buffalo, NY (14) 30 31.10% 11.20% 5,891

Springfield, MA (15) 34.4 32.30% 10.50% 3,091 Cincinnati, OH (16) 55 33.90% 13.10% 5,282 New Haven, CT (17) 28.7 34.70% 9.80% 3,255 Indianapolis, IN (18) 33 35.40% 14.20% 7,068

Albany, NY (19) 32 36.20% 12.00% 3,003 Akron, OH (20) 30 38.00% 17.40% 3,396

Allentown, PA (21) 30.1 38.50% 11.50% 3,415 Dayton, OH (22) 28 39.00% 14.30% 4,577

Milwaukee, WI (23) 40.4 40.20% 19.30% 6,269 Los Angeles, CA (24) 91 40.40% 30.10% 26,026

Dallas, TX (25) 48 41.30% 18.10% 17,196 Kansas City, MO (26) 27 41.90% 12.80% 9,562

Rochester, NY (27) 24 42.50% 12.00% 5,510 Portland, OR (28) 31 44.80% 18.00% 9,140 Houston, TX (29) 32 46.10% 22.00% 25,058

Grand Rapids, MI (30) 23 46.50% 16.30% 4,699 Riverside, CA (31) 20.4 46.70% 15.80% 18,254

San Francisco, CA (32) 35.2 48.20% 14.90% 13,177 Phoenix, AZ (33) 30.9 48.80% 17.00% 17,811 Atlanta, GA (34) 23 54.00% 16.10% 28,961

Columbus, OH (35) 23 54.00% 29.90% 8,966

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Urbanized Area (rank) Districts(wtd) 4-dist ratio 1-dist ratio kids/district McAllen, TX (36) 15 55.50% 19.00% 8,671 Toledo, OH (37) 16 60.20% 29.50% 6,135

Sacramento, CA (38) 21.5 60.50% 20.60% 13,224 Virginia Beach, VA (39) 12 63.10% 27.00% 22,524

San Diego, CA (40) 23.6 64.90% 22.40% 21,110 San Jose, CA (41) 23.6 66.80% 29.20% 11,443

Oklahoma City, OK (42) 15 68.80% 29.80% 9,309 Denver, CO (43) 14 69.80% 30.10% 26,247 Omaha, NE (44) 12 74.50% 43.90% 10,282

San Antonio, TX (45) 18 76.00% 26.00% 15,099 Tulsa, OK (46) 12 77.10% 39.80% 8,742

Washington, DC (47) 16 80.60% 28.50% 43,835 Austin, TX (48) 11 85.20% 48.50% 14,182

Birmingham, AL (49) 11 85.30% 38.70% 11,076 Richmond, VA (50) 10 86.50% 36.20% 15,266

Tucson, AZ (51) 9 87.10% 52.70% 14,436 El Paso, TX (52) 9 87.90% 42.30% 17,493

Louisville, KY (53) 9 90.00% 65.80% 17,069 Concord, CA (54) 12.7 90.40% 29.00% 7,837

Nashville, TN (55) 7 92.70% 63.30% 18,139 Baltimore, MD (56) 7 96.90% 38.20% 54,128

Fresno, CA (57) 9.7 96.90% 53.60% 13,396 Memphis, TN (58) 7 98.40% 54.30% 28,751

New Orleans, LA (59) 5 98.60% 50.00% 38,898 Charlotte, NC (60) 7 99.40% 80.60% 19,576

Mission Viejo, CA (61) 6 99.90% 62.70% 16,504 Miami, FL (62) 4 100.00% 33.60% 212,883

Sarasota, FL (63) 4 100.00% 48.40% 18,281 Tampa, FL (64) 3 100.00% 52.50% 111,666

Salt Lake City, UT (65) 4 100.00% 49.80% 47,838 Orlando, FL (66) 3 100.00% 66.80% 71,458

Jacksonville, FL (67) 3 100.00% 80.90% 56,985 Albuquerque, NM (68) 4 100.00% 84.40% 27,880

Raleigh, NC (69) 4 100.00% 99.80% 23,854 Las Vegas, NV (70) 1 100.00% 100.00% 238,408

(Bold denotes UAs in the South; italics denotes arid [<20 inches precipitation/year].)

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§4. Racial Segregation and Arid Climates Made for Larger School Districts The names of the Urbanized Areas in Table 2 are coded to reveal two geographic regularities.

The UAs in bold type are in the South. This includes the states that joined the Confederacy in the Civil War plus Delaware, Maryland, Kentucky, and Oklahoma. All of these states at one time practiced racial segregation in schooling, and in all of them blacks were a large enough group for segregation to affect the structure of school districts. Segregation was practiced in other states by local option. The states the South all had statewide segregated schools at least up to the 1930s.

The reason for the South’s unusually large districts (often entire counties) is that operating two separate school systems over the same geographic area lost important economies of scale (Harlan 1958, p. 15; Bond 1934, p. 231; Margo 1990, p.22). A district of 36 square miles with 2000 students who were integrated by race could typically have three elementary schools and one high school. But if half of these students were black and half were white and they were to be segregated in separate schools, the number of elementary and high schools would double. So would the number of principals and bus routes and, in states that segregated textbooks (sic!), the number of textbook storage facilities.

The legacy of segregation thus left the Urbanized Areas in the South with large-area school districts. One might ask why the South has not broken up the school districts since desegregation began in earnest in the 1960s. One reason is that it is difficult to break up any school district or any other geographically-defined political entity. Most school district consolidations were consented to by the voters in the areas affected (Barron 1997, pp. 47-67). The same laws normally require that voters in the proposed districts must approve break-ups, and mutual approval is rare. The other reason is particular to the South, most of which is subject to the Voting Rights Act of 1965. Reorganizations of any political body require the approval of the U.S. Justice Department, and it has steadfastly refused to accommodate school-district reorganizations that have even a possibility of increasing racial segregation (Motomura 1983).

The other cause of variation in school-district size is associated with rainfall. In arid areas, the density of rural populations is low. In high-rainfall areas (typically but not exclusively in the North and South), farmers could have relatively small farms and still make a living. In arid areas (mostly in the West), farming or, more typically, ranching required a larger land area for a family to make a living. When cities in the arid West began to grow outward, the rural districts that they incorporated were relatively large, simply because a larger area had been required to collect enough students to run rural, age-graded schools. Since it was rare to break up an existing district, the land-area of the now-suburban district remained large even as the population density rose.

Besides this, many cities at the beginning of the twentieth century ran their schools, as opposed to having the now-common “independent school district.” As cities expanded, they also took their school districts with them, which accounts of the large size of central-city school districts in the North (e.g., New York, Chicago, Philadelphia, Detroit, and Cleveland). In the arid West, early-twentieth-century cities were able to expand their boundaries over a wider area because they had a monopoly over water supplies, and so central-city school districts also became larger. It should be noted that “rainfall” is used instead of just “west of the 100th Meridian” because there are some well-watered places in the West such as Seattle (# 12 in Table

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2) and Portland (#28), and these Urbanized Areas do indeed have more school districts than cities of similar size in more arid areas, such as Sacramento (# 38) and Phoenix (#33).

The array of Urbanized Areas in Table 2 strongly suggest that regional variation in school district size is accounted for by two historical factors, climate (which determined rural population densities) and a history of racial segregation. More systematic evidence is presented in Table 3, which summarizes a linear regression using as data the seventy cities in Table 2. The dependent variable is the 4-district concentration ratio. The independent variables are a dummy variable for UAs located in the South, which is positive and clearly statistically significant. (Positive in this case means less competitive structure, since the concentration ratio rises as there are fewer school districts.)

The variable “rainfall” in Table 3 is the average annual precipitation (in inches) in the main city of the Urbanized Area from 1961 to 1990. (Rainfall averages do not change much, so the modern figures are reasonable proxies for earlier times of settlement.) Wetter cities are likely to have had higher rural densities in the early 1900s, when age-graded districts were formed. The higher rural densities were the result of smaller average farm size. In dry areas, grazing and dry farming (wheat) were predominant. The suburbs of dry-area cities were also more likely to have been dependent on central-city water, which would make them more likely to consolidate with the city than remain independent. (Cities once normally controlled their school districts, but such “dependent” districts have become rare since the 1930s [Henry and Kerwin 1938]). “Rainfall” is clearly negative and statistically significant, indicating more school-district competition in wetter areas outside of the South. (The South itself is among the highest rainfall areas in the nation, which supports the idea that racial segregation was the driving force behind larger district size.)

The last variable is simply the number of children between ages 5 and 19 within the Urbanized Area. “UA kids” is negative, indicating the larger UAs are more likely to be more competitive in their school district structure than smaller UAs. It should be noted that the minimum size UA in the sample is half a million people (not just children), so “smaller” is not tiny. It is often noted in the Tiebout literature that smaller cities and rural areas have fewer jurisdictions simply because there are usually some minimum size in area and population for establishing a modern school district. Indeed, many smaller Urbanized Areas have fewer than four districts in total, so that their “four-district ratio” is hardly meaningful. Of the UAs listed in Table 2, only four have fewer than four districts: Las Vegas (1 district), Tampa (3), Orlando (3), and Jacksonville (3). Note also that the bottom of Table 2 lists five UAs that have exactly four districts—all in the South or arid West.

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Table 3: OLS Regression to explain variation in district concentration

Dependent variable is the 4-District Ratio (higher values mean less competition)

Regression Statistics Multiple R 0.769 R Square 0.591 Adjusted R Square 0.572 Standard Error 0.191 Observations 70

Coefficients Standard Error t Stat Intercept 0.8300 0.063540 13.06 South 0.4709 0.054907 8.58 rainfall -0.0096 0.001877 -5.10 UA kids -1.569E-07 4.68E-08 -3.36

The positive effect of total Urbanized Area population (as represented by “UA kids” in Table

3) on competition, independent of climate and segregation, might suggest some limitations on the measure of competition adopted here. One objection might be that it is obvious that a larger Urbanized Area would have more school districts, so that district population should not itself be an independent variable. But other countries often have school administrative units that encompass the entire metropolitan area. As the area expands, the center’s district lines are moved outward. So it is not “obvious” in a technical or comparative sense that larger American Urbanized Areas should necessarily have more districts, and there is actually considerable variation.

A different objection to population size as an explanatory variable relates to commuting distances between home jurisdiction (which is where the school district is defined) and work jurisdiction. The New York UA is the second most competitive in the nation by the metric adopted here, but the area’s immense geographic size—stretching more than 120 miles from eastern Long Island to Pennsylvania—surely limits the choices that any in-moving family would have. Columbus, Ohio, has a 54 percent concentration ratio, but it is arguable that most of its 23 school districts are realistic choices for a family with employment somewhere in Columbus. But this bias is less critical if one keeps in mind that average commuting distance is greater in larger urban areas. Someone with a job in Manhattan and an inclination to live in the suburbs really can choose among a large number of suburban districts on Long Island, Westchester, Connecticut, and New Jersey. The agglomeration economies of larger cities are manifested in the number of school districts as well as in the variety of employment and recreational opportunities.

Table 2 also lists two alternative measures of competition, the percent of land occupied by the largest districts (usually but not always the central city district) and the average district size. The simple correlation between the single-largest and the four-district concentration ratios is .87, which suggests that one could get a pretty good idea of competitiveness just by calculating the

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area of the biggest district in the UA to the total UA. This high correlation also suggests that the more sophisticated measure of competition, the Herfindahl index, would not add much to the 4-district ratio. (The Herfindahl squares the percentage market share of the districts and so would give greater weight to the largest than to the next three districts.)

The other potential measure of concentration, the average population of a district (UA kids/district), does not seem to be a good measure. The simple correlation between kids/district and the 4-district ratio is only .47, which indicates that it would account for less than a quarter of the variation in size between the two measures (.47 squared is .22). This is important for economic research because many if not most empirical studies have used average district size or some variant of it as their measure of competition among school districts. Average district size tends to make smaller UAs appear more competitive. Including UA size as an independent variable along with district size would offset this understatement, but the inclusion of UA size in regressions is often as a control for other economic effects besides school-district competitiveness. It would seem to be more productive to use a measure of competition that is meaningful on its own terms, and the four-district concentration ratio looks most appropriate for that purpose.

§5. The Persistence of Regional Variations in School-District Structure

Table 2 allows some insights into the degree of competition available to the population at large. Within industrial organization, a four-firm concentration ratio of 40 percent or less is usually deemed to be competitive. We can take Table 2 and cumulate the school-age population from the lowest ratio-UA (Boston, rank #1) to that with a 40 percent concentration ratio (Los Angeles, #24). This number is about 13 million, which is about half of the total school-age population of this group of large UAs. (Keep in mind that Table 2 lists all UAs in excess of half a million people in 2000.) In other words, about half of the population living in these moderate-to-large-sized Urbanized Areas has a lot of Tiebout-choice with respect to school districts.

If we turn to the unambiguously concentrated (tending toward monopolistic) structures at the bottom of Table 2, a common cut-off point is a 4-district ratio of 80 percent. This group ranges from Washington, DC’s UA (rank #47, 80.6 percent) to Las Vegas (rank #70, 100 percent.) This monopolistic group contains about 5 million school-age children, which is about 20 percent of the school-age population of this group of UAs. While it can be said that a majority of urban children live in areas in which there is a fair amount of competition among school districts, a nontrivial fraction live in large urban areas where the alternatives to the largest district are quite limited and in one case, Las Vegas, nonexistent.

What is most impressive about Table 2, however, is not absolute levels of competitiveness but the enormous variation by region of the country. Economists expect some regional variation in the structure of industries that provide goods that are not traded among regions. For example, the structure of the homebuilding industry, which has always been competitive, nonetheless displays differences among metropolitan areas. In one recent study, the twenty largest (by most building activity, not most people) housing markets were examined by their five-firm concentration ratio, where the measure was number of building permits. The range of the top twenty markets was 47 percent (Denver) to 12 percent (Atlanta), with the vast majority of those in between being between 20 and 40 percent. In school districts, on the other hand, the range of 4-district ratios is from 8.5 percent (Boston) to 100 percent (Las Vegas and six others). Even if

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one examines those at the (unweighted) interquartile level, the variation is huge: New Haven (rank #17) at 35 percent versus Louisville (#53) at 90 percent.

The other extraordinary fact about regional variations is that they appear to be due to, or at least closely associated with, historical factors from the now-distant past. Legally-enforced racial segregation has long been struck down by the courts, and families have not chosen their home locations on the basis of agricultural factors for an even longer time. Although it is clear that the U.S. Justice Department and the Federal Courts retard breaking up the countywide districts that contribute to much of the South’s high concentration ratios, it is not entirely clear that these districts would become fragmented even if this constraint were removed. Very large districts in the West where racial segregation is much less of a constraint (or impetus) show little sign of breaking up. It cannot be that water is much of a constraint on local government formation anymore, since districts have long since been detached from most large cities, and most suburbs have their own independent sources of water.

Nor is the stasis in district size due to a widespread belief that there are important scale economies that would be lost if the largest districts were broken up. Scale economies are important in consolidating very small (under 3000 students) districts, but they are irrelevant for almost any of the four-largest districts in the Urbanized Areas examined in this study (Andrews, Duncombe, and Yinger 2002). The most interesting question about large school districts is not how they got to their present size, but why these boundaries are so resistant to breaking up to a size that almost all school patrons think is preferable.

§6. Conclusion and Comparison to Hoxby’s Rivers

The primary contribution of this study to the literature on school district competition is to generate a national, urban-centered measure of school district competition. Our measure is based on land area rather than population, but within Urbanized Areas, the two measures should not differ greatly. Urbanized Areas do not include the low-density areas of MSAs (which is our point in using UAs), and the population density of central cities and the close-in suburbs that make up the Urbanized Area has almost converged by the 2000 Census for all but the largest cities. We have made no effort to determine the effects of school-district competitiveness on student achievement. Our empirical contribution to the substantive issues has only been to show that there is (a) a lot of competition among public school districts in many large urbanized areas and (b) a great deal of variation in competition among regions of the country.

It would seem logical to compare our measure with those of others who have used a competition variable. These comparisons would not reveal much of interest, however, because other studies have usually looked at small as well as large urban areas (usually MSAs but sometimes counties), confined themselves to particular states or regions, or imposed other constraints on the scope of their data (e.g., examined only unified districts). Our effort is not to discredit any particular study. We only point out that competition is most relevant in Urbanized Areas rather than all parts of MSAs, and that a simple measure borrowed from industrial organization, the four-firm concentration ratio, offers a useful alternative to simply counting all school districts without regard to size or location within the MSA.

Our explanation for the substantial regional variations in district competition have to do with farming conditions and racial segregation, both of which were influential when urban and suburban districts were established. History seems to matter a great deal. The durability of formative patterns from the early to mid twentieth century reflects the fact that it is difficult to

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break up existing school districts. School district consolidation is a one way street. We do not know whether this is because of population and technological trends favoring larger districts or, as we suspect, because of the political and social difficulties of agreeing to split up.

We close with a brief note about a well-know measure for competition among school districts that was developed first by Hoxby (2000) and later incorporated into several other papers. To avoid the econometric biases created by simply counting the number and size of school districts to measure competition, Hoxby created an indirect (“instrumental variable”) measure of competitiveness. Her story is that districts in urban areas are influenced by a pre-existing geography. Cities that were riven by numerous rivers and streams and other physical barriers (though in practice streams were the important one) would be likely to have more school districts.

The reason is that streams are costly to bridge, so that using them as boundaries for school districts that had to transport children to a few schools would minimize transportation costs. An Oklahoma historian (Davison 1949) described how one newly-formed county in his state first established its school districts (circa 1900). The county superintendent “drew an imaginary line in any direction which presented the least resistance. If he found the line tending to cross an unabridged stream, he drew it in and started downstream. That was cheaper than building a bridge and safer than swimming school children across swollen streams in time of high water.” (The “swimming” was not facetious; it referred to how horse-drawn school wagons—the predecessors of school buses—forded streams in high water. By an “imaginary” line he meant a line on a map rather than markers on the land itself.)

Our account of school-district variation outside the South is related to Hoxby’s, though we did not contemplate this relationship until Jon Sonstelie pointed it out to us when we informally told him of our results. We emphasize the pre-existing pattern of rural settlement when urban areas were growing and suburbanizing. The rural pattern of the late 1920s is remarkably persistent in the suburban parts of Urbanized Areas, as Alesina, Baqir, and Hoxby (2004) demonstrate with their maps of the Cleveland and Cincinnati areas from that era. Initial residents of newly-built suburbs in the 1920 appear largely to have adopted the pre-existing rural district boundaries as their own and not altered them after the 1920s. In high-rainfall places, this rural pattern had relatively small-area districts because farms could be small and thus population density could be higher than in low-rainfall areas.

But of course high-rainfall areas also have more streams and rivers, which would have formed the logical boundaries for many rural areas. Arid areas have fewer rivers and the “imaginary line” that the Oklahoma official drew could have gone on for a longer distance without hitting a stream. In one sense our explanation is complementary to and thus difficult to distinguish from Hoxby’s. Those who established school district boundaries in well-watered (and well-rivered) areas did not have to include too much territory in order to get an adequate-sized district, so turning the boundary line aside at a natural barrier such as a local stream was a cost-minimizing strategy.

One advantage of our account is that it can explain the countywide districts that characterize much of the South. (Alesina et al do not explicitly exclude the South, but because they focus on district changes within counties, they effectively delete countywide districts. Hoxby does not exclude such districts.) Prior to the 1930s, when the NAACP began winning lawsuits based on inequality of resources for black schools, most Southern states relegated black students in rural areas (where most blacks lived) to ungraded, one-room schools that did not require

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transportation. Age-graded schools for whites were established after 1900 within cities and higher-density county areas, so there were typically numerous districts within Southern counties, just as in the North. In response to the increasingly successful NAACP litigation, Southern states began to consolidate school districts so as to provide blacks with some semblance of equal facilities (Donohue, Heckman, and Todd 2002). Thus most countywide districts in the South were not created until after World War II, though the county had always been an important basis for the distribution of state funds in the South.

The South is a well-watered region with many streams and rivers, so on both of our and Hoxby’s account, the South ought to have competitive districts. Our account, though, offers a economies-of-scale-based reason for the South’s larger districts and less competitive structure. By insisting on racially segregated schools, the South made itself like an arid area. In most of the South, the density of total population was similar to that of the rural North. But the density of the white population, taken by itself, and the black population, taken by itself, made each potential school district more like those of the arid West. (In many rural counties in the South the black population exceeded that of whites in the early twentieth century.) Blacks were not usually geographically segregated from whites in the rural South (they had to work in proximity to one another, and transportation was costly), so school districts that created separate black and white schools had to be much larger.

Thus when a Southern official who drew up school districts ran the “imaginary line” from a central point, and the line ran into a stream, he could not easily stop and follow the “line of least resistance” paralleling the river. If he did, he would not have a population large enough to create a black and a white school district. Once white politicians decided they had to provide graded schools and high schools for both blacks and whites, Southern school districts had to be almost twice as large as their Northern counterparts to operate with the same economies of scale. § References Able, J.F. 1923. Consolidation of Schools and Transportation. Bulletin 41, U.S. Bureau of

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