A Note on Student Academic Performance: In Rural versus Urban Areas
Borland, Melvin V., Howsen, Roy M., The American Journal of Economics and Sociology
There is a considerable body of literature (Broomhall and Johnson, 1994; Broomhall, 1993; DeYoung, 1985) that concludes that rural students perform less well than urban students on standardized tests of educational achievement. One hypothesis for the existence of this condition is that expenditures on education do matter, and they are smaller in rural areas than in urban areas (Mulkey, 1993; McDowell, et al, 1992; Jansen, 1991; Reeder, 1989; and DeYoung, 1985). A second hypothesis for the existence of the difference in educational achievement between rural and urban areas involves the relationships between the values in use of particular inputs and the level of such achievement (Hanushek, 1991). And a third hypothesis is that differences by location in attitudes of individuals, parents, and peers about education exist and result in the observed differences in educational achievement by location (Broomhall and Johnson, 1994; and Hanson and Ginsburg, 1988).
While previous studies have focused on the rural versus urban areas issue, this demarcation may be misleading. The fundamental issue explaining student educational achievement is not the rural versus urban areas issue, but the determination of variables within which differences explain the significant variation in student achievement in any area. Students would be expected to perform similarly, if the associated values of explanatory variables are similar, irrespective of location. If the distributions of values of explanatory variables differ by location, the demarcation simply substitutes for the difference in the distributions of such variables and is of little help in the development of appropriate policy.
The intent of this article is twofold. First, we intend to determine if students from both highly rural and highly urban areas with similar associated explanatory variables perform similarly, but less well, on student achievement tests than students from other areas. Second, we intend to show that studies that analyze student achievement should include measures of both cognitive skills and educational market competition as explanatory variables.
The state of Kentucky provides a unique setting in which to determine the relationship between educational achievement and population density. There are 120 counties within the state in which population density varies from 21 people per square mile (in the Robertson County district) to 7,774 people per square mile (in the Bellevue district in Campbell County). The average population density for the state is 591 people per square mile. Coal mining dominates the eastern part of the state known as the Appalachia area. As well, several counties in western Kentucky are noted for their coal mining. At the other extreme, highly populated areas surround Covington, Lexington, and Louisville. Thus, Kentucky provides an excellent setting in which to determine the effect of population density.
The low population density areas of Kentucky tend to be the coal-producing areas. Kraybill, et al, (1987) and Duncan and Tickameyer (1983) compared values of quality-of-life measures in coal-producing areas of Virginia and Kentucky and found that quality-of-life measures in the coal-producing areas tend to be lower than the quality-of-life measures found elsewhere in these two states. Their quality-of-life variables included income, employment, education, health care, and housing. Thus, the rural areas of Kentucky tend to be less appealing in terms of living habitat.
At the other extreme are the areas of high population density. The values of inner-city quality-of-life measures are low and have been declining over the past several years, as well. Conditions with respect to crime, gangs, and deteriorating structures are considered to have led to these declining quality-of-life measures within the inner cities. These conditions have resulted in what is commonly referred to as "urban flight." Therefore, quality-of-life measures are considered to be low in both highly rural and highly urban areas relative to other areas.
To the extent that quality-of-life measures are low both in highly rural and highly urban areas relative to other areas of the state and that such measures reflect actual perceptions by location, one would expect out-migration of relatively mobile resources from these areas to have occurred. The individuals who are more likely to out-migrate would be those who have greater career opportunities and stronger incentives for higher educational achievement (Broomhall, 1995). Such individuals tend to come from high-level socioeconomic backgrounds that correlate highly with mental abilities (Charters, 1963). Thus, individuals with higher cognitive skills would be expected to have out-migrated from both highly rural and highly urban areas to other areas of the state. This out-migration leaves those areas with resources that are potentially less mobile and individuals who exhibit lower socioeconomic characteristics. These individuals have generally been considered not to place a high regard on education because of their inability to foresee high returns to education within such regions (Broomhall and Johnson, 1994).
The statistical model employed in this article is an extension of a basic statistical model of student performance developed in earlier articles (Hanushek, 1986). Previous results suggest that, in general, three types of variables significantly contribute to student performance: parental variables, school variables, and financial variables. Given the simultaneity of student performance and teacher salary, the system of equations below describes the specific form of the model:
sa = f(csi, col, att, ptr, c, pbl, u, ts, dnsdv) (1)
ts = g(adm, rank, lfi, c, u, sa) (2)
where sa represents student achievement, csi is a measure of cognitive skills, col represents the percentage of students who graduate from high school and go on to college, att represents daily average attendance, ptr represents the pupil-teacher ratio, c is a measure of the degree of educational market competition, pbl is the quotient of the population that is black divided by the total population, u represents the presence of a teachers' union, ts is teacher salary, dnsdv represents the absolute value of the deviation of population density from that value of population density that maximizes the t-value on the estimated coefficient for dnsdv, adm is defined as the quotient of administration cost divided by total expenses, rank is defined as the percentage of teachers within the school district who possess at least a master's degree, and lfi is the quotient of local revenue per child in average daily attendance divided by the assessed property value per child in average daily attendance. All data is for third-grade students throughout the state of Kentucky for the academic year ending in 1990. A total of 170 school districts were employed in the analysis. See the Appendix below for a detailed description of the data.
Within eq. (1), the signs on the coefficients of the csi, col, and art variables are expected to be positive. That is, increases in student cognitive skills along with increases in attendance and increases in the percentage of students who graduate from high school and go on to college, are expected to lead to higher student performance.
The ptr and c variables are expected to have negative influences on student achievement. As the pupil-teacher ratio increases, student achievement scores should be expected to decline to the extent that class size indeed matters. Similarly, as educational competition among the school districts increases, student achievement scores are expected to increase (Borland and Howsen, 1992).
Table 1 Two Stage Least Squares Estimates of the Student Achievement and Teacher Salary Equations Student Teacher Variables Achievement Eq. Salary Eq. intercept -74.63895 17840(*) (-1.85) (12.72) density -0.000943(*) (-1.95) competition -1.862699(**) -766.8397(*) (-1.30) (-2.28) cognitive skill 1.030654(*) (8.24) college 0.055372(**) (1.81) teacher salary -0.001337 (-1.43) attend 0.529600 (1.39) pblack -10.71332 (-1.07) union 1.796939 964.3882(*) (1.21) (2.97) pupil/teacher ratio 0.068034 (0.33) student achievement 78.44555(*) (3.93) administration exp. -17641(*) (-2.43) teacher rank 30.2609(*) (3.15) tax effort 1389.312(*) (2.79) [R.sup.2] 0.56 0.35 * 0.05 level of significance, two-tail test ** 0.10 level of significance, one-tail test Number in parenthesis is t-statistic
Finally, highly rural and highly urban areas that have low associated quality-of-life measures may translate into an apparent low expected return to education for individuals in school (Broomhall, 1995; and Broomhall and Johnson, 1994). Given a low expected return to education, low student achievement scores relative to those in other areas would be expected. Such a phenomenon would suggest that the coefficient on the variable, dnsdv, will be negative. Such results imply that the relationship between student educational achievement and population density is inverted U-shaped.
The system of equations was estimated using a two-stage least squares procedure. Table 1, above, depicts the results of that estimation. The claim by McCloskey and Ziliak (1996) that economists consider statistical significance to be the same as economic significance certainly overstates the extent to which economists imply significance on the basis of statistical significance alone. Although some economists may always view statistical significance as equal to economic significance, such an acknowledgment, however, neither implies that all economists always view statistical significance as such or even that some economists always view statistical significance as the same as economic significance.
Nevertheless, it is important, as McCloskey and Ziliak suggest, to consider the economic implication of changes in statistically significant variables. After all, "it makes a difference, only if it makes a difference." In this article, the economic impact of statistically significant variables is indicated in the final section.
The results suggest that the coefficient on the csi variable is positive and highly significant at the 0.01 level. The coefficient on the col variable is significant at the 0.05 level for a one-tail test. The att, ts, u, pbl, and ptr variables are all insignificant at the 0.05 level. To the extent, however, that statistically insignificant variables may nevertheless be influential depending on the absolute size of estimated coefficients, respectively, elasticities were computed. None was greater than 1.00.
The estimated coefficient of the competition variable, c, suggests that counties with fewer school districts that provide educational services have lower student achievement scores on their tests than would otherwise be expected. This finding is not at all too uncommon. Hoxby (1994), Couch, et al, (1993), and Borland and Howsen (1992) have each discovered that increased competition among schools within given areas leads to higher student performance.
The estimated coefficient of the density deviation variable, dnsdv, is negative and significant at the 0.05 level. This result suggests that low density areas and high density areas have lower student achievement scores than areas of moderate density. Thus, after accounting for the influences of csi, col, att, ptr, c, pbl, u, and ts, students who live in very high density and very low density areas performed similarly, but less well on standardized tests than students from moderate density areas. Broomhall (1995) finds that students who perceive local job opportunities to be few and who exhibit an unwillingness to relocate expect a low rate of return to education to exist, reducing the incentive to perform well in school. In addition, Broomhall (1995) suggests that this is true, in particular, for rural areas in central Appalachia. This study suggests that the finding could be true for rural areas in Kentucky as well as urban areas in Kentucky. That is, the rural areas do not have a monopoly position when it comes to performing relatively poorly on student achievement tests.
This article's main objectives were (1) to determine if students who live both in highly rural and highly urban areas perform similarly, but less well, in terms of educational achievement than students who live in other areas, and (2) to show the impact of the inclusion of both cognitive skills and educational market competition variables in equations in which one is attempting to explain the variation in student achievement. The results of this article suggest that highly rural and highly urban area students do perform similarly on tests of educational achievement, but less well than students from other areas, and that studies which omit measures of cognitive skills and educational market competition as explanatory variables may be overstating the effects of the remaining variables in associated models.
These findings suggest the following policy recommendations. First, policymakers should realize that students from both highly rural and highly urban areas perform less well in terms of student performance than students from moderately dense areas, even after taking into account the effect of other socioeconomic variables. Policies that are intended to affect only rural students are at best one-sided. To the extent that the quality of resources remaining in highly rural and highly urban areas is less than that in moderate density areas, even at similar nominal prices, differential subsidies may be necessary to equate expected student achievement. Further research with respect to the dynamics of educational resource migration is, of course, suggested. At this time one can only offer conjecture.
A second policy recommendation suggested by the results is the establishment of competitive educational market systems that allow educational consumers at least some choice in the acquisition of educational services. Such a condition would create within counties the necessary environment in the educational market that would be expected to lead to higher student performance.
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Appendix: Description of Variables
sa: student achievement. Student achievement is defined as the mean total battery normal curve equivalent score for third-grade students within a school district.
csi: cognitive skill. Cognitive skill is represented by the mean of a cognitive skills index for students in a school district.
col: college. College is defined as the percentage of students within a school district who go on to college.
att: attendance. Attendance is defined as the aggregate days attendance divided by the aggregate days membership.
ptr: pupil-teacher ratio. The pupil-teacher ratio is defined as enrollment at the district level divided by the number of classroom teachers at the district level.
c: competition. Competition is defined as a Herfindahl index. This index takes on values greater than zero but equal to or less than one. A value of one implies that there is only one school district, i.e., monopolist, which supplies education within a county. As the Herfindahl index declines, i.e., approaches zero, then the educational market within a county becomes more competitive. Kentucky allows parents to send their children to a school outside one's district for a nominal fee. For instance, in Warren County, county residents can send their children to a city school for approximately $175 per academic year. This would result in up to a $3,200 gain for the city school at the expense of the county school system. This gain/loss occurs because of the funding formula used by the state to allocate school finances (Borland and Howsen, 1992).
pbl: percent of population that is black. The percentage of the population that is black is defined as black population divided by total population.
u: unionization. The unionization variable is defined as a dummy variable that takes on a value of one, if the union bargains for the local teachers, and is equal to zero otherwise.
ts: teacher salary. Teacher salary is defined as the average teacher salary within a school district.
dnsdv: absolute value of the deviation in population density. This value was determined by taking the absolute value of the difference between 2565 and population density for a county.
adm: administration cost. Administration cost is defined as the quotient of administration cost divided by total expenses.
rank: rank earned. Rank earned is defined as the percentage of teachers within a school district who possess at least a master's degree.
lfi: tax effort. Tax effort is defined as the quotient of local revenue per child in average daily attendance divided by the assessed property value per child in average daily attendance.
Melvin V. Borland and Roy M. Howsen are professors in the Department of Economics, Western Kentucky University, Bowling Green, Kentucky 42101. E-mail addresses are firstname.lastname@example.org and email@example.com, respectively.] Their current research is concerned with the effects of alternative market structures and other variables on student academic achievement. Recent publications include "Student Academic Achievement and the Degree of Market Concentration in Education," Economics of Education Review, 11:1, 1992.…
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Publication information: Article title: A Note on Student Academic Performance: In Rural versus Urban Areas. Contributors: Borland, Melvin V. - Author, Howsen, Roy M. - Author. Journal title: The American Journal of Economics and Sociology. Volume: 58. Issue: 3 Publication date: July 1999. Page number: 537. © 1999 American Journal of Economics and Sociology, Inc. COPYRIGHT 1999 Gale Group.
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