PAGE 1
EDUCATIONAL PRODUCTION IN COLORADO: ACHIEVING THE 90% HIGH SCHOOL GRADUATION RATE GOAL by Greg F. Gregory B.S., Arizona State University, 1987 A thesis submitted to the Faculty.of the Graduate School of the University of Colorado at Denver in partial fulfillment of the requirements for the degree of Master of Arts Economics 1994 @
PAGE 2
This thesis for the Master of Arts degree by Greg F. Gregory has been approved for the Graduate School by Daniel Rees
PAGE 3
Gregory, Greg F. (M.A., Economics) Educational Production in Colorado: Achieving the 90% High School Graduation Rate Goal Thesis directed by Assistant Professor Daniel Rees ABSTRACT Colorado has adopted the national goal of increasing the public high school graduation rate to 90% by the year 2000. Between 198992 Colorado increased its graduation rate from 77.0% to 79.9%, or 0.97% per year. To achieve a 90% graduation rate by the year 2000, Colorado needs to accelerate the graduation rate to a 1.26% increase per year. In this paper, linear probability and modified logit models of educational production functions were used to estimate the sign and significance of educational inputs. Crosssectionai .data was collected across 175 public school districts in Colorado. The linear probability model estimates a significant (at the 0.2% level) negative coefficient (0.01) .between the studentteacher ratio and the graduation rate. In 198990 there were 103 districts achieving below the 90% graduation rate goal. These 103 districts contained 504,584 students and 21,194 teachers, or a mean studentteacher ratio of 23.8. The decrease of studentteacher ratio per district required to raise each iii
PAGE 4
district's graduation rate to 90.0% is calculated: DISTRICT DECREASE OF = STUDENTTEACHER RATIO [90 0% _ACTUAL DISTRICT] GRADUATION RATE 0.01 Accordingly, the mean studentteacher ratio for these 103 districts is reduced from 23.8 to 9.7. This policy would increase the number of teachers by 145%, from 21,194 to 52,006. Thus, the total number of new teachers required to achieve the 90% graduation rate goal in Colorado is 30,813, an average increase of 299 teachers per district. The large increase (145%) in additional teachers demonstrates the weakness of the studentteacher ratio as a costeffective policy variable. Each one unit reduction of the studentteacher ratio only yields a .01 percentage point increase in the graduation rate. Therefore, lowering the studentteacher ratio is not an efficient solution to Colorado's problem of reaching a 90% graduation rate by the year 2000. Continued research is needed to find improved measures of the qualitative effectiveness of teachers, curriculum, and technology in order to determine the most efficient allocation of educational resources. This abstract accurately represents the content of the candidate's thesis. I recommend its publication. Signed Daniei Rees iv
PAGE 5
CONTENTS Tables CHAPTER 1. INTRODUCTION 2. LITERATURE REVIEW Educational Achievement in Colorado Trends in Educational Policy Development of Educational Production Functions . . 3. THE DATA .. Variable Descriptions 4. ESTIMATION TECHNIQUES Linear Probability Model Modified Logit Model 5. EMPIRICAL RESULTS 6. POLICY IMPLICATIONS 7. CONCLUSIONS BIBLIOGRAPHY v vi 1 3 3 4 7 12 12 15 15 16 17 21 24 26
PAGE 6
TABLES Table 1. 198990 Educational Production Function 2. 3. 4. Data Base 198990 High School Graduation Rate Regression . . . . . . Colorado High School Graduation Rates StudentTeacher Ratio Decrease by District vi 28 32 33 34
PAGE 7
CHAPTER 1 INTRODUCTION The purpose of this paper is to assists Colorado administrators in creating educational policies that generate a 90 percent high school graduation rate1 by the year 2000. In 1989, the President and governors selected six national goals to enhance public school education by the year 2000. Increasing the high school graduation rate to at least 90 percent is one of the six national goals adopted by Colorado.2 The ensuing calculations demonstrate that Colorado needs to accelerate its actual graduation rate increase by 30.3 percent per year in order to achieve the 90 percent graduation rate goal by the year 2000: ACTUAL GRADUATION RATE INCREASE = 79.9%77.0% 1992 1989 = REQUIRED GRADUATION_ 90.0% 79.9% = RATE INCREASE 2000 1992 2.9% 3 YEARS .1% 8 YEARS = = 0. 97% YEAR 1.26% YEAR ACELLERATION = 1. 26%/YEAR 0. 97%/YEAR = REQUIRED 0.97%/YEAR 30. 3%/YEAR 1The 198990. Colorado high school graduation rates, by school district, ranged between 100% and 30% (See Table 1) 2Colorado Department of Education "State Report Card 1993: Meeting the Challenge" (Denver 1994) pp. 1114. 1
PAGE 8
Administrators base their educational policies on the premise of a cause and effect relationship existing between the quality of educational inputs and student achievement. Regression analyses may yield inferences about these causal relationships between educational inputs and the high school graduation rate. Therefore, linear and logarithmic models of educational production functions are developed, using 198990 crosssectional data from 175 Colorado districts, to estimate the sign and significance of key educational inputs. The educational production functions use the 198990 Colorado high school graduation rate as the dependent variable. The independent variables are divided into vectors of student socioeconomic background and educational inputs. The educational inputs represent the policy variables that school administrators have the most control over. Thus, educational inputs with correctly signed and significant (at the 5% level) coefficients have potential policy implications.3 The incidence of high school graduation should accelerate as significant educational inputs are more efficiently. 3The coefficients of independent variables in the linear probability model measure the proportional change in the high school graduation rate associated with a one percentage point change in the independent variables. Negative coefficients indicate the input variable decreases the high school graduation rate. 2
PAGE 9
CHAPTER 2 LITERATURE REVIEW Educational Achievement in Colorado The overall high school graduation rate4 for the state of Colorado has increased from 76 percent in 1987 to 79.9 percent in 1992. At this rate of increase, the high school graduation rate in the year 2000 will be 86.1 percent, which is 3.9 percent short of the national goal. In the 198990 school year, only 72 Colorado districts representing 57,754 students had reached the goal of a 90 percent high school graduation rate. The remaining 103 districts representing 504,584 students were achieving below the 90 percent goal. The 1992 high school completion rate5 for Colorado increased to 81.0 percent from the 1991 rate of 79.8 percent. The high school completion rate of minorities was substantially below the state average, with American Indians at 59.7 percent, Blacks at 69.9 percent, and Hispanics at 65.9 percent.6 4The high school graduation rate is the percentage of students receiving a regular diploma in relation to students entering grade nine, adjusted for transfers. 5The high school completion rate includes graduates plus students receiving other certificates from a Colorado high school. 6colorado Department of Education, State, pp. 1925. 3
PAGE 10
In 1992, Colorado voters turned down a one penny sales tax increase for public school funding. Amendment 1, the Taxpayer's Bill of Rights was also approved by a 5446 percent margin in the 1992 general election. This amendment limits the growth of public school expenditures per district to the annual rate of inflation, measured by the Consumer Price Index for DenverBoulder. Therefore, educational resources for the state of Colorado must be lookedat as a zerosum scenario. If Colorado is to meet the goal of a 90 percent high school graduation rate by the year 2000, then the available educational resources should be allocated in the most efficient manner possible. Trends in Educational Policy In the United States as a whole, current expenditures (i.e., excluding capital expenditures and interest on debt) per steadily inbreased between 1963 and 1983. Measured in 1983 dollars, current expenditures per student increased 135 percent in real dollars from $1,262 in 1960 to $2,960 in 1983. A large proportion of the increase in expenditures per student went towards reducing national studentteacher ratios.7 7Eric Hanushek, "The Economics of Schooling: Production and Efficiency in Public Schools" Journal of Economic Literature (September 1986) 24: 114648. 4
PAGE 11
Between 1960 and 1980, a combination of falling enrollment and policy efforts to reduce class size by hiring more teachers resulted in a 25 percent reduction in national studentteacher ratios8 (i.e., decreasing from 25.8 in 1960 to 19.0 in 1980, based on "all classroom teachers"). The studentteacher ratio in Colorado continued to decline during the period 198489, and then rose between 199092. The studentteacher ratio decline during 198489 followed deliberate policy efforts to reduce class size and increase the number of special education and special subject teachers. The studentteacher ratio increase since 1989 is a result of public school budget restrictions and growth in the student population of coiorado.9 Educational policy has changed the characteristics of American public school teachers between 196083. The 8studentteacher ratioscan be calculated by dividing the number of students enrolled in a district by .either the total number of "all classroom teachers" or the total number of "selected classroom teachers". The definition of "all classroom teachers" consists of any staff member assigned the professional activities of instructing students in selfcontained classes or courses. The definition of "selected classroom teachers" consists of all classroom teachers with the exception of special education teachers, Chapter I, II teachers and teachers in specialized subject areas such as music, art, physical education, driver education, and ROTC. The educational production functions estimated in this paper calculate the studentteacher ratio based on "selected classroom teachers", since this definition excludes courses not generally considered as barriers to obtaining a regular high school diploma. 9colorado Department of Education "Pupil Membership and Related Information: Fall 1990" (Denver 1991) pp. 16. 5
PAGE 12
median years of teacher experience has increased from 9 to 13 years. The percentage of teachers with a master's degree increased fr6m 26.1 to 53.0 percent.w These changes in teacher characteristics are often influenced by educational policies based on a priori reasoning. Public school administrators have inadequate evidence to support their premises that student achievement can be improved by increasing either average teacher experience or teacher education beyond a bachelor's deg;ree.11 The trends in these public school policies imply that educational achievement can be maximized by finding the most efficient allocation of instructional inputs, subject to public school budget constraints. The dilemma associated with these public school policies is finding a method of verifying the causal relationships flowing from educational inputs to high school achievement. The technique used here to infer these causal relationships is regression analysis motivated by educational production functions. 10u.s. Department of Commerce, Bureau of the Census "Statistical Abstract of the United States, 1985" (Washington D.C. 1986). 11Eric Hanushek, "Conceptual and Empirical Issues in the Estimation of Educational Production Functions" Journal of Human Resources (Summer 1979) 37274. 6
PAGE 13
Development of Educational Production Functions The first major statistical study concerning the relationship between educational inputs and student achievement was the Coleman Report. 12 The Coleman Report was commissioned by the Civil Rights Act of 1964 to study the distribution of educational resources by ethnic background across the United States. This survey of 500,000 students in 3,000 schools generated the controversial belief that family background and peer characteristics of students were the most consequential input factors affectingeducational achievement. The original inputoutput analyses performed for the .coleman Report have since evolved into the estimation of "educational production functions" by economists. These educational production functions attempt to reveal the maximum amount of educational achievement possible for alternative combinations of educational inputs .13 By interpreting the sign and significance of coefficients associated with educational inputs, new public school policies that improve technical and allocative efficiency can be implemented. 12d.s. Coleman, et al., Equality of Educational Opportunity (Washington D.C. 1966). 13David Monk, Educational Finance: An Economic Aooroach (New York: McGrawHill Publishing Company, 1990) pp. 32530. 7
PAGE 14
.The functional relationships between educational inputs and the high school graduation rate must be specified prior to estimating the regression coefficients. Even though there is inadequate guidance for economists to follow when selecting a functional form of educational production function, the general model14 most often used in educational production function analyses is specified: A= iF;I,P,S} (1) where: A is the dependent variable for educational achievement. F is a vector of independent variables representing student's family characteristics. I is an independent variable representing student's intellectual capa6ity prior to entering high school. P is a vector of independent variables representing student's social class. S is a vector of independent variables representing teacher and school characteristics. The data used in this research is aggregated at the district level and no measure of mean student intellectual capacity prior to high school is available. With the exception of intellectual capacity, the linear and logarithmic educational production functions estimated in this paper follow the general model (1) 14oaniel Luecke and Noel McGinn, "Regression Analyses and Education Production Functions: Can They Be Trusted?" Harvard Education Review (August 1975) 45: 32550. 8
PAGE 15
In order to specify the educational production functions for the entire state of Colorado, according to the general mo.del ( 1) the variables selected require the measurement of average district characteristics for students and teachers. Hanushek finds the variation of average district data to cause a second order problem when distinguishing between functional forms of educational production functions .15 The conceptual general model measures the characteristics of individual students, while most estimates of educational production functions use aggregate level data. The most detailed educational and socioeconomic data available for the entire state of Colorado is collected at the district level. Averaging district characteristics is a drawback since this method eliminates internal variation within districts. The misleading implicit assumption is that every student in the district receives an equal amount of inputs, or that atypical inputs.balance each other out. This problem in the level of aggregation can only be solved by new efforts to collect individual level data across Colorado. 15Hanushek, "Conceptual," pp. 37274. 9
PAGE 16
The causation between teaching inputs and educational outcome is complicated by teacher selection effects. Teacher selection effects occur when systematic methods are used to evaluate, select and address students with different learning characteristics. Teachers evaluate the academic level of their students when choosing the method of teaching a particular class. A class with poorly prepared students may receive easier tests, and then be passed on to the next level without the proper training. Teaching biases may channel students into effortless classes that inhibit students from completing the classes required for graduation. Hanushek finds the most intelligent or best educated teachers may select to teach advanced students, thus reversing the flow of causation from educational achievement to teacher inputs .16 Therefore, a policy that increases.the level of teacher education may not yield the entire benefit to achievement that is expected from the estimated correlation. This .problem of teacher selection is diminished if a surplus of teachers limits their influence on classroom assignment. To explain the entire educational process the independent variables must include nonschool inputs such 16Ibid., pp. 37274. 10
PAGE 17
as socioeconomic background and expectations. The difficulty in obtaining these input variables often leads to the use of indirect proxies, which may result in measurement errors. The lack of reliable deductive theory contributes to an inductive approach to specifying independent variables for educational production functions. This manipulating of coefficient significance specifying regression models creates variation in the results. Independent variables should be select based on education theory instead of intercorrelation problems. The expected results for an educational production function should a positive relationship between student achievement and traditional instructional quality inputs. Hanushek presents the findings of 147 separately estimated educational production functions. 17 The sign and significance (at the 5 percent level) of the estimated coefficients generated unexpected results indicating that there is no systematic relationship between increased school expenditures and improvements in student performance. 17Ibid. 11
PAGE 18
CHAPTER 3 THE DATA Variable Descriptions This paper compares cross sectional data from 175 districts in Colorado for the 198990 school year .18 The Hinsdale County RE.1 district was excluded since it contained no students enrolled in grades 7 through 12. The 198990 school year was selected since it coincided with the collection of 1990 census data, which provides independent variables for a vector of student socioeconomic background across Colorado's districts. The dependent variable is the high school graduation rate for Colorado, defined as the percentage of students receiving a regular high school diploma in relation to students entering grade nine, adjusted for transfer students .19 The Class of 198990 grac].uation rate is calculated by dividing the number of graduates by the membership base. The membership base is the number of 18see Table 1 for a listing of the dependent and independent variables by school district. The Mean values for these variables are located at the bottom of Table 1. 19Colorado Department of Education "Colorado Graduation Rates for Class of 1990 and 198990 Annual Dropout Rates for Grades 712" (Denver 1991) pp. 1386. 12
PAGE 19
eighth graders from the spring of 1987, adjusted for the number of transfer students in grades 912. The graduation rate does not include students receiving nontraditional certificates or a general equivalency certificate (GED) The independent variables can be divided into two categories: 1) Student socioeconomic background, and 2) Instructional quality measures. Student socioeconomic background is measured for each distiict by the following independent variables: 1. Median household income. 2. Percentage of single parent households.20 Instructional quality is measured for each school district by the following independent variables: 1. Total student enrollment in grades K12. 2. Student to teacher ratio. 3. Teacher turnover rate. 4. Percentage of nonwhite teachers. 5 Teacher experience in years 6. Percentage of teachers with a master's degree.21 The average teacher experience per district and the percent of teachers with a master's degree includes 20u. S. Department of Commerce, Bureau of the Census "1990 Census of Population and Housing: Summary Social, Economic, and Housing Characteristics Colorado" (Washington, D.C. 1993) Table 4 and Table 10. 21colorado Department of Education "Certified Personnel and Related Information: Fall 1990" (Denver 1991) pp. 1858. 13
PAGE 20
all staff members assigned the professional activities of instructing pupils in selfcontained classes or courses. The number of students enrolled in grades K12 per district includes alternative education students and transfer students. A student is considered a transfer to another district or educational program if the receiving school or program sends for the students records, or if the sending district can document that the legal guardian has provided information regarding the school or education program into which the student is transferring. The ratio for grades K12 per district is calculated by dividing the number of selected full time equivalent classroom teachers by the total number of students. Selected classroom teachers include all teachers with the exception of special education teachers, Chapter I, II teachers and teachers in specialized subject areas such as music, art, physical education, driver education and ROTC. The teacher turnover rate is the rate at which personnel whose primary function is classroom teaching leave or separate from the district, or change from their classroom teaching to another position from one school year to another. This rate is determined by comparing the classroom teachers reported in the currerit year against those reported in the previous year. 14
PAGE 21
CHAPTER 4 ESTIMATION TECHNIQUES Linear Probability Model The linear probability model uses crosssectional data from 139 districts. The estimated coefficients from the linear probability model are easy to interpret; however, 36 districts.with a 100% high school graduation rate have been from this model. The linear probability model is not defined when the estimated dependent variable equals 1 or 0. 22 For this reason the modified logit model is also presented. The equation for the linear probability model is: (2) where: yi is the high school graduation rate for district i. Xi is a vector of explanatory variables for district i. ei is the distuxban9e term. A weighted leastsquares method is used to estimate the coefficients in (2) by multiplying all data variables by the following weight: I N1 w1 = =c.....,r1 .....,(=1=r1=> (3) where: is the weighiing factor for district i. Yi is the high school graduation rate for district i. N is the student enrollment grades K12 for district i. nG.S. Maddala, LimitedDependent and Qualitative Variables in Econometrics (New York: Cambridge University Press, 1983) p. 30. 15
PAGE 22
Modified Logit Model The modified logit model uses crosssectional data from 175 districts. The estimated coefficients from the modified logit model can be used to verify the sign and significance of the linear probability model results. The advantage of the modified logit model over the linear probability model is that logits are defined even when the dependent variable equals 1 or 0. 23 The equation for the modified logit model is: (4) where: Yi is the high school graduation rate for district i. Ni is the student enrollment grades K12 for district i. Xi is a vector of expianatory variables for district i. ei is the disturbance term. A weighted leastsquares method is used to estimate the coefficients in (4) by multiplying all data variables by the following weight: where: wi is yi is N is the the the (NI CY1 + 1/N1 ) (1 Y1 + 1/N1 ) (N1 + 1) (N1 + 2) weighting factor for district i. (5) high school graduation rate for district i. student enrollment grades K12 for district i. 23D.R. Cox, Analysis of Binary Data (London: Methuen, 1970) p. 33; 16
PAGE 23
CHAPTER 5 EMPIRICAL RESULTS The results of the ordinary least squares regression for both the linear probability and modified logit models can be found in Table 2. The two socioeconomic variables contain substantially significant coefficients that support established educational production theory. Both models estimate a significant (at the 1% level) positive coefficient for median household income. As median household income increases the high school graduation rate also increases. This may be due to the increased expectations and financial resources associated with students from higher income households. Both models estimate a significant (at the 0.2% level) negative coefficient for the percentage of single parent households. Consequently, an increase in the number of single parent households in a district decreases the high school graduation rate. Students from single parent households tend to have had less parental attention at home which results in lower expectations and skill levels. The empirical results for the instructional quality variables support the established educational production theory. These independent variables contain the expected 17
PAGE 24
sign in both the linear and modified logit models; however, only the studentteacher ratio was significant at the 10% level. The studentteacher ratios in both models contain a substantially significant (at the 0.2% level) negative coefficient. This result confirms the inverse relationship between studentteacher ratios and the high school graduation rate. Therefore, a decrease in studentteacher ratios should increase the high school graduation rate. This causation may be due to the reduced individual attention students receive in larger classes. The remaining instructional input variables containedless than 10% significance, due to moderate levels of multicolinearity. Multicolinearity creates wide confidence intervals which may lead. to a type 1 error (i.e., rejecting the significance of these independent variables when they should be accepted) Highly intercorrelated explanatory variables complicate the causation between instructional inputs and the high school graduation rate. Teacher experience in the linear probability model estimates a positive coefficient with 84% confidence. This positive coefficient suggests that an increase in the average years of teacher experience may cause the 18
PAGE 25
high school graduation rate to increase. However, the modified logit model only estimates this positive relationship with 64% confidence. The modified logit estimates a negative coefficient (significant at the 10.4% level) for the teacher turnover rate. This insinuates that stable teachers who remain in the same district have a positive impact on the high school graduation rate. The linear probability model estimates a substantially lower 36.5% significance level for the teacher turnover rate. Total student enrollment contains a negative coefficient (significant at the 20.5% level in the linear probability model) This implies a weak relationship between an increase in total student enrollment per district and a decrease in the high school graduation rate. This relationship may be caused by the urban characteristics (e.g., high incidence of minority students, crime and substance abuse) of large districts. The insignificant negative coefficient estimated for the percentage of nonwhite teachers implies that employing more minority teachers may decrease the high school graduation rate. Traditional education theory contends minority teachers have a positive impact on minority students, but may decrease the educational achievement of white students. 19
PAGE 26
The percentage of teachers with a master's degree or higher is positively correlated with an increase in the graduation rate at the 38.9% level of significance in the linear probability model. The low level of significance associated with this instructional input provides some possible policy implications. Teacher salary is directly tied to years of experience and level of education beyond a bachelor's degree. Current educational policy encourages teachers to continue their education beyond a bachelor's degree. Most districts in Colorado increase teacher salary at intervals for each 15 semester hours completed beyond a bachelor's degree. The low level of significance associated between thelevel of teacher education beyond a bachelor's degree and the high school graduation rate indicate that this policy may be both futile and expensive. Educational policies that reallocate resources towards significant teaching inputs should result in greater efficiency and a higher incidence of graduation among high school students in Colorado. 20
PAGE 27
CHAPTER 6 POLICY IMPLICATIONS In order to achieve a 90% graduation rate by the year 2000, Colorado needs to increase the graduation rate by 1.26% per year. The linear probability model estimates a significant (at the 0.2% level) negative coefficient (0.01) between the studentteacher ratio and the graduation rate. Consequently, each one unit reduction of the studentteacher ratio correlates to a .01 percent (i.e., dividing the studentteacher ratio coefficient of 0.01 by the 198990 graduation rate of 0.77) increase in the Colorado graduation rate. In 198990 there were 103 districts achieving below the 90% graduation rate goal. 24 These 103 districts contained 504,584 students and 21,194 teachers, or a mean studentteacher ratio of 23.8. The decrease of studentteacher ratio per district required to raise each district's graduation rate to 90.0% is calculated: DISTRICT DECREASE OF STUDENTTEACHER RATIO= [9 0. 0% 0.01 Table 4 for the studentteacher ratios of Colorado's 103 districts achieving below the 90% high school graduation rate goal. 21
PAGE 28
Accordingly, the mean studentteacher ratio for these 103 districts is reduced from 23.8 to 9.7. A review of Table 4 indicates the problems associated with reducing the studentteacher ratio in each of the 103 districts achieving below the 90% graduation rate goal. The first 8 districts in Table 4 are subject to the minimum 1.0 studentteacher ratio even though this does not achieve the 90% graduation rate goal. The predicted studentteacher ratio for these 8 districts is actually negative, which required hiring more teacher than students for these districts. If the studentteacher ratio drops below 1.0, then a very small decrease in studentteacher ratio results in an inordinate increase in the number of new teachers required. The difficulty with these districts exists in their low high school graduation rates or low studentteacher ratios, which can make the studentteacher ratio ineffective as a policy variable. The policy to reduce studentteacher ratios in the 103 districts achieving below the 90% graduation rate goal, subject to a minimum studentteacher ratio of 1.0, increases the number of teachers in Colorado by 145%, from 21,194 to 52,006. Thus, the total number of new teachers required to achieve a 90% graduation rate in 22
PAGE 29
Colorado is 30,813, an average increase of 299 teachers per district. The large increase (145%) in additional teachers required to reach the 90% graduation rate goal demonstrates the weakness of the studentteacher ratio as a costeffective policy variable. Although the studentteacher ratio is substantially significant in the linear probability model, its low 0.01 coefficient only yields a .013 increase in the graduation rate for each one unit reduction of the studentteacher ratio. Therefore, lowering the studentteacher ratio is not an efficient solution to Colorado's problem of reaching a 90% graduation rate by the year 2000. The only resolution to this problem of large decreases in studentteacher ratios is to set a reasonable minimum value (e.g., 18.0, 19.0, 20.0) per district, and then modify other policy variables in order to increase the graduation rate to the 90% goal. This requires policy makers to uncover other significant policy variables that can be modified along with the studentteacher ratio. Continued research is needed to find improved measures of the qualitative effectiveness of teachers, curriculum, and technology in order to determine the most efficient allocation of educational resources. 23
PAGE 30
CHAPTER 7 CONCLUSIONS The national education goal of obtaining a 90 percent high school graduation rate by the year 2000 does not appear to be realistic. The majority of urban school districts in Colorado are too far below the 90 percent graduation rate to meet this goal by the year 2000; however, this paper indicates that reducing the studentteacher ratio may assist in reaching this goal. A reduction in the studentteacher ratio is not the panacea to Colorado's problem of reaching the 90% high school graduation rate by the year 2000. Other qualitative instructional variables need to be modified in collaboration with the studentteacher ratio. The following policy recommendations may help Colorado in achieving a 90 percent. high school graduation rate by the year 2000: 2 Tail Policy Recommendation Level of Significance Decrease studentteacher ratio 0.0000 Decrease percentage of single 0.0008 parent households Increase median family income 0.0065 Increase average years of teacher 0.1600 experience Decrease teacher turnover rate 0.6347 24
PAGE 31
The empirical evidence that high studentteacher ratios adversely affect the high school graduation rate coincides with education theory and the continuing trend in education policy to reduce the average number of students per teacher. However, the regression results could beimproved with the use of panel data. A fixedeffects model could be used with panel data, holding students' socioeconomic backgrounds constant over time. The data set also lacks qualitative independent variables for instructional quality. Variables for teacher performance are hard to find, especially in time series data. A variable for teacher verbal skills or teacher capability would help the data set. Other qualitative independent variables that might help the regression results w6uld include: peer and parent expectations, crime rate, and substance abuse rate. Education policies such as head start programs for young children should eventually help the high school graduation rate. Policies at the preschool and primary levels can have a significant impact on future high school graduation rates. The data set used here does not include variables on nonsecondary level teachers or programs. This type of data may enhance educational production function theory and empirical results. 25
PAGE 32
BIBLIOGRAPHY Brown, C. "Equalizing Differences in the Labor Market." The Quarterly Journal of Economics. (February 1980): 94: 11334. Coleman, J.S., et al., Equality of Educational Opportunity. Washington D.C. 1966. Colorado Department of Education. "State Report Card 1993: Meeting the Challenge." (Denver 1994). "Certificated Personnel and Related Information: Fall 1990." (Denver 1991). "Colorado Graduation Rates for the Class of 1990 and 198990 Annual Dropout Rates for Grades 712." (Denver 1991). "Pupil Membership and Related Information: Fall 1990." (Denver 1991). Cox, D.R. Analysis of Binary Data. London: Methuen, 1970. Hanushek, E. "The Economics of Schooling: Production and Efficiency in Public Schools." Journal of Economic Literature. (September 1986) 24: 114648. "Conceptual and Empirica.l Issues in the Estimation of Educational Production Functions." Journal of Human Resources. (Summer 1979) 37274. Luecke, Daniel F., and McGinn, Noel F. "Regression Analyses and Education Production Functions: Can They Be Trusted?" Harvard Education Review. (August 1975) 45: 32550. Maddala, G.S. LimitedDependent and Qualitative Variables in Econometrics. New York: Cambridge University Press, 1983. Monk, David. Educational Finance: An Economic Approach. New York: McGrawHill Publishing Company, 1990. 26
PAGE 33
U.S. Department of Commerce, Bureau of the Census. "1990 Census of Population and Housing: Summary Social, Economic, and Housing CharacteristicsColorado." (Washington, D.C. 1993). "Statistical Abstract of the United States, 1985." (Washington, D.C. 1986). 27
PAGE 34
t0 OJ COLORADO COJNTY TABLE 1: 198990 EDUCATIONAL PRODUCTION FUNCTION DATA BASE COLORADO SCHOOL DISTRICT JUlESBURG SOURCE: COLORADO DEPT OF EDUCATION & U.S. DEPT OF COMMERCE1990 CENSUS
PAGE 35
(:1...) 1.0 TABLE 1: 198990 EDUCATIONAL PRODUCTION FUNCTION DATA BASE COLORADO COONTY COLORADO SCHOOL DISTRICT SOURCE: COLORADO DEPT OF EDUCATION & U.S. DEPT OF COMMERCE1990 CENSUS PERCENT I TEACHER I "' TEACHERS NONWHITE EXPERIENCE WITH
PAGE 36
w 0 COLORADO COUNTY PROWERS I WILEY TABLE 1: 198990 EDUCATIONAL PRODUCTION FUNCTION DATA BASE COLORADO SCHOOL DISTRICT SOURCE: COLORPDO DEPT OF EDUCA llON & U.S. DEPT OF COMMERCE 1990 CENSUS TEACHER EXPERIENCE RS'
PAGE 37
w ....... TABLE 1: 198990 EDUCATIONAL PRODUCTION FUNCTION DATA BASE SOURCE: COLORADO DEPT OF EDUCATION & U.S. 0 EPT OF COMMERCE 1990 CENSUS
PAGE 38
TABLE 2: 198990 HIGH SCHOOL GRADUATION RATE REGRESSION IMMIW#flm!Wtfll!@l!l ';" SIGNIFICANT VARIABLE AT THE 5% LEVEL LINEAR PROBABILITY MODEL ( n = 139 SCHOOL DISTRICTS) MODIFIED LOGIT MODEL EXOGENOUS VARIABLES VARIABLE WEIGHllNG FACTOR MEDIAN HOUSEHOLD IN COllE 'l!.SINGLE PARENT HOUSEHOLDS TOTAL STlDENTS ENROllED STlDENT TEACHER RAllO TEACHER TtJRNOVER RATE PERCENT NONWHITE TEACHERS TEACHER EXPERIENCE (YEARS) 'J!.TEACHERS WITH MADEGREE NOTES: COEFRCIENT TSTAT 0.0000003101 1.27 0.0007518000 0.48 0.0789458000 1.01 0.0040273000 1.41 0.0484442000 0.86 ( n = 175 SCHOOL DISTRICTS) 2TAIL SIGNIFICANCE COEFFICIENT TSTAT 2 TAIL SIGNIFICANCE === 0.2051 0.0000004650 0.34 0.7344 0.6347 0.0161348000 1.64 0.1038 0.3120 0.1463056000 0.31 0.7532 0.1600 0.0156631000 0.92 0.3578 0.3890 0.2482513000 0.77 0.4407 1) TliE DEPENDENT VARIABLE IS TliE 198990 HIGH SCHOOL GRADUATION RATE PER SCHOOL DISTRICT. 2) BOlli MODELS EXCLUDE TliE HINSDALE COUNTY RE.1 SCHOOL DISllUCT, WHICH HAD NO snJDENTS ENROLLED IN GRADES 711iROUGH 12. 3) THE UNEAR MODEL EXCLUDES 38 SCHOOL DISTRICTS WHICH HAVE A 100% GRADUATION RATE. 4) SEE CHAPTER 3 FOR VARIABLE DESCRIPTIONS. 5) SEE CHAPTER 4 FOR ECONOMETRIC ESTIMATION TECHNIQUES. 32
PAGE 39
TABLE 3: COLORADO HIGH SCHOOL GRADUATION RATES SCHOOL GRADUATION STUDENTTEACHER FTE YEAR RATE RATIO TEACHERS 198889 77.0% 23.6 23,703 198990 77.9% 23.4 24,042 199091 78.9% 23.6 24,308 199192 79.9% 23.9 24,822 NOTES: 1) IN 1989, THE PRESIDENT AND. GOVERNORS SELECT SIX NATIONAL GOALS TO ENHANCE PUBLIC EDUCATION BY THE YEAR 2000. INCREASING THE HIGH SCHOOL GRADUATION RATE TO 90 PERCENT IS ONE OF THE SIX GOALS. 2) THE GRADUATION RATE IS THE NUMBER OF STUDENTS WHO RECEIVE A REGULAR HIGH SCHOOL DIPLOMA AS A PERCENT OF THOSE WHO WERE IN MEMBERSHIP DURING THE PREVIOUS FOURYEAR PERIOD FROM GRADES 912. 3) AT THE END OF THE 198990 SCHOOL YEAR, 40.9% OF SCHOOL DISTRICTS REPRESENTING 20.3% OF STUDENTS IN COLORADO WERE AT OR ABOVE THE GRADUATION RATE GOAL OF 90%. THE AVERAGE STUDENTTEACHER RATIO FOR THE DISTRICTS AT OR ABOVE THE 90% GRADUATION RATE WAS 20.3, WHILE THOSE DISTRICTS BELOW THE 90% GRADUATION RATE AVERAGED A 23.8 STUDENTTEACHER RATIO. THIS DATA ALONG WITH THE REGRESSION RESULTS SUGGEST THAT LOWER STUDENTTEACHER RATIOS ARE ASSOCIATED WITH HIGHER HIGH SCHOOL GRADUATION RATES. 4) AT THE END OF THE 199192 SCHOOL YEAR, 41.1% OF SCHOOL DISTRICTS, AND 35.0% OF SCHOOLS IN COLORADO WERE AT OR ABOVE THE GRADUATION RATE GOALOF90%. 33
PAGE 40
w """ YEARS I COLORADO COUNTY TABLE4: COLORADO SCHOOL DISTRICT STUDENTTEACHER RATIO DECREASE BY DISTRICT ( SlmJECTTO A MINIMUM STUDENTTEACHBl RATIO OF 1.0) (103 COLORADO SCHOOL DISlRICTS ACHIEVING BB.OWTHE 90% HIGH SCHOOL GRADUATlON RATE GOAL) ACTUAL PREDICTED PREDICTED ACTlJAL DEatEASE PREDICTED ACTlJAL ACTlJAL INCREASE PREDICTED PERCENT 1911990 GRAD.RATE GRAD RATE 1911990 IN ACTUAL STWENT1911990 1911990 IN ACTUAL TEACJERS INCREASE HIGH W/ 1911990 W/ DESIRED STUlENT1911990 TEACHER STWENTS TEACHERS 1911990 PER IN SCHOOL STWENTSTWENTTEACHER STUlENTRAllO PER PER TEACHERS DISDUCT TEACHERS GRADUAllON 1EACIR 1EACIR RAllO TEACHER DISTRICT DISTRICT PER PER RATE RAllO RAllO RAllO DIST 511.0 918 !168.0 80 89.0 714 755.0 Slffl 5981.0 49 60.0 590 621.0 655% PREDICTED VALUES ARE ESTIMATED USING THE REGRESSION COEFFICIENTS FROM THE UNEAR PROBABILilY MODEL
PAGE 41
w lJ1 TABLE4: STUDENTTEACHER RATIO DECREASE BY DISTRICT SI.IUECT TO A MINIMUM ST\JDENT lEACHBt RAllO OF 1.0_1 I (103 COLORADO SCHOOL DISlRICTS ACHIEVING BB.OWTHE 90% HIGH SCHOOL GRADUAllON RATE GOAL) YEARS I COlDRADO I COlDRADO I ........_ "'""""' '"B>""" ......._ .,..,.._ """""" [""""'""""[ ,_,. """"""' COUNTY SCHOOLDISTRICT 198990 GRAORATE GRAORATE 198990 INAClUAL SllDENT198!190 198990 INACTUAL TEACIRS INatEASE HIGH w/ 198990 w/ DESIRED SllDENT198990 TEACHER SllDENTS TEACHERS 198990 PER IN SCHOOL SllDENTSllDENTTEACHER SllDENTRATIO PER PER TEACHERS DISffliCT TEACHERS! GRADUATION TEACHER TEACHER RATIO TEACHER DISffliCT DISffliCT PER PER RATE RATIO RATIO RATIO __ DISlHICT DISlHICT 41 80% 86% 96% 20.6 1sl 41.4 tr':::o rrrr :rrr#%: ""':: ....... ,,,,._.,. "' GARFIELD RE2 43 76% 79% 94% 25.6 iiiiAiiifui::= ::::: .. := : .. : ,::,;,,, :::::,M \\\\\ !2[ 215.1 i4 109.7 198990lCAFFEE SAl.IDA 45 79% 83% 94% 22.2 10.9 11.3 1241 56 :==:::. .'''' ) ??t!i:i?i/Wi' :/)))( ooi' : \\\\! i/''':i\\\#k'\/\ ... .. :.= ... .... : : :::: )( ::: : :::,,:;:,:::: r:::::::::>u:::::::;., :=:: :::::::r::: :i='r:::::::::::::=:JJ;: t::::=iii'<:=::: ::::::::::::::: }:::=:M .....,,. 48 79% BO% 91% 22.3 10.8 11.5 2088 94 BB 11 ................ ... .. ........... . ::::::::::::.:::: .:;:;:: .... :::::. .. ,;::24.0 12.4 11.6 2268 95 101 195.3 107% ?i ar:ii : :;:;::::::::n::: :::::: .::::i t:=:::=:::::::::::=:::w ::::::=::::::::r nM ::::::: ::::::::::=::::::nmiii 12.3 0.5 11.8 227 18 1 19.2 4% ::::: ')'====== ::::;:i'i ,.; =:=)ii'sa ,.,,:::::;., :::::::::: ?'$. 14.9 2.5 12.4 284 19 4 22.9 20% :=::::?:::::: ::::;;1x ::=::::::::. ::=:::=::ii : =::=:::::=:=:::ww i: 21.1 7.9 13.2 412 20 12 31.2 60% #:M*i\i=t: i;t@l&Jiii#.(f(')//}} /)iii:::!'\!? ::0//J!!iiii :::!:iff :::::> > :::= ;:::::=;::::=:JM ::::::::::::::::::::::=:t!!? ::::::::::::::::::::::n?o :::=:::::=::::=::::::=:::::=:?.: 198990 PROWERS GRANADA 59 BB% 85% 87% 15.2 1.8 13.4 259 17 2 19.3 13% gJ?MQ::=:::=:t :::::::;:,:;::::: :::=:\':!iii ::::=:::: :::: ::;::})ii:iilii' :<=::::Y =: :=:::::::==:: : ::t:=::::::=:::.!o= :: ::::tt?WM ::::: : )4$ ::::: :::::::::: ::==:: 198990 LARIMER 'THOMPSON et BO% 85% 95% 23.5 9.9 13.6 11783 501 364 865.6 73% Wii!!F \ ::::::: ;:::;=n:::::M% :::::: ::)::=::::: :,:::: :::: /=i\:M =:: ::::.:::::: =::::2.s... > = =:i=i:::;: >hi: :::::::::::::: ) \ j :;;::::=:::: 198990 BOULDER BOUlDERVAUFi 63 79% 83% 94% 24.7 11.0 13.7 21013 851 682 1532.2 80% =::: =::::::::::: :::=::=::::: :::: ::::::::::: ::::=::::. n::::H ::::::::: ::::=:::::r =:::::::=::::::: t'?@ :==:::::::: 198990 AlAMOSA AlAMOSA 65 82% 78% 85% 22.0 7.8 14.2 23fS 108 59 166.7 55% //)//{\\ /)i!: ::=;::::::':':}:i//#ilii' '\\ :: :::::. :: :=:::'('\' ''2o: s ... :.:: } :: //?\ =:':A?? ?\\ : ':"\::: \:!:iii.? .. 198990 lAKE lAKE ff7 83% 88% 95% 21.3 6.7 14.6 1159 54 25 79.3 46% .,.,.,,.,.,.;c.,.,., ,,,:;;:;o:;;,::':'::::,::::: ,;:::;;;ili:::;;;,:;;;,;c''';;;''"lli'"'''''' ,:,:::cc' :,:,,,:,:,,,:,,,,,, ... ,,,;,; ;,,,,. ,;:;:}'A'=i:iiil \}):0: ;}){9'1:5: ,:;:':;:}:;:. /:J!'f" .,,,,,,,,,,,,,,:,:. ,;:: ,.::::. ,.,.,.,.,.,., :::: .,.,.,.,<.,;>'
PAGE 42
TABLE4: YEARS I COIDRADO I COLDRADO COUNTY SCHOOL DISTliiCT STUDENTTEACHER RATIO DECREASE BY DISTRICT ( SIBJECTTO A MINIMUM STUDENT TEACHER RAllO OF 1.0) (103 COLORADO SCHOOL DISlRICTS ACHIEVING BaOWTHE 90% HIGH SCHOOL GRADUAllON RATE GOAL) I ACTUAL PREDICTED PREDICTED ACTUAL DEaiEASE PREDICTED ACTUAL ACTUAL INaiEASE PREDICTED 198990 GRAD RATE GRAD RATE 198990 IN ACTUAl STUlENT198990 198990 IN ACTUAL TEACIRS HIGH w/198990 w/ DESIRED STUJENT198990 TEACIR STUJENlS l"EADRS 198990 PER SCHOOL STUJENTSTUJENTTEACK:R STUJENTRAllO PER PER TEACIRS DISTIIICT GRADUAllON TEACIR TEACIR RAllO TEACK:R DISTRICT DISTRICT PER RATE RAllO RAllO RAllO DISTRICT PERCENT INmEASE IN TEACIRS PER DISTRICT 1911190 COS1IUA SIERRAGRANCE 13 88% 80% 82% 18.4 2.5 15.9 309 17 3 19.4 16% ir::=tt=== :!iiJi;iM:tt\':=t:=:r=:::rrt:=t:::==: t:w ===:trrr::::;:ri!: :r=ttttti$.:ii r=t:r=tt:=::ta: t:::rrrH:atii ::=:::rt\' : '!ii'iii 1911190 PUEBLD RJEBLDCITY 75 80% 74% 85% 26.8 10.5 16.3 18403 687 441 1128.1 64% =r=r::=:::n:=%: ::::=:=:::=t'tdw r:t:nrrM 191!990 KJTCARSCN 8URINGTON 77 86% 84% 88% 20.3 3.8 16.5 853 42 10 51.7 23% :=rw t::::::rt := r::r:=tr:r:::m* :=:::t=r::==:::t;t::Q: ::::=:=:=:rttM$: r:::::::::rruw. 1911190 MOFFAT MOFFAT 711 84% 86% 92% 23.4 6.1 17.3 2613 112 39 151.0 35% =:::::::::::':::: :/i!it :=::: :=:::=:::=::: =t= :::=:::=t:::;;ij;a: :::=:::::=:rtt)b =ttttwws: tttttiiiiii :tt::=:tJMM r:::r=:::t::.lt'iii 1911190 RIO GRANDE 140NTEVISTA. 81 86% 77% 60% 21.4 3.6 17.8 1363 65 13 77.7 20% 1M.;w MiliWtm=:::: :::=:=: :ttt ::::=rr:::::rr=wi ::=:tt':=::::::::::Io :rtr:=::taM ::::r::: n. tr =: rt==:t:r::::::::::r: 1911190 EI..PASO J.MSPAIJooiER 83 83% 69% 96% 24.8 6.9 17.9 2313 93 36 129.2 38% ::::: r:::=::r=r:::t::='::=:i=:::=:::::::::::r=::::i =:::=::::=:=::::r::?% 1911190 WElD EATON 85 87% 88% 91% 21.0 3.0 16.0 1124 54 9 62.4 17% w ::/iiii)I: :;::::::::::=:tiilliiidt\tttt::lia% tt=::::::: 'itilHt:=:=::tttiiHi:::=:::::=:t=:=:::=tif tt:=:=::t:::::::ilo:t: 0"\ 191!990 JEFFERSON JEFFERSON liT 82% 81% 90% 26.9 8.4 18.5 75164 2794 1266 4060.6 45% :::::::::::::::::t/t@ii :::::::::::::::::t::rMi tit:::==: :=M!i ::::::::::::::td@t::::::::::::::::::=::::::::.: i:It::::=:::tt::)p:::::::: ::::::::tMiL:=::::t:= (;M:%. 1911190 ARAPAHOE lfiTl.ETON 89 83% 87% 94% 25.6 7.2 18.6 15356 595 230 825.2 39% rr =:rrrt ::::": rttr:n:au r:r:::::::sP.il: =:r':r=t=:::::Hu :::=:::::::::::::::=:hii ::::::::::=:::=:tt ;u. : ::::::::::: :::::::::::::?. 1911190 ADAMS BENNETT D1 90% 67% 88% 19.4 0.2 19.2 610 42 0 42.2 1% =r:=rr t)i: :r==:::::::::=:::=:::=:::t!!i;: =rrrrtiiPH =:::=:=:::=:tt'/@;ii:
