_{1}

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This study uses Gini coefficient and the different decomposition of Gini coefficient to investigate the equality of distribution of human capital and endowment. The result shows that neither the amount of endowment nor the number of teachers indeed causes a great deal of inequality in different schools. The contribution from full-time teachers is more than the contribution from the part-time teachers to the inequal distribution of teachers. For the inequal distribution of endowment, the contribution from the between-group is greater than the contribution from with-group.

In 1999, the Chinese government made decision to expand the scale of enrollment in Colleges and universities, and in the subsequent years of continuous expansion, the size of enrollment is unprecedented. The expansion of enrollment in colleges and universities increases the opportunity for higher education and the higher education transform from elite education to mass education. According to 1996-2008 panel date, Jun’s [

Since 1999, 72 Chinese universities belonging to the Ministry of Education (MOE) were selected as “985 Project” and “211 Project” universities; it aims to develop some outstanding universities to set a good example in teaching, research, and service to society for other. These MOE universities are distributed in 18 provinces, among which, Beijing, Shanghai, Jiangsu and Hubei have the largest amount. Till 2013, though accounting for only 8.5% of all Chinese universities (879 undergraduate universities), MOE universities occupy nearly total resources of Chinese higher education. In addition, since 2011, no more other universities were permitted to join in “985 Project” and “211 Project” by the ministry of education universities in China.

In this paper, we will study the distribution of endowment and teachers’ equality in the US, as the United States is the world’s most developed countries. The total investment in higher education and its diversified financing channels are in the world’s leading position. The practice of higher education funding in the United States is known as the typical model of the western countries, and the source of higher education investment can basically points into four major blocks: one is government investment, including federal, state, and local government investment; second, personal and family involvement, namely, colleges and universities, the tuition and fees; the third is from the social investment, mainly including donation income; the fourth is the sales and service income. Due to the lack of date, we use the endowment in each school. In the US, the teachers are divided into part-time teachers and full-time teachers. The main difference between full-time teachers and part-time teachers is that full-time teachers have a job security, enjoy the basic benefits of the school, only to participate in teaching management, not to participate in other management work. Part time teachers have no job security, do not enjoy the benefits of the school, do not participate in any management work, and have been paid remuneration according to the course. According to China’s terms, they are “temporary workers”. At present, these “temporary workers” have accounted for 50% of the teaching staff of American University.

With regard to the consumption of special consumer goods, A. Druckman (2008) [

The rest of the paper is organized as follows. In Section 2, we review the earlier literatures. Section 3 presents the method of Gini coefficient, and also the Gini coefficient decomposition data are presented in Section 3. We discuss our empirical results in Section 4, and Section 5 concludes.

Equity and efficiency are two obviously important consideration in the analysis of the education sector all the time. Jill Johnes and Li Yu (2008) [

As for equity, Many researchers in the field of education (Bottani & Benadusi, 2006 [

Besides, Hong (2009) [

How can measure education resource equality? Prior to the study of human capital and material capital have an important impact on the education results, we select the human capital and material capital to study the distribution of the unfair. Schultz founded the theory of human capital, and defined the human capital is the knowledge, skills, experience, creativity and health status of the economic value of the human capital. In Colleges and universities, teachers and researchers are the most important human capital, in particular, the professor (Senior Teachers) with a wealth of knowledge, skills and experience; young teachers (senior and intermediate teachers) have a very strong innovation. Material capital refers to the form of long-term production, is the material basis of human capital. In Colleges and universities, material capital is all kinds of educational resources and facilities. Among them, laboratory, library, the library and the classrooms (Teaching Department of education, 2009) and school covers an area, laboratory equipment and teaching etc. is an important place for teaching and research activities and the basic conditions; and according to the fixed assets management system, buildings, vegetation, electronic equipment, medical, office equipment, sports goods of fixed assets in Colleges and universities are also indispensable for the development of the elements; in particular, education and scientific research funds is an important component of the material capital.

Due to the limitation of data, we just analyze the full-time teachers and part- time teachers separately as for the human capital and the endowment as for the material capital. The endowment data are from the National Association of College and University Business Officers (NACUBO), which consist of those gathered from 832 U.S. colleges and universities for the 2014 NACUBO-Commonfund Study of Endowments. Eliminating five schools belonged to Canad and the two that the data was defected. We just choose the top 100 schools, which listed in

There are multiple ways to measure degrees of inequality, such as the Theil-L Index, the coefficient of variation,, and the Gini index. The main reasons this study chooses the Gini coefficient as the measurement are that, first, the Gini index is used widely to measure multiple types of distribution difference (Sen, 1997) [

Gini coefficient of total and different types of teacher

G = 1 2 n 2 η ∑ i = 1 n ∑ j = 1 n | y end-stu i − y end-stu j | (1)

G = 1 2 n 2 η ∑ i = 1 n ∑ j = 1 n | y tea-stu i − y tea-stu j | (2)

G full-stu = 1 2 n 2 η ∑ i = 1 n ∑ j = 1 n | y full-stu i − y full-sti j | (3)

The name of university | The name of university |
---|---|

University of Tennessee System | University of Wisconsin Foundation |

The University of Georgia Foundation | University of Missouri System |

University of Florida Foundation, Inc. | University of Illinois and Foundation |

Texas Tech University System | University of Nebraska |

University of Alabama System | University of Oklahoma |

University of Arkansas-Fayetteville | University of Cincinnati |

University of Kentucky | Purdue University |

Virginia Commonwealth University | Michigan State University |

Baylor University | University of Minnesota and Foundation |

Georgetown University | The Kansas University Endowment Association |

Tulane University | Saint Louis University |

Southern Methodist University | Indiana University and Foundation |

University of Texas System | University of Michigan |

Texas Christian University | Case western Reserve University |

Wake Forest University | The University of Tulsa |

University of Virginia | Washington University in St. Louis |

Vanderbilt University | Northwestern University |

Duke University | University of Chicago |

Emory University | University of Notre Dame |

Trinity University (Texas) | Swarthmore College |

University of Richmond | University of Colorado Foundation |

Baylor College of Medicine | University of California |

Washington & Lee University | The UCLA Foundation |

Rice University | University of California, Berkeley Foundation |

Berea College | University of Washington |

University of Lowa and Foundation | The George Washington University |

Boston University | University of Southern California |

Tufts College | The Rockefeller University |

Boston College | California Institute of Technology |

Brown University | Stanford University |

Middlebury College | Pomona College |

Smith College | University of Pennsylvania |

Dartmouth College | Rutgers, the State University of New Jersey |

Bowdoin College | Carnegie Mellon University |

Wellesley College | Johns Hopkins University |

William College | University of Pittsburgh |

Grinnell College | Yeshiva University |

Amherst College | University of Rochester |

Harvard University | Cornell University |

Yale University | Columbia University |

Massachusetts Institute of Technology | University of Delaware |

Princeton Theological Seminary | Syracuse University |

University of California-San Francisco Foundation | New York University |

The Texas A&M University System and Foundations | Lehigh University |

The University System of Maryland Foundation, Inc. | Vassar College |

Georgia Institute of Technology and Related Foundations | Princeton University |

University of North Carolina at Chapel Hill and Foundation |

G part-stu = 1 2 n 2 η ∑ i = 1 n ∑ j = 1 n | y part-stu i − y part-stu j | (4)

where, in formula (1), y^{i} and y^{j} are the numbers of total endowment per unit of students in the ith and jth school. η is average numbers and there are n schools. similar to formula (1), formula (2) is the calculation equation for the Gini coefficient of the total teachers per units of students. Formula (3) is the calculation equation for the Gini coefficient of the full-time teachers per units of students. (4) is the calculation equation for the Gini coefficient of the part-time teachers per units of students.

Decomposition contribution rate and its increment according to different types of teacher

In this subsection, we study further the contribution of different types of teacher to the degree of unbalanced of teachers in different universities. The study uses formulas 5 - 6 to decompose the Gini coefficient of teachers of per students according to the different types of teacher, as follows:

G = ∑ n = 1 4 E n G ′ n = ∑ n = 1 4 R n E n G n (5)

where G represents the Gini coefficient of summed numbers of teacher of per student; En represents the proportion of the number of teachers of type n to the total teachers; G_{n} represent the Gini index of type n; and G ′ n represents the concentration index (also called the pseudo Gini coefficient) of type n. when the total number of teacher are ranked from lowest to highest, a rank of teachers of type n is possible not strictly from lowest to highest; in this situation, G ′ n is called the pseudo Gini coefficient, and G ′ n does not equal G_{n}. because there are 96 schools involved in this study, q = (1, 2, ∙∙∙, 96), and then, the teacher of type n in unit q is x_{qn}.

R = n ∑ q = 1 96 ( q − 96 + 1 2 ) x q n ∑ q ′ = 1 96 ( q ′ − 96 + 1 2 ) x q n = cov ( x n , q ) cov ( x n , q ′ ) _{ }

is the Gini correlation coefficient between type n numbers of teachers and total number of teachers (Larman and Yitzhaki, 1985 [

Then, the contribution of type n teacher’s imbalance to overall unbalanced

teacher can be expressed as E n G ′ n G .

Then, we can obtain the dynamic results of the decomposition:

Δ G = G t 1 − G t 0 = ∑ n = 1 2 G n t 0 Δ E n + ∑ n = 1 2 E n t 0 Δ G n + ∑ n = 1 2 Δ E n Δ G n (6)

where Δ E n = E n t 1 − E n t 0 represents the change of the proportion of type n teacher’s number to the total number of teacher from the base period to the current period. Δ G n = G n t 1 − G n t 0 represents the change of the concentration index (pseudo Gini coefficient) of the numbers of teacher per student from the base period to current period. Thus, the change of the Gini coefficient of summed teachers per student can be decomposed into three parts: first, the construction effect caused by the structural changes of teachers per students of all types of teachers; second, the concentration effect caused by the change of the concentration index of teachers per students of all types of teachers; and third, the comprehensive effect of these two effects.

Decomposing Gini coefficient according different regions

In this section, we study the impact of different regions on the distribution of endowment. There are diverse way to decompose Gini coefficient, such as the method putted forward by Zhang and Li (2002) [

G = G ( y 1 , y 2 , ⋯ , y m ) = 2 n 2 μ ∑ k = 1 m ∑ j ∈ N k r i ( y i − μ ) = 2 n 2 μ ∑ k = 1 m { ∑ i ∈ N k i ( y i − μ k ) + ∑ i ∈ N k i ( μ k − μ ) + ∑ i ∈ N k ( r i − i ) y i } = W + B + R (7)

where

W = 2 n 2 μ ∑ k = 1 m ∑ i ∈ N k i ( y i − μ k ) = ∑ k = 1 m v k 2 b k G ( y k ) (8)

B = 2 n 2 μ ∑ k = 1 m ∑ i ∈ N k i ( μ k − μ ) = ∑ k = 1 m b k v k [ ∑ j = 1 k v j − ∑ j = k m v j ] = G ( y i ¯ , ⋯ , y m ¯ ) (9)

i occurs in the ith position when the teacher distribution is written y = (y^{1}, y^{2}, ∙∙∙, y^{m}), and in position r_{i} when all teacher in increasing order. The first term of the right-hand side in Equation (7) is the within-group contribution, while the second term is the between-group component of education inequality. R is a residual, which is zero if the subgroup observation ranges do not overlap. When we aim to analyze inequality caused by school type, schools should be divided into two subgroups. In the other situation, it should be divided into three.

In

First, we measure and calculate the Gini coefficient of the endowment, full- time, part-time and total teachers per student, using the date in 2014 because of the lack of data for other years, but it is meaningful to measure the trends of the distribution with the change of the time if the data is available.

As we all know that Gene coefficient was initially used to calculate the income inequality which ranges from 0 to 1. When the Gini coefficient is 0, it represent that it is the perfect equity, when the Gini coefficient is 1, it represent complete inequity. And the bigger Gene coefficient, the more unfair. In general, The Gini coefficient is between 0.36 and 0.24 in developed country. In accordance with the provisions of the relevant United Nations organizations, 0.4 is the picket line, which means that when the Gini coefficient beyond 0.4, the distribution is largely inequality. In our paper, the Gini coefficient of endowment per student is 0.682, and the Gini coefficient of total teachers per student is 0.4863 (see

In the next section, we analyze the effect of part-time teachers per student and the full-time teachers per student to the total teacher-student. And then we analyze whether the distribution of endowment is affected by regions or not.

Decomposition contribution rate and its increment according to different types of teacher

According to data, the teacher is consisted by two types, the first one is full-

Variable | Mean | Std. Dev. | Min | Max |
---|---|---|---|---|

Number of students in school | 29046.16 | 38356.18 | 208 | 247534 |

Number of full time teacher | 2747.677 | 2967.38 | 40 | 23451 |

Number of part time teacher | 817.6882 | 1079.868 | 20 | 6602 |

Number of endowment | 3990999 | 5872323 | 916828 | 3.59e+07 |

Source: IPEDS and NACUBO (National Association of College and University Business Officers).

The number of school | 5 | 6 - 25 | 26 - 50 | 51 - 75 | 76 - 93 |
---|---|---|---|---|---|

Endowment-students | 0.398 | 0.389 | 0.156 | 0.0145 | 0.0116 |

Full-time teachers-students | 0.187 | 0.321 | 0.385 | 0.119 | 0.077 |

Part-time teachers-students | 0.0875 | 0.367 | 0.039 | 0.208 | 0.121 |

Total teachers-students | 0.169 | 0.319 | 0.008 | 0.136 | 0.085 |

Variable | Gini |
---|---|

Endowment-students | 0.682 |

Total teachers-students | 0.4863 |

time teacher and the second one is part-time teachers. The part-time teachers is the one who only need to fulfill the responsibility of teaching, be responsible for teaching, and do not need to participate in all activities of the school.

We calculate the contribution of different types of teachers per student, the result listed in

There are two reasons to interpret the phenomenon. First, according to

Besides, if we have the data in other years, we can analyze the change of the Gini efficient and the contribution of different types using the approach mentioned in the section of method.

Decomposing Gini coefficient according different regions

In this section, we study the factor of regions. As we all know, the Chinese is sort into east, west and central. Similarly, the United States is also divided into different regions. Though there are many way to divided the, we use a combination of basic and conventional way, which it was divided into five regions―New England, The central coast of the Atlantic, South, Midwest, West. The schools distributed into different regions, the New England consist 16 schools, the central coast of the Atlantic consist 18 schools while the south, midwest, west include 28 schools, 20 schools, 11 schools respectively, which is listed in

Full-time teachers-students | Part-time teachers-students | Proportion | |
---|---|---|---|

Contribution | 0.867 | 0.133 | 6.5 |

Variable | Gini coefficient |
---|---|

Full-time teachers-students | 0.51 |

Part-time teachers-students | 0.4624 |

Type of teachers | Full-time teachers per student | Part-time teachers per student | F/P |
---|---|---|---|

Percentile | 0.82 | 0.18 | 4.56 |

Subgroups | Within-group Contribution (%) | Between-group Contribution (%) | R(%) | W/B |
---|---|---|---|---|

17.2 | 49.6 | 35.7 | 2.89 |

District | New England | central coast of the Atlantic | South | Midwest | West |
---|---|---|---|---|---|

number | 16 | 18 | 28 | 20 | 11 |

endowment | 0.268 | 0.381 | 0.154 | 0.101 | 0.097 |

End-stu | 0.293 | 0.370 | 0.096 | 0.088 | 0.154 |

When decomposing for the new England, central coast of the Atlantic, south, midwest and west regions, empirical results show that the contribution rate from within-group components is triple than that of between-group component. The comparison in

The purpose of this study is to analyze the situation and the reason of the higher education resource inequality in US. At the beginning, we adopt the Gini coefficient to measure the higher education resource inequality in US. The result shows that neither the amount of endowment nor the number of teachers, there is a great deal of unfairness in different schools.

Next, based on the Gini coefficient decomposition method by different types of teacher, we decomposed education inequality for variables of part-time teachers and full-time teachers. The finding is that the contribution from full-time is so big because the famous schools have more attraction and more ability to apply the position to teachers. Besides, the number of full-time teachers is more than part-time teachers.

Then, we decompose the Gini coefficient of endowment by the variable of regions. The result shows the contribution from between-group is much greater than that from within-group. The New England and the central coast of the Atlantic have more endowment than South, Midwest and West.

Liu, Y.Y. (2017) The Equality of Distribution of Education Resources―The Case of 96 Universities in the US. Open Journal of Social Sciences, 5, 180-190. http://dx.doi.org/10.4236/jss.2017.51014