Complexity

Volume 2018, Article ID 3528206, 9 pages

https://doi.org/10.1155/2018/3528206

## An Unintended Effect of Financing the University Education of the Most Brilliant and Poorest Colombian Students: The Case of the Intervention of the* Ser Pilo Paga* Program

^{1}Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile^{2}CeiBA Complexity Research Center, Bogotá, Colombia^{3}President, Universidad de los Andes, Bogotá, Colombia^{4}Fondo de Financiamiento de Infraestructura Educativa, Ministerio de Educación Nacional, Bogotá, Colombia^{5}Center for Development of Nanoscience and Nanotechnology (CEDENNA), Santiago, Chile^{6}Departamento de Ingeniería Industrial, Universidad de los Andes, Bogotá, Colombia

Correspondence should be addressed to Pablo Medina; oc.ude.sednainu@idem-bap

Received 29 June 2018; Accepted 1 November 2018; Published 2 December 2018

Academic Editor: Guido Caldarelli

Copyright © 2018 Pablo Medina et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In this paper, we show an unintended effect of the program* Ser Pilo Paga* (SPP) that was a flagship program of the Colombian government between 2014 and 2018. It was designed as an intervention in the Colombian Higher Education System (CHES) by awarding, in the steady state, individual funding to about 40,000 students. Every year, 10,000 new students were chosen from the best applicants in the top decile of the population in the entrance exam to higher education in Colombia that also came from families that live under the level of poverty according to a national survey. Our approach, based on an intensive study of the changes in the statistical distributions of the exam scores during these four years, provides evidence of student performance improvements not only of the beneficiaries of the program, but also of the whole student population. This shows that the program opened similar opportunities for all the students, especially for the poorest ones. The program drove a reduction in the gap between students of the upper strata of the population and those of the lowest strata that usually did not access a high quality institution of higher education due to the lack of funding. This result has opened a debate about the optimal way of funding higher education.

#### 1. Introduction

In October 2014, the President of Colombia announced the program Ser Pilo Paga (SPP for the Spanish acronym) (the name of the program uses the Colombian adjective “pilo” that denotes a particular characteristic of a person, which will be explained later in the introduction). SPP is one of the programs designed and implemented by the Minister of Education (Gina Parody, coauthor of this paper) to contribute to the objective of turning the country into the most educated country in Latin America by 2025. SPP focuses on a specific group of academically high achievers that had no access to a higher education due to their low income [1–3].

In this manuscript, we report an unintended effect in the Colombian education system that was produced by this program. As we will analyze below, the SPP program has had some direct and some indirect effects in the Colombian Higher Education System (CHES), such as a clear improvement in the results of the entrance examination to the CHES, not only of the SPP students, but also of the whole student population.

SPP is the result of a previous research, conducted by the authors of this article, that concluded with the design and implementation of the program. The design of the program articulates efforts from the following four institutions of the Colombian system: (i) the Colombian agency (ICETEX) created in the 1950s to offer financial loans to pay higher education of individual students; (ii) the agency (ICFES) that has designed a compulsory entrance examination to access higher education, now named SABER 11, since 1968; (iii) the accreditation commission (CNA) created by law in 1992 that accredits the quality of the academic programs of both the official and the nonprofit private academic institutions; and (iv) the National Planning Department (DNP) that has run a national survey that characterizes groups to focus the need of subsidies (SISBEN) since 1995.

The origin of this research was the observation of a reduction in the quality of the students that access the CHES. In particular, we observed that the proportion of students that entered the CHES with a high score in SABER 11 was reduced from 32% to 16% in the first 14 years of the 21st century. This tendency implied that somehow there was a reduction of the proportion of talented students that enter the CHES. Therefore, we had to find a way to reverse that tendency because we felt that a characteristic of the quality of a system of higher education is the access of highly qualified students [4]. Furthermore, from a point of view of “justice as fairness,” it is important to educate this set of students so that they can contribute to the progress and fairness of society [5].

In the context of the reduction of the proportion of students with high scores in SABER 11, we studied the set of students with a score in the entrance examination of one and a half standard deviations above the mean. We found that the number of students in this set was 7.5% of the total number of students that had taken the examination. In the subset of this 7.5% of students, we studied the access to the CHES of the students with a SISBEN score under the level of poverty. The result was that 32.5% of the students in the subset did not enter the CHES in the year immediately after they had taken the examination in spite of the fact that they had the academic merit.

Hence, the result of our analysis was that around 14,000 students did not access the CHES in an accredited institution in spite of the fact that they had the merit. With this fact, we designed the SPP program to reverse the situation. In this paragraph we will clarify our understanding of the characteristics of a student that we term “pilo,” which has been studied in a similar way in other contexts [1, 4, 6]. The Colombian expression “pilo” characterizes a student that believes that if he/she makes the necessary effort, then he/she will construct the context to achieve high academic standards. SPP means that if he/she has the capacity to make the effort to construct the context in which he/she will achieve the academic objectives that he/she has declared for him/herself, then he/she will have the financial support to achieve a professional degree.

Thus, SPP is a merit-based program that offers financial aid that covers full tuition costs and some living expenses for each student. The program benefits 10,000 new students every year for four years. To be eligible, a student should fulfill three requirements: (i) a score in SABER 11 in the top 7.5% of the population, (ii) a score in SISBEN under the level of poverty in the area where he/she lives, and (iii) acceptance into one of the Colombian accredited universities (public or private).

The financial aid is administered by ICETEX. The aid is a loan that will be condoned when the student is awarded his/her professional degree.

In this paper, we show one unintended effect of SPP that is related to the overall improvement in the scores of SABER 11. We studied the cohorts of students that took SABER 11 in the second semester of the four years from 2014 to 2017. Among others, we studied the evolution of simple statistical measurements like mean and standard deviation in the four years of the program.

With the observation of the evolution of these measurements we studied the performance, and its improvement, of three different sets of students: (i) the entire group of students that took the entrance examination; (ii) the set of students that took the entrance examination and that had a score in the SISBEN survey that set them under the level of poverty, henceforth named SISBEN students; and (iii) the set of students that could not be beneficiaries of SPP due to their SISBEN score (it was higher than the level of poverty or did not have a SISBEN score), henceforth named non-SISBEN students.

In the case of the SPP beneficiaries, we separated them into three subsets, corresponding to the three geographical areas defined by the survey: (i) 14 biggest cities of the country, (ii) urban cities and towns not included in the 14 biggest cities category, and (iii) rural areas.

With the analysis of the measurements in this article we show that the beneficiaries of SPP drove the system in two ways: (i) every year the performance of the SPP students was better than in the previous year and (ii) there was an increment of the* speed* of the improvement of the whole student population.

For the analysis we developed a Pareto approximation of the right tail of the distribution. In the analysis we compared the temporal variation of the performance and the improvement of the different sets of students.

After this introduction (Section 1) we have organized the article in the following three sections: (i) in Section 2, we explain the data and the methodology that we used to study the performance of the population; (ii) in Section 3, we present the results obtained from our analysis; and, (iii) in Section 4, we analyze the competition between students to show the results and possible future consequences due to this intervention.

#### 2. Materials and Methods

##### 2.1. Beneficiary Conditions and the Data

In the study we use the data of the results of SABER 11. ICFES (these administrative data are provided by ICFES after approval request) provided the data of the students that took the test in the second semester of each of the four years from 2014 to 2017. In each cohort there are approximately 575,000 students. We used a weighted average of the performance of each student in different components of the test. In future studies, we may analyze the student performance in individual components of the test. ICFES provides the scores in a range from the minimum of 0 to the maximum of 500, and for each cohort we found the minimum score required to be a beneficiary, namely, above one and a half standard deviations from the mean. The minimum scores in the examination were (i) 310 in 2014, (ii) 318 in 2015, (iii) 342 in 2016, and (iv) 348 in 2017.

In the database we also included scores of SISBEN. DNP provided the scores of SISBEN to determine the socioeconomic characteristic of the set of beneficiaries, as it classifies the socioeconomic situation of the student. The SISBEN is further categorized according to three geographic areas, so that the score is different for each area. The three areas and their respective SISBEN scores are (i) 57.21 for the 14 biggest cities of the country, (ii) 56.32 for the urban areas not included in the 14 biggest ones, and (iii) 40.75 for rural areas.

Each year, the CNA provides the list of institutions that have an institutional accreditation.

For the analysis of the beneficiaries we also use administrative data of the program. This information allows us to compare a variety of properties of the students in the three different areas of the SISBEN students, and their statistical analysis is presented in the article. The SPP program selects 10,000 new students every year.

##### 2.2. The Measurements of Performance and Improvement

For the analysis we constructed the sets of the whole population that took the entrance examination (SABER 11) in the second semester of the years 2014 to 2017. In each of these sets we identified two subsets: (i) the set of students with a SISBEN equal to or less than the score for a person to become a possible beneficiary of SPP and (ii) the set of students with a SISBEN greater than the score for a person to become a possible beneficiary of SPP. For each year we identified the subset of students in set (ii) that were beneficiaries of SPP. In each of these 4 subsets, one for each year, we further separated them into the three subsets of the beneficiaries for each of the three classification areas of the SISBEN. In each of these 12 sets of students we conducted a basic descriptive statistical analysis to study the performance and the improvement of each set based on the right tail of probability distribution of the scores of the students. To study the performance and the improvement of a set of students, we proposed our own definition of these two quantities. Our assumption, as we may observe from the data, is that analyzing the set of students that are classified in the right tail of the distribution provides a strong hint of the behavior of the entire population. We also complemented our analysis using common statistical measurements like the mean and the standard deviation. Moreover, we made a special analysis of the subsets of students in the three areas of the SISBEN observing the changes in the SPP scores.

As we have said, studying the tail of the distributions allows us to measure the rate of performance and improvement in time. We consider that the right tail of the distribution of the examination scores has a statistical behavior similar to a Pareto distribution. The Pareto distribution is defined by the function . The function represents the probability density distribution of the variable , which in this case represents test scores, while represents the parameter of the distribution. In other words, gives an idea of how “extreme” the values of the scores are. The greater of the distribution is, in general, the lower the scores we may expect. In other contexts, power-law distribution has been widely accepted to describe the wealth distribution in different economies, as well as to characterize other extreme or critical phenomena like earthquakes, the Internet network, and so forth [7–29]. If for two sets we obtain , we may deduce that members of set 2 have obtained in general lower scores on the examination, while students of set 1 have obtained in general higher results because the distribution has more “extreme” scores. Therefore, we propose to use the exponents as an estimation of a measurement of performance:

According to our approach, the fraction should convey a reasonable notion of performance. We expect that populations described with a lower value of have in general better results than populations with a higher value of , so that the expression of (1) will be greater than in the second cases. In Figure 1(a) we show an example for the scores of two sets of students that can be described by Pareto distributions with and , respectively. Although both sets of students have similar mean, the set characterized with (the blue ones) has more people with higher scores than those characterized with (red). In the same way, this figure suggests that if the test would consider higher examinations scores, on average the first population (the blue ones) may obtain higher scores. Because we are considering normalized distributions (i.e., ), it is then possible to compare sets with different population sizes.