1. Introduction

After the appearance of the epidemic caused by the SARSCov-2 virus, later named COVID-19 disease, at the end of 2019 in Wuhan, China, a great effort has been made to contain the contagion in the region where it first appeared.

That effort was fruitless, and the infections spread throughout the world. The World Health Organization (WHO) declared a pandemic on March 11, 2020. From that moment on, measures were taken in Colombia to reduce the effects of the epidemic, especially in terms of public health. The National University of Colombia suspended face-to-face classes as of March 15, 2020 and theretofore all classes were held remotely. All the tasks that required the presence of people one way or another, including all laboratory courses and practices, were suspended. At the national level, a generalized mandatory confinement was decreed, which accentuated the difficulties, especially for students with fewer resources.

The university temporarily modified the student statute to prevent students with little or no internet access from being harmed by this. As a result, the period to drop a registered course without penalty was extended to the very end of the semester. In practice, this meant that there would be no failing grades while the remote class regime lasted. In addition, several initiatives were organized in several schools to find sources of financial aid, mainly through voluntary faculty financial contributions, for those students from out of town without the means either to sustain themselves or participate in remote learning.

During the rest of the year 2020, it became evident that more students than usual were having academic difficulties. Nevertheless, the temporary relaxation of the student regulations avoided a major catastrophe in terms of failing courses and student outcomes. However, some program advisory committees reported higher dropout rates for reasons not directly associated with academic performance, which may be attributable to the pandemic. The increase in reported cases of emotional problems has also been notorious.

This situation reflects a trend detected worldwide that shows that many people, including students, have been affected in different ways during the months of the pandemic because of stress caused by fear of infection and mobility restrictions. Several publications have analyzed how different population groups have been differently affected. Reference ^[1], for example, emphasizes that the impacts can be very different, depending on social and economic conditions.

At an international level, numerous studies have been carried out on the impact experienced by students from different countries and educational levels. Most of the studies that have been undertaken on college students have focused on the psychological effects experienced as a consequence of the conditions derived from the pandemic ^[2-4].

Several studies have analyzed the effects of inequalities and social inequities in different contexts, especially among university students ^[2,5]. Flack ^[5], for instance, made an extensive analysis of the ways in which Australian students perceived the pandemic, controlling for socio-economic conditions, ethnicity, location, type of school (private, religious, public).

Another group of studies has been dedicated to evaluating conditions associated with delays in graduation and other conditions that lead to loss of income, due to lost wages, once students graduate ^[3].

All the studies that we have analyzed are based on surveys or interviews. At this time, we do not have any study where objective variables related to the direct effects of the pandemic on the academic performance of the student community are evaluated.

This project aims to estimate the effects that the pandemic and its treatment have had on the academic progress, grades and dropout rates of students from the School of Engineering of the National University of Colombia, campus Bogotá. We considered the two academic periods of 2020 and compared them to the previous ten semesters in order to gauge the effect that the new course drop policy has had.

2. Methods and data preparation

The main source of data was the University Registrar's official record files with all the information on courses registered by undergraduate students from the Bogota campus. Additional files containing data on courses that were dropped and, therefore, do not appear in students' transcripts were then added, to analyze changes in patterns of course completion and passing. This information was combined with personal and socioeconomic student information. All records were anonymized, to protect students' personal information prior to any processing or analysis. Records for students of the school of Engineering were then selected and studied as presented below.

2.2 Causal model

In order to establish causal links between the different variables, a causal model needs to be established. The usual representation of causal relationships is by means of a Directed Acyclical Graph (DAG). In this type of graphs, nodes represent variables and arrows represent causal influences. The effect of the pandemic can be thought of as a natural experiment since the apparition of this treatment is independent of all other variables. Therefore, a DAG representing the effect of the pandemic and two main additional variables (sex and family income) affecting a student's result (outcome) is shown in Fig.1 A causal model like this allows us to establish causal relationships from statistical estimands ^[6]. The only assumption that is necessary for this DAG is the fact that Sex and Family income are independent variables. Based on this graph, all impacts estimated in this work are, in fact, causal effects.

Source: Own work

Figure 1 Causal model of the effects of the pandemic. 

All statistical models featured from now on are presented in standard form, which makes explicit the assumptions made in the construction of the model. The ~ symbol indicates a distribution assumed for the data (a likelihood function) and an equal sign defines a parameter of the distribution in terms of other variables. In this work we only consider two types of models: linear regression models where residuals are normally distributed and logistic regressions with a Bernoulli distribution and a logistic link function. Bayesian goodness of fit tests were performed based on Bayesian factors. All were satisfactory, which was somehow expected, given the large sample size.

2.4 Population characteristics

During the period being considered, a total of 13617 students were registered in engineering programs. A breakdown, by sex and curricular program, of the evaluated population is presented in Fig.2. It may be observed that the number of female students is relatively low in all engineering programs, as is common in Colombian schools of engineering.

Source: Own work.

Figure 2 Composition of Engineering programs, by sex. 

The current COVID-19 pandemic has forced many changes in the way of living of the population in general. We were interested in knowing how it affected the students in our school. A very important issue was the effects of the pandemic on the total number of attending or registered students each semester, since there were fears that many students would drop out because of the aggravation economic hardships that took place at the time for them. Fig. 3 shows the number of students registered each semester, divided by sex. It may be noticed that the number of students has, in fact, rose slightly during 2020, but decreased in 2021, for reasons to be discussed in the results section.

Source: Own work.

Figure 3 Number of students registered at the school of Engineering by sex. 

3. Academic performance

Being a public school, the university has a very diverse student population, in economic and social characteristics. One measure the university utilizes for summarizing the economic means of each student is what we call Basic Tuition Points (PBM, by its Spanish initials). It is used to decide the amount a student must pay each semester for tuition and other fees. For modeling purposes, we will use a centered version of this variable: PBMc is a normalized (zero mean, unitary standard deviation) PBM.

The project analyzed the impacts or effects of the COVID-19 pandemic from the point of view of the student's academic performance, as characterized by (i) the course grades and (ii) the progress in the program measured as the ratio bet