Beyond the Covid-19 pandemic: remote learning and education inequalities

Abstract

Is remote learning associated with education inequalities? We use PISA 2018 data from five European countries—France, Germany, Italy, Spain and the United Kingdom—to investigate whether education outcomes are related to the possession of the resources needed for distance learning. After controlling for a wide set of covariates, fixed effects, different specifications and testing the stability of coefficients, we find that remote learning is positively associated with average education outcomes, but also with strong and significant education inequalities. Our results show that negative gaps are larger where online schooling is more widespread, across countries, locations, and school types. More generally, remote learning inequalities appear to be associated with technological network externalities: they increase as digital education spreads. Policy makers must guarantee to all students and schools the possession of the resources needed for remote learning, but to reach this goal efficiently they must adapt their actions to the characteristics of countries, areas and school systems.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10663-022-09556-7.

Introduction

Several developed countries had already adopted some form of remote learning when the Covid-19 pandemic struck in 2020 and, abruptly, turned it into the main form of schooling. Many governments reacted rapidly, providing various degrees of support to schools and students lacking the resources needed to online schooling, but the urgency of these actions lead to uneven results across areas, schools and students’ populations. With the ebb of the pandemic and the reopening of schools, the sense of urgency subsided and government interventions slowed.

On the research side, the pandemic gave rise to many studies on the effects of remote learning on education. However, most of them restrict the analysis to online education during school closures, without extending its reach beyond pandemic times. A different branch of research on the use of ICT tools in schooling is based on experimental or quasi-experimental tests, but also in this case the investigation does not produce results that can be generalized to the impact of remote and online learning on education.

The present research investigates whether an uneven possession of the resources needed for remote learning by students and schools is associated with inequalities in education. It differs from the studies inspired by school closures during the Covid-19 pandemic (Kuhfeld et al. 2020; Schleicher 2020) as well as from the experimental and quasi-experimental research measuring the performance students—often from disadvantaged socioeconomic backgrounds or in developing economies—who are provided with computers or internet access. Overall, the results of these studies are heterogeneous, with computer and internet in some cases leading to improved and in other cases to poorer education outcomes (Banerjee et al. 2007; Leuven et al. 2007; Fairlie 2012; Carter et al. 2017; Comi et al. 2017; Malamud et al. 2019). Instead, we focus on remote learning and students’ education outcomes during non-critical times and use a very comprehensive and large dataset that covers a relatively homogenous group of developed countries.

More specifically, we use the 2018 wave of the Program for International Student Assessment (PISA) survey to assess whether the educational outcomes of students unable to learn remotely are significantly different from those of their peers. The PISA dataset provides comparable data within and across countries and is representative of countries’ entire students’ populations of 15-year-olds. It measures students’ ability to use their reading, mathematics and science knowledge and skills every three years and is characterized by features of standardization and comprehensiveness that allow the implementation of cross-country comparisons over several dimensions, including the one that motivates this study, remote learning. To our knowledge, this is the first time that this type of research is based on such a wide dataset. We focus on the scores in mathematics and consider countries—France, Germany, Italy, Spain and the United Kingdom—that share the economic, institutional and social characteristics of the western European area, while at the same time partially differ in their educational systems. This allows results to be independent from structural differences in the level of development of countries, but at the same time lets them vary with schooling systems.

Our variables of interest are, at home, the availability of a computer for schoolwork, an internet connection and a quiet place to study, and, at school, of a platform for online schooling. Since the possession of these resources can be expected to be correlated with the characteristics of students and of their families and schools, we control for a wide array of potential confounders, fixed effects and specifications. In fully controlled regressions, we find negative strong and significant gaps in the education of students unable to learn remotely. Perhaps unexpectedly, they are larger in the United Kingdom, where students and schools are best endowed with the resources needed for digital learning, and smaller in Spain, where digital education is less widespread. Specifically, the lack of a computer for schoolwork is associated with negative gaps in mathematics that range from the equivalent to half of a school year in the United Kingdom to about a sixth of a year in Spain. Moreover, gaps tend to be larger in urban areas, where the use of ICT resources is more common, and in the best endowed schools. In general, our results suggest that there are network technological externalities in remote learning that make the losses of outsiders larger where online learning is more widespread. We also find that a quiet place to study is significantly related to students’ scores. Composition analyses show that gap variations are partly explained by school types in countries where school tracking starts earlier, by grade repetition where repeating grades is more frequent, and by socioeconomic factors in other cases. In countries where grade repetition is frequent, remote learning inequalities are also associated with students’ joint probabilities of repeating grades and planning to abandon education early. Our results evidence correlations rather than causal relationships, but our sets of controls on socioeconomic factors, individual characteristics, school systems and fixed effects contribute to make them quite robust.

While several covariates help to explain part of the variations in remote learning gaps, these inequalities tend to remain strong and significant even in the fully controlled regressions, which points to a direct relationship between the scarcity of the resources needed to remote learning and school outcomes. Hence, our results signal the necessity of decisive policy actions even in non-pandemic times, aimed at ensuring that all students and schools possess the resources needed for online learning. The findings on the correlates of these gaps show how these actions can be tailored according to the characteristics of countries, areas and school systems, but the fact that gaps can remain strong and significant even after all correlates have been accounted for, indicates that these actions must also be quite direct. The rest of the paper is structured as follows: Sect. 2 discusses the related literature, Sect. 3 presents the data and main descriptive statistics, Sect. 4 is dedicated to the empirical methodology, results are provided in Sects. 5, and 6 concludes.

Related literature

The impact of digital and remote schooling on students’ outcomes has been widely debated for at least the last two decades. A group of publications frequently cited is based on a randomized control experiment performed in 2006. It consisted into a random assignment to first-year community college students in California of computers to be used at home, and aimed to estimate educational outcomes and labour market returns. Since the goal was the evaluation of the effects of home computers alone, no training, other assistance or resources were provided. Fairlie (2012) finds that the treatment group who received home computers developed substantially better computer skills than the control group, and Fairlie and London (2012) that the treated students experienced small, positive, short-run effects on educational outcomes. However, Fairlie and Robinson (2013) show that, although computer use increased substantially among the treated, there were no effects on educational outcomes, including grades, standardized test scores, or others. Fairlie and Grunberg (2014) evidence that the treatment group of students had a higher probability of taking transfer courses—allowing them to move from community college to university—than the control group. Finally, Fairlie and Bahr (2018) examine the short- to medium-term effects on earnings, employment and college enrolment, without finding significant effects of computer skills on college enrolment or short- or medium-run earnings.

Among studies focusing on developing countries, Banerjee et al. (2007) analyse the impact of two different programs, implemented in 1998 and in 2000, that provided supplementary inputs to children from poor families in urban India: a remedial education and a computer-assisted learning program. The second intervention offered children in grade four two hours of shared computer time per week during which they played games that involved solving math problems. Results show that both programs had a substantial positive effect on children’s academic achievement, at least in the short run.

Malamud et al. (2019) study the effects of home internet access by considering a broad range of child outcomes in Peru during the years 2011 to 2013. Data derive from an experiment consisting into randomly providing low-cost laptops (XO) for home use to children enrolled in low-achieving public primary schools, and into selecting among them a subgroup to whom also supply a free high-speed internet access. They find that children with internet access improved their computer and internet proficiency relative to those without computers, and improved their internet proficiency relative to those with computers only. However, there were no significant effects of internet access on math and reading achievements, cognitive skills, self-esteem, teacher perceptions, or school grades when compared to either group. Beuermann et al. (2015) focus on the short-term effects—approximately five months after performing the experiment—of providing children with XO laptops but not internet access. Results are that scores in an objective test measuring proficiency in using the XO laptop increased, but math and reading scores did not significantly change.

Malamud and Pop-Eleches (2011) estimate the effect of home computers on child and adolescent outcomes in Romania by exploiting a voucher program, subsidized in 2008 by the Romanian Ministry of Education, which awarded approximately 35,000 vouchers worth 200 Euros towards the purchase of a personal computer to low-income students enrolled in public schools. They employ a regression discontinuity design that allows comparisons across students who are very similar in family income and other respects but markedly differ in their possession of a computer at home. Their results indicate both positive and negative effects of home computers on the human capital development: children who won a voucher to purchase a computer had significantly lower school grades but showed improved computer skills.

Among researchers considering more developed economies, Leuven et al. (2007) evaluate the effects of two types of subsidies provided in Netherlands in 2000 to schools where large proportions of students had parents with low levels of education. The first scheme provided extra funding for personnel, the second for computers and software. To identify the effect of the two programs on pupils’ achievement, they exploit regression discontinuities in a local difference-in-differences framework. They find that the effects of both types of subsidies are negative and, in some cases, significant. Moreover, computer subsidies worsened girls’ achievements.

Carter et al. (2017) analyse the short-term effects of using ICT tools at school by employing data from an experiment performed in 2015 in the United States Military Academy, a four-year undergraduate institution. By considering final exam scores as the outcome variables, they randomized classrooms into a control group, where students were not allowed to use laptops or tablets, and two treatment groups, one where students were allowed to freely use them during class for note-taking and classroom participation, the other where students could use them, but could be monitored by lecturers. They find negative effects in both types of treatment, suggesting that using these ICT devices at school can harm classroom performance even when their utilization is monitored.

A few studies are based on wider samples. One is Yanguas (2020), who examines the early-adulthood educational outcomes of students who were provided laptops and internet access as school children in 2007 during the Plan Ceibal in Uruguay. This nationwide one-laptop-per-child program delivered a laptop to each student in primary and middle schools within the public education system and equipped all public schools with wireless internet access. She finds negative effects of the program on educational attainment. Students who were exposed to the program were less likely to apply for scholarships and to enrol in technology-related majors relative to health and social sciences majors.1

Vigdor et al. (2014) rely on a longitudinal sample consisting on students enrolled in grades five through eight in public schools in North Carolina between the years 2000 and 2005. They address concerns of non-random selection by employing a within-student estimator and using local variation in the timing of the introduction of broadband internet services; then they trace the impact of home computer introduction for a period of up to three years. They document broad racial and socioeconomic gaps in home computer access and use, and find that the introduction of home computer technology is associated with modest, but statistically significant and persistently negative relationships with students’ math and reading test scores. Moreover, the introduction of broadband internet is associated with widening racial and socioeconomic achievement gaps. They speculate that broadband internet access can reduce the efficiency of the time spent on homework, presumably by introducing distractions and new options for leisure time. Using longitudinal data from years 2001 to 2006 and a difference-in-difference approach Cristia et al. (2014) find that the introduction of computers in a school in Peru have no significant effects on students’ repetition, dropout and enrolment rates.

Comi et al. (2017) analyse whether ICT-related teaching practices affect students’ achievement in the Lombardy region in Italy by using standardized survey data (INVALSI) and an ad-hoc ICT survey performed in 2012 on a representative sample of students and teachers from 100 classrooms in the second year of upper secondary school (10th grade). To address issues of endogeneity, they use a within-student between-subject estimator, which controls for unobserved heterogeneity in schools, classrooms and students. They find that computer-based teaching practices increase student performance if they are aimed at increasing students’ awareness of ICT use and at improving their navigation critical skills, ability to distinguish between relevant and irrelevant material and access, locate, extract, evaluate and organize digital information. On the other hand, they report a negative impact of practices requiring an active role of students in classes using ICT.

Hence, the results of the above studies are heterogeneous. Several of them are based on experimental or quasi-experimental approaches that focus on samples of students from disadvantaged backgrounds, or from less well-off areas or countries where the use of ICT technologies for schoolwork is limited. Moreover, in some experiments students are supplied with ICT tools without being provided with previous training, which can affect results. In some cases, regarding developed economies, the experiments have been performed at times when online learning was still uncommon, so that results can hardly apply to present times. A few studies are based on broad samples, but results between them also diverge. Overall, the findings on the effects of the use of ICT tools in education differ strongly, partly because of the heterogeneity of the samples, methodologies and periods of time considered, and partly because the underlying research questions also vary. Several research approaches and findings on this topic are excellently reviewed in Escueta et al. (2020).

Data and descriptive statistics

We use data from the 2018 wave of PISA assessment on students’ test scores in mathematics.2 Overall, we consider 73,305 students enrolled in over 2577 schools in the five countries. The PISA dataset is the result of a two-stage stratified design, where, first, individual schools are sampled, and secondly, students are randomly sampled within schools. Given that each participating student in the PISA survey answers a limited amount of questions taken from the total test item pool, OECD provides ten test scores (known as plausible values), which can be interpreted as multiple imputed values of students’ performance based on students’ answers to the test and their background questionnaires. The difficulty of each item represents a weight, used to compute the weighted averages of correct responses. This approach allows having a measure of an individual’s proficiency for each student in each subject area, regardless of the questions actually answered. We employ the recommended OECD strategy for the estimation of coefficients and their variances, making use of all ten plausible values (OECD 2018). As a result, the number of students in the nationally defined target populations represented by our analytical samples covers from 85% (United Kingdom and Italy) to 99% (Germany) of the five countries’ populations of 15-year-olds (more details are in the Online Appendix).

Regarding the effective possibility of learning remotely, we select from the PISA Student’s Questionnaire the following questions: Which of the following are in your home: A computer you can use for schoolwork, A quiet place to study, A link to the internet, with responses that can be ‘Yes’ or No’, and from the School’s Questionnaire: To what extent do you agree with the following statements about your school’s capacity to enhance learning and teaching using digital devices? An effective online learning support platform is available, with answers that vary from ‘Strongly disagree’ to ‘Strongly agree’.3 Concerning the planned length of students’ education, from the Students’ Questionnaire we consider: Which of the following do you expect to complete? Answers range from lower secondary to advanced tertiary and research education programs. Our main control variables concern student’s individual characteristics (gender, immigrant status, age at arrival if born abroad, and repetition of one or more school years), family’s socioeconomic status (parents’ education and occupation, number of books and e-books at home), type of school attended (general, technical or professional, and private or public) and its location (city, town or rural). A detailed definition of variables is in Table 6. In further specifications we add school fixed effects.

Table A2.

Definition of variables

Variable	Definition
Math score	Continuous variable representing the students’ score in mathematics
Leaving education early	Binary variable taking value 1 when the student plans to complete at most ISCED levels 3C or 3B and 0 otherwise
Repeated grade	Binary variable taking value 1 when the student has repeated a grade and zero otherwise
No computer	Binary variable taking value 1 when the student states that she/he does not possess a computer at home to use for schoolwork and 0 otherwise
No internet	Binary variable taking value 1 when the student states that she/he does not have an access to the internet at home and 0 otherwise
No quiet place to study	Binary variable taking value 1 when the student states that she/he does not a quiet place to study at home and 0 otherwise
No school ICT	Binary variable taking value 1 when the school administrator states that the school does not possess an effective online learning support platform and 0 otherwise
Female	Binary variable taking value 1 for female 0 for male
Age	Continuous variable representing the students’ age at the time of interview, in years and months
Low education level	Binary variables representing the highest education level among parents. They take value 1, respectively, if; High, at least one parent has tertiary education, Average, neither parent has more than upper secondary education, Low, both have less than secondary education, and zero otherwise
Average education level
High education level
Low occupational level	Binary variables representing the highest occupational status among parents. Based on the ISEI classification of occupations, the occupational level is divided into Low, Average, and High by splitting the observations into tertiles. Dummy variables take value 1 in accordance to each level and 0 otherwise
Average occupational level
High occupational level
0–25 books	Binary variables taking value 1 in correspondence to each number of books at home and 0 otherwise
26–200 books
More than 200 books
None	Binary variables, taking value 1 in correspondence to each number of e-books at home and 0 otherwise
1–2 e-books
3 or more e-books
Immigrant status	Binary variables taking value 1 if the student is foreign born or his/her citizenship differs from that of the country of the test and 0 otherwise
Age of arrival	Continuous variable indicating the age of the arrival of the student in years and moths. It equals 0 if the student is native
General school	Binary variables taking value 1 in correspondence to each type of school and 0 otherwise
Technical school
Vocational school
Public school	Binary variables taking value 1 if the student attends a public school, and 0 otherwise
Rural area	Binary variables indicating taking value 1 in correspondence to each size of the municipality where the school is located and 0 otherwise. City comprises more than 100,000, Town between 100,000 and 3000 Rural area less than 3000
Town
City
Lack of infrastructure	Binary variable taking value 1 if the school administrator states that the physical infrastructure of the school is inadequate and 0 otherwise
Inadequate infrastructure	Binary variable taking value 1 if the school administrator states that the quality of the physical infrastructure is poor and 0 otherwise

Descriptive statistics are summarised in Table 5 and correlations between our main variables are in Table S1. The latter shows, in particular, that there is a weak correlation between our four variables of interest. It also shows that the less abundant resource is the ICT endowment at school: its scarcity is highest in Germany and lowest in the United Kingdom. If only home ICT resources—computer for schoolwork, an internet connection—are considered, the country with the highest proportions of students lacking them is Italy and the one with the lowest scarcity is the United Kingdom. The latter, however, has the highest proportion of students without a quiet place to study at home. If the proportion of students lacking at least one of the four resources needed for remote learning is considered—a computer, an internet connection, a quiet place to study at home, a school with a platform for online teaching—Figure S1-A evidences that it varies from 50% in the United Kingdom (42% if a quiet place to study is excluded) to 74% in Germany (70% considering only ICT resources).

Table A1.

Descriptive statistics

	France			Germany			Italy			Spain			United Kingdom
	Obs.	Mean	Std. Dev.	Obs.	Mean	Std. Dev.	Obs.	Mean	Std. Dev.	Obs.	Mean	Std. Dev.	Obs.	Mean	Std. Dev.
Math score	6308	495.41	92.57	5451	500.04	95.39	11,785	486.59	93.78	35,943	481.39	88.4	13,818	501.77	93.02
Reading score	6308	492.61	101.18	5451	498.28	105.75	11,785	476.28	96.87	–	–	–	13,818	503.93	100.21
Leave educ. Early	5930	0.12	0.32	4408	0.31	0.46	10,943	0.06	0.23	34,406	0.09	0.28	12,750	0.13	0.33
Repeated grade	6215	0.17	0.37	4674	0.20	0.4	11,495	0.13	0.34	35,449	0.29	0.45	13,306	0.03	0.16
No computer	6193	0.09	0.29	4711	0.08	0.27	11,485	0.10	0.3	35,391	0.09	0.28	13,250	0.08	0.27
No internet	6203	0.02	0.12	4721	0.02	0.14	11,491	0.03	0.17	35,371	0.02	0.14	13,262	0.01	0.09
No quiet place to study	6186	0.06	0.24	4723	0.05	0.21	11,491	0.09	0.28	35,372	0.07	0.26	13,204	0.11	0.31
No school ICT	5458	0.65	0.48	4718	0.67	0.47	11,291	0.54	0.5	34,738	0.48	0.5	11,331	0.34	0.47
Female	6308	0.49	0.5	5451	0.46	0.5	11,785	0.48	0.5	35,943	0.49	0.5	13,818	0.51	0.5
Age	6308	15.86	0.29	5451	15.83	0.29	11,785	15.77	0.29	35,943	15.84	0.29	13,818	15.76	0.28
Parents' education	6133			4481			11,439			34,925			12,391
Low education level	6133	0.08	0.26	4481	0.21	0.41	11,439	0.15	0.36	34,925	0.16	0.37	12,391	0.03	0.17
Average education level	6133	0.21	0.41	4481	0.25	0.43	11,439	0.42	0.49	34,925	0.14	0.34	12,391	0.32	0.47
High education level	6133	0.71	0.45	4481	0.54	0.5	11,439	0.43	0.5	34,925	0.70	0.46	12,391	0.65	0.48
Parents' occupation level	5806			4437			11,053			34,246			11,992
Low occupation level	5806	0.33	0.47	4437	0.34	0.47	11,053	0.34	0.47	34,246	0.34	0.47	11,992	0.34	0.47
Average occupation level	5806	0.34	0.47	4437	0.33	0.47	11,053	0.33	0.47	34,246	0.33	0.47	11,992	0.33	0.47
High occupation level	5806	0.33	0.47	4437	0.33	0.47	11,053	0.33	0.47	34,246	0.33	0.47	11,992	0.33	0.47
Books at home	6157			4722			11,459			35306			13,196
0–25 books	6157	0.37	0.48	4722	0.25	0.43	11,459	0.27	0.45	35,306	0.25	0.43	13,196	0.36	0.48
26–200 books	6157	0.41	0.49	4722	0.47	0.5	11,459	0.50	0.5	35,306	0.52	0.5	13,196	0.45	0.5
More than 200 books	6157	0.22	0.41	4722	0.28	0.45	11,459	0.23	0.42	35,306	0.23	0.42	13,196	0.19	0.39
e-Books at home	6110			4684			11,409			35,198			13,230
None	6110	0.80	0.4	4684	0.66	0.31	11,409	0.72	0.45	35,198	0.59	0.49	13,230	0.50	0.5
1–2 e-Books	6110	0.17	0.38	4684	0.31	0.46	11,409	0.26	0.44	35,198	0.38	0.48	13,230	0.43	0.5
3 or more e-Books	6110	0.03	0.17	4684	0.03	0.18	11,409	0.02	0.13	35,198	0.03	0.17	13,230	0.07	0.25
Immigrant status	6167	0.14	0.35	4727	0.22	0.42	11,354	0.10	0.3	34,844	0.12	0.33	12,979	0.20	0.4
Age of arrival	6177	0.51	2.29	4798	0.71	2.81	11,479	0.43	1.95	35,419	0.66	2.48	13,293	0.84	2.86
School type	6308			5451			11,785			35,943			13,818
General school	6308	0.64	0.48	5451	0.55	0.5	11,785	0.48	0.5	35,943	0.99	0.1	13,818	1.00	–
Technical school	6308	0.30	0.46	5451	0.38	0.49	11,785	0.31	0.46	35,943	–	0.01	13,818	–	–
Vocational school	6308	0.60	0.24	5451	0.07	0.26	11,785	0.20	0.4	35,943	0.01	0.1	13,818	–	–
Public school	5602	0.80	0.4	4690	0.96	0.19	11,575	0.96	0.19	34,911	0.68	0.47	11,888	0.34	0.47
Location of school	5602			4663			11,575			34,884			11,859
Location: Rural area	5602	0.03	0.16	4663	0.11	0.11	11,575	0.04	0.19	34,884	0.04	0.21	11,859	0.07	0.26
Location: Town	5602	0.75	0.43	4663	0.72	0.45	11,575	0.72	0.45	34,884	0.59	0.49	11,859	0.62	0.49
Location: City	5602	0.22	0.42	4663	0.27	0.44	11,575	0.24	0.42	34,884	0.36	0.48	11,859	0.31	0.48
Lack of infrastructures	5515	0.29	0.46	4695	0.37	0.48	11,416	0.53	0.5	34,743	0.42	0.49	11,179	0.34	0.47
Inadequate infrastructures	5515	0.28	0.45	4668	0.42	0.49	11,433	0.55	0.5	34,636	0.39	0.49	11,240	0.33	0.47

All plausible values employed. All results are weighted and replication weights are taken into account

Grade repetition is unusual in the United Kingdom but common in the other four countries, especially Spain and Germany, where 29 and 20% of students repeat grades, respectively. Educational systems also differ in the degree of tracking between schools: the age at which students are tracked for the first time is 10 years in Germany, 14 in Italy, 15 in France and 16 in the United Kingdom and Spain (in the latter, however, some of vocational schools start at 15; Woessmann 2009). The proportion of students planning to leave education early varies from about 30% in Germany (where vocational school can be attended while working part-time) to six percent in Italy. Since secondary studies can be completed at a different age in each of the five countries—compulsory education ends at the ages of 18 or 19 in Germany (depending on each länder) and at 16 in the other four countries—the definition of what is early varies with each institutional setting.

Empirical strategy

To gauge the links between remote learning and education outcomes, we test, separately for each country, the relationships between the students’ scores in mathematics and the lack of the resources needed to learn remotely by using the following specification:

$$\begin{array}{cc}\hfill \text{Test}{\text{scores}}_{\text{ij}}& ={\alpha }_1+{\beta }_1\text{No}{\text{computer}}_{\text{ij}}+{\beta }_2\text{No}{\text{internet}}_{\text{ij}}+{\beta }_3\text{No}\text{quiet}{\text{place}}_{\text{ij}}\hfill \\ \hfill & +{\beta }_4\text{No}\text{school}{\text{ICT}}_{\text{j}}+{\text{X}}_{\text{ij}}\mathrm{\Pi }+{\text{Z}}_{\text{ij}}\mathrm{\Lambda }+{\text{S}}_{\text{ij}}\mathrm{\Gamma }+{\lambda }_{\text{j}}+{\epsilon }_{\text{ij}}\hfill \\ \hfill \end{array}$$ 1

where Test score is the weighted test score in mathematics of student i in school j, No computer, No internet, No quiet place, No school ICT are the variables of interest. X_ij, Z_ij and S_ij are sets of covariates concerning, respectively, student’s characteristics, family’s socio-economic status, and the type of school attended. Specifically, the vector of student’s characteristics, X_ij, includes Female, a dichotomous variable taking value one if the student is female and zero otherwise, Age, in months, Immigrant status, the student’s status of immigration (a dichotomous variable taking value one if the student is immigrant and zero otherwise), Age at arrival in months (taking value zero if native) and Repeated grade if the student repeated one or more school years; the vector concerning the family’s socio-economic status, Z_ij, includes Parents’ education (the highest level of education among parents, HISCED in PISA), Parents’ occupation (the highest occupational status among parents, HISEI) and the number of Books and of e-Books at home; S_ij are school characteristics, denoting general, technical or professional schools, and private or public schools; λ_j are school fixed effects, and ε_ij are error terms clustered at the school level.

$$\begin{array}{cc}\hfill \text{Leaving}\text{education}{\text{early}}_{\text{ij}}^{\ast }& ={\alpha }_1+{\beta }_1\text{No}{\text{computer}}_{\text{ij}}+{\beta }_2\text{No}{\text{internet}}_{\text{ij}}\hfill \\ \hfill & +{\beta }_3\text{No}\text{quiet}{\text{place}}_{\text{ij}}+{\beta }_4\text{No}\text{school}{\text{ICT}}_{\text{j}}\hfill \\ \hfill & +{\text{W}}_{\text{ij}}\mathrm{\Pi }+{\text{Z}}_{\text{ij}}\mathrm{\Lambda }+{\text{S}}_{\text{ij}}\mathrm{\Gamma }+{\epsilon }_{1\text{ij}}\hfill \\ \hfill \end{array}$$ 2

In Sect. 5.5, we use separate Probit specifications to gauge the correlations between the probabilities of leaving education early and of repeating a grade (except for the United Kingdom, where grade repetition is uncommon) with our four variables of interest. The variable on the students’ planned length of investment in education takes value one when it stops at lower secondary studies or at upper secondary levels leading directly to the labour market, and zero otherwise.Subsequently, we use a Bivariate Probit specification to test whether the joint probabilities of planning to leave school early and repeating a school year are correlated with the lack of the resources needed to learn remotely. The Probit and Bivariate Probit specifications on leaving school early and repeating a school year are:

$$\begin{array}{cc}\hfill \text{Repeated}{\text{grade}}_{\text{ij}}^{\ast }& ={\alpha }_1+{\beta }_1\text{No}{\text{computer}}_{\text{ij}}+{\beta }_2\text{No}{\text{internet}}_{\text{ij}}+{\beta }_3\text{No}\text{quiet}{\text{place}}_{\text{ij}}\hfill \\ \hfill & +{\beta }_4\text{No}\text{school}{\text{ICT}}_{\text{j}}+{\text{W}}_{\text{ij}}\mathrm{\Pi }+{\text{Z}}_{\text{ij}}\mathrm{\Lambda }+{\text{S}}_{\text{ij}}\mathrm{\Gamma }+{\epsilon }_{1\text{ij}}\hfill \\ \hfill \end{array}$$ 3

With planning to leave education early:

$$\left\{\begin{array}{c}\text{Leaving}\text{education}{\text{early}}_{\text{ij}}=1\text{if}\text{Leaving}\text{education}{\text{early}}_{\text{ij}}^{\ast }>0\\ \text{Leaving}\text{education}{\text{early}}_{\text{ij}}=0\text{if}\text{Leaving}\text{education}{\text{early}}_{\text{ij}}^{\ast }\le 0\end{array}\right)$$

And Repeated grade:

$$\left\{\begin{array}{c}\text{Repeated}{\text{grade}}_{\text{ij}}=1\text{if}\text{Repeated}{\text{grade}}_{\text{ij}}^{\ast }>0\\ \text{Repeated}{\text{grade}}_{\text{ij}}=0\text{if}\text{Repeated}{\text{grade}}_{\text{ij}}^{\ast }\le 0\end{array}\right)$$

The error terms ε_1ij and ε_2ij are assumed to be independently and identically distributed as bivariate normal. The vector W_ij comprises the same covariates on individual characteristics included in X_ij except for Repeated grade, which is now one of the two dependent variables. Since these models are nonlinear, we do not include school fixed effects (Cameron and Trivedi 2005).

Results

Home and school resources for remote learning

Table 1 presents the results of estimating Eq. (1) with a separate sample for each country. Coefficients on our variables of interest are the differences between the scores of students unable to learn remotely and those of their peers. They can also be interpreted as proportions of school years by considering that, on average in OECD countries, the cognitive content of one school year corresponds to about 40 score points (on a mean of 500; OECD 2019). Base regressions include only our four variables of interest, No computer, No internet, No quiet place to study and No school ICT. Each column between the base and full regressions comprises also one group of covariates (included one at a time: individual characteristics, socioeconomic factors or school types). The last two columns include, respectively, all controls and all controls plus school fixed effects (detailed results are in Table S2 in the Online Appendix).

Table 1.

Remote learning resources

	France						Germany
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
	Base	Individual	Socioeconomic	School type	Full	Full—FE	Base	Individual	Socioeconomic	School type	Full	Full—FE
No computer	− 62.533***	− 41.282***	− 38.440***	− 28.252***	− 20.631***	− 19.347***	− 71.246***	− 52.432***	− 39.492***	− 57.387***	− 33.163***	− 20.849***
	(5.273)	(3.825)	(5.226)	(3.976)	(4.159)	(3.977)	(6.287)	(5.702)	(6.709)	(6.876)	(6.499)	(5.729)
No internet	− 10.569	0.162	− 18.283	− 12.905	− 15.982	− 3.937	− 51.702***	− 38.863***	− 43.308***	− 38.766***	− 28.775***	− 31.554***
	(13.691)	(11.136)	(13.760)	(10.833)	(11.530)	(13.084)	(10.515)	(10.473)	(10.907)	(10.967)	(10.549)	(10.272)
No quiet place to study	− 37.640***	− 18.175***	− 18.148***	− 16.236***	− 5.280	− 3.422	− 31.932***	− 15.253**	− 18.847**	− 22.817***	− 8.973	− 1.283
	(5.418)	(4.978)	(4.772)	(4.203)	(4.453)	(4.405)	(6.877)	(7.288)	(7.951)	(7.163)	(7.643)	(7.898)
No school ICT	− 4.631	0.610	− 3.544	− 1.488	− 0.833		− 14.058	− 16.183**	− 11.285*	− 10.539	− 12.553**
	(7.670)	(5.812)	(5.162)	(4.636)	(3.463)		(9.921)	(7.763)	(6.791)	(7.890)	(5.426)
Constant	510.761***	426.139***	519.638***	561.847***	496.900***	459.339***	523.869***	104.506	534.609***	560.337***	66.588	15.171
	(5.346)	(65.001)	(6.675)	(5.705)	(56.620)	(54.655)	(7.238)	(99.103)	(6.488)	(20.295)	(86.303)	(81.055)
Individual characteristics	No	Yes	No	No	Yes	Yes	No	Yes	No	No	Yes	Yes
Parents characteristics	No	No	yes	No	Yes	Yes	No	No	Yes	No	Yes	Yes
School characteristics	No	No	No	Yes	Yes	No	No	No	No	Yes	Yes	No
School FE	No	No	No	No	No	Yes	No	No	No	No	No	Yes
Observations	5341	5277	4889	5341	4852	4852	4077	3986	3616	4049	3544	3570
R2	0.059	0.264	0.265	0.406	0.476	0.528	0.071	0.203	0.239	0.204	0.343	0.52

	Italy						Spain
	(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)	(21)	(22)	(23)	(24)
	Base	Individual	Socioeconomic	School type	Full	Full—FE	Base	Individual	Socioeconomic	School type	Full	Full—FE
No computer	− 47.097***	− 36.129***	− 30.398***	− 31.749***	− 20.058***	− 13.635***	− 47.789***	− 15.847***	− 23.467***	− 44.420***	− 6.857*	− 6.085*
	(6.204)	(5.152)	(5.570)	(4.763)	(4.516)	(4.186)	(3.287)	(3.485)	(3.508)	(3.321)	(3.635)	(3.604)
No internet	− 43.378***	− 36.380***	− 28.543***	− 28.029***		− 4.651	− 20.642**	− 4.538	− 2.960	− 17.365**	4.770	4.300
	(10.444)	(10.515)	(9.711)	(9.213)	(9.588)	(8.729)	(8.112)	(7.840)	(8.241)	(8.046)	(7.889)	(7.925)
No quiet place to study	− 15.754***	− 8.063	− 4.177	− 5.443	3.535	1.287	− 8.917**	− 3.355	− 2.024	− 8.221*	− 0.682	0.476
	(5.554)	(5.678)	(5.768)	(5.236)	(5.575)	(5.054)	(4.176)	(4.028)	(4.329)	(4.212)	(4.154)	(4.005)
No school ICT	− 3.507	− 2.991	− 6.76	− 12.906*	− 10.031		− 5.846**	− 2.112	− 2.503	− 3.897	− 0.456
	(9.568)	(8.885)	(7.498)	(6.866)	(6.130)		(2.818)	(2.280)	(2.006)	(2.575)	(1.853)
Constant	497.262***	296.172***	514.277***	554.359***	431.558***	357.889***	489.972***	358.087***	507.958***	505.281***	364.337***	366.909***
	(6.690)	(76.540)	(6.688)	(19.812)	(70.823)	(63.723)	(2.049)	(40.661)	(3.554)	(2.848)	(41.464)	(43.433)
Individual characteristics	No	Yes	No	No	Yes	Yes	No	Yes	No	No	Yes	Yes
Parents characteristics	No	No	Yes	No	Yes	Yes	No	No	Yes	No	Yes	Yes
School characteristics	No	No	No	Yes	Yes	No	No	No	No	Yes	Yes	No
School FE	No	No	No	No	no	Yes	No	No	No	No	No	Yes
Observations	10,979	10,806	10,386	10,979	10,256	10,256	34,033	33,415	32,182	33,958	31,611	31,680
R2	0.039	0.13	0.154	0.219	0.298	0.524	0.03	0.286	0.174	0.055	0.33	0.395

	UK
	(25)	(26)	(27)	(28)	(29)	(30)
	Base	Individual	Socioeconomic	School type	Full	Full—FE
No computer	− 43.098***	− 43.256***	− 22.015***	− 42.167***	− 21.913***	− 22.253***
	(5.232)	(5.089)	(5.303)	(5.472)	(5.506)	(5.604)
No internet	− 93.290***	− 76.370***	− 67.620***	− 93.002***	− 70.242***	− 64.219***
	(15.029)	(12.407)	(15.808)	(15.088)	(17.348)	(15.487)
No quiet place to study	− 23.206***	− 21.763***	− 10.029**	− 23.419***	− 9.151*	− 8.057*
	(5.069)	(4.880)	(4.573)	(5.034)	(4.768)	(4.620)
No school ICT	− 18.617**	− 17.795**	− 12.442**	− 16.733**	− 11.229**
	(7.504)	(7.260)	(5.117)	(7.391)	(5.129)
Constant	519.002***	145.815	530.446***	526.627***	232.335**	285.673***
	(4.090)	(111.011)	(4.574)	(4.840)	(105.235)	(90.028)
Individual characteristics	No	Yes	No	No	Yes	Yes
Parents characteristics	No	No	Yes	No	Yes	Yes
School characteristics	No	No	No	Yes	Yes	No
School FE	No	No	No	No	No	Yes
Observations	10,728	10,376	9170	10,699	8930	8954
R2	0.052	0.072	0.169	0.067	0.197	0.321

Dependent variable is student’s scores in mathematics. Standard errors are clustered at the school level. ***p < 0.01, **p < 0.05, *p < 0.1. All plausible values employed. All results are weighted and replication weights are taken into account. Covariates are: gender, age in months, repeated grade, immigrant status, age of arrival as individual characteristics; highest parents’ level of education, highest parents’ level of employment, books at home, e-books at home as parents characteristics; school characteristics are technical, vocational, lyceums; public or private

Table 1 shows that the first of our variables of interest, not having a computer at home for schoolwork, is negatively and significantly associated with students’ scores in all countries and specifications. In fully controlled regressions, negative coefficients equal the loss of about half a school year in France, Germany and the United Kingdom, and a third and a sixth of a school year, respectively, in Italy and Spain (or, respectively, of 19.3, 20.8 and 22 negative score points). The size and robustness of these coefficients across countries and specifications evidence, symmetrically, that having a computer at home for schoolwork is positively associated with education outcomes. In the full regressions, the coefficients on the variable evidence the gap that remains after the indirect incidence of covariates on scores channelled by the lack of the possession of a computer has been controlled for.

To check for the possibility that these strong relationships are still driven by omitted confounding factors concerning, for example, unobserved socio-economic characteristics, we performed the Oster (2019) test statistic, δ, on our variables of interest. The Oster test assesses the coefficient stability and the potential importance of unobserved variables by comparing a regression without controls with the full regression and with a hypothetical regression that includes both the observed and unobserved controls. A value of δ greater than one implies a selection on observed that is at least as important as a selection on unobserved, and indicates a result robust to omitted variable bias. Following the approach suggested by Oster (2019), we assume a maximum obtainable R-squared equal to 1.3 times the R-squared of the full model. Our results on No computer, show that coefficients in Table 1 are robust and unlikely to be confounded by unobserved characteristics. The values of δ are 3.31 for France, 1.94 for Germany, 1.12 for Italy, 6.57 for Spain, and 14.79 for the United Kingdom. Test results on the other three variables of interest are similar.

Findings on the lack of an internet connection at home present more variability across countries. Specifically, coefficients are always negative and significant in the United Kingdom: in the fully controlled within-school regression (column 30) the education loss corresponds to more than one and a half school year (64.2 score points). In Germany results are equally robust and the fully controlled gap equals about 75% of a school year. Coefficients are significant in Italy except for the within-school regression (column 18), which indicates that differences between students in the availability of internet connections at home are correlated with the specific schools attended. However, it can also be observed that the type of school attended (column 17), before school fixed effects are included (in column 18), contributes to explain much of the variation in the coefficient with respect to the base regression (column 13). In Spain, coefficients on No internet are significant in the initial specification, but shrink and lose significance as individual characteristics are considered (columns 19 and 20). Among them, having repeated a grade has a strong and significant negative relationship with scores (Table S2). Coefficients have the expected signs in France, but are not significant.

The United Kingdom is the only country where a negative association between the lack of a quiet place to study and students’ scores is significant in all specifications. In the fully controlled regression (column 30) it corresponds to a loss in education of about 20% of a school year. In the other four countries, coefficients are significant in the base regression, but shrink and lose significance especially in relation to socioeconomic conditions and school types in France, Germany and Italy, and to grades repetition in Spain.4

Regarding schools, No school ICT is negatively and robustly associated with students’ scores, again, only in the United Kingdom. Coefficients in Germany are significant in the full regression (column 11), but not in all specifications. In both countries, attending a school without a platform for online teaching implies an education loss of almost 30% of a school year (about 12 score points). Coefficients have the expected signs in the other three countries, but their significance is weak or nil.

School locations

Among the ICT resources needed to learn remotely, those possessed by schools are as crucial as those available in students’ homes but, as evidenced by the descriptive statistics of Table A1 and Figure S1-B, are scarcer. Moreover, as seen above, coefficients on this variable are weakly significant in all countries except the United Kingdom. This low significance can hide heterogeneities at more disaggregated levels concerning, for example, school locations. Among these, since cities are generally better endowed with internet and broadband infrastructures than rural areas, it can be reasonably expected that urban schools make a higher or more efficient use of platforms for remote teaching than rural ones. Also, in urban locations, the networks of students and schools linked through online teaching can be expected to be stronger. If this is so, everything else equal, the education losses of students unable to access online classes can be expected to be bigger in these locations than in rural areas, where remote learning is less widespread. To test this hypothesis, we use the question in the School Questionnaire: Which of the following definitions best describes the community in which your school is located? to build a categorical variable, Location, where rural areas are populated by less than 3000 people, towns by a number between 3000 and 100,000 people  and cities by more than 100,000 people. Then, we interact this variable with No school ICT.

Results in Table 2 concerning the fully controlled regressions show that the coefficients on the interactions of No school ICT with Location (rural areas are in the intercept) are strongly negative and significant in Italy and the United Kingdom, and, although to a lesser degree, also in Spain. Specifically, living in a city or town positively affects scores, but attending a city or town school that does possess a platform for teaching online is associated to strong negative score gaps, which correspond to 52.4 and 48.8 negative scores in Italian cities and towns respectively, and to 32 and 36.9 in the United Kingdom. In Italy, these losses are well above a school year and in the United Kingdom to almost a year. This supports our expectation that students attending schools located where the use of digital devices is more common but that lack the resources needed to teach remotely experience larger cognitive losses than those living in rural locations, where digital education networks are less widespread. In France and Germany locations appear to matter less: neither coefficients on the interacted variables, nor on them separately, are significant. These results can be due to a more homogenous distribution of ICT resources between schools across different areas in these countries.

Table 2.

No school ICT resources and school locations

	France	Germany	Italy	Spain	UK
	(2)	(4)	(6)	(8)	(10)
No computer	− 20.743***	− 32.137***	− 20.397***	− 6.928*	− 21.742***
	(4.164)	(6.555)	(4.458)	(3.645)	(5.522)
No internet	− 15.941	− 29.524***	− 18.253*	4.903	− 70.753***
	(11.466)	(10.690)	(9.552)	(7.880)	(17.262)
No quiet place	− 5.774	− 9.581	3.363	− 0.728	− 9.465**
	(4.384)	(7.674)	(5.606)	(4.142)	(4.770)
No school ICT	− 9.136	− 74.769	35.809	12.978*	22.130**
	(17.747)	(57.093)	(22.317)	(7.560)	(10.970)
(No school ICT)*(Town)	6.745	68.319	− 43.766*	− 12.219	− 36.867***
	(18.570)	(56.759)	(24.135)	(7.819)	(12.305)
(No school ICT)*(City)	14.759	52.215	− 52.455**	− 16.131*	− 31.953**
	(20.071)	(59.479)	(24.662)	(8.628)	(14.185)
Town	− 9.278	− 43.755	18.923	0.415	18.175***
	(8.861)	(33.830)	(18.568)	(5.621)	(6.172)
City	− 11.811	− 48.963	26.013	7.799	16.740**
	(9.810)	(36.741)	(20.816)	(6.085)	(7.172)
Constant	503.277***	103.476	411.688***	360.925***	216.580**
	(57.680)	(97.967)	(71.748)	(42.264)	(104.961)
Covariates	Yes	Yes	Yes	Yes	Yes
Observations	4852	3522	10,256	31,557	8930
R2	0.476	0.351	0.299	0.331	0.199

Dependent variable is student’s scores in mathematics. Standard errors are clustered at the school level. ***p < 0.01, **p < 0.05, *p < 0.1. All plausible values employed. All results are weighted and replication weights are taken into account. The base level of Location is Rural area. Covariates are: gender, age in months, repeated grade, immigrant status, age of arrival, highest parents’ level of education, highest parents’ level of employment, books at home, e-books at home, school types (technical, vocational, lyceums; public or private)

Correlates of school fixed effects

The lack of significant coefficients on No school ICT in the full regressions of all countries except Germany and the United Kingdom could also, more generally, depend on ICT school resources being in fact proxies of other factors, such as school wealth or school characteristics. For example, if No school ICT were a proxy of school wealth, the coefficient on the variable would include the effects of schools’ infrastructures and economic resources. All these factors, together with other school characteristics, are absorbed into school fixed effects. Hence, to control whether our results on the associations between the variable No school ICT and students’ scores effectively depend on the lack of a school platform for remote teaching, we regress the coefficients of the school fixed effects (estimated from the full fixed-effects regressions of Table 1: columns 6, 12, 18, 24 and 30) on the variable No school ICT, while controlling for the other school characteristics. Coefficients on fixed effects in the full regressions measure each school’s outcome in terms of scores once all characteristics of schools and individuals have been controlled for.

Specifically, to take into account school wealth indicators, we consider two questions in the School Questionnaire: Is your school’s capacity to provide instruction hindered by any of the following issues? The first is: A lack of physical infrastructure (e.g. building, grounds, heating/cooling, lighting and acoustic systems), and the second is: Inadequate or poor quality physical infrastructure (e.g. building, grounds, heating/cooling, lighting and acoustic systems). Answers range from ‘Not at all’ to ‘A lot’. With these, we build two binary variables, Lack of infrastructures and Inadequate infrastructures, which take value one when answers are ‘A lot’ or ‘To some extent’ and zero otherwise. Other than these two variables on school infrastructures, we also control for school types and school locations.

Results in Table S3 show that, after controlling for school wealth, school types and locations, the relationship between school outcomes and students’ scores are negatively and significantly related to the lack of a platform for remote teaching across all countries. These results further support the finding in Table 1 that No school ICT has a direct relationship with school outcomes and is it not just an indirect indicator of school wealth. Moreover, they show that when platforms are available they are also effectively used; otherwise, their presence or absence would be just an indicator of other factors and, again, would not be directly correlated with school scores.

The results of Table 1, plus those on school locations and on the correlates of the coefficients on school fixed effects evidence that gaps associated to the lack of the ICT resources needed for remote schooling, No computer, No internet and No school ICT, are larger where the use of ICT resources is more widespread: among countries, in the United Kingdom, and among locations, in cities and towns. In particular, the lack of a computer for schoolwork is significant in all countries, but losses in education are bigger where their use is more widespread: United Kingdom, Germany and France. Together, these results are consistent with the existence of technological network externalities in education.

Gelbach decomposition

Results in Table 1 and Table S2 show that coefficients on our four variables of interest vary across specifications as the different groups of covariates are included into the regressions. They also show also that coefficient variations are not driven by the same sets of covariates across countries. For example, when compared with the base regressions, coefficients on the variables of interest in France vary more with school types (Table 1, column 4) than with other covariates, while in the United Kingdom they vary especially with socioeconomic factors. However, while these and other gap variations can be directly observed in Table 1, their relationships with covariates can be precisely computed by using the Gelbach (2016) decomposition method. It shows how much of the variation of coefficients from the base to the full regressions are due to each cofactor, while at the same time, it is independent from the order in which covariates are added to the regressions. Table 3 shows the decomposition of coefficient variations in relation to the three groups of covariates—concerning individual, socioeconomic and school factors—while Table S4 in the Online Appendix presents detailed results on each variable.

Table 3.

Gelbach decomposition by country

	∆ coefficient	Individual	(%)	Socioeconomic	(%)	School	(%)	Total explained
		(1)		(2)		(3)		(4)
France	No computer	− 5.18***	11.54	− 14.77***	32.90	− 24.94***	55.56	− 44.89***
	No internet	− 0.25		6.06		0.6		6.41
	No quiet place to study	− 6.21***	20.53	− 9.06***	29.95	− 14.98***	49.52	− 30.25***
	No school ICT	− 1.17		− 0.6		− 2.14		− 3.92
Germany	No computer	− 7.65***	20.92	− 20.47***	55.97	− 8.46***	23.13	− 36.57***
	No internet	− 10.18*	46.89	− 4.98	22.94	− 6.55**	30.17	− 21.71**
	No quiet place to study	− 9.13***	31.31	− 13.85***	47.50	− 6.18**	21.19	− 29.16***
	No school ICT	1.06		− 2.87		− 4.16		− 5.98
Italy	No computer	− 3.32**	14.41	− 8.18***	35.50	− 11.54***	50.09	− 23.04***
	No internet	− 3.63	14.94	− 8.34***	34.32	− 12.34**	50.78	− 24.30***
	No quiet place to study	− 3.52**	20.34	− 5.43***	31.37	− 8.37***	48.35	− 17.31***
	No school ICT	− 2.24*		2.14		7.54*		7.45
Spain	No computer	− 26.28***	62.45	− 14.96***	35.55	− 0.84**	2.00	− 42.08***
	No internet	− 15.83***	60.08	− 10.11***	38.37	− 0.42	1.59	− 26.35***
	No quiet place to study	− 3.86***	49.42	− 3.78***	48.40	− 0.17	2.18	− 7.81***
	No school ICT	− 3.67***	53.34	− 2.60***	37.79	− 0.62	9.01	− 6.88***
United Kingdom	No computer	0.33	− 1.70	− 18.95***	97.63	− 0.8	4.12	− 19.41***
	No internet	3.07		− 13.94**		− 1.7		− 12.58
	No quiet place to study	− 1.60*	11.39	− 12.71***	90.46	0.26	− 1.85	− 14.05***
	No school ICT	− 0.27	3.71	− 5.64**	77.47	− 1.37	18.82	− 7.28**

The dependent variable is computed as the average of the ten plausible values in mathematics. Standard errors are clustered at the school level. ***p < 0.01, **p < 0.05, *p < 0.1. All results are weighted. Covariates, indicated in column headers are: Individual factors: gender, age (in months), repeated grade immigrant status, age of arrival; socioeconomic: highest parents’ level of education, highest parents’ level of occupation, books and e-books at home; School includes: types (general, technical, vocational), public or private, and location (city, town or rural)

Table 3 evidences that in France, about 56 and 50% of the variations between the base and the full model of the coefficients on No computer and No quiet place, respectively, are due to school characteristics (column 3). Likewise, in Italy, about 50% of the variations in the coefficients on the variables concerning home resources are related to school types. In both countries, socioeconomic factors have a smaller but also important role: they explain about 30% of the variation of coefficients. In Germany, variations in the scores’ gaps related to No computer and No quiet place are especially due to socioeconomic covariates (about 50%, column 2), while variations of No internet coefficient are especially linked to school types and individual characteristics (among which the age of arrival of immigrant students, Table S4). Hence, in countries where tracking starts earlier, France, Italy and Germany, school type variables contribute considerably to explain variations in remote learning gaps. How this happens is shown in detail in the columns concerning General, Technical and Vocational school in Table S4. Interestingly, the negative variation is entirely due to the schools best endowed and with the highest average education levels, which are the general schools, or lyceums. In our data, students who lack the resources needed to learn remotely are also more likely to attend technical and vocational schools, but Table S4 shows that students who lack a computer or a quiet place to study and attend schools where they are common, i.e. lyceums, experience the highest losses in education. This finding is similar to the one seen above regarding cities and rural areas, and is also consistent with the role of technological networks in education.

In Spain, individual characteristics (and among them, especially grades repetition, Table S4) explain coefficients’ variations more than in other countries, while socioeconomic factors follow. This indicates that students in Spain who are unable to learn remotely because of a lack of resources are also more likely to repeat grades. These results are consistent with the country’s system of comprehensive schools combined with a high frequency of grades retention. Finally, variations of the four coefficients, from the base to the full model, are small in the United Kingdom, but are mostly due to socioeconomic factors, which contribute to explain about 90% of the total variations. Specifically, Table S4 shows that important among them are the jobs and cultural status of parents (proxied by the number of books at home). In turn, this is consistent with the late tracking and low frequency of grade retention of the country.

Interestingly, across countries, being an immigrant student explains more of the variations in the coefficients on No computer or No quiet place than of those on No internet (Table S4). A possible explanation of this discrepancy that immigrant families tend to maintain communication links with people in their home country and, therefore, have a higher access to internet than expected. Another individual variable that leads to somewhat unexpected results is gender. Being female is always negatively correlated with the outcome in mathematics (Table 1), but it counteracts the negative variation of the coefficient on No computer. This can be seen in Table S4, where the coefficient on the female variable is always positive, and is significant in France, Germany and Spain. This is partly due to an average possession of computers for schoolwork that in all countries is higher for females than for males. However, both characteristics, gender and immigrant status explain very small portions of the variation of the coefficients on the variables of interest, smaller than that explained by school types or parents’ occupations.

In sum, results up to now show that the gaps in mathematics due to the lack of resources needed to learn remotely are partly explained by covariates, such as school locations, school types, socioeconomic factors or individual characteristics, in proportions that can vary across countries, but also that, after all their effects have been considered, part of the direct correlations between the lack of the resources needed to learn remotely and education outcomes remains strong and significant.

Repeating grades and planning to leave education early

Not being able to learn remotely can have longer run consequences than those on score gaps. For example, students unable to attend online classes who see their scores falling considerably below those of their peers may form pessimistic expectations regarding the length of their future education. They may plan to drop out of school altogether, or to stop studying when completing their compulsory schooling cycle of secondary school. As already said, we use the question Which of the following do you expect to complete? with which we build a dummy variable taking value one if the student expects to complete at most the lower secondary (ISCED level 2) or upper secondary levels providing direct access to the labour market (ISCED levels 3C or 3B), and zero if the student plans to complete higher levels. Moreover, if falling behind may reduce students’ planned investments in education, repeating grades may reinforce these plans. Hence, we expect students unable to attend remote learning to be more likely to plan to cut their planned investments in education early if they are also likely to repeat grades.

We first test separately whether our four variables of interest are associated with the probabilities of forming plans to stop education early and with repeating, and, second, we test whether they are correlated with the joint probabilities of the two events. As stated in Eqs. (2) and (3) above, we use Probit specifications for the first two tests and Bivariate Probit regressions for the latter. In the Probit specification, the coefficients of the marginal probabilities on each variable of interest are in columns 1 to 4 of Table 4. The base regressions include only our four variables of interest, while the full specifications control for all covariates of Eqs. (2) and (3). The results on the Bivariate Probit regressions are in columns 5 and 6. The Rho coefficients report the correlation between the residuals of the regressions having Leaving education early and Repeated grades as dependent variables.

Table 4.

Repeating grades and planning to leave education early

Dependent variable:		Probit								Bivariate probit
		Leaving education early				Repeated grade				Leaving education early &  Repeated grade
		Base		Full		Base		Full		Base		Full
		(1)		(2)		(3)		(4)		(5)		(6)
France	No computer	0.06**	(0.025)	0.02	(0.021)	0.179***	(0.028)	0.02***	(0.008)	0.04***	(0.009)	0.01	(0.001)
	No internet	0.01	(0.046)	0.01	(0.50)	0.02	(0.045)	0.00	(0.015)	0.00	(0.008)	0.00	(0.001)
	No quiet place to study	0.02	(0.021)	− 0.01	(0.02)	0.119***	(0.024)	0.00	(0.008)	0.02***	(0.006)	0.00	(0.001)
	No school ICT	0.01	(0.013)	0.01	(0.01)	0.04	(0.03)	0.01	(0.011)	0.00	(0.004)	0.00	(0.001)
	Rho									0.01	(0.04)	− 0.26***	(0.06)
	Predicted mean y1, y2	0.12		0.11		0.14		0.07		0.10		0.05
	Observations	5128		4718		5330		4852		5121		4716
Germany	No computer	0.24***	(0.036)	0.09**	(0.036)	0.13***	(0.036)	0.04	(0.028)	0.13***	(0.028)	0.04**	(0.015)
	No internet	0.17**	(0.083)	0.11**	(0.083)	0.07	(0.053)	0.03	(0.060)	0.07*	(0.043)	0.03	(0.031)
	No quiet place to study	0.08**	(0.040)	0.08**	(0.040)	0.09***	(0.031)	0.04	(0.031)	0.06***	(0.022)	0.01	(0.013)
	No school ICT	0.01	(0.046)	− 0.01	(0.035)	0.00	(0.029)	− 0.02	(0.022)	0.00	(0.021)	− 0.01	(− 0.001)
	Rho									0.42***	(0.038)	0.24***	(0.039)
	Predicted mean y1, y2	0.31		0.19		0.19		0.13		0.10		0.05
	Observations	3778		3370		4017		3544		3770		3367
Italy	No computer	0.06***	(0.018)	0.03**	(0.013)	0.09***	(0.024)	0.04*	(0.019)	0.03***	(0.01)	0.01**	(0.005)
	No internet	0.02	(0.023)	0.00	(0.016)	0.04	(0.040)	0.01	(0.032)	0.01	(0.01)	0.00	(0.004)
	No quiet place to study	0.03**	(0.013)	0.00	(0.001)	0.07***	(0.021)	0.03*	(0.017)	0.02***	(0.006)	0.00	(0.003)
	No school ICT	0.01	(0.001)	0.01	(0.001)	0.00	(0.016)	0.02*	(0.001)	0.00	(0.004)	0.01*	(0.001)
	Rho									0.49***	(0.049)	0.34***	(0.051)
	Predicted mean y1, y2	0.07		0.04		0.13		0..09		0.03		0.01
	Observations	10,438		9820		10,962		10,256		10,431		9817
Spain	No computer	0.15***	(0.013)	0.05***	(0.008)	0.31***	(0.017)	0.186***	(0.018)	0.148***	(0.011)	0.05***	(0.007)
	No internet	0.04***	(0.013)	0.01	(0.010)	0.15***	(0.03)	0.07**	(0.03)	0.047***	(0.011)	0.01*	(0.007)
	No quiet place to study	0.03***	(0.01)	0.015**	(0.008)	0.05***	(0.016)	0.01	(0.015)	0.025***	(0.007)	0.01**	(0.005)
	No school ICT	0.01	(0.001)	0.00	(0.005)	0.04***	(0.013)	0.02**	(0.011)	0.01**	(0.005)	0.00	(0.003)
	Rho									0.90***	(0.049)	0.76***	(0.029)
	Predicted mean y1, y2	0.08		0.08		0.25		0.03		0.07		0.07
	Observations	33,041		30,801		34,004		31,611		33,030		30,795
United Kingdom	No computer	0.14***	(0.02)	0.07***	(0.014)
	No internet	0.13*	(0.073)	0.01	(0.038)
	No quiet place to study	0.07***	(0.02)	0.04**	(0.02)
	No school ICT	0.03**	(0.013)	0.01	(0.009)
	Predicted mean y1, y2	0.15		0.13
	Observations	10,271		8721

The dependent variables, Leaving education early (y1) and Repeated grade (y2)are dichotomous variables taking, respectively, value one when the student plans to leave education early and zero otherwise, and value one when grades are repeated and zero otherwise. Rho coefficients report the correlation between the residuals of the regressions having Leaving education early and Repeated grades as dependent variables. Standard errors are clustered at the school level. ***p < 0.01, **p < 0.05, *p < 0.1. All plausible values employed. All results are weighted and replication weights are taken into account. ‘Base' columns 1, 3 and 5 include only the variables of interest, while 'Full' columns 2, 4 and 6 include all covariates of Eqs. (2) and (3). Margins are computed at mean values of covariates

Results from Table 4 show that in all countries the lack of ICT resources, especially No computer, significantly increase the separate probabilities of repeating grades (except for the United Kingdom) and of planning to leave education early. In the full regressions of columns 2 and 4, No computer increases the probability of repeating a grade in France by two percentage points (from the average probability of seven percent, shown by the predicted mean of Repeated grade, in column 4). In Germany it rises the probability of planning to leave education early by nine percentage points (the average being 19%; column 2), while the joint probability of planning to leave education early and repeating a grade rises by four percentage points (on an average of 24%; column 6). In Italy, No computer is associated with a higher probability of planning to leave education early that corresponds to three percentage points and repeating a grade to four, while it increases their joint probability by one percentage point. Similar results on the joint probabilities apply to No school ICT. In Spain most coefficients on our variables of interest are strong and significant. In the fully controlled regressions, No computer is associated with an increase in the joint probability of repeating a grade and planning to leave education early of five percentage points, No internet and No quiet place are related to increases of one percentage point. The Rho coefficient, indicating the degree of correlation between the two probabilities is higher than in the other countries. Finally, in the United Kingdom, No computer and No quiet place to study increase the probability of planning to leave school early by seven and four percentage points, respectively.

In sum, being unable to learn remotely is strongly associated with grades repetition, except for the United Kingdom, and with students planning to leave school early. Moreover, it is correlated with the joint probability of both events in the three countries where grades repetition is more frequent, namely Germany, Italy and Spain.

Sensitivity and further robustness checks

The wide range of controls included in Table 1, the corroborating results of the Gelbach decomposition, Oster tests and subsequent checks on school types and characteristics support the robustness of our findings. However, to further check that the coefficients on our variables of interest are not in fact driven by unobserved family’s socioeconomic factors we interacted our variables of interest with three different levels of these covariates. The underlying hypothesis is that if coefficients on our variables of interest were just absorbing the effect on scores of family conditions, then the coefficients on the variables interacted with a low socioeconomic status level would be negative, indicating that their relationship with scores worsens when socioeconomic conditions are low, while the opposite would hold for higher levels.

Table S5 in the Online Appendix reports the coefficients of all our variables of interest interacted with three proxies levels of income: parents’ education, parents’ jobs, and number of books and of e-books at home. The intermediate socioeconomic status is in the intercept. Results show that coefficients on the interacted variables are mostly non-significant, and in the few cases in which they are, their signs do not support the above hypothesis and in several cases go against it.5Among socioeconomic indicators, we also controlled for the number of cars owned by the student’s family, but since this variable entails a substantial loss of observations, we chose not to include it among the covariates of Table S5.6

Another possibility is that lacking the resources needed for learning remotely might matter less when neither the school the student attends possesses ICT tools for education. In this case, the inequality within schools deriving from the scarcity of resources at home should weaken, while that between schools can persist. We tested this hypothesis by interacting the variable No school ICT with the other three variables of interest, but found that the coefficients on these interactions are generally non-significant. As shown in Table S6, one exception is Italy, where in the full regression the coefficient on the interaction of No internet at home and No school ICT is positive and significant (column 5). As expected, not having an internet connection at home is correlated with a smaller gap in education when, everything else given, the school attended does not make use of ICT resources for teaching. Even in the case of Italy, however, when school fixed effects are included into the regression, both coefficients, on No internet and on its interaction with No school ICT shrink and become non-significant (column 6).7

In further checks of the robustness of our findings, we repeated our regressions with supplementary sets of covariates, comprising language spoken at home, different types of ICT resources available at school, and teachers’ digital training. Moreover, we substituted the dependent variable with the scores in reading, and rerun all regressions. Both for mathematics and reading,  repeated all tests with balanced samples based on the observations of the full regressions. Next, we repeated the mafter imputing the values of the missing observations in the full samples. All these checks provided support for our main results and are available upon request.

Conclusions

This study uses PISA 2018 data on mathematics from five European countries to investigate whether education inequalities can be related to the lack of the resources needed to learn remotely—a computer for schoolwork, an internet connection, a quiet place to study, a school with a platform for online teaching—. After controlling for a wide set of cofactors, fixed effects and different specifications, we find that students lacking these resources score significantly below their peers. Symmetrically, and differently from previous studies pointing at negative or null effects of the use of computers or internet in schooling (Leuven et al. 2007; Malamud and Pop-Eleches 2011; Vigdor et al. 2014; Carter et al. 2017), we find that the relationships between remote learning and education outcomes, both at the students’ and schools’ levels, are positive and significant.

Part of the negative gaps are explained by education systems, school types, locations and individual or socioeconomic factors, with the importance of each of them varying across countries. In cities, the use of ICT resources for schooling is more common than in towns and rural areas, and in countries with early tracking, general schools (lyceums) are better endowed, but both register the larger negative gaps of students unable to learn remotely. In countries with late tracking, socioeconomic and individual factors play a more direct role in explaining gap variations, but, also in this case, the correlation is stronger for students with better-off families who lack the resources needed for online learning. Further results from our research show that education inequalities can have long-lasting consequences, especially in countries where grade retention is more frequent. Students not possessing the resources needed for learning remotely and repeating grades are more likely to plan to end their education early or/and drop out from school.

These findings point to a more general result: there are technological network externalities in remote and online learning that make the losses of outsiders larger as it spreads and becomes an integral part of education. The positive correlation between the use of these resources and average education levels together with the fact that gaps can remain significant even after all cofactors have been controlled for, imply that even in non-pandemic times governments must decisively promote the use of remote learning at a general level, and at the same time especially focus on those students and schools that lack the resources needed to participate into it. The nature of externalities implies that low-level education equilibria, where both schools and students lack these resources, are self-sustaining. The Covid-19 pandemic accelerated the use of remote learning in several countries but spread unevenly across areas, schools and families, which makes the need of corrective policy actions now even stronger than before.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Appendix

6.