Abstract

RGE

Revista Galega de Economía

1132-2799 2255-5951

Universidade de Santiago de Compostela

España sepinter@usc.es

10840

https://doi.org/10.15304/rge.35.1.10840

Articles

From educational reforms to skills in the labour market: the case of Spanish adults

Das reformas educativas ás competencias no mercado laboral: o caso dos adultos españois

https://orcid.org/0009-0006-9817-1036

Ávila Gómez

Irene Inés

Conceptualization Methodology Analysis and interpretation Writing – Preparation of the draft Software ¹ ^a

https://orcid.org/0000-0002-0906-3206

López Agudo

Luis Alejandro

Methodology Analysis and interpretation Writing – Review & Editing ¹ ^b

https://orcid.org/0000-0003-0939-5064

Marcenaro Gutiérrez

Óscar David

Conceptualization Data acquisition Analysis and interpretation Writing – Review & Editing ¹ ^c

¹ Department of Applied Economics (Statistics and Econometrics). University of Malaga, Málaga University of Malaga Department of Applied Economics (Statistics and Econometrics) Spain

Málaga

29013

^a ireneavilagomez@uma.es ^b lopezagudo@uma.es ^c odmarcenaro@uma.es

2026

30 05 2026

35 1

10840

05 08 2025 12 03 2026

2026

Universidad de Santiago de Compostela

https://creativecommons.org/licenses/by-nc-nd/4.0/

This is an open access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) License

Abstract

This study examines the long-term consequences of early school leaving and years of education on adult cognitive skills in Spain. Using an instrumental variable approach that leverages historical policy reforms—introducing minimum compulsory dropout school-leaving ages of 14 and later 16—we isolate the influence of dropout and education on literacy and numeracy skills. The analysis of data from the Programme for the International Assessment of Adult Competencies (PIAAC) 2012 and 2023 reveals that, when accounting for bias due to endogeneity, early school leavers may suffer significant declines in cognitive performance, with literacy scores dropping 1.72 standard deviations (SDs) and numeracy scores falling by 1.64 SDs. Furthermore, 1 year of additional education (above the average) appears to significantly raise cognitive performance by 0.26 SDs in literacy and 0.21 SDs in numeracy. However, we remain cautious with the interpretations, as secular trends may be present in our instrument. Associations reinforce that the accumulation of formal education is essential for skill development, emphasising the need for policies aimed at reducing (increasing) dropout rates (years of education) of the population, while considering the heterogeneity across socio-economic groups.

Resumo

Este estudo examina as consecuencias a longo prazo do abandono escolar prematuro e os anos de escolarización nas habilidades cognitivas dos adultos en España. Mediante un enfoque de variables instrumentais que aproveita as reformas políticas históricas —a introdución de idades mínimas de escolarización obrigatoria de 14 e, posteriormente, de 16 anos—, illamos a influencia do abandono escolar e a educación nas habilidades de lectura, escritura e aritmética. A análise dos datos do Programa para a Avaliación Internacional das Competencias dos Adultos (PIAAC) de 2012 e 2023 revela que, ao ter en conta o rumbo debido á endoxeneidade, as persoas que abandonan prematuramente a escola poden sufrir un descenso significativo no seu rendemento cognitivo, cunha caída de 1,72 desviacións estándar (DE) nas puntuacións de alfabetización e de 1,64 DE en as de aritmética. Ademais, un ano de educación adicional (por encima da media) parece elevar significativamente o rendemento cognitivo en 0,26 DE en alfabetización e 0,21 DE en aritmética. Con todo, mantémonos cautelosos coas interpretacións, xa que poden existir tendencias seculares no noso instrumento. As asociacións reforzan a idea de que a acumulación de educación formal é esencial para o desenvolvemento de habilidades, o que pon de relevo a necesidade de políticas destinadas a reducir (ou aumentar) as taxas de abandono escolar (ou os anos de educación) da poboación, tendo en conta ao mesmo tempo a heteroxeneidade entre os distintos grupos socioeconómicos.

Keywords Educational reform Dropout Literacy skills Numerical skills Instrumental variables

Palabras chave Reforma educativa Abandono escolar Habilidades de lectura e escritura Habilidades numéricas Variables instrumentais

JEL Classification I21 C21

Fundación Bancaria BBVA - Programa Prismas y Problemas 2023

PPRO-SEJ645-G-2023

Fundación Ramón Areces

PPRO-SEJ645-G-2023

Andalusian Regional Government

PPRO-SEJ645-G-2023

1. INTRODUCTION

Education has proven to be a key factor in shaping people's position in the labor market and, consequently, its impact on the development of cognitive skills has attracted increasing attention in the Economics of Education research field over recent decades. In particular, understanding how early school leaving and the accumulation of formal schooling years affect later-life competencies such as numeracy and literacy is essential – not only for academic inquiry but also for designing effective public policies. This paper seeks to examine the influences of early dropout and total years of education on cognitive skills among Spanish adults, using the two available datasets from the 2012 and 2023 cycles of the Programme for the International Assessment of Adult Competencies (PIAAC).

In this context, Spain has experienced considerable educational reforms. Specifically, two major legislative changes, the LGE (Ley General de Educación) and the LOGSE (Ley Orgánica de Ordenación General del Sistema Educativo) – have fundamentally restructured the compulsory education system in the country. Whereas under the previous LEP (Ley de Enseñanza Primaria) and LOE reform (Ley Orgánica del Derecho a la Educación) there was no minimum dropout age (BOE, 1945; BOE, 1953), the LGE and LOGSE established minimum dropout ages of 14 (BOE, 1970) and 16 (BOE, 1991). These reforms seem to generate a source of exogenous variation in educational attainment that provide an opportunity to disentangle the influence of education on cognitive outcomes through an instrumental variable (IV) approach.

The relevance of this research is further underscored by striking national statistics. According to the latest data from the National Institute of Statistics (INE, 2025), Spain’s dropout rate among individuals aged 18 to 24 has declined from 30.9% in 2002 to 13% in 2024; however, even with this improvement, dropout rates remain approximately 3.5 percentage points higher than the European Union average (INE, 2025), with recent research also highlighting that ethnically marginalised students are particularly affected by these high dropout rates in Spain (Moreira et al., 2023).

Furthermore, it seems necessary to distinguish between the impacts of categorical educational failure – such as not completing lower secondary education – and marginal reductions in educational exposure – losing one year of formal schooling – could be particularly crucial for developing targeted policy interventions. For instance, while both scenarios generally represent educational shortfall, they may operate through different mechanisms that require distinct policy responses. While not completing lower secondary education represents a fundamental disruption to the educational trajectory, which may potentially affect not the quantity of learning and the access to subsequent educational opportunities and social networks; losing a single year of schooling may primarily affect the accumulation of specific skills and knowledge without necessarily altering the structural pathways through the education system.

This research makes several key contributions to the existing literature. First, unlike previous studies that typically rely on a single educational law as an instrument and analyse smaller portions of available data, this study utilizes all four major Spanish educational reforms across the full available birth cohort range (1947-2004), providing greater statistical power and more comprehensive coverage of policy variation. Additionally, this research explicitly differentiates between the effects of categorical dropout and the marginal impact of losing one year of education – a distinction that has not been largely studied in prior work. Finally, by employing instrumental variables methodology, the study aims at addressing the potential endogeneity concerns in educational attainment that may bias conventional estimates. This comprehensive approach allows us to address two persistent questions:

Is early school dropout negatively associated with literacy and numeracy skills in adulthood?

What is the return to an additional year of schooling in terms of later-life literacy and numeracy skills?

Two questions that can have far-reaching implications for both the formulation of educational policies and the broader understanding of human capital development and labour market mismatch.

This paper proceeds as follows: we first examine the existing literature on this topic, then describe our data sources and methodological framework. After presenting our empirical findings, we compare these results with previous research and discuss their relevance for policy formulation.

2. LITERATURE REVIEW

The relationships between education and the development of cognitive skills has long been a subject of research with numerous studies showing that formal schooling helps students become more proficient in numeracy and literacy competencies. The influential research by Hanushek (2009) has established that education is a key determinant in the development of cognitive skills, a finding that has been reinforced by more recent studies, although recent research by Calero et al. (2019) demonstrates that the effectiveness of converting schooling into cognitive competencies varies significantly across both education levels and birth cohorts, suggesting that schools have become more effective at developing cognitive skills over time across consecutive generations, with intermediate education levels showing more stable improvements compared to higher education.

When using large-scale assessments to analyse this issue, particularly PIAAC, many studies for the Spanish case have enriched our understanding of the determinants and long-term impacts of education. For instance, Montes-Pineda et al. (2021) provide updated evidence on how variations in early formal education translate into variations in cognitive performance. Furthermore, Brindusa et al. (2020) demonstrate that Spain’s cognitive skills gap relative to other European Union countries stems significantly from differences in educational attainment and socio-economic background, with these factors explaining approximately one-third and one-fourth of the gap, respectively. Their findings reveal that these disparities are particularly pronounced at the lower end of the skill distribution, where educational and socio-economic disadvantages compound to create larger performance gaps. This literature underlines that more education generally translates into better outcomes in later life, although it is important to consider its quality for an effective and immediate skill acquisition (Benito & Romera, 2020).

Another important strand of the international literature examines the determinants of school dropout and its subsequent impact on cognitive development in western countries. The literature consistently finds that individuals who do not complete at least compulsory education tend to exhibit lower levels of cognitive proficiency. Early work by Vaughn et al. (2010) provided evidence for the United States on how dropout is associated with diminished skill formation later in life, which may result in lower earnings (Tyler et al, 2000). Furthermore, it has been linked to an increase in the likelihood of substance abuse in the same country (Reingle Gonzalez et al., 2016) and criminal activity among men in Sweden (Bäckman, 2017). These studies have emphasised that dropout not only affects immediate educational outcomes, but also has long-lasting consequences on labour market and life performance.

However, the endogeneity of education is a methodological issue that has been present throughout the research in the field. Unobserved factors such as innate ability or family background may simultaneously influence both educational attainment and cognitive outcomes. While this concern has been extensively documented in the broader economics of education literature regarding earnings returns (e.g. Griliches, 1977 for the case of the United States), similar methodological challenges apply to studies examining cognitive skills, as individuals with higher unobserved ability may be more likely to both pursue additional education and perform better on cognitive assessments.

To address this issue, several studies have implemented instrumental variables approaches using exogenous policy changes as instruments and PIAAC 2012 data. For example, Marcenaro-Gutiérrez and Lopez-Agudo (2024) for Spain use the LGE reform in a regression discontinuity framework to estimate the influence of dropout, finding a negative association of dropout with literacy and numeracy skills of around 1.5 standard deviations. Furthermore, Cappellari et al. (2024) exploit variations in exposure to educational reforms across birth cohorts and the participating countries of PIAAC (including Spain) using a recursive model, to show that an extension of 1 standard deviation in schooling was positively associated with a 22% increase in earnings, although these returns vary significantly by socio-economic background.

Along these lines, the potential impact of educational reforms on educational outcomes also needs consideration. Robles-Zurita (2017) exploits the variability in the rate of implementation of the LOGSE in Spain among cohorts and regions and found a non-significant effect on cognitive outcomes. In contrast, Bellés-Obrero and Duchini (2021) employ a cohort fixed effect model and found a significant positive effect of the LOGSE on occupational outcomes in Spain, only for middle and high skilled individuals.

Furthermore, an experiment by Green and Navarro-Paniagua (2012) suggest that raising the compulsory school leaving age may negatively affect teacher effort in Spain, thereby influencing the overall quality of education received and implying that policy reforms might have unintended consequences that could bias estimates of the returns to education, if not properly accounted for. In this vein, Psacharopoulos and Patrinos (2018) and Psacharopoulos (2024) argue that externalities and institutional factors can bias estimates by increasing the size effect of instruments constructed with past cohorts, which may be capturing trends in the economy along with the returns to education. For instance, they mention the work by Brinch and Galloway (2012), which found that a change in a national educational law in Norway during the 1960s that raised the compulsory school leaving age from 7 to 9 years old, had an important raise in the IQ of the students when they were 19 years old, suggesting that schooling affects general ability. This dilemma will be considered in our paper, accounting estimates as associations and not as causal interpretations, as we will describe.

Finally, in addition to methodological improvements the literature also emphasises the importance of controlling for socio-economic factors that potentially mediate this effect. For instance, Bussolo et al. (2023) demonstrated that family background appears to remain as a critical determinant of the likelihood of dropping out and later occupational outcomes in European countries. Similarly, Fernandez-Enguita et al. (2010) and Serrano et al. (2013) highlighted the significant role of the Spanish socio-economic disparities in shaping educational outcomes, and Leist et al. (2021) found that greater inequality in educational opportunities is associated with lower levels of cognitive functioning across Europe, reinforcing the necessity of accounting for these variables when estimating the returns to education, including in terms of cognitive skills.

In summary, the literature reviewed establishes a link between educational attainment and adult cognitive skills in the field of Economics of Education, while recognising the need of isolating causal pathways, and controlling for factors that may affect the outcome variables through the predicted channels of our variables of interest. Furthermore, existing research has largely overlooked the distinction between categorical dropout and the loss of a single year of education, a gap that this study directly addresses. By leveraging a broader set of policy instruments and the available PIAAC cycles, the present research contributes to a more nuanced understanding of how the Spanish historical trajectories in the compulsory education system shape cognitive development across the life course, with direct implications for the design of inclusive and effective public policy.

3. MATERIALS AND METHODS

The data used for our analysis is that from the Programme for the International Assessment of Adult Competencies (PIAAC), an international study led by the OECD that seeks to examine the educational and socio‐labour characteristics of the working‐age population (16 to 65 years) across countries and link these traits to the application of key skills; particularly in literacy, numeracy, and adaptive problem-solving. To this date, PIAAC has conducted two rounds: the first round (OECD, 2013a) involved 25 participating countries and collected data between September 2011 and May 2012, the second round (OECD, 2025) expanded to 31 countries, with data collection spanning from September 2022 to June 2023.

According to PIAAC Technical Report (OECD, 2013b; OECD, 2025), PIAAC’s sampling process consisted of a stratified multistage clustered area sample with a self-weighted design with three sampling stages on census sections, dwelling units and persons. Specifically, Spain used a population registry, as its sampling frame for the first two sampling stages only and used a household screener for the third sampling stage, with a 0.5% of the targeted population not being covered by main study sampling frames, corresponding to those living in dangerous areas. The sample selection followed a stratified and multi-stage probabilistic design. The first stage consisted of selecting census sections using systematic sampling with probability proportional to size from a sorted list within explicit strata (stratification was done by autonomous community and municipality size, with implicit stratification applied by sorting by province, income level, and dwelling size). In the second stage, dwellings were selected by the use of systematic random sampling. In the third and final stage, eligible individuals within households were selected by simple random sampling (eligible individuals were ordered by age before random selection).

The estimating process for competencies was based on item response theory, multivariate Rasch models, and OECD scaling process, creating 10 plausible values for each domain (literacy, numeracy and adaptive problem solving in 2023); more information on this procedure can be found in OECD (2013b) and OECD (2025).

The sampling error is estimated in PIAAC sample using Balance Repeated Replication Methods with Fay’s adjustment and replicate weights. Furthermore, the survey accounts for sample measurement error based in latent skill estimates using plausible values, also arising from imputation procedures and potential measurement errors by language of assessment.

Using these data, this study focuses on how early school dropout, and an extra year of schooling are associated with later-life outcomes in Spain, specifically literacy and numeracy skills, using a sample confined to individuals born between 1947 and 2004. This filter ensures that respondents have had sufficient time to complete their formal education, as those born after 2004, during the 2011-2012 and 2022–2023 data collection, were still in the process of completing their education, which could confound dropout with ongoing studies.

In PIAAC 2012 survey for Spain, 5,971 participants were selected from the standard age range of 16 to 65 years, while for PIAAC 2023 the number of individuals participating in the survey was 5,871. This yields a representative cross-section of the adult population in Spain of 11,842 individuals. The datasets comprise detailed information from two primary components: a cognitive assessment and an extensive background questionnaire. The cognitive assessment evaluates participants’ literacy and numeracy skills through several tests that provide standardised scores to facilitate cross-country comparisons. By contrast, the background questionnaire collects comprehensive data on socio-economic characteristics, the development and maintenance of cognitive skills, and the use of information and communication technologies (ICTs).

For our analysis, the outcome variables include standardised literacy competence scores and standardised numeracy competence scores, facilitating international comparisons². Key explanatory variables involve dropout status, years of education, gender, immigrant status, and a standardised Economic, Social, and Cultural Status (ESCS) index, which incorporates socioeconomic variables that are available in both databases: parental education levels (for both father and mother) and the number of books available at home when the respondent was 14. Finally, the model controls for the respondent’s Spanish autonomous region³. To preserve the chronological ordering, outcome variables measured in 2012 or 2023 are analysed alongside control variables collected at earlier stages of the respondents’ lives.

A central innovation of our study is the exploitation of exogenous variations in dropout behaviour arising from four pivotal educational reforms in Spain that cover all the available sample cohort ages. Specifically, our analysis leverages shift in compulsory education – from a non-mandatory system under the Law of Primary Education (LEP, adopted in 1945) and the Organic Law on Education (LOE, adopted in 1953), to the introduction of a dropout age of 14 under the 1970 General Education Law (LGE), and finally to the extension of compulsory education until age 16 following the 1990 Organic Law for the General Organization of the Educational System (LOGSE). This approach could bring us closer to isolating the influence of education on later-life cognitive outcomes.

Furthermore, it is important to note that, due to variations in the implementation of these reforms across Spain’s autonomous communities and schools (e.g. Robles-Zurita, 2017), the birth-year cut-offs do not align with the formal enactment dates of these laws that can be found in their official implementation calendars, which are detailed in Tables A1 and A2 (Appendix A). However, we control for autonomous regions in our estimations, to capture these heterogeneities, along with other regional characteristics.

PIAAC data require specialised methodologies to account for its complex sampling design. Specifically, the application of replicate weights (using jackknife or balanced repeated replication methods), and ten plausible values for the cognitive assessments (OECD, 2025) is essential for obtaining unbiased estimates and accurate standard errors⁴ (as indicated by the OECD technical report (OECD, 2025); or by other research works such as e.g. Jerrim et al., 2017).

Our variables of interest are dropout and years of education. Dropout is a binary variable, which takes the value 1 if the respondent’s highest level of education is ISCED 2, following the standardised classification that ensures comparability across countries and cohorts. In contrast, years of education is a continuous variable representing the respondent’s formal schooling duration, excluding any additional year due to grade repetition⁵.

3.1. Instrumental variables

To better isolate the influence of early school dropout and years of education on adult literacy and numeracy skills, we employ an instrumental variable (IV) strategy that leverages historical changes in Spanish educational policy. Specifically, our approach utilises three binary instrumental variables for years of education and dropout, defined as follows:

ZLEP+LOE,i=1 for respondents born before 1969 (reflecting the period when education was non-compulsory under the Law of Primary Education, LEP, and the Organic Law on Education, LOE);

ZLGE,i=1 for respondents born between 1969 and 1975 (corresponding to the implementation of the 1970 General Education Law, LGE, which established a dropout cut-off at age 14);

ZLOGSE,i=1 for respondents born after 1975 (capturing the period following the 1990 Organic Law for the General Organization of the Educational System, LOGSE, that extended compulsory education until age 16).

These instruments are designed to isolate exogenous variations in the years of education and dropout decisions, thereby mitigating potential bias from unobserved factors such as innate ability or family dynamics. However, our estimations will control for socio-economic background variables following the previous literature review on factors which were found to condition educational attainment in Spain (Choi & Calero, 2013; Serrano et al., 2013; González-Rodríguez et al., 2019; Marcenaro-Gutiérrez & Lopez-Agudo, 2024). In particular, our regressions we use as our key explanatory variables the decision to drop out (Vaughn et al., 2010; Choi & Calero, 2013; Marcenaro-Gutiérrez & Lopez-Agudo, 2024) and years of education (OECD, 2013a; Crespo et al., 2014; Hanushek et al., 2015; Cappellari et al., 2024). As controls, we include gender (as suggested by e.g. OECD, 2014; Rodríguez-Martínez, & Gallardo Gil, 2019), socioeconomic status (Fernandez-Enguita et al., 2010; Serrano et al., 2013; Brindusa et al., 2020; Bussolo et al., 2023), immigrant status (Choi & Calero, 2013; Dustmann et al., 2012; Zinovyeva et al., 2014; Moreira et al., 2023), and autonomous community (Calero & Escardíbul, 2016; OECD, 2018). These controls are described as follow and Summary Statistics can be found in Appendix A (Table A3), where we can already see mean differences between cohorts in all variables selected, specially between the first and last cohorts:

Standardised literacy competence scores: constructed variable with mean close to 0 and standard deviation close to 1 that captures the respondent measured competence in literacy. The mean increases across cohorts from −0.28 in the earliest cohort to 0.20 in the latest cohort.

Standardised numeracy competence scores: constructed variable with mean close to 0 and standard deviation close to 1 that captures the respondent measured competence in mathematics. The mean increases across cohorts from –0.24 to 0.10.

Dropout: takes value 1 if the respondents’ highest educational level is up to an ISCED 2. The proportion of respondents who dropped out of school falls substantially across cohorts from 46% to 20%.

Years of education: continuous variable representing respondent’s schooling duration, excluding additional years due to grade retention. The means increase from 13.35 to 15.38 across cohorts. Gender: takes the value 1 when the respondent is a female. Gender composition is stable across cohorts, around 50%.

Standardised Economic, Social, and Cultural Status (ESCS) index: manually constructed from parental education levels (for both father and mother) and the number of books available at home when the respondent was 14 to have mean 0 and a standard deviation of 1. Statistics indicate higher status for younger cohorts with means growing from -0.30 to 0.26.

Immigrant status: whether the respondent reported to be born in Spain and have Spanish parents (native), immigrant parents (second-generation immigrant) or be born in another country (second-generation immigrant), with native as the reference group. Immigrant representation increases over time from a mean of 0.09 to 0.18 for the case of first-generation immigrants, and from 0.01 to 0.04 for second-generation immigrants.

Autonomous Community: a dummy variable for each Autonomous Region in Spain, representing in which region did the respondent answered the questionnaire. It presents similar values across cohorts.

Entries marked with “S” denote statistically significant discontinuities reported in the table. Overall, the cohorts differ meaningfully in educational attainment and socioeconomic composition, which motivates controlling for these covariates in the regression and discontinuity analyses.

3.1.1. Testing for exogenous variation

One of the fundamental requirements for our IV approach is that the instruments must be “as good as randomly assigned” – that is, the three educational regimes must be uncorrelated with the error term. In our study, we assume that the instruments are exogenous based on their nature as historical educational laws. Since these laws were enacted independently of individual characteristics, they provide a strong theoretical basis for assuming exogeneity.

To further ensure that the instruments capture only exogenous variation in dropout rates and years of education, and do not serve as proxies for other unobserved determinants, we assess the balance of key socio-economic and demographic characteristics across the instrument-defined groups. Specifically, we test for differences in gender, immigrant status, ESCS index and autonomous community. The results, along with the descriptive statistics (see Table A3 in Appendix A), indicate significant differences across the LEP+LOE, LGE, and LOGSE regimes, particularly in socio-economic variables. These discrepancies may reflect structural changes over time, such as rising immigration, differences in cohort age, and the expansion of education. To strengthen the assumption that differences in outcomes are primarily driven by educational policy changes rather than pre-existing disparities, we control for all selected covariates in the analysis that could influence the outcome variables through the predicted dropout and schooling years’ channel.

3.1.2. Testing for instrument relevance

The second fundamental requirement for the validity of our IV approach is that the instrument must be strongly correlated with the endogenous variables (dropout and years of education). Using the PIAAC 2012 and 2023 data, we provide preliminary evidence supporting the relevance assumption by presenting in Figure 1 dropout rates and years of education plotted by year of birth.

Furthermore, the data reveal a statistically significant negative correlation at the 1% significance level between birth year and dropout (–0.28 at the individual level; –0.92 when aggregated by birth year) and a statistically significant positive correlation at the 1% significance level between birth year and years of education (0.24 at the individual level; 0.84 when aggregated by birth year).

Additionally, dropout is significantly correlated at the 1% significance level with the LEP+LOE, the LGE and the LOGSE educational reform variables. Conversely, years of education are significantly correlated at the 1% significance level with the LEP+LOE and the LOGSE, while it does not appear to be significantly correlated with the LGE at any significance level.

Figure 1 Dropout rates and years of education by birth year Figure 1. Dropout rates and years of education by birth year

Notes: The procedures indicated in OECD (2016) (weighting and plausible values) have been employed. The bold vertical lines represent the cut-off years for the education law instruments.

Source: Authors’ own calculations.

3.1.3. Testing the Monotonicity Property

Furthermore, our education law instrumental variable should accomplish the monotonicity property (Fiorini & Stevens, 2014; Barua & Lang, 2016, or Dhuey et al., 2019). Following Barua and Lang’s (2016) definition, this property can be defined as “while the instrument may have no effect on some individuals, all of those who are affected should be affected unidirectionally”⁶. In Figure 2 we can see that, in fact, our data may accomplish this property as those who started primary education once the 1970 law was completely implemented (those born in 1969), actually seemed to perform higher than those who started during the implementation process or before, while the same appears to happen with the 1990 education law.

Figure 2 Relationship between standardised scores in literacy and numerical skills with year of birth Figure 2. Relationship between standardised scores in literacy and numerical skills with year of birth

Notes: The procedures indicated in OECD (2016) (weighting and plausible values) have been employed. The bold vertical lines represent the cut-off years for the education law instruments.

Source: Authors’ own calculations

3.1.4. Testing secular trends

Nevertheless, from Figures 1 and 2 we can also observe nearly linear trends for both of our dependent variables across years, which could suggest that there may be secular trends in co-occurring factors such as improvements in the educational system or increased access to information (this is an issue highlighted by authors such as e.g. Psacharopoulos & Patrinos, 2018, and Psacharopoulos, 2024). Due to this potential bias that may cause our estimates to capture the influence of these externalities, apart from the associations of the changes in the educational laws with our dependent variables, we remain cautious at interpreting our 2SLS estimators as causal.

3.2. Estimation Strategy

Given the potential endogeneity of the decision to drop out and years of education, we estimate its influence on adult outcomes using a Two-Stage Least Squares (2SLS) instrumental variable (IV) approach, considering the adjustments required on PIAAC estimations (replicate weights, jackknife, balanced repeated replication values and ten plausible values on scores). Accordingly, we aim to correct omitted variables bias that may be affecting OLS estimates (e.g. innate ability). Moreover, we conduct a robustness check that eliminates first-generation immigrants from the sample, ensuring the sample is formed by individuals whose education was developed in the same nation, and assessing whether our strategy still works when obtaining associations of educational attainment on long-term educational cognitive skills.

3.2.1. Baseline Regression Model

We begin by considering the baseline model, in which the influence of early school dropout and years of education on adult outcomes is estimated via ordinary least squares (OLS), separately. For cognitive outcomes, specifically literacy and numeracy skills, the model is specified as:

(1) s i = α + β DO i + γ X i + ε i

(2) s i = α + δ Edu i + γ X i + ε i

where i represents each individual. s_i are literacy and numerical standardised scores, alternatively; in equation (1) DO_i is a dummy variable which takes the value “1” if the individual dropped out their studies before finishing ISCED 2 level and “0” otherwise; X_i are individual’s socio-economic background characteristics; ε_i is the idiosyncratic error term. For equation (2), Edu_i represents the respondent’s formal years of education, ranging from 3 to 24, depending on their highest level of education attained.

However, β and δ coefficients in both estimations would be biased given the potential endogeneity of the dropout and years of education decision with the idiosyncratic error term ε_i (e.g., due to the correlation with the omitted variable of ability), needing an Instrumental Variable (IV) strategy.

3.2.2. Instrumental V Regression Specification

Given the potential endogeneity of the dropout and years of education decision, we instrument both DO_i and Edu_i using the previously defined three binary variables corresponding to the key educational reforms. The first-stage regression estimates the decision to drop out and the schooling years as a function of these instruments and control variables, separately:

(3) Pr ( D O i = 1 ) = π 0 + π 1 Z LEP + LOE , i + π 2 Z LGE , i + π 4 X i + ϑ i

(4) E d u i = π 0 + π 1 Z LEP + LOE , i + π 2 Z LGE , i + π 4 X i + ϑ i

where ϑ_i is the first-stage idiosyncratic error term. The predicted values of both dropout DO^i and years of education (Edu^i) obtained from equations (3) and (4), are then substituted into their respective second-stage equations, based on (1) and (2). Thus, the reduced form specifications for cognitive outcomes are estimated as follows:

(5) s i = α + β D O ^ i + γ X i + ε i

(6) P s i = α + δ E d u ^ i + γ X i + ε i

Obtaining coefficient β that represents the influence of school dropout and δ presenting the long-life cycle returns of one more year of education on the outcomes under analysis.

To further validate our instruments, we conduct several diagnostic tests; we apply the Hansen J test (1982)⁷ to assess the validity of the selected instruments in our overidentified model, and the Kleibergen–Paap F statistic (2006)⁸ weak instrument test to evaluate the strength of our instruments. We applied these tests as our estimations yield from the usage of replicate weights⁹, results from these tests confirm that our instruments satisfy the necessary relevance and exclusion restrictions for consistent IV estimation, although testing for overidentifying restrictions and exogeneity of the instruments in the model for the decision to drop out is limited to the extent that we use a probit estimation strategy in the first stage, not being able to directly obtain these results.

Still, our methodology has some limitations: our analysis does not account for potential changes resulting from lifelong learning or job-related training, our sample exhibits a highly asymmetrical distribution between educational laws, and the variables used are self-reported (hence potentially affected by measurement or computational errors), later treated by the OECD, and were selected to coincide between both datasets. Because of that, although we employ a quasi-experimental methodology to reduce endogeneity, we are still cautious and interpret our results as associations.

4. RESULTS

We begin our analysis by estimating a series of models using the Two-Stage Least Squares (2SLS) instrumental variables (IV) approach, which exploits exogenous variation in dropout rates and years of education, induced by historical changes in Spanish educational policy. Our complete sample consists of 11,123 observations using missing flags¹⁰ in our estimations to recover missing data from the autonomous communities and ESCS index controls. The reduction in sample size results from the exclusion of 103 observations from Ceuta and 85 from Melilla, 444 individuals that were 18 or less at the moment of the survey, as well as the removal of 87 cases with missing values in the year of birth variable (used to construct the dropout variable).

To ensure that the omitted observations do not introduce selection bias, we conduct difference tests comparing observable characteristics between included and excluded cases, except for second generation immigrant status. All tests fail to reject the null hypothesis at conventional significance levels, indicating no systematic differences between groups¹¹. Within our sample, 3,370 individuals dropped out of basic education, while 7,753 did not. The sample is further disaggregated by educational regime: 3,793 individuals were subject to the LEP+LOE (born before 1969), 1,963 to the LGE (born between 1969 and 1975) and 5,367 to the LOGSE (born after 1975).

4.1. Results with an Ordinary Least Squares Approach

We first estimate the influence of education and dropout on cognitive outcomes by using ordinary least squares (OLS). For years of education, Table 1 demonstrates that an additional year of education is associated with increases of δ of 0.13 standard deviations (SDs) in literacy and 0.14 SDs in numeracy scores (each significant at the 1% level). When we add controls for autonomous community, immigrant status, gender, and the ESCS index, the coefficients attenuate to 0.11 for literacy and 0.12 for numeracy (both significant at the 1% level).

In terms of dropout – defined as a binary variable equal to 1 if the respondent’s highest education is ISCED 2 – OLS estimates without controls indicate that dropping out is associated with a reduction of β of 0.82 SDs in literacy and 0.85 SDs in numeracy (each significant at the 1% level). Once controls are included, the negative influence of dropout decreases to 0.64 SDs for literacy and 0.67 SDs for numeracy (both significant at the 1% level).

4.2. Results with an Instrumental Variable Approach

To address potential endogeneity in educational attainment and dropout, we employ a two‐stage least squares (2SLS) instrumental variable approach that exploits exogenous variation from Spanish educational reforms (LEP+LOE, LGE, and LOGSE). In Table 2 we can see the first-stage coefficients of the instruments in our baseline model and our model with controls, where instruments yield statistically significant coefficients for both, years of education and the dropout endogenous variables, except for the LGE reform in the years of education specification with controls. This suggests that the selected instruments significantly explain a portion of the variation in these variables, thereby satisfying the relevance assumption.

For the years of education specification without controls (using 11,123 observations), the first‐stage estimates are -1.90 years for LEP+LOE and -0.45 years for LGE (all significant at the 1% level; π₁, π₂, respectively. Furthermore, results in Table 3 show that, in the second stage, an additional year of education is positively related to literacy by 0.23 SDs and numeracy by 0.20 SDs (both significant at the 1% level). Furthermore, the Hansen J test for overidentified models yield a non-significant χ² of 0.32 for both literacy and numeracy equations, not rejecting instrument validity at conventional levels. The Kleibergen-Paap Wald rk F statistic yield a value of 213.10 for both literacy and numeracy equations, supporting the strength of our instruments according to Stock and Yogo (2005) and Andrews et al. (2019) critical values.

Table 1 The influence of years of education and dropping out on Spanish literacy and numeracy skills

Variables Specification I. Without controls Specification II. With controls

Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills

Dropout (Ref.: did not drop out)

The student dropped out -0.822*** -0.852*** -0.635*** -0.665***

(0.021) (0.021) (0.020) (0.021)

Years spent on education 0.134*** 0.137*** 0.114*** 0.116***

(0.002) (0.002) (0.003) (0.003)

Standardized Economic, Social and Cultural Status (ESCS)

ESCS Index 0.188*** 0.193*** 0.276*** 0.281***

(0.010) (0.010) (0.010) (0.010)

Missing Flag -0.770*** -0.777** -1.025*** -1.035***

(0.151) (0.368) (0.161) (0.379)

Gender (Ref.: male)

Female -0.096*** -0.256*** -0.076*** -0.236***

(0.017) (0.017) (0.018) (0.018)

Immigrant status (Ref.: native)

First-generation immigrant -0.500*** -0.453*** -0.559*** -0.514***

(0.027) (0.027) (0.029) (0.028)

Second-generation immigrant -0.024 -0.130** -0.104 -0.213***

(0.061) (0.063) (0.064) (0.066)

Missing Flags 0.410*** 0.049 0.505*** 0.134***

(0.031) (0.031) (0.034) (0.034)

Autonomous Community (Ref.: Andalusia)

Aragon -0.169*** -0.070 -0.146*** -0.049

(0.044) (0.043) (0.047) (0.046)

Asturias -0.071 -0.066 0.016 0.022

(0.052) (0.051) (0.052) (0.051)

Balearic Islands -0.051 0.001 -0.094 -0.044

(0.070) (0.065) (0.078) (0.071)

Canary Islands -0.094** -0.106** -0.097* -0.109**

(0.047) (0.049) (0.051) (0.052)

Cantabria -0.033 -0.016 0.030 0.048

(0.091) (0.091) (0.098) (0.098)

Castile La Mancha -0.139*** -0.075* -0.085** -0.020

(0.038) (0.040) (0.040) (0.042)

Castile Leon 0.143*** 0.188*** 0.191*** 0.235***

(0.040) (0.038) (0.042) (0.040)

Catalonia -0.054* 0.008 -0.016 0.047

(0.031) (0.031) (0.033) (0.033)

Valencian Community 0.178*** 0.153*** 0.211*** 0.186***

(0.032) (0.033) (0.034) (0.034)

Extremadura -0.158** -0.168*** -0.181** -0.190***

(0.070) (0.064) (0.076) (0.069)

Galicia 0.054 0.077** 0.069* 0.091**

(0.037) (0.036) (0.039) (0.038)

Madrid -0.085*** -0.052* -0.031 0.002

(0.030) (0.030) (0.032) (0.032)

Murcia 0.063 0.103** 0.082 0.122**

(0.047) (0.046) (0.050) (0.050)

Navarra -0.020 0.101* 0.001 0.123*

(0.071) (0.060) (0.076) (0.063)

Basque Country -0.198*** -0.059 -0.116*** 0.023

(0.041) (0.039) (0.043) (0.041)

La Rioja 0.132 0.066 0.209** 0.144*

(0.081) (0.071) (0.087) (0.082)

Missing Flag -0.503*** -0.693*** -0.410*** -0.605**

(0.046) (0.117) (0.159) (0.235)

Constant -1.954*** -1.977*** 0.251*** 0.272*** -1.501*** -1.475*** 0.316*** 0.382***

(0.037) (0.038) (0.012) (0.012) (0.043) (0.044) (0.024) (0.024)

Observations 11,123 11,123 11,123 11,123 11,123 11,123 11,123 11,123

Notes

Dependent variable: Standardised scores in literacy and numerical skills (standardised using Spanish mean and standard deviation).

Estimation method: Ordinary Least Squares (OLS).

Coefficient: ***

Significant at 1%,

significant at 5%,

significant at 10%.

Source: Authors’ own calculations.

Table 2 First-stage regression results for years of education and dropout

Specification I. Without Controls Specification II. With Controls

Variables Years of Education Dropout Years of Education Dropout

LEP+LOE -1.898*** 0.746*** -1.148*** 0.553***

(0.092) (0.031) (0.086) (0.033)

LGE -0.451*** 0.323*** 0.071 0.175***

(0.104) (0.040) (0.095) (0.042)

Standardized Economic, Social and Cultural Status (ESCS)

ESCS Index 1.506*** -0.548***

(0.035) (0.021)

Missing Flag -2.748** 0.402

(0.952) (0.511)

Gender (Ref.: male)

Female 0.379*** -0.125***

(0.072) (0.030)

Immigrant status (Ref.: native)

First-generation immigrant -0.620*** 0.051

(0.104) (0.044)

Second-generation immigrant -0.595*** -0.089

(0.228) (0.106)

Missing Flag 5.205***

(0.140)

Autonomous Community (Ref.: Andalusia)

Aragon 0.689*** -0.263***

(0.179) (0.080)

Asturias 1.277*** -0.296***

(0.223) (0.100)

Balearic Islands -0.157 -0.092

(0.294) (0.118)

Canary Islands -0.016 -0.025

(0.217) (0.087)

Cantabria 0.794*** -0.127

(0.264) (0.112)

Castile La Mancha 0.407** 0.026

(0.187) (0.071)

Castile Leon 0.866*** -0.256***

(0.159) (0.072)

Catalonia 0.528*** -0.099*

(0.135) (0.053)

Valencian Community 0.412*** -0.065

(0.135) (0.057)

Extremadura -0.642*** 0.227**

(0.243) (0.095)

Galicia 0.268* -0.072

(0.159) (0.061)

Madrid 0.737*** -0.152***

(0.123) (0.051)

Murcia 0.170 -0.002

(0.221) (0.078)

Navarra 0.543** -0.232**

(0.240) (0.108)

Basque Country 1.271*** -0.313***

(0.196) (0.077)

La Rioja 0.669 -0.019

(0.410) (0.154)

Missing Flag 2.503**

(1.083)

Constant 15.340*** -0.888*** 14.482*** -0.738***

(0.049) (0.022) (0.097) (0.040)

Observations 11,123 11,123 11,123 11,120

Notes

Estimation method: First stage of Two-Stages Least Squares (2SLS).

Coefficient: ***

Significant at 1%,

significant at 5%,

significant at 10%.

Source: Authors’ own calculations.

Table 3 The influence of years of education and dropping out on Spanish literacy and numeracy skills

Variables Specification I. Without controls Specification II. With controls

Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills

Dropout (Ref.: did not drop out)

The student dropped out -1.675*** -1.501*** -1.717*** -1.643***

(0.082) (0.083) (0.088) (0.088)

Years spent on education 0.226*** 0.197*** 0.262*** 0.208***

(0.012) (0.011) (0.019) (0.017)

Standardized Economic, Social and Cultural Status (ESCS)

ESCS Index -0.055* 0.043 0.110*** 0.131***

(0.033) (0.029) (0.016) (0.016)

Missing Flag -0.352 -0.517 -0.915*** -0.936**

(0.240) (0.371) (0.125) (0.368)

Gender (Ref.: male)

Female -0.149*** -0.289*** -0.110*** -0.267***

(0.022) (0.020) (0.018) (0.018)

Immigrant status (Ref.: native)

First-generation immigrant -0.437*** -0.415*** -0.578*** -0.532***

(0.033) (0.030) (0.029) (0.028)

Second-generation immigrant 0.040 -0.090 -0.157** -0.261***

(0.072) (0.069) (0.063) (0.066)

Missing Flag -0.293*** -0.388***

(0.095) (0.086)

Autonomous Community (Ref.: Andalusia)

Aragon -0.265*** -0.130*** -0.234*** -0.128***

(0.053) (0.047) (0.048) (0.047)

Asturias -0.244*** -0.173*** -0.060 -0.047

(0.071) (0.062) (0.052) (0.050)

Balearic Islands -0.017 0.022 -0.123 -0.069

(0.081) (0.071) (0.077) (0.071)

Canary Islands -0.091 -0.104** -0.097* -0.109**

(0.059) (0.053) (0.051) (0.052)

Cantabria -0.137 -0.081 0.003 0.023

(0.096) (0.095) (0.099) (0.099)

Castile La Mancha -0.200*** -0.113** -0.072* -0.009

(0.050) (0.046) (0.040) (0.042)

Castile Leon 0.025 0.114*** 0.117*** 0.168***

(0.050) (0.044) (0.042) (0.040)

Catalonia -0.125*** -0.036 -0.041 0.024

(0.038) (0.034) (0.033) (0.032)

Valencian Community 0.119*** 0.116*** 0.190*** 0.167***

(0.040) (0.036) (0.034) (0.034)

Extremadura -0.061 -0.107 -0.094 -0.111

(0.077) (0.067) (0.077) (0.070)

Galicia 0.021 0.056 0.049 0.074*

(0.043) (0.038) (0.039) (0.038)

Madrid -0.185*** -0.114*** -0.069** -0.032

(0.037) (0.034) (0.032) (0.032)

Murcia 0.032 0.083* 0.073 0.113**

(0.054) (0.048) (0.049) (0.049)

Navarra -0.094 0.056 -0.057 0.070

(0.077) (0.064) (0.076) (0.064)

Basque Country -0.379*** -0.172*** -0.212*** -0.065

(0.055) (0.048) (0.043) (0.042)

La Rioja 0.016 -0.006 0.189** 0.125

(0.097) (0.070) (0.088) (0.085)

Missing Flag -0.895*** -0.937***

(0.095) (0.063)

Constant -3.284*** -2.856*** 0.502*** 0.463*** -3.593*** -2.776*** 0.683*** 0.714***

(0.170) (0.161) (0.027) (0.027) (0.275) (0.244) (0.038) (0.037)

Observations 11,123 11,123 11,123 11,123 11,123 11,123 11,120 11,120

Instrumental variables analysis

Hansen J overidentification test 0.316 0.317 11.771*** 9.638*** 0.106 0.487 17.668*** 28.425***

Kleibergen-Paap rk LM 213.103*** 213.103*** 289.520*** 289.520*** 100.415*** 100.229*** 151.143*** 151.143***

Notes

Standard errors are in parentheses. The procedures indicated in OECD (2016) (weighting and plausible values) have been employed. Missing flag has been included to prevent missing information on the autonomous community, immigrant status and ESCS index. The null hypothesis of the Hansen J overidentification test is that the instruments of the overidentified model are valid. The Kleibergen-Paap Wald rk F statistic yield the values to be compared with the critical values for strong instruments.

Dependent variable: Standardised scores in literacy and numerical skills (standardised using Spanish mean and standard deviation).

Estimation method: Two-Stages Least Squares (2SLS).

Coefficient: ***

Significant at 1%,

significant at 5%,

significant at 10%.

Source: Authors’ own calculations.

When controls are included, the first-stage estimates adjust to -1.15 years for LEP+LOE (significant at the 1% level) and 0.07 years for LGE (not significant). In the second stage, results suggest that an extra year of education is positively related to literacy by 0.26 SDs and numeracy by 0.21 SDs (both significant at the 1% level). The Hansen J test for overidentified models yield a non-significant χ2 of 0.11 for literacy and 0.49 for the numeracy equation, again not rejecting instrument validity at conventional levels. Moreover, the Kleibergen-Paap Wald rk F statistic yield a value of 100.42 for both literacy and numeracy specifications, respectively, supporting the strength of our instruments. These results align with Schleicher (2023) report on PISA 2022 data, who found that an additional year is associated with a 0.20 SD cognitive development. For the dropout specification without controls, the instruments provide first-stage coefficients of 0.75 for LEP+LOE, 0.32 for LGE (all significant at the 1% level; π₁, π₂, respectively). In the second stage, dropout is negatively related to literacy by 1.68 SDs and numeracy by 1.50 SDs (both significant at the 1% level). The Hansen J test manually computed yield a significant χ2 of 11.77 for literacy and 9.64 for the numeracy equation, rejecting instrument validity at conventional levels. By contrast, due to the nature of our model, the Kleibergen-Paap Wald rk F statistic cannot be computed with a probit specification, but considering a linear model the statistic yields a value of 289.52.

With controls, the first-stage coefficients are 0.55 for LEP+LOE and 0.18 for LGE (both significant at the 1% level). The second stage indicates that dropout is negatively related to literacy by 1.72 SDs and numeracy by 1.64 SDs (both significant at the 1% level). The Hansen J test manually computed yield a significant χ2 of 17.69 for literacy and 28.43 for the numeracy equation, rejecting instrument validity at conventional levels, Finally, the Kleibergen-Paap Wald rk F statistic from the linear specification yields a value of 151.143, supporting the strength of instruments in the models with and without controls. Coefficients align with the work conducted by Marcenaro-Gutiérrez & Lopez-Agudo (2024), who found negative associations of around 1.5 SD of the decision to drop out and cognitive development.

4.3. Robustness Check

To further check our results, we eliminated respondents that stated to be first-generation immigrants from the sample, to eliminate the probability of a potential bias from respondents who did not leave any educational law during their schooling years. The reduction of the sample leaves us with 9,489 observations at the end.

We again estimate the influence of education and dropout on cognitive outcomes by using ordinary least squares (OLS) while accounting for our controls. For years of education, Table A4 (Appendix) demonstrates that an additional year of education is associated with an increase of 0.12 SDs in literacy and numeracy scores (each significant at the 1% level). In terms of dropout, OLS estimates indicate that dropping out is associated with a reduction of 0.67 SDs in literacy and 0.69 SDs in numeracy (each significant at the 1% level).

Moreover, when employing our 2SLS instrumental variable approach, in Table A5 (Appendix) we can see the first-stage coefficients of the instruments in our model with controls, where instruments yield statistically significant coefficients for both, years of education and the dropout endogenous variables, except for the LGE reform in years of education, which again is not significant at any level. This suggests that the selected instruments significantly explain a portion of the variation in these variables, thereby satisfying again the relevance assumption.

For the years of education specification, the first‐stage estimates are -1.30 years for LEP+LOE (significant at the 1% level) and 0.03 years for LGE (not significant at any level). By contrast, for the dropout specification, the first-stage estimates yield 0.58 for LOE and 0.17 for LGE (all significant at the 1% level).

Furthermore, results in Table A4 (Appendix) show that, in the second stage, an additional year of education is positively related to literacy by 0.26 SDs and numeracy by 0.22 SDs (both significant at the 1% level). The Hansen J test for overidentified models yield a non-significant χ2 of 0.001 for literacy and 0.92 for the numeracy equation, again not rejecting instrument validity at conventional levels. Moreover, the Kleibergen-Paap Wald rk F statistic yield a value of 112.15 for literacy and 111.69 for the numeracy specification, further supporting the strength of our instruments.

In contrast, the decision to drop out is associated with a decrease of 1.85 SDs in literacy and 1.78 SDs in numeracy (both significant at the 1% level). The manual-computed Hansen J test for overidentified models shows a significant χ2 of 15.40 for literacy and 25.22 for the numeracy equation, rejecting instrument validity at conventional levels to the extent that the first stage is a probit model. Finally, the Kleibergen-Paap Wald rk F statistic yield a significant value of 145.98 for both literacy and numeracy specifications.

These results almost perfectly align with our main specifications with little changes in values, specifically in terms of dropout, where its association with literacy and numeracy skills increases almost 0.14 SDs when not accounting for first-generation immigrants. However, the similarity is undeniable, proving the robustness of our main findings in the analysis.

5. DISCUSSION

This research has rigorously examined and updated the relationship of early school dropout and years of education on adult cognitive outcomes – specifically, literacy and numeracy skills – using an instrumental variable (IV) approach that leverages exogenous variation induced by historical educational reforms in Spain. Our methodology, which instruments the endogenous variables of dropout and formal schooling years through three distinct policy changes (LEP+LOE, LGE, and LOGSE) has allowed us to address biases arising from unobserved heterogeneity, such as innate ability. In doing so, our study contributes to the growing literature on the long-life cycle returns to education and underscores the importance that educational trajectories still play in shaping cognitive skills, as demonstrated by our analysis of the two available PIAAC cycle.

Furthermore, considering Psacharopoulos and Patrinos (2018) and Psacharopoulos (2024) works, while OLS estimations may contain endogeneity bias due to factors affecting the dependent and independent variables of interest simultaneously (e.g. innate ability or family dynamics), the IV estimates may suffer the same issue as our instruments may be capturing external factors affecting the trend in the dependent variables. In this context, we need to limit our interpretations to be associations and not causal effects.

Nevertheless, the empirical results and our robustness are consistent with a broad body of literature. In line with Hanushek (2009), our findings confirm that additional years of education are associated with significant improvements in cognitive performance. Moreover, although we utilized PIAAC dataset for the analysis, our results perfectly align to 2022 PISA report (Schleicher, 2023), which states that an additional year of schooling is almost equivalent to 0.20 SDs increase in PISA tests. Additionally, our IV estimates reveal that an extra year of schooling yields substantially higher returns – in terms of both literacy and numeracy scores – than those estimated using ordinary least squares (OLS), suggesting that traditional OLS approaches may underestimate the true influence of educational attainment on cognitive skills, in terms of years of education. Furthermore, we found associations of the laws with PIAAC scores, contrasting Robles-Zurita (2017) analysis, and results were similar in our robustness check, that eliminated the probability of a potential bias due to the accountability of first-generation immigrants that may have not completely experienced the educational reforms under analysis.

At the same time, our main empirical analysis highlights the severe adverse effects of early school dropout on cognitive outcomes. Consistent with Vaughn et al. (2010), our findings show that dropout markedly reduces skills in later life, with our instrumental variable (IV) approach indicating reductions on the order of several standard deviations. Similarly, Marcenaro-Gutiérrez and Lopez-Agudo (2024) identified dropout effects of approximately 1.5 SDs using an IV framework around the implementation of the LGE. However, our results also reveal that the influence of dropout is not uniform across all demographic groups as Brindusa et al. (2020) documented, with our estimations using the ESCS index supporting this heterogeneity found in the literature. Therefore, the socio-economic factors taken into account – parental education, the number of books in the home, regional disparities, and gender (Fernández-Enguita et al., 2010; Serrano et al., 2013; Bussolo et al., 2023; Rodríguez-Martínez & Gallardo, 2019).– still play a significant role in conditioning school attainment.

6. CONCLUSIONS

Although our main estimation strategy falls into estimates that may be affected by bias due to endogeneity in both the OLS and IV strategies, we can interpret our results as associations instead of causal effects. With the information from our main analysis, it seems necessary to underscore the importance of targeted policy interventions, considering that increasing the duration of compulsory education, as implemented through the LGE and the LOGSE, may yield significant cognitive and economic benefits. However, our findings also indicate that such policy reforms can have unintended consequences and for example, while Bellés-Obrero and Duchini (2021) found that the LOGSE has a positive influence on occupational outcomes among middle- and high-skilled individuals, Robles-Zurita (2017) did not observe a significant effect on cognitive outcomes. These divergent findings could suggest that educational reforms might interact with other socio-economic factors, such as the quality of education and teacher effort, as highlighted by Green and Navarro-Paniagua (2012). Consequently, enhancing educational quality – as argued by Benito and Romera (2020)—is essential to ensure that extended schooling translates effectively into cognitive capital.

Our study also emphasises the importance of applying rigorous econometric techniques when evaluating the returns to education. By employing replicate weights, jackknife or balanced repeated replication methods, and accounting for plausible values in the PIAAC (2013b; 2023) data (Jerrim et al., 2017), we have taken crucial steps to obtain unbiased estimates and accurate standard errors. Furthermore, diagnostic tests, including the Hansen J overidentification test and the Kleibergen-Paap Wald rk F statistic, have generally confirmed the validity and relevance of our instruments while using replicate weights, although caution is warranted as potential endogeneity concerns remain (as suggested by Green & Navarro-Paniagua, 2012; and Psacharopoulos and Patrinos, 2018; Psacharopoulos, 2024) and the results from specifications for dropout suggested the rejection of our overidentifying restrictions to the extent that the first stage was estimated with a probit model and the diagnosis tests had to be computed manually considering a linear model in the first stage.

In this vein, despite its contributions, this study has certain limitations. First, as we mentioned before, our estimates are limited to be interpreted as associations and not causal effects. Second, the external validity of our findings may be restricted to the Spanish context as we only use data and educational reforms for Spain. Additionally, our analysis relies on cross-sectional measures of cognitive skills measured through the PIAAC 2012 and later 2023 survey, which does not account for potential changes resulting from lifelong learning or job-related training, as highlighted by recent research from Hanushek et al. (2025). Furthermore, our sample exhibits a highly asymmetrical distribution of educational laws, specifically in the LGE reform, which accounts for fewer than 18% of the sample and may be influencing the generalisability of our results. Finally, the variables used in this research are self-reported (hence potentially affected by measurement or computational errors), and were selected to coincide between both datasets, not including characteristics as school funding or labour status of the parents when the respondent was a student, which may introduce measurement errors or bias that could be influencing the estimated relationships and limiting the causal interpretations of our findings.

In summary, even when limiting our estimates to associations, the evidence presented in this study supports the hypothesis that both additional schooling and avoidance of early dropout have significant, positive influence on cognitive outcomes. These findings not only corroborate and extend existing research in the Economics of Education, but also carry important policy implications. To maximise the cognitive and economic benefits of education, future policies should prioritise interventions aimed at reducing dropout rates – particularly among vulnerable groups – while simultaneously improving the quality of education delivered. Such a dual approach would contribute to narrowing socio-economic disparities and fostering a more skilled, adaptable workforce in the long run. In addition, companies should receive tax benefits linked to the training of their employees throughout their lives as a means of promoting the development of their skills and improving company productivity.

While our research has advanced the understanding of the long-life cycle returns to education in Spain, in the terms of cognitive development, it also highlights the inherent complexities in disentangling the mechanisms at play. Future research should continue to explore the interplay between educational quantity and quality, and further refine methodological approaches to address persistent issues of endogeneity that capture ability, institutional characteristics and general trends in the economy where the educational system analysed is developed, particularly among those subpopulations where the presented instruments may be less robust. Besides, it would be interesting to assess a regional study within the autonomous community, giving attention to spatial autocorrelation effects on different metropolitan areas. Through these continued efforts, we can work toward designing educational systems that not only extend learning, but also ensure that every additional year of schooling effectively contributes to the development of cognitive abilities and human capital.

Acknowledgement

This work has been partly supported by Fundación Bancaria BBVA - Programa Prismas y Problemas 2023 - “La inequidad socioeconómica derivada de la ineficiencia de los sistemas educativos (INESOCEF)”), by the Fundación Ramón Areces and by the Andalusian Regional Government (PPRO-SEJ645-G-2023). We also acknowledge the training received from the University of Malaga PhD Programme in Economy and Business [Programa de Doctorado en Economía y Empresa de la Universidad de Malaga].

Authors’ contributions

Conceptualization, O. D. M.-G., and I. I. A.-G.; Methodology, L. A. L.-A., and I. I. A.-G.; Software, I. I. A.-G.; Data acquisition, O. D. M.-G.; Analysis and interpretation, I. I. A.-G., L. A. L.-A., and O. D. M.-G.; Writing – Preparation of the draft, I. I. A.-G.; Writing – Review & Editing, L. A. L.-A., and O. D. M.-G. All authors have read and agreed to the published version of the manuscript.

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Notas ²

Standardisations of scores were performed with the mean and the standard deviation for Spain in PIAAC in 2012 and 2023. For PIAAC 2023, in literacy skills the mean is 247.2 and the standard deviation 48.6, while for numeracy skills the mean is 249.7 and the standard deviation 52.3 (OECD, 2024). For PIAAC 2012, the mean of literacy skills is 251.8 and the standard deviation 49.0, while in numeracy skills the mean is 245.8 and the standard deviation 51.3 (OECD, 2013a). The aim of these transformations is to interpret the results as effect sizes, to facilitate international comparisons.

Spain is composed of 17 autonomous communities (Andalusia, Aragon, Asturias, Balearic Islands, Basque Country, Canary Islands, Cantabria, Castile and León, Castilla–La Mancha, Catalonia, Extremadura, Galicia, Community of Madrid, Murcia, Navarre, La Rioja, Valencian Community) and 2 autonomous cities (Ceuta and Melilla).

⁴

These adjustments are necessary because PIAAC is based on a sample of individuals. Sampling weights are used to scale the sample to the size of the population, while jackknife and balanced repeated replication weights are employed to obtain robust standard errors. Moreover, plausible values account for the uncertainty inherent in large-scale assessments like PIAAC, where respondents answer only a subset of the literacy and numeracy items, and the remaining responses are generated via multiple imputation. Consequently, each estimation is performed ten times, with the final result obtained by averaging these iterations (OECD, 2016), following the multiple imputation combining or Rubin’s rules (Rubin, 1987).

⁵

Grade repetition is not considered as it does not necessarily correspond to additional knowledge acquisition or an improvement in cognitive skills. Rather, it typically indicates a delay in educational progress due to academic difficulties.

⁶

Other definition for the monotonicity property by Fiorini and Stevens 2014 is that “for a given change in the value of the instrument, it cannot be that some individuals increase treatment intensity while others decrease treatment intensity” (p. 2).

⁷

The Hansen J test assesses whether the instruments in an overidentified GMM model satisfy the orthogonality conditions—that is, whether they are valid (uncorrelated with the error) and correctly excluded from the structural equation. It is based on the minimized value of the GMM criterion function (the J‑statistic) which under the null hypothesis follows a chi-squared (χ2) distribution with degrees of freedom equal to the number of overidentifying restrictions. The null hypothesis states that all instruments are valid and any extra instruments add no new information beyond that required for identification.

⁸

The Kleibergen–Paap rk Wald F statistic evaluates the strength of instruments in the presence of heteroskedasticity or clustering, testing whether the excluded instruments are sufficiently correlated with the endogenous regressors to achieve identification. It is computed as a Wald F‑ (adjusted for non‑ errors) based on the smallest canonical correlation between instruments and endogenous variables after partialling out exogenous controls. Under the null hypothesis of weak identification, this statistic follows an approximate F‑ with smaller values indicating that the instruments may be too weak to yield reliable IV estimates.

⁹

Normally, the tests used for instrument validity are the Sargan-Basmann overidentification test (Sargan, 1958; Basmann, 1960) and the Stock and Yogo (2005) weak instrument test which requires errors to be homoskedastic and independent and identically distributed (i.i.d.), but the use of replicate weights generally violates these assumptions, requiring alternative methods (StataCorp, 2023).

¹⁰

This approach involves creating binary indicator (dummy) variables, known as missing flags, for observations with missing values in specific covariates. Instead of dropping these observations, the missing values are replaced with zero values, and a corresponding missing flag variable is added to the regression to indicate that the original value was missing with the value 1. This method helps retain a larger sample size while controlling for potential bias introduced by missing data, by assuming that missingness itself carries meaningful information, rather than occurring completely at random (Jones, 1996).

¹¹

These tests will be provided from authors upon request.

Appendix A

Table A1 Calendar of implementation for the 1970 education law for primary education

Academic year Implemented grades Birth year of those who started the grade in the new education system while it was being implemented (Spanish students start compulsory education at the age of six)

1970/71 1st, 2nd, 3th and 4th grades 1st grade − 1964

2nd grade − 1963

3th grade − 1962

4th grade − 1961

1971/72 5th grade 5th grade − 1961

1972/73 6th grade 6th grade − 1961

1973/74 7th grade 7th grade − 1961

Source: Authors’ own calculations using the implementation calendar of the 1970 education law (BOE 1970).

Academic year	Implemented grades	Birth year of those who started the grade in the new education system while it was being implemented (Spanish students start compulsory education at the age of six)
1970/71	1st, 2nd, 3th and 4th grades	1st grade − 1964
2nd grade − 1963
3th grade − 1962
4th grade − 1961
1971/72	5th grade	5th grade − 1961
1972/73	6th grade	6th grade − 1961
1973/74	7th grade	7th grade − 1961

Table A2 Calendar of implementation for the 1990 education law

Academic Year Implemented Grades Birth Year of those who started the grade in the new education system while it was being implemented (Spanish students start compulsory education at the age of six)

1990/91 Minimum dropout age 1974

1991/92 Preschool education 1988

1992/93 1st and 2nd grade 1st grade 1986

2nd grade 1985

1993/94 3rd and 4th grade 3rd grade 1985

4rd grade 1984

1994/95 5th grade 1984

1995/96 6th grade 1984

1996/97 7th grade 1984

1997/98 8th grade 1984

1998/99 9th grade 1984

1999/00 10th grade 1984

Source: Authors’ own calculations using the implementation calendar of the 1990 education law (BOE 1991).

Academic Year	Implemented Grades	Birth Year of those who started the grade in the new education system while it was being implemented (Spanish students start compulsory education at the age of six)
1990/91	Minimum dropout age	1974
1991/92	Preschool education	1988
1992/93	1st and 2nd grade	1st grade 1986
2nd grade 1985
1993/94	3rd and 4th grade	3rd grade 1985
4rd grade 1984
1994/95	5th grade	1984
1995/96	6th grade	1984
1996/97	7th grade	1984
1997/98	8th grade	1984
1998/99	9th grade	1984
1999/00	10th grade	1984

Table A3 Descriptive Statistics and Balance Analysis: Testing for Discontinuity in Covariates

Variables Sample born between 1947-1968 Sample born between 1969-1975 Sample born between 1976-2004

Obs. Mean S.d. Obs. Mean S.d. Obs. Mean S.d.

Competences Reading 3,793 (-0.28)^S 0.98 1,963 0.10^S 0.97 5,367 0.20^S 0.96

Mathematics 3,793 (-0.24)^S 1.00 1,963 0.10^S 0.96 5,367 0.18^S 0.95

The respondent dropped out Yes 3,793 0.46^S 0.50 1,963 0.28^S 0.45 5,367 0.20^S 0.40

No 3,793 0.54^S 0.50 1,963 0.72^S 0.45 5,367 0.80^S 0.40

Years spent on education 3,793 13.35^S 4.38 1,963 14.98^S 3.65 5,367 15.38^S 3.24

Gender Female 3,793 0.53^S 0.50 1,963 0.53 0.50 5,367 0.53^S 0.50

Male 3,793 0.47^S 0.50 1,963 0.47 0.50 5,367 0.47^S 0.50

Immigrant status Native 3,793 0.89^S 0.31 1,963 0.84^S 0.37 5,367 0.78^S 0.41

First-generation immigrant 3,793 0.09^S 0.29 1,963 0.15^S 0.36 5,367 0.18^S 0.39

Second-generation immigrant 3,793 0.01^S 0.12 1,963 0.01^S 0.11 5,367 0.04^S 0.19

Standardized Economic, Social and Cultural Status (ESCS) ESCS Index 3,793 (-0.30)^S 0.81 1,963 (-0.10)^S 0.91 5,367 0.26^S 1.04

Missing flag 3,793 0.00^S 0.02 1,963 0.00^S 0.02 5,367 0.00^S 0.04

Autonomous Community Andalusia 3,793 0.18 0.39 1,963 0.19 0.39 5,367 0.21 0.41

Aragon 3,793 0.04 0.19 1,963 0.04 0.19 5,367 0.04 0.18

Asturias 3,793 0.03^S 0.17 1,963 0.02 0.16 5,367 0.02^S 0.14

Balearic Islands 3,793 0.02 0.17 1,963 0.02 0.13 5,367 0.02 0.13

Canary Islands 3,793 0.03 0.18 1,963 0.04 0.20 5,367 0.03 0.16

Cantabria 3,793 0.03 0.16 1,963 0.02 0.15 5,367 0.02 0.13

Castile la Mancha 3,793 0.05 0.22 1,963 0.04 0.20 5,367 0.05 0.21

Castile Leon 3,793 0.06 0.23 1,963 0.05 0.22 5,367 0.05 0.21

Catalonia 3,793 0.11 0.31 1,963 0.11 0.32 5,367 0.12 0.33

Valencian Community 3,793 0.09 0.28 1,963 0.10 0.30 5,367 0.11 0.31

Extremadura 3,793 0.03 0.17 1,963 0.03 0.17 5,367 0.02 0.14

Galicia 3,793 0.07 0.26 1,963 0.07 0.26 5,367 0.06 0.24

Madrid 3,793 0.14 0.35 1,963 0.14 0.35 5,367 0.15 0.35

Murcia 3,793 0.04 0.18 1,963 0.04 0.21 5,367 0.04 0.20

Navarra 3,793 0.02 0.15 1,963 0.02 0.13 5,367 0.02 0.12

Basque Country 3,793 0.04 0.21 1,963 0.05 0.21 5,367 0.05 0.21

La Rioja 3,793 0.02 0.13 1,963 0.02 0.13 5,367 0.01 0.11

Missing flag 3,793 0.00^S 0.02 1,963 0.00^S 0.00 5,367 0.00^S 0.01

Notes

Variables		Sample born between 1947-1968		Sample born between 1969-1975		Sample born between 1976-2004
Competences		Reading		3,793	(-0.28)^S	0.98		1,963	0.10^S	0.97		5,367	0.20^S	0.96
		Mathematics		3,793	(-0.24)^S	1.00		1,963	0.10^S	0.96		5,367	0.18^S	0.95
The respondent dropped out		Yes		3,793	0.46^S	0.50		1,963	0.28^S	0.45		5,367	0.20^S	0.40
	No		3,793	0.54^S	0.50		1,963	0.72^S	0.45		5,367	0.80^S	0.40
Years spent on education		3,793	13.35^S	4.38		1,963	14.98^S	3.65		5,367	15.38^S	3.24
Gender		Female		3,793	0.53^S	0.50		1,963	0.53	0.50		5,367	0.53^S	0.50
		Male		3,793	0.47^S	0.50		1,963	0.47	0.50		5,367	0.47^S	0.50
Immigrant status		Native		3,793	0.89^S	0.31		1,963	0.84^S	0.37		5,367	0.78^S	0.41
	First-generation immigrant		3,793	0.09^S	0.29		1,963	0.15^S	0.36		5,367	0.18^S	0.39
	Second-generation immigrant		3,793	0.01^S	0.12		1,963	0.01^S	0.11		5,367	0.04^S	0.19
Standardized Economic, Social and Cultural Status (ESCS)		ESCS Index		3,793	(-0.30)^S	0.81		1,963	(-0.10)^S	0.91		5,367	0.26^S	1.04
	Missing flag		3,793	0.00^S	0.02		1,963	0.00^S	0.02		5,367	0.00^S	0.04
Autonomous Community		Andalusia		3,793	0.18	0.39		1,963	0.19	0.39		5,367	0.21	0.41
		Aragon		3,793	0.04	0.19		1,963	0.04	0.19		5,367	0.04	0.18
		Asturias		3,793	0.03^S	0.17		1,963	0.02	0.16		5,367	0.02^S	0.14
		Balearic Islands		3,793	0.02	0.17		1,963	0.02	0.13		5,367	0.02	0.13
		Canary Islands		3,793	0.03	0.18		1,963	0.04	0.20		5,367	0.03	0.16
		Cantabria		3,793	0.03	0.16		1,963	0.02	0.15		5,367	0.02	0.13
		Castile la Mancha		3,793	0.05	0.22		1,963	0.04	0.20		5,367	0.05	0.21
		Castile Leon		3,793	0.06	0.23		1,963	0.05	0.22		5,367	0.05	0.21
		Catalonia		3,793	0.11	0.31		1,963	0.11	0.32		5,367	0.12	0.33
		Valencian Community		3,793	0.09	0.28		1,963	0.10	0.30		5,367	0.11	0.31
		Extremadura		3,793	0.03	0.17		1,963	0.03	0.17		5,367	0.02	0.14
		Galicia		3,793	0.07	0.26		1,963	0.07	0.26		5,367	0.06	0.24
		Madrid		3,793	0.14	0.35		1,963	0.14	0.35		5,367	0.15	0.35
		Murcia		3,793	0.04	0.18		1,963	0.04	0.21		5,367	0.04	0.20
		Navarra		3,793	0.02	0.15		1,963	0.02	0.13		5,367	0.02	0.12
		Basque Country		3,793	0.04	0.21		1,963	0.05	0.21		5,367	0.05	0.21
		La Rioja		3,793	0.02	0.13		1,963	0.02	0.13		5,367	0.01	0.11
		Missing flag		3,793	0.00^S	0.02		1,963	0.00^S	0.00		5,367	0.00^S	0.01

The procedures indicated in OECD (2016) (weighting and plausible values) have been employed. “Obs.” stands for “Observations” and “S.d.” for “Standard Deviation”. The values in bold indicate that there are significant differences (at 5% or less) between population born between 1958–1968, the population born between 1969–1975 and the population born between 1976-2004.

Source: Authors’ own calculations.

Table A4 Robustness Check. First-stage regression results for years of education and dropout

Specification I. Without Controls Specification II. With Controls

Variables Years of Education Dropout Years of Education Dropout

LEP+LOE -2.161*** 0.796*** -1.304*** 0.576***

(0.097) (0.034) (0.092) (0.036)

LGE -0.559*** 0.338*** 0.029 0.169***

(0.111) (0.044) (0.102) (0.047)

Standardized Economic, Social and Cultural Status (ESCS)

ESCS Index 1.482*** -0.567***

(0.039) (0.024)

Missing Flag -2.054* 0.038

(1.167) (0.620)

Gender (Ref.: male)

Female 0.339*** -0.119***

(0.077) (0.032)

Immigrant status (Ref.: native)

Second-generation immigrant -0.614*** -0.084

(0.226) (0.107)

Missing Flag -5.264***

(0.147)

Autonomous Community (Ref.: Andalusia)

Aragon 0.715*** -0.227***

(0.193) (0.084)

Asturias 1.390*** -0.379***

(0.225) (0.106)

Balearic Islands 0.078 -0.147

(0.335) (0.144)

Canary Islands -0.166 0.017

(0.230) (0.091)

Cantabria 0.804*** -0.167

(0.273) (0.119)

Castile La Mancha 0.420** 0.003

(0.197) (0.075)

Castile Leon 0.911*** -0.252***

(0.168) (0.076)

Catalonia 0.596*** -0.105*

(0.149) (0.058)

Valencian Community 0.395*** -0.075

(0.145) (0.062)

Extremadura -0.740*** 0.256***

(0.252) (0.098)

Galicia 0.204 -0.046

(0.169) (0.065)

Madrid 0.903*** -0.212***

(0.132) (0.057)

Murcia 0.357 -0.056

(0.230) (0.086)

Navarra 0.637** -0.218*

(0.269) (0.119)

Basque Country 1.553*** -0.407***

(0.188) (0.081)

La Rioja 0.682 -0.022

(0.435) (0.168)

Missing Flag 3.230***

(1.166)

Constant 15.340*** -0.922*** 14.521*** -0.725***

(0.049) (0.025) (0.100) (0.043)

Observations 9,489 9,489 9,489 9,486

Notes

Estimation method: First stage of Two-Stages Least Squares (2SLS).

Coefficient: ***

Significant at 1%,

significant at 5%,

significant at 10%.

Source: Authors’ own calculations.

Table A5 Robustness Check. The influence of years of education and dropping out on Spanish literacy and numeracy skills

Variables Specification I. Estimations with OLS and controls Specification II. Estimations with IV and controls

Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills Literacy Skills Numeracy Skills

Dropout (Ref.: did not drop out)

The student dropped out -0.666*** -0.693*** -1.854*** -1.777***

(0.022) (0.022) (0.088) (0.088)

Years spent on education 0.115*** 0.117*** 0.264*** 0.215***

(0.003) (0.003) (0.018) (0.016)

Standardized Economic, Social and Cultural Status (ESCS)

ESCS Index 0.174*** 0.177*** 0.258*** 0.260*** -0.071** 0.016 0.070*** 0.089***

(0.010) (0.010) (0.011) (0.011) (0.030) (0.028) (0.017) (0.017)

Missing Flag 0.949*** -1.012* -1.228*** -1.295** -0.596** -0.780 -1.235*** -1.302**

(0.180) (0.585) (0.198) (0.605) (0.303) (0.588) (0.141) (0.594)

Gender (Ref.: male)

Female 0.102*** -0.262*** -0.085*** -0.245*** -0.147*** -0.292*** -0.119*** -0.276***

(0.018) (0.018) (0.019) (0.019) (0.022) (0.020) (0.019) (0.019)

Immigrant status (Ref.: native)

Second-generation immigrant -0.020 -0.125** -0.102 -0.208*** 0.044 -0.082 -0.157** -0.259***

(0.061) (0.063) (0.064) (0.066) (0.071) (0.069) (0.063) (0.066)

Missing Flag 0.389*** 0.027 0.467*** 0.094*** -0.322*** -0.441***

(0.033) (0.032) (0.036) (0.036) (0.089) (0.082)

Autonomous Community (Ref.: Andalusia)

Aragon -0.102** 0.013 -0.071 0.043 -0.199*** -0.051 -0.152*** -0.031

(0.045) (0.042) (0.047) (0.045) (0.054) (0.048) (0.048) (0.046)

Asturias -0.066 -0.039 0.017 0.044 -0.253*** -0.163** -0.093* -0.057

(0.053) (0.053) (0.054) (0.053) (0.071) (0.064) (0.054) (0.053)

Balearic Islands -0.041 -0.064 -0.074 -0.098 -0.044 -0.066 -0.134 -0.153*

(0.076) (0.078) (0.084) (0.082) (0.091) (0.088) (0.082) (0.083)

Canary Islands -0.094* -0.124** -0.105* -0.135** -0.070 -0.108* -0.092* -0.123**

(0.051) (0.051) (0.054) (0.054) (0.064) (0.056) (0.054) (0.054)

Cantabria -0.043 -0.004 0.011 0.050 -0.143 -0.070 -0.030 0.012

(0.094) (0.097) (0.101) (0.103) (0.102) (0.102) (0.102) (0.104)

Castile La Mancha 0.128*** -0.059 -0.077* -0.008 -0.189*** -0.099** -0.072* -0.003

(0.039) (0.041) (0.041) (0.042) (0.053) (0.048) (0.041) (0.042)

Castile Leon 0.175*** 0.221*** 0.226*** 0.272*** 0.054 0.142*** 0.149**** 0.203***

(0.040) (0.039) (0.042) (0.041) (0.051) (0.044) (0.042) (0.040)

Catalonia -0.012 0.057* 0.031 0.100*** -0.088** 0.006 0.002 0.073**

(0.033) (0.032) (0.035) (0.034) (0.041) (0.036) (0.035) (0.034)

Valencian Community 0.184*** 0.170*** 0.213*** 0.200*** 0.124*** 0.131*** 0.183*** 0.173***

(0.033) (0.034) (0.035) (0.035) (0.040) (0.037) (0.035) (0.035)

Extremadura -0.152** -0.157** -0.179** -0.182*** -0.042 -0.084 -0.072 -0.085

(0.071) (0.064) (0.077) (0.070) (0.078) (0.068) (0.079) (0.071)

Galicia 0.045 0.077** 0.057 0.089** 0.022 0.062 0.045 0.078*

(0.039) (0.038) (0.041) (0.040) (0.046) (0.041) (0.040) (0.040)

Madrid -0.062* -0.019 -0.001 0.042 -0.181*** -0.098*** -0.059* -0.011

(0.032) (0.032) (0.034) (0.034) (0.039) (0.037) (0.033) (0.034)

Murcia 0.070 0.105** 0.097* 0.132** 0.009 0.065 0.063 0.101**

(0.048) (0.048) (0.052) (0.052) (0.055) (0.049) (0.050) (0.051)

Navarra 0.029 0.192*** 0.064 0.226*** -0.055 0.136** 0.008 0.174***

(0.074) (0.061) (0.082) (0.066) (0.078) (0.065) (0.082) (0.066)

Basque Country 0.182*** -0.039 -0.087* 0.057 -0.399*** -0.182*** -0.217*** -0.062

(0.043) (0.041) (0.045) (0.043) (0.056) (0.049) (0.045) (0.044)

La Rioja 0.122 0.061 0.199** 0.139* 0.006 -0.015 0.175** 0.117

(0.078) (0.071) (0.079) (0.080) (0.115) (0.080) (0.079) (0.084)

Missing Flag 0.491*** -0.677*** -0.402** -0.591** -0.891*** -0.940***

(0.048) (0.120) (0.165) (0.242) (0.093) (0.060)

Constant 1.538*** -1.511*** 0.314*** 0.375*** -3.629*** -2.889*** 0.719*** 0.745***

(0.045) (0.046) (0.025) (0.024) (0.254) (0.228) (0.038) (0.038)

Observations 9,489 9,489 9,489 9,489 9,489 9,489 9,486 9,486

Instrumental variables analysis

Hansen J overidentification test 0.001 0.922 15.396*** 25.220***

Kleibergen-Paap rk LM 112.153*** 111.686*** 145.976*** 145.976***

Notes

Variables	Specification I. Estimations with OLS and controls
Dropout (Ref.: did not drop out)
The student dropped out			-0.666***	-0.693***			-1.854***	-1.777***
			(0.022)	(0.022)			(0.088)	(0.088)
Years spent on education	0.115***	0.117***			0.264***	0.215***
	(0.003)	(0.003)			(0.018)	(0.016)
Standardized Economic, Social and Cultural Status (ESCS)
ESCS Index	0.174***	0.177***	0.258***	0.260***	-0.071**	0.016	0.070***	0.089***
	(0.010)	(0.010)	(0.011)	(0.011)	(0.030)	(0.028)	(0.017)	(0.017)
Missing Flag	0.949***	-1.012*	-1.228***	-1.295**	-0.596**	-0.780	-1.235***	-1.302**
	(0.180)	(0.585)	(0.198)	(0.605)	(0.303)	(0.588)	(0.141)	(0.594)
Gender (Ref.: male)
Female	0.102***	-0.262***	-0.085***	-0.245***	-0.147***	-0.292***	-0.119***	-0.276***
	(0.018)	(0.018)	(0.019)	(0.019)	(0.022)	(0.020)	(0.019)	(0.019)
Immigrant status (Ref.: native)
Second-generation immigrant	-0.020	-0.125**	-0.102	-0.208***	0.044	-0.082	-0.157**	-0.259***
	(0.061)	(0.063)	(0.064)	(0.066)	(0.071)	(0.069)	(0.063)	(0.066)
Missing Flag	0.389***	0.027	0.467***	0.094***	-0.322***	-0.441***
	(0.033)	(0.032)	(0.036)	(0.036)	(0.089)	(0.082)
Autonomous Community (Ref.: Andalusia)
Aragon	-0.102**	0.013	-0.071	0.043	-0.199***	-0.051	-0.152***	-0.031
	(0.045)	(0.042)	(0.047)	(0.045)	(0.054)	(0.048)	(0.048)	(0.046)
Asturias	-0.066	-0.039	0.017	0.044	-0.253***	-0.163**	-0.093*	-0.057
	(0.053)	(0.053)	(0.054)	(0.053)	(0.071)	(0.064)	(0.054)	(0.053)
Balearic Islands	-0.041	-0.064	-0.074	-0.098	-0.044	-0.066	-0.134	-0.153*
	(0.076)	(0.078)	(0.084)	(0.082)	(0.091)	(0.088)	(0.082)	(0.083)
Canary Islands	-0.094*	-0.124**	-0.105*	-0.135**	-0.070	-0.108*	-0.092*	-0.123**
	(0.051)	(0.051)	(0.054)	(0.054)	(0.064)	(0.056)	(0.054)	(0.054)
Cantabria	-0.043	-0.004	0.011	0.050	-0.143	-0.070	-0.030	0.012
	(0.094)	(0.097)	(0.101)	(0.103)	(0.102)	(0.102)	(0.102)	(0.104)
Castile La Mancha	0.128***	-0.059	-0.077*	-0.008	-0.189***	-0.099**	-0.072*	-0.003
	(0.039)	(0.041)	(0.041)	(0.042)	(0.053)	(0.048)	(0.041)	(0.042)
Castile Leon	0.175***	0.221***	0.226***	0.272***	0.054	0.142***	0.149****	0.203***
	(0.040)	(0.039)	(0.042)	(0.041)	(0.051)	(0.044)	(0.042)	(0.040)
Catalonia	-0.012	0.057*	0.031	0.100***	-0.088**	0.006	0.002	0.073**
	(0.033)	(0.032)	(0.035)	(0.034)	(0.041)	(0.036)	(0.035)	(0.034)
Valencian Community	0.184***	0.170***	0.213***	0.200***	0.124***	0.131***	0.183***	0.173***
	(0.033)	(0.034)	(0.035)	(0.035)	(0.040)	(0.037)	(0.035)	(0.035)
Extremadura	-0.152**	-0.157**	-0.179**	-0.182***	-0.042	-0.084	-0.072	-0.085
	(0.071)	(0.064)	(0.077)	(0.070)	(0.078)	(0.068)	(0.079)	(0.071)
Galicia	0.045	0.077**	0.057	0.089**	0.022	0.062	0.045	0.078*
	(0.039)	(0.038)	(0.041)	(0.040)	(0.046)	(0.041)	(0.040)	(0.040)
Madrid	-0.062*	-0.019	-0.001	0.042	-0.181***	-0.098***	-0.059*	-0.011
	(0.032)	(0.032)	(0.034)	(0.034)	(0.039)	(0.037)	(0.033)	(0.034)
Murcia	0.070	0.105**	0.097*	0.132**	0.009	0.065	0.063	0.101**
	(0.048)	(0.048)	(0.052)	(0.052)	(0.055)	(0.049)	(0.050)	(0.051)
Navarra	0.029	0.192***	0.064	0.226***	-0.055	0.136**	0.008	0.174***
	(0.074)	(0.061)	(0.082)	(0.066)	(0.078)	(0.065)	(0.082)	(0.066)
Basque Country	0.182***	-0.039	-0.087*	0.057	-0.399***	-0.182***	-0.217***	-0.062
	(0.043)	(0.041)	(0.045)	(0.043)	(0.056)	(0.049)	(0.045)	(0.044)
La Rioja	0.122	0.061	0.199**	0.139*	0.006	-0.015	0.175**	0.117
	(0.078)	(0.071)	(0.079)	(0.080)	(0.115)	(0.080)	(0.079)	(0.084)
Missing Flag	0.491***	-0.677***	-0.402**	-0.591**	-0.891***	-0.940***
	(0.048)	(0.120)	(0.165)	(0.242)	(0.093)	(0.060)
Constant	1.538***	-1.511***	0.314***	0.375***	-3.629***	-2.889***	0.719***	0.745***
	(0.045)	(0.046)	(0.025)	(0.024)	(0.254)	(0.228)	(0.038)	(0.038)

Observations	9,489	9,489	9,489	9,489	9,489	9,489	9,486	9,486
Instrumental variables analysis
Hansen J overidentification test					0.001	0.922	15.396***	25.220***
Kleibergen-Paap rk LM					112.153***	111.686***	145.976***	145.976***

Standard errors are in parentheses. The procedures indicated in OECD (2016) (weighting and plausible values) have been employed. Missing flag has been included to prevent missing information on the autonomous community. The null hypothesis of the Hansen J overidentification test is that the instruments of the overidentified model are valid. The Kleibergen-Paap Wald rk F statistic yield the values to be compared with the critical values for strong instruments.

Estimation method: First stage of Two-Stages Least Squares (2SLS).

Coefficient: ***

Significant at 1%,

significant at 5%,

significant at 10%.

Source: Authors’ own calculations.

Variables	Specification I. Without controls				Specification II. With controls
Variables	Literacy Skills	Numeracy Skills	Literacy Skills	Numeracy Skills	Literacy Skills	Numeracy Skills	Literacy Skills	Numeracy Skills
Dropout (Ref.: did not drop out)
The student dropped out			-0.822***	-0.852***			-0.635***	-0.665***
			(0.021)	(0.021)			(0.020)	(0.021)
Years spent on education	0.134***	0.137***			0.114***	0.116***
	(0.002)	(0.002)			(0.003)	(0.003)
Standardized Economic, Social and Cultural Status (ESCS)
ESCS Index					0.188***	0.193***	0.276***	0.281***
					(0.010)	(0.010)	(0.010)	(0.010)
Missing Flag					-0.770***	-0.777**	-1.025***	-1.035***
					(0.151)	(0.368)	(0.161)	(0.379)
Gender (Ref.: male)
Female					-0.096***	-0.256***	-0.076***	-0.236***
					(0.017)	(0.017)	(0.018)	(0.018)
Immigrant status (Ref.: native)
First-generation immigrant					-0.500***	-0.453***	-0.559***	-0.514***
					(0.027)	(0.027)	(0.029)	(0.028)
Second-generation immigrant					-0.024	-0.130**	-0.104	-0.213***
					(0.061)	(0.063)	(0.064)	(0.066)
Missing Flags					0.410***	0.049	0.505***	0.134***
					(0.031)	(0.031)	(0.034)	(0.034)
Autonomous Community (Ref.: Andalusia)
Aragon					-0.169***	-0.070	-0.146***	-0.049
					(0.044)	(0.043)	(0.047)	(0.046)
Asturias					-0.071	-0.066	0.016	0.022
					(0.052)	(0.051)	(0.052)	(0.051)
Balearic Islands					-0.051	0.001	-0.094	-0.044
					(0.070)	(0.065)	(0.078)	(0.071)
Canary Islands					-0.094**	-0.106**	-0.097*	-0.109**
					(0.047)	(0.049)	(0.051)	(0.052)
Cantabria					-0.033	-0.016	0.030	0.048
					(0.091)	(0.091)	(0.098)	(0.098)
Castile La Mancha					-0.139***	-0.075*	-0.085**	-0.020
					(0.038)	(0.040)	(0.040)	(0.042)
Castile Leon					0.143***	0.188***	0.191***	0.235***
					(0.040)	(0.038)	(0.042)	(0.040)
Catalonia					-0.054*	0.008	-0.016	0.047
					(0.031)	(0.031)	(0.033)	(0.033)
Valencian Community					0.178***	0.153***	0.211***	0.186***
					(0.032)	(0.033)	(0.034)	(0.034)
Extremadura					-0.158**	-0.168***	-0.181**	-0.190***
					(0.070)	(0.064)	(0.076)	(0.069)
Galicia					0.054	0.077**	0.069*	0.091**
					(0.037)	(0.036)	(0.039)	(0.038)
Madrid					-0.085***	-0.052*	-0.031	0.002
					(0.030)	(0.030)	(0.032)	(0.032)
Murcia					0.063	0.103**	0.082	0.122**
					(0.047)	(0.046)	(0.050)	(0.050)
Navarra					-0.020	0.101*	0.001	0.123*
					(0.071)	(0.060)	(0.076)	(0.063)
Basque Country					-0.198***	-0.059	-0.116***	0.023
					(0.041)	(0.039)	(0.043)	(0.041)
La Rioja					0.132	0.066	0.209**	0.144*
					(0.081)	(0.071)	(0.087)	(0.082)
Missing Flag					-0.503***	-0.693***	-0.410***	-0.605**
					(0.046)	(0.117)	(0.159)	(0.235)
Constant	-1.954***	-1.977***	0.251***	0.272***	-1.501***	-1.475***	0.316***	0.382***
	(0.037)	(0.038)	(0.012)	(0.012)	(0.043)	(0.044)	(0.024)	(0.024)

Observations	11,123	11,123	11,123	11,123	11,123	11,123	11,123	11,123

	Specification I. Without Controls		Specification II. With Controls
Variables	Years of Education	Dropout	Years of Education	Dropout
LEP+LOE	-1.898***	0.746***	-1.148***	0.553***
	(0.092)	(0.031)	(0.086)	(0.033)
LGE	-0.451***	0.323***	0.071	0.175***
	(0.104)	(0.040)	(0.095)	(0.042)
Standardized Economic, Social and Cultural Status (ESCS)
ESCS Index			1.506***	-0.548***
			(0.035)	(0.021)
Missing Flag			-2.748**	0.402
			(0.952)	(0.511)
Gender (Ref.: male)
Female			0.379***	-0.125***
			(0.072)	(0.030)
Immigrant status (Ref.: native)
First-generation immigrant			-0.620***	0.051
			(0.104)	(0.044)
Second-generation immigrant			-0.595***	-0.089
			(0.228)	(0.106)
Missing Flag			5.205***
			(0.140)
Autonomous Community (Ref.: Andalusia)
Aragon			0.689***	-0.263***
			(0.179)	(0.080)
Asturias			1.277***	-0.296***
			(0.223)	(0.100)
Balearic Islands			-0.157	-0.092
			(0.294)	(0.118)
Canary Islands			-0.016	-0.025
			(0.217)	(0.087)
Cantabria			0.794***	-0.127
			(0.264)	(0.112)
Castile La Mancha			0.407**	0.026
			(0.187)	(0.071)
Castile Leon			0.866***	-0.256***
			(0.159)	(0.072)
Catalonia			0.528***	-0.099*
			(0.135)	(0.053)
Valencian Community			0.412***	-0.065
			(0.135)	(0.057)
Extremadura			-0.642***	0.227**
			(0.243)	(0.095)
Galicia			0.268*	-0.072
			(0.159)	(0.061)
Madrid			0.737***	-0.152***
			(0.123)	(0.051)
Murcia			0.170	-0.002
			(0.221)	(0.078)
Navarra			0.543**	-0.232**
			(0.240)	(0.108)
Basque Country			1.271***	-0.313***
			(0.196)	(0.077)
La Rioja			0.669	-0.019
			(0.410)	(0.154)
Missing Flag			2.503**
			(1.083)
Constant	15.340***	-0.888***	14.482***	-0.738***
	(0.049)	(0.022)	(0.097)	(0.040)

Observations	11,123	11,123	11,123	11,120

Variables		Sample born between 1947-1968			Sample born between 1969-1975			Sample born between 1976-2004
Variables		Obs.	Mean	S.d.	Obs.	Mean	S.d.	Obs.	Mean	S.d.
Competences	Reading	3,793	(-0.28)^S	0.98	1,963	0.10^S	0.97	5,367	0.20^S	0.96
	Mathematics	3,793	(-0.24)^S	1.00	1,963	0.10^S	0.96	5,367	0.18^S	0.95
The respondent dropped out	Yes	3,793	0.46^S	0.50	1,963	0.28^S	0.45	5,367	0.20^S	0.40
The respondent dropped out	No	3,793	0.54^S	0.50	1,963	0.72^S	0.45	5,367	0.80^S	0.40
Years spent on education		3,793	13.35^S	4.38	1,963	14.98^S	3.65	5,367	15.38^S	3.24
Gender	Female	3,793	0.53^S	0.50	1,963	0.53	0.50	5,367	0.53^S	0.50
	Male	3,793	0.47^S	0.50	1,963	0.47	0.50	5,367	0.47^S	0.50
Immigrant status	Native	3,793	0.89^S	0.31	1,963	0.84^S	0.37	5,367	0.78^S	0.41
	First-generation immigrant	3,793	0.09^S	0.29	1,963	0.15^S	0.36	5,367	0.18^S	0.39
	Second-generation immigrant	3,793	0.01^S	0.12	1,963	0.01^S	0.11	5,367	0.04^S	0.19
Standardized Economic, Social and Cultural Status (ESCS)	ESCS Index	3,793	(-0.30)^S	0.81	1,963	(-0.10)^S	0.91	5,367	0.26^S	1.04
Standardized Economic, Social and Cultural Status (ESCS)	Missing flag	3,793	0.00^S	0.02	1,963	0.00^S	0.02	5,367	0.00^S	0.04
Autonomous Community	Andalusia	3,793	0.18	0.39	1,963	0.19	0.39	5,367	0.21	0.41
	Aragon	3,793	0.04	0.19	1,963	0.04	0.19	5,367	0.04	0.18
	Asturias	3,793	0.03^S	0.17	1,963	0.02	0.16	5,367	0.02^S	0.14
	Balearic Islands	3,793	0.02	0.17	1,963	0.02	0.13	5,367	0.02	0.13
	Canary Islands	3,793	0.03	0.18	1,963	0.04	0.20	5,367	0.03	0.16
	Cantabria	3,793	0.03	0.16	1,963	0.02	0.15	5,367	0.02	0.13
	Castile la Mancha	3,793	0.05	0.22	1,963	0.04	0.20	5,367	0.05	0.21
	Castile Leon	3,793	0.06	0.23	1,963	0.05	0.22	5,367	0.05	0.21
	Catalonia	3,793	0.11	0.31	1,963	0.11	0.32	5,367	0.12	0.33
	Valencian Community	3,793	0.09	0.28	1,963	0.10	0.30	5,367	0.11	0.31
	Extremadura	3,793	0.03	0.17	1,963	0.03	0.17	5,367	0.02	0.14
	Galicia	3,793	0.07	0.26	1,963	0.07	0.26	5,367	0.06	0.24
	Madrid	3,793	0.14	0.35	1,963	0.14	0.35	5,367	0.15	0.35
	Murcia	3,793	0.04	0.18	1,963	0.04	0.21	5,367	0.04	0.20
	Navarra	3,793	0.02	0.15	1,963	0.02	0.13	5,367	0.02	0.12
	Basque Country	3,793	0.04	0.21	1,963	0.05	0.21	5,367	0.05	0.21
	La Rioja	3,793	0.02	0.13	1,963	0.02	0.13	5,367	0.01	0.11
	Missing flag	3,793	0.00^S	0.02	1,963	0.00^S	0.00	5,367	0.00^S	0.01