## Abstract

Most low- and middle-income countries have implemented mass education reforms in the last few decades. Demographers and policymakers have posited that mass schooling would enhance women's autonomy and, therefore, accelerate population transformations in the Global South. However, gains in women's schooling may have unexpected implications for female autonomy in contexts where hypergamy norms—the ideal that men should marry down and women should marry up in education and other markers of status—are still dominant. This study addresses difficulties in evaluating the causal impact of additional education on women's autonomy by leveraging the timing of compulsory schooling reforms in three Latin American countries: Bolivia, Colombia, and Peru. Using Demographic and Health Surveys, I implement an instrumental variable design using random exposure to compulsory schooling laws as an instrument for years of education. Results show that for women who entered the school system as a result of compulsory reforms, further schooling decreased their level of autonomy in all countries—especially among women from rural Bolivia and Peru. Additional analyses suggest these results are explained by changes in the selection into schooling and the formation of unions defying hypergamy norms. Together, these findings highlight the importance of examining the returns to mass schooling considering population heterogeneity and the contextual meaning of women's education.

## Introduction

In the last few decades, compulsory school reforms have been implemented across most low- and middle-income countries (LMICs) (Buchmann and Hannum 2001). A direct consequence of these policies has been a dramatic rise in women's schooling and a reduction in the gender gap in education (Dorius and Firebaugh 2010; Grant and Behrman 2010). Scholars have investigated the effects of further schooling on women's marriage timing, child mortality, and intimate partner violence, among other outcomes (Andriano and Monden 2019; Grant 2015; Weitzman 2017); however, less is known about the impact of mass education on female autonomy, an important predictor of women's health, reproductive behavior, and overall well-being (Balk 1994; Dyson and Moore 1983; Oppenheimer 1997; Upadhyay and Hindin 2005).

Demographers and development scholars have argued that mass schooling accelerates population transformations by increasing women's status in the home and enabling them to make decisions about their health, earnings, and movement (Caldwell 1980; Inkeles 1969; Therborn 2004). Similarly, aid agencies and multilateral organizations have embraced mass schooling as an effective policy for increasing women's autonomy in countries with high gender inequality (Murphy-Graham and Lloyd 2016). However, gains in women's schooling may have unexpected implications for female autonomy in contexts where hypergamy norms—the ideal that men should marry down and women should marry up in education and other markers of social status—are still dominant. The prevalence of these expectations has been associated with lower marriage rates among educated women and high tensions within couples who do not conform to this ideal—including higher rates of intimate partner violence (Behrman 2019; Jewkes 2002; Vyas and Watts 2009). Thus, if women's gains in education represent a challenge to men's dominant status in families, mass schooling may unexpectedly hinder women's autonomy in these contexts.

Scholarship on the effect of mass schooling on women's autonomy in the Global South is inconclusive. While some studies show that education is associated with increased autonomy (Acharya et al. 2010; Basu 1992; Jejeebhoy and Sathar 2001; Oropesa 1997), others find it ineffective (Heaton et al. 2005; Malhotra and Mather 1997; Wolf 1985). The heterogeneity of these findings may be because of the endogeneity of schooling. As women's education and autonomy are both predicted by family background, cognitive ability, and other unobserved differences, establishing a causal effect on the outcome of interest is especially difficult. Additionally, research has mostly centered on the case of married women, as changes in female empowerment tend to occur in relation to husbands. Focusing on this subpopulation, however, also introduces selection biases, given the correlation between education and union formation patterns (Raymo 2003; Schwartz and Mare 2005).

This article addresses these challenges by investigating three questions. First, what is the effect of mass schooling on women's autonomy? Second, does the impact of schooling vary according to women's background? Third, are changes in women's union formation a potential pathway through which education affects their autonomy? I answer these questions by leveraging quasi-experimental variation in compulsory schooling reforms enacted in Bolivia, Colombia, and Peru. These Latin American countries implemented such reforms during the 1990s, at similar stages of development and amid the prevalence of hypergamy norms in families, especially among rural populations (García and de Oliveira 1994; Ingoldsby 1991). However, these societies differed in their level of gender inequality in key domains. For instance, while gender gaps in education were still sizable in Bolivia and Peru at the time of these reforms, Colombia already had a female advantage in primary and secondary education (IPUMS 2020). Thus, this comparison allows me to examine the effects of mass schooling on women's autonomy across contexts that share similar socioeconomic and cultural conditions but vary in their degree of educational gender inequality.

In this analysis, I first assess the changes in the returns to schooling for women's autonomy across birth cohorts that were differentially exposed to educational expansion. I then focus on the effects of compulsory schooling reforms via an instrumental variable (IV) design, using random exposure to these laws as an instrument for years of education. This approach allows me to disentangle the effect of schooling on women's autonomy from other unobserved factors that could confound this relationship.

My findings first show that women's schooling is positively associated with greater autonomy; however, these returns progressively diminish as educational systems expand. Once I address endogeneity via instrumental variables, I find that women who complied with compulsory laws and gained further education experienced a decrease in their autonomy in all countries, although this effect was notably smaller in Colombia. Additional analyses confirm that while education was a means of empowerment for most women, for those who were less likely to continue their education without compulsory reforms, further schooling did not fulfill the promise of greater autonomy. I then show that selection into schooling and union formation behavior may be important pathways explaining these effects. This study contributes to a growing literature documenting the unexpected implications of rapid increases in women's status in contexts where hypergamy norms and gender inequality are still ubiquitous.

## Literature Review

### Mass Education and Women's Autonomy

The enhancement of women's autonomy and decision-making has long been theorized as one of the benefits of educational expansion. Drawing on the experience of high-income countries, modernization scholars promoted mass schooling in the Global South as an effective tool to diffuse the values and motivations associated with development, including women's emancipation from subordinate roles (Inkeles 1969; Portes 2015). Indeed, the promotion of “developmental idealism”—including the notion that modern nuclear families are the root of development—had a significant influence on the adoption of mass schooling policies in LMICs (Thornton 2001; Thornton et al. 2015).

Demographers also viewed mass schooling as a unique policy to speed up demographic change and socioeconomic prosperity in these contexts. In his seminal article on education and fertility decline, Caldwell (1980) posited that the greatest effect of schooling would be on the transformation of family relationships and norms. Education was expected to increase women's autonomy and decision-making relative to traditional sources of authority in families—namely, parents and husbands. Population scholars further argued that women's enhanced autonomy would play an essential role in their demographic behavior and in the reduction of fertility, in particular (Caldwell 1980; Cleland and van Ginneken 1988).

Different mechanisms have been hypothesized to explain the relationship between mass education and increases in women's autonomy. Some argued that education would empower women by exposing them to gender-egalitarian attitudes (Bledsoe et al. 1999; Caldwell 1980), enhancing their cognitive abilities to make informed decisions (Kabeer 2005) and increasing their socioeconomic resources (Jejeebhoy 1995). However, as educational expansion unfolded in the Global South, several limitations of schooling for the enhancement of women's autonomy became apparent. The most alarming issues were the continuous enforcement of gender biases in schools (King and Hill 1993; Ohsako 1997; Stromquist 2001), as well as the persistent low quality of educational institutions (Pritchett 2013; Willms and Somer 2001).

In addition, mass education may also increase women's autonomy via the type of households and partnerships that educated women form in adulthood. Who women marry may affect their autonomy and decision-making, especially because changes in these domains occur relative to other household members—most importantly, their husbands (Basu 1992). Because partners may have conflicting interests and preferences, the bargaining position of each spouse shapes who has more agency and decision-making power to pursue those preferences (Agarwal 1997; Kabeer 2007). From a resource-exchange perspective, each spouse's bargaining power is a function of their relative resources, such as income or education, and their ability to effectively leave the marriage, if necessary (Cook and Whitmeyer 1992). In most high-income countries, highly educated women tend to marry equally educated men (Blossfeld 2009; Schwartz and Mare 2005), leading to unions with lower intramarital differences and, therefore, more balanced power relations. More highly educated women also tend to form unions with smaller intramarital age gaps (Baird et al. 2010), which tend to be more symmetrical in education and economic standing (Malhotra and Mather 1997; Pyke and Adams 2010). Thus, women exposed to compulsory laws may be more likely to enter unions with more egalitarian power relations in which husbands are more prone to share household decisions and foster women's autonomy.

Lastly, most prior scholarship has assumed that the benefits of education for women's autonomy do not change over time. Yet, the positive effects of schooling may vary as the number of educated women increases across birth cohorts. Recent analyses in Europe and the United States show that as education expands and more individuals obtain an educational credential, the marginal effect of such credentials declines (Horowitz 2015); these relative effects of education have been found for labor market outcomes (Bol 2015; Horowitz 2018) and civic participation (Horowitz 2015). Although few studies have investigated how the benefits of schooling on women's autonomy change throughout educational expansion, many have shown that the social meaning of women's schooling is shaped by their relative position in the educational distribution of their own cohort (Frye and Lopus 2018; Kravdal 2002; Schofer and Meyer 2005). Consequently, the positive effect of schooling on female autonomy may diminish as educational systems expand and higher proportions of women have more schooling.

### Women's Education, Hypergamy Norms, and Rural Contexts

Women's education, however, is not always an attractive trait in the marriage market. This is especially the case in contexts of high gender inequality. Hypergamy norms have historically structured marriage markets in Latin America (Esteve et al. 2016). Across contexts, the prevalence of educational hypergamy norms has been associated with lower marriage rates among educated women and with higher stress and tensions among couples in which wives are more educated than their husbands (Frye and Urbina 2020; Jewkes 2002; Vyas and Watts 2009). For example, violation of educational hypergamy norms in marriages has been associated with the limitation of women's autonomy (Koenig et al. 2003), increases in intimate partner violence (Behrman 2019; Oduro et al. 2015; Weitzman 2014), and husband's pursuit of other sexual partners (Hunter 2007; Morrell 2001).

In Latin America, and especially in rural contexts, hypergamy norms are prevalent and expressed in popular discourse as “machismo” (Chant 2002). Beyond the marriage market, this set of gendered beliefs structures families by assigning domestic responsibilities to wives and bread-winning activities to husbands, and by encouraging submissive behavior from women while promoting exaggerated masculinity among men (Ingoldsby 1991; Orgill and Heaton 2005). Although Latin American women have made important gains in educational attainment, labor participation, and economic independence in recent decades, behaviors consistent with hypergamy ideals remain prevalent (Chant 2002; García and de Oliveira 2011). Across the region, men often resist the desire of wives and daughters to work outside the home (Safa 1995), downplay women's financial contributions (García and de Oliveira 1994; Kabeer 2007), and engage in gender-based violence at higher rates than in most other countries (Friedemann-Sánchez and Lovatón 2012). Scholars of Latin America have interpreted these behaviors—including the use of violence—as responses to reaffirm masculine authority when men's dominant status in the home is undermined (Menjívar 2011; Safa 1995).

In this context, particularly in rural areas, women's schooling may not always be welcomed by families, nor attractive for bachelors. Indeed, before compulsory reforms, families in rural regions were more prone to resist women's education. Studies in Peru and Bolivia showed that parents tended to favor boys' schooling, and girls often left school to aid with domestic work and farming tasks (Ames 2005; Zapata et al. 2011). Across Latin America, more educated women are still less likely to get married, and those that enter a union are more prone to “marry down” in education (Ganguli et al. 2014). These trends may mean that educated women are penalized in the marriage market because of the perceived threat of their education, or that educated women opt out of marriage as it becomes an increasingly unattractive arrangement for them—a phenomenon also documented in other parts of the world (Raymo 2003; Raymo and Park 2020).

In sum, the interaction between women's schooling and the prevalence of hypergamy norms may shape the effects of education on women's autonomy in unexpected ways. Instead of marrying equally educated men who are more welcoming of women's autonomy, female students exposed to these reforms may enter unions that violate hypergamy norms, which in turn may hinder their autonomy and decision-making.

### Prior Research and the Present Study

The relationship between women's education and autonomy has received extensive scholarly attention. Several studies in LMICs have found that more educated women have higher levels of autonomy and decision-making (Acharya et al. 2010; Basu 1992; Cheng 2019; Jejeebhoy and Sathar 2001). However, other investigations have shown that education does not substantively enhance women's empowerment (Heaton et al. 2005; Malhotra and Mather 1997; Wolf 1985). Quantitative studies in Latin America have found a similar set of findings. In Mexico, Oropesa (1997) showed that education was crucial in increasing wives' decision-making power relative to their husbands. Heaton et al. (2005) found that schooling moderately increased women's autonomy and decision-making in Bolivia but had no effects in Peru and Nicaragua.

The heterogeneity of these findings may be due to multiple factors. Because most studies do not address the endogeneity of schooling, it is unclear whether these results are causal. For example, it may be that women with higher schooling are more likely to come from advantaged families, who espouse gender-egalitarian beliefs and are more prone to enroll their daughters in school. In these situations, we cannot know whether the positive effects of education on autonomy are due to women's schooling or unobserved differences in their family background. Also, prior scholarship has focused on the implications of education for women in marital unions. This seems like a natural choice, as changes in women's empowerment occur relative to other decision-makers in the family, usually their husbands. Nevertheless, because demographers have shown that schooling also shapes women's chances of entering a union and with whom they do so, focusing solely on married women also introduces selection biases.

The present study addresses these two issues by implementing an IV approach using exposure to compulsory schooling laws in Bolivia, Colombia, and Peru as an instrument. Compulsory laws have often been used in the demographic literature as instruments to uncover the causal effects of schooling (Andriano and Monden 2019; Behrman 2015; Grant 2015; Weitzman 2017). The next section provides further details on the context in which compulsory laws were implemented in the three countries.

## Background: Compulsory Schooling in Bolivia, Colombia, and Peru

During the 1990s, most Latin American governments implemented compulsory schooling laws. Bolivia, Colombia, and Peru each did so between 1991 and 1994, raising requirements for primary and lower secondary attainment.1 For a detailed description of these reforms, see the online appendix.

I study the effects of mass schooling on women's autonomy in Bolivia, Colombia, and Peru for several reasons. First, these reforms significantly increased women's educational attainment in all countries, a necessary condition to analyze the impact of greater schooling on female autonomy. Second, these countries shared several important socioeconomic characteristics when these reforms were implemented. At that time, each had a large rural population, a medium-high human development index,2 and a per capita GDP below the Latin American average (see Table A1 in the online appendix). In terms of education, Colombia was slightly behind Bolivia and Peru in mean years of schooling (5.5 vs. 6.4 and 6.6 in 1990, respectively), and in each country less than half of the population older than 25 had any secondary education (United Nations Development Programme 2020). Moreover, all three had wide education gaps between urban and rural populations, which were expected to be reduced via compulsory education reforms (UNESCO 2004). Rural populations in Bolivia and Peru tended to be indigenous communities, which in the early 1990s represented 55% and 35% of the population, respectively (IPUMS 2020). This was not the case in Colombia,3 where the largest minority group—representing 9% of the population—were Afro-descendants, who mostly lived in urban areas (IPUMS 2020).

Third, beyond these similarities, Bolivia, Colombia, and Peru also varied in the level of educational gender inequality when these reforms were implemented. Although the countries shared a common set of gendered beliefs promoting hypergamy and men's dominance in families (García and de Oliveira 2011), Colombia was the most gender-egalitarian in some key domains. At the time of compulsory reforms, Colombian women had almost equalized men's mean years of education (see Table A1 in the online appendix), and those born after 1960 had already surpassed men's educational attainment (IPUMS 2020). In Bolivia and Peru, women had almost two fewer years of education and were significantly less likely to have a secondary education (UNESCO 2020). Moreover, dropout rates were especially high among girls from rural populations, who often left school to help their families with domestic duties (Stromquist 2001; Zapata et al. 2011). Thus, comparing these countries offers the opportunity to analyze the effect of compulsory schooling on women's autonomy across contexts with similar socioeconomic and cultural characteristics, but that vary in key aspects of educational gender inequality.

## Research Design

### Data and Sample

For this analysis, I pool data from the Demographic and Health Surveys (DHS) collected between 2000 and 20164 (Heger Boyle et al. 2019). The analytic sample includes all women aged 20–49 years at the time of the survey.5 The central analysis compares a subsample of women who were just below the average exit age in primary school at the time of compulsory reforms (ages 9–11) with respondents just above the exit age at the time of implementation (ages 12–14). In Bolivia, this criterion yields a sample of 3,583 unexposed (born 1980–1982) and 2,289 exposed (born 1983–1985) women. In Colombia, the sample consists of 11,208 unexposed (born 1977–1979) and 11,680 exposed (born 1980–1982) respondents. Lastly, in Peru, the sample comprises 15,585 unexposed (born 1979–1981) and 16,601 exposed (born 1982–1984) women. Note that Colombia and Peru have much larger sample sizes as the number of DHS surveys available for each country is four and six waves, respectively, while Bolivia has only two surveys available for this analysis.

The analytic sample includes women in different household arrangements. Although most were either married or cohabiting, 20–34% were single.6 The majority of the latter lived with their parents (70% pooled across countries) at the time of the survey, while only 12% lived with other relatives and 13% were the head of household. Given that women's schooling is associated with union formation outcomes, the central analyses of this study make inferences about women's autonomy in the full universe of household configurations. In addition, secondary analyses explore whether women's union formation patterns may be a pathway explaining the effects of schooling on autonomy.

### Measures

#### Outcomes

Following prior demographic literature, this study defines autonomy as a woman's ability to execute decisions regarding her personal affairs and those concerning close family members (Ghuman 2003; Kabeer 1999). To measure women's autonomy, I use a series of questions7 about the control over their freedom of movement (item 1), own health (item 2), major household purchases (item 3), and own money (item 4). To read more about the validity and limitations of these measures, see the online appendix.

To improve the comparability of these questions across countries, I transform each of these items into binary indicators (Cavaille and Marshall 2019). I code each answer as 1 if women responded that they made each decision by themselves alone, by themselves and their partner, or by themselves and someone else, and as 0 if the decision was made either by their partner or by someone else alone. In the case of women not in a union, “someone else” generally refers to their parents or other relatives, as only 20% of unmarried respondents lived alone or with a nonfamily member. Moreover, this coding strategy captures whether women have a say in but not absolute dominance over decisions regarding personal and household matters. In that sense, it conceptualizes shared decision-making and negotiated autonomy as indicators of women's empowerment, relative to scenarios in which they do not have any say at all on these issues.8

I use these binary outcomes both as separate items and as an additive scale. In particular, I generate a scale of women's autonomy to capture its multidimensional nature. The autonomy scale is generated by summing the country-specific standardized scores of each recoded item in Table A3 in the online appendix. The resulting scale is sufficiently reliable, having a Cronbach's alpha score higher than .60 in all countries (Cortina 1993).9Table A4 contains descriptive statistics of autonomy measures by exposure to compulsory reforms.

#### Control Variables

Given that I pool different DHS rounds, I include survey year as a categorical variable in all models to account for period effects. I also control for respondents' ethnicity, given the existence of relevant schooling gaps among indigenous and Afro-descendant students. Ethnicity was operationalized as a categorical variable that included “Spanish/White,” “Quechua,” “Aymara,” and “Other Indigenous” for the case of Bolivia and Peru, and “Spanish/White,” “Indigenous,” “Afro-descendant,” and “Other” for Colombia.10 To control for potential regional differences in school construction, models include the current region of residence under the assumption that respondents have not moved since initiating primary schooling; given that these regions are broad geographic divisions in all countries, this assumption seems plausible. Results without regional controls are substantively the same but contain larger standard errors (see Table A5 in the online appendix).

Lastly, to examine heterogeneous treatment effects by women's background, I use a dichotomous version of the ethnicity variable—being indigenous or Afro-descendant versus not—and respondents' residence in childhood. The latter was operationalized as a categorical variable coded 1 if the respondent lived in a rural area during her childhood and 0 if she lived in a city or town. Because this measure was available only for some survey waves, I could not use it as a pretreatment measure for region of residence in the main IV models.

#### Pathways

I explore how union formation and partner characteristics may explain the effect of education on women's autonomy. I first examine respondents' likelihood of being in a marital union measured as a dichotomous indicator coded 1 if the respondent has never been married or cohabited and 0 if she has. The second set of measures focuses on partner characteristics among married respondents. I include (1) a dichotomous indicator for educational homogamy coded 1 if husbands and wives have equal years of education, (2) a dichotomous indicator for educational hypergamy coded 1 if husbands have at least one more year of schooling, and (3) a dichotomous indicator for educational hypergamy coded 1 if husbands have at least three more years of schooling. I also include (4) a dichotomous indicator for educational hypogamy coded 1 if wives have at least one more year of schooling and (5) a dichotomous indicator for educational hypogamy coded 1 if wives have at least three more years of schooling. Lastly, I construct (6) a dichotomous indicator of whether the respondent's partner is five years older. To further explore the role of partner characteristics for women's autonomy, I construct a dummy variable measuring whether husbands engage in controlling behavior, coded 1 if women report their husband engaging in any of the following behaviors: (1) being jealous or angry if she talks or talked to other men, (2) frequently accusing her of being unfaithful, and (3) trying to limit her contact with her family.

These measures do not distinguish between cohabitation and marriage because of the long tradition of coexistence between these two types of unions in Latin America (Esteve et al. 2012). Indeed, excluding the more economically advanced countries, cohabitation remains common at later stages of the life cycle, and unmarried couples usually bear children together (Palloni et al. 1996). In Bolivia, Colombia, and Peru, cohabitation accounts for almost two fifths of all marital unions and is not associated with lower levels of education (Esteve et al. 2012). Given the special status of cohabitation in Latin America, recent scholarship considers it as having a similar standing as marriage (Castro Martín 2002; Torche 2010). Thus, when using the term marriage in this article, I will also be referring to nonmarital unions.

### Analytic Strategy

To examine the relationship between mass schooling and women's autonomy in adulthood, I conduct two analyses. First, I examine the association between years of education and women's autonomy and how it changes across birth cohorts. The goal of this analysis is to assess how the autonomy returns of schooling shift as higher proportions of women access education. To this end, I estimate a series of ordinary least-squares (OLS) models in which I interact years of schooling with five-year grouped-birth cohorts born between 1970 and 1990. This set of birth cohorts encompasses women exposed to different stages of school expansion, providing a broader view of the relationship between mass education and women's position in the household. For each country, I estimated the following model:

$Yic=β0+β1Schoolingic+β2Cohortic+β3School×Cohortic+β4Xic+εic,$
(1)

where $Xic$ is a vector of covariates of individual $i$ in country $c$, including survey year, the region of residence, and ethnicity (in Peru and Bolivia11), and $εic$ are standard errors clustered by survey clusters.

The second analysis estimates the causal effect of women's schooling on their autonomy in the home via an IV approach. As mentioned, I compare birth cohorts that were young enough to be exposed to compulsory reforms with cohorts that were barely too old to be impacted by these laws. I use respondents' exposure to these reforms as an instrument for their total years of schooling using a two-stage least-squares (2SLS) estimation strategy in each country. Importantly, this approach yields the effect of an extra year of education among respondents who comply with compulsory laws, namely, the local average treatment effect (LATE) among compliers. To read about the specific assumptions underlying this analysis, see the online appendix.

In the first stage, I regress individual $i$ years of completed schooling on a dummy indicator of exposure to compulsory reforms $Exposedic$ in each country $c$, where $Xic$ is a vector of covariates for individual $i$, and $uic$ are standard errors clustered by survey cluster:

$Schoolingic=α0+α1Exposedic+α2Xic+uic.$
(2)

The second stage is a linear probability model where the outcome of interest is regressed on the predicted value of years of completed schooling from the first stage. The key parameter is $β1$, which yields the treatment effect of one extra year of education on women's autonomy, among respondents who complied with compulsory schooling laws:

$Outcomeic=β0+β1School^ingic+β2Xic+uic.$
(3)

All IV models control for survey year, region, and ethnicity (in Peru and Bolivia), and include robust standard errors, clustered by survey cluster.

To estimate heterogeneous treatment effects according to respondents' residence in childhood, I conduct the same IV procedure for each subgroup separately. Similarly, for the exploration of pathways, I use the same IV approach in which instead of estimating the effect of an extra year of schooling on women's autonomy, I assess the effect of education on women's likelihood of entering a union and, if in a union, their husbands' characteristics. There are two significant limitations to this supplementary analysis. First, although it can establish a causal link between schooling and each pathway, it cannot do so between each pathway and women's autonomy. Second, this analysis is only exploratory given that these pathways are not mutually exclusive, nor do they encompass all possible mechanisms that may explain these results.

Researchers using IV typically pay little attention to the characteristics of compliers and noncompliers (Marbach and Hangartner 2020). However, characterizing these groups is an important first step to assess the external validity of the estimated effects. To this end, I use the approach developed by Marbach and Hangartner (2020), which allows recovering mean values for pretreatment covariates for compliers and noncompliers.

The logic of this procedure is the following. When using IV, researchers can estimate the covariate means of individuals who are assigned to the control group but still take the treatment—these are the always-takers–—and of subjects who are assigned to treatment but do not take the treatment—these are the never-takers. Assuming there are no defiers12 and that the instrument is independently assigned, by subtracting the weighted covariate means of always-takers and never-takers from the entire sample, we can recover the covariate mean for compliers (for more information, see Marbach and Hangartner 2020). I implement this procedure in Stata, estimating the mean values and bootstrap standard errors for two pretreatment covariates—respondents' type of childhood residence and their ethnicity—for compliers, always-takers, and never-takers. Since this method is only compatible with binary treatments, I dichotomize the treatment variable at the educational level at which the first stage is strongest in each country.13 Across all contexts, the strongest effect of compulsory reforms was on increasing the probability of having eight or more years of education (see Table A6 in the online appendix).

## Descriptive Results

### Expansion Reforms and Women's Schooling

Figure 1 provides an overview of women's educational attainment by birth cohort. Women in all countries have significantly increased their years of schooling over time. For instance, women born in the 1960s had an average of seven years of education in Colombia and Peru, and around six years in the case of Bolivia. By the 1985 cohort, which was fully exposed to expansion reforms in all countries, women's mean years of schooling was 10 years. While these improvements shortened the gender gap in schooling in Bolivia and Peru, women still attained fewer years of education than men—for the 1980 cohort, the gap was 0.3 years in Bolivia and 0.4 years in Peru. In contrast, Colombian cohorts were already exhibiting a female advantage of 0.7 years of education (author's calculations from IPUMS 2020).

### Schooling and Women's Autonomy Across Cohorts

Table 1 (columns 1, 3, and 5) contains the estimates from OLS models between women's years of schooling and their autonomy in the home, pooled across cohorts. As expected, education does enhance women's autonomy in all countries. In particular, an extra year of schooling is associated with a rise in the autonomy scale, with increases ranging from 0.006 to 0.021 standard deviations (both p < .001).

To examine how the returns to schooling change as school expansion unfolds, I include a series of interaction terms between women's schooling and their birth cohorts (Table 1, columns 2, 4, and 6). Models contain grouped-birth cohorts born between 1970 and 1990, comprising women who were and were not exposed to these policies. For women born between 1970 and 1974 (the reference category), an extra year of schooling increases their autonomy in all three countries. Nevertheless, interaction terms reveal that these positive returns decline in younger birth cohorts. In Bolivia, the magnitude of this decline is noticeable in the 1980–1984 cohort, for which the association between one extra year of schooling and women's autonomy decreases by almost two percentage points (p$<$ 0.001) when compared with the 1970–1974 cohort. In the case of Colombia and Peru, interaction terms for the 1985–1989 cohorts show a decrease in the positive effect of schooling of 1.1 (p$<$ 0.001) and two percentage points (p$<$ 0.001), respectively.

Consistent with prior observational studies, these results demonstrate that an extra year of schooling is associated with an increase in women's autonomy in Bolivia, Colombia, and Peru. However, we see that as educational systems expand, the positive returns of schooling for women's empowerment tend to diminish. Since these models are unable to control for individuals' unobserved characteristics and selection processes, we cannot solely attribute these results to women's schooling and its interaction with expansion reforms.

## Main Findings

### Compulsory Schooling Increases Education

Table 2 contains results from OLS models regressing total years of schooling on cohort exposure to these policies. We can see that expansion reforms significantly increased women's educational attainment in all countries. The effect is largest in Bolivia, where girls exposed to the reform have an average of 0.56 more years of education (p$<$ .001) than unexposed students; exposed cohorts in Colombia increase their education by 0.47 years (p $<$ .001), while exposed girls in Peru gain 0.37 more years of schooling (p$<$ .001). Given that the average schooling in all countries was already more than eight years, the magnitudes of these effects are sizable.

Importantly, these results confirm that compulsory reforms in Bolivia, Colombia, and Peru are sufficiently strong instruments for examining how schooling affects women's autonomy. For instance, in all countries, reforms have a p value lower than .001, a t value larger than 4.0, and an F value of a considerable magnitude (Stock et al. 2002).

### The Effect of Mass Schooling on Women's Autonomy

Table 3 provides the estimated effects of one extra year of schooling on the autonomy scale, as well as on separate items. In all countries, point estimates indicate a negative effect of one extra year of education—that is, exposed women have less autonomy relative to those unexposed to these reforms. These effects are statistically significant in Colombia and Peru. Peruvian women who attended school an extra year experience a decrease in their autonomy of −0.37 standard deviations in the autonomy scale (p$<$ .001), while in Colombia, a one-year increase in education leads to a decrease in women's autonomy of −0.10 (p$<$ .001). In the case of Bolivia, point estimates also reveal a negative effect of an extra year of schooling among compliers, −0.67 standard deviations in the autonomy scale.

We can take a closer look at these findings by focusing on the separate autonomy items in Table 3. Findings show that schooling has a consistently negative effect on women's control of major household purchases in all countries. These effects are significant in Peru and Colombia, where one extra year of schooling has a negative effect of 25 and 12 percentage points (p$<$ .001), respectively. Schooling among compliers also negatively affects women's ability to decide about family visits: in Peru, one extra year of education has a negative effect of almost 21 percentage points on decisions about family visits (p$<$.001). In addition, women who attain one more year of education experience a decrease in their ability to decide about their health care in Colombia (1.7 percentage points; p$<$.057) and Peru (12 percentage points; p$<$ .036). Schooling does not affect women's ability to make decisions about their money.

### Mass Schooling and Women's Background

Instrumental variables allow researchers to make causal inferences only about individuals who comply with the treatment. Investigating whether this group differs from students who would have attended school regardless of these reforms (always-takers) or who did not comply with the treatment (never-takers) may be relevant to contextualize my main findings. Following the approach developed by Marbach and Hangartner (2020), I examine whether compliers, always-takers, and never-takers differ in their pretreatment characteristics, namely, their ethnicity and whether they live in an urban or rural area.

Figure 2 shows that in Bolivia and Peru, a higher proportion of compliers than of always-takers lived in rural areas. Among women who continue their schooling because of compulsory laws, 45% in Bolivia and 52% in Peru lived in rural areas during their childhood, compared with only 13% and 19% of always-takers, respectively. The proportion of students from rural backgrounds is even larger among never-takers. These findings are consistent with prior studies showing higher dropout rates among girls from rural areas in both countries. Nevertheless, these estimates also show that compulsory laws successfully kept girls from rural backgrounds in school. In Colombia, we do not see significant differences between compliers and always-takers, but we do between always-takers and never-takers.

Figure 3 shows the distribution of respondents according to their ethnicity. Although in Bolivia and Peru, the proportion of compliers from a minority background is higher than that of always-takers, these differences are only statistically significant in Peru. However, among never-takers, we do observe a larger proportion of indigenous or Afro-descendant women compared with always-takers across all countries.

This analysis suggests that compliers to compulsory reforms in Bolivia and Peru are different from women who would have continued their education regardless of these laws (always-takers). Indeed, compliers were more likely to come from rural backgrounds and be indigenous (in the case of Peru). In Colombia, however, differences between compliers and always-takers are less noticeable.

Given the relevance of having a rural background for treatment compliance, I also explore if there are heterogeneous effects of mass schooling according to respondents' residential context in childhood. Because only Bolivia and Peru had valid first stages,14 I conduct this analysis only for these two countries (see Table A7 in the online appendix). Findings show that an extra year of schooling decreases women's autonomy for students who grew up in a rural area in these countries (Table 4). Bolivian women with an extra year of education experience a decline of 0.13 standard deviations (p$<$ .05) in their shared decision-making and autonomy, while in Peru the decline is 0.06 standard deviations (p $<$ .05). In contrast, an extra year of schooling does not significantly impact women's autonomy for those who spent their childhood in urban environments. These results further confirm that—at least in Bolivia and Peru—the treatment of compulsory schooling and its negative effects on autonomy were concentrated among women who grew up in rural contexts.

### Women's Schooling and Union Formation

Because schooling may impact women's autonomy by affecting their likelihood of entering a union and the type of partners they marry (Basu 1992), I now explore these pathways. As shown in Table 5, I find that women with one extra year of schooling are more likely to be never-married in all countries.15 This effect is especially sizable in Bolivia and Peru, where exposed women are 27 and 28 percentage points, respectively, more likely to be never-married. These estimates show that women who were exposed to compulsory reforms are less likely to marry than those who were not. Importantly, this finding has two possible interpretations: either more educated women are less attractive in the marriage market and do not marry or their education enables them to opt out of marriage.

Looking at the type of husbands that women who are exposed to educational reforms marry provides further clues about how compulsory schooling may have restricted female autonomy. In the case of Colombia, women with an extra year of schooling are more likely to marry men with more years of education (Table 6, columns 2 and 4). In Peru and Bolivia, we see the opposite pattern: exposed women are more likely to enter hypogamous unions—in other words, they are more prone to “marry down” in education. This is the case when the difference in schooling is of one or more years (column 3), and when the gap is of three or more years (column 5). Conversely, exposed Bolivian and Peruvian women are less likely to form hypergamous unions—marrying men with more schooling than themselves (columns 2 and 4). Both results suggest that women with further schooling are more likely to enter unions that deviate from hypergamy expectations, which in contexts of high gender inequality has been associated with a series of detrimental outcomes for women. Lastly, no significant effects were found pertaining to the age of partners in any country.

Given these findings in Bolivia and Peru, I further explore whether autonomy restrictions were concentrated among married respondents. To this end, I estimated the heterogeneous treatment effects of schooling on women's autonomy by marital status in all countries. Because relationship status is affected by respondents' education, these findings should be evaluated with caution. Table A9 (see online appendix) shows that greater education has a positive effect on autonomy for unmarried women (either living alone or with parents) in Bolivia and Peru. In contrast, point estimates for married and cohabiting respondents are negative in all countries, although they are not statistically significant. That the negative effects of compulsory schooling appear to be focused among married respondents suggests that a compensatory dynamic may be driving the curtailment of women's autonomy among couples—a dynamic that has been documented among unions that deviate from educational hypergamy. To further assess this pathway, I examine whether married women exposed to compulsory schooling were more likely to experience controlling behaviors from their husbands. Estimates in Table A10 show that women's greater schooling increases these types of behaviors among partners, especially in Bolivia and Peru, where effects are sizable but not significant.

Together, these results suggest that the limitation of female autonomy in Bolivia and Peru was partly driven by compensatory responses among couples seeking to reaffirm masculine authority when threatened by their wife's greater education. The fact that exposure to these reforms increased women's likelihood of educational hypogamy (among respondents who got married) and that education's negative effects on autonomy were concentrated among married women further reinforce the plausibility of this pathway.

Lastly, IV findings are robust to a series of sensitivity tests. The latter include the definition of exposed cohorts, the use of calendar year cutoffs and partial treatment exposure, and secular time trends. For details on these and more robustness checks, see the online appendix.

## Discussion

Social scientists have long argued that mass education is a critical policy by which to socialize individuals regarding new ideas about family norms and gender relations in LMICs (Caldwell 1980; Inkeles 1969). Mass schooling was expected to accelerate family change by increasing women's bargaining power in the home and enhancing their autonomy. As expansion reforms unfolded, however, several limitations as a policy to raise women's autonomy became apparent. One was the prevalent view that women's education challenges men's status in families and threatens hypergamy norms in contexts of high gender inequality. Scholars found that in these settings, educated women were less prone to marry and those who did marry down in education were more likely to experience higher stress in their relationships (Behrman 2019; Vyas and Watts 2009). These findings led me to alternatively hypothesize that mass education may have adverse effects on women's autonomy in contexts where hypergamy norms are widespread.

In this study, I examine these claims by analyzing the effect of compulsory schooling laws enacted in Bolivia, Colombia, and Peru on women's autonomy. I contribute to prior scholarship by leveraging the timing of these reforms and identifying the causal effect of women's schooling on their autonomy later in adulthood. In addition, I explore the role of population heterogeneity and union formation patterns as potential explanations for these findings.

My first set of analyses relying on OLS models indicate that education is positively associated with a higher degree of female autonomy in Bolivia, Colombia, and Peru. However, results of these models also show that the positive returns of women's schooling diminish as educational systems expand and a larger proportion of women are educated in each cohort. Indeed, the decreasing returns of schooling as educational systems grow has also been documented in the case of labor market outcomes and civic participation (Bol 2015; Horowitz 2015). Once endogeneity is addressed via instrumental variables, I find that the cohorts of women exposed to compulsory laws experienced a decrease in their autonomy. The effect's direction is consistent across all countries, with statistically significant effects in Colombia and Peru. Importantly, IV results pertain to compliers of compulsory education laws and not necessarily to those who would have continued their schooling regardless of these reforms. In Bolivia and Peru, I show that compliers to compulsory laws were more likely to come from rural areas or a minority background and that the decrease in autonomy was stronger among women from rural contexts.

In contrast to classic demographic and modernization theories, these findings reveal that mass education did not enhance women's empowerment. In fact, for vulnerable groups of women, extending their years of schooling resulted in the curtailment of their autonomy. I interpret these findings as being consistent with two nonexclusive explanations for compulsory schooling's inability to increase women's autonomy. One concerns the tradeoff between school expansion and student selectivity. I find that women's schooling is positively associated with a higher degree of autonomy across all countries. Nevertheless, as school systems expanded and incorporated more vulnerable populations via compulsory laws, these effects increasingly diminished. As qualitative studies suggest, it may be that schools did not offer the proper learning conditions or materials to enhance women's autonomy among disadvantaged students (King and Hill 1993; Ohsako 1997; Stromquist 2001), whose families and communities were already hesitant about keeping their daughters in school (Ames 2013). A similar argument was made by Grant (2015), who found that further schooling had no effects on age at first birth among compliers of universal primary education policies in Malawi. Thus, these findings highlight the importance of examining the differential returns to schooling according to population heterogeneity, in terms of both individuals' preexisting conditions and heterogeneous treatment effects (Brand and Xie 2010). The case of women's autonomy suggests that respondents who were less likely to continue their education in the absence of compulsory reforms—women from rural and indigenous backgrounds in Bolivia and Peru—perceived lower returns to schooling in this particular outcome. These changes in selectivity may be relevant to assess the effects of compulsory schooling in LMICs for other demographic outcomes, such as fertility timing and age at marriage, among others.

A secondary explanation relates to the interaction between women's education and union formation patterns. I argue that compulsory schooling in contexts where women's education is viewed as a threat to marital norms may generate the unexpected consequence of curtailing married women's autonomy. Findings show that exposed students were less likely to get married in all three countries, suggesting that (1) women are penalized in the marriage market as a result of their increased schooling and their potential threat to hypergamy norms and/or (2) educated women purposely choose not to marry to protect their autonomy. Moreover, I found that in Bolivia and Peru, exposed women who get married are more likely to “marry down” in education, violating hypergamy expectations. Unions in which wives have more schooling than their husbands have shown to be problematic for women in a myriad of contexts (Behrman 2019; Cools and Kotsadam 2017; Frye and Urbina 2020; Hunter 2007). Following this literature, my results suggest that the greater restriction of women's autonomy in Bolivia and Peru may result from a compensatory response among couples who transgress educational hypergamy norms. Indeed, I find that the negative effects of compulsory schooling were concentrated among married respondents in Bolivia and Peru and that this subgroup of women were also more likely to experience controlling behaviors from their husbands. Because I cannot causally test this hypothesis here, I invite future research to do so, especially as hypogamous unions are becoming more prevalent in LMICs (Esteve et al. 2016; Lin et al. 2020).

Although my main findings are consistent across contexts, some differences between countries are important to note. The negative effects of compulsory schooling on women's autonomy and marriage entry were considerably smaller in Colombia. Moreover, in contrast to Bolivia and Peru, further schooling increased women's likelihood of marrying more educated men in Colombia. Identifying the source of these cross-country differences is beyond the scope of this study, but Colombia's greater gender equality in education at the time of compulsory reforms may be an explanatory factor. Future research should examine the role of gender gaps in education and other macro-level characteristics on the impact of compulsory schooling on women's status.

Several important caveats are necessary to qualify these results. First, this study focuses on only one dimension of women's status—their autonomy—and, therefore, cannot conclude that exposed women would have been in a better position in the absence of compulsory schooling. Prior scholarship has demonstrated education's positive effects on women's health, employment, and social mobility. Hence, it may be that further schooling did not enhance women's autonomy, but it may have improved their standing in other status dimensions. Second, this study explored only one set of pathways—changes in selection into schooling and the effects of women's education on union formation. However, prior research has detected other mechanisms, such as school quality and gender biases in classrooms, that may further limit mass schooling's ability to increase women's autonomy. Third, because of data limitations, the conclusions of this study pertain only to women and cannot explain how mass schooling affects men. Because changes in women's autonomy in the home occur in relation to their partners, learning about the impact of schooling on men's gender-egalitarian behaviors is critical.

Together, these findings are important for several reasons. Despite its limitations, this study was able to identify the causal effect of compulsory schooling on women's autonomy in Bolivia, Colombia, and Peru. Although there is a significant body of work examining the implications of schooling for women's empowerment in LMICs, most of these studies do not address issues of endogeneity. My analytic strategy allowed me to identify how the positive returns of schooling for women's autonomy diminished as school systems expanded and ultimately how—for vulnerable groups complying with compulsory reforms—further schooling did not fulfill the promise of empowerment. These findings highlight the importance of examining the differential returns to mass schooling considering population heterogeneity and the contextual meaning of women's education.

## Acknowledgments

I thank Dalton Conley, Margaret Frye, Arun Hendi, Jennifer Jennings, and James Raymo for their helpful feedback and encouragement. Pablo Argote, Jeremy Cohen, Ian Lundberg, Janet Xu, and Simone Zhang provided insightful comments on early drafts. This work has greatly benefited from feedback received at the Family Workshop at Princeton University, the Woodrow Wilson Scholars Series at Princeton University, the 2020 annual meeting of the American Sociological Association, the 2020 IUSSP Population, Poverty and Inequality Research Conference, and the 2021 annual meeting of the Population Association of America.

## Notes

1

Bolivia implemented reforms in 1994, raising the years of mandatory schooling from five to eight beginning with the cohort born in 1983; Colombia did so in 1991, raising the years from five to 10 beginning with the cohort born in 1981; and Peru did so in 1993, raising the years from five to 10 years beginning with the cohort born in 1982.

2

In 1990, the United Nations defined an index between .43 and .57 as medium development.

3

Only 3.3% of the Colombian population self-identified as indigenous (IPUMS 2020).

4

For Bolivia, I use the 2003 and 2008 surveys; for Colombia, I use the 2000, 2005, 2010, and 2015 surveys; and for Peru, I use the 2004, 2007, 2009, 2010, 2011, and 2012 surveys.

5

I focus solely on women because DHS questions on decision-making and autonomy were answered only by female respondents in all countries.

6

See Table A2 in the online appendix for descriptive statistics of the analytic sample.

7

See Table A3 in the online appendix for the exact wording of these questions.

8

As a robustness check, I adopt a “stricter” conceptualization of autonomy, achieved only when women are in complete control of their autonomy and decision-making. I code each item as 1 only if women alone were making these decisions and as 0 if they were doing so with their husbands, together with someone else, or the decision was made either by the husband or someone else alone. Results do not substantively change using this alternative coding strategy.

9

The Cronbach’s alpha was .70 in Bolivia, .63 in Colombia, and .68 in Peru.

10

In the main analyses, ethnicity was not included for Colombia given its high proportion of missing values.

11

Colombia collected ethnicity information in only some survey waves, resulting in a high proportion of missing values.

12

Defiers are those who do the opposite of what they are assigned to do; they take the treatment when they are assigned not to take it, and do not take the treatment when they are assigned to take it.

13

I specifically considered the size, significance, and F test of each estimate.

14

In Colombia, first-stage estimates do not yield evidence of expansion reforms as a strong instrument.

15

In 2000, the median age at marriage/cohabitation for women was 22.6 in Bolivia, 23.1 in Colombia, and 23.6 in Peru (World Bank 2020). Similar findings were found when estimating this model only among women between the ages of 25 to 34. See Table A8 in the online appendix.

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