Identifying the mechanisms through which the testing environment affects the gender gap in math

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Internal Validity of the Empirical Strategy

The internal validity of the RDD requires that there is no endogenous sorting on either side of grant eligibility cutoffs. The forcing variable is the relative distance to the household after–tax income cutoff. This type of endogenous sorting is more likely to occur in the common case where the treatment assignment rule is public knowledge Imbens and Lemieux (2008), as in this paper. As precise thresholds are public information and have not changed since 2010, a concern of manipulation at the cutoff arises especially for the first income-eligibility threshold (fee waiver). In incentives in need-based grants contrast, manipulation is less likely at higher cutoffs, since students have incentives to apply on either side given the fact that students on both sides are eligible for a positive amount of aid. Montalvo (2018) highlight the fact that after–tax income is more difficult to manipulate than income, and in Spain the changes in the tax code are frequent.
vicinity of the cutoffs, displaying that it does not seem to be systematic manipulation of household parental income around the thresholds. The density of applicants increased as parental income decreased in T1 grant, given the fact that more students may be encouraged to apply as they were closer to the cutoff. Density estimates at T2 grant were roughly constant, since applicants have incentives to apply on both sides as they would be awarded with s positive cash allowance. The test statistics proposed by McCrary (2008) fail to reject a statistically significant jump at the eligibility cutoffs for any of the treatment samples used in this paper (i.e. period, gender, or predetermined ability).
An additional test for local random assignment is to check whether applicants baseline characteristics are “locally” balanced on either side of the thresholds. If some groups of students are more likely to sort on the “high” side of a threshold may indicate endogenous sample selection, and treatment assignment cannot influence variables that are predetermined with respect to the treatment. Local linear regressions are performed for each of the applicants’ observable characteristics (i.e., gender, nationality, parental income, PAU score, or parents’ occupation) as dependent variable. Panel A of Table 1.B.3 presents the regression results, showing that the observable characteristics of applicants are well balanced, since less than 10 percent of the variables do change discontinuously at income eligibility thresholds. Furthermore, a chi-squared test based on a system of seemingly unrelated regression with as many equations as baseline characteristics is performed. Panel B indicates that the null hypothesis that the discontinuity gaps are jointly equal to zero cannot be rejected.
An additional concern is that parental income, at constant prices of 2015, is samples. highly correlated over time (regressing applicants’ income in a given year on income the year before leads to a coefficient estimate of 0.73), which may lead to a persistent sorting of applicants on either side of eligibility cutoffs and may confound the effects of current year discontinuities in grant amounts with those from previous years. In fact, there is variation in income, since the fraction of applicants who reported the same parental income than the one registered the year before is only 3.2 percent. Students’ who were awarded a grant in a given year might be more likely to re–apply the next year. It might be that impacts would be driven by this group, with no density break for applicants at the cutoffs but so for re–applicants. A robustness check testing the discontinuity in the density of re-applicants cannot reject the null hypothesis of zero discontinuity in the density of re-application.

Discontinuities in Grant Amounts

In this subsection, I examine the discontinuities in average grant amounts awarded of the income-eligibility thresholds, which is a necessary condition for the empirical design to identify the causal effects of grants on student outcomes.
T1 or T2 grant plotted against the relative income-distance to the relevant eligibility thresholds. The figure indicates that approximately 98 percent of the theoretical eligible applicants received the grant. samples as a function of applicants’ relative distance to the thresholds separately for the two periods under study. The results indicate a clear discontinuity in the average conditional cash allowance for T1 and T2 grants in both periods, which is confirmed by the statistically significant results showed in Table 1.B.4 (Panel A). T1 grant provides not statistically significantly different average grant amount for both periods, with an average cash amount of 675 euros in Period I and 825 euros in Period II (relatively to been awarded with fee waiver). T2 grant reports a drastic decrease in the average grant amounts awarded across periods, with an average increment in 32See online appendix, section B.

Impact on Dropout

Most of the literature focuses on the extensive margin effect of grants on enrollment. When there is an effect on enrollment (which is often stronger for freshmen students), disentangling the intensive margin response on performance is challenging (due to the potential selection bias that the enrollment effect provides). An advantage of the setting under study is the specific timing of grant applications in Spain, which allows to estimate the effects of grants on students who are already enrolled, and for whom dropout rates are relatively small. Table 1.B.5 displays the RDD estimates on dropout from higher education. The null hypothesis of a zero effect of cash allowance on dropout cannot be rejected for all types of grants and periods. The results are suggesting that the effect of grant on student performance do not seem to be biased by dropout effects. This result is consistent with Montalvo (2018), finding no effect on dropout of a sharp increase in tuition fees in a highly comparable setting.

Impact on Student Performance

I focus on the average GPA, which in Spain can take values between 0 (the minimum grade) and 10 (the maximum)33 and the fraction of credits that the student passed among the total attempted credits as measures of student performance.
Figure 1.A.6 plots the average GPA for all treatment samples as a function of applicants’ relative income-distance to the thresholds separately for both periods studied. The solid black lines are the fitted values from a linear projection. The average GPA is slightly different across periods for the two samples of applicants (around the T1 and T2 grant thresholds respectively). The average GPA was around 5.9 points in Period I and 6.15 points in Period II. Table 1.B.4 presents the non-parametric RDD estimates.

Heterogeneous Effects of Grants on Student Performance

Despite of the robust baseline estimates, investigating the existence of heterogeneous results for academic term (Fall vs. Spring grades) and different subgroups of population (gender, predetermined academic ability and residence status) is necessary to understand the implications of the estimated effects. Student Performance by Academic Term. Students are already enrolled at
the higher education institution when they apply, and the vast majority of grant decisions are not notified before the end of the first term of the academic year. In addition, conceded grants were divulged between February-March on average. This unique process may create an unclear view of when the grant incentives are created to improve student performance, due to the fact that students faced a different timing of acceptance/rejection disclosure. An ideal way to test whether there is heterogeneous 38For further analysis of this robustness check see online appendix, section D. effects of the grant on student performance before or after the student received the notification, it is to compare the effect on students who received it before the term exams versus those who were informed after. Unfortunately, this sample split creates endogenous selection at the eligibility cutoffs, since denied grants were disclosed before accepted grants on average, leading to a significant break in the density at income thresholds.
An alternative way to test it is to look at the impact of the grant on student performance by academic term (Fall and Spring). Students had a higher probability to get an answer on the second rather than on the first term. Then, it is reasonable to believe that student reaction to the allowance would be stronger for Spring than Fall grades. Table 1.B.6 presents the non-parametric estimates by academic term, confirming this hypothesis. The effect sizes are larger for the second than first term.
Although the difference is not statistically significant, the estimates for Fall Term seem to be more sensitive to the functional form, as can be seen in Figure 1.A.7 and Figure 1.A.8.
Student Performance by Subgroups of Population. Table 1.B.7 and Table 1.B.8 presents the RDD estimates for T1 and T2 grants by period and subgroups of applicants. The positive effect of the T1 grant on student performance coupled with more stringent performance incentives are found for both males and females, but the magnitudes differ (Panel A). The point estimate is statistically significant for males, but it is not statistically different of female’s.

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Impact on Degree Completion

Table 1.B.10 expands the analysis by investigating the impact of financial aid on degree completion. The table focuses on students who applied for the grant in the final year of a degree program, i.e., in their fourth year of a bachelor’s degree. The non–parametric estimates indicate that being eligible for 825 euros (relatively to the tuition waiver) in the period when performance requirements were more stringent, increases student’s chances of obtaining a degree in 12.5 and 11 percent with respect to the baseline mean for all applicants and if the applicant is on the graduation year respectively. In contrast, the null hypothesis of zero effect on degree completionunder a setting with weak academic requirements cannot be rejected.

Comparability between Period I and Period II

. An important concern corresponds to the degree of comparability between applicants for a need-based grant in Period I and Period II. I test whether the students’ observable characteristics of the comparison group at T1 and T2 grant in Period I are similar to applicants in Period II. I test the comparability of these students performing a t-test of the difference in observable characteristics between period. Table E1 presents the results of this analysis. The null hypothesis of equality of the observable characteristics between periods cannot be rejected for three quarters of the variables at T1 grant, and for more than half in T2 grant.

Academic requirements for BCG grant

This section summarizes the academic standards for being eligible for a BCG grant over the six-year period studied (2010–2015). In order to be eligible for a need-based grant, students must have complied with a minimum fraction of credits earned and average GPA the year before application. Table F1 shows a summary of the different performance standards required by year, degree and cohort. It is remarkable the increase in the fraction of credits earned required in 2012, and the posterior change of the entire framework of academic incentives in 2013, which incorporates the average GPA of the year before application plus a variable component which depends on performance and family income the year of grant application (the variable component formula is described in equation 11). Figure displays a graphical summary of academic requirements for non-freshmen students. Academic incentives varied between the two periods:
• Period I (2010–2012): incentives were based on the fraction of credits earned the year before application.
• Period II (2013–2015): academic standards were based on the fraction of credits earned the year before application, the average GPA the year before application and in the application year (through the grant’s individual variable component).

Table of contents :

1 Countering moral hazard in higher education : The role of performance incentives in need-based grants 
1.1 Introduction
1.2 Institutional Background
1.2.1 Higher Education in Spain
1.2.2 The Becas de Carácter General Need-Based Grant Program .
1.3 Data .
1.4 Empirical Strategy
1.5 Theoretical Framework
1.6 Results .
1.6.1 Internal Validity of the Empirical Strategy
1.6.2 Discontinuities in Grant Amounts
1.6.3 Impact on Dropout
1.6.4 Impact on Student Performance
1.6.5 Robustness Checks
1.6.6 Heterogeneous Effects of Grants on Student Performance
1.6.7 Mechanisms
1.6.8 Impact on Degree Completion
1.7 Discussion
1.7.1 External Validity
1.7.2 Interpretation of Results: Efficiency and Equity
1.7.3 Potential confounding factors
1.8 Conclusion
Appendix 1.A Appendix: Main Figures
Appendix 1.B Appendix: Main Tables
Appendix 1.C Additional Figures and Tables
1.C.1 Low-Income Students’ Performance in Higher Education
1.C.2 Validity of the Research Design: McCrary (2008) Test
1.C.3 Discontinuities in Awarded Grants
1.C.4 Robustness Checks
1.C.6 Comparability between Period I and Period II
1.C.7 Equity Effects
1.C.8 Academic requirements for BCG grant
2 The Gender Gap in Student Performance: The Role of the Testing Environment 
2.1 Introduction
2.2 Institutional Background
2.2.1 Standardized Testing in Spain
2.2.2 A Randomized Intervention in the Administration of Standardized Testing .
2.3 Data and Descriptive Statistics
2.4 Empirical Strategy
2.5 Results .
2.5.1 Baseline Results
2.5.2 Robustness Checks and Heterogeneity Analysis
2.5.3 Ruling out alternative explanations
2.6 Identifying the mechanisms through which the testing environment affects the gender gap in math
2.7 Conclusion
Appendix 2.A Main Figures and Tables
Appendix 2.B Additional Figures and Tables
2.B.1 Additional Balancing Tests
2.B.2 Description of Variables
2.B.3 Additional Heterogeneous Effects
3 School Choice Priorities and School Segregation: Evidence from Madrid 
3.1 Introduction
3.2 Institutional Background
3.3 Data and Summary Statistics
3.3.1 Data .
3.3.2 Summary statistics of applicants
3.4 Empirical Strategy
3.4.1 Out of School District Choice and Assignment Event Study: First Difference Approach Difference-in-Difference Analysis
3.4.2 School Segregation
3.4.3 Identification Threats
3.5 Results .
3.5.1 Out of District Choice and Assignment Event Study: First Difference Approach Difference-in-Difference Analysis
3.5.2 School Segregation
3.6 Robustness Check: Phasing-in of the Reform in other Municipalities .
3.6.1 Out-of-Municipality Assignment and Distance to Assigned School
3.6.2 School Segregation by Immigrant Status
3.7 Conclusion
Appendix 3.A Main Figures
Appendix 3.B Main Tables
Appendix 3.C Additional Figures and Tables
3.C.1 Description of priority criteria
3.C.2 Section Example
3.C.3 Years of Schooling
3.C.4 Population trends in the Region of Madrid
3.C.5 Housing Prices and School Average Performance.
3.C.6 To which schools are pupils assigned?
3.C.7 Sample Restrictions
3.C.8 Theoretical Properties of the Boston Mechanism
3.C.9 Difference-in-Difference Approach
3.C.10 Alternative measure of segregation by parental education
3.C.11 School Classification


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