CONTROL DE EXENCIONES Y EXONERACIONES Capítulo Único

Before starting with the analysis of the relationship between retention and student achievement let us briefly discuss the issue of tracking (see, for example, Rothstein, 2010) that has been detailed in recent education literature and that may possibly bias the results if it is not accounted for. The idea is that teacher value added models may produce biased estimates when students are not randomly assigned to teachers but are assigned based on observed or unobserved characteristics. As an example, a class of students who obtain higher test scores on average may be assigned to a different teacher than a class with low average scores. As the skills of these teachers may differ they may affect the future outcomes of students, which are the object of this analysis. Even more so, regarding this analysis, repeaters may be sorted into different classes (for example, lower-achieving ones to reduce the within- class variation). The latter could be the reason for differences in future outcomes between promoted students and repeating ones in lieu of the treatment variable grade retention. The data used do not allow for experimental analysis of this issue such as was conducted by Kane and Staiger (2008) who show that the value added model they implement does not suffer from biased estimates. I can, however, show that selection of repeating and promoted students into classes of different average scores does not seem to occur in the data used.

Figure 2.1 shows the relationship between the share of repeaters and the mean score of students per class for second graders.15 The fitted line has a slight and insignificant positive

15 _{This figure and the corresponding ones (Figures A1, A2 and A3) in Appendix A are based on grade 2 as the}

data structure does not allow for similar analyses in other grades. As there is no reason to believe that this pattern changes over time, I conjecture that it remains the same across the panel.

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slope. This suggests that repeating students are not assigned into low-achieving classes to separate them from high-achieving students. Several similar exercises can be found in Appendix A. Based on these results I do not believe that there is a particular rule for assigning repeaters to different classes than promoted students.16 Furthermore, possible sources of bias are alleviated from assignment of classes to teachers based on mean scores and share of repeaters on the class level by including these variables as additional covariates in the estimation of the propensity score, as indicated in the variable description of subsection 2.3.1.

Figure 2.1: Relationship between share of repeaters and mean score per class

It is important to note that there are two differing concepts in comparing the treatment and control observations in the post-treatment period (see Holmes, 1989, p.21). They reflect the varying views on the purpose that is attributed to grade retention. The first one (concept (a)) analyzes how much a student should learn during one year of schooling. Therefore, if a

16 _{Since the figures show that classes with a higher or lower percentage of repeaters do not differ systematically}

in their mean test scores, they also deliver suggestive evidence that there are no peer effects stemming from repetition.

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student repeats grade 3, her achievement one year later (she is still in grade 3) is compared to a non-repeating student who is in grade 4 by then. The idea is to analyze the changes in student achievement from one year to the next given repetition and non-repetition.

The second concept (concept (b)) reflects the idea that a student should have a certain level of knowledge by a specific grade. Therefore, if a student repeats grade 3, her achievement two years later (i.e. in grade 4) is compared to a non-repeating student one year later who at that time is in grade 4. This kind of comparison aims at finding out if repeating enabled the student to reach the same level of knowledge in grade 4 as the non-repeating student. Note that in this case the repeating student had one more year of schooling to reach this level. The different possibilities of comparison are illustrated in Figure 2.2.

It shows a grade 2 retention decision and follows the students till the end of the panel. Only those students have been selected who have not dropped out during the panel. The squares indicate students who repeated grade 2 and therefore lag one grade behind the grade 2 non-repeating students, which are shown by triangles. Concept (a) translates to a vertical comparison (solid circles) where the students had the same amount of schooling since the retention decision. Concept (b) can be applied by horizontal comparison (dashed circles), where a repeater when in grade 3 is compared to a non-repeater when in grade 3 and so on. As the mean test scores of non-repeaters are generally considerably higher (circular dots), I have selected those non-repeaters who roughly start at the mean of the promoted students in the first wave of the panel, i.e. approximately have the same starting point in terms of test scores. Referring to the vertical comparison we can clearly see that the repeating students build up a substantial negative gap in the post-retention years towards their old peers. As a consequence, for the same amount of schooling the promoted students will achieve higher scores than the retained students even though they started at the same initial level.

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Figure 2.2: Comparing retained and promoted students (I)

The circles encompass the observations to be compared. The solid circles represent concept (a): The students compared have the same amount of schooling since the point of the repetition decision. The dashed circles represent concept (b): A grade 2 repeater when in grade 3 is compared to a promoted student when in grade 3, etc. N=22 for repeaters and N=58 for non-repeaters starting at mean score of repeaters.

Following the rationale of concept (b), we may now look at the horizontal comparisons. The retained students when in grade 3 have slightly higher test scores than the promoted ones had when in grade 3. So far, if the policy is meant to guarantee a certain level of knowledge by a certain grade, retention could be seen as a successful means to achieve this aim. Even in this context, it is important to note that the retained student had one more year of schooling to obtain this level. Moreover, looking at grades 4 and 5 the score of the retained students falls below that of the promoted student despite the additional year of schooling.

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Therefore, we have to be more cautious about supporting retention even in the case of a same- grade comparison in line with concept (b).17

Even though other variables are not controlled for so far, we can make an attempt to answer the first hypothesis based on Figure 2.2. The figure shows the pathway in terms of the test scores of students repeating grade 2. Let us assume that the mean score in grade 2 remained constant over time, i.e. the mean score of second graders in the first year of the panel (which is known from the data) is the same as the mean score of second graders in the following year. Using this assumption we can simply compare the mean score of repeaters when they attend grade 2 the second time to their mean score when they attended grade 2 in the first year of the panel. As the mean score of the repeaters has increased, we can state that the repeater will be better in relative terms when compared to her new grade 2 peers than when compared to her old grade 2 peers. This does not come as a surprise as the repeaters had an additional year of schooling and there was some improvement of scores during that year. The result of this simple and straightforward analysis corroborates the perception that teachers may believe retention to be useful as they can see the relative improvements of repeaters in their new class (see Bernard et al., 2005, p.64).

17 _{For variations of this figure with different starting points for promoted and retained students, see Figures A4}

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