Promotion with and without Learning: Effects on Student Enrollment and Dropout Behavior Elizabeth M. King, Peter F. Orazem, and Elizabeth M. Paterno Automatic promotion policy presumes that grade retention discourages continuation in school and that the lenient promotion of students with poor performance does not hamper their ability to do well in the next grade. However, promoting students into grades for which they are not prepared may backfire, leading to early dropouts. An econometric decomposition of promotion decisions into a component that is based on merit (attendance and achievement in tests) and another component that is uncorrelated with those indicators allows a test of whether parental decisions to keep their child in school is influenced by merit-based or nonmerit-based promotions. Results suggest that the enrollment decision is significantly influenced by whether learning has taken place. The effect of grade promotions uncorrelated with merit on persistence in school is only 20 to 33 percent as large as the effect attributed to merit-based promotion. JEL codes: I20, I21, I28 Education policy-makers have long debated the relative benefits of social promo- tion versus grade retention. Social promotion is the policy or practice of promot- ing students from one grade to the next, irrespective of their academic performance. Grade retention is the practice of holding back underperforming students in the same grade until they attain minimum grade-appropriate skills. Social promotion advocates claim that even low-performing students would benefit from staying with and learning from their peer (or age) group, whereas grade retention harms students’ self-esteem, does not improve their performance, Elizabeth M. King (corresponding author) is a nonresident senior fellow at the Brookings Institution, Washington, DC; her email address is bethking1818@gmail.com. Peter F. Orazem is a university professor of economics at Iowa State University; his email address is pfo@iastate.edu. Elizabeth M. Paterno is an economist at the Ministry of Community and Social Services, Government of Ontario, Canada; her email address is Elizabeth.Paterno@ontario.ca. Useful comments on earlier versions of this paper from Felipe Barrera-Osorio, Halsey Rogers, Guilherme Sedlacek, and participants at meetings of the Population Association of America and the Midwest Economics Association are gratefully acknowledged. The paper benefitted tremendously from the careful comments of the referees and the editor. The research was funded through a grant from the World Bank’s Research Support Budget and the Economics Department of Iowa State University. The opinions and conclusions expressed in this paper are those of its authors and do not necessarily reflect positions of the World Bank and its member governments. THE WORLD BANK ECONOMIC REVIEW, VOL. 30, NO. 3, pp. 580– 602 doi:10.1093/wber/lhv049 Advance Access Publication December 17, 2015 # The Author 2015. Published by Oxford University Press on behalf of the International Bank for Reconstruction and Development / THE WORLD BANK. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com. 580 King, Orazem, and Paterno 581 and increases their likelihood of dropping out of school. In contrast, proponents of grade retention believe that waiting until students have attained mastery of the curriculum will better prepare them for advanced work at the higher grades whereas social promotion will doom them to falling ever farther behind their classmates.1 To varying degrees, social promotion is practiced in countries such as Denmark, Japan, Korea, Norway, Sweden, and many states in the United States. Other countries, among them France and many developing countries, instead use grade retention extensively as a means to improve student performance. I. SOCIAL PROMOTION OR GRADE RETENTION? REVIEW OF THE L I T E R AT U R E There is mixed evidence about the relative merits of social promotion and grade retention—and these policies remain controversial. Two studies that use a regres- sion discontinuity design to estimate the impact of grade retention reach opposite conclusions: Roderick and Nagaoka (2005) find that third-grade students who were retained under Chicago’s high-stakes testing policy did no better than earlier cohorts of third-grade students who were automatically promoted, and re- tained sixth-graders underperformed their earlier counterparts who had been promoted. Grissom and Shepard (1989) find that grade retention increased dropout rates by as much as 20–30 percent, even after controlling for achieve- ment, socioeconomic status and gender, and Eide and Showalter (2001) conclude that grade retention had a negative but statistically insignificant impact on the probability of dropout in their study. In contrast to these studies, Jacob and Lefgren (2004) find that grade retention, plus summer remedial programs, sub- stantially increased academic achievement among third-graders, although not among sixth-graders. And yet another study on Chicago’s high-stakes, testing- based promotion policy, which increased the grade retention rate of eighth- graders from 1 percent to 10 percent, actually lowered later dropout rates because fewer students entered high school ill-prepared (Allensworth 2004). Studies on developing countries also report contradictory findings. In impov- erished areas such as Brazil’s rural northeast, retained grade-two students per- formed more than half a standard deviation below average before repetition, but performed slightly above average after repetition (Gomes-Neto and Hanushek 1994).2 In Senegal, however, second-graders who do not perform well and are re- quired to repeat the grade are more likely to drop out before completing primary 1. Holmes’ (1989) and Jimerson’s (2001) reviews of multiple studies concluded that retained children score one-third of a standard deviation below promoted students on later achievement tests. However, many reviewed studies did not adequately control for other differences between promoted and retained students. Studies that best controlled for such differences found the largest negative effects of grade retention on test scores. 2. The study tracked a sample of schools during the period 1981–85 (Gomes-Neto and Hanushek 1994). Of 2,619 students in the second grade in 1981, 127 students were still in the second grade in 1985. 582 THE WORLD BANK ECONOMIC REVIEW school than those students who perform equally poorly but are allowed to pro- gress to the next grade (Glick and Sahn 2010). There is a fundamental problem with studies that try to relate the act of a child being promoted from one grade to the next with the probability that the child stays in school or drops out. At least some, and likely the majority, of the chil- dren who are promoted would have met the standards for promotion even when there is a policy of total or partial social promotion. That means that the re- searcher has to distinguish between merit-based promotions and the rest. A second problem is that, unless compulsory basic education is fully enforced, it is typically parents who make the decision of whether their child will stay in school, at least at the primary level. If parents are primarily interested in whether their child is learning, then their decision will depend on their perception of this learning outcome, regardless of whether or not the school promotes the child. Thus, studies have to model how parents discern whether or not their child is learning and also how parents react to promotion decisions by the school. This study examines a different aspect of the debate about grade retention and promotion—how parents process the information that grade promotion or reten- tion provides about student achievement—and integrates that information into parental decisions about their child’s schooling.3 Even at the earliest grades, parents implicitly evaluate the value of schooling relative to the opportunity cost of child time spent in school, and these assessments may be influenced by whether the child is perceived to be learning from school. The study addresses this question in the context of first-grade and second-grade students in the Northwest Frontier Province (NWFP), the smallest and northernmost of Pakistan’s four main provinces, now officially called the Khyber Pakhtunkhwa. First, the analysis establishes the extent to which promotions are based on student performance in the classroom. The teacher’s decision to retain or promote a child could be based on factors other than academic performance, in- cluding student deportment, policies on automatic promotion, and parental pres- sure. This leads to a decomposition of promotions into two components—one based on observed academic merit and the other based on factors other than merit—and the components are then related to either continued enrollment or student dropout. The analysis uses a unique data set collected in the NWFP in 1994. At that time, the NWFP Education Management Information System (NEMIS) was ex- ploring the use of a student assessment system. Prior to that time, there had not been any formal means by which parents or teachers could compare student per- formance across schools or even across students within a school. Despite this lack of prior knowledge of relative student learning, teacher promotion decisions 3. Eide and Showalter (2001) evaluated parental decisions regarding grade retention in their study of the returns to grade retention for high school students in the United States. They modeled the parental decision as depending on whether the child’s earnings net of schooling costs are higher or lower from grade retention. Controlling for endogeneity of grade retention, white students do get a benefit from grade retention in lower dropout rates and higher labor market earnings. King, Orazem, and Paterno 583 in primary schools were based primarily on student attendance and on student skills as measured by performance on tests of mathematics and language skills. The relationship to test scores is particularly interesting in that the teachers never saw the students’ performance on those tests, so they must know which children have mastered the material even without the aid of formal assessments. More striking is that largely illiterate parents appear to have based their own decision to send their child to school for another year largely on merit-based promotions. Promotions that were not correlated with measured student cognitive attain- ments had a much smaller positive impact on the probability of school continua- tion or persistence. This finding implies that parents make their decisions regarding a child’s continued schooling on the basis of perceived learning in the previous year, rather than on promotion or retention per se. It also suggests that if a child’s ability to learn in future years is reduced by being placed in a grade for which the child is unprepared, then promotion could lead to increased dropout. Increasingly, researchers and development agencies have been exploring school- based management reforms and increased parental involvement in schools as mechanisms for improving school quality and student learning. One of the con- cerns about decentralized control of local schools, however, is that uneducated parents are not able to assess quality and would therefore be unable to advocate for quality schools.4 The findings here suggest that, even without external sources of information, parents may be better judges of school quality than has been pre- viously thought. II. THE MODEL This section presents a model of demand for education in the household, fol- lowed by a model of the decisions made by teachers and schools about whether or not to promote students to the next grade. As first proposed by Becker (1967) in his Woytinsky Lecture, households choose levels of human capital investments by equating the (discounted) expected marginal private benefits and the expected marginal private costs of these investments. Applying this framework to the demand for child education, parental decisions about child schooling depend on the direct and indirect costs of schooling, family income, and expected hedonic and/or pecuniary returns to schooling.5 This model generally assumes that costs, income, and returns are all known at the time of the decisions. In reality, infor- mation on these factors is revealed over time and parental decisions can better be modeled as a sequential one. Part of the revelation process for parents is learning more about their child’s ability and aptitude for school by observing the child’s performance in school. Each school year, parents observe the child’s progress in school through two 4. These concerns, among others, are reviewed by Ahmad et al. (2005) and Bardhan (2002, 2005). 5. See, for example, Behrman and Deolalikar (1991); Alderman, Orazem, and Paterno (2001); Anderson, King, and Wang (2003) for studies on developing countries. 584 THE WORLD BANK ECONOMIC REVIEW indicators, whether the child is promoted to the next grade and how much the child learns. Conditional on new information, parents update their decision (as well as aspirations) regarding how many years the child will remain in school. Abstracting from any compulsory education law, this model implies that if the child’s progress is below parental expectations, then parents will reduce the addi- tional number of years the child will be in school, leading to early dropout. Another part of the revelation process is parents discovering more about the quality of the school their child attends, including the extent to which the school is able to impart new knowledge and skills to their child, and about how the school (teachers) assesses student performance and decides on which students to promote or retain at each grade. The model below incorporates grade promotion decisions into parental decision-making about schooling. Length of Time in School The human capital model suggests that parents will choose length of time in school in order to maximize their child’s lifetime discounted utility from school- ing and earnings. Parental utility is assumed to be increased by their child’s schooling through two potential avenues, the child’s cognitive attainment and progression through the grades. Below are two cases of the value of promotion to parents: first, a simplistic case where parents care only about cognitive achieve- ment (and not years of schooling completed), and second, a case where parents also care about grade progression and the credential associated with promotion. Case A1: Only child cognitive attainment raises parental utility. If parents care only about whether their child is learning in school and not about completed years of schooling per se, then lifetime discounted utility at time t will depend solely on the human capital acquired, qit. This would characterize parental utility if, for example, parents value only the future earnings potential of their child and if firms pay only for cognitive achievement and not for years of school- ing. In fact, Glewwe (2002), Hanushek and Kimko (2000), and Hanushek and Woessmann (2012) present evidence that it is cognitive achievement, not years of schooling, that increase earnings.6 Akresh et al. (2012) also show that in Burkina Faso parents are more likely to send more able children to school compared with their less able siblings. The parents’ net discounted utility from sending child i to school in year t þ 1 is: V S ðqit ; Wtþ1 ðqit ; tÞ; Citþ1 ; tÞ: ð1Þ The net value of an additional year in school should rise with the child’s past accu- mulation of knowledge, qit, but decreases with the child’s opportunity cost of time, Wit þ 1, and the direct costs of schooling, Cit þ1. The opportunity cost of schooling, 6. Why years of schooling and cognitive achievement do not have the same effect on growth is partly explained by Pritchett (2013) who presents compelling evidence that increases in schooling years, as in India, do not produce similar increases in achievement or learning in many developing countries. King, Orazem, and Paterno 585 Wit þ1, increases with the child’s age, t, and with the child’s past accumulated knowledge, qit. Finally, the net present value also depends directly on t; with finite lifetimes, the length of the remaining years of potential returns from another year of schooling decreases with age (that is, each year that labor force entry is delayed due to schooling reduces lifetime earnings). Provided that V S ðqit ; Wtþ1 ðqit ; tÞ; Citþ1 ; tjt ¼ 0Þ . 0 and that there are diminishing marginal returns to schooling, @VS , 0, there will be a unique optimal t* such that V S ðqità ; Wtà þ1 ðqità ; tà Þ; @t Cità þ1 ; tÃ Þ ¼ 0; after which the child will leave school. The parents’ utility from the t þ 1st year of schooling as implied by (1) assumes that parents can observe the child’s human capital stock, qit, but qit is almost certainly observed with error. Instead, the child’s academic progress is proxied by a series of promotion outcomes from grade to grade which informs parents of their child’s learning. However, these promotion decisions may not signal learning accurately if they depend on factors other than merit. At one extreme, promotions may be automatic for all students and do not provide infor- mation on the child’s acquired knowledge, leaving parents to assess the child’s qit on their own. Case A2: Both promotion and child cognitive attainment raise parental utility. If parents get utility from their child’s promotion independent of cognitive achievement ( perhaps because the labor market rewards the number of complet- ed years of schooling irrespective of learning levels), then promotion also enters the parents’ discounted utility from the t þ 1st year of schooling: V S ðqit ; Wtþ1 ðqit ; t; Pit Þ; Citþ1 ; t; Pit Þ ð2Þ where Pit indicates if child i was promoted in year t. Optimal length of time in school will be to set t** such that V S ðqitÃà ; WtÃà þ1 ðqitÃà ; tÃà ; PitÃà Þ; CitÃà þ1 ; tÃà ; PitÃÃ Þ ¼ 0: The case for social promotion rests on the presumption that children learn best when they are among their age peers. Promotion raises a child’s self-esteem and confidence which in turn will raise the marginal product of additional time in school. But this increase in self-confidence could raise also the child’s value in production activities, thus raising the opportunity cost of time in school. For this reason, the optimal length of time in school will not necessarily rise. However, if the social promotion has no impact on the child’s opportunity cost of time, then t** . t* as long as parents place a value on the promotion itself, independent of what the child has learned in school.7 7. Grade retention, however, can dilute marginal returns to each year spent in school. Behrman and Deolalikar (1991) examined the effect of high retention rates on returns to primary education in Indonesia and found those rates to be extremely overestimated. Under alternative estimates of grade retention rates, these rates are overstated by 82 –114 percent for the below-completed-primary level and by 38 –78 percent for the completed primary category. 586 THE WORLD BANK ECONOMIC REVIEW This discussion demonstrates two views of the value of promotions to parents. In case (1), promotions measure the child’s qit which parents use in deciding how long the child should remain in school. In case (2), promotions raise parents’ utility from schooling beyond the utility they get from the child’s qit. Distinguishing between these two views empirically will require a mechanism to distinguish between a promotion decision that is based purely on merit and a promotion decision based on factors other than the child’s performance (non- merit factors). Promotion Decisions There are two polar cases to consider with respect to how teachers make their promotion decisions: In the first case, promotions are based exclusively on student performance; in the second, promotions are based solely on factors other than merit. Actual promotions will be a convex combination of these two ex- tremes (a third case). Case B1. Merit-based promotion. Suppose that student i’s merit in year t and school j is given by qijt and merit is determined by a human capital production process qijt ¼ f ðAijt ; Mijt ; Lijt Þ; ð3Þ where Aijt is student attendance during the year and Mijt and Lijt are math and language skills measured at the end of the year. Conditional on Aijt, Mijt, and Lijt, the teacher derives an estimate of merit, qeijt , which differs from actual merit, qijt, by a random error, 1ijt. There is also a threshold level of merit, qmin j , necessary to justify promotion to the next grade in school j.8 Hence, the promotion decision can be written as, Pijt ¼ 1 if qe min ijt À qj ¼ qijt À 1ijt À qmin j !0 ¼ 1 if qijt À qmin j ! 1ijt ð4Þ ¼ 0; otherwise: Pijt is a dichotomous variable that equals one if the teacher decides to promote the student. Assuming that a teacher’s ability to evaluate student performance is not perfect and that the error 1ijt is distributed as N ð0; sÞ, (4) can be estimated as a probit equation with the elements of qijt and qmin j as regressors. When promo- tions are based strictly on merit, observed promotions will send correct signals to 8. Bedi and Marshall (2002) modeled day-to-day school attendance as an outcome of parental schooling decisions, and like parental decisions about enrollment, they found it is affected by the expected benefits as measured by an associated increase in test scores and by the quality of school facilities. King, Orazem, and Paterno 587 the parents about their child’s performance, except when there is a large positive or negative evaluation error, 1ijt.9 Case B2. Nonmerit-based promotion. Teachers may also base promotions partly on the parents’ status in the community or on a school policy (or practice) to keep grade retention rates to a minimum (or at zero). In this case, only non- merit factors, Zijt, affect promotion, so the teacher’s promotion decision is Pijt ¼ 1 if Zijt b ! jijt ð5Þ ¼ 0; otherwise where jijt represents random variation in the teacher’s evaluation of a student. In this extreme case, the promotion decision provides no information to the parents about their child’s performance. Case B3. Hybrid promotion. Promotion decisions are unlikely to follow either of the two polar cases above but are far more likely to be a combination of merit- based and nonmerit-based factors. Using g as the weight placed on merit factors, the promotion policy might be characterized as Pijt ¼ 1 if g½qijt À qmin j Š þ ð1 À gÞ½Zijt bŠ ! g1ijt þ ð1 À gÞjijt ¼ eijt ð6Þ ¼ 0; otherwise: This hybrid promotion decision returns the strict merit-based decision if g ¼ 1 and the strict nonmerit-based decision if g ¼ 0. Without tests that measure student performance against common standards and thresholds, even if the school or a teacher wants to base promotions on merit, large measurement error variances in the process governing 1ijt will bias the merit weight g toward zero. One result of the absence of student assessments that are perceived to be fair and accurate is that parents (and students) may get the impression that merit is not valued. Performance, Promotion, and Persistence Parental decisions regarding how long to keep their child in school can be driven by the child’s performance in school as in equation (1), or by both performance and promotion as in equation (2). Promotion will be positively correlated with a child’s performance as long as g . 0 in equation (6), even if promotion is not solely merit-based. To distinguish between equations (1) and (2), the incidence of promotion is decomposed into a component that is correlated with merit and another component that is uncorrelated with merit. This can be accomplished by 9. In their study on Brazil, Gomes-Neto and Hanushek (1994) found that promotion rates were directly related to students’ test scores. A one-point increase in the Portuguese achievement test reduced the probability of grade retention by 1 percent. The impact of increases in the mathematics test score were half as large. Since the mean observed grade retention rate in the sample was only 4 percent, these merit effects are significant. 588 THE WORLD BANK ECONOMIC REVIEW predicting promotion on the basis of equation (4), the strict merit-based model, 10 which measures the merit-based component as PM ijt ¼ EðPijt jAijt ; Mijt ; Lijt Þ. An N alternative would be to include only nonmerit factors such that Pijt ¼ EðPijt jZijt Þ: A third alternative is labeled residual promotion, PR ijt , the promotion component uncorrelated with all merit and nonmerit factors that affect the probability of promotion. That can be specified as PR ijt ¼ Pijt À EðPijt jAijt ; Mijt ; Lijt ; Zijt Þ: Using these alternative components of the observed promotion decision, a linear ap- proximation to (2), the parents’ utility from enrolling the child in school the next year can be modeled as S M N R Vijt þ1 ¼ dM Pijt þ dN Pijt þ dR Pijt þ dW Wijtþ1 þ dC Cijtþ1 þ uijtþ1 : ð7Þ S Parents will keep their child in school as long as Vijt þ1 . 0, which corresponds to the probit equation Eijtþ1 ¼ 1 if dM PM N R ijt þ dN Pijt þ dR Pijt þ dW Wijtþ1 þ dC Cijtþ1 . Àuijtþ1 ð8Þ ¼ 0 otherwise; where Eijtþ1 is a dichotomous variable indicating whether or not the child is en- rolled in the following year. The coefficients dM , dN , and dR represent the weights that parents place on merit, nonmerit, and random information contained in the promotion when they decide whether or not to keep their child in school. If parents care about promotion as well as learning, they might place equal weight on the components such that dM ¼ dN ; if merit matters more, dM would be larger. Note that the residual component (with coefficient dR Þ could be measuring unob- served merit factors, thus underestimating the importance of merit on the parents’ decision to keep the child in school. This possibility is addressed in section IV. I I I . D ATA S O U R C E S The empirical analysis is based on data from a series of survey questionnaires de- signed by the authors and fielded by NEMIS. The survey covered a representative sample of 257 government, mosque, and private schools that were first surveyed by Ali and Reed (1994) as part of a textbook study. In each school, one teacher was selected in each of the first three grades; this selection was random if there was more than one teacher in a grade. Although data were collected for kachi or kindergarten, pakki or grade one, and grade two, the analysis uses data only on grades one and two as the kachi pupils were too young to take the tests. The school survey obtained information on teachers’ socioeconomic background. 10. Including attendance as a merit factor allows us to include children who were missing on the day of the exam. Similar results are obtained when only the subset of children who took the exam are included and only test scores are included in the merit vector. King, Orazem, and Paterno 589 For the household survey, two students from the school were randomly selected and information was collected on the socioeconomic attributes of each student’s family. Variable definitions and sample statistics are reported in table 1.11 The NWFP school year begins in April, schools close from June–August, and then the school year continues through March of the following year. The enu- merators surveyed the teachers and students at the start of the school year in April and May. The first-grade exams were administered to second-graders at that time, effectively within 1 –2 months after they completed the first grade. These exams were administered also to the first-graders at the end of the school year. The enumerators returned to the schools after the schools reopened in April. At that time, they collected the official information on student and teacher attendance from the attendance register and information on the children who re- enrolled for that year. If a student was not enrolled again in the same school, enu- merators obtained information on whether that student had transferred to another school or had dropped out. Enumerators were able to find the enroll- ment status of all but nine of the original sample children; those nine observa- tions were excluded from the analysis of persistence in school. During the course of the school year, the enumerators conducted two unan- nounced or spot checks of teacher and student absenteeism. The first check oc- curred in the first two months of the school year, and the second occurred in the final two months. Data on monthly student and teacher attendance over the school year were also obtained from the school’s attendance register. According to the spot visits, the average teacher absence rate was 19 percent, which is com- parable to the absence rates found by Chaudhury et al. (2006) for six developing countries using similar methods to that employed in our study. Students had a lower average absence rate of 10 percent.12 Students with absent teachers were often supervised by other teachers present on the day. The first-grade tests were designed by the late Sar Khan. Based on the official curriculum which all schools, public or private, were expected to follow, the tests assessed student achievement of the minimum competencies set by the curricu- lum for each grade level.13 The language test was conducted in the language of 11. Our choice of which school and household measures to use is related to the frequency of response. For example, distance from the home to the school was not answered by twenty-five households. Our results are not affected by the inclusion or exclusion of the distance to school (the average is under one kilometer, so this is not surprising), and so only results using the larger sample excluding school distance are reported. 12. Das et al. (2007) also found that in Zambia spot-check absenteeism rates were lower for students than teachers. In Zambia, the higher teacher absenteeism was due to AIDS-related illnesses and deaths. In NWFP, the absenteeism is apparently a result of an implicit contract in which present teachers take on the burden of their absent colleagues, allowing teachers to be absent more frequently in multiple-teacher schools than in single-teacher schools. 13. The ability of tests to measure student learning accurately is a topic of much debate in the field of education. Because the aim was to have a measure of achievement that is independent of the teacher and teachers’ promotion decisions, a standardized but curriculum-based test was the best available option. These tests should adequately capture relative learning across schools and children as the sampled pupils were all in the first two grades and were tested at a very basic level of reading and arithmetic. 590 THE WORLD BANK ECONOMIC REVIEW T A B L E 1 . Definition and Summary Statistics of Variables All Variable Definition children Boys Girls Promotion ¼ 1 if the child is promoted 0.91 0.92 0.89 (0.29) (0.27) (0.31) Persistence ¼ 1 if the child is enrolled the next 0.92 0.94 0.88 school year (0.27) (0.23) (0.32) Male 0.67 (0.47) Student attendance Average monthly attendance 0.90 0.91 0.87 taken from school records (0.13) (0.11) (0.14) Math achievement test 14.3 14.2 14.5 score (5.4) (5.3) (5.6) Language achievement 11.3 11.0 12.0 test score (6.3) (6.0) (4.6) Took test ¼ 1 if child took achievement tests 0.82 0.84 0.76 (0.39) (0.36) (0.43) Grade 2 ¼ 1 if child is in grade 2 0.49 0.50 0.47 (0.50) (0.50) (0.50) Teacher attendance Average spot-check attendance, 0.81 0.82 0.80 by school (0.16) (0.16) (0.16) Number of students Total number of students in school 24.2 22.8 27.2 (16.2) (15.4) (18.2) Single parent Either only one parent or parent reports 0.39 0.41 0.36 no schooling (0.49) (0.49) (0.48) Mother’s education Mother’s highest grade attended 0.96 0.91 1.06 (2.46) (2.37) (2.62) Father’s education Father’s highest grade attended 4.72 4.28 5.60 (4.9) (4.67) (5.29) Younger siblings Number of younger siblings 1.61 1.52 1.82 (1.23) (1.16) (1.34) Usually healthy? ¼ 1 if the child is usually healthy 0.94 0.94 0.94 (0.24) (0.23) (0.24) Household income Estimated household income 5.28 5.01 5.83 (Rs. 1000) (3.73) (3.30) (4.42) Note: Standard errors in parentheses. Source: Authors’ analysis based on data sources discussed in the text. instruction to avoid giving undue advantage to any one language group.14 Out of a possible score of twenty-five, the average scores for the math and language tests were 14.3 and 11.3, respectively. The analysis is based on a working sample of 904 children, 90.9 percent of whom were promoted and 92.2 percent of whom remained in school the follow- ing year (table 2). Of those not promoted, 40.7 percent dropped out of school; of those promoted, only 4.5 percent dropped out of school. As discussed in the 14. Although Pashto is the main language in the NWFP, the province has many other languages spoken, including Hindko, Punjabi, Persian, and Urdu. King, Orazem, and Paterno 591 T A B L E 2 . Distribution of Children, Merit-based Promotion, and Nonmerit-based Promotion, by Promotion and Continuation Status (%) Continued Promoted No Yes Total No 40.7 [3.7] 59.3 [5.4] 100 [9.1] PM ijt ¼ 50.3 PM ijt ¼ 79.6 PM ijt ¼ 67.7 PN ijt ¼ 89:2 PN ijt ¼ 89:4 PN ijt ¼ 89:4 Yes 4.5 [4.1] 95.5 [86.8] 100 [90.9] PM ijt ¼ 90.0 PM ijt ¼ 93.4 PM ijt ¼ 93.2 PN ijt ¼ 90.7 PN ijt ¼ 91:1 PN ijt ¼ 91:1 Total [7.8] [92.2] [100.0] PM ijt ¼ 71.4 PM ijt ¼ 92.5 PM ijt ¼ 89:8 PN ijt ¼ 90:0 PN ijt ¼ 91.0 PN ijt ¼ 91:0 Notes: The top number in each cell is the percentage continuing or not continuing in school the following year by the promotion status listed in the first column. The number in brackets is the number of children in the promotion/continuation cell as a percentage of the total sample. The last two numbers are the predicted probabilities of promotion based solely on merit (using table 3, column 4) or based solely on the nine nonmerit factors. These totals are based on the sample used in the regression analysis for which complete household data is available. The complete sample had very similar percentages. Source: Authors’ analysis based on data sources discussed in the text. model above, the positive correlation between promotion and persistence to the next grade may be due to learning or simply to being promoted. About 18 percent of the children did not take the exam. Earlier versions of the paper focused only on the sample for which test scores were available. Because of the concern that the fraction continuing in school might be correlated with sitting for the exam, the analysis now uses the full sample. The conclusions derived from the smaller sample and the full sample are similar; this is probably because the teachers did not have advance warning about the exam and had no fi- nancial incentive to discourage weak students from attending on the exam day. I V. E M P I R I C A L A N A L Y S I S AND R ES ULT S The first part of the analysis identifies the determinants of student promotion, and the second part uses those findings to embed predicted promotions into the analysis of student persistence in school. Student Promotion Two versions of the promotion equation are estimated: the pure merit-based specification (4) and the hybrid specification (6). Student performance is mea- sured by the test scores for mathematics and language and reflects the extent to which students have learned the material required by the nationally approved 592 THE WORLD BANK ECONOMIC REVIEW curriculum. Student performance is also measured by the student’s attendance rate, as captured in the official record, on the assumption that regular school at- tendance affects learning.15 A school’s required performance for promotion, qmin j , is assumed to vary with the school’s average score on the math and language tests. This would imply that it would be harder for a student to pass in a school in which students, on average, perform better. Since the performance level required for promotion should rise with grade level, a dummy variable for grade two is also added. Anything that raises the performance standard should lower the probability of promotion. Measures of Zijt include the mother’s and the father’s highest grades attained, whether there is only a single parent living in the household, and household income. Past studies in various countries have found that grade retention is higher for children who come from poorer homes and schools (Bonvin 2003; Eide and Showalter 2001; Glick and Sahn 2010; Gomes-Neto and Hanushek 1994; Hauser, Pager, and Simmons 2004; Mete 2004; Patrinos and Psacharopoulos 1996), a reason why appropriate identification has been a methodological issue for the studies that estimate the impact of grade retention on student performance. Parents with more education or higher income are expected to have more power or ability to influence teachers. Variables that might reflect parental incen- tives to do so include the number of younger siblings a child has (since parents may have a particular interest in the success of their first-born child), whether the child is male (since parents may have a stronger desire for their sons to succeed), and whether the child is healthy (since education may be more valuable if the child is expected to be able to reap the benefits of schooling for a longer period of time). Finally, two measures of how well the teacher can assess student perfor- mance are used, the teacher’s own attendance in class and class size.16 The more frequently the teacher is absent and the larger the class, the less the teacher is able to know a given child’s performance and the less likely that the promotion decision is influenced by merit. The first important result is the test of the null hypothesis that the coefficients are all zero for elements of the nonmerit vector Zijt (table 3). That test is equivalent to a test of the null hypothesis that g ¼ 1 in equation (6). The results reported below the regressions show that, for the full sample and for the subsample of boys, the null hypothesis that the coefficients on the vector Zijt are jointly equal to zero cannot be rejected at standard significance levels. For the subsample of girls, this null hypothesis is rejected only at the 10th percentile significance level, largely because the presence of younger siblings and teacher attendance also affect girls’ promotion. In contrast, the joint hypothesis that the coefficients on the merit vector qijt are jointly equal to zero is rejected, suggesting that the null hypothesis 15. The official attendance record is a complete record of student effort. Spot checks of student attendance confirmed that the official student attendance records were accurate. 16. Spot check observations on teacher attendance are used rather than the official teacher attendance. The official attendance was nearly 95 percent, but the spot check attendance averaged only 80 percent. King, Orazem, and Paterno 593 that g ¼ 0 in equation (6) is strongly rejected. In short, the evidence strongly sup- ports the view that teachers promote mainly on the basis of merit. Superior perfor- mance on either the math or language test significantly increases promotion probability, even though the teachers were never given the results of these exams. The elasticities of promotion probability with respect to the math and language scores range from 0.04 to 0.06 for all samples, except that math scores do not affect girls’ promotion. More informative are the predicted promotion probabili- ties as the scores vary from one standard deviation below to one standard devia- tion above the mean, holding all other factors at their sample means. A student who scores one standard deviation below the mean math score has a 95-percent probability of promotion, while a student with the same attributes who scores one standard deviation above the mean has a 99-percent probability of promotion. Language scores are even more important, with an interquartile range of promo- tion probability of six percentage points. Promotion is not strongly tied to a stu- dent’s performance relative to other students within a school. Average test scores have a small and statistically insignificant effect on promotion, suggesting that pro- motion standards may not differ significantly across schools. Promotions are more strongly tied to student attendance. Going from one stan- dard deviation below the mean to one above the mean increases the probability of promotion from 91 to 98 percent. Attendance is particularly important for girls’ promotion while language and math scores are relatively more important for boys. Each of these three merit-based measures has a stronger effect on promotion than any other factor considered except teacher attendance, the only nonmerit factor with an elasticity of comparable magnitude. Neither test scores nor attendance has to be exogenous to promotion in order to decompose promotion into merit- and nonmerit-based components. It is en- tirely plausible that parents send their child to school more regularly when that child is learning, but that does not mean that attendance is an inappropriate factor in assessing whether the child merits promotion. The method here only re- quires a measure of promotion that is uncorrelated with the child’s performance. Nevertheless, when the model is estimated without attendance, the results indi- cate that the test scores are the dominant factors that drive promotions. Two factors stand out in the vector of nonmerit influences on promotion. First, students with younger siblings are more likely to be promoted. This is consistent with the presumption that schools may face pressure to promote older children so as not to discourage the enrollment of younger children in the family.17 Nevertheless, this effect on promotion is very small, with an elasticity of just 0.025. Second, student promotion is influenced by teacher attendance with an elasticity of 2 0.055. The direction of the effect is surprising. As teacher attendance increases, 17. As noted by a referee, it is possible that the presence of younger siblings could simply reflect the advantage that first-born children have from the undivided attention of their parents, and so this too could be a merit-related factor. If true, the merit share used in this analysis understates the true merit share of promotions. 594 THE WORLD BANK ECONOMIC REVIEW all else equal, the probability of promotion decreases. A plausible explanation is that teachers who are frequently absent have little merit-related information upon which to base promotion decisions and thus cannot defend a decision to hold back a child for another year.18 Alternatively, these teachers may feel they need to curry favor with the parents in order to avoid complaints. Because of significant gender differences in schooling in Pakistan, promotion is analyzed separately for boys and girls. The null hypothesis that the process governing promotions is the same for boys and girls is not rejected. The coeffi- cients are very consistent in sign and significance across the boys’ and girls’ equa- tions. For both, it is test scores and attendance that drive differences in promotion so g is set close to one. Nonmerit factors play only minor roles in nu- merical impact, even when they have significant coefficients. The decision to discontinue the child’s education is unrelated to the vector Zijt, the nonmerit factors that might affect promotion (shown in table 2). The proba- bility of remaining in school conditioned on Zijt is about 90 percent. However, the decision to keep the child in school is correlated with the child’s test scores, even if the child is not promoted. The second number from the bottom of each cell in table 2 is the average probability of promotion as predicted by merit factors alone.19 The largest difference is that the students who were not promot- ed but stayed in school have predicted merit-based promotion rates that are 30 percentage points higher than their not promoted counterparts who did not con- tinue in school. Their predicted merit-based promotion is only 13 percentage points lower than that of the promoted students. Of the promoted students, the ones who dropped out performed only marginally below the ones who stayed in school, suggesting that their dropping out was driven by nonacademic reasons. Student Persistence Promotion decisions can affect the probability that a student persists or continues in school. One specification that examines this relationship includes the dummy variable, Pijt, which indicates whether or not the child was promoted. A second specification decomposes the observed promotion decision into: PM ijt , the merit component predicted by the first three terms in table 3 (column 1); PN ijt , the non- merit component of the promotion explained by the last nine terms in table 3; and PRijt , the residual component of promotions that are uncorrelated with the re- gressors. Because the estimations using the decomposed promotions require a two-step process, the standard errors were corrected using a bootstrapping pro- cedure.20 18. Das et al. (2007) find that a 5-percent increase in teacher’s absence rate in Zambia reduces learning by 4– 8 percent of average gains over the school year. They explain this reduction in learning not only being due to a reduction in contact time but also due to a decrease in preparation time for class by teachers. 19. Predicted promotion is based on the model in column 4 of table 2. 20. Bootstrapped standard errors are nearly identical to the original standard errors. The estimation using a linear probability model yields similar results. T A B L E 3 . Probit Analysis of Merit and Nonmerit Factors Affecting Student Promotion 1 2 3 4 5 6 Variable Full sample Boys Girls Full sample Boys Girls Merit factors: qijt Student monthly attendancea 0.278** 0.192** 0.301** 0.315** 0.226** 0.457** (6.11) (3.51) (5.78) (6.57) (4.01) (5.47) Math achievement test score/100a 0.388** 0.417** 0.197 0.439** 0.468** 0.225 (2.25) (2.19) (0.80) (2.18) (2.20) (0.56) Language achievement test score/100a 0.582** 0.542** 0.568** 0.629** 0.566** 0.807** (2.97) (2.29) (2.68) (2.83) (2.18) (2.13) Took testc 2 0.038** 2 0.037** 2 0.028 2 0.044** 2 0.042** 2 0.038 (2.85) (2.43) (1.39) (2.70) (2.27) (1.16) School average math score/100c 0.089 0.328 2 0.139 0.107 0.296 2 0.212 (0.32) (0.88) (0.42) (0.34) (0.72) (0.40) School average language score/100c 2 0.350 2 0.426 2 0.117 2 0.371 2 0.456 2 0.148 (1.31) (1.12) (0.38) (1.24) (1.08) (0.30) Grade 2c 2 0.014 2 0.013 2 0.017 2 0.013 2 0.011 2 0.021 (1.21) (0.90) (1.32) (0.95) (0.66) (0.89) Nonmerit factors: Zijt Teacher spot-check attendance b 2 0.065* 2 0.053 2 0.084* (1.74) (1.27) (1.68) Number of students/100b 2 0.005 2 0.013 2 0.010 (0.13) (0.26) (0.29) Maleb 0.004 . . (0.27) Mother’s educationb 2 0.001 2 0.002 2 0.001 (0.65) (0.90) (0.47) Father’s educationb 2 0.002 2 0.002 2 0.001 (1.02) (1.06) (0.60) King, Orazem, and Paterno Single parent at homeb 2 0.007 2 0.003 2 0.006 (0.35) (0.12) (0.26) Number of younger siblingsb 0.015** 0.012* 0.016** 595 (2.99) (2.08) (3.59) 596 Usually healthy?b 2 0.003 2 0.014 0.030 (0.10) (0.57) (0.70) Household incomeb 0.002 0.001 0.002 (1.02) (0.44) (0.79) Log Likelihood 2 188.5 2 125.1 2 55.8 2 194.9 2 129.6 2 60.9 Pseudo R2 0.31 0.26 0.46 0.29 0.24 0.41 N 904 604 300 904 604 300 H0 : equal coefficients between genders 15.2 8.8 H0 : Merit factors qijt ¼ 0 i.e. g ¼ 0 69.2** 42.9** 38.2** H0 : Nonmerit factors Zijt ¼ 0 i.e. g ¼ 1 13.8 11.6 15.3* THE WORLD BANK ECONOMIC REVIEW Estimated Effects Full sample Boys Girls Elasticity +1 s Elasticity +1 s Elasticity +1 s Math Score 0.05 0.95 to 0.99 0.06 0.94 to 0.99 0.01 0.98 to 0.99 Language Score 0.06 0.93 to 0.99 0.04 0.94 to 0.99 0.05 0.97 to 0.99 Attendance 0.26 0.91 to 0.98 0.19 0.93 to 0.98 0.26 0.88 to 0.99 Notes: All results are converted into marginal effects of the variable on the probability of promotion. Z-statistics corrected for clustering at the school level are reported in parentheses. **Significant at 5% *Significant at 10% a Element of the merit vector qijt. b Element of the nonmerit vector Zijt. c Control Source: Authors’ analysis based on data sources discussed in the text. King, Orazem, and Paterno 597 The enrollment status of all but nine of the students with promotion data from the prior school year was obtained, bringing the sample size to 895. The first striking result is that being promoted raises the probability of persisting in school by 36 percentage points (table 4). On the other hand, the joint exclusion test that the household, school or child attributes that make up Zijt cannot be rejected in the first column, and none of the coefficients is individually significant. When the coefficients on the elements of Zijt are restricted to be zero, the estimates of promotion on continuation are virtually unchanged. For these reasons, Zijt is ex- cluded from the remaining analysis, and the focus is on the effects of the subcom- ponents of promotion. As shown in the ranges below, going from one standard deviation below to one standard deviation above the realized promotion probability shifts the pre- dicted probability of persisting in school for an otherwise average child from 88 to 96 percent. The high correlation between promotion and persistence in school would seem to support an automatic or social promotion policy. However, a pro- motion may signal only that the child is prepared for more advanced schooling, leading parents to continue to enroll their child in school, in which case the pro- motion per se would have no impact on the child’s persistence in school. When the observed promotion Pijt is replaced with a three-part decomposition into merit, nonmerit, and residual components, it is the merit-based component of the promotion that drives the persistence effect (table 4, column 3). The marginal effect of the merit component is more than three times larger than the marginal effects of the other two components. One standard deviation above or below the mean varies the probability of persistence by 12 percentage points, double the range due to the residual component. The nonmerit-based component has almost no impact on school persistence. The interpretation of the residual promotion component is not straightfor- ward. This component reflects unobserved factors that are uncorrelated with either the observed merit or nonmerit promotion factors. If it is wholly due to unobserved nonmerit-based promotion factors, then such factors matter but have only a relatively small numerical effect on student persistence. If the residual component is wholly due to unobserved merit factors, then the importance of merit is understated. The cautious interpretation of these results is still that even mostly illiterate parents place the greatest weight on merit when deciding whether or not to keep their child in school. This suggests that automatic or social promotion has at most a small impact on persistence rates. The effect of merit-based promotion on persistence is significantly larger for girls than for boys (52 versus 24 percent), suggesting that parents are particularly sensitive to whether their daughters are learning and use this information to decide on their continuing in school. While the test that boys and girls respond equally to signals contained in promotion decisions could not be rejected at stan- dard significance levels, this is mainly because girls are unaffected by the nonmerit-based and random components of promotion. For boys, the marginal 598 T A B L E 4 . Probit Analysis of the Effect of Student Promotion on School Persistence Variable Full Sample Full Sample Full Sample Boys Girls Boys Girls Actual promotion: Pijt 0.361** 0.362** 0.25** 0.52** (7.59) (7.45) (4.81) (6.27) Merit-based promotion: PM ijt 0.331** 0.245** 0.518** (7.03) (4.034) (6.40) Nonmerit-based promotion: PN ijt 0.071 2 0.004 2 0.229 (0.25) (0.01) (0.54) Residual promotion: PR ijt 0.106** 0.085** 0.118 (3.82) (2.98) (1.57) Zijt Yes No No No No No No THE WORLD BANK ECONOMIC REVIEW Log likelihood 2 199.4 2 205.3 2 203.4 2 118.1 2 82.9 2 114.7 2 74.7 Pseudo R2 0.188 0.164 0.17 0.11 0.23 0.14 0.31 N 895 895 895 598 297 598 297 H0 : Zijt ¼ 0 11.8 H0 : equal coefficients between genders 6.83** 7.76 +1s Range: Pijt [0.88,0.96] [0.87,0.95] [0.91,0.96] [0.79,0.94] +1s Range: PM ijt [0.86,0.98] [0.90,0.98] [0.77,0.98] +1s Range: PN ijt [0.94,0.95] [0.96,0.95] [0.93,0.90] 0 +1s Range: PN ijt [0.91,0.97] [0.93,0.97] [0.88,0.94] Notes: The results are converted into marginal effects of the variable on the probability of continuing in school. Z-statistics corrected for clustering at the school level are reported in in parentheses. The z-statistics are estimated using a bootstrapping procedure with 200 draws with replacement in the columns using a two-step estimation procedure. The estimated ranges reflect predicted probabilities of student persistence from one standard deviation below to one standard deviation above the associated promotion measure. **significant at 5%; *significant at 10% Source: Authors’ analysis based on data sources discussed in the text. King, Orazem, and Paterno 599 effect on school persistence of merit-based promotion is nearly thrice that of pro- motion based on residual criteria. The probability of persistence for each promoted or not-promoted student rises rapidly with academic performance as indexed by the merit-based promotion component (figure 1). The gap between promoted and not-promoted students becomes smaller as merit-based promotion rises, consistent with the presumption that parents respond to information about how much their child is learning. One might be concerned that teachers are deciding to promote the children whom they expect will stay in school the following year. The instruments for pro- motion mitigate against this problem: The two tests were administered by the enumerators, and the teachers never saw the test results, so the tests were outside the teacher’s influence. Student attendance registers were validated by spot checks of student attendance, so they also appear to have been outside the teacher’s control. Consequently, the merit-based promotion measure will not be clouded by possible teacher motives to promote children who intend to return to school. On the other hand, the two nonmerit-based promotion components would be clouded by such incentives insofar as they represent promotion decisions that are not based on student performance. Of those two components, only the residual component matters for continuing in school the following year, and only for boys. Note that even if the residual component is entirely made up of unobserved nonmerit factors, the upper-bound measure of the effect of social promotion on student persistence is just 8.5 percent, or roughly one-third the effect of merited F I G U R E 1. Relationship between Persistence in School and Merit-Based Promotion, by Whether the Child was Promoted Source: Authors’ analysis based on data sources discussed in the text. 600 THE WORLD BANK ECONOMIC REVIEW promotions for boys, and 11.8 percent, or roughly one-fifth of the effect of merited promotions for girls. Alternatively, if the residual component is also merit based, then the upper-bound measure of the total effect of merit-based pro- motions on student persistence in school would be 33 percent for boys and 63 percent for girls. V. C O N C L U S I O N S High grade repetition rates, reaching 20 percent or higher in some countries (e.g., Brazil, Nepal, Senegal), increase the number of years it takes to produce a cohort of primary school completers and impose heavy costs on education systems (in terms of additional classroom space and teachers) and on households. Researchers have argued also that grade retention lowers students’ self-esteem and thus their persistence to learn. These considerations imply that grade repeti- tion works against education goals to increase school enrollment and completion rates and to promote learning. But is automatic or social promotion then the right policy to achieve these goals? The economic model of demand for schooling is based on the assumption that it is parents (and students) who determine ultimately how much a policy mandate or incentive will affect their schooling decisions. Whether or not the returns to edu- cation outweigh the (direct and opportunity) costs of going to school is relevant to whether children enroll in school, how long they stay enrolled, and how much they learn (Glewwe 2002; Behrman et al. 2008; Hanushek et al. 2008; Pritchett 2013). Expanded school supply, for example, is often not enough to nudge schooling de- cisions. Parents are willing to bypass a low-quality public school in favor of a better-quality, albeit more remote, public school (Gertler and Glewwe 1990) or even a private school that charges fees but is of better quality (Alderman et al. 2001; Andrabi et al. 2008). The large number of school-aged children not in school in developing countries where primary schooling is compulsory and largely tuition-free is at least partial evidence that parents do make decisions about their children’s schooling. This paper examined whether an automatic or social promotion policy that reduces the price of each year of schooling completed but that is not accompa- nied by better school quality will induce higher school enrollment and school continuation rates. In estimating the relationship between grade promotion and student performance, the analysis distinguished between promotion that is based on student performance (merit) and promotion that is based on nonmerit factors. While the evidence on the impact of grade promotion is not derived from a random experiment, it is based on teacher promotion decisions, student test scores that are not shared with the teachers or parents, and student persistence decisions made given the promotion decisions. 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