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Grade retention is a major issue in the ongoing debate over how to improve primary and secondary education in the United States. This paper examines the retention decision and its empirical effects using an economic framework. Within our model, the retention decision is endogenous with respect to such observables as dropping out of school and labor market earnings and this endogeneity needs to be accounted for in empirical work. In the empirical section of the paper we use the High School and Beyond (HSB) data set to examine the effects of retention on the probability of dropping out of high school and on labor market earnings several years after the student has entered the workforce. We account for the endogeneity of grade retention by using instrumental variables (IV) estimation where the key instrument is based on exogenous variation across states in kindergarten entry dates.

Grade retention is a major issue in the ongoing debate over how to improve primary and secondary education in the United States. Also known as ‘flunking’ or ‘being held back’, grade retention generally refers to the educational practice of having a child repeat a grade in school. For 1995, the National Center for Education Statistics (NCES) estimated that over 13% of individuals aged 16 to 24 had repeated at least one grade. For blacks, the estimate is nearly one in five (National Center for Educational Statistics, 1997a, Table 24). The NCES estimates are low compared with other studies. The NCES estimates imply that roughly 1% of students are retained each year.1 By contrast, a study by Rose, Medway, Cantrell and Marus (1983) using data from the 1980s estimates that 5.5% of all students in grades K–12 are retained each year. With a sample of 15 states, several states had rates that implied over 50% of students would be retained at least once by the tenth grade. As for more recent evidence, Table 1 gives estimates derived from the October educational supplement of the 1997 Current Population Survey (CPS). The survey asked of each child in a household what grade they were enrolled in during the current year and what grade they were enrolled in during the previous year, and we used this information to calculate retention rates. These estimates show that retention rates are substantially higher in the first grade than in subsequent grades, that blacks tend to be retained at higher rates than whites, and that males are retained more frequently than females. Table 1. Estimated retention rates (ages 14 and under) Grade All Whites Blacks Males Females 1 6.69 5.70 14.59 7.81 5.54 2 2.22 2.26 1.86 2.87 1.48 3 1.57 1.20 3.32 1.78 1.37 4 1.62 1.52 2.42 1.68 1.56 5 1.23 0.99 2.07 1.42 1.01 6 1.36 1.03 2.66 1.71 1.03 7 1.80 1.89 1.28 2.49 1.08 8 1.10 0.99 2.02 1.60 0.58 Average 2.24% 1.97% 3.98% 2.71% 1.74% Source: Current Population Survey, October 1997, authors' computations. Table options Although there are no systematic national estimates of either the number of students held back each year or of the cost to the public of this practice, a rough estimate of the direct dollar cost can be made. In 1996, the NCES estimated there were 44.7 million students in grades K–12 in the US and that the average expenditure per child was almost $5800 (National Center for Educational Statistics, 1997b). Using a conservative estimate of 1% annual retention rate, the estimated cost for retention is approximately $2.6 billion per year and affects about 450,000 children. Credible estimates of 5% annual retention rates imply an annual cost of approximately $13 billion and over 2 million children affected. By way of comparison, the federal Head Start program (Head Start, 1998) had appropriations of approximately $3.6 billion in fiscal year 1997 and served approximately 800,000 children. The retention cost estimates also obviously ignore the private costs of retention, such as the delay of entry into the labor force or matriculation into post-secondary education, which are likely to be substantial. Despite its widespread use, retention is a very controversial practice.2 Opponents of retention contend there is a causal link between retention and negative outcomes such as dropping out of school (Cairns, Cairns & Neckerman, 1989; Fine, 1991; Grissom & Shepard, 1989, Chap. 3; Rumberger, 1987; Wagenaar, 1987), low self-esteem and poor academic performance generally (Kellam, Branch, Agrawal & Ensminger,1975; Royce, Darlington, & Murray, 1983). For example, Grissom and Shepard (1989) estimate that retaining a student increases the probability of not completing high school by 20 to 30%. Holmes (1989) surveyed 47 empirical studies using a variety of academic achievement measures. He found that retained students tended to score 0.19 to 0.31 standard deviations below comparable students who had not been retained. House (1989, p. 209) summarized the research as follows: “It would be difficult to find another educational practice on which the evidence is so unequivocally negative”. However, there does exist a small body of empirical evidence suggesting there are beneficial effects to retention. Most notable is the recent research by Alexander, Entwisle and Dauber (1994) which documents the educational progress of a cohort of several hundred students in the Baltimore school system over an eight-year period and finds that retention has a positive effect on academic achievement as well as on more subjective measures such as self-esteem. In other work, Kerzner (1982) and Pierson and Connell (1992) also find some positive effects on academic outcomes, although the evidence tends to be mixed. One key element that is missing in the current debate is a serious discussion about how retention decisions are made and how to account for the decision process in measuring the effects of retention. If retention is based solely upon a student passing a well-defined academic standard, that will likely have a different set of implications than if the decision is based on some guess as to how much a given student would benefit from an additional year in a particular grade. Economists have not contributed much to this lively and important debate although the heart of the problem is a resource allocation decision.3 This paper examines the retention decision and its empirical effects within an economic framework. We model the decision to retain a child as a parental decision with a parent deciding to hold a child back based on the net gain to the child, where the benefit of retention is higher expected earnings and the cost includes both the deferred entry into the job market and non-pecuniary considerations. With such a framework, the retention decision is clearly endogenous with respect to such observables as dropping out of school and labor market earnings, and this endogeneity needs to be accounted for in empirical work. In the empirical section of the paper we use the High School and Beyond (HSB) data set to examine the effects of retention on the probability of dropping out of high school and on labor market earnings several years after the student has entered the workforce. This empirical work adds to the existent literature on grade school retention in several dimensions. First, the data set is nationally representative and thereby provides some generality that is lacking in much of the current literature, which typically consists of case studies of individual schools or districts. Second, since the HSB is a panel of students tracked since their sophomore year in 1980 up to 1992, we are able to examine the relatively long-run impact of retention on eventual labor market earnings, which no previous study has been able to measure. Third, we account for the endogeneity of grade retention by using instrumental variables (IV) estimation where the key instrument is based on exogenous variation across states in kindergarten entry dates. The outline of the paper is as follows. Section 2 presents the model, Section 3 describes the data and estimation approach, Section 4 gives empirical results, and Section 5 concludes.

Grade retention is a widely used, yet controversial practice. Supporters argue that retention provides students an additional year to gain important academic skills and emotional maturity. However, many researchers assert that repeating a grade negatively affects a student's educational career. In this paper we examine the retention decision and its empirical effects within an economic framework, focusing on the effect of retention on eventual labor market earnings, paying particular attention to the potential endogeneity of the retention decision. For all demographic groups, the OLS estimates show a statistically significant positive correlation between retention and dropping out of high school and a statistically significant negative correlation between retention and post-high school labor market earnings. These findings are consistent with much of the previous empirical research on grade retention. However, the IV estimates which account for endogeneity differ markedly from the OLS estimates. For whites, the estimated IV coefficients are opposite in sign from the OLS coefficients which suggests that grade retention may have some benefit to students by both lowering dropout rates and raising labor market earnings. We cannot strongly state, however, that grade retention is a useful policy since the IV estimates tended to be statistically indistinguishable from zero, although it is important to note that the parameter estimates hinted at relatively large effects. For blacks, the IV approach gave very poor first-stage results and the resulting IV estimates are not informative. The difference in estimation results between blacks and whites is somewhat puzzling and potentially troubling. The first-stage regression results for whites suggest that our IV identification strategy works reasonably well and is consistent with our theoretic framework of altruistic decision-makers optimizing on behalf of a child. However, for blacks the first-stage results yield insignificant results with no clear pattern. One possible explanation is that the sample size for blacks is substantially smaller and thus if we had more observations we could expect similar results to those for whites. But when we reduced the sample size for whites, the pattern of the coefficients remains much the same and in the unreduced sample, although statistical significance unsurprisingly declines. This leads us to wonder whether sample size is the primary reason for the difference. The other possibility is that the retention decision process for blacks is fundamentally different from whites. We emphasize that we do not currently have good evidence on this so we can only make conjectures. One conjecture within the context of the model is that parents or decision-makers in black households use a different algorithm than in white households. Another possibility is that school officials use a different criterion for blacks than whites. Obviously other explanations are also possible, but this seems like an area worthy of further investigation. Another policy issue raised by this research is whether decision-making for retention can be considered optimal in any sense. We modeled the decision being made by parents equating expected marginal costs and benefits, but these will necessarily be private costs and benefits. Since the vast majority of children in the US are educated in public schools, a parent's decision to retain a child will ignore the cost to the public treasury in spending another year educating that child and that cost is not factored into the decision process. The prediction would then be that retention is done too often because parents to not face the full marginal cost. A fuller examination of this topic is also probably worth considering.