Have We Put an End to Social Promotion? Changes in School Progress among Children Aged 6 to 17 from 1972 to 2005

Abstract

We examine trends over time in the proportion of children below the modal grade for their age (BMG), a proxy for grade retention, and in the effects of its demographic and socioeconomic correlates. We estimate a logistic regression model with partial constraints predicting BMG using the annual October school enrollment supplements of the Current Population Survey. This model identifies systematic variation in the effects of social background across age and time from 1972 to 2005. While the effects of socioeconomic background variables on progress through school have become increasingly powerful as children grow older, that typical pattern has been attenuated across the past three decades by a steady secular decline in the influence of those variables across all ages. A great deal of concern has been expressed about rising levels of economic and social inequality in the United States since the middle 1970s, and about the potential intergenerational effects of such inequality. However, there has been an opposite trend in the effects of social origins on being BMG. A trend is not a law, and there is reason to be concerned about the recent deceleration of the secular decline in effects of social background on being BMG.

Despite the availability of other methods to assist poorly performing students, grade retention is often proposed and used to help them catch up to their better performing peers. However, most research on the effects of grade retention portrays it as a practice that, at best, provides no lasting benefit to the students and, at worst, is considered a damaging practice. The lack of compelling evidence about the causal effects of retention, whether beneficial or harmful, raises the following questions. What proportion of the school-aged population experiences retention? How do demographic and social background characteristics of students affect retention? Have these effects changed across time as school populations and educational practices have changed?

Identifying potential disparities in retention by demographic and social background characteristics is important for two reasons. First, educational attainment is a fundamental dimension of population composition. It affects many other population processes throughout the life course. The experience of retention in grade is a powerful predictor of later success in schooling and beyond. Thus, the predictive power of retention warrants tracking both retention rates and disparities in them. The second reason follows from the first. Official national and even state-level statistics on either the incidence or prevalence of retention are scarce. Documenting retention at the population level allows us to place the findings of studies about the effects of retention into the context of the actual practices of retention. The more common the practice of retaining students in grade, the more the effects of being retained will be magnified at the population level.

Nationally, estimates of the proportion of students who have experienced at least one retention vary from 10% to 30% depending on the age of students, time period, and data source (Bianchi 1984; Corman 2003; Wheelock 2007). Despite the dearth of information about the prevalence of retention, there is some agreement among researchers that the proportion of children who have ever been retained is growing, but this evidence is sparse. In their study of 12 elementary schools in the state of New York, Allington and McGill-Franzen (1992) found that the proportion of students retained in kindergarten through second grade increased between 1979 and 1989. However, this increase was offset by a decline in the proportion of children retained in the upper elementary grades.

There are two series of estimates of national trends in grade retention rates. One series collects official grade-specific retention statistics from state education agencies (Hauser, Frederick, and Andrew 2007; National Research Council 1999; Shepard and Smith 1989). Only 29 states and the District of Columbia reported any retention data from 1977–1978 to 2004–2005. It is difficult to draw systematic conclusions from these incidence rates because coverage of years and grades is incomplete and because definitions of retention vary across state (and district) lines. These statistics do not show substantial increases in retention rates. The main conclusions to be drawn from the official reports of retention are that retention rates in different states vary widely, and within each state, the rates vary by grade and show no stable trend over time. However, consistent indications of increasing retention rates have occurred at the earliest grade levels in some states.

In a second series analyzing trends in the prevalence of retention (Hauser 2001, 2004; Hauser, Pager, and Simmons 2004), Hauser and colleagues identified children in the October Current Population Survey’s annual school enrollment supplement who were below the modal grade for their age (hereafter, BMG) as a proxy for ever having been retained. They found that the proportion of children who were BMG increased dramatically over time for each age group. Discerning changes in the prevalence of retention over time with this proxy measure is difficult because children can be BMG due to either a past retention or late entry into formal schooling, among other reasons. The evidence suggests that the increases are driven by children who are BMG at the youngest ages, most likely due to the increasing average age at school entry (Frey 2005; Shepard 1989). As a result, the authors inferred retention by subtracting the initial prevalence of BMG in the cohort from the prevalence of BMG in that same cohort at older ages. Using this conservative measure, Hauser and colleagues found that the prevalence of retentions actually decreased between 1972 and 1996.

This article extends their series of estimates temporally and methodologically. First, we update the time series with data through 2005. Second, we explicitly estimate changes over time in the effects of social background characteristics on being BMG using a logistic regression with interaction constraints (discussed in the Models section below).

The question of how retained children compare with those who are not is relevant to the contemporary policy environment in which test-based accountability is expanding and the desire to end social promotion is strong (Bush 2004; Clinton 1999; National Commission on Excellence in Education 1983; National Education Goals Panel 2007). However, the academic literature on the individual-level effects of grade retention implies that if retention has any effects, they are harmful: lower academic achievement (Hong and Raudenbush 2005; Nagaoka and Roderick 2004), dropping out of high school (Allensworth 2004; Hauser, Simmons, and Pager 2004; Jimerson 1999), lower likelihood of attending college, and earning lower wages (Jimerson 1999).1 In his meta-analysis on retention research in the 1990s, Jimerson (2001:434–35) concluded that

[S]tudies examining the efficacy of grade retention on academic achievement and socioemotional adjustment that have been published during the past decade report results that are consistent with the converging evidence and conclusions of research from earlier in the century that fail to demonstrate that grade retention provides greater benefits to students with academic or adjustment difficulties than does promotion to the next grade.

These negative effects of retention become more important when one considers that retention is correlated with student background characteristics. Differential retention rates by gender, for example, mean that boys are more likely to suffer the negative outcomes discussed above because they are more likely to be retained.

Unfortunately, none of these studies used an experimental design, and without this, these findings must contend with uncertainty in attributing causality to the fact that a particular student has been retained. This is especially true for studies of the effects of retention on academic achievement because, ostensibly, retention decisions are made because of poor academic performance. With these weaknesses in mind, the weight of the evidence does suggest that retention fails to provide long-term benefits to students.

Although this article will not solve the inconsistency between the policy environment and research findings, it does inform the debate by documenting changes in both the overall prevalence of retention over time and the influence of social background characteristics on retention. This new information will allow us to judge how much social promotion exists. Furthermore, if a large proportion of the school-aged population experiences grade retention, these findings may lend support to future efforts to design experiments evaluating the causal effects of retention.

Specifically, this article addresses the following four research questions: (1) Has the prevalence of children who are BMG increased over time? (2) If so, is the increase driven by changes in the prevalence of BMG at certain ages? (3) What are the effects of social background characteristics on being BMG? (4) Finally, how do social background effects differ over time and age? We find that the odds of being BMG have increased over time after controlling for age and social background characteristics. We also find increasing social background differences in the odds of being BMG as children age, but, simultaneously, these differences diminish over time.

In the next section, we describe the data and discuss the use of BMG as a proxy for grade retention. The third section sets forth the modeling strategy employed in our analyses. We present the model estimates in the fourth section. Finally, we situate our findings in the grade retention literature and their implications for the future of the debate over the practice of retaining students in grade.

DATA

The research questions above require a consistent measure of grade retention that is repeated over a long period of time. Curiously, given the prominence of the standards and accountability movement across three decades, there has been no concerted effort to monitor the success of efforts to end social promotion (Hauser 2001, 2004; Shepard and Smith 1989). Because comparable direct measures of grade retention do not exist, we use the October school enrollment supplement to the Current Population Survey (CPS). The CPS data on school enrollment come from a nationally representative probability sample of the civilian noninstitutional population each October. We are able to construct a uniform CPS file from 1972 onward because a common set of social background questions has been asked every year, along with information about age and grade enrollment of school-aged persons.2 Although the data do not contain detailed educational measures, such as the previous year’s enrollment (prior to 1994), academic achievement, or information about transitional or special education classrooms, the data do provide repeated cross-sectional observations of the national population over an extended period of time. The fact that the data are repeated cross sections, rather than true longitudinal observations, does not pose a problem because we are interested in aggregate retention rates rather than the consequences of retention for individuals.

A further complication in documenting trends in grade retention over time is that some research uses measures of the incidence of retention—the proportion of students retained in the previous year. Others use the prevalence of retention—the proportion of students who have experienced at least one retention. Ideally, we would use incidence rates to measure changes in retention rates because prevalence measures for a given year incorporate the sum of an individual’s history of exposure to being retained. However, incidence measures are unavailable in the October school supplement to the CPS prior to 1994, and they have been included regularly only since 1995 (see Hauser et al. [2007] for a similar analysis using this measure). Limiting ourselves to this measure would eliminate almost two-thirds of the time series available. We proceed with the prevalence measure in our analyses in order to exploit the full range of data available.

Measuring Retention

Consistent with past research on the prevalence of grade retention, we compare a student’s age and grade of enrollment to construct a proxy for retention (Bianchi 1984). Children who are BMG are assumed to have experienced retention at some point in their educational careers prior to the survey date.

Table 1 compares the constructed BMG measure with a direct retrospective report of whether the student has ever been retained.3 If we assume the latter is the true measure, more than 80% of children are correctly classified by their BMG status. The overwhelming majority of misclassified children are false positives (classified as BMG without having been retained). Why would the BMG measure err in the direction of false positives? First, the direct measure is likely an underestimate (although the impact of this is unknown) owing to the respondent’s failure to report retention because they forgot or were too embarrassed to do so. More importantly, our measure cannot distinguish between children who had been retained in grade and those whose parents decided to delay school entry. Other reasons could be birthdays that occur between state-mandated cut-off dates and the administration of the survey, or missing a year of school for health reasons.

Table 1.

Comparison of Retention Measures in the CPS

BMG	Direct Measure of Retention
	Yes	No
Yes	5,768	12,418
No	822	49,792

The practice of delaying school entry is known as academic redshirting. Whether the decision to redshirt children is made by their parents alone or with teacher input, the reasons given are similar to those given for retaining children. Either the child needs more time to mature, or the extra year would give a lower-performing student a chance to catch up to meet the expectations of kindergarten. The effects of redshirting are similar to effects of retention in that there is a temporary advantage to the redshirted child, but it disappears by third grade. Redshirted children are also more likely to be placed in special education classes than are comparable peers (Marshall 2003). Thus, the error introduced by the false positive identifications is reduced to the extent that academic redshirting is effectively a form of preemptive retention.

Cascio (2005) estimated the bias introduced by using BMG as a proxy for grade retention in regression estimates of the effects of social background using the October CPS. Her sample included children aged 7 to 15 in 1992, 1995, and 1999. She used the direct report of ever having been retained and found that when BMG is used as a dependent variable, the effect of the misclassification of students in the CPS data set attenuates the magnitude of the true coefficients of the independent variables by as much as 35%. The attenuation bias is greater for males (38% vs. 32%) and for older ages (41% for ages 12 to 15 vs. 30% for ages 7 to 11). The attenuation bias decreased over time, from 40% in 1992 to 32% in 1999. The attenuation bias is highest for non-Hispanic blacks (45%), followed by non-Hispanic whites (34%), Hispanics (31%), and the group of other races (28%). However, the coefficients we present are biased toward zero only when interpreted as the effect of a given social background characteristic on grade retention per se. There is no such bias when they are interpreted as the effect on being BMG.

Despite the shortcomings of using BMG as a proxy for having experienced one or more retentions, there are three reasons why such analyses are justified. First, the lack of direct retention data makes this the only way to study the prevalence of retention since the early 1970s. This fact, combined with the possibility of increasing numbers of children being exposed to the negative consequences of retention, makes continued monitoring of retention levels crucial. Finally, we make comparisons within birth cohorts in order to minimize the impact of the recent trend of increasing ages at school entry. Looking at changes relative to one’s own cohort allows us to control for initial levels of being BMG due to academic redshirting, much like the practice of subtracting out initial levels of BMG that Hauser and colleagues employed (Hauser 2001, 2004; Hauser, Pager, and Simmons 2004).

Covariates

We include two sets of covariates in the analysis: demographic and social background characteristics. These covariates serve a dual purpose in the multivariate analyses, depending on the research question being addressed. In terms of the first research question, the role of the covariates is to adjust the observed rates of being BMG for changes in the composition of the school-aged population over the period of study. Compared with the earliest cohorts involved in these analyses, later cohorts tend to include, among other things, larger proportions of racial and ethnic minorities, as well as those who come from single-parent families (Kominski and Adams 1993; Lapkoff and Li 2007).

Retention decisions do not affect all subpopulations equally. Retained students tend to be male (Corman 2003; Hauser, Pager, and Simmons 2004; Zill, Loomis, and West 1997), black or Hispanic (Alexander et al. 2003; Hauser, Pager, and Simmons 2004; Jimerson et al. 1997; Zill et al. 1997), and young relative to their peers (Corman 2003; Shepard and Smith 1986). Certain family characteristics have also been shown to be related to retention decisions, such as coming from single-parent homes with lower family income and fewer years of education (Corman 2003; Hauser 2001; Hauser, Pager, and Simmons 2004).4 Therefore, compositional changes with respect to these characteristics need to be controlled in order to measure net changes across time in the proportion of children who are BMG.

Not coincidentally, the demographic and social background covariates that we include are characteristics that have been shown to be consequential for the status attainment process (Featherman and Hauser 1978; Hauser and Featherman 1976; Mare 1980). Differential progress through graded school may be one pathway by which social background influences ultimate educational attainment and later life chances. That is, grade retention versus promotion is a fork in the road to educational success or failure. If certain demographic and social background characteristics increase the chances of being BMG, then they are likely to limit later attainments unless retention or academic redshirting has a compensatory effect.

Table 2 lists the two sets of covariates used in the analysis. In addition to the social background characteristics discussed in the previous paragraphs, we include measures of age, birth cohort, region, metropolitan status, number of children in the household, the occupational status of the household head and his or her spouse, and whether or not the child’s family owns their home. Age is included as a rough measure of exposure. We expect older students to have a higher prevalence of BMG because of their greater exposure to the risk of grade retention. Age is measured by the respondent’s last birthday as of the end of the survey week.

Table 2.

Covariate Proportions, Means, and Standard Deviations for Complete Case and Imputed Data: October Current Population Surveys, 1972–2005

Variable	Complete Case			Imputed		Observed Values
	Proportion	Mean	SD	Mean	SD
White	.734		.44			912,526
Black	.133		.34			912,526
Hispanic	.089		.29			912,526
Other Race	.043		.20			912,526
Male	.510		.50			912,526
Major Central City	.088		.28			912,526
Major Suburb	.131		.34			912,526
Other Central City	.133		.34			912,526
Other Suburb	.222		.42			912,526
Rural	.426		.49			912,526
East	.213		.41			912,526
Midwest	.258		.44			912,526
South	.299		.46			912,526
West	.230		.42			912,526
Home Ownership	.719		.45			912,526
Single-Parent Household	.256		.44			912,526
Total Children in the Household		2.713	1.44			912,526
Logged Income		9.919	0.85	9.918	0.85	844,371
Head’s K-12 Education		11.116	2.06	11.116	2.06	911,476
Heads Postsecondary Education		1.279	1.96	1.279	1.96	911,476
Spouse’s K-12 Education		11.307	1.81	11.302	1.82	679,229
Spouse’s Postsecondary Education		1.068	1.74	1.067	1.74	679,229
Head’s Occupational Status		38.001	20.33	37.989	20.32	811,052
Spouse’s Occupational Status		39.791	18.79	39.751	18.79	443,903

The birth cohort measure is constructed by subtracting the respondent’s age from the year of the survey. Because the survey was administered in October, the birth cohort measure assigns those with birthdays between the survey week and the end of the year to the year after they were born. For example, a 10-year-old child surveyed in 1990 with a birthday in December would be placed in the 1980 cohort instead of the 1979 cohort, as she should be. This error in the birth cohorts should be minimal because we group the sample into five-year birth cohorts so that at least 80% of the sample will always fall into the correct cohort group. The error is further reduced because over 60% of the state cutoff dates that Cascio (2005) could collect occur in or before October. Thus, most of the cases that are possibly misclassified are placed in the same cohort as the classmates with whom they started school.

The education measures in the CPS varied over time. Through 1991, the variable was measured in years of education, from zero to six years of college or more. From 1992 forward, education was measured as highest category of school or degree completed. Hauser (1997) discussed the incompatibilities and inconsistencies of these two measures of education. For the analysis presented here, we converted the educational credentials to the metric of putative years of school completed. This introduces a degree of measurement error by assuming, for example, that 16 years of education is equivalent to a bachelor’s degree.

There are two education variables for each “parent” in the final model. The first captures the number of years completed through high school graduation, and the second captures college education. Thus, a person who completed the 10th grade has a value of 10 for the first variable and 0 for the second. The corresponding scores for high school graduates with no college and those with a bachelor’s degree are (12, 0) and (12, 4), respectively. This scheme was used to allow for piecewise linear effects of education before and after the transition from high school to college, especially in light of the differences in college attendance over time among the parents of children in the October CPS samples.

Analytic Sample

The CPS data include 912,526 children aged 6 to 17 clustered within 276,124 households over 34 years. Due to limits of computational power, in the multivariate analyses below, we report results from a one-half random subsample stratified by age, period, gender, and race. This subsample contained 457,038 observations clustered within 214,206 households. All of the models reported here were estimated using robust standard errors that have been adjusted for household clustering. There were missing data in some observations on seven continuous variables. The second column of Table 2 shows the means or proportions of each demographic and social background variable used in the analysis before accounting for missing data. The fourth column shows the means of the covariates with missing data after imputation for those variables with missing values. The final column of Table 2 shows the total number of nonmissing observations for each variable. Appendix Table A1 shows the percentage missing on each variable by year.

There are two types of missing data on the variables used in this analysis. Data on household income and head’s education are sometimes missing, but there are actual values of these characteristics.5 We used multiple imputation to replace this type of missing data. When data are not missing completely at random (MCAR), listwise deletion can yield biased results (Allison 2001:6).6 Multiple imputation yields consistent, asymptotically efficient, and asymptotically normal estimates under the weaker assumptions that the data are missing at random (MAR) and the model is correctly specified. Of the two variables with this type of missing data, income is the only one for which there is evidence that it is not MAR. However, only 7% of cases lack income data, so this violation should not strongly affect the estimates.

Some data on spouse’s education and occupational status as well as head’s occupational status are missing for a different reason; values do not exist because of unemployment or because there is no spouse in the household. In order to account for this type of missing data, we use a dummy variable adjustment technique. We substitute the missing data on these variables with mean values of nonmissing cases, conditional on the age and birth cohort of the child. Then we include a dummy variable in each model that we estimate, indicating whether the observation has missing values. Where missing observations truly do not exist, this method of accounting for missing data is statistically sound (Allison 2001; King et al. 2001).

MODELS

There are two prototypical ways to estimate trends over time and age using conventional logistic regression (logit) models. Eq. (1) is a logit model with BMG as the response variable, where i indexes individuals, j indexes age, and k indexes birth cohort. The social background variables are indexed by l.

$$\text{logit}[P(Y_{ijk}=1)]={\alpha }_{jk}+\sum _l{\beta }_l{x}_{il}.$$ (1)

Our analytic sample contains data on 45 birth cohorts. We divide these birth cohorts into nine groups spanning five years each (1955–1959, 1960–1964,. . ., 1995–1999). Thus, α represents separate intercepts for each age by birth cohort group combination, the variables of interest in this simple model. The β terms are the main effects for the l demographic and social background variables, x. This model is unsatisfactory because change can occur only in different levels of the intercepts; the effects of social background characteristics do not change.

In a more nuanced treatment, Hauser, Pager, and Simmons (2004) used separate logistic regressions at selected ages to examine the effects of demographic and social background variables as well as time on being BMG. This allowed them to look at how the effects differed among children aged 6, 9, 12, 15, and 17. A similar set of logistic regressions is required to assess differences in how the effects of social background variables change with age and time. Eq. (2) generalizes this strategy. This “full interaction” model allows the social background effects to vary independently in each age by birth cohort category.

$$\text{logit}[P(Y_{ijk}=1)]={\alpha }_{jk}+\sum _l{\beta }_l{x}_{il}+\sum _l{\gamma }_{jkl}{x}_{il}.$$ (2)

Again, α represents differential intercepts. Now β represents the effects of social background variables at the baseline category, age = 6 and birth cohort = 1965–1969, and γ contains the differences in effects over each age and cohort combination. This model allows all the effects to vary freely and thus uses many more degrees of freedom, especially as the number of categories of j and k increases. An equivalent method is to estimate the logit model in Eq. (1) for each age by birth cohort combination. Either way, this model yields unwieldy results because there are more than 2,000 estimated parameters.

Eq. (3) is a logit model with interaction constraints (LIC), the main model of interest in this article.7 This model was developed to improve upon these two standard approaches. Specifically, it improves upon them in three ways. First, we wanted to model the changes in social background characteristics over time directly instead of drawing conclusions based on “eye-balling” the magnitudes of the coefficients in the full interaction model. Second, we wanted to isolate the trends across birth cohorts from trends across age. Thus, we are able to estimate the changes in the effects of household income on being BMG over time net of the changes in the effects of household income as children age. Finally, this model substantially reduces the number of estimated coefficients from the full interaction model, thus making it more parsimonious, while still allowing the magnitudes of the social background coefficients to vary systematically.

$$\text{logit}[P(Y_{ijk}=1)]={\alpha }_{jk}+\sum _l{\beta }_l{x}_{il}+{\lambda }_j\left(\sum _l{\beta }_l{x}_{il}\right)+{\lambda }_k\left(\sum _l{\beta }_l{x}_{il}\right).$$ (3)

The α term represents an intercept for each level of age, indexed by j, and birth cohort, indexed by k. The β_l parameters in the next three terms capture the effects of the explanatory variables, x_il, for the same baseline category as the full interaction model. The parameters λ_j and λ_k capture the proportional change in the linear predictor separately for each level of j and k. The proportional change, λ_j, is the factor by which the linear predictor changes as age increases, while λ_k is the factor by which the linear predictor changes for each birth cohort.

If λ is positive, the effects of the explanatory variables increase in magnitude. Similarly, if λ is negative, the effects decrease in magnitude. This can be shown by factoring the linear predictor out of the final three terms:

$$\text{logit}[P(Y_{ijk}=1)]={\alpha }_{jk}+(1+{\lambda }_j+{\lambda }_k)\sum _l{\beta }_l{x}_{il}.$$ (4)

The λ variables can be continuous or categorical. When the lambda variable is continuous, λ₅ is half the size of λ₁₀. When lambda is categorical, the interpretation of λ_k is relative to an omitted baseline category. In order to test for model fit, we ran four different models in which we treated both age and birth cohort as continuous variables, both as categorical variables, and with one categorical and one continuous variable. We report results only from the models in which age and birth cohort are categorical because they fit the data best. Consistent with this specification, Morris (1993) found that changes in retention rates across grade levels were not linear, but were better described by a negative exponential growth function.

Preliminary analyses showed that the unconstrained model is preferred to the LIC model in this case.8 However, there was a group of variables for which the constraints worked well. We decided to relax the constraints on the ill-fitting covariates and derived a hybrid of the models in Eqs. (2) and (4). We call this model (Eq. (5)) a logit with partial interaction constraints (LPIC).

$$\text{logit}[P(Y_{ijk}=1)]={\alpha }_{jk}+\left(1+{\lambda }_j+{\lambda }_k\right)\sum _1^l{\beta }_l{x}_{il}+\sum _{l+1}^L{\gamma }_{jkl}{x}_{il}.$$ (5)

In this equation, the explanatory variables are separated into two groups. There are l explanatory variables with constrained interactions. The remainder of the explanatory variables, from l + 1 to L, have unconstrained interactions. We divided the variables post hoc according to previous empirical work mentioned earlier. The seven constrained variables are gender, income, home ownership, head’s K–12 education, head’s occupational status, spouse’s occupational status, and the total number of children in the household.

Table 3 lists the F statistics of the model comparison test for multiple imputed data proposed by Allison (2001:68). Both the LPIC model and the unconstrained model are preferred over the simple logistic regression (Eq. (1)). The last row of Table 3 tests the hypothesis that the LPIC model fits as well as the unconstrained model. The p value of 0.02 in the last column indicates that the unconstrained model does significantly improve the fit over the LPIC model at the conventional p < .05 level. However, the statistical power of more than 450,000 observations warrants a level far less than p < .001 (Raftery 1995:140–41). Using either of these criteria, the fully constrained model fails to significantly improve the fit relative to the LPIC model. Based on this statistical evidence and its greater parsimony, we limit our discussion to estimates from the LPIC model.9

Table 3.

F Statistics for Nested Model Tests^a

Test	Value	df, Numerator	df, Denominator	p Value
Eq. (1) nested in Eq. (2)	3.119	2,047	1,294.054	.000
Eq. (1) nested in Eq. (5)	3.885	1,443	3,324.259	.000
Eq. (5) nested in Eq. (2)	1.278	604	198.876	.020

^aThese statistics are obtained using the SAS macro (COMBCHI) written by Allison (2001), available online at http://www.ssc.upenn.edu/~allison/combchi.sas.

FINDINGS

Prevalence of Being BMG

Before turning to the estimates from the multivariate models, we discuss the changes in prevalence of BMG over time and age. Figure 1 shows the proportion of children at selected ages who are enrolled below the modal grade for their age. The trend lines are three-year moving averages in order to smooth the data, and the horizontal axis indicates the year in which the cohort was born. Read vertically, Figure 1 shows the within-cohort change in the prevalence of BMG. As expected, the proportion of BMG children increases at each age except for a crossover between ages 12 and 15 for the 1982 through 1984 birth cohorts. Through the 1988 cohort, the last year for which we have complete cohort data, the later cohorts have higher overall prevalence levels than their earlier counterparts, but the increases occur over different periods of time. For 6-year-old children, there is a steady increase until the 1982 birth cohort, which declines through the 1988 cohort. Similar patterns hold for children aged 9 and 12, although the declines start earlier. There is a short period of increase surrounded by fairly stable proportions who are BMG for the two oldest ages. After 1988, the proportion of children who are BMG remains steady before the appearance of short upward trends during the last few observed years among the three youngest ages shown. The largest gap between ages occurs between 6- and 9-year-olds. This difference is larger than the difference between 9- and 17-year-olds, suggesting that most retention occurs during the first few years of schooling.

Figure 1.

Proportion of Children Below Modal Grade for Age, by Birth Cohort^a

^aTrend lines are three-year moving averages.

However, as discussed above, this measure is an imperfect indicator of retention history. The trend lines in Figure 1 are nearly parallel to the trend line for 6-year-olds, suggesting that the overall BMG rates are driven by a mix of age at school entry, academic redshirting, and retention at early ages. Figure 2 updates the series of Hauser and colleagues (Hauser 2004; Hauser, Pager, and Simmons 2004) in which the prevalence of BMG 6-year-olds has been subtracted from the same cohort at later ages. The horizontal axis is the birth year of the cohort. The trend lines are three-year moving averages in order to smooth fluctuations.

Figure 2.

Proportion of Children Below Modal Grade, Adjusting for BMG 6-Year-Olds^a

^aTrend lines are three-year moving averages.

Figure 2 makes explicit the influence on the overall prevalence of BMG of the increasing proportion of BMG 6-year-olds. It is evident that the rise in retention is driven by pre-first-grade retentions or delays in school entry. Once the proportion of the population who may have entered school BMG for any reason is removed, the proportion of additional 9-year-olds who become BMG after school entry remains fairly steady at around 13% through the 1976 birth cohort. After this point, the proportion of 9-year-olds who become BMG drops to between 5% and 10% after the 1983 birth cohort. The three most recent birth cohorts of 9-year-olds return to the original levels of BMG prevalence. Older children follow the same general pattern, although the periods of decline occur for slightly earlier cohorts. Only the proportion of 15-year-olds who are BMG fails to recover to original levels. These trends are consistent with Shepard (1989:65), who observed that “[h]olding children back in kindergarten in large numbers is a phenomenon of the 1980s.” She concluded that retention in kindergarten is still retention; some of the increase in BMG 6-year-olds is attributable to retention per se. It appears that retentions at older ages are being replaced by retentions at younger ages.

Odds of Being BMG

The odds of being BMG reinforce what we have seen in Figures 1 and 2. The omitted age by birth cohort category is 6-year-olds born between 1965 and 1969. This cohort of children graduated on time from high school between 1973 and 1977. The estimates of the age by cohort intercepts from the LPIC model are shown in Table 4.10 Each estimate is significant at the p < .001 level except the intercept for 6-year-olds in 1970–1974, which is only marginally significant at the p < .10 level. Generally, the odds of being BMG increase with age within each cohort and increase over time within each age. This suggests that the increases are not related to the changing composition of the student population over the past three-and-a-half decades.

Table 4.

Predicted Odds of Being BMG by Age and Birth Cohort From the LPIC Model^a

Birth Cohort	Age
	6	7	8	9	10	11	12	13	14	15	16	17
1955–1959								3.391	3.804	4.715	6.008	5.963
1960–1964			2.455	3.388	3.252	3.693	4.071	4.495	4.050	5.158	6.166	7.453
1965–1969	1.000b	2.098	3.235	3.174	4.195	4.411	4.502	4.967	4.887	6.210	7.083	6.609
1970–1974	1.331c	3.140	3.821	4.701	4.862	5.439	6.142	6.691	6.204	6.814	7.882	8.845
1975–1979	2.047	4.021	5.109	6.036	7.018	7.299	7.212	8.021	8.009	8.299	8.800	9.340
1980–1984	3.391	5.064	5.751	7.114	7.284	8.433	8.914	8.671	8.747	9.407	10.818	11.106
1985–1989	3.224	4.425	4.991	6.285	6.722	6.826	7.411	7.808	6.724	8.033	9.592	11.372
1990–1994	3.670	4.739	5.791	6.382	6.641	7.696	6.887	8.128	7.548	7.307
1995–1999	3.857	5.490	5.761	8.309	7.149

^aAll other covariates are held constant at their means.

^bThis is the omitted category.

^cStatistically significant only at the 10% level.

Table 4 also suggests that retentions are being shifted to younger ages. The odds ratios of being BMG among 6-year-olds are increasing faster than the corresponding odds ratios among 17-year-olds. This can be seen by dividing the odds ratios of the latter by the odds ratios of the former within cohorts. The increase in odds ratios is sharpest during the early cohorts, a ratio of 6.6 for the 1965–1969 cohorts compared with a ratio of 3.4 for the 1985–1989 cohorts. The smaller relative increase among this latest fully observed cohort shows that the increase in the odds of being BMG was lower. This implies that fewer children are becoming BMG after age 6 in later cohorts, confirming the trend lines observed in Figure 2. This comparison is only suggestive because we did not explicitly test whether the included intercepts were statistically distinct.

The size of the odds ratios is large. While the increase in odds is real in substantive terms, their magnitude is partly driven by the relative infrequency (about 5%) of being BMG in the omitted category. For example, the largest difference in the odds of being BMG is between 17-year-olds born between 1985 and 1989 and the omitted category. The odds ratio suggests that the odds of the former being BMG are more than 11 times larger than the latter. The average observed odds of being BMG in the omitted category are 0.054 (authors’ calculations). The model predicts odds of being BMG as a 17-year-old born during 1985–1989 as being about 0.61, which implies that 38% of students in the age by cohort category should be BMG. This is very close to the observed value of 34%. Looking at changes as children age within the 1965–1969 birth cohort shows a steep increase in the odds of being BMG through age 10 followed by a more gradual increase. Similarly, the odds of BMG among 6-year-olds increased steadily across observed cohorts except for a minor reversal for cohorts born between 1985 and 1989.

Constrained Effects

Based on previous research, the coefficients on the constrained variables are all in the expected directions. Boys are more likely than girls to be BMG.11 Each additional child in the household increases the chances of being BMG. Children in families who own their home, who have higher income, in which the household head has higher education, and in which both the head and the spouse have higher occupational status scores are all less likely to be BMG. These coefficients are shown in the third column of Table 5.

Table 5.

Interaction Constraint Factors and the Estimated Effects of Social Background Characteristics

Age	λj (Age)		Cohort	λk (Year)		Variable	β
	Coefficient	SE		Coefficient	SE		Coefficient	SE
6	0	––	1955–1959	0	––	Male	.385	.036
7	.298	.089	1960–1964	–.016	.077	Logged Income	–.134	.013
8	.331	.092	1965–1969	–.012	.077	Home Ownership	–.225	.022
9	.281	.089	1970–1974	–.095	.072	Head’s K-12 Education	–.048	.005
10	.397	.096	1975–1979	–.102	.072	Head’s Occupational Statusa	–.032	.004
11	.474	.102	1980–1984	–.326	.061	Spouse’s Occupational Statusa	–.029	.004
12	.474	.103	1985–1989	–.425	.058	Total Children in Household	.064	.006
13	.410	.098	1990–1994	–.614	.063
14	.577	.112	1995–1999	–.491	.091
15	.551	.112
16	.624	.118
17	.684	.125

^aOccupational status coefficients represent a change of 10 points.

The first and second columns of Table 5 list the estimated constraint factors for age and birth cohort, respectively. The constraint factors for age are all statistically significant at the p < .001 level and show a steady increase as children grow older. Not only are children more likely to be BMG as they age, but the differences between those students who are regularly promoted and those who are not increase as well, with respect to these seven social background characteristics. In order to calculate the magnitude of the coefficients for other ages and/or birth cohorts, we must multiply them by the interaction constraint factor, 1 + λ_j + λ_k. For example, holding birth cohort (λ_k) constant, the magnitude of the constrained coefficients for 17-year-olds is 1.684 times as large as those for 6-year-olds. The odds of being BMG for an average boy aged 6 in the sample are 47% higher than those for an average 6-year-old girl. Nine years later, the difference in the odds grows to 91%.12 Each additional year of education for the household head through high school reduces the chances that a 6-year-old is BMG by 5%. This advantage grows to 6%, 7%, 7%, and 8% for children aged 9, 12, 15, and 17, respectively.

Changes in the effects of the constrained variables between birth cohorts are in the opposite direction; the effects of the constrained social background characteristics decrease in successive birth cohorts. However, the only constraint factors that are statistically distinguishable from those in the first cohort (1955–1959) are in the final four birth cohort groups (1980–1999). This time period corresponds to the decrease observed in Figure 2. Continuing with the previous examples, the odds of being BMG for boys born between 1980 and 1984 are only 30% higher than among girls, holding age constant. The gender differences are 25%, 16%, and 22% in the 1985–1989, 1990–1994, and 1995–1999 cohorts, respectively. The reduction in the odds of being BMG associated with an additional year of education through high school for the household head drops to 3% for those born between 1980 and 1989 and 2% for those born between 1990 and 1999.

Unconstrained Variables

No such unifying trends were found for the rest of the covariates. In the rest of this section, we discuss differences associated with those unconstrained covariates with statistically significant main effects.13 However, not all of the interaction terms discussed below are statistically significant from zero, and as a result, we only outline general trends rather than interpret coefficients. We discuss racial differences in being BMG because of the importance of racial gaps in educational achievement and attainment. We discuss geographical differences in the prevalence of being BMG for two reasons. First, school practices have traditionally differed by both geographic region and urbanicity. Second, these are the only other set of variables that follow a trend, although it is distinct from the one identified for the constrained variables.

The only statistically significant racial main effect is between blacks and whites. Table 6 lists the odds ratios of being BMG for black children relative to non-Hispanic whites, holding everything else constant. Overall, most of the odds ratios are between 0.8 and 1.2. For most age by cohort groups, the black-white difference in being BMG is half of the main effect for gender. Within each age, the differences between blacks and whites are unstable over time with no discernible trends. Over time, black children are less likely to be BMG than non-Hispanic whites until age 10 or 11, net of cohort and the other variables in the model. After these ages, black children are somewhat more likely than whites to be retained, except at age 15.

Table 6.

Odds Ratios of Being BMG for Blacks Relative to Non-Hispanic Whites^a

Birth Cohort	Age
	6	7	8	9	10	11	12	13	14	15	16	17
1955–1959								1.156	1.204	0.860	0.948	1.286*
1960–1964			1.076	1.039	1.035	0.966	0.924	0.984	0.958	0.897	1.004	0.981
1965–1969	0.533*	0.904	0.852	0.991	0.974	1.152	1.115	1.087	1.148	0.858	1.020	1.076
1970–1974	0.553*	0.919	0.896	0.958	1.303*	1.221*	1.313*	1.015	1.181	1.247*	1.123	1.352*
1975–1979	0.686*	0.843	0.955	1.210	1.035	1.047	0.998	1.264*	1.172	0.869	1.153	1.084
1980–1984	0.689*	0.828	0.732*	1.184	0.838	0.916	0.914	1.187	1.150	0.849	1.245*	1.017
1985–1989	0.750*	0.851	0.916	0.999	0.938	1.020	1.001	1.176	0.984	1.119	1.124	1.295*
1990–1994	0.641*	0.775	0.726*	0.836	1.014	1.013	0.981	1.361*	0.904	0.927
1995–1999	0.546*	0.841	0.857	1.079	1.308

^aAll other covariates are held constant at their means.

^*Statistically significant at the p < .05 level.

Our evidence suggests that black children are more likely than white children to progress regularly through grades during the first few years of schooling, but that is followed by a rapid increase, during which they surpass their white counterparts in the likelihood of being BMG. Future work is needed to investigate the cause of this pattern, which is not discussed in most research on retention. This evidence is consistent with more academic redshirting among white parents, but it also could be attributable to successful preschool programs in inner cities, to a narrower achievement gap between white and black students at younger ages, or to less rigorous academic standards. Unfortunately, the CPS data do not allow us to assess the merits of these explanations.

The geographic differences in being BMG are the only other group of covariates that follow a distinct pattern. The differences between the Midwest and the Northeast generally decline with age. Midwestern children are between 1.5 and 2.5 times more likely to be BMG than Northeasterners at age 6. By age 13, the differences between the two regions generally disappear. Over time, the trend within each age level is generally U-shaped. Midwestern children are more likely than Northeastern children to be BMG in the earliest and latest cohorts. Comparing the South to the Northeast, there is no discernible trend in the changes in magnitude as children age. The most consistent change over time at most ages is that there is an increase in the likelihood of being BMG in the South in cohorts born after 1985. The odds ratios comparing the West to the Northeast bounce above and below 1. There is a small general decline in the difference as children age.

Although the main effects are not statistically significant, the differences between children in major cities and those elsewhere follow the same general trend as those in the Midwest and West. Children in major suburban, smaller metropolitan, and rural areas begin school with much higher proportions of children who are BMG than in the major central cities, but these differences are eliminated around ages 9 and 10. Subsequently, the proportions of children who are BMG outside major central cities continue to fall relative to the proportion in such cities. By the time they are 17, children in central cities are more likely to be BMG. There is no discernible trend in the differences between major central cities and elsewhere over time.

DISCUSSION

In general, these findings confirm past research on the prevalence of retention that used children who are below the modal grade for their age as a proxy for having been retained in the past. How robust are they to model specification decisions? The most influential decision we made in this analysis involved collapsing the 45 birth cohorts into nine five-year groups. Shifting these groups ahead two years would alter the findings somewhat. However, we ran an alternative set of models that organized the data by survey year instead of birth cohort. In these auxiliary models, years were collapsed to coincide with presidential terms, and the findings from all models were very similar with respect to the age by cohort intercepts, the effects of constrained and unconstrained variables, and the interaction constraint factors. Based on this evidence, we believe that our findings are not an artifact of this particular grouping of birth cohorts.

Despite our confidence in it, the preceding analysis does have some limitations. First, as discussed above, BMG remains an imperfect proxy for retention per se, even when comparing students in the same birth cohort. As a result, the estimated coefficients are biased toward zero: as little as two-thirds of the population parameters for retention per se because we do not have direct measures of retention (Cascio 2005). Second, CPS data lack any measure of cognitive ability or academic performance. This introduces omitted variable bias that is likely quite important because the decision to retain a student is often made in response to poor academic performance. The bias introduced by the omission of cognitive ability inflates the magnitude of the demographic and social background coefficients that are correlated with cognitive ability and retention, especially in the case of socioeconomic standing and race/ethnicity.

The increase in the importance of the constrained covariates (gender, income, home ownership, head’s K–12 education and occupational status, spouse’s occupational status, and the number of children in the household) as children age could be interpreted as a consequence of the increased use of test-based criteria for retention as children progress through school. That is, the background effects may increase because retention decisions are increasingly based on test scores and grades.

The ability/performance explanation is less convincing when one looks at the changes in the effects of social background across cohorts because those effects decline from the 1980 through 1999 birth cohorts. This would imply that the importance of test scores has declined for students born between 1980 and 1999—the period during which calls to end social promotion were widespread. If anything, one would expect the importance of test scores to increase as the school accountability movement leads to promotion decisions increasingly based on academic performance.

We checked this apparent contradiction against long-term trend data from the National Assessment of Educational Progress (NAEP; U.S. Department of Education 2005). If there were decreasing test score gaps between girls and boys or by parental education, then the decline of social background differences in BMG experienced by the latest cohorts would be consistent with lower rates of social promotion. In fact, the NAEP trend data show that the male-female gap in reading converges only among 9-year-olds, and the gender gap in math converges only for 17-year-olds. The differences in NAEP scores by parental education have not appreciably changed for 13- and 17-year-olds born after 1979 and 1981, respectively. Thus, it appears that the omission of academic achievement is not responsible for the declining social background effects on BMG. Only the reversal of this decline in the post-1994 birth cohorts supports the supposition that social promotion is in decline, and not to a level below that observed for the earliest birth cohorts in the CPS data.

Given these caveats, our findings confirm previous results regarding the shift toward earlier retention (or increasing age at entry to regular school). Social background differences between retained and regularly promoted students are smallest during this period of their educational careers. Looking at it from the other end of the age spectrum, the group of retained students appears to be more selective at the oldest ages. This pattern appears inconsistent with the school transitions literature, which has found waning effects of social background characteristics at higher transitions (Hauser and Andrew 2006; Lucas 2001; Mare 1980; Raftery and Hout 1993). However, the analysis in this article employed unconditional logits, whereas the school transitions literature used conditional logistic regressions. The regular increase in the effects of social background characteristics as children age is a combination of the effects of social background accumulating across multiple transitions and larger transition-specific effects of social background in grade 3 and grades 6 and later (see Hauser et al. 2007: table 5-2).

One explanation consistent with this finding is that parents, school decision-makers, or both view retention at older ages as having more serious consequences than retention at earlier ages.14 Alternatively, early retentions might be made to ameliorate developmental issues other than academic performance. If the maturity level of children is less correlated with social background than academic achievement is, this process would produce the strengthening effects of social background that we observe. Future research is needed to identify how prevalent this form of “social retention” is at different levels of schooling.

Our findings regarding the decreasing social background differences for later birth cohorts between students who are BMG and those who are “on time” run counter to the trends of increasing social and economic inequality that took place over the time period covered in this analysis (Fischer and Hout 2006). Perhaps this indicates that being BMG is not a sharp fork in the road to educational success or failure but merely an early signal of other determinants of social stratification; however, our data do not speak to this.

The constrained socioeconomic differences decrease for each successive cohort except the 1995–1999 cohort; the point estimate for this cohort is still less than that of the first cohort. By itself, this pattern does not provide many answers to the title question—have we ended social promotion? However, combined with decreasing levels of the prevalence of becoming BMG after age 6, it appears that retention has declined. Children over age 6 are less likely to be retained today than they were in the past.

Reconciling this trend with “an end to social promotion” would require either the existence of many inappropriate retentions under the previous regime and/or that those retentions were based disproportionately on social background rather than on appropriate academic criteria. The first possibility seems unreasonable if we believe arguments for ending social promotion. According to that diagnosis, there were too few retentions. The second possibility is more plausible. Schools may be making high-stakes decisions about students based on putatively appropriate criteria (but see National Research Council 1999:40–41). Under such a system, the power of middle- and upper-class parents to overrule the promotion decisions about their children might be reduced, thereby reducing socioeconomic differences. Although plausible, this explanation does not hold up because it would imply increasing rates of retention. Based on our results, the only conclusion to be drawn is that efforts to end social promotion remain unfulfilled.

By using the LPIC model, we were able to simultaneously estimate the changes in the likelihood of being BMG and isolate the changes in the effects of social background and demographic characteristics. To answer the questions with which we began this article, the proportion of children who are BMG has increased steadily for all age groups in every birth cohort. Accompanying this growth has been a decline in the social background and demographic differences between students who are BMG and those who are not. These simple generalizations fail to tell the whole story. The increases are driven primarily by the increase in BMG among 6-year-olds. While we cannot show that efforts to end social promotion have failed, the evidence indicates that there has not been a surge of children older than 6 who have been retained in the last three decades. This study highlights the need for further investigation of the effects and correlates of academic redshirting and other reasons for delayed school entry as well as retention.

Appendix Table A1.

The Percentage of Missing Values on Each Variable by Year

Year	Income	Education		Occupational Status
		Head	Spouse	Head	Spouse
1972	6.00	0	18.26	10.15	60.52
1973	6.95	0	18.41	9.87	58.94
1974	6.72	0.03	19.70	10.92	58.54
1975	7.50	0	20.60	11.23	58.08
1976	7.86	0	20.32	10.74	56.77
1977	7.78	0	20.87	10.46	55.09
1978	7.95	0	22.16	10.55	53.57
1979	7.46	0	22.25	9.72	52.68
1980	5.91	0	23.17	10.74	53.06
1981	4.78	0	23.96	10.82	52.47
1982	4.97	0	24.49	10.88	51.87
1983	4.30	0	24.92	10.95	52.45
1984	4.38	0	25.18	11.10	51.06
1985	3.56	0	25.36	11.09	49.61
1986	2.36	0	26.00	10.41	49.15
1987	3.43	0	26.44	10.79	48.94
1988	4.88	0	26.84	10.99	48.04
1989	6.40	0	26.89	10.98	47.27
1990	6.60	0	26.93	11.01	47.61
1991	5.22	0.13	27.78	12.49	48.26
1992	5.33	0.14	28.31	12.44	48.05
1993	5.68	0.18	28.17	11.81	47.44
1994	6.93	0.08	28.51	13.20	47.50
1995	8.64	0.26	28.38	13.16	47.18
1996	8.57	0.17	28.52	11.91	46.52
1997	8.85	0.17	28.72	11.49	47.47
1998	9.57	0.33	29.27	10.83	47.82
1999	10.82	0.40	29.68	11.18	48.47
2000	12.66	0.33	30.14	11.09	49.02
2001	12.21	0.35	30.22	10.89	48.43
2002	12.31	0.39	30.75	10.97	49.68
2003	14.70	0.48	30.27	11.48	49.79
2004	14.13	0.53	31.00	11.67	50.14
2005	14.47	0.51	31.12	12.05	50.41