The twelfth century rabbinic scholar Maimonides proposed a maximum class size of 40. This same maximum induces a nonlinear and nonmonotonic relationship between grade enrollment and class size in Israeli public schools today. Maimonides' rule of 40 is used here to construct instrumental variables estimates of effects of class size on test scores. The resulting identification strategy can be viewed as an application of Donald Campbell's regression-discontinuity design to the class-size question. The estimates show that reducing class size induces a significant and substantial increase in test scores for fourth and fifth graders, although not for third graders.
This paper estimates the effects of school quality--measured by the pupil/teacher ratio, average term length, and relative teacher pay--on the rate of return to education for men born between 1920 and 1949. Using earnings data from the 1980 census, the authors find that men who were educated in states with higher-quality schools have a higher return to additional years of schooling. Rates of return are also higher for individuals from states with better-educated teachers and with a higher fraction of female teachers. Holding constant school quality measures, however, the authors find no evidence that parental income or education affects average state-level rates of return.
Based on Baumol's cost-disease model, we develop two alternative measures of the change in the productivity of schooling. Both productivity measures are based on changes in the relative price of schooling. We find that in most OECD countries the price of schooling has increased faster in 1970-94 than would be compatible with constant schooling productivity. In addition, we show that the average performance of pupils has remained constant at best in most OECD countries. Our results imply a larger decline in the productivity of schooling in many OECD countries than in the United States.
I identify the effects of class size on student achievement using longitudinal variation in the population associated with each grade in 649 elementary schools. I use variation in class size driven by idiosyncratic variation in the population. I also use discrete jumps in class size that occur when a small change in enrollment triggers a maximum or minimum class size rule. The estimates indicate that class size does not have a statistically significant effect on student achievement. I rule out even modest effects (2 to 4 percent of a standard deviation in scores for a 10 percent reduction in class size)
This paper analyzes data on 11,600 students and their teachers who were randomly assigned to different size classes from kindergarten through third grade. Statistical methods are used to adjust for nonrandom attrition and transitions between classes. The main conclusions are (1) on average, performance on standardized tests increases by four percentile points the first year students attend small classes; (2) the test score advantage of students in small classes expands by about one percentile point per year in subsequent years; (3) teacher aides and measured teacher characteristics have little effect; (4) class size has a larger effect for minority students and those on free lunch; (5) Hawthorne effects were unlikely.
Classroom education has public good aspects. The technology is such that when one student disrupts the class, learning is reduced for all other students. A disruption model of educational production is presented. It is shown that optimal class size is larger for better-behaved students, which helps explain why it is difficult to find class size effects in the data. Additionally, the role of discipline is analyzed and applied to differences in performance of Catholic and public schools. An empirical framework is discussed where the importance of sorting students, teacher quality, and other factors can be assessed.
This chapter summarizes the recent literature on peer effects in student outcomes at the elementary, secondary, and post-secondary levels. Linear-in-means models find modest sized and statistically significant peer effects in test scores. But the linear-in-means model masks considerable heterogeneity in the effects experienced by different types of students. Using nonlinear models, one prevalent finding is larger peer effects in which high ability students benefit from the presence of other high ability students. Studies that stratify students by race and ability often find that students are affected both by the racial composition of their peers and by the achievement of their same-race peers. At the university level, several studies find modest sized effects from dormmate and roommate background on own academic performance. For both university and high school students, the measured peer effects on “social” outcomes such as drinking are larger than the effects on academic outcomes. Many authors find substantial peer effects in drinking, drug use, and criminal behavior. This chapter suggest areas for future investigation and data collection.
Class-Size Effects in School Systems Around the World: Evidence from Between-Grade Variation in TIMSS: We estimate the effect of class size on student performance in 18 countries, combining school fixed effects and instrumental variables to identify random class-size variation between two adjacent grades within individual schools. Conventional estimates of class-size effects are shown to be severely biased by the non-random placement of students between and within schools. Smaller classes exhibit beneficial effects only in countries with relatively low teacher salaries. While we find sizable beneficial effects of smaller classes in Greece and Iceland, the possibility of even small effects is rejected in Japan and Singapore. In 11 countries, we rule out large class-size effects.
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