Download Class Size Effects on Student Performance: An Analysis by Kruger and more Exercises Economics of Education in PDF only on Docsity! Lecture 14 Kruger: In his analysis, he takes individual raw scores on the Stanford Achievement Test and converts them into percentile scores Independent variables: -Dummy variable for small class size -Dummy variable for regular class size plus TA -Dummy variable for free lunch -Dummy variable for gender -Dummy variable for race/ethnicity -Dummy variable for having a teacher with a master’s -Teacher’s years of experience -School fixed effects The restricted model only includes the dummy variables for different class sizes. The complete model includes all of the above-mentioned independent variables. Restricted Model Complete Model Small Class Size 8.43 7.40 (1.21) (1.19) Regular class w/ TA 2.22 1.78 (1.00) (.99) Free lunch --- -13.61 --- (.87) Race/ethnicity --- 6.97 --- (1.19) Teacher w/ Masters --- .48 --- (1.07) Teacher experience --- .05 --- (.06) How should we interpret the restricted model results? A student in a small size class scores 8.43 percentile points higher than a student in a regular sized class, all other things equal. In the complete model, we might be worried that the control variables Kruger added will collapse the effects of class size from the restricted model. For example, a master’s degree may have no relevance to classroom performance or many master’s degrees could be from very low quality schools. Boiling down the wide range of programs and experiences into a 0 or 1 dummy variable is difficult. Do the effects of class size get larger over time? K 5.37 1 6.37 2 5.26 3 5.24 docsity.cmo Are the same students tested each year? No. There is a lot of turnover in these classrooms so, each year, the group of students tested are new to the program/experiment. Using the whole sample: Was your initial class (K) a small class? (0,1) 3.16 (.9) Was your initial class a regular class w/ TA? (0,1) .49 (.67) Cumulative years in small class 1.05 (.38) Cumulative years in regular class w/ TA .25 (.37) If you’re first assignment is a small class, according to the results above, your percentile score increases by 3.16 percentile points. The Value Added Model: 06,07, )()( JuneJune TestScoreTestScore − = change in test score over a year Problems with applying the value added model? If the major benefits of small classes accrue after the first year of the program, then the benefit will be built into the test scores in subsequent years. How big is the overall effect? In the complete model, the effect of being in a small class is 7.4 percentile points. Is that a big magnitude? A small magnitude? How much money would you spend to get that effect? In other words, in order to interpret these results, you may want to run a cost-benefit analysis. Alternatively, you could compare the small class size effect from the complete model to the effects of other important control variables you are interested in such as race/ethnicity. The coefficient on race/ethnicity is 6.97, which is quite close to 7.40. Could small classes for minority students overcome the White/Asian and minority test gap? Well, we must first factor in the rest of our variables, especially the coefficient on the “free lunch” variable, which has an even larger magnitude. Average gain from being in a small class sized: .22 SD Basic Black/White test score gap: 1 SD How would you do a cost-benefit analysis? Money is not free. Neither is managerial and administrative time. iiiii TestScoreAgeEdw εδββα ++++= )()()()ln( 21 See paper for Krugman’s full cost-benefit analysis. docsity.cmo
