A variance decomposition in the evaluation of the effects of educational policies in economic education

Abstract

A student's grade is decomposed into a part due to ability plus a part due to random guessing. Holding the variance of the ability distribution constant, we show that the introduction of a positive educational policy will increase the mean but decrease the variance of the grade distribution.

Acknowledgement

Comments from Ted Joyce and Frank Tansey are gratefully acknowledged.

Notes

¹ There is a substantial literature on the class size and performance relationship. For theoretical models, see e.g. Lippman (1990), Correa (1993) and Kennedy and Siegfried (1996). For empirical studies, see e.g. Kennedy and Siegfried (1997), Hoxby (2000) and Arias and Walker (2004).

² The concept of an education production function, while popular in empirical studies, is vague. Different studies might include different set of variables. See also discussions in Hoxby (2000) and Rivkin et al. (2005).

³ While the point estimates using the sample variances indicate a smaller variance with smaller class size, Arias and Walker (2004) found that a F-test for the equality of variance with data pooled from the two semesters marginally fails to reject the hypothesis of equal variance (p-value = 0.121). However, it is well known that the F-test is not robust and its size is extremely sensitive to the assumption of normality (Lehmann, 1986, pp. 207). Further, the result is obtained only by pooling the data from two semesters.