Using Panel Data to Improve Estimates of the Determinants of Educational Achievement

Abstract

Single equation models of educational achievement that have been estimated by OLS have tended to ignore the effects of omitting relevant variables. These omitted variables may lead to biased and inconsistent estimates. Further, past research frequently obscures the correct interpretation of the estimated coefficients. This paper considers three frequently estimated models of educational achievement: the case when only cross-sectional data are available, the case when pre and post measures of achievement are available, and the case where one has more complete panel data. Starting from a general cumulative model of achievement, we outline sufficient assurmptions to produce readily interpretible OLS estimates which have good statistical properties. With only cross-sectional data, these assumptions are almost certainly not met in most research. With two measures of achievement, useful estimates with good statistical properties can be obtained if we make quite restrictive assumptions concerning the relationships among the explanatory variables. With panel data, simple OLS can produce coefficients with good statistical properties underfairly general conditions. The use of multiple measures, however, may lead to multicollinearity which one must balance off against the gain in efficiency.