As a numerical indicator, the latter is typically termed the School Life Expectancy (SLE) and serves educational statisticians and policy-makers as a measure of the performance of an education system. While seemingly straightforward concepts, a number of problems arise that highlight the need for a critical appraisal of this and related indicators. This study aims to demonstrate the existence and nature of these problems, explain under which conditions they occur, and how they can be resolved. The United Nations’ routinely approximates SLE by the sum of age-specific enrolment rates (UIS, 2009, p. 257). This is justified on the grounds that en- rolment data are more readily available than full flow data (intake, repetition, drop-out and promotion) by age and grade. Operationalised in this way, it is not, however, possible to unambiguously derive the population MYS from time series data on SLE. The reason becomes obvious from a demographic perspective: MYS is a ‘cohort’ measure (more precisely a mean of cohort measures), while the idea of SLE as a property of the education system intrinsically refers to a given point in time; it is a ‘period’ measure in demographic terminology (Siegel, Swanson and Shryock, 2004). The approximate SLE defined above conflates both period and cohort perspectives. However, the impossibility of unambiguously deriving cohort from period conclusions and vice-versa have been studied extensively in the demographic context. In particular, technical demography provides us with the knowledge that the cohort and period perspectives are equivalent when transition rates are stationary, and that the numerical and interpretational gap widens, the faster conditions are changing. This study addresses the question, to which degree the standard SLE indicator and related measures, such as the student-years-per-graduate, can be misleading under plausible scenarios of change in the student flow rates. The customary measure of SLE is an approximation with relatively low data requirements. The data necessary to calculate the ‘ideal’ period measure are not always available. Accordingly, the aim here is not to suggest abandoning the approximation, but to offer an assessment of the possible margin of error, both analytically and with numerical computer simulation. The relative performance of estimating SLE using a reconstructed cohort (Education Policy and Data Center (EPDC), 2009) based on two consecutive years of enrolment data is assessed.

The study takes as a starting point a comprehensive overview of conceptual and operational definitions of measures of duration and attainment in the educational statistics and economics literature. The differences between these measures are critically discussed, both substantively and theoretically, from the point of view of human capital theory and educational research, as well as methodologically. With respect to the latter, it is particularly instructive to take into account techniques for dealing with flow and incidence rates in fertility and mortality. The distinction between cohort and period measures in demography is explained and illustrated, and the implications for education indicators discussed. This analysis is illustrated through computer simulation, drawing on empirical country case-study data on student flows from the Education Policy and Data Center (EPDC) database. Some bounds on the size of the error are derived mathematically.

SLE as currently operationalised suffers from considerable conceptual ambiguity that limits its usefulness for quality assessment and policy-analysis. In particular, it fails to be consistent as either a period or cohort indicator, being less sensitive to change than the ideal period measure and more sensitive than the true cohort measure of school life expectancy. Under plausible scenarios of changing transition rates, the common SLE indicator can be biased in either direction by several years. Approximate formulae for the direction and magnitude of the bias are provided based on overall repetition and drop-out rates at two points in time (as opposed to class- and age-specific rates required for the analytically correct calculation). Both period and cohort perspectives are required to judge school reforms and to relate institutional performance indicators to population measures of educational attainment. Pure cohort indicators react too slowly to allow the monitoring of policy effects (Cameron, 2005); real period measures or approximations to them that are valid under the conditions of educational reform are required. Statistical data collection and reporting should be geared towards allowing their calculation. In the meantime, policy-makers and researchers should beware of the limitations of the approximate SLE indicator as an improper period measure.