plausible value. That should guarantee that all imputation errors, one in plausible values and the others in imputed covariates, will be taken into account (see OECD 2002, 2005). The final set of variables from the PISA dataset used in this analysis are re-sampling replicate weights used in the calculation of standard errors. Intra-cluster correlation violates an assumption needed for the unbiasedness of the analytical method of calculating standard errors based on the variation of the sample. Re-sampling methods such as bootstrapping, Jackknifed Repeated Replication and Balanced Repeated Replication serve as alternative means of calculating standard errors. These methods calculate sampling variance by re-sampling the same sample to mimic re-sampling of the original population. Replicate weights are alternative sample weights which represent a subsample based on the original sampling design. PISA provides replicate weights compatible with Fay’s adjusted Balanced Repeated Replication. These weights were constructed to reflect the sampling design including any country specific modifications, as well as non-response by students or schools (OECD 2002: 89-98). Standard errors were obtained by the BRR method. In our case, the additional benefit of using BRR weights is that these were produced by survey organizers who used confidential information not available for external users.

# <u>Decompose Change over Time</u>

A simple decomposition analysis is undertaken in order to attempt to explain one of the possible pathways be which the reform may have led to improved student achievement. We decompose reading scores over time PISA 2000 and 2006 to explain to what extent the increase in scores is due to changes in characteristics and what proportion is due to changes in returns to characteristics. A simple education production function is estimated (Hanushek 1986, 2002; Todd and Wolpin 2003; Glewwe 2002), which relates various inputs affecting student learning to measured outputs, the PISA standardized reading test score. Past empirical research does not always agree on which school and family inputs improve children’s achievement. Examples are the disagreements found on the role of schooling inputs such as class-size, teacher experience, teacher education and mother’s employment. Nevertheless, although a child’s achievement is inherently individual in nature, a large body of evidence points to the existence of persistence effects in educational achievement across generations (Fertig 2003; Fertig and Schmidt 2002; Currie and Thomas 1999). Consequently, one must control for individual pupil characteristics as well as family background. Finally, one needs to control for characteristics on school environment as well as institutional arrangements. Evidence also suggests that socioeconomic and family background variables, such as parent’s education and the number of books a child has, are very important determinants of test scores at early ages (Fryer and Levitt 2002). Therefore, we specify and estimate education production functions that relate students’ achievement to individual, family and school inputs. We then proceed to decompose the over time test score gap into an explained component (accounting for student, family, and school characteristics) and an “unexplained” – or returns, or the efficiency by which the country is able to convert characteristics into student learning outcomes as measured by test scores – component, using the traditional Oaxaca (1973)-Blinder (1973) decomposition method.

The model specification for the estimation of the production function for cognitive achievement is as follows: 15