family structure, have a small number of missing observations. To keep the sample size and performance distribution untouched by the matching exercise, missing values for matching covariates were imputed through multiple imputation models (Royston 2004).

We use the Poland’s data from the OECD’s Program for International Student Assessment (PISA), an internationally comparable standardized student test conducted every three years to test reading, mathematics and science achievement of 15-year-olds. PISA assesses and compares student achievement based on a standardized and highly reliable framework. It assesses the knowledge and skills essential for full participation in society and the world of work. It is conducted near the end of compulsory education. In all cycles, the domains of reading, mathematical and scientific literacy are covered not merely in terms of mastery of the school curriculum, but in terms of important knowledge and skills needed in adult life. This makes the PISA framework attractive as a basis for international comparisons.

The detailed description of the assessment framework, cautious procedures of translation and supervision of country specific implementation, and careful calibration of student scores based on response item theory and collected background variables all support the view of PISA as a valid framework for international comparisons of student achievement. Depending on population and country involvement there are approximately 2,500 to nearly 30,000 students tested in each participating country. The survey is realized as a representative to the population of interest with a two-stage stratified sample with random sampling of schools and within each school. Survey weights are provided by the organizers that reflect the different probabilities of schools and students to be sampled (OECD 2001).

The PISA survey has a complex structure, similar to methods commonly used in other educational surveys such as the International Association for the Evaluation of Educational Achievement’s (IEA) Trends in International Mathematics and Science Study (TIMSS) and Progress in International Reading Literacy Study (PIRLS), or the United States’ National Assessment of Educational Progress (NAEP), with sampling conducted with different probabilities in two stages within separate strata. This complexity should be taken into account by using probability weights when calculating point estimates and by adjusting for clustering and strata design when estimating standard errors. However, there is little advice in the literature on how to account for survey design in matching methods (see Zanutto 2006, for example, of analysis with survey weights and stratification matching). In our case, we used survey weights when calculating average outcomes for the treated students in PISA 2000. This way the results are representative for the population of 15-year-olds in 2000. Also, students are answering a randomly assigned groups of test items (so-called booklets), but responses are put into one common scale using psychometric models. The performance of each student is reflected by five plausible values which give equally probable performance scores for individuals. Plausible values should not be used to judge individual performance but provide unbiased estimates of achievement for whole populations of interest. Each analysis should be repeated five times with each plausible value used once to take into consideration measurement error in student performance. We follow this strategy in this paper by repeating each analysis five times, once with each plausible value of reading performance. When using the multiple imputation method, we imputed missing values once for each plausible value and then repeat any estimation five times, once with each dataset containing one plausible value and imputations obtained with this 14