Peer effects and measurement error: The impact of sampling variation in school survey data (evidence from PISA)

Investigation of peer effects on achievement with sample survey data on schools may mean that only a random sample of the population of peers is observed for each individual. This generates measurement error in peer variables similar in form to the textbook case of errors-in-variables, resulting in the estimated peer group effects in an OLS regression model being biased towards zero. We investigate the problem using survey data for England from the Programme for International Student Assessment (PISA) linked to administrative microdata recording information for each PISA sample member's entire year cohort. We calculate a peer group measure based on these complete data and compare its use with a variable based on peers in just the PISA sample. We also use a Monte Carlo experiment to show how the extent of the attenuation bias rises as peer sample size falls. On average, the estimated peer effect is biased downwards by about one third when drawing a sample of peers of the size implied by the PISA survey design.