Thesis

Chapter 3. Primary School Skill Development: from First to Sixth Grade 3.4.2 IV approach While we first estimate model 3.3 with OLS, we also apply an IV approach. Measurement error in the test scores used as independent variables may lead to attenuation bias with OLS estimation (e.g., Holm et al., 2025; Jerrim & Vignoles, 2013; Passaretta et al., 2022). Measurement error occurs when children perform unusually well or poorly during an assessment (e.g., due to luck or a bad day). Failure to account for measurement error in initial test scores can lead to misleading estimates that are biased toward zero. Prior research has discussed challenges in estimating achievement gaps based on error-prone early achievement measures (Jerrim & Vignoles, 2013). OLS estimates that ignore measurement error tend to underestimate the persistence of relative achievement over time and overestimate the role of other factors in our equation (e.g., parental education) on achievement (e.g., Van Huizen, 2018). To address measurement error, we use an IV approach, which reduces attenuation bias (Bradbury et al., 2015) and which is used in related previous research (e.g., Passaretta & Skopek, 2018a; Passaretta et al., 2022; Skopek & Passaretta, 2018; Van Huizen, 2018). The approach uses an earlier skill score as an instrumental variable to predict the initial skill score in the first stage, and then substitutes this predicted initial skill score into equation 3.3. For this approach to work, the earlier skill score must be strongly correlated with the initial skill score, and the errors in the two scores must be uncorrelated. We confirm that the earlier skill score is indeed closely aligned with the initial skill score, as both scores assess the same skills and are separated by only a six-month gap (F-values are always above 10, indicating that the instruments are 58

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