Chapter 4. The Interplay of Reading, Spelling, and Math in Primary Education: A Panel VAR Analysis skills, while the measurement error in earlier periods is assumed to be uncorrelated with current errors, helping to filter out noise. As a result, panel VAR GMM helps mitigate classical measurement error when it is random and uncorrelated over time. However, if measurement error is systematic, persistent, or correlated with true skills, GMM may not fully eliminate this bias. 4.3.3 IRFs Based on our panel VAR model, we derive IRFs. These IRFs are used as a form of thought experiment to examine how reading, spelling, and math skills vary together over time. By introducing a hypothetical shock in one skill11, the IRFs trace how all three skills tend to fluctuate in subsequent periods. This approach does not imply causation but provides a structured way to explore the patterns of co-movement among skills. This allows us to observe how changes in one skill are accompanied by shifts in others, illustrating the interconnected nature of skill development and offering insights that go beyond what can be seen in single-time-point analyses or simple correlations. For readability, the remainder of the chapter refers to the shock to the residual of a specific variable as a shock to the variable itself. As the reduced panel VAR allows the covariates of the errors to move 11The shocks applied to the system of equations are exogenous, meaning they are introduced to the error term and assumed to originate from outside the system. So, as panel VAR models consider the skill’s own lag and the lags of other skills in the system, the residuals in these models capture what is not explained by past values of skills; and a shock to one of the residuals introduces new, unpredictable information to the system. However, in the context of an educational intervention, it is unlikely that the shock would impact only one skill in isolation. Educational interventions typically target multiple skills, and their effects often extend to related areas due to the interconnected nature of these skills. 92
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