Chapter 4. The Interplay of Reading, Spelling, and Math in Primary Education: A Panel VAR Analysis 4.4.4 Cumulative effects in skill development What we ultimately want to know is to what extent a shock to one skill relates to lasting changes in all skill levels over time. We examine this using cumulative IRFs. While the GIRFs show how a variable moves in each period following a hypothetical shock, the cumulative IRFs aggregate these movements, providing insight into how long the changes persist over time. In this way, we examine the net results of this hypothetical shock after several time periods. Figure 4.3 shows the cumulative IRFs. A hypothetical shock to one skill relates to persistent changes for all skills, as the cumulative response gradually builds and eventually stabilizes above zero. This indicates that skill levels remain elevated in subsequent periods, suggesting that changes in one skill are associated with persistent adjustments in the other skills. After ten time periods, or five years, the cumulative movement of a hypothetical shock on a skill itself is around 0.70 SD, indicating that the movement remains substantial over time. This 0.70 SD movement is larger than the change observed after a single time period. In contrast, the cumulative movement of a shock in one skill on another skill is around 0.10-0.20 SD, which is noticeably smaller and less pronounced than the movement observed for the skill directly affected. The cumulative IRFs highlight that focusing only on short-run movements can underestimate the total magnitude of skill changes, as accumulation over time can produce much larger overall changes than initially apparent. This underestimation is particularly evident when compared to conventional approaches, such as fixed-effects 100
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