Chapter 4. The Interplay of Reading, Spelling, and Math in Primary Education: A Panel VAR Analysis an unexpected, hypothetical shock to one of the skills in the system of equations. These IRFs act as a thought experiment showing how reading, spelling, and math skills evolve together over time after a hypothetical shock. In this way, they visualize how changes in one skill are associated with subsequent responses in the other skills over time. These responses do not represent causal effects, but rather illustrate typical patterns of variation and co-movement among the skills. Fixed-effects regressions indicate that reading, spelling, and math skills are positively related at the same point in time. An increase of one standard deviation in reading skills relates to an increase of spelling skills of around 0.10 SD, and vice versa the relation is also positive and of similar magnitude. For all the other skills, this contemporaneous relationship is almost or more than twice as strong. Besides these contemporaneous relationships, this chapter, moreover, finds that skills are dynamically related to each other. Reading, spelling, and math skills Granger-cause each other, meaning that past values of one skill contain useful information for predicting another. Generalized IRFs show that an unexpected, exogenous positive shock to one type of skill is associated with increases in the other skills. Skills respond most strongly to a shock in the skill itself, but also move together with other skills. Over time, shocks are linked with lasting changes in the system. Five years after a positive shock, improvements remain evident. While the cumulative improvements were strongest in the skill that experienced the shock (around 0.7 SD), the observed changes in other skills (0.1-0.2 SD) also indicate notable transfer across skills. These results show that skills do not develop in isolation, nor can skill deficits be addressed independently. Because skills tend to develop together, investments in one area may 80
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