Thesis

an increase of around 0.10 SD in spelling and reading in the next period. Two periods after the shock, the response decreases to 0.06 SD for spelling and 0.01 SD for reading. The second row shows the response to a shock in reading skills. Math and spelling increase in the first period by around 0.10 SD and 0.07 SD, respectively. In the second period, these responses are roughly halved. The last row shows the response to a shock in spelling skills. Reading and math increase by about 0.05-0.10 SD in the first period. In the following periods, the responses gradually decrease, similar to the patterns observed for the shocks in reading and math. Generally, the responses remain observable for about 3 to 4 periods, with one exception: the response of reading to a shock in math nearly returns to zero after the first period. It is notable that the GIRF shows a positive response of reading to a shock in math, despite the panel VAR estimates indicating a negative coefficient for the lag of math on reading. The positive GIRF response indicates that an unexpected increase in math is associated with an initial increase in reading, which approaches zero in subsequent periods. In contrast, the negative coefficient in the VAR model reflects a longerterm association, where higher levels of math tend to coincide with lower levels of reading over time. This apparent discrepancy arises because the GIRF captures short-term dynamics following a shock, while the panel VAR model reflects persistent, long-term patterns. The negative association of reading after a shock in math appears to be offset by positive associations from the other variables in the system. 99

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