4.3 Methodology 4.3.1 Fixed-effects regressions We first investigate the static, contemporaneous relationship between reading, spelling, and math skills. We do so using three fixed effects regressions: Rit =β R 0 +β R 1 Sit +β R 2 Mit +ε Rit (4.1) Sit =β S 0 +β S 1 Rit +β S 2 Mit +ε S it (4.2) Mit =β M 0 +β M 1 Rit +β M 2 Sit +ε Mit (4.3) withεj it =v j i +u j it ∀j ∈{R,S,M} (4.4) Equations 4.1-4.3 model the reading (Rit), spelling (Sit), and math (Mit) score of student i in time period t in a multivariate model. εj it is the idiosyncratic error term, consisting of an unobserved time-invariant individual fixed effect (vj i ) and an unobserved time-varying error term (uj it). The former, the individual fixed effect, controls for unobserved, time-invariant characteristics that relate to a student’s skill score. These characteristics, for instance, could include factors such as a student’s innate ability or background 89
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