together, normal IRFs do not model the result of an individual shock. One way of focusing on isolated shocks, is constructing orthogonal IRFs. The recursive panel VAR and its orthogonal IRFs impose shortrun relationships by imposing contemporaneous skill variables in the equations.12 For this purpose, the order of the variables in the panel VAR system becomes crucial. Therefore, we need to argue which variables are more exogenous in the system, and so are ordered earlier. Literature on this is, however, lacking and, in the setting of skills, it is rather difficult to assign a clear and definitive order because the relationships among these skills are often bidirectional or simultaneous. Therefore, imposing a strict ordering for orthogonal IRFs could be artificial or misleading. For that reason, we construct generalized IRFs (GIRF), as proposed by Pesaran and Shin (1998). GIRFs account for the potential correlations between shocks, making them more realistic for systems where variables influence each other in interconnected ways. 4.4 Results 4.4.1 Fixed-effects regressions We first analyze the contemporaneous relationship between reading, spelling, and math skills using fixed effects regressions (see Equations 4.1-4.3). Table 4.2 shows the estimation results of these regressions. 12To make the residuals orthogonal, the Cholesky decomposition of the variancecovariance matrix of the residuals can be used, which decomposes a positivedefinite matrix into the product of a lower triangular matrix and its conjugate transpose. 93
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