Institut für Volkswirtschaftslehre

Permanent URI for this collectionhttps://hohpublica.uni-hohenheim.de/handle/123456789/24

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Browsing Institut für Volkswirtschaftslehre by Sustainable Development Goals "4"

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    A generalized representation of Faà Di Bruno'S formula using multivariate and matrix‐valued Bell polynomials
    (2025) Evers, Michael P.; Kontny, Markus
    We provide a generalization of Faà di Bruno’s formula to represent the 𝑛-th total derivative of the multivariate and vector-valued composite 𝑓 ∘𝑔. To this end, we make use of properties of the Kronecker product and the 𝑛-th derivative of the left-composite 𝑓 , which allow the use of a multivariate and matrix-valued form of partial Bell polynomials to represent the generalized Faà di Bruno’s formula. We further show that standard recurrence relations that hold for the univariate partial Bell polynomial also hold for the multivariate partial Bell polynomial under a simple transformation. We apply this generalization of Faà di Bruno’s formula to the computation of multivariate moments of the normal distribution.
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    Metropolitan, urban, and rural regions: how regional differences affect elementary school students in Germany
    (2025) Schwerter, Jakob; Bleher, Johannes; Doebler, Philipp; McElvany, Nele
    This study examined how regional differences affect elementary school students using the representative German Progress in International Reading Literacy Study (PIRLS) 2016 data (N = 3,959 fourth-grade students; M_{Age} = 10.34 years; 49% girls; 71% from a nonimmigrant background) by combining bootstrapping, multiple imputations, principal component analysis, and the least absolute shrinkage and selection operator (LASSO). Grouping regions into rural, (sub-)urban, and metropolitan, we found that students from rural and metropolitan areas are 10.9% and 15.1% more likely, respectively, to receive an academic track recommendation than their urban counterparts. Similarly, rural and metropolitan students are 0.2 to 0.3 standard deviations more likely to enjoy school and be interested in reading than their urban counterparts. Aside from students’ backgrounds and skills, many of the characteristics explaining this regional difference are structural, directly affected by policy decisions. Variables directly and indirectly influenced by policy help explain regional differences, but nonpolicy variables reduce regional differences in academic track recommendations the most.