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Institut für Volkswirtschaftslehre

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

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Browsing Institut für Volkswirtschaftslehre by Classification "510"

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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; Evers, Michael P.; Department of Economics, University of Hohenheim, Stuttgart, Germany; Kontny, Markus; Deutsche Bundesbank, Frankfurt, Germany
    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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    Modelling and diagnostics of spatially autocorrelated counts
    (2022) Jung, Robert C.; Glaser, Stephanie
    This paper proposes a new spatial lag regression model which addresses global spatial autocorrelation arising from cross-sectional dependence between counts. Our approach offers an intuitive interpretation of the spatial correlation parameter as a measurement of the impact of neighbouring observations on the conditional expectation of the counts. It allows for flexible likelihood-based inference based on different distributional assumptions using standard numerical procedures. In addition, we advocate the use of data-coherent diagnostic tools in spatial count regression models. The application revisits a data set on the location choice of single unit start-up firms in the manufacturing industry in the US.