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In this theoretical study we investigate the efficiency potential of monolithic white light emitting diodes (LEDs) that are free of wavelength-converting phosphors and are based solely on the InGaN material system. For that purpose we develop a numerical model that handles multiple active layers of different emission wavelength and takes photon reabsorption and -emission as well as internal non-radiative and optical losses into account. It is applied both to thin film structures as well as novel nanorod LEDs featuring disc-like active layers. In both cases, the active layers may either consist of multiple thin quantum wells or a single thick, bulk-like InGaN layer.