We present a statistical analysis of the X-ray luminosity of rotation powered pulsars and their surrounding nebulae using the sample of Kargaltsev & Pavlov (2008) and we complement this with an analysis of the gamma-ray-emission of Fermi detected pulsars. We report a strong trend in the efficiency with which spin-down power is converted to X-ray and gamma-ray emission with characteristic age: young pulsars and their surrounding nebulae are efficient X-ray emitters, whereas in contrast old pulsars are efficient gamma-ray emitters. We divided the X-ray sample in a young (Tau < 1.7x10^4 yr) and old sample and used linear regression to search for correlations between the logarithm of the X-ray and gamma-ray luminosities and the logarithms of the periods and period derivatives. The X-ray emission from young pulsars and their nebulae are both consistent with L_X ~ Pdot^3/P^6. For old pulsars and their nebulae the X-ray luminosity is consistent with a more or less constant efficiency eta = L_X/Edot = ~ 8x10^-5. For the gamma-ray luminosity we confirm that L_gamma ~ Edot^(1/2). We discuss these findings in the context of pair production inside pulsar magnetospheres and the striped wind model. We suggest that the striped wind model may explain the similarity between the X-ray properties of the pulsar wind nebulae and the pulsars themselves, which according to the striped wind model may both find their origin outside the light cylinder, in the pulsar wind zone.
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