Getting Rental Prices Right for Computers

National statistical agencies frequently assume very high geometric depreciation rates in order to capture the fact that computers are usually retired after 3 or 4 years of use. However, typically the service flow that a computer generates over its useful life is roughly constant, which contradicts the geometric model of depreciation where the service flow falls at a constant rate forever. Thus a one hoss shay or light bulb model of depreciation seems to be more appropriate for computers. The paper uses Australian data on computer investment over the past 25 years to construct one hoss shay estimates of computer capital stocks and flows and considers how best to approximate these more realistic models of depreciation with a geometric model. The paper shows that under certain simplifying assumptions, a geometric model of depreciation can provide an exact approximation to an underlying one hoss shay model. This exactness result is extended to a more general model of depreciation, the Constant Efficiency Profile model. Finally, using Australian data, the paper shows how well the geometric approximation fits a one hoss shay model when the simplifying assumptions are not satisfied.