The dynamic properties of micro based stochastic macro models are often analyzed through a linearization around the associated deterministic steady state. Recent literature has investigated the errors made by such a deterministic approximation. Complementary to this literature we investigate how the linearization affects the stochastic properties of the original model. We consider a simple real business cycle model with noisy learning by doing. The solution has a stationary distribution that exhibits moment failure and has an unbounded support. The linear approximation, however, yields a stationary distribution with possibly a bounded support and all moments finite.

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Keywords ARCH process, Linearization, Real business cycles model, Stochastic difference equation
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Babus, A.M, & de Vries, C.G. (2010). Global stochastic properties of dynamic models and their linear approximations. Journal of Economic Dynamics and Control, 34(5), 817–824. doi:10.1016/j.jedc.2010.02.001