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 error 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.

ARCH process, Linearization, real business cycle model, stochastic difference equation
Time-Series Models; Dynamic Quantile Regressions (jel C22), Existence and Stability Conditions of Equilibrium (jel C62), Business Fluctuations; Cycles (jel E32)
Tinbergen Institute
Tinbergen Institute Discussion Paper Series
Discussion paper / Tinbergen Institute
Tinbergen Institute

Babus, A.M, & de Vries, C.G. (2010). Global Stochastic Properties of Dynamic Models and their Linear Approximations (No. TI 2010-081/2). Discussion paper / Tinbergen Institute. Tinbergen Institute. Retrieved from