Global Stochastic Properties of Dynamic Models and their Linear Approximations - Ana Babus; Casper G. de Vries (Tinbergen Institute, 2010)
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 momentsfinite.
Keywords: C22; C62; E32; 330; Linearization; ARCH process; Real business cycles model; Stochastic difference equation; Dynamisches Modell; Real Business Cycle; Stochastischer Prozess