Appendix to Accompany VCauses of Nonlinearities in Low% Order Models of the Real Exchange RateV

摘要: Suppose the linearized (to the first order) model takes the form u0'b $# b% x0L%# b&ε0(1a) x0'a $# a% x0L%# a&ε0(1b) where u0 is a (non% predetermined endogenous) control variable; x0 represents a (predetermined endogenous) state variable, and ε0 is an exogenous innovation with mean zero and standard deviation σ& drawn indepen% dently and identically from an underlying distribution with bounded support. For illustrative purposes, we assume that the same shock affects the state and control variables, and the magnitude of its impact is given by the known parameters a& and b&, respectively. Such a system adequately represents the output from Dynare. In order to rewrite the system (1) as an autoregressive process for the control variable u0, we lag the equation (1b) by one period, substitute the resulting expressions into (1a), and collect like terms. We can express u0 as a function of its own lag and the exogenous shock as follows: u0'(!% a%" b $# a $ b%)# a% u0L%#! a&b% a% b&" ε0L%# b&ε0