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242 CHAPTER 8. THE MUNDELL-FLEMING MODELThe long-run or the steady-state is not conveniently characterized ina stochastic environment because the economy is constantly being hitby shocks to the non-stationary exogenous state variables. Instead of along-run equilibrium, we will work with an equilibrium concept given bythe solution formed under hypothetically fully ßexible prices. Then aslong as there is some degree of price-level stickiness that prevents completeinstantaneous adjustment, the disequilibium can be characterizedby the gap between sticky-price solution and the shadow ßexible-priceequilibrium.Let the shadow values associated with the ßexible-price equilibriumbe denoted with a ‘tilde.’ The predetermined part of the price level isE t−1˜p t which is a function of time t-1 information. Let θ(˜p t − E t−1˜p t )represent the extent to which the actual price level p t responds at datet to new information where θ is an adjustment coefficient. The stickypriceadjustment rule isp t =E t−1˜p t + θ(˜p t − E t−1˜p t ). (8.20)According to this rule, goods prices display rigidity for at most oneperiod. Prices are instantaneously perfectly ßexible if θ =1andtheyare completely Þxedone-periodinadvanceifθ = 0. Intermediatedegrees of price Þxity are characterized by 0 < θ < 1 which allowthe price level at t to partially adjust from its one-period-in-advancepredetermined value E t−1 (˜p t ) in response to period t news, ˜p t − E t−1˜p t .The exogenous state variables are output, money, and the aggregatedemand shock and they are governed by unit root processes. Outputand the money supply are driven by the driftless random walksy t = y t−1 + z t , (8.21)m t = m t−1 + v t , (8.22)iidwhere z t ∼ N(0, σz)andv 2 iidt ∼ N(0, σv). 2 The demand shock d t also is aunit-root processd t = d t−1 + δ t − γδ t−1 , (8.23)where δ tiid∼ N(0, σ 2 δ). Demand shocks are permanent, as represented byd t−1 but also display transitory dynamics where some portion 0 < γ < 1