Consider a classical economy with an exogenous real interest rate process {rt}. Discuss the conditions under which the equilibrium will be (locally) unique and solve for the equilib- rium level of inflation when the central bank follows the rules: (a) Rule #1: Partial adjustment i₁ = $¡it−1 + (1 − $;)ii where ; € [0,1] and it is a reference interest rate given by, ϋ =ρ+Φαπε (b) Rule #2: Moving average inflation targeting

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Equilibrium indeterminacy and interest rate rules
Consider a classical economy with an exogenous real interest rate process {rt}. Discuss the
conditions under which the equilibrium will be (locally) unique and solve for the equilib-
rium level of inflation when the central bank follows the rules:
(a) Rule #1: Partial adjustment
i = pit-1+ (1 – 4:)i:
where o e [0,1] and i; is a reference interest rate given by,
(b) Rule #2: Moving average inflation targeting
it = p+ Prīt
where 7 = (1– 8) Lo oK Tq-k-
(c) Show the equivalence between the two rules.
Transcribed Image Text:Equilibrium indeterminacy and interest rate rules Consider a classical economy with an exogenous real interest rate process {rt}. Discuss the conditions under which the equilibrium will be (locally) unique and solve for the equilib- rium level of inflation when the central bank follows the rules: (a) Rule #1: Partial adjustment i = pit-1+ (1 – 4:)i: where o e [0,1] and i; is a reference interest rate given by, (b) Rule #2: Moving average inflation targeting it = p+ Prīt where 7 = (1– 8) Lo oK Tq-k- (c) Show the equivalence between the two rules.
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