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Monetary/Fiscal Interactions: Nominal Indeterminacy Behzad Diba University of Bern May 2011 (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 1/7 A Classical Question Classical economists analyzed long-run equilibrium in models that incorporated the Classical Dichotomy (long-run neutrality of money): (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 2/7 A Classical Question Classical economists analyzed long-run equilibrium in models that incorporated the Classical Dichotomy (long-run neutrality of money): 1 The long-run equilibrium values of real variables (e.g., real wages, employment, output, real interest rates) don’t depend on monetary conditions (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 2/7 A Classical Question Classical economists analyzed long-run equilibrium in models that incorporated the Classical Dichotomy (long-run neutrality of money): 1 2 The long-run equilibrium values of real variables (e.g., real wages, employment, output, real interest rates) don’t depend on monetary conditions The long-run equilibrium values of nominal variables (e.g., the price level, nominal wages) are determined by monetary conditions and the equilibrium values of the relevant real variables (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 2/7 A Classical Question Classical economists analyzed long-run equilibrium in models that incorporated the Classical Dichotomy (long-run neutrality of money): 1 2 The long-run equilibrium values of real variables (e.g., real wages, employment, output, real interest rates) don’t depend on monetary conditions The long-run equilibrium values of nominal variables (e.g., the price level, nominal wages) are determined by monetary conditions and the equilibrium values of the relevant real variables Neoclassical models of long-run equilibrium (with no nominal rigidity) re‡ect the same fundamental view in a more sophisticated setting (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 2/7 A Classical Question Classical economists analyzed long-run equilibrium in models that incorporated the Classical Dichotomy (long-run neutrality of money): 1 2 The long-run equilibrium values of real variables (e.g., real wages, employment, output, real interest rates) don’t depend on monetary conditions The long-run equilibrium values of nominal variables (e.g., the price level, nominal wages) are determined by monetary conditions and the equilibrium values of the relevant real variables Neoclassical models of long-run equilibrium (with no nominal rigidity) re‡ect the same fundamental view in a more sophisticated setting Classical Monetary Theory was about how monetary conditions pin down the price level and other nominal variables (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 2/7 A Classical Question Classical economists analyzed long-run equilibrium in models that incorporated the Classical Dichotomy (long-run neutrality of money): 1 2 The long-run equilibrium values of real variables (e.g., real wages, employment, output, real interest rates) don’t depend on monetary conditions The long-run equilibrium values of nominal variables (e.g., the price level, nominal wages) are determined by monetary conditions and the equilibrium values of the relevant real variables Neoclassical models of long-run equilibrium (with no nominal rigidity) re‡ect the same fundamental view in a more sophisticated setting Classical Monetary Theory was about how monetary conditions pin down the price level and other nominal variables The Quantity Theory of Money (MV = PY ) was typically the link between the money supply and the price level (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 2/7 A Classical Question Classical economists analyzed long-run equilibrium in models that incorporated the Classical Dichotomy (long-run neutrality of money): 1 2 The long-run equilibrium values of real variables (e.g., real wages, employment, output, real interest rates) don’t depend on monetary conditions The long-run equilibrium values of nominal variables (e.g., the price level, nominal wages) are determined by monetary conditions and the equilibrium values of the relevant real variables Neoclassical models of long-run equilibrium (with no nominal rigidity) re‡ect the same fundamental view in a more sophisticated setting Classical Monetary Theory was about how monetary conditions pin down the price level and other nominal variables The Quantity Theory of Money (MV = PY ) was typically the link between the money supply and the price level But some classical (neoclassical) economists addressed the question of price-level determinacy when the central bank sets the nominal interest rate (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 2/7 Speci…cations of Monetary Policy We can model monetary policy as a rule for setting either the money supply or the nominal interest rate (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 3/7 Speci…cations of Monetary Policy We can model monetary policy as a rule for setting either the money supply or the nominal interest rate In our simple cash-in-advance model, a monetary policy that sets an exogenous path for the money stock pins down the price level (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 3/7 Speci…cations of Monetary Policy We can model monetary policy as a rule for setting either the money supply or the nominal interest rate In our simple cash-in-advance model, a monetary policy that sets an exogenous path for the money stock pins down the price level But a policy that sets an exogenous path for the nominal interest rate (e.g., pegs the nominal rate) does not pin down the price level (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 3/7 Speci…cations of Monetary Policy We can model monetary policy as a rule for setting either the money supply or the nominal interest rate In our simple cash-in-advance model, a monetary policy that sets an exogenous path for the money stock pins down the price level But a policy that sets an exogenous path for the nominal interest rate (e.g., pegs the nominal rate) does not pin down the price level The same point can be made in an exchange economy with the ad-hoc speci…cation mt pt = yt ηit as the equilibrium condition in the market for money (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 3/7 Speci…cations of Monetary Policy We can model monetary policy as a rule for setting either the money supply or the nominal interest rate In our simple cash-in-advance model, a monetary policy that sets an exogenous path for the money stock pins down the price level But a policy that sets an exogenous path for the nominal interest rate (e.g., pegs the nominal rate) does not pin down the price level The same point can be made in an exchange economy with the ad-hoc speci…cation mt pt = yt ηit as the equilibrium condition in the market for money The left-hand side is the (logarithm of the) real money stock (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 3/7 Speci…cations of Monetary Policy We can model monetary policy as a rule for setting either the money supply or the nominal interest rate In our simple cash-in-advance model, a monetary policy that sets an exogenous path for the money stock pins down the price level But a policy that sets an exogenous path for the nominal interest rate (e.g., pegs the nominal rate) does not pin down the price level The same point can be made in an exchange economy with the ad-hoc speci…cation mt pt = yt ηit as the equilibrium condition in the market for money The left-hand side is the (logarithm of the) real money stock The right-hand side is the (logarithm of) demand for real money balances (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 3/7 Nominal Indeterminacy With the ad-hoc speci…cation mt pt = yt ηit a policy that sets an exogenous path for the nominal interest rate pins down real money balances (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 4/7 Nominal Indeterminacy With the ad-hoc speci…cation mt pt = yt ηit a policy that sets an exogenous path for the nominal interest rate pins down real money balances And the Fisher equation, nominal interest rate = (expected) real interest rate + (expected) in‡ation pins down expected in‡ation (because the real rate is determined by the real side of the model) (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 4/7 Write the Euler equations for real and nominal bonds as h u0 (Ct+1 ) 1 = Et 0 Rt u (Cth ) h u0 (Ct+1 ) 0 u (Cth ) 1 = Et It Pt Pt+1 where Rt and It are the gross real and nominal interest rates. Rede…ne rt and it to represent the continuously compounded rates rt = log(Rt ) De…ne t+1 let t = log( bond as t) and = h u0 (Ct+1 ) 0 u (Cth ) = log( t and t ), it = log(It ) and = t+1 Pt+1 Pt and write the Euler equation for the nominal expf it g = Et expf t+1 g expf t+1 g Note that in a steady-state equilibrium, we get expf ig = expf g expf g and the Fisher equation i=r+ The …rst-order terms in the Taylor approximation satisfy expf ig[it i] = expf g expf gEt ([ t+1 i t+1 Et ] which simpli…es to it = + Et and it = rt + Et 1 t+1 t+1 [ t+1 ]) Nominal Indeterminacy With the ad-hoc speci…cation mt pt = yt ηit a policy that sets an exogenous path for the nominal interest rate pins down real money balances And the Fisher equation, nominal interest rate = (expected) real interest rate + (expected) in‡ation pins down expected in‡ation (because the real rate is determined by the real side of the model) But the equilibrium price level is not determined (the model exhibits nominal indeterminacy) (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 4/7 Nominal Determinacy To get nominal determinacy, we often con…ne our analysis to suitably bounded equilibria. In this case, the price level is pinned down if we specify monetary policy as (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 5/7 Nominal Determinacy To get nominal determinacy, we often con…ne our analysis to suitably bounded equilibria. In this case, the price level is pinned down if we specify monetary policy as an interest-rate rule (reacting to in‡ation) that obeys the Taylor Principle (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 5/7 Nominal Determinacy To get nominal determinacy, we often con…ne our analysis to suitably bounded equilibria. In this case, the price level is pinned down if we specify monetary policy as an interest-rate rule (reacting to in‡ation) that obeys the Taylor Principle or a policy that sets an exogenous path for the money supply (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 5/7 Nominal Determinacy To get nominal determinacy, we often con…ne our analysis to suitably bounded equilibria. In this case, the price level is pinned down if we specify monetary policy as an interest-rate rule (reacting to in‡ation) that obeys the Taylor Principle or a policy that sets an exogenous path for the money supply In our simple cash-in-advance model, the determinacy implication of a money-supply rule is straightforward (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 5/7 Nominal Determinacy To get nominal determinacy, we often con…ne our analysis to suitably bounded equilibria. In this case, the price level is pinned down if we specify monetary policy as an interest-rate rule (reacting to in‡ation) that obeys the Taylor Principle or a policy that sets an exogenous path for the money supply In our simple cash-in-advance model, the determinacy implication of a money-supply rule is straightforward but there are issues, in other models, that are beyond the scope of this course (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 5/7 Nominal Determinacy To get nominal determinacy, we often con…ne our analysis to suitably bounded equilibria. In this case, the price level is pinned down if we specify monetary policy as an interest-rate rule (reacting to in‡ation) that obeys the Taylor Principle or a policy that sets an exogenous path for the money supply In our simple cash-in-advance model, the determinacy implication of a money-supply rule is straightforward but there are issues, in other models, that are beyond the scope of this course and major central banks don’t target the money stock anyway (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 5/7 Nominal Determinacy To get nominal determinacy, we often con…ne our analysis to suitably bounded equilibria. In this case, the price level is pinned down if we specify monetary policy as an interest-rate rule (reacting to in‡ation) that obeys the Taylor Principle or a policy that sets an exogenous path for the money supply In our simple cash-in-advance model, the determinacy implication of a money-supply rule is straightforward but there are issues, in other models, that are beyond the scope of this course and major central banks don’t target the money stock anyway Our discussion will focus on interest-rate rules (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 5/7 The Taylor Principle An interest-rate rule obeys the Taylor Principle if it responds to in‡ation with a coe¢ cient greater than unity (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 6/7 The Taylor Principle An interest-rate rule obeys the Taylor Principle if it responds to in‡ation with a coe¢ cient greater than unity this can serve to stabilize aggregate demand in models with nominal rigidity (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 6/7 The Taylor Principle An interest-rate rule obeys the Taylor Principle if it responds to in‡ation with a coe¢ cient greater than unity this can serve to stabilize aggregate demand in models with nominal rigidity it makes in‡ation dynamics explosive and implies a unique bounded solution for the in‡ation rate (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 6/7 The Taylor Principle An interest-rate rule obeys the Taylor Principle if it responds to in‡ation with a coe¢ cient greater than unity this can serve to stabilize aggregate demand in models with nominal rigidity it makes in‡ation dynamics explosive and implies a unique bounded solution for the in‡ation rate For concreteness, suppose the central bank has a zero-in‡ation target in the long run and sets it = ρ + φπ π t where ρ is the real interest rate in the steady-state equilibrium (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 6/7 The Taylor Principle An interest-rate rule obeys the Taylor Principle if it responds to in‡ation with a coe¢ cient greater than unity this can serve to stabilize aggregate demand in models with nominal rigidity it makes in‡ation dynamics explosive and implies a unique bounded solution for the in‡ation rate For concreteness, suppose the central bank has a zero-in‡ation target in the long run and sets it = ρ + φπ π t where ρ is the real interest rate in the steady-state equilibrium Using, the Fisher equation, rt = it Et π t +1 , the dynamics of in‡ation are governed by Et π t + 1 = φ π π t (Institute) ( rt ρ) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 6/7 Determinacy under the Taylor Principle The dynamic equation Et π t + 1 = φ π π t ( rt ρ) generates explosive dynamics if φπ > 1 (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 7/7 Determinacy under the Taylor Principle The dynamic equation Et π t + 1 = φ π π t ( rt ρ) generates explosive dynamics if φπ > 1 So, an interest-rate rule that obeys the Taylor Principle implies a unique bounded solution for the in‡ation rate, and this determines the price level (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 7/7 Determinacy under the Taylor Principle The dynamic equation Et π t + 1 = φ π π t ( rt ρ) generates explosive dynamics if φπ > 1 So, an interest-rate rule that obeys the Taylor Principle implies a unique bounded solution for the in‡ation rate, and this determines the price level There are, however, historical episodes (e.g., the US before 1979) for which the data suggest the Taylor Principle was not satis…ed (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 7/7 Determinacy under the Taylor Principle The dynamic equation Et π t + 1 = φ π π t ( rt ρ) generates explosive dynamics if φπ > 1 So, an interest-rate rule that obeys the Taylor Principle implies a unique bounded solution for the in‡ation rate, and this determines the price level There are, however, historical episodes (e.g., the US before 1979) for which the data suggest the Taylor Principle was not satis…ed We will discuss nominal determinacy during these episodes later (Institute) Monetary/Fiscal Interactions: Nominal Indeterminacy May 2011 7/7