Monetary policy regime formalization: instrumental rules

Transcription

1 Monetary policy regime formalization: instrumental rules PhD program in economics 2009/10 University of Rome La Sapienza Course in monetary policy (with G. Ciccarone) University of Teramo

2 The monetary policy regime The simple model: x = σ 1 (i π e ) + x e + ε D π = β π e + γ x + ε S Three variables (x, π, i) and two equations!!! We need another equation to close the model. How is the interest rate set? Monetary regime 2

3 More in detail: 3 approaches 3 Instrumental rule The policy-maker commits to a (simple) feedback rule. Standard approach (discretion) Each instant of time (no commitment), the policy-maker behaves by minimizing an approximate social loss derived from the micro-founded model. Targeting rule Each instant of time, the policy-maker behaves by minimizing a different loss based on target deviations different from those derived from the micro-founded model. It commits to the targets.

4 Definitions Possible sources of confusion 1. Activist vs. Non-Activist Rule (Friedman) 2. Rule (contingent plan) vs. Discretion (optimization period by period) 3. Targeting vs. Instrumental Rules 4. Old view (rules vs. discretion): the inflation bias and central bank independence 4

5 Instrumental rule implementation If a rule that describes how the monetary authority sets the nominal interest rate is added to the model, this must be done with care to ensure that the policy rule does not render the system unstable or introduce multiple equilibria. 5

6 Instability due to self-fulfilling expectations Consider what would happen if expected inflation were to rise. Et π(t+1) [i(t) Et π(t+1)] x(t) π(t) Since there is no endogenous feedback from this rise in expected inflation to the nominal interest rate, the real interest rate must fall. This decline in the real rate is expansionary and the output gap increases. The rise in output increases actual inflation. 6

7 Taylor rule (Taylor, 1993) 7 The most famous instrument rule is the Taylor one: i(t) = i + π(t) x(t) [ π(t) π T ] where π T was the target level of average inflation (Taylor assumed it to be 2%) and i was the equilibrium nominal rate of interest (Taylor assumed the real rate was equal to 2%); x(t) is the potential output gap (linear deterministic trend). Please notice (Taylor rule): i(t) = 1.5 π(t) x(t)

8 A formal analysis in a NK model A simple New Keynesian (Neo Wicksellian) model x = E x σ i Eπ ( ) 1 t t t+ 1 t t t+ 1 π = βeπ + κx t t t+ 1 t Augmented by a Taylor Rule i = aπ + a x t 1 t 2 t 8

9 Rearranging Etβπ = t 1 π + t κxt 1 a2 a1 Ex t t+ 1+ Etπ t+ 1 = 1+ xt + π t σ σ σ σ Ex t t a x 2σ a1σ t 0 β Etπ = t+ 1 κ 1 π t 9

10 Stability analysis AEY EY = t t+ 1 BYt = t t+ 1 MYt M = [ ] Y = x π t t t 1 A B σ Ex t t a x 2σ a1σ t 0 β Etπ = t+ 1 κ 1 π t Ex t t+ 1 1 σ 1+ a x 2σ a1σ t Etπ = t+ 1 0 β κ 1 π t M a2β + γ a1β 1 1+ θβ θβ = γ 1 β β 10

11 The two eigenvalues of Matrix M λ 1 ( M ) a+ b 2β = λ ( M ) 2 = a b 2β. γ + β a a = + β + > θ γ a2 1 β γ β 2 2 b= + β + + β + ( a1γ + a2) θ θ θ θ λ ( M ) λ ( M )

12 We look at the second eigenvalue only a b 2β ( ) 2 > 1 a b > 2β a 2β > b a 2β > b. 2 2 γ + βa2 γ a2β γ β β + > + β + + β + ( a1γ + a2) θ θ θ θ θ Stability requires ( a ) γ ( β) a > a 1 β + a > 1 γ

13 13 Taylor Principle Setting a 1 > 1 is referred to as the Taylor Principle, because John Taylor was the first to stress the importance of interest rate rules that called for responding more than one-forone to changes in inflation. With Taylor s original coefficients, 1.5, so that the nominal rate is changed more than onefor-one with deviations of inflation from target. Thus, the rule satisfies the Taylor Principle.

14 Taylor Rule stability: Summary I Suppose the central bank responds to both inflation and the output gap according to: i(t) = a1 π(t) + a2 x(t) + v(t) With this policy rule, the condition to ensure the economy has a unique, stationary equilibrium becomes: a1 + (1 β) a2 / κ > 1 Stability depends on both the policy parameters. 14

15 Taylor Rule stability: Summary II 15 Self-fulfilling expectations: Et π(t+1) [i(t) Et π(t+1)] x(t) π(t) This suggests that a policy which raised the nominal interest rate enough to increase the real interest rate when inflation rose would be sufficient to ensure a unique equilibrium the Taylor Principle. A feedback rule satisfies the Taylor Principle if it implies that in the event of a sustained increase in the inflation rate by k percent, the nominal interest rate will eventually be raised by more than k percent.

16 Taylor Rule with interest-rate inertia A similar result is obtained in the case of a rule that incorporates interest-rate inertia of the kind characteristic of estimated Fed reaction functions (e.g., Judd and Rudebusch, 1997): i(t) = i (t) + a1 [π(t) π ] + a2 [x(t) x ] + ρ [i(t 1) i (t 1)] 16 With this policy rule, the condition to ensure the economy has a unique, stationary equilibrium becomes: a1 + (1 β) a2 / κ > 1 ρ Once again it corresponds precisely to the

17 Taylor Rule & NK approach The Taylor rule may result from the Social Loss minimization. Zero inflation target. Flexible price output gap (unit labor cost) instead of de-trended output. Non-constant intercept. 17

18 18 Estimated Taylor rules & co In general, the basic Taylor Rule, when supplemented by the addition of the lagged nominal interest rate, does quite well in matching the actual behavior of the policy interest rate. But since they at most explain 2/3 of the empirical instrument-rate changes, central banks in practice deviate substantially from such a rule. Moreover, Ophanides (2000) that when estimated using the data on the output gap and inflation actually available at the time policy actions were taken (i.e., using real-time data), the Taylor Rule does much more poorly in matching the U.S. funds rate.

19 The advantages The rule can easily be verified by outside observers and a commitment to the rule would therefore be technically feasible. Variants of the Taylor rule have been found to be relatively robust to different models, in the sense that they perform reasonably well in simulations with different models and rarely result in very bad outcomes 19

20 The disadvantages The rule will not result in an optimal outcome, for several reasons (sub-optimal). No central bank has made a commitment to follow it (never observed). Empirical estimates of Taylor-type reaction functions show that they at most explain 2/3 of the empirical instrument-rate changes. Thus, central banks in practice deviate substantially from such a reaction function. 20

21 Is the Taylor rule enough? It is difficult to think that a rule can be followed automatically Monetary policy management is more complex and flexible Central element the role of projections (forecast-based targeting) Flexible Inflation Targeting (Svensson, Bernanke)

22 22 Money rules (stable demand for money) The quantity of money is not totally absent from the underlying model, since equation money demand must equal money supply in equilibirum (LM curve). In a linearized form: m(t) p(t) = 1/(σb) x(t) 1/σ i(t) Given the nominal interest rate chosen by the monetary policy authority, this equation endogenously determines the nominal quantity money.

23 Example Alternatively, if the policy-maker sets the nominal quantity of money, the model can be solved jointly for x(t), π(t), and i(t). E.g. the Taylor rule i(t) = a1 π(t) + a2 x(t)) becomes: m(t) = 1/σ a1 π(t) + 1/σ (1/b + a2) x(t) + p(t) 23