Discussion of. "Indeterminacy with Inflation-Forecast- Based Rules in a Two-Bloc Model" N. Batini, P. Levine and J. Pearlman

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1 Discussion of "Indeterminacy with Inflation-Forecast- Based Rules in a Two-Bloc Model" N. Batini, P. Levine and J. Pearlman Marc Giannoni Columbia University International Research Forum on Monetary Policy November

2 Contribution Analyze stability and determinacy of equil. with Inflation-Forecast-Based (IFB) rules or i t i t1 1 E t tj i t i t1 1 E t H,tj for given j 0, and 0 1, 0 Micro-founded open economy model Builds on BB (2001), CGG (2002) tractable two-country model Add "realistic" features * persistence (habit, inflation indexing) * bias for consumption of home-produced goods 2

3 Analysis of Determinacy: Why is it Important? IFB rules: relevant good description of actual policy in US (CGG, 2000), Europe (Castelnuovo, 2003) approximation of optimal rule If generate indeterminacy: potentially very bad outcomes arbitrary large fluctuations in inflation, output... regardless of size of fundamental disturbances Need to look for rules that guarantee a determinate equilibrium! We know many conditions for determinacy in closed economies how do they generalize to open-economies? 3

4 What Do BLP Do? Log-linearize model s equations Two decoupled blocks of difference equations (M. Aoki): sum system ( S,...):sameas for closedeco. difference system ( D,...) For open economy: both systems must be saddle-path stable for stable and determinate equil. Use "root locus technique" (Batini & Pearlman, 2002) analyze how roots of characteristic polynomial change as one policy parameter is changed ( 4

5 Findings For particular policy rules considered: In sum system (as in closed economy): * 1: necessary cond. for determinacy (Taylor principle) * 1: also sufficient if forecast horizon j 0 * Indeterminacy for any, if horizon j lies too far in future * Larger reduces region of indeterminacy New results: In difference system * Problem of indeterminacy "intrinsically" more serious * Even more so when CB responds to expected consumer price inflation: if no home bias, indeterminacy for all,,j Very interesting and important! 5

6 Rest of Discussion Perfect foresight model: unclear / misleading A few issues with simple IFB A possible solution to the problem of indeterminacy (plus some more) 6

7 Perfect Foresight Model: Unclear / Misleading Analysis of determinacy refers to transition matrix of dynamic system shocks are irrelevant Uncertainty may be removed a priori BUT: dynamic equations need to correctly reflect underlying uncertainty! In paper, structure of underlying asset markets unclear asset markets appear incomplete 7

8 Perfect Foresight Model: Unclear / Misleading Combining Euler equation with UIP: S t P t C t hc t1 S t C S t1p t1 t hc t1 S t1 C t1 hc t hc t C t1 (22) BLP argue (22) is equivalent to S t P t C t hc t1 S t C t hc t1 1 (23) But in stochastic setting: true only with complete asset markets (risk-sharing condition for consumption) In general, determinate equilibrium with (23) may not be determinate with (22)! 8

9 A Few Issues with Simple IFB Why Inflation-Forecast-Based (IFB) rules? BLP: "current inflation predetermined" But inflation is not predetermined in model! Instead, desirable to respond to forecasts when current variables depend on lagged state variables (Giannoni-Woodford, 2002) Whywouldrestrictto 1? * Optimal policy rules i t i t1 E t tj typically have 1 in forward-looking models! (Rotemberg-Woodford, 1999) * 1: Expands the region of determinacy (closed eco.) 9

10 A Few Issues with Simple Rules ("Taylor", IFB) Perform well in wide range of models (Levin, Wieland, Williams, 1999, 2001) BUT, coefficients of optimal simple IFB (or Taylor) rules are extremely sensitive to exogenous shock processes (autocorrelation) embed how fast shocks are expected to dissipate work well to extent that shocks of new kind won t appear! 10

11 Sensitivity of Optimal Simple Rules to Shock Process Example: Optimal Taylor Rule i t t x y t in "sum model" when h 0, and shocks on IS and AS equations are AR(1) (Giannoni-Woodford, 2002) Plotof, x for different degree of serial correlation in shocks 11

12 5 Optimal Taylor Rules φ x ρr=0.6 ρu=0 ρr=0.6 ρu= Indet. ρr=0.6 ρu=0.6 1 ρr=0.35 ρu=0 ρr= ρu=0.35 ρr=0 ρr=0.35 ρr=0 ρu=0 ρu=0.35 ρr=0 ρu=0.6 ρu= φ π Sum system (AR(1) shocks, h 0) 12

13 Simple IFB rules: Likely to generate indeterminacy in open-economy model Optimal simple rule sensitive to assumption about particular shock process Any solution? 13

14 A Possible Solution: Robustly Optimal Rules Giannoni-Woodford (2002, 2003) Optimal policy under cooperation Maximize 0 0,where 0 E 0 t0 s.t. model s restrictions z t1 E t x t1 A t t 2 y y t k 2 i i t 2 z t x t B where z t : vect. of predetermined variables (lags) x t : vect. of non-predet. variables e t : vect. of exogenous shocks Obtain a set of FOCs i t i t Ce t 14

15 Optimal Policy Model equilibrium conditions and FOCs: characterize equilibrium t, t, y t, y t, i t, i t Representation of optimal policy matters: e.g., i t i t j0 D j e tj generates an indeterminate equilibrium! An alternative: Manipulate FOCs to obtain policy rules 15

16 Robustly Optimal Rules BLP model with 1 2, h 0: FOCs can be expressed as i t i i t1 i t1 F t y F t y t q t where i t i i t1 i t1 F t y F t y t q t q t 1 2 sf 0 t s s1 F 1 t1 s t E t2 s t1 F t z j0 z,j E t z tj, y 0, i, 1 16

17 Properties of Robustly Optimal Rules i t i i t1 i t1 F t y F t y t q t i t i i t1 i t1 F t y F t y t q t Yield a determinate equilibrium Optimal Robust to the specification of shock processes 17

18 Conclusion BLP paper: very interesting analysis of indeterminacy in relevant open-economy model Important new results: indeterminacy more prevalent in open-economy model However conclusions limited to particular class of policy rules analyzed Can avoid indeterminacy problem by adopting optimal rule of a particular form 18

19 REFERENCES For derivation and properties of robustly optimal rules in general LQ framework: See Giannoni and Woodford, "Optimal Interest-Rate Rules: I. General Theory," NBER w.p. 9419, December For characterization of robustly optimal rule in model similar to "sum model" presented here: See Giannoni and Woodford, "Optimal Interest-Rate Rules: II. Applications," NBER w.p. 9420, December 2002, or "How Forward-Looking is Optimal Monetary Policy," forthcoming in Journal of Money, Credit, and Banking. 19