by Richard Mash Ulf S oderstr om IGIER, Bocconi University

June 2007

The issue

I How explain the behavior of in ation over the business cycle? I Standard sticky-price models (NKPC) counterfactual: I Disin ation costless I In ation not persistent I In ation jumps in response to shocks

I Mankiw (2001): \Although the NKPC has many virtues, it also has one striking vice: It is completely at odds with the facts."

The issue

I Quick x: some prices indexed to past in ation

Gal and Gertler (1999), Christiano, Eichenbaum and Evans (2005)

I Empirical criticism: hard-wires in ation persistence

In practice, in ation persistence depends on monetary regime Ball (2000), Mankiw and Reis (2002), Benati (2007) I Ball, Mankiw and Reis (2002): \Yet this compromise [the hybrid NKPC] may yield the worst of both worlds. Like the NKPC, the hybrid model yields an immediate jump in in ation in response to monetary policy shocks (unless all agents are backward looking). Like the accelerationist Phillips curve, the hybrid model fails to explain the absence of in ation inertia under earlier monetary regimes (unless no agents are backward looking). That is, by taking a weighted average of two awed models, the hybrid model of the Phillips curve ends up with the

aws of each."

This paper

I Theoretical/methodological criticism of indexing models: ad hoc

schemes, not optimal given constraints

I GG and LAPI models constrained optimal (t 1 only state) LOPI model not constrained optimal

I Optimal indexing ) depends on in ation persistence

I Hybrid NKPC with exogenous indexing not structural, vulnerable to Lucas critique I Utility-based welfare criteria with constant indexing may be misleading

I Optimal indexing ) no in ation persistence in equilibrium I Model

Comment 1: Methodology

I Using ad hoc rule rather than optimal behavior given constraint can be misleading

I Lucas (1980): \I am attracted to the view that it is useful, in a general way, to be hostile toward theorists bearing free parameters. . . "

I What constraints could lead rms to use simple rules of thumb? Costs of optimization, or information collection? I Learning (Honkapohja and Evans, Milani) I Rational inattention (Sims, Woodford, Ball, Mankiw-Reis)

I Indexing simpli cation, perhaps misleading I But more important than other simpli cations?

Comment 2: Utility-based welfare criteria

I Models are simpli ed descriptions of reality, misspeci ed by construction

I I I I

Utility-based welfare criteria should be handled with care Useful to understand welfare implications of distortions Careful with practical policy advice Is indexation more misleading than other simpli cations?

Comment 3: The Lucas critique

I Many model features are not really structural, e.g., time-dependent price-setting

I Does this matter in practice? Empirical issue I Empirical support for Lucas critique mixed

(Linde, 2001; Rudebusch, 2005; Lubik-Surico, 2006)

I Size matters:

I Modest interventions: 25 basis points I Large-scale regime shifts

Comment 4: Can the hybrid NKPC lead us wrong?

I Sometimes the degree of persistence really matters I In ation target v. Price level target I The value of commitment: publishing interest rate forecasts

I Degree of indexation signi cant ) CB may erroneously conclude that the value of commitment is small, price level target welfare-reducing

I What if persistence is endogenous? I Ball, Mankiw and Reis (2002): Flexible price level target optimal I Williams (2006): Learning can undermine the eectiveness of price level target

Final words

I I I I

Interesting and thought-provoking paper Most results intuitive, some (zero persistence) less so Potentially important policy implications Call for more research

The model

I Calvo price setting: each rm faces constant probability 1 of being allowed to change its price in a given period

I Some rms set price as a function of past in ation (rule of thumb) I Here: Firms choose degree of indexation optimally given constraint on price setting

Three indexing schemes

I GG (1999): Fraction 1 ! of Calvo rms set optimal price xt , fraction ! index to past in ation, non-Calvo rms keep prices xed xjr;t = pt 1 + r t 1 (1) pt = (1 ) [(1 ! )xt + ! xtr ] + pt 1 (2) I CEE (2005): Non-Calvo rms index price to own price and past in ation (LOPI)

xjc;t pt

= xjc;t 1 + c t 1 = (1 )xt + xtc

(3) (4)

I Alternative CEE (LAPI): Non-Calvo rms index price to aggregate price and past in ation

xja;t pt

= pt 1 + a t 1 = (1 )xt + xta

(5) (6)

The model

I Real marginal cost

mt

= yt + "t

(7)

I Reduced form in ation and output gap t = t 1 + k "t yt = y t 1 + c "t

I Optimal Calvo price xt

= (1

)Et

X1 [ + + j

j

I Optimal exible price

xt

j

=0

= p t + mt

pt

j

(8) (9)

mt +j ]

(10)

(11)

Optimal indexing

I Firms choose degree of indexation such that = Et 1 xt

(12)

+ (1 )y 1

(13)

xj ;t

I GG model:

r =

I CEE LAPI model ( exible prices):

a = + y

I GG and LAPI models constrained optimal (t 1 only state) LOPI model not constrained optimal

I Optimal degree of indexation depends on in ation persistence

(14)

Phillips curves

I All schemes imply hybrid Phillips curves of the form t = f Et t +1 + b t 1 + (yt + "t )

(15)

All parameters depend on degree of indexation, which depends on in ation persistence

I Phillips curve models vulnerable to Lucas critique I Utility-based welfare criteria with constant indexation may be misleading

I Intuitive results

Reduced-form solutions

I Weak assumptions on monetary policy:

I Monetary policy does not introduce new state variables I No indexation ) No persistence I Monetary policy leans against the wind: > 0 ) y < 0 I LAPI: 1 = a + y (16)

I I I I

a = + y Only equilibrium: a = = y = 0

GG: Similar result No persistence in equilibrium Less intuitive Comments

(17)