How tough should you beInflation targeting, fiscal feedbacks, and multiple equilibria

Alexandre Schwartsman

Unibanco

The model structure

Model consists of 2 blocks

The reaction function block

A “minimalist” inflation targeting model

1. Phillips Curve

2. “IS” function

3. Loss function

The fiscal/arbitrage block

Explicit modeling of:

1. Arbitrage between sovereign and risk –free debt instruments

2. Relationship between domestic interest rates, fiscal policy and

probability of default

Transmission mechanisms and efficacy usually

associated to parameters

The reaction function block - 1

Phillips curve

“IS” function

Loss function

ttttt ey 1

ttttt rEiy

0

2

nnt

ntEL

The reaction function block - 2

Modeling the exchange rate requires 2 assumptions

Uncovered interest parity

Mean reversal

Thus, the current exchange rate behavior is given by

*1 ttt iie

11 tt eee

ttt iie *

The reaction function block - 3

Reduced form for the Central Bank’s reaction function

11

* )( tttt

iri

i TR

i*

The fiscal/arbitrage block

Assume 2 other assets, in addition to the local bond

Risk-free bond with yield iUS

Risky sovereign bond with yield i*

Risk neutral agents equate expected return

where (1-) is the probability of default

USii *

Modeling the default risk - 1

1. Primary surplus is random variable with support [sL, sH]

2. Default rule: if primary surplus is higher than real debt service [s (i-)b], pay; otherwise total default

Zero probability of default

100% probability of default

0)( 1 tLL bissP 1t

LL b

si

1)( 1 tHH bissP 1t

HH b

si

Modeling the default risk - 2

Repayment probability can be expressed as a function of domestic interest rate

0)(;0)(

;0)(

;1)(

iiiii

iii

iii

HL

H

L

(i)

"<0

" = 0

iL iH i

Arbitrage

The arbitrage equation then becomes

USiii )(* )( *ii

0)(

)(*

ii

i

02*

2*

i

i

*lim iHii

LUS iiii ;*

iiH

SS

iL

iUS i*

Multiple equilibria and stability

i TRiH

iBAD SSB

iGOOD A

iL

iUS i*GOOD i* i*BAD

i TRiH

SSB

A

iL

iUS i*

Comparison to standard case

Interest rates are higher than in standard case (exogenous i*)

Fiscal feedback reduces efficiency of monetary policy instrument

i

SS (standard) TR

i*iUS

SS (feedback)

Comparative staticsi TRiHiH' SS

B SS'B'

A'A

iLiL'

iUS i*

i TRiH

SSB

A'A

iLSS'

iUS iUS ' i*

TR'i TRiH

B' SSB SS'

A'

A

iL

iUS i*

TR'i TRiH

B' SSB SS'

A'

A

iL

iUS i*

Fiscal policy Risk-free rate

ShocksUsual

transmission channels

Existence

For simplicity assume primary surplus uniformly distributed

H

L

HLLH

H

iii

iii

iiiii

iii

;0)(

;1)(

;)(

USLHtt

H

iiiri 4

)(2

11 c

1

11)(2

t

HttUS

LHc

b

sriii

Implication of inflation “floor”Setting the inflation target below the critical

threshold implies no possible equilibrium

i TRiH

SS

iL

iUS i*

Determinants of inflation “floor”

Inflation floor depends essentially on 3 determinants

1. Primary surpluses2. Public debt

3. Size of supply and demand shocks

1

11)(2

t

HttUS

LHc

b

sriii

Unstable equilibrium properties

“Bad” equilibrium associated to weaker currency due to higher interest rate

differential

i TRiH

iBAD SSB

iGOOD A

iL

iUS i*GOOD i* i*BAD

Bizarre shock responses

Responses to fiscal policy and shocks at odd with the data

i TRiHiH' SS

B SS'B'

A'A

iLiL'

iUS i*

TR'i TRiH

B' SSB SS'

A'

A

iL

iUS i*

Saddlepath properties?

Model does not have saddlepath properties, that is, Central Bank behavior is myopic

(converges to stable equilibrium)

If Central Bank were to choose the equilibrium, why would it choose the “bad” one?

i TRiH

SSB

A

iL

iUS i*

Extension

Possibility of further equilibria, depending on primary surplus distribution (if second order

condition fails)Stable high-interest rate equilibrium (C)

i

C TR

SSB

A

i*iUS

Concluding remarks

1. Multiple equilibria, at least in this setting, do not seem to be the cause behind high real interest rate

2. Fiscal feedbacks, nonetheless, imply higher interest rates than standard exogenous interest rate case

3. Feedbacks depend on sensitivity of default likelihood to domestic interest rates, which is an empirical issue. Other forces may be at work (global “risk aversion”)

4. Future direction of research: Central Bank reaction when output gap enters loss function; possibility of further equilibria depending on the primary surplus distribution