Robust Monetary Policy

Student: Adam Altar – SamuelCoordinator: Professor Ion Stancu

Robust control

Allows policymakers to formulate policies that guard against model misspecification.

Provides a set of tools to assist decisionmakers confronting uncertainty.

Allows private agents to express concern, or pessimism, when forming expectations.

Relevant literature

Hansen and Sargent (1999, 2001, 2002, 2006)

Svensson (1997) Dennis, Leitemo and Soderstrom (2004,

2005, 2006) Giordani and Soderlind (2004)

Robust control problems

can be solved using: State – space methodsStructural methods

Two distinct equilibria of interest:“Worst – case” equilibrium“Approximating” equilibrium

“Worst – case” equilibrium

is the equilibrium that pertains when the policymaker and private agents design policy and form expectations based on the worst-case misspecification and the worst-case misspecification is realized

“Approximating” equilibrium

is the equilibrium that pertains when the policymaker and private agents design policy and form expectations based on the worst-case misspecification, but the reference model transpires to be specified correctly

State – space form

(1)

(2)

where zt - vector of endogenous variables

,2maxmin0

110

ttttttttt

t

vuvvQuuUuzRzzE

tt

111~

ttttt CCvBuAzz

State – space form

ut – vector of control variables εt – vector of white – noise innovations vt+1 – vector of specification errors θ – shadow price, inversely related to the

budget for misspecification

Structural form

(3)

(4)

,4312110 tttttt AuAyEAyAyA

,][maxmin0

0

ttttttt

t

vuvvQuuWyyE

tt

An empirical New Keynesian model

Variables:π – inflation ratey – output gap i – interest rateεπ – supply shockεy – demand shock

Equations

(5)

(6)

Objective function:(7)

tttttt yE ,11 )1(

tyttttyttyt EiyEy ,111 )()1(

0

2220}{

)(mint

tttt

iviyE

t

Solution method

The problem is, both in the nonrobust and in the robust case, a discrete – time stochastic LQ problem.

The optimal control is given by (8)

where F is the optimal feedback matrix.

ttt KzFzu

Solution method

In the nonrobust case:

In the robust case:

tt iu

1,

1,

ty

t

t

t

vvi

u

ResultsInflation responses to unit supply shock

Nonrobust Robust

ResultsOutput gap responses to unit supply shock

Nonrobust Robust

ResultsInterest rate responses to unit supply shock

Nonrobust Robust

ResultsInflation responses to unit demand shock

Nonrobust Robust

ResultsOutput gap responses to unit demand shock

Nonrobust Robust

ResultsInterest rate responses to unit demand shock

Nonrobust Robust

Conclusions

In the robust case, the optimal policy of the central bank is more activist than in the nonrobust case