Optimal Monetary and Fiscal Policy at the ZLB in a Small Open Economy

Optimal Monetary and Fiscal Policy at the ZLB in a Small Open Economy

Saroj Bhattarai Konstantin Egorov

Pennsylvania State University

Norges Bank/HEC Montreal Workshop on

New Developments in Business Cycle Analysis June 20, 2014

Motivation-Data

I ZLB a concern recently for several SOEs

Motivation-Data

I Real exchange rate appreciation

Motivation-Theory

I Large recent literature on policy implications of hitting the ZLB

I Negative output gap and de‡ation; govt spending powerful; credibility problem of optimal commitment policy severe

I This literature typically discards the open-economy aspect

I Allow for non-trivial open-economy aspects in a SOE model

I No restrictive parameterization (log utility and unit trade elasticity)

I Do not shut down the terms of trade externality (no balanced trade)

I Open economy problem no longer “isomorphic” to the closed economy

Research Questions

I How does trade elasticity a¤ect outcomes at the ZLB?

I Comparison of optimal policy under commitment and discretion

I What is the role played by (real) exchange rate dynamics in ZLB?

I In addition to the “de‡ationary bias” of discretionary policy at the ZLB, what new “bias” emerges in an open economy?

I Joint consideration of optimal monetary and …scal policy

I What is the role for govt spending at the ZLB?

I How does trade elasticity a¤ect the extent of increase in govt spending?

Households

I Two-country model with a limiting case of a “small open economy”

I Foreign variables exogenous

I Representative household at home maximizes Et

X1 s=0

s u Ct+s; _t+s Z 1

0

v ht+s(i); _t+s di

I Consumption good is an aggregate of home and foreign goods

Ct = (1 )¹ C

1

H;t + ¹C

1 F;t

1

; Pt =h

(1 )P_H;t¹ + P_F;t¹ i₁¹ I C_H;t andC_F;t in turn aggregates of a continuum of varieties with an

elasticity of substitution"

I Perfect international risk-sharing

Firms

I Continuum of …rms produce di¤erentiated varieties y_t(i) =f(h_t(i); _t)

I Dynamic price-setting problem due to adjustment costsd _p^pH;t(i)

H;t 1(i) I The …rm maximizes (steady-state production subsidy(1+s))

E_t X1 s=0

t;t+sZ_t+s(i)

Z_t(i) = (1+s)p_H;t(i)y_t(i) n_t(i)h_t(i) d p_H;t(i)

p_{H;t 1}(i) P_H;t

I Focus on a symmetric equilibrium

International Pricing

I No price discrimination

p_H;t(i) =Stp_H;t(i); p_F;t(i) =Stp_F;t(i)

whereSt is the nominal exchange rate

I PPP does not hold because of “home bias”

I De…nitions of the real exchange rate(Q_t) and the terms of trade(&_t) Q_t = StP_t

P_t ; &_t = PF;t

P_H;t

I Re-write

r(&_t) = P_t PH;t

; Q_t = &_t

r(&t) =q(&_t)

Private Sector Equilibrium

I Asset-pricing condition

1 1+it

=Et

"

uC Ct+1; _t+1 uC(Ct; _t)

1 t+1

#

; it 0 I Optimal pricing equation

"Yt

" 1

" (1+s)uC(Ct; _t) ~vy(Yt; _t)r(&t) +uC(Ct; _t)d⁰( H;t) H;t

= Et uC Ct+1; _t+1 r(&t)

r(&t+1)d⁰( H;t+1) H;t+1

I International risk-sharing

q(&t) =uC(Ct; _t) uC(Ct; _t) I Accounting

t H;t

= r(&t) r(&t 1)

Government and Market Clearing

I Government budget constraint (lump-sum taxes) B_t = (1+i_{t 1})B_{t 1} P_tT_t

I Resource constraint and net exports

Yt = (1 )r(&t) Ct + &_tC_t +d( H;t)

NX_t = (YtP_H;t CtPt)

P_H;t = (Y_t C_tr(&_t))

E¢ cient Equilibrium (First-best)

I The SOE planner maximizes

u(Ct; _t) v~(Yt; _t)

st

Y_t = (1 )r(&_t) C_t + &_tC_t

q(&t) = uC(C_t; _t) u_C(Ct; _t)

I Solution can be characterized in closed-form

I Important benchmark for later as we express “gaps” as deviations from the e¢ cient equilibrium

Commitment Equilibrium (Ramsey)

I The central bank maximizes Et

X1

s=0

su Ct+s; _t+s v Y~ t+s; _t+s st

"Yt

" 1

" (1+s)uC(Ct; _t) v~y(Yt; _t)r(&t)

= r(&t)Et uC Ct+1; _t+1 d⁰( H;t+1) ^H;t+1

r(&t+1) uC(Ct; _t)d⁰( H;t) H;t

1 1+it

= Et

"

uC Ct+1; _t+1 uC(Ct; _t)

1 t+1

#

; it 0 Yt = (1 )r(&t) Ct+ &_tCt +d( H;t) q(&t) = uC(Ct; _t)

uC(Ct; _t)

I Dynamic time-inconsistency due to forward-looking variables

Discretion Equilibrium (Markov)

I The central bank maximizes

u(Ct; _t) ~v(Yt; _t) st

"Yt

" 1

" (1+s)uC(Ct; _t) v~y(Yt; _t)r(&t)

= r(&t)Et uC Ct+1; _t+1 d⁰( H;t+1) ^H;t+1

r(&t+1) uC(Ct; _t)d⁰( H;t) H;t

1 1+it

= Et

"

uC Ct+1; _t+1 uC(Ct; _t)

1 t+1

#

; it 0 Yt = (1 )r(&t) Ct+ &tCt +d( H;t) q(&t) = uC(Ct; _t)

uC(Ct; _t)

I Period-by-period problem and take expectations as given

Functional Forms

I Period-utility

u(C; ) = ^CC¹

1 ; v(h(i); ) = ^Ch(i)¹⁺

1+

I Production function

y(i) = ^Ph(i)

I Price-adjustment cost

d( _H) =d₁( _H 1)²

I Shocks

P

t = ^P_{t 1}+"^P_t

C

t = ^C_{t 1}+"^C_t

Steady-State and Subsidy

I We consider a non-stochastic steady-state

I Linearize around this steady-state to analyze dynamic responses to shocks

I Allow an appropriate production subsidy such that the First-best, Ramsey, and Markov steady-states coincide

I Convenient choice to compare various equilibria

I In this (symmetric) steady-state

I H = =&=1;(1+i) ¹= ;C =C =Y =1; and =1

Steady-State and Subsidy

Theorem

The following production subsidy ensures that the First-best, Ramsey, and the Markov steady-states coincide

1+s =h

1 (1 )² + (1 )²i 1

(1 ) "

" 1 :

I Previous literature

I Closed-economy ( =0); Gali and Monacelli (2005) ( = =1)

I Farhi and Werning (2012)

I Accounts for both “internal” and “external” distortions

I The weight on the terms of trade externality depends on openness

I Higher and lead to terms of trade appreciation motive

I Subsidy is higher than(1 )_"^"₁ when <1

Private Sector Equilibrium

I Linearized PSE (“canonical” representation)

^

xt =Etxt+1^

(1 )

^

r_t^gap+ 2

1 ^q_t^gap Et^q_t^gap₊₁

^{t 1 1

^_H;t = E_t^_H;t+1+ ₁x^_t + ₂^q_t^gap+ ₃^^P

t

^

x_t = 2

1 + 1

1

1 ^q_t^gap

^_t = ^_H;t +

1 q^^gap_t ^q_t^gap₁ + ₄ ^^P

t ^^P

t 1

where ₃=0 under = =1.

Optimal Targeting Rule-Commitment

Theorem

The targeting rule under commitment takes the form of a time-varying price level target where the central bank chooses it to achieve

pH;t =pH;t+ ~

~~xt

if possible. Otherwise, it sets it =0:The target for next period is determined as pH;t+1=pH;t+1+ ~ ~

~ pH;t pH;t

~

~xt 1

~ pH;t 1 pH;t 1

~

~xt 1 : Here,

~

xt = 1x^t+ 2^q^gapt + 3^^P

t

^

xt = 2

1 + 1

1

1 q^^gapt

where 3=0under = =1.

Optimal Targeting Rule-Discretion

Theorem

The targeting rule under discretion takes the form of an in‡ation target where the central bank chooses i_t to achieve

^_H;t = ^_H;t + ~

~x~t =0 if possible. Otherwise, it sets i_t =0:Here,

~

x_t = ₁x^_t+ ₂^q_t^gap+ ₃^^P

t

^

x_t = 2

1 + 1

1

1 q^^gap_t

where ₃=0under = =1.

Calibration

I Standard calibration (Faia and Monacelli (2008)) Parameter Value Parameter Value

0.99 0.7, 1, 2

1 1

0.4 d₁ 75/2

3 " 7.5

I Deterministic simulation where a large one-time unexpected shock ( =0:95) makes the ZLB bind

I Piece-wise linear algorithm with guess-and-verify for duration of ZLB

I Follow Jung, Teranishi, and Watanabe (2005)

Commitment-Role of Trade Elasticity

10 20 30 40

0 0.2 0.4 0.6 0.8

Panel A: Conventional Variables 1. i (Nominal Interest Rate, in levels)

% points

10 20 30 40

-0.20 0.00 0.20 0.40

2.Π_H (Home Inflation)

% points

10 20 30 40

-2 -1 0 1

3. Ygap (Output gap)

%

10 20 30 40

-1.2 -1 -0.8 -0.6 -0.4 -0.2

Time

4. reff (Efficient Real Interest Rate)

% points

10 20 30 40

0 0.2 0.4

Time

5. rgap (Real Interest Rate Gap)

% points

η=0.7 η=1 η=2

Commitment-Role of Trade Elasticity

10 20 30 40

5 10 15 20 25

Panel B: Open Economy Variables 1. qeff (Efficient Real Exchange Rate)

%

10 20 30 40

-1.5 -1 -0.5 0

2. qg ap (Real Exchange Rate Gap)

%

10 20 30 40

-5 0 5 10

Time 3. nx_eff (Efficient Net Exports)

% of output

10 20 30 40

0 0.1 0.2 0.3 0.4 0.5

Time 4. nx_{g ap} (Net Exports Gap)

% of output

η=0.7 η=1 η=2

Discretion-Role of Trade Elasticity

10 20 30 40

0 0.2 0.4 0.6 0.8

Panel A: Conventional Variables 1. i (Nominal Interest Rate, in levels)

% points

10 20 30 40

-30 -20 -10 0

2.Π_H (Home Inflation)

% points

10 20 30 40

-40 -20 0

3. Y_{g ap} (Output gap)

%

10 20 30 40

-1.2 -1 -0.8 -0.6 -0.4 -0.2

Time

4. r_eff (Efficient Real Interest Rate)

% points

10 20 30 40

0 5 10

Time 5. rg ap (Real Interest Rate Gap)

% points

η=0.7 η=1 η=2

Discretion-Role of Trade Elasticity

10 20 30 40

5 10 15 20 25

Panel B: Open Economy Variables 1. qeff (Efficient Real Exchange Rate)

%

10 20 30 40

-30 -20 -10 0

2. qg ap (Real Exchange Rate Gap)

%

10 20 30 40

-5 0 5 10

Time 3. nx_eff (Efficient Net Exports)

% of output

10 20 30 40

0 5 10

Time 4. nx_{g ap} (Net Exports Gap)

% of output

η=0.7 η=1 η=2

Commitment vs. Discretion

I =1 and iid shock (lack of history dependence)

2 4 6 8 10

0 0.5 1

P ane l A: Conventional Variable s 1. i (Nom inal Intere st Rate , in levels)

% points

2 4 6 8 10

-8 -6 -4 -2 0 2

2.Π_H (Hom e Infla tion)

% points

2 4 6 8 10

-30 -20 -10 0

3. Y_gap (Output ga p)

%

2 4 6 8 10

-20 -10 0

Time

4. r_eff (E fficient Rea l Intere st Rate )

% points

2 4 6 8 10

0 10 20

Time

5. r_gap (Re al Intere st Rate Ga p)

% points

Commitment Discretion

I Usual “de‡ation bias” of discretionary policy

Commitment vs. Discretion

I =1 and iid shock

2 4 6 8 10

0 5 10 15 20

P ane l B: O pen Economy Variables 1. q_eff (E ffic ie nt Re a l E xc ha nge Rate )

%

2 4 6 8 10

-20 -15 -10 -5 0

2. q_gap (Re a l E xc hange Rate Ga p)

%

2 4 6 8 10

0 0.2 0.4 0.6 0.8 1

Time 3. nx

eff (E ffic ient Net E xports)

% of output

2 4 6 8 10

0 0.2 0.4 0.6 0.8 1

Time 4. nx

gap (Ne t E xports Ga p)

% of output

Commitment Discretion

I New “overvaluation bias” of discretionary policy

Optimal Monetary and Fiscal Policy

I Discretion outcomes worse but commitment policy is time-inconsistent

I Allow for optimal govt spending under discretion

I Govt spending yields utility

I u Ct+s; _t+s R1

0 v ht+s(i); _t+s di +g Gt+s; _t+s

I Govt spending an aggregate of the two goods

I Gt = (1 )¹ G

1

H;t + ¹G

1

F;t

1

I Main mechanism

^r_t = _yh

Y^_t E_tY_t^₊₁i

+ _Gh

G^_t E_tG_t+1^ i

Optimal Monetary and Fiscal Policy-Discretion

I Countercyclical govt spending (level depends on )

10 20 30 40

1 2 3 4 5

Pa nel C: Fiscal Va riables

Time

1. G_eff (Efficient Government Expen ditures)

% of output

10 20 30 40

0 5 10 15

Time

2. G_gap (Governmen t Expend itu res Gap)

% of output

η=0.7 η=1 η=2

Optimal Monetary and Fiscal Policy-Discretion

I Comparison with setting govt spending equal to e¢ cient level ( =0:7)

10 20 30 40

0 0.2 0.4 0.6 0.8

Panel A: Conventional Variables 1. i (Nominal Interest Rate, in levels)

% points

10 20 30 40

-20 -10 0

2.Π

H (Home Inflation)

% points

10 20 30 40

-30 -20 -10

3. Y_{g ap} (Output gap)

%

10 20 30 40

-1.2 - 1 -0.8 -0.6 -0.4 -0.2

Time

4. r_{ef f} (Efficient Real Interest Rate)

% points

10 20 30 40

2 4 6 8

Time 5. rg ap (Real Interest Rate Gap)

% points

Optimal polic y Zero G gap

Optimal Monetary and Fiscal Policy-Commitment

10 20 30 40

1 2 3 4 5

Panel C: Fiscal Variables

Time

1. G_eff (Efficient Government Expenditures)

% of output

10 20 30 40

0 0.5 1 1.5

Time

2. G_{g ap} (Government Expenditures Gap)

% of output

η=0.7 η=1 η=2

Conclusion

I ZLB leads to an appreciated real exchange rate

I Negative outcomes are more severe with lower trade elasticity

I Discretionary policy su¤ers from an “overvaluation” bias

I Countercyclical govt spending is optimal …scal policy response

I The increase in govt spending is lower with higher trade elasticity

Related Literature

I Optimal targeting rule under commitment in ZLB

I Eggertsson and Woodford (2003) (price level target)

I Comparison of commitment with discretion in ZLB

I Eggertsson (2006) (de‡ation bias)

I Optimal monetary and …scal policy in ZLB

I Eggertsson (2001) and Werning (2011)

I Optimal monetary policy in a small open economy without ZLB

I Gali and Monacelli (2003) (restrictive parameterization)

I Faia and Monacelli (2008) and De Paoli (2009) (generalization)

I Optimal monetary policy in a small open economy in ZLB

I Svensson (2002) (without welfare-theoretic loss function)

Future work

I Law of one price deviation in traded goods

I Departure from perfect risk-sharing across countries

I Could …xed exchange rates be optimal under discretion?

I Optimal choice of composition of govt spending?