Steady State Analysis of an Open Economy General Equilibrium

Model for Brazil

Mirta Noemí Sataka Bugarin (Eco/UnB)Roberto de Goes Ellery Jr(Eco/UnB)

Victor Gomes Silva(UCB/UnB)Marcelo Kfoury Muinhos (DEPEP/Bacen)

Objective

• Numerical characterization of steady state equilibrium for an open general equilibrium model, parameterized for the Brazilian economy.

• Quantify how monetary and fiscal policies affect the model economy long-run equilibrium.

Main feature of the Model economy

• Transaction technology, Ljungqvist and Sargent (2001), is introduced in order to obtain monetary equilibrium.

• Production included in the model economy.

• Small open economy.

Model set up

• Households

),(max0

,,,, 011tt

t

t

bimhclcu

tdttttt

0)1.(. 11 tqP

mic

R

bts t

t

ttt

t

dt

t

tdtttttt P

mbkrhwq ])()[1(

s.t. (2) 1 = lt + ht + s(ct,,mt+1/Pt)

0/'/),/'(/;0)/'(/),/'(/,/,/ 22222 PmcsPmsPmsPmscscs

In particular transaction technology takes the form: s(ct, mt+1/Pt) = ct [1/(1+ mt+1/Pt)].

Given law law of motion for capital formation:

ttt ikk )1(1

as well as initial conditions (k0, m0, b0) > 0, assuming:

ttt lccu ln1ln)(

• Productive sector

Competitive firms, competitive factor’s market and constant return to scale technology:

)1(,1

1

tttt

tt

t

t

t

ttt

AkwkAr

AkH

KA

H

Y

HAKY

• Government

Tax revenue:

Seignorage:

Debt financing:

))(( ttttt khwT

t

tt

t

tt

t

t

t

t

t

t

t

t

t

tt

P

PRm

P

MRm

P

M

P

M

P

P

P

M

P

MMSt 111

1

11 ;

t

dt

dt

P

BBdbt

1

*1 )(

t

ft

ft

P

BBfbt

• Government (cont.)

Public expenses:

Assuming PPP holds, e($/R$)=P*/P.

Government budget constraint, all t ≥ 0:

*t

ftf

tt

dtb

ttttt P

Br

P

BrGsGsGcG

GsGcfbtdbtStTt

• Allocation of resources

Total production allocation:

Balance of Payment:

ttdtttt

fttt

dt

dt

ft

dtt

cmccygyygicy

yyy

;;;

ttt AccCapCABP .*t

ftf

ttt P

BrTBCA

*t

ftf

tttt P

cyMXTB *

1 )(.

t

ft

ft

t P

BBAccCap

Definition: competitive general equilibrium

Sequences of

0010100 ,/,, t

dttttt iandbPmhc , such that given

(i) exogenous sequences for 0

*00 ,, t

ft

ft Pry

and policy parameters, i.e.

,

Rm,,

0,0,0)/()/((ii) 0000 mkPbPB

(iii) the law of motion for assets

problem, sRF' thesolves

problem, sRA' thesolve and

,/, sequences The 1.

0101

01010

tt

tttt

kk

bPmc

ft

dtt yyy

=

rkwhTBigc tttt

0*

t

ftf

ttt P

BrTBCA

i.e., PPP. assuming satisfied, is

y consistenc agrgregate clear, markets All 2.

Strategy to compute GCE

• Formulate DPP.• Derive Euler equations (set of necessary

conditions) using differentiability property of Value Function.

• Obtain algebraic steady state solution for endogenous variables.

• Calibrate model economy with parameter values derived from observed economy.

• Compute numerical solution.

Parameterization

Parameters Values

Preferences = 0.6 ; = 0.96

Technology = 0.05; = 0.35; A = 1;

Fiscal and Monetary Policy

= 0.2; , = 0.17;

Long run relationships = 0.079; =0.09;

K/Y = 1.73

Foreign Variables rf = 5.03% ; P* = 1

Steady State Real Variables

Variable Value at Long Run Equilibrium

Capital Stock, k 3.1925

Aggregate Product, y 1.5012

Private Investment/Aggregate Output

0.1060

Real Wage 0.9758

Capital Real Rental Price

0.1646

Fig. 1 Aggregate Debt Output

Ratios at Alternative Steady States

Fig 2. Operational Deficit Output Ratio at Alternative Steady States

Fig. 3 Domestic Debt Output Ratio at

Alternative Steady States

Fig. 4 Seignorage Revenue, Operational Deficit and Aggregate Debt as Ratios to Aggregate Output at

Alternative Steady States

Fig 7 Tax rate, Interest Rate and D/Y

Fig. 8 Tax rate, Interest rate and Operational Debt – Output ratio.

Fig 9. Tax rate, Interest rate and Domestic debt – output ratio

Fig. 10 Seignorage, Operational Deficit and D/Y

Conclusion1. Under adopted parameterization, an aggregate D/Y ratio of 0.3387 is attained at the steady state equilibrium. This equilibrium is supported by a tax share on aggregate output of 17.87%, given a tax rate of 20% and a participation of government expenses of about 17% in aggregate output.

2. Simulation of alternative steady states has shown a clear trade off between higher interest rates (low inflation rates) and higher debt output ratios in the long run.

ExtensionExtensions to analyze short run dynamics of the system are under development. Impulse responses to demand shocks (via monetary policy interventions) and to supply shocks (via exogenous productivity shocks) can be introduced to compute a rational expectation competitive equilibrium.