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.