Download Steady State Analysis of an Open Economy General

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

max


d 
ct , ht , mt 1 , it , b t 1 t 0
t

 u (ct , lt )
t 0
btd1
mt 1
s.t.(1)
 ct  it 
 qt
Rt
Pt
t  0
mt
qt  (1   )[ wt ht  (rt   )kt ]  b 
Pt
d
t
s.t. (2) 1 = lt + ht + s(ct,,mt+1/Pt)
s / c,  2 s / c 2 , s / (m' / P),  2 s / (m' / P) 2  0; s / (m' / P),  2 s / cm' / P  0
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:
kt 1  (1   )kt  it
as well as initial conditions (k0, m0, b0) > 0, assuming:
u (ct )   ln ct   1    ln lt

• Productive sector
Competitive firms, competitive factor’s market and constant return to
scale technology:
Yt  AK t H t1

 Kt 
Yt

 A


Ht
H
 t 
 Akt
rt  A kt 1 , wt  Akt (1   )
• Government
Tax revenue:
Tt   ( wt ht  ( t   )kt )
Seignorage:
St 
M t 1  M t M t 1 Pt 1 M t M t 1
M



Rmt  t ;
Pt
Pt 1 Pt
Pt
Pt
Pt
Debt financing:
Btd1  Btd
dbt 
Pt
( Bt f1  Bt f )
fbt 
*
Pt
Rmt 
Pt 1
Pt
• Government (cont.)
Public expenses:
Gt  Gct  Gst
d
f
B
B
Gst  rtb t  rt f t*
Pt
Pt
Assuming PPP holds, e($/R$)=P*/P.
Government budget constraint, all t ≥
0:
Tt  St  dbt  fbt  Gc  Gs
• Allocation of resources
Total production allocation:
yt  ytd  ytf
ytd  ctd  it  gt ; ytf   yt ; gt   yt ; ctd  ct  cmt
Balance of Payment:
Bt f
Pt *
BPt  CAt  Cap. Acct
CAt  TBt  rt
ctf
TBt  X t  M t  yt  *
Pt
( Bt f1  Bt f )
Cap. Acct 
Pt *
f
f
Definition: competitive general equilibrium
Sequences of
 c  , h  , m
t

0
t

0
t 1
(i) exogenous sequences for
and policy parameters, i.e.
 
/ Pt  0 , btd1 0 and  it  0 , such that given
y  , r  ,  P 
f 
t 0
 , , Rm
(ii) ( B / P)0  (b / P)0  0, k0  0, m0  0
,
(iii) the law of motion for assets
f 
t 0
* 
t 0
1. The sequences
and
c 
t
 kt 1 0 solve

0
,
 mt 1 / Pt  0 ,  bt 1 0
the RA' s problem,
 kt 1 0
solves the RF' s problem,
=
2. All markets clear, agrgregate consistenc y
is satisfied, assuming PPP. i.e.,
yt  ytd  ytf
CAt  TBt  rt
ct  gt  it  TBt  wh  rk
f
Bt f
0
*
Pt
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
Long run relationships
 = 0.2; ,
Foreign Variables
= 0.17;

= 0.079;  =0.09;
K/Y = 1.73
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/Aggrega
te 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
Conclusion
1. 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.
Extension
Extensions 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.