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Samba: Stochastic Analytical Model with a BayesianApproach
DSGE Model Project for Brazil�s economy
Working in Progress - Preliminary results
DSGE team: Solange Gouvea, André Minella, Rafael Santos,Nelson Souza-Sobrinho, and Tomiê Sugahara
Banco Central do Brasil �Research DepartmentX Seminar on In�ation Targeting
August 4th, 2008
Purposes of the project
� Provide the Banco Central do Brasil with a Dynamic Stochastic General Equi-librium (DSGE) model to be used as a tool for:
� policy analysis
� framework for policy discussions; qualitative and quantitative assessmentof shock e¤ects, monetary policy decisions and di¤erent scenarios, etc.
� medium-term forecast
� �All models are wrong! Some are useful�George Box
� Models and judgement are complements, not substitutes
Model features
� Microfounded model developed for the in�ation targeting period (started inmid-1999)
� Small open economy model
� Aggregate demand (C + I + G + X - M):
� Households -> private consumption and investment
� Firms -> import demand
� Government -> government consumption
� Rest of the world -> export demand
Model features
� Supply side (Y)
� Competitive �rms -> assemble di¤erentiated goods supplied by monopo-listic competitive �rms and sell them in
� Local markets (domestic consumption and investment goods)
� Abroad (export goods)
� Monopolistic competitive �rms -> production of di¤erentiated goods
� Inputs: labor, capital services, and imports
� Price rigidity (à la Calvo) with forward- and backward-looking behavior(Galí and Gertler, 1999)
Model features
� Government:
� Monetary policy: Taylor rule
� Fiscal policy rule
� Rest-of-the-world variables: interest rate, in�ation, world imports, and foreigninvestors�"risk aversion".
Main loglinear equations
� Aggregate Demand: Consumption
� Optimizing households
cot =�
1
1 + h
�Et�cot+1
�+�
h
1 + h
�cot�1 �
1
�
�1� h
1 + h
�Et (rt � �t+1) +
:::+1
�
�1� h
1 + h
�(1� �c) z
ct
� Rule-of-thumb households
crott = wrt + nrott
� Aggregate consumption
ct = (1�$c) cot +$cc
rott
rt - interest rate; �t - in�ation; zct - shock to consumption;wrt - real wages; n
rott - employment
� Aggregate Demand: Investment:
it =1
�s (1 + �)qIt +
�
1 + �Etit+1 +
1
1 + �it�1 +
1� �I�
1 + �
!zIt
Shadow price of capital
qIt = Etn� (1� �) qIt+1 + (1� �(1� �)) brkt+1 � (rt � �t+1)
o
� Aggregate Demand: Net Exports
� Exports
xt = m�t + {qt
� Imports
mt = yt � % (qt �mct)
brkt - rental rate of capital; zIt - shock to investment; m�t - world imports;qt - real exchange rate; yt - (gross) output; mct - real marginal cost
� Aggregate Supply
� Production function
yt = f (kt; ut; nt;mt; at)
� Labor market
� Labor supply
nt = (1�$n)not +$nn
rott
� Labor demand
nt = yt � [(1� %) + %sd] at � [�+ % (1 + sd) (1� �)]wrt +
+� [1� % (1� sd)] rkt + %(1� sd)qt
kt - physical capital; ut - rate of capital utilization; at - productivity shock
� Capital services
� Demand
kt + ut = yt � [(1� % (1� sd)] at � [(1� �) + �% (1� sd)] brkt +:::+ (1� �) [(1� % (1� sd)]w
rt + %(1� sd)qt
� Supply
ut =1
�abrkt
� Law of motion for capital
kt+1 = (1� �)kt +�I
K
�it
� Phillips curve
�t = �mct + �b�t�1 + �fEt�t+1
where:
mct = sdh�brkt + (1� �)wrt � at
i+ (1� sd)qt
��; �b; �f
�= f (�;$b; �)
� Financial variables
� Real exchange rate (UIP)
qt = Etqt+1 �h�rt � Et�t+1)� (r�t + �t � Et�
�t+1
�i� Country-risk premium
�t = � by�t+1 + �z
��t + z
�t
r�t - world interest rate; ��t - world in�ation;
z��t - international investors�risk averstion; z�t - shock to country-risk premium
� Government
� Monetary policy (Taylor rule)
rt = rrt�1 + (1� r)h �Et (�t+1 � �t+1) + �t + yy
V At
i+ zrt
� Fiscal policy rule
gyt = gg
yt�1 +
�1� g
� � sbsyt�1 � bb
yt
�+ z
gt
�t - in�ation target; zrt - shock to monetary policy;gyt - government consumption-to-GDP ratio; s
yt - primary �scal surplus target;
zgt - shock to �scal policy; bsyt�1 - primary �scal surplus deviation from the target
� Shocks and rest-of-the-world variables:
zt = �zt�1 + "t
� Value added (GDP) - Equilibrium:
yV At = scct + siit + sggt + sxxt � smmt
Estimation technique
� Bayesian estimation:
Estimated parameter distribution = prior distribution + likelihood information fromthe data
It is a bridge between calibration and maximum likelihood
Results: Model + Data + Priors
Estimation
� Sample period: 1999Q2 to 2008Q1 (36 obs)
� Data: 25 series:
� Data treatment: HP �lter
� Number of model parameters: 58
� 41 estimated: 17 structural parameters and 24 shock parameters
� 17 calibrated: 3 structural parameters and 14 steady-state relationships
Posteriors distributions for selected parameters
0 0.2 0.4 0.6 0.80
2
h
0 0.2 0.4 0.6 0.80
2
h
0.4 0.6 0.8 10
10
θ
0.4 0.6 0.8 10
10
θ
1 1.5 20
1
2
γπ
1 1.5 20
1
2
γπ
Challenges
� Common to DSGE models and their estimation:
� Generation of slower and more persistent dynamics (enough propagationmechanisms, lags in the transmission mechanisms, etc.)
� Identi�cation of the main model channels in place
� Large number of parameters to be estimated �calibration versus estimation
Challenges
� Brazilian economic features:
� Small sample size
� Speci�c features: administered prices
� Large changes in some ratios over the sample (ex.: net external debt-to-GDP ratio)
Next steps
� Re�ning model setup:
� Add nominal and real rigidities: wage rigidity, price rigidity in the importand export sectors, �rm-speci�c capital
� Disaggregate CPI in�ation into administered and non-administered prices
� New estimation and model implementation