Introduction to a Small Macro Model
EVROPSKÝ SOCIÁLNÍ FOND
PRAHA & EU
INVESTUJEME DO VAŠÍ BUDOUCNOSTI
Jiri Lukac
jiri.lukac@gmail.com
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Outline
• Motivation
• Economic Background
• New Keynesian Theory
• Lucas Critique
• Model Equations in our Model
• Conclusion
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Motivation
• The model enables to produce economically consistent projections
• Without model, the forecast is purely an extrapolation of historical data or
judgements
• The model is built to be transparent and simple
• Central Bank models usually much more complicated
• Broader analysis and judgments can be incorporated in the forecast
• The model provides (i) common language and represents (ii) a
consensual view on the transmission mechanism
• Used for forecasting and monetary policy analysis (FPAS)
• „The only function of economic forecasting is to make astrology look
respectable.“ J.K. Galbraith (US Canadian-born economist)
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Economic Background
• The model is based on New Keynesian theory
• Nominal and real rigidities
• Monopolistic competition and sticky-prices in the short-run
• Rational expectations
• Derived from microeconomic foundations
• But...coefficients are not derived from the microfounded model or
using econometric approach
• We uses a semi-structural or ‚gap‘ model
• Low maintanace cost
• Very flexible and intuitive
• Easy to calibrate
• Mainly medium-term forecasting
• Equations in log-linearized form
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Economic Background (ii)
• Model ...
• ... is structural
• Every equation has economic interpretation
• ...is general equilibrium
• supply = demand
• ... is stochastic
• Random shocks affect each endogenous variable
• ... incorporates rational expectations
• There is no way to consistently fool economic agents
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Lucas Critique
• Lucas improved the use of conventional models
• His legacy: the expectation of the individuals about the system has
to be incorporated in the model
• Expectation is a social behaviour
• With an change of the regime, the individuals also change their
expectations
• Most economic decision are forward looking
• Forward looking model vs econometric model
• Without rational expectation the model can‘t be good for mediumup-to-long-term
forecasting
• Might lead to wrong calibration
• This type of model is immune towards Lucas critique
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Model Equations in our Model (i)
• Works with only flow variables and has an exogenously
well-defined long-run “steady-state” (equilibrium/trend)
• It analyses the business cycle around the “steady-state”
(trend) values using “gaps”
• A “gap” is deviation of a particular variable from the
“steady-state” (trend) value
• Log-linearized approximation
ttttt ylylyyy __)/log(*100ˆ 
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Model Equations in our Model (ii)
• A core model consists of 4 main behavioral equations:
• Agregate demand (Real sector)
• Agregate supply (Real sector)
• Uncovered interest parity (UIP)
• Policy Rule
• ...and External equations plus identities.
• Each real variable is decomposed to trend (equilibrium)
• The model express each variable in terms of deviation from equilibrium
• Forward-looking (model-consistent expectations)
• Inflation and exchange rate
• Policy analysis (Central bank part of the model)
• Open structure
• Expert Judgments can be incorporated
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Model Equations in our Model (iii)
• Transmition mechanism in gap model
Shocks
hitting the
economy
Financial shocks:
Foreign interest rates
Portfolio changes
Demand shocks:
Foreign demand
Fiscal policy
Inflation shocks:
Indirect taxes
Energy prices
LR interest rates
Ex rate
RMCI Output gap
3 Month interest
rate Inflation
Inflation expectations
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Aggregate demand (Output Gap)
• Relates monetary policy and real economic activity:
• Own lagged value
• Allows for inertia in the system  shocks which have persisting
effects
• Monetary policy
• Nominal interest rate – sticky prices - real interest rate
• Nominal exchange rate – sticky prices – real exchange rate
• External developments
1 2 3 41
ˆ ˆ ˆˆ ˆ
y
t t tt t ta a a ay y yr z 
    
Output
gap Monetary condition index Foreign output
gap
Aggregate demand
shock
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Aggregate Demand (ii)
Output gap
GDP
Persistence
Deviations of real
int rates
Deviation of real
ex rate
Potential level of
GDP
Backward
looking
Intertemporal
substitution
Intratemporal
substitution
Foreign output Gap
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Aggregate Demand Parameters (iii)
• 𝑎3
• Impact of foreign demand on the output gap
• Typically varies between 0.1 and 0.5
• Calibration: base the calibration on OLS regression of the domestic
output gap on foreign and or on the export to GDP ratio
y
ttttt yamciayay  
*
3211 ˆˆˆ
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Aggregate Demand Parameters (iv)
• 𝑎4
• The relative weight of the real interest rate and real exchange
rate in real monetary conditions in the IS curve (monetary
conditions index … mci).
• The value varies between 0.3 (open economy) and 0.8 (closed
economy)
• Calibration: Expert assessment.
)ˆ)(1(ˆ 44 ttt zaramci 
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Aggregate Demand – Ghana, 2002Q1 –
2012Q4
• Relatively stable negative relationship between real interest rate
and output
2002:1 2003:1 2004:1 2005:1 2006:1 2007:1 2008:1 2009:1 2010:1 2011:1 2012:1
-10
-5
0
5
10
15
Output Gap and Real Interest Rate Gap, percent
Output Gap
RIR Gap
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Aggregate Demand – Ghana, 2005Q1 –
2011Q4
2002:1 2003:1 2004:1 2005:1 2006:1 2007:1 2008:1 2009:1 2010:1 2011:1 2012:1
-8
-6
-4
-2
0
2
4
6
8
10
12
Output Gap and Real Exchange Rate Gap, percent
Output Gap
RER Gap
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Aggregate Supply
• Depends on
• Expectations  backward- and/or forward-looking
• World food prices and exchange rate – mainly
• Domestic real economic activity – a little
• Cost push shocks
• Monopolistic competition and sticky prices

 tt
e
ttt rmcbbb   21111 )1(
Headline
Inflation
Expected inflation Real marginal cost
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Aggregate Supply – Real Marginal Cost
• Output gap approximates domestic inflationary pressure
• Real marginal cost of domestic producers
• Real exchange rate gap approximates external
inflationary pressure
• Real marginal cost of importers
Output gap
Real
Exchange
rate gap
ttt zbybrmc ˆ)1(ˆ 33 
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Aggregate Supply Parameters
• Inflation persistence. Share of forward looking agents on the goods
markets
• Varies between 0.4 (low persistence) and 0.9.
The higher is the share of forward looking agents the less
pronounced policy reactions are required
• Calibration: start with 0.5 and adjust according to the model
performance

 tt
e
ttt rmcbbb   21111 )1(
1b
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Aggregate Supply Parameters (ii)
• Monetary policy influences inflation through its effects on output
and the exchange rate thus, the coefficients on the output and
exchange rate gaps must be greater than zero or else MP has no
effect on inflation.
• higher in economies that are very open
• Higher exchange rate pass-through is associated with countries
where MP credibility is low
• What factors impact the exchange rate pass-through?

 tt
e
ttt rmcbbb   21111 )1(
3b
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Aggregate Supply (iii)
Core Inflation
Persistence
Behavioural
components
Backward
looking
Imported
inflation
Relative price
movements
Business cycle
Forward looking
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Aggregate Supply (ii)
• Two Phillips curves
• The Phillips curve describes the trade-off between prices
and output
• Summed based on the weight of their relative
components
• In developed countries, weight of food in CPI is about 10-
20%. In emerging countries, the weight of food ranges
between 30-50%
food food food core
t t tw (1 w )     
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Exchange Rate (Uncovered Interest rate
Parity -- UIP)
• Relates domestic and foreign interest rate with expected change in
the exchange rate (capital inflows)
• Domestic/foreign interest rate
• Country premium
• Current and expected exchange rate
• The expected return on a short-term investment is the same when
ignoring country risk premiums at home and abroad.
s
tttt
e
tt premiiss   4/)( *
1
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Policy Rule (Taylor Rule)
• Monetary Reaction Function
• Describes the manner in which monetary policy is conducted
• Neutral nominal rate = trend real interest rate + model-consistent
inflation expectations
• Monetary authority sets a path for interest rates that anchors inflation
expectations to the target.
• Lagged term provides interest smoothing where CB responds
gradually.
• Output gap: policy decisions depend on more than just inflation
expectations.
i
tt
Te
t
n
ttt yffififi    )ˆ)()(1( 312111
e
t
n
t ri 1 
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Policy Rule (ii)
3 Month interest
rate
Policy neutral
level
Persistence
Reaction
to business cycle
Equlibrium real
rates
Inflation
expectations
Output
gap
Expected
deviation
from
target
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Policy Rule – Ghana, 2002Q1 – 2012Q4
• The interest rate reacts nicely to inflation, with a slight
lag only
2005:1 2006:1 2007:1 2008:1 2009:1 2010:1 2011:1 2012:1
-10
-5
0
5
10
15
20
25
Inflation (percent, QoQ annualized), output gap (percent), nominal interest rate (percent p.a.
Inflation
Output Gap
Interest rate
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Model limitations
• No explicit modeling of the supply side and current
account
• Captured indirectly through other endogenous variable
• No stock-flow consistency…
• From investment to capital level, output level and back
• No stock and assets equilibriums
• How to model crises?
• No explicit modeling of central bank “credibility”
However, all these limitations can be at least partially
overcome by extending and adjusting the framework
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Calibration
• Calibration of a model should reflect stylized facts
about the economy and the dynamics between
variables
• Parameters are set on the basis of model
properties
• Restriction from economic theory
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Literature
Berg, Andrew, Philippe D. Karam, and Douglas Laxton,
2006, “Practical Model-Based Monetary Policy Analysis—
A How-To Guide,” IMF Working Paper 06/81
(Washington: International Monetary Fund).
Beneš, Jaromír, Jaromír Hurník, and David Vávra, 2008,
“Exchange Rate Management and Inflation Targeting:
Modeling the Exchange Rate in Reduced-Form New
Keynesian Models,” Czech Journal of Economics and
Finance, Vol. 3-4/2008.
IMF, 2010, “Handout for the Modeling Workshop”
(unpublished; Washington: IMF Institute).
Thank you for your attantion!
xxx