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Introduction to a Small
Macro Model
Jaromir Hurnik
Monetary Policy and Business Cycle
April 2009
“All models are wrong! Some
are useful.”
George Box
George E.P. Box and Norman R. Draper, “Empirical Model-Building and Response
Surfaces” (Wiley 1987), pp. 424.
Outline
 Basic equations
 Calibration versus estimation
 Forecast uncertainty
The Model
 A canonical gap model (reduced-form newKeynesian model)




Aggregate demand
Aggregate supply
Uncovered interest rate parity (simple/extended)
Policy rule
 Work horse at many central banks
 Developed countries: Bank of Canada, Reserve Bank
of New Zealand
 Emerging economies: Czech Republic, Ukraine,
Romania, Colombia, Peru, Guatemala, Botswana
The Model
 Distinguishes between the observed value and a
trend (≈ steady-state values of the system)
 Forward-looking
 Model consistent expectations
 Inflation
 Exchange rate
 Policy analysis
 Central bank is part of the model
 Open structure
 Expert views may be easily incorporated
Schematic Transmission
Mechanism
Transmission Mechanism
Inflation expectations
LR interest rates
SR interest
rate
RMCI
Output gap
Inflation
Ex rate
Shocks
hitting the
economy
Financial shocks:
Foreign
rates
Portfolio changes
Demand shocks:
Foreign demand
Fiscal policy
Inflation shocks:
Indirect taxes
Energy prices
Aggregate Demand
 Relates monetary policy and real economic activity
 Depends on
 Own lagged value
 Monetary policy
 Nominal interest rate – sticky prices - real interest rate
 Nominal exchange rate – sticky prices – real exchange rate
 External developments
yˆ t  a1 yˆ t 1  a2 mcit  a yˆ  
*
3 t
mcit  a4 zˆt  (1  a4 )rˆt
y
t
Aggregate Demand
 Real interest rate affects
 Substitution between consumption today and in the future
 Investment activity
 Real exchange rate
 Substitution between home and foreign goods
Aggregate Demand
Russia, 2000Q1 – 2008Q4
Output Gap and Real Interest Rate Gap
5
Output Gap
RIR Gap
Rolling correlation
between the real interest
rate and output gaps
0
Output Gap<->RIR Gap (time shift)
0.4
0.2
-5
0
2001:1 2002:12003:1 2004:12005:1 2006:12007:1 2008:1
-0.2
Relatively stable negative relationship
between real interest rate and output
-0.4
-0.6
-4
-3
-2
-1
0
1
Time shift
2
3
4
Aggregate Demand
Russia, 2000Q1 – 2008Q4
Output Gap and Real Exchange Rate Gap
20
15
Output Gap
RER Gap
Rolling correlation between
the real exchange rate and
output gaps
10
Output Gap<->RER Gap (time shift)
0.6
5
0.4
0
0.2
0
-5
-0.2
-10
2001:1 2002:1 2003:1 2004:1 2005:1 2006:1 2007:1 2008:1
Counter intuitive relationship between real
exchange rate and output in the data. Not
surprising. Closed economy and
appreciation (depreciation) driven by
commodity prices.
-0.4
-0.6
-0.8
-4
-3
-2
-1
0
1
Time shift
2
3
4
Aggregate Supply




Relates real economic activity and inflation
Monopolistic competition
Sticky prices
Depends on
 Expectations  Backward- and/or forward-looking
 Real marginal costs
 Cost push shocks
 t  b1 t 1  (1  b1 )
e
t 1

 b2 rmct   t
Aggregate Supply
 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
rmct  b3 yˆt  (1  b3 ) zˆt
Aggregate Supply
Russia, 2001Q1 – 2008Q4
Inflation (detrended) and Real Marginal Cost Gap
8
6
Inflation (q-o-q)
RMC Gap
4
Rolling correlation between
inflation and real marginal
cost
Inflation (detrended)<->RMC Gap (time shift)
2
0.6
0.5
0
0.4
-2
0.3
0.2
-4
0.1
-6
2001:1 2002:1 2003:1 2004:1 2005:1 2006:1 2007:1 2008:1
0
-0.1
Stable relationship. High real
marginal cost are followed by higher
inflation with a lag of 1-2 quarters
-0.2
-4
-3
-2
-1
0
1
Time shift
2
3
4
Uncovered Interest Rate Parity
 Relates domestic and foreign interest rate with
the expected change in the exchange rate




Domestic interest rate
Foreign interest rate
Current and expected exchange rate
Exchange rate shocks
st  s
e
t 1
 (i  it  premt ) / 4  
*
t
s
t
Uncovered Interest Rate Parity
Russia, 1991Q1 – 2006Q4
Exchange Rate (q-o-q) and Money-Market Interest Rate
80
Exchange rate (q-o-q)
Interest Rate
60
40
20
0
-20
-40
2001:1
2002:1
2003:1
2004:1
2005:1
2006:1
2007:1
2008:1
Weak relationship between
the money
market and the
exchange rate.
Not surprising,
because the
nominal
exchange rate
served as the
nominal anchor
Modified UIP
 Extension for a more rigid exchange rate regime
 Smoothness
 Interventions
st  e1 stT1  (1  e1 )( ste1  (it*  it  premt ) / 4)   ts
where the exchange rate target is defined as
stT1  st 1  2 / 4(~  ~*  ~
z)
Policy Rule
 Describes behavior of the central bank
 Reacts when inflation deviates from the price stability
 Smoothes its reaction to inflation or the output gap
(uncertainty about real-time estimates of output gap)
 Takes into account real economic activity
 Policy shocks
 Neutral nominal rate = trend real rate + model-consistent
inflation forecast
it  f1it 1  (1  f1 )(itn  f 2 ( te1   T )  f 3 yˆ t )   ti
n
e
~
i  r 
t
t
t 1
Policy Rule
Russia, 2001Q1 – 2008Q4
Output Gap, Inflation (q-o-q) and Money-Market Interest Rate
30
25
Output Gap
Inflation (q-o-q)
Interest Rate
20
15
10
5
0
-5
2001:1 2002:1 2003:1 2004:1 2005:1 2006:1 2007:1 2008:1
Interest rate seems
to react to both
inflation and output,
however with a lag
only
Policy Rule Digression
 The Taylor-type rule can make policy
scenarios difficult to compare
 One option: replace the rule with a loss
function (ála Norges Bank):
Min ℓ = var() + l*var(y)
 Policymaker decides the value of l
Model Limitations
 No explicit modeling of the supply side
 The choice of the inflation target value does not
affect potential output growth
 No stock and assets equilibria
 How to model crises?
 No stock-flow consistency…
 From gaps back to the levels
 No explicit modeling of central bank “credibility”
Calibration Versus Estimation
 Estimation




Short data sample
Changes in economy
Policy regime changes
Some parameters are difficult to
estimate because of endogeneity of
policy actions
Endogeneity of policy actions (1)
 The AD equation predicts a negative
relationship between r and y
 Timeline:




Expected economic slowdown
Policymaker cuts the interest rate
The economy still slows down
Econometrician observed positive correlation
between interest rate and output gap
 Do rate cuts slow down the economy?
Endogeneity of policy actions (2)
 UIP predicts a positive correlation
between E(Δst+1) and r-r*
 Timeline:
 Inflation increased
 Exchange rate depreciated
 Policymaker hiked the rate to combat
inflation
 Econometrician observed negative correlation
between interest rate and exchange rate
 Do rate cuts appreciate the currency?
Calibration Versus Estimation
 Econometricians reduce our forward-looking
model into a backward-looking one:
 t  1 *  t 1  2 * yˆt 1  3 * rt 1  1 * controls  ...
 Such model cannot predict future inflation:
 Ignores reactions of the policymaker to shocks
 Coefficients often contradict theory
 Adaptive expectations of inflation


 Inflation ≈ past output gaps:  
yˆ  
t

i 0
t i
t i
Calibration Versus Estimation
 Calibration




Parameters set on the basis of model properties
Restriction from economic theory
Responses to typical shocks
Adaptive strategy
 Verification




Reactions to shocks
Residuals
In-sample simulation
Data versus model-implied correlations
Estimate
precision
Estimating Versus Calibrating
Estimated
regression
Calibrated
model
time horizon
There are
instances to
use estimated
models, but
not for longrun forecasts!