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Evaluating an estimated new Keynesian
small open economy model
Malin Adolfson, Stefan Laséen, Jesper Lindé,
Mattias Villani
Marc Goñi – 19 th April
Introduction Model Methodology Results Conclusion
Motivation
During the last years, the use of DSGE models for forecasting and
policy recommendations has grown.
However, key macroeconomic series aren’t still fitted:
- Persistence and volatility of real exchange rate
- International transmission of business cycles
This paper estimates a NK small open economy for Sweden using
Bayesian techniques and accounting for the Swedish monetary
policy regime shift.
By modifying the UIP condition the model is able to account for
realistic persistence and volatility of the exchange rate.
Introduction Model Methodology Results Conclusion
Literature Review
Christiano et al (2005) “Nominal rigidities and the dynamic
effects of a shock to monetary policy”
Smets and Wouters (2003) “An estimated DSGE for the Euro
Area”
Smets and Wouters (2004) “Forecasting with a BDSGE model.
An application to the Euro area”
Adolfson et al (2007) “Forecasting performance of an open
economy DSGE model with incomplete pass through”
Introduction Model Methodology Results Conclusion
Outline
1. Model
Modified UIP
Monetary Policy regime shift
2. Methodology
Estimate the DSGE model using Bayesian techniques
Use Del Negro, Schorfheide (2004), Del Negro (2007) for
misspecification evaluation
3. Results
Posterior probabilities and Impulse Responses
Forecasting ability
Misspecification
Introduction Model Methodology Results Conclusion
Firms
1. Domestic Goods Firms
The domestic final good is a composite of intermediate goods
produced using capital K and labor H subject to price
stickyness and an externally financed wage bill. Moreover, it is
exposed to technology shock.
Introduction Model Methodology Results Conclusion
Firms
•
Final Domestic Good
•
Intermediate Domestic Good Demand
Introduction Model Methodology Results Conclusion
Firms
•
Production Function
•
Marginal Cost
Introduction Model Methodology Results Conclusion
Firms
•
Optimization problem
•
Phillips Curve for the domestic Goods Sector
Introduction Model Methodology Results Conclusion
Firms
2. Import and Export Sector
The are import consumption and investment firms and export
firms
Each firm buys the homogeneous foreign (home) good at price
P* (Pd) and converts it to a differentiated good through brand
naming technology
Nominal rigidities in the local currency price imply short run
incomplete pass-through
Introduction Model Methodology Results Conclusion
Firms
•
Final Import (Export) Good
•
Intermediate Good Demand
•
Production function
Introduction Model Methodology Results Conclusion
Firms
•
Marginal Cost
for the importing firms
for the exporting firm
•
Optimization problem
•
Phillips curves for Consumption and Investment Imports
and Exports
Introduction Model Methodology Results Conclusion
Households
The economy is populated with a continuum of Households
which attain utility from consumption, leisure and real cash
balances.
To purchase these commodities they invest in physical capital
and supply capital and labor to firms
Introduction Model Methodology Results Conclusion
Households
•
Preferences
where,
Introduction Model Methodology Results Conclusion
Households
•
Capital Accumulation
where,
Introduction Model Methodology Results Conclusion
Households
•
Labor Decision
Introduction Model Methodology Results Conclusion
Households
•
Bond Holdings
The choice between domestic and Foreign bonds balances into
a no arbitrage condition (UIP).
- Nominal interest rate difference equals expected
change in exchange rate
Not much empirical support for UIP:
- Persistent hump-shaped response of the exchange rate
to monetary shock
Introduce negative correlation between expected change in
exchange rate and risk premium to get this persistence
(forward premium puzzle)
Introduction Model Methodology Results Conclusion
Households
•
Bond Holdings
–
Risk Premium
–
MUIP
Introduction Model Methodology Results Conclusion
Central Bank
As Sweden went from a fixed to a floating exchange rate in
1992 we need to account for this break
•
Pre 1992
Generalized Taylor Rule
Introduction Model Methodology Results Conclusion
Central Bank
•
Post 1992
Allow for three different policy specifications and let the
data tell the most appropriate.
–
Fixed exchange rate rule
–
Semi-Fixed exchange rate rule
Introduction Model Methodology Results Conclusion
Central Bank
–
Inflation Targeting
with parameters
that is, no break in the monetary policy.
Introduction Model Methodology Results Conclusion
Shocks
where
Introduction Model Methodology Results Conclusion
Government
The Government spends resources in consuming the domestic
good, collects taxes from households and transfers the
surplus/deficit plus the seigniorage to the households via lump
sum taxes
Introduction Model Methodology Results Conclusion
Foreign Economy
Foreign prices, output and interest rate are exogenously given
by a 4-lag VAR estimated using un-informative priors
Introduction Model Methodology Results Conclusion
Model Solution
To solve the model consider the market clearing conditions
To compute the equilibrium decision rules,
-
Stationarize all variables
-
Log linearize around the steady state
-
Use the AIM algorithm to calculate the numerical reduced
form solution
Introduction Model Methodology Results Conclusion
Data
Use quarterly Swedish data for the period 1980Q1-2004Q4
For the foreign variables weight Sweden’s 20 largest trading
partners in 1991 according to IMF
Introduction Model Methodology Results Conclusion
Bayesian Estimation
Previously, compute the reduced form solution
Construct the observed data vector
Transform the reduced form solution into a state-space
representation mapping the unobserved state variables to the
observed data
Introduction Model Methodology Results Conclusion
Bayesian Estimation
1. Prior Distribution
Set priors for unobserved state variables using 1980Q11985Q4 a training sample
For the majority of the estimated parameters, use Adolfson et
al (2007)
Set some priors (stickiness and markup shocks) based on
micro evidence and on educated guesses
Set identical priors for the parameters in the monetary policy
rule (allows to compare them disregarding any “prior” effect)
Introduction Model Methodology Results Conclusion
Bayesian Estimation
2. Likelihood function
To compute the Likelihood function apply the Kalman filter to
the state space transformation of the reduced form solution
The structural shocks and the exogenous fiscal al foreign VAR
shocks enter in such a way that there is no singularity of the
Likelihood function
Introduction Model Methodology Results Conclusion
Bayesian Estimation
3. Posterior distribution
Obtain the joint posterior distribution in two steps:
-
The posterior mode and the Hessian matrix (evaluated at
the mode) is computed by standard numerical routines
-
This Hessian is used in a Metropolis Hastings algorithm to
generate a sample for the posterior distribution
Introduction Model Methodology Results Conclusion
Bayesian Estimation
Notes
- Calibrate
identification
those
parameters
suspicious
of
weak
- Work with a large number of variables to facilitate
Identification of parameters and shocks
Introduction Model Methodology Results Conclusion
Misspecification
Following Del Negro, Schorfheide (2004), Del Negro (2007)
-
Estimate a more flexible empirically oriented VAR with a
prior centered at the DSGE with tightness
-
Find the optimal
-
If the
(maximum likelihood)
is large, that is the DSGE-prior pushes the VAR
towards the implied cross-equation restrictions, then the
model is compatible with the data and, thus, the DSGE is
well specified
Introduction Model Methodology Results Conclusion
Posterior Distribution
Table 1
•
Monetary policy rules
Taylor based rule with a break in parameters gets the best fit
Evidence for a break but not for a strong fix exchange rate
policy
•
Parameters
In general, similar parameter estimation across specification
Wage stickiness and lagged inflation response equal the prior
Policy rule parameters similar in the two regimes
Introduction Model Methodology Results Conclusion
Posterior Distribution
•
UIP Condition
Need to separately identify the risk premium shock from its
propagartion
Modifying the UIP condition allows to generate the desired
exchange rate persistence
Introduction Model Methodology Results Conclusion
Impulse Responses
Introduction Model Methodology Results Conclusion
Forecasting Performance
Introduction Model Methodology Results Conclusion
Forecasting Performance
Introduction Model Methodology Results Conclusion
Forecasting Performance
Introduction Model Methodology Results Conclusion
Model Misspecification
Introduction Model Methodology Results Conclusion
Model Misspecification
Introduction Model Methodology Results Conclusion
Conclusions
- Improve the NK small open economy model by modifying
the UIP condition
- By improving the acknowledgement of the workings of the
economy the CB is now able to derive policy implications a
part from forecasting
- However, it seems that misspecification should be more
considered