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Euro Area Persistence in an Estimated
Nonlinear DSGE Model
Gianni Amisano, Universita di Brescia
Oreste Tristani, European Central Bank
Discussant: Sumru G. Altug
Koc University and CEPR
Conference on Estimation and Empirical Validation of Structural Models
for Business Cycle Analysis, Zurich, August 29-30, 2006
Introduction
This paper takes to data a small dynamic
stochastic general equilibrium model for the
purpose of explaining the persistence in Euro
area inflation.
The model incorporates nominal rigidities in the
adjustment of goods prices as well as frictions
influencing the behavior of real variables. The
formulation of the nominal rigidities follow from
Woodford (2003) while the real side of the
economy is similar to Christiano, Eichenbaum
and Evans (2005).
Motivation
One of the important issues regarding
Euro area inflation persistence has to do
with breaks in the inflation rate.
The paper adds to this literature by
considering a model that tries to generate
variation in inflation persistence through
the existence of nonlinearities in the model
as opposed to exogenously specified
breaks in the inflation rate.
Methodology
Unlike many recent applications of DSGE modeling, the
paper does not employ a linearized solution to the
original model. Instead it allows second-order moments
(or variances) to influence the first moments of the
generated series.
The model that is postulated is “small”. For example, it
abstracts from the foreign sector and the exchange rate
for the purpose of explaining inflation persistence.
The paper also departs from much of the recent
macroeconomics literature by estimating the model
using a Bayesian simulation approach.
Issues to Think About
The approach used in the paper raises a
number of methodological issues:
– The role of linearity versus nonlinearity
– The role of “size”
– Full versus limited information approaches
– The role of frictions
In the remainder of my discussion, I will
elaborate on these points.
Linearity
Developed as part of the Cowles Commission approach
to macro-econometric modeling. Much of the interest lay
in the identifiability of the structural model from the
reduced form.
Linear Rational Expectations models sought to account
for the impact of expectations of future exogenous
variables on the variables of interest. The focus shifted
to non-linear cross-equation restrictions.
Dynamic factor models: impose little economic structure
aside from the hypothesis of a small number of common
unobservable factors and uncorrelated shocks
Affine models of the term structure in the Finance
literature: impose counterfactual restrictions on risk
premia
Let’s keep the nonlinearity in our
(nonlinear) models
Most recent papers with nominal rigidities and real frictions of the
type considered in this paper have employed linearization around a
non stochastic steady state. See, for example, Christiano,
Eichenbaum and Evans (2005).
Even in models that examine the asset pricing implications of
DSGE models, approximate linear laws of motion are generated for
the “real” series and the (nonlinear) asset pricing relations are
evaluated using these linear solutions. As an example, see
Jermann (1997).
By contrast, this paper uses a second-order approximation around
a non- stochastic steady state. The second-order approximation
allows for inflation persistence to depend on how far the economy is
away from the steady state instead to postulating breaks for
inflation. Thus, the nonlinear model generates endogenous regimes
for inflation and inflation persistence.
This approach is much more in the spirit of the original nonlinear
model.
Small is beautiful
The advantage of postulating a “small’ model is that the
effects of the different features that drive economy-wide
dynamics – the internal habit, adjustment costs, etc. –
are well understood.
The nominal side of the economy is also well studied –
price stickiness with Taylor type monetary policy rules.
What remains is to see whether inflation persistence can
arise endogenously once non-linearity is accounted for.
The “test” of the model then becomes predicated on a
simple fact: Does the nonlinear model produce a more
persistent inflation rate starting from a high inflation level
than a low one?
Full versus limited information
methods
All models in Economics are conditional models. That is,
they are conditional on a given structure, which itself
depends on a set of unknown parameters. Our
formulation of the likelihood function in statistics or
econometrics makes this notion explicit.
The model is in this paper is estimated using a full
information method. Hence, whereas the model is
relatively simple, the estimation approach is based on all
the information generated by the model.
Recent applications of RBC/DSGE modeling have
followed the approach of writing down relatively
elaborate economic structures, which are then linearized
and calibrated or estimated with information on a subset
of the moments or variables.
Full versus limited information
methods
For example, Christiano and Eichenbaum (AER, 1992)
estimate a subset of the parameters based on the
steady-state properties of the model with GMM
estimation. Likewise, Christiano, Eichenbaum and Evans
(JPE, 2005) use a subset of the impulse response
functions implied by the model for estimation.
One problem with limited information methods, as
Canova and Sala (2005) have shown, is that model
identification may fail. In other words, estimation based
on a limited set of moments or variables may yield the
same parameter estimates across different models.
Hence, this paper contributes to the existing literature by
extending the use of full information methods to a DSGE
model of inflation persistence.
The role of frictions
Another way in which this paper differs from many recent DSGE
models is that it does not possess a full set of “real” frictions such
as adjustment costs. This is partly due to the problems in fully
estimating the existing model.
Many recent DSGE models that employ frictions for describing the
“real” side of the economy employ investment adjustment costs and
habit formation, among other features. Yet adjustment costs models
have been shown to be ad hoc because they imply constant costs of
adjusting the capital stock.
Irreversibility in investment – even if only in some sectors of the
economy as in Kogan (JFE, 2001) – provides a theoretically more
appealing way of generating the smooth response of investment to
shocks since it implies an endogenous, time-varying adjustment cost
or risk premium.
The role of frictions (cont.d)
Irreversibility also provides a role for the impact of risk, uncertainty
and learning. Hence, irreversibility allows for changes in the
exogenous environment facing firms to affect real outcomes.
Irreversibility also is a statement about the nature of markets that
economic agents face. For example, complete irreversibility implies
that re-sale markets for existing capital do not exist. When an
economist (versus an engineer) thinks about a friction or an
imperfection, it must surely have to do with the nature of markets or
the types of trades that agents can enter into.
Calvo contracts were motivated in this way, at least as an
observable feature of actual labor markets.
When one follows the business news (which is typically concerned
about the impact of political and economic uncertainty on investors’
decisions), one cannot help thinking that a more satisfactory
approach to modeling “real” frictions is called for.