Euro Area Persistence in an Estimated Nonlinear DSGE Model

1
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

2
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).

3
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.

4
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.

5
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.

6
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

7
Lets 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.

8
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?

9
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.

10
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.

11
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.

12
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.