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.