RICERCA ITALIANA     

New directions in the theoretical and empirical modelling of inflation

Università degli Studi di Torino

Abstract

The proposed research concerns the theoretical and empirical analysis of the inflationary process.

At the theoretical level, we will study the determinants of inflation persistence, within the framework of the "new-keynesian Phillips curve", analysing in particular the effect of alternative assumptions about the staggering of price decisions and on the presence of a positive steady-state inflation rate on the robustness of the results of this class of models about optimal monetary policy design.

On the empirical side, the general purpose of the project is to develop forecasting models and more general methodological tools to support the monetary policy decision-making process, particularly in the Euro area. Several specific topics will be addressed, namely: the estimation of the long-run behaviour of inflation ("core" inflation measurement); the application of various modelling tecniques (non-linear models and models with time-varying parameters) to inflation forecasting; the analysis of inflation dynamics in the European Union accession countries. <<<

Principal Investigator

Fabio Cesare BAGLIANO Università degli Studi di TORINO

Research Objectives

The proposed research aims at studying several, theoretical and empirical, issues in inflation modelling, In the existing literature in this field there are still some important open issues that our project intends to address.

In summary, the main (and closely related) research fields in which our project aims to produce original contributions, are the following:

(1) the theoretical analysis of the observed persistence of the inflationary process, with particular reference to alternative staggering schemes of price setting decisions, and to the presence of a positive long-run, trend inflation rate in the economy;

(2) the construction of empirical models of the inflationary process, directly derived from the relevant economic theory, as useful tools for short- and long-term forecasting to be employed in the policy decision-making process, particularly in the Euro area. The empirical part of the project, in turn, will develop along several lines of research, mainly concerning the following topics:
(a) the specification of non-linear forecasting models for inflation;
(b) the use of several time-varying parameters models in the empirical analysis of inflation;
(c) the development of new methodologies to measure the core inflation rate;
(d) the construction of models to explain and forecast inflation in the EU accession countries;
(e) the development of new methodologies for short-run forecasting of economic activity. <<<

Timescale

24 months

National and international background

Over the last two decades, in the economic literature about monetary policy and in the practical monetary policy conduct by several Central Banks, controlling inflation has become the main final goal for monetary authorities. Inflation targeting policies, setting explicit quantitative targets for monetary policymakers, have been recently implemented in several countries.

The strong emphasis on inflation control in monetary policy design has motivated recent developments in the theoretical and empirical analysis of the inflationary process, aimed at studying the nature, propagation mechanisms and persistence of inflationary shocks and at improving inflation measurement techniques and inflation forecasting models. Both those lines of investigation motivate our research project, which is aimed at addressing some open issues in the theoretical literature on inflation and optimal monetary policy, and at improving the inflation measurement and forecasting techniques used by policymakers.

For ease of exposition, in what follows we deal first with the theoretical issues more directly related to our research, and then we turn to the main empirical issues.

At the theoretical level, several aspects of our research are based on the recent dynamic, stochastic, general equilibrium models combining typical elements of the real business cycle literature (microfoundations and intertemporal optimisation) and characteristic features of the new-keynesian literature (monopolistic competition and nominal rigidities in goods and labour markets). In particular, by introducing staggered price decisions by monopolistic competitive firms in a stochastic dynamic general equilibrium model, the so-called "New-Keynesian Phillips Curve" (NKPC) is derived (see Galí and Gertler 1999, Galì et al. 2001, and Woodford, 2003). The main and substantial difference between a standard Phillips Curve and the NKPC rests on the forward-looking nature of the latter, whereby current inflation depends on future expected inflation and not from the past inflation levels. The standard equation is obtained from Calvo's (1983) model, log-linearized around the zero inflation steady state. Adding a standard Euler equation for consumption derived from the household's intertemporal maximisation, an elegant and tractable microfounded IS-AS model is obtained.
Whitin this class of models, a strand of literature (see Clarida et al. 1999, Galì 2003 and Woodford 2003 for surveys of the main results) analyses the optimal behaviour of a monetary authority endowed with an output and inflation stabilization objectives. Several results crucially rely on the relative price and inflation dynamics embedded in the NKPC derived from a Calvo-style price staggering. On the basis also of theoretical ann empirical papers advoceting the inclusion of a backward-looking component in inflation dynamics in order to obtain the high persistence observed in the data (Fuhrer and Moore 1995, Christiano et al. 2005), the robustness of such results with respect to alternative models of price staggering has been investigated. Guerrieri (2002) shows that a backward-looking component in the inflation equation naturally arises in the Taylor (1980) model without the need of assuming myopic agents (i.e., Galí and Gertler, 1999) or backward-looking indexation (i.e., Christiano et al., 2001). Moreover, Wolman (1999) and Kiley (2002) show that the Taylor and Calvo models deliver very different dynamics of output and prices in response to demand shocks. Wolman (1999) concludes that the Calvo model is an extreme special case, not just a convenient simplification. Ascari (2004) further investigates the robustness of the NKPC with respect to the assumption of zero inflation in steady state. Indeed, assuming zero trend inflation to model post-war inflation data can hardly be justified. Ascari (2003) shows that in the Calvo's (1983) model the properties of both steady state and dynamics are crucially determined by the level of trend inflation, even for very low inflation levels. The same is not true for Taylor's (1980) model. The results obtained by models employing Calvo pricing and log-linearised around a zero inflation steady state are therefore not robust to realistic changes in the underlying price setting assumptions. This issue deserves further attention, given the relevance that the features and determinants of inflation dynamics have in shaping monetary policy decisions.

On the empirical level, the emphasis on inflation control as the primary goal for monetarey policy has motivated research aimed at refining the techniques used for measuring and forecasting the short- and long- run behaviour of the price level. In this field, some lines of research are directly relevant to our project.
First, the fact that the conventionally measured inflation rate may fluctuate in the short-run due to only temporary disturbances, with little impact on the long-run inflation rate, poses new problems to monetary policy. In fact, the latter should forecast and react in advance only to such long-run inflation prospects, disentangling them from the purely transitory inflation components, to which monetary policy should not react. Short-run changes in the observed inflation rate should then be carefully analyzed in order to extract the long-run, trend component of inflation, commonly referred to as the "core" inflation rate.
One of the approaches followed to measure core inflation applies time-series analysis techniques to the aggregate price change data. In particular, using a bivariate VAR model including output and inflation, Quah and Vahey (1995) defined core inflation as that component of the observed inflation rate that has no long-run effect on output. This definition is consistent with a vertical long-run Phillips curve, showing no long- run trade-off between inflation and output. More recently, Bagliano and Morana (2003a, 2003b) and Bagliano et al. (2004) extended the Quah-Vahey (1995) approach to a multivariate framework. Here, core inflation is interpreted as the long-run forecast of the inflation rate obtained from a small-scale macroeconomic system of relevant variables. Such forecast is built around long-run equilibrium relations between the inflation rate and two main sources of inflationary pressures, namely the rates of growth of monetary aggregates and nominal wages, using the common trends methodology of King et al. (1991).
The main advantage of this "common trend" measure of core inflation is its forward-looking nature, capturing the persistent element in the inflation process, and the fact that it is based on theoretical relationships, linking inflation to money and wage growth in the long-run. However, this approach may be applied only to a non-stationary observed inflation series, yielding a "core inflation" rate evolving over time as a random walk stochastic process. The non-stationarity of the inflation rate can hardly be an appropriate initial assumption in general, and especially when a price-stability oriented monetary policy has effectively reduced over time the fluctuations of the inflation rate around a given target level. Thus, it seems necessary to improve the already applied techniques in order to extend the forward-looking core inflation measure also to a strongly persistent (but stationary) inflation process, characterized by "long memory" and possible "structural breaks". The relevance of such features for the analysis of the inflation rate is supported by numerous recent empirical studies for several countries (e.g. Bos et al. 2002, Morana 2005). Their common finding is that inflation is a "long memory" process, displaying mean reversion in the long-run and subject to regime changes.
At the more general level of inflation forecast model building, the likely presence of structural breaks creates difficulties in specifying and using traditional models, based for example on the relationship between inflation and the "non accelerating inflation unemployment rate" (NAIRU) (Staiger et al. 1997, Atkenson and Ohanian 2001, Canova 2002). A potential solution is the use of non-linear, univariate and multivariate, models (possibly suggested by the NKPC and capable of identifying different regimes) to analyze inflation dynamics and to forecast the inflation process. A similar approach has been followed recently by Cogley and Sbordone (2005) to estomate a structural NKPC.

Beside the above general methodological issues, since the research projects aims at providing useful tools for monetary policy analysis in the Euro area, it seems interesting to address two additional issues: the development of forecasting models based on VARs with time-varying parameters (following Doan et al. 1984 and successive developments); and the specificatio of inflation forecasting models for the European Union accession countries.
As for the first line of research, our research will build on several contributions from the recent econometric literature, namely: (a) the comparative analysis of different time variation schemes (the standard approach of Amisano and Serati 2002, Amisano and Federico, 2004; state equation heteroskedastic errors as in Canova and Ciccarelli, 2003, Amisano and Serati, 2002, 2004; switching regimes in the state equation as in Kim and Nelson, 1999; stochastic volatility in the measurement equation as in Cogley and Sargent 2002; the imposition of restrictions to limit the dimensions of the parameter space with the aim of obtaining better forecasting properties as in Amisano and Federico, 2004, Canova and Ciccarelli, 2003); (b) the use of Bayesian techniques, based on informative prior distributions obtained from theoretical considerations (Amisano and Serati 2003).
As for inflation analysis in EU accession countries, research has followed two main directions, that our project will pursue further. On the one hand, "cointegrated VAR" models (Golinelli and Orsi 2002, for Poland, the Czech Republic, and Hungary) mainly analyse the dynamic relationships among the variables of interest. Golinelli and Orsi (2002) stresses the relevance of the Balassa-Samuelson effect to interpret the links between the exchange rate and the inflation rate in those countries. Therefore, it allows for further research in the field of matching the specific institutional aspects nof those countries with the statistical features of data. On the other hand, "structural modelling" (Golinelli and Rovelli 2005, for the same countries) often uses quarterly data in order to better measure structural relationships (Svensson 2000) between the inflation rate (supply equation), the output gap (demand equation), the effective exchange rate (uncovered interest parity) and the short term interest rate (the Taylor rule).

Extending the analysis to several macroeconomic variables, particularly GDP, raise some problems to the specification of forecasting models since national accounts are (a) published with a lag, and (b) periodically subject to revision (Orphanides 2001). Point (a) raises the issue of how to exploit the timely information of monthly indicators in order to better forecast GDP one- and two-quarters ahead. To this aim, Baffigi, Golinelli and Parigi (2004) introduce the so-called "Bridge Models" (BM), intended to "bridge the gap" between timely-updated monthly indicators and quarterly national accounts. BM have a better forecasting ability that all alternative benchmark models and suggest to extend this approach to more countries in order to forecast GDP for the G7 group, and to study in more depth the links between BM and time disaggregation methods.

At several junctures in our proposed research project, the focus will be on the comparative assessment of competing forecasting models of the inflation rate. Recently, the literature about out-of-sample forecast evaluation has witnessed a renaissance, and a number of authors have proposed formal testing procedures for comparing the predictive ability of competing forecasts, given a general loss function (Diebold and Mariano 1995, Clark and McCracken 2001). More recently, Giacomini and White (2003) proposed a general method for out-of-sample predictive ability testing and model selection that can be applied to multi-step point, interval, probability or density forecast evaluation for a general loss function. Contrary to previous contributions, their "conditional predictive ability tests" are specifically designed to handle heterogeneity (including possible structural breaks) in the data and thus are well suited for evaluating the forecast performance of the class of models that we consider in this research proposal. <<<