Inflation Dynamics in a Small Open Economy

• Author: Anders Rygh Swensen,Ådne Cappelen,Pål Boug
• Date: 01 October 2017
• DOI: http://doi.org/10.1111/sjoe.12194
• Published date: 01 October 2017

Inflation Dynamics in a Small Open

Economy∗

P˚

al Boug

Statistics Norway, NO-0033 Oslo, Norway

pal.boug@ssb.no

˚

Adne Cappelen

Statistics Norway, NO-0033 Oslo, Norway

aadne.cappelen@ssb.no

Anders Rygh Swensen†

University of Oslo, NO-0316 Oslo, Norway

swensen@math.uio.no

Abstract

We evaluate the empirical performance of forward-looking models for inflation dynamics

in a small open economy. Using likelihood-based testing procedures, we find that the exact

formulation is at odds with Norwegian data. Moreover, some of the parameters in the

model are not well identified. We also find that the inexact formulation is not rejected

statistically using a test based on a minimum distance method. However, confidence regions

also reveal an identification problem with this model. Instead, we find a well-specified

backward-looking model with imperfect competition underlying the price setting, which is

a model that outperforms an alternative forward-looking model in-sample. The backward-

looking model also forecasts somewhat better than the alternative forward-looking model,

during and after the recent financial crisis.

Keywords: Backward-looking; cointegrated vector autoregressive models; equilibrium correc-

tion models; forward-looking; likelihood-based methods; minimum distance method

JEL classification:C51; C52; E31; F31

I. Introduction

Forward-looking models – based on rational expectations, optimizing

agents, and imperfect competition in markets for goods – have long played

a central role in understanding inflation dynamics in the economics pro-

fession and in central banks conducting inflation targeting. Since the in-

fluential papers by Roberts (1995), Fuhrer and Moore (1995), Gal´

ı and

∗We are grateful to two anonymous referees for helpful comments and suggestions on an

earlier draft.

†Also affiliated with Statistics Norway.

©The editors of The Scandinavian Journal of Economics 2016.

Scand. J. of Economics 119(4), 1010–1039, 2017

DOI: 10.1111/sjoe.12194

Gertler (1999), Gal´

ıet al. (2001), and Sbordone (2002), a large num-

ber of studies have been devoted to testing the role of expectations in

inflation dynamics based on data from both closed and open economies;

see Mavroeidis et al. (2014) and An and Schorfheide (2007) for

reviews of the literature. Studies differ with respect to the data used, the

sample period studied, and the econometric methods applied. The sup-

portive evidence on forward-looking behavior in price formation is rather

mixed.

In this paper, we follow Mavroeidis et al. (2014), among several oth-

ers, and we evaluate the empirical performance of forward-looking mod-

els based on Norwegian data and using a limited-information approach.

Building on Sbordone (2002), our forward-looking models relate current

inflation to expected future inflation and the difference between the actual

price and the steady-state value of levels as a theory-consistent forcing

variable. The steady-state value is specified as a mark-up over marginal

costs, which, in turn, are determined by costs of both labor and imported

intermediate goods along the lines of the open economy models in Mc-

Callum and Nelson (1999), Kara and Nelson (2003), and Batini et al.

(2005). We contribute to the empirical literature by studying both the exact

formulation, in the sense of Hansen and Sargent (1991), and the inexact

formulation, in which a stochastic error term is included in the model. For

the exact formulation, we employ the likelihood-based testing procedures

suggested by Johansen and Swensen (1999, 2008). Because a similar treat-

ment of the inexact formulation is more complicated to handle, we rely on

a test based on a minimum distance approach along the lines of Sbordone

(2002) and Magnusson and Mavroeidis (2010). Consequently, we are able

to shed some light on the importance of introducing a stochastic error

term to the empirical model, an econometric issue that is often neglected

in the literature. Unlike most related studies (e.g., Gal´

ı and Gertler, 1999;

Gal´

ıet al., 2001; Batini et al., 2005), we pay particular attention to time

series properties of the variables involved, and the possible existence of

unit roots, and we search for statistically well-specified underlying models

as premises for valid statistical inference on the forward-looking models

(cf. Mavroeidis et al., 2014). Another issue that has been little addressed in

the literature is forecasting performance. Recently, Rumler and Valderrama

(2010) and King and Watson (2012) have discussed this issue. King and

Watson (2012) find a large gap between inflation predicted by the Smets

and Wouters (2007) forward-looking model for US and actual inflation.

The gap can only be closed by assuming large and exogenous mark-up

shocks. They recommend devoting more attention to detailed analysis of

the structural inflation equation in order to detect imperfect specifications.

In our study, we also compare and contrast specifications of a reduced-form

forward-looking model with a backward-looking model counterpart as two

P. Boug,



A. Cappelen, and A. R. Swensen 1011

©The editors of The Scandinavian Journal of Economics 2016.