8

The Long Swings Puzzle: What the Data

Tell When Allowed to Speak Freely

Katarina Juselius

Abstract

The persistent movements away from long-run benchmark values in real exchange rates that are
often observed in many real exchange rates during periods of currency float have been subject
to much empirical and theoretical research without resolving the underlying puzzle. This chapter
demonstrates how the cointegrated VAR approach of grouping together components of similar
persistence can be used to uncover structures in the data that ultimately may help to explain
theoretically the forces underlying such puzzling movements. The characterization of the data
into components which are empiricallyI(0),I(1) andI(2) is shown to be a powerful organizing
principle, allowing us to structure the data into long-run, medium-run, and short-run behavior. Its
main advantage is the ability to associate persistent movements away from fundamental bench-
mark values in one variable/relation with similar persistent movements somewhere else in the
economy.

8.1 Introduction 350
8.2 The VAR model 352
8.3 The persistent movements in real exchange rate data 353
8.3.1 The long swings puzzle 354
8.3.2 Pulling and pushing forces in the cointegrated VAR model 354
8.3.3 Approximating persistent behavior withI( 1 )orI( 2 ) 356
8.4 ModelingI( 2 )data with theI( 1 )model: does it work? 357
8.5 AnI( 1 )analysis of prices and exchange rates 359
8.5.1 Specification 359
8.5.2 Rank determination and general model properties 360
8.5.3 Estimating the long-run structure 363
8.6 Representing theI( 2 )model 365
8.6.1 The basic structure 365
8.6.2 Deterministic components 366
8.7 Estimation in theI( 2 )model 369
8.7.1 The ML procedure 369
8.7.2 LinkingI( 1 )withI( 2 ) 370
8.8 Two hypothetical scenarios 372
8.9 AnI( 2 )analysis of prices and exchange rates 373
8.9.1 Determining the two rank indices 373
8.9.2 The pulling forces 374

349