Palgrave Handbook of Econometrics

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Palgrave Handbook of

Econometrics

Volume 2: Applied Econometrics

Edited By

Terence C. Mills

and

Kerry Patterson

Editorial and selection matter © Terence C. Mills and Kerry Patterson 2009

Individual chapters © Contributors 2009

All rights reserved. No reproduction, copy or transmission of this

publication may be made without written permission.

No paragraph of this publication may be reproduced, copied or transmitted

save with written permission or in accordance with the provisions of the

Copyright, Designs and Patents Act 1988, or under the terms of any licence

permitting limited copying issued by the Copyright Licensing Agency,

Saffron House, 6–10 Kirby Street, London EC1N 8TS.

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and Patents Act 1988.

First published in 2009 by

PALGRAVE MACMILLAN

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Printed and bound in Great Britain by

CPI Antony Rowe, Chippenham and Eastbourne

Contents

Notes on Contributors

viii

Editors’ Introduction

xi

Part I The Methodology and Philosophy of Applied Econometrics

1

2

3

The Methodology of Empirical Econometric Modeling: Applied

Econometrics Through the Looking Glass

David F. Hendry, Nufﬁeld College, Oxford University

How Much Structure in Empirical Models?

Fabio Canova, Universitat Pompeu Fabra

Introductory Remarks on Metastatistics for the Practically Minded

Non-Bayesian Regression Runner

John DiNardo, University of Michigan

3

68

98

Part II Forecasting

4

5

Forecast Combination and Encompassing

Michael P. Clements, Warwick University, and David I. Harvey,

School of Economics, University of Nottingham

Recent Developments in Density Forecasting

Stephen G. Hall, University of Leicester, and James Mitchell,

National Institute of Economic and Social Research

169

199

Part III Time Series Applications

6

7

8

9

10

Investigating Economic Trends and Cycles

D.S.G. Pollock, University of Leicester

Economic Cycles: Asymmetries, Persistence, and Synchronization

Joe Cardinale, Air Products and Chemicals, Inc., and Larry W. Taylor,

College of Business and Economics, Lehigh University

The Long Swings Puzzle: What the Data Tell When Allowed to

Speak Freely

Katarina Juselius, University of Copenhagen

Structural Time Series Models for Business Cycle Analysis

Tommaso Proietti, University of Rome ‘Tor Vergata’

Fractional Integration and Cointegration: An Overview and an

Empirical Application

Luis A. Gil-Alana and Javier Hualde, Universidad de Navarra

v

243

308

349

385

434

vi

Contents

Part IV

11

12

13

Discrete Choice Modeling

William Greene, Stern School of Business, New York University

Panel Data Methods and Applications to Health Economics

Andrew M. Jones, University of York

Panel Methods to Test for Unit Roots and Cointegration

Anindya Banerjee, University of Birmingham, and Martin Wagner,

Institute forAdvanced Studies, Vienna

Part V

14

15

Cross-section and Panel Data Applications

473

557

632

Microeconometrics

Microeconometrics: Current Methods and Some Recent Developments

A. Colin Cameron, University of California, Davis

Computational Considerations in Empirical Microeconometrics:

Selected Examples

David T. Jacho-Chávez and Pravin K. Trivedi, Indiana University

729

775

Part VI Applications of Econometrics to Economic Policy

16

17

18

The Econometrics of Monetary Policy: An Overview

Carlo Favero, IGIER-Bocconi University

Macroeconometric Modeling for Policy

Gunnar Bårdsen, Norwegian University of Science and Technology,

and Ragnar Nymoen, University of Oslo

Monetary Policy, Beliefs, Unemployment and Inﬂation: Evidence

from the UK

S.G.B. Henry, National Institute of Economic and Social Research

821

851

917

Part VII Applications to Financial Econometrics

19

20

21

22

Estimation of Continuous-Time Stochastic Volatility Models

George Dotsis, Essex Business School, University of Essex,

Raphael N. Markellos, Athens University of Economics and Business,

and Terence C. Mills, Loughborough University

Testing the Martingale Hypothesis

J. Carlos Escanciano, Indiana University, and Ignacio N. Lobato,

Instituto Tecnológico Autónomo de Mexico

Autoregressive Conditional Duration Models

Ruey S. Tsay, Booth Business School, University of Chicago

The Econometrics of Exchange Rates

Efthymios G. Pavlidis, Ivan Paya, and David A. Peel,

Lancaster University Management School

951

972

1004

1025

Contents

vii

Part VIII Growth Development Econometrics

23

24

25

The Econometrics of Convergence

Steven N. Durlauf, University of Wisconsin-Madison,

Paul A. Johnson, Vassar College, New York State, and

Jonathan R.W. Temple, Bristol University

The Methods of Growth Econometrics

Steven N. Durlauf, University of Wisconsin-Madison,

Paul A. Johnson, Vassar College, New York State, and

Jonathan R.W. Temple, Bristol University

The Econometrics of Finance and Growth

Thorsten Beck, European Banking Center, Tilburg University, and CEPR

Part IX

26

27

28

29

1119

1180

Spatial Econometrics

Spatial Hedonic Models

Luc Anselin, School of Geographical Sciences and Urban Planning,

and Nancy Lozano-Gracia, GeoDa Center for Geospatial

Analysis and Computation, Arizona State University

Spatial Analysis of Economic Convergence

Sergio J. Rey, Arizona State University, and Julie Le Gallo,

Université de Franche-Comté

Part X

1087

1213

1251

Applied Econometrics and Computing

Testing Econometric Software

B.D. McCullough, Drexel University

Trends in Applied Econometrics Software Development 1985–2008:

An Analysis of Journal of Applied Econometrics Research Articles,

Software Reviews, Data and Code

Marius Ooms, VU University Amsterdam

1293

1321

Author Index

1349

Subject Index

1374

Notes on Contributors

Luc Anselin is Foundation Professor of Geographical Sciences and Director

of the School of Geographical Sciences and Urban Planning at Arizona State

University, USA.

Aninyda Banerjee

Birmingham, UK.

is

Professor

of

Econometrics

at

the

University

of

Gunnar Bårdsen is Professor of Economics at the Norwegian University of Science

and Technology, Norway.

Thorsten Beck is Professor of Economics and Chair at the European Banking

Center, Tilburg University and Research Fellow, CEPR.

Colin Cameron is Professor of Economics at the University of California,

Davis, USA.

Fabio Canova is ICREA Research Professor in Social Science at Universitat Pompeu

Fabra, Barcelona, Spain.

Joe Cardinale is a Manager, Economics at Air Products and Chemicals, Inc., USA.

Michael P. Clements is Professor of Economics at Warwick University, UK.

John DiNardo is Professor of Economics and Public Policy at the University of

Michigan, Ann Arbor, USA.

George Dotsis is Lecturer in Finance at the Essex Business School, University of

Essex, UK.

Steven N. Durlauf is Professor of Economics at the University of WisconsinMadison, USA.

Juan Carlos Escanciano is Assistant Professor of Economics at Indiana University,

Bloomington, USA.

Carlo A. Favero is Professor of Economics at IGIER-Bocconi University, Italy.

Julie Le Gallo is Professor of Economics and Econometrics at the Université de

Franche-Comté, France.

Luis A. Gil-Alana is Professor of Econometrics at the University of Navarra, Spain.

William Greene is Professor of Economics at the Stern School of Business,

New York, USA.

Stephen G. Hall is Professor of Economics at University of Leicester, UK.

David I. Harvey is Reader in Econometrics at the School of Economics, University

of Nottingham, UK.

David F. Hendry is Professor of Economics and Fellow, Nufﬁeld College, Oxford

University, UK.

viii

Notes on Contributors

ix

Brian Henry is Visiting Fellow at the National Institute of Economic and Social

Research, NIESR, UK.

Javier Hualde is Ramon y Cajal Research Fellow in Economics at the Public

University of Navarra, Spain.

David Jacho-Chávez is Assistant Professor of Economics at Indiana University,

Bloomington, USA.

Paul A. Johnson is Professor of Economics at Vassar College, New York State, USA.

Andrew M. Jones is Professor of Economics at the University of York, UK.

Katarina Juselius is Professor of Empirical Time Series Econometrics at the

University of Copenhagen, Denmark.

Ignacio N. Lobato is Professor of Econometrics at the Instituto Tecnológico

Autónomo de México, Mexico.

Nancy Lozano-Gracia is Postdoctoral Research Associate in the GeoDa Center for

Geospatial Analysis and Computation at Arizona State University, USA.

Raphael N. Markellos is Assistant Professor of Quantitative Finance at the Athens

University of Economics and Business (AUEB), Greece.

Bruce D. McCullough is Professor of Decision Sciences and Economics at Drexel

University, Philadelphia, USA.

Terence C. Mills is Professor of Applied Statistics and Econometrics at

Loughborough University, UK.

James Mitchell is Research Fellow at the National Institute of Economic and Social

Research, UK.

Ragnar Nymoen is Professor of Economics at University of Oslo, Norway.

Marius Ooms is Associate Professor of Econometrics at the VU University,

Amsterdam, The Netherlands.

Kerry Patterson is Professor of Econometrics at the University of Reading, UK.

Efthymios G. Pavlidis is Lecturer in Economics at the Lancaster University

Management School, Lancaster University, UK.

Ivan Paya is Senior Lecturer in Economics at the Lancaster University Management

School, Lancaster University, UK.

David A. Peel is Professor in Economics at the Lancaster University Management

School, Lancaster University, UK.

D. Stephen G. Pollock is Professor of Economics at the University of Leicester, UK.

Tommaso Proietti is Professor of Economic Statistics at the University of Rome

‘Tor Vergata’, Italy.

Sergio Rey is Professor of Geographical Sciences at Arizona State University, USA.

Larry W. Taylor is Professor of Economics at the College of Business and

Economics, Lehigh University, Pennsylvania, USA.

x Notes on Contributors

Jonathan R.W. Temple is Professor of Economics at Bristol University, UK.

Pravin Trivedi is Professor of Economics at Indiana University, Bloomington, USA.

Ruey S. Tsay is Professor of Econometrics and Statistics at the University of Chicago

Booth School of Business, USA.

Martin Wagner is Senior Economist at the Institute for Advanced Studies in

Vienna, Austria.

Editors’ Introduction

Terence C. Mills and Kerry Patterson

The Palgrave Handbook of Econometrics was conceived to provide an understanding of major developments in econometrics, both in theory and in application.

Over the last twenty-ﬁve years or so, econometrics has grown in a way that few

could have contemplated, and it became clear to us, as to others, that no single person could have command either of the range of technical knowledge that

underpins theoretical econometric developments or the extent of the application

of econometrics. In short, econometrics is not, as it used to be considered, a set of

techniques that is applied to a previously well-deﬁned problem in economics; it is

not a matter of ﬁnding the “best” estimator from a ﬁeld of candidates, applying

that estimator and reporting the results. The development of economics is now

inextricably entwined with the development of econometrics.

The ﬁrst Nobel Prize in Economics was awarded to Ragnar Frisch and Jan Tinbergen, both of whom made signiﬁcant contributions to what we now recognize as

applied econometrics. More recently, Nobel Prizes in Economics have been awarded

to Clive Granger, Robert Engle, James Heckman and Daniel McFadden, who have

all made major contributions to applied econometrics. It is thus clear that the discipline has recognized the inﬂuential role of econometrics, both theoretical and

applied, in advancing economic knowledge.

The aim of this volume is to make major developments in applied econometrics accessible to those outside their particular ﬁeld of specialization. The response

to Volume 1 was universally encouraging and it has become clear that we were

fortunate to be able to provide a source of reference for others for many years to

come. We hope that this high standard is continued and achieved here. Typically,

applied econometrics, unlike theoretical econometrics, has always been rather

poorly served for textbooks, making it difﬁcult for both undergraduate and postgraduate students to get a real “feel” for how econometrics is actually done. To

some degree, the econometric textbook market has responded, so that now the

leading textbooks include many examples; even so, these examples typically are

of an illustrative nature, focusing on simple points, simply exposited, rather than

on the complexity that is revealed in practice. Thus our hope is that this volume will provide a genuine entry into the detailed considerations that have to be

xi

xii Editors’ Introduction

made when combining economics and econometrics in order to carry out serious

empirical research.

As in the case of Volume 1, the chapters here have been specially commissioned

from acknowledged experts in their ﬁelds; further, each of the chapters has been

reviewed by the editors, one or more of the associate editors and a referee. Thus,

the process is akin to submission to a journal; however, whilst ensuring the highest

standards in the evaluation process, the chapters have been conceived of as part

of a whole rather than as a set of unrelated contributions. It has not, however,

been our intention to provide just a series of surveys or overviews of some areas of

applied econometrics, although the survey element is directly or indirectly served

in part here. By its very nature, this volume is about econometrics as it is applied

and, to succeed in its aim, the contributions, conceived as a whole, have to meet

this goal.

We have organized the chapters of this volume of the Handbook into ten parts.

The parts are certainly not watertight, but serve as a useful initial organization of

the central themes. Part I contains three chapters under the general heading of

“The Methodology and Philosophy of Applied Econometrics.” The lead chapter is

by David Hendry, who has been making path-breaking contributions in theoretical

and applied econometrics for some forty years or so. It is difﬁcult to conceive how

econometrics would have developed without David’s many contributions. This

chapter ﬁrst places the role of applied econometrics in an historical context and

then develops a theory of applied econometrics. As might be expected, the key

issues are confronted head-on.

In introducing the ﬁrst volume we noted that the “growth in econometrics is to

be welcomed, for it indicates the vitality and importance of the subject. Indeed,

this growth and, arguably, the dominance over the last ten or twenty years of

econometric developments in taking economics forward, is a notable change from

the situation faced by the subject some twenty-ﬁve years or so ago.” Yet in Chapter

1, Hendry notes that, next to data measurement, collection and preparation, on the

one hand, and teaching, on the other, “Applied Econometrics” does not have a high

credibility in the profession. Indeed, whilst courses in theoretical econometrics or

econometric techniques are de rigueur for a good undergraduate or Masters degree,

courses in applied econometrics have no such general status.

The intricacies, possibly even alchemy (Hendry, 1980), surrounding the mix of

techniques and data seem to defy systematization; perhaps they should be kept

out of the gaze of querulous students, who may – indeed should – be satisﬁed with

illustrative examples! Often to an undergraduate or Masters student undertaking a

project, applied econometrics is the application of econometrics to data, no more,

no less, with some relief if the results are at all plausible. Yet, in contrast, leading

journals, for example, the Journal of Econometrics, the Journal of Applied Econometrics and the Journal of Business and Economic Statistics, and leading topic journals,

such as the Journal of Monetary Economics, all publish applied econometric articles

having substance and longevity in their impact and which serve to change the

direction of the development of econometric theory (for a famous example, see

Nelson and Plosser, 1982). To some, applying econometrics seems unsystematic

Terence C. Mills and Kerry Patterson

xiii

and so empirical results are open to question; however, as Hendry shows, it is

possible to formalize a theory of applied econometrics which provides a coherent basis for empirical work. Chapter 1 is a masterful and accessible synthesis and

extension of Hendry’s previous ideas and is likely to become compulsory reading

for courses in econometrics, both theory and applied; moreover, it is completed by

two applications using the Autometrics software (Doornik, 2007). The ﬁrst application extends the work of Magnus and Morgan (1999) on US food expenditure,

which was itself an update of a key study by Tobin (1950) estimating a demand

function for food. This application shows the Autometrics algorithm at work in a

simple context. The second application extends the context to a multiple equation

setting relating industrial output, the number of bankruptcies and patents, and real

equity prices. These examples illustrate the previously outlined theory of applied

econometrics combined with the power of the Autometrics software.

In Chapter 2, Fabio Canova addresses the question of how much structure there

should be in empirical models. This has long been a key issue in econometrics, and

some old questions, particularly those of identiﬁcation and the meaning of structure, resurface here in a modern context. The last twenty years or so have seen

two key developments in macroeconometrics. One has been the development of

dynamic stochastic general equilibrium (DSGE) models. Initially, such models were

calibrated rather than estimated, with the emphasis on “strong” theory in their

speciﬁcation; however, as Canova documents, more recently likelihood-based estimation has become the dominant practice. The other key development has been

that of extending the (simple) vector autoregression (VAR) to the structural VAR

(SVAR) model. Although both approaches involve some structure, DSGE models,

under the presumption that the model is correct, rely more on an underlying theory than do SVARs. So which should be used to analyze a particular set of problems?

As Canova notes: “When addressing an empirical problem with a ﬁnite amount of

data, one has . . . to take a stand on how much theory one wants to use to structure

the available data prior to estimation.” Canova takes the reader through the advantages and shortcomings of these methodologies; he provides guidance on what to

do, and what not to do, and outlines a methodology that combines elements of

both approaches.

In Chapter 3, John DiNardo addresses some philosophical issues that are at

the heart of statistics and econometrics, but which rarely surface in econometric textbooks. As econometricians, we are, for example, used to working within

a probabilistic framework, but we rarely consider issues related to what probability actually is. To some degree, we have been prepared to accept the axiomatic

or measure theoretic approach to probability, due to Kolgomorov, and this has

provided us with a consistent framework that most are happy to work within.

Nevertheless, there is one well-known exception to this unanimity: when it comes

to the assignment and interpretation of probability measures and, in particular, the

interpretation of some key conditional probabilities; this is whether one adopts a

Bayesian or non-Bayesian perspective. In part, the debate that DiNardo discusses

relates to the role of the Bayesian approach, but it is more than this; it concerns

metastatistics and philosophy, because, in a sense, it relates to a discussion of the

xiv Editors’ Introduction

theory of theories. This chapter is deliberately thought-provoking and certainly

controversial – two characteristics that we wish to encourage in a Handbook that

aims to be more than just an overview. For balance, the reader can consult Volume

1 of the Handbook, which contains two chapters devoted to the Bayesian analysis of

econometric models (see Poirier and Tobias, 2006, and Strachan et al., 2006). The

reader is likely to ﬁnd familiar concepts here, such as probability and testing, but

only as part of a development that takes them into potentially unfamiliar areas.

DiNardo’s discussion of these issues is wide-ranging, with illustrations taken from

gambling and practical examples taken as much from science, especially medicine,

as economics. One example from the latter is the much-researched question of the

causal effect of union status on wages: put simply, do unions raise wages and, if so,

by how much? This example serves as an effective setting in which to raise issues

and to show that differences in approach can lead to differences in results.

For some, the proof of the pudding in econometrics is the ability to forecast

accurately, and to address some key issues concerning this aspect of econometrics Part II contains two chapters on forecasting. The ﬁrst, Chapter 4, by Michael

Clements and David Harvey, recognizes that quite often several forecasts are available and, rather than considering a selection strategy that removes all but the best

on some criterion, it is often more fruitful to consider different ways of combining

forecasts, as suggested in the seminal paper by Bates and Granger (1969). In an

intuitive sense, one forecast may be better than another, but there could still be

some information in the less accurate forecast that is not contained in the more

accurate forecast. This is a principle that is ﬁnding wider application; for example,

in some circumstances, as in unit root testing, there is more than one test available

and, indeed, there may be one uniformly powerful test, yet there is still potential

merit in combining tests.

In the forecasting context, Clements and Harvey argue that the focus for multiple forecasts should not be on testing the null of equal accuracy, but on testing

for encompassing. Thus it is not a question of choosing forecast A over forecast B,

but of whether the combination of forecasts A and B is better than either individual forecast. Of course, this may be of little comfort from a structuralist point of

view if, for example, the two forecasts come from different underlying models; but

it is preferable when the loss function rewards good ﬁt in some sense. Bates and

Granger (1969) suggested a simple linear combination of two unbiased forecasts,

with weights depending on the relative accuracy of the individual forecasts, and

derived the classic result that, even if the forecasts are equally accurate in a mean

squared error loss sense, then there will still be a gain in using the linear combination unless the forecasts are perfectly correlated, at least theoretically. Clements and

Harvey develop from this base model, covering such issues as biased forecasts, nonlinear combinations, and density or distribution forecasts. The concept of forecast

encompassing, which is not unique in practice, is then considered in detail, including complications arising from integrated variables, non-normal errors, serially

correlated forecast errors, ARCH errors, the uncertainty implied by model estimation, and the difﬁculty of achieving tests with the correct actual size. A number of

recent developments are examined, including the concept of conditional forecast

Terence C. Mills and Kerry Patterson

xv

evaluation (Giacomini and White, 2006), evaluating quantile forecasts, and relaxing the forecast loss function away from the traditional symmetric squared error.

In short, this chapter provides a clear, critical and accessible evaluation of a rapidly

developing area of the econometrics literature.

Chapter 5 is by Stephen Hall and James Mitchell, who focus on density forecasting. There has been a great deal of policy interest in forecasting key macroeconomic

variables such as output growth and inﬂation, some of which has been institutionally enshrined by granting central banks independence in inﬂation targeting. In

turn, there has been a movement away from simply reporting point forecasts of

inﬂation and GDP growth in favor of a fan chart representation of the distribution

of forecasts. A density forecast gives much more information than a simple point

forecast, which is included as just one realization on the outcome axis. As a corollary, forecast evaluation should also include techniques that evaluate the accuracy,

in some well-deﬁned sense, of the density forecast. However, given that generally

we will only be able to observe one outcome (or event) per period, some thought

needs to be given to how the distributional aspect of the forecast is evaluated. Hall

and Mitchell discuss a number of possibilities and also consider methods of evaluating competing density forecasts. A further aspect of density forecasting is the

ability of the underlying model to generate time variation in the forecast densities. If the underlying model is a VAR, or can be approximated by a VAR, then,

subject to some qualiﬁcations, the only aspect of the forecast density which is able

to exhibit time variation is the mean; consequently, models have been developed

that allow more general time variation in the density through, for example, ARCH

and GARCH errors and time-varying parameters. This chapter also links in with the

previous chapter by considering combinations of density forecasts. There are two

central possibilities: the linear opinion pool is a weighted linear combination of

the component densities, whereas the logarithmic opinion pool is a multiplicative

combination. Hall and Mitchell consider the problem of determining the weights

in such combinations and suggest that predictive accuracy improves when the

weights reﬂect shifts in volatility, a characteristic of note for the last decade or so

in a number of economies.

Part III contains four chapters under the general heading of “Time Series Applications.” A key area in which the concept of a time series is relevant is in

characterizing and determining trends and cycles. Chapter 6, by Stephen Pollock,

is a tour de force on modeling trends and cycles, and on the possibilities and

pitfalls inherent in the different approaches. In the simplest of models, cyclical

ﬂuctuations are purely sinusoidal and the trend is exponential; although simple,

this is a good base from which to understand the nature of developments that

relax these speciﬁcations. Such developments include the view that economic time

series evolve through the accumulation of stochastic shocks, as in an integrated

Weiner process. The special and familiar cases of the Beveridge–Nelson decomposition, the Hodrick–Prescott ﬁlter, the Butterworth ﬁlter and the unifying place of

Weiner–Kolgomorov ﬁltering are all covered with admirable clarity. Other considerations include the complications caused by the limited data that is often available

in economic applications, contrary to the convenient assumptions of theory. In an

xvi

Editors’ Introduction

appealing turn of phrase, Pollock refers to obtaining a decomposition of components based on the periodogram “where components often reside within strictly

limited frequency bands which are separated by dead spaces where the spectral

ordinates are virtually zeros.” The existence of these “spectral dead spaces” is key

to a practical decomposition of an economic time series, however achieved. In

practice, trend ﬁtting requires judgment and a clear sense of what it is that the

trend is capturing. Other critical issues covered in this chapter include the importance of structural breaks, a topic that has been inﬂuential elsewhere (for example,

in questioning the results of unit root testing: Perron, 1989); and to aid the reader,

practical examples are included throughout the exposition.

Chapter 7, by Joe Cardinale and Larry Taylor, continues the time series theme of

analyzing economic cycles whilst focusing on asymmetries, persistence and synchronization. This is a particularly timely and somewhat prophetic chapter given

that we are currently experiencing what is perhaps the deepest recession in recent

economic history. How can we analyze the critical question “When will it end?”

This chapter provides the analytical and econometric framework to answer such a

question. The central point is that cycles are much more interesting than just marking their peaks and troughs would suggest. Whilst “marking time” is important, it

is just the ﬁrst part of the analysis, and should itself be subjected to methods for distinguishing phases (for example, expansions and contractions of the output cycle).

Once phases have been distinguished, their duration and characteristics become

of interest; for example, do long expansions have a greater chance of ending than

short expansions? Critical to the analysis is the hazard function: “the conditional

probability that a phase will terminate in period t, given that it has lasted t or more

periods.” Cardinale and Taylor consider different models and methods of estimating the hazard function and testing hypotheses related to particular versions of it.

They also consider tests of duration dependence, the amplitudes of cycles, and the

synchronization of cycles for different but related variables; for example, output

and unemployment. Their theoretical analysis is complemented with a detailed

consideration of US unemployment.

No handbook of econometrics could be without a contribution indicating the

importance of cointegration analysis for non-stationary data. In Chapter 8, Katerina Juselius considers one of the most enduring puzzles in empirical economics,

namely, if purchasing power parity (PPP) is the underlying equilibrium state that

determines the relationship between real exchange rates, why is there “pronounced

persistence” away from this equilibrium state? This has been a common ﬁnding of

empirical studies using data from a wide range of countries and different sample

periods. Juselius shows how a careful analysis can uncover important structures in

the data; however, these structures are only revealed by taking into account the

different empirical orders of integration of the component variables, the identiﬁcation of stationary relationships between non-stationary variables, the dynamic

adjustment of the system to disequilibrium states, the appropriate deterministic

components, and the statistical properties of the model. As Juselius notes, and

in contrast to common approaches, the order of integration is regarded here as

an empirical approximation rather than a structural parameter. This opens up a

Terence C. Mills and Kerry Patterson

xvii

distinction between, for example, a variable being empirically I(d) rather than

structurally I(d); a leading example here is the I(2) case which, unlike the I(1)

case, has attracted some “suspicion” when applied in an absolute sense to empirical series. The challenging empirical case considered by Juselius is the relationship

between German and US prices and nominal exchange rates within a sample that

includes the period of German reuniﬁcation. The methodology lies ﬁrmly within

the framework of general-to-speciﬁc modeling, in which a general unrestricted

model is tested down (see also Hendry, Chapter 1) to gain as much information

without empirical distortion. A key distinction in the methodological and empirical analysis is between pushing and pulling forces: in the current context, prices

push whereas the exchange rate pulls. PPP implies that there should be just a single stochastic trend in the data, but the empirical analysis suggests that there are

two, with the additional source of permanent shocks being related to speculative

behaviour in the foreign exchange market.

In an analysis of trends and cycles, economists often characterize the state of

the economy in terms of indirect or latent variables, such as the output gap, core

inﬂation and the non-accelerating rate of inﬂation (NAIRU). These are variables

that cannot be measured directly, but are nevertheless critical to policy analysis.

For example, the need to take action to curb inﬂationary pressures is informed by

the expansionary potential in the economy; whether or not a public sector budget deﬁcit is a matter for concern is judged by reference to the cyclically adjusted

deﬁcit. These concepts are at the heart of Chapter 9 by Tommaso Proietti, entitled

“Structural Time Series Models for Business Cycle Analysis,” which links with the

earlier chapters by Pollock and Cardinale and Taylor. Proietti focuses on the measurement of the output gap, which he illustrates throughout using US GDP. In the

simplest case, what is needed is a framework for decomposing a time series into a

trend and cycle and Proietti critically reviews a number of methods to achieve such

a decomposition, including the random walk plus noise (RWpN) model, the local

linear trend model (LLTM), methods based on ﬁltering out frequencies associated

with the cycle, multivariate models that bring together related macroeconomic

variables, and the production function approach. The estimation and analysis of a

number of models enables the reader to see how the theoretical analysis is applied

and what kind of questions can be answered. Included here are a bivariate model

of output and inﬂation for the US and a model of mixed data frequency, with quarterly observations for GDP and monthly observations for industrial production, the

unemployment rate and CPI inﬂation. The basic underlying concepts, such as the

output gap and core inﬂation, are latent variables and, hence, not directly observable: to complete the chapter, Proietti also considers how to judge the validity of

the corresponding empirical measures of these concepts.

To complete the part of the Handbook on Times Series Applications, in Chapter

10 Luis Gil-Alana and Javier Hualde provide an overview of fractional integration

and cointegration, with an empirical application in the context of the PPP debate.

A time series is said to be integrated of order d, where d is an integer, if d is the minimum number of differences necessary to produce a stationary time series. This is

a particular form of non-stationarity and one which dominated the econometrics

xviii

Editors’ Introduction

literature in the 1980s and early 1990s, especially following the unit root literature. However, the integer restriction on d is not necessary to the deﬁnition of an

integrated series (see, in particular, Granger and Joyeux, 1980), so that d can be a

fraction – hence the term “fractionally integrated” for such series. Once the integer

restriction is relaxed for a single series, it is then natural to relax it for the multivariate case, which leads to the idea of fractional cointegration. Gil-Alana and Hualde

give an overview of the meaning of fractional integration and fractional cointegration, methods of estimation for these generalized cases, which can be approached

in either the time or frequency domains, the underlying rationale for the existence

of fractionally integrated series (for example, through the aggregation of microrelationships), and a summary of the empirical evidence for fractionally integrated

univariate series and fractionally cointegrated systems of series. The various issues

and possible solutions are illustrated in the context of an analysis of PPP for four

bivariate series. It is clear that the extension of integration and cointegration to

their corresponding fractional cases is not only an important generalization of the

theory, but one which ﬁnds a great deal of empirical support.

One of the most signiﬁcant developments in econometrics over the last twenty

years or so has been the increase in the number of econometric applications involving cross-section and panel data (see also Ooms, Chapter 29). Hence Part IV is

devoted to this development. One of the key areas of application is to choice situations which have a discrete number of options; examples include the “whether

to purchase” decision, which has wide application across consumer goods, and the

“whether to participate” decision, as in whether to enter the labor force, to retire, or

to join a club. Discrete choice models are the subject of Chapter 11 by Bill Greene,

who provides a critical, but accessible, review of a vast literature. The binary choice

model is a key building block here and so provides a prototypical model with which

to examine such topics as speciﬁcation, estimation and inference; it also allows the

ready extension to more complex models such as bivariate and multivariate binary

choice models and multinomial choice models. Models involving count data are

also considered as they relate to the discrete choice framework. A starting point

for the underlying economic theory is the extension of the classical theory of consumer behavior, involving utility maximization subject to a budget constraint, to

the random utility model. The basic model is developed from this point and a host

of issues are considered that arise in practical studies, including estimation and

inference, speciﬁcation tests, measuring ﬁt, complications from endogenous righthand-side variables, random parameters, the use of panel data, and the extension

of the familiar ﬁxed and random effects. To provide a motivating context, Greene

considers an empirical application involving a bivariate binary choice model. This

is where two binary choice decisions are linked; in this case, in the ﬁrst decision

the individual decides whether to visit a physician, which is a binary choice, and

the second involves whether to visit the hospital, again a binary choice: together

they constitute a bivariate (and ordered) choice. An extension of this model is to

consider the number of times that an individual visits the doctor or a hospital. This

gives rise to a counts model (the number of visits to the doctor and the number of

visits to the hospital) with its own particular speciﬁcation. Whilst a natural place to

Terence C. Mills and Kerry Patterson

xix

start is the Poisson model, this, as Greene shows, is insufﬁcient as a general framework; the extension is provided and illustrated with panel data from the German

health care system. A second application illustrates a mixed logit and error components framework for modeling modes of transport choice (air, train, bus, car).

Overall, this chapter provides an indication, through the variety of its applications,

as to why discrete choice models have become such a signiﬁcant part of applied

econometrics.

The theme of panel data methods and applications is continued in Chapter 12

by Andrew Jones. The application of econometrics to health economics has been

an important area of development over the last decade or so. However, this has not

just been a case of applying existing techniques: rather, econometrics has been able

to advance the subject itself, asking questions that had not previously been asked

– and providing answers. This chapter will be of interest not only to health economics specialists, but also to those seeking to understand how treatment effects in

particular are estimated and to those investigating the extent of the development

and application of panel data methods (it is complemented by Colin Cameron

in Chapter 14). At the center of health economics is the question “What are the

impacts of speciﬁc health policies?” Given that we do not observe experimental

data, what can we learn from non-experimental data? Consider the problem of

evaluating a particular treatment; for an individual, the treatment effect is the difference in outcome between the treated and the control, but since an individual is

either treated or not at a particular time, the treatment effect cannot be observed.

“Treatment” is here a general term that covers not only single medical treatments

but also broad policies, and herein lies its generality, since a treatment could equally

be a policy to reduce unemployment or to increase the proportion of teenagers

receiving higher education. In a masterful understanding of a complex and expanding literature, Jones takes the reader through the theoretical and practical solutions

to the problems associated with estimating and evaluating treatment effects, covering, inter alia, identiﬁcation strategies, dynamic models, estimation methods,

different kinds of data, and multiple equation models; throughout the chapter

the methods and discussion are motivated by practical examples illustrating the

breadth of applications.

A key development in econometrics over the last thirty years or so has been the

attention given to the properties of the data, as these enlighten the question of

whether the underlying probability structure is stationary or not. In a terminological shorthand, we refer to data that is either stationary or non-stationary. Initially,

this was a question addressed to individual series (see Nelson and Plosser, 1982);

subsequently, the focus expanded, through the work of Engle and Granger (1987)

and Johansen (1988), to a multivariate approach to non-stationarity. The next

step in the development was to consider a panel of multivariate series. In Chapter

13, Anindya Banerjee and Martin Wagner bring us up to date by considering panel

methods to test for unit roots and cointegration. The reader will ﬁnd in this chapter

a theoretical overview and critical assessment of a vast and growing body of methods, combined with practical recommendations based on the insights obtained

from a wide base of substantive applications. In part, as is evident in other areas

xx Editors’ Introduction

of econometric techniques and applications, theory has responded to the much

richer sources of data that have become available, not only at a micro or individual level, as indicated in Chapter 12, combined with increases in computing

power. As Banerjee and Wagner note, we now have long time series on macroeconomic and industry-level data. Compared to just twenty years ago, there is thus a

wealth of data on micro, industry and macro-panels. A panel dataset embodies two

dimensions: the cross-section dimension and the time-series dimension, so that,

in a macro-context, for example, we can consider the question of convergence not

just of a single variable (say, of a real exchange rate to a comparator, be that a

PPP hypothetical or an alternative actual rate), but of a group of variables, which

is representative of the multidimensional nature of growth and cycles. A starting

point for such an analysis is to assess the unit root properties of panel data but,

as in the univariate case, issues such as dependency, the speciﬁcation of deterministic terms, and the presence of structural breaks are key practical matters that, if

incorrectly handled, can lead to misleading conclusions. Usually, the question of

unit roots is a precursor to cointegration analysis, and Banerjee and Wagner guide

the reader through the central methods, most of which have been developed in

the last decade. Empirical illustrations, based on exchange rate pass-through in

the euro-area and the environmental Kuznets curve, complement the theoretical

analysis.

Whilst the emphasis in Chapter 13 is on panels of macroeconomic or industrylevel data, in Chapter 14, Colin Cameron, in the ﬁrst of two chapters in Part

V, provides a survey of microeconometric methods, with an emphasis on recent

developments. The data underlying such developments are at the level of the

individual, households and ﬁrms. A prototypical question in microeconometrics

relates to the identiﬁcation, estimation and evaluation of marginal effects using

individual-level data; for example, the effect on earnings of an additional year of

education. This example is often used to motivate some basic estimation methods, such as least squares, maximum likelihood and instrumental variables, in

undergraduate and graduate texts in econometrics, so it is instructive to see how

recent developments have extended these methods. The development of the basic

methods include generalized method of moments (GMM), empirical likelihood,

simulation-based methods, quantile regression and nonparametric and semiparametric estimation, whilst developments in inference include robustifying standard

tests and bootstrap methods. Apart from estimation and inference, Cameron considers a number of other issues that occur frequently in microeconometric studies:

in particular, issues related to causation, as in estimating and evaluating treatment

effects; heterogeneity, for example due to regressors or unobservables; and the

nature of microeconometric data, such as survey data and the sampling scheme,

with problems such as missing data and measurement error.

The development of econometrics in the last decade or so in particular has been

symbiotic with the development of advances in computing, particularly that of personal computers. In Chapter 15, David Jacho-Chávez and Pravin Trivedi focus on

the relationship between empirical microeconometrics and computational considerations, which they call, rather evocatively, a “matrimony” between computing

Terence C. Mills and Kerry Patterson

xxi

and applied econometrics. No longer is it the case that the mainstay of empirical

analysis is a set of macroeconomic time series, often quite limited in sample period.

Earlier chapters in this part of the volume emphasize that the data sources now

available are much richer than this, both in variety and length of sample period.

As Jacho-Chávez and Trivedi note, the electronic recording and collection of data

has led to substantial growth in the availability of census and survey data. However,

the nature of the data leads to problems that require theoretical solutions: for example, problems of sample selection, measurement errors and missing or incomplete

data. On the computing side, the scale of the datasets and estimation based upon

them implies that there must be reliability in the high-dimensional optimization

routines required by the estimation methods and an ability to handle large-scale

Monte Carlo simulations. The increase in computing power has meant that techniques that were not previously feasible, such as simulation assisted estimation

and resampling, are now practical and in widespread use. Moreover, nonparametric and semiparametric methods that involve the estimation of distributions rather

than simple parameters, as in regression models, have been developed through

drawing on the improved power of computers. Throughout the chapter, JachoChávez and Trivedi motivate their discussion by the use of examples of practical

interest, including modeling hedonic prices of housing attributes, female labor

force participation, Medicare expenditure, and number of doctor visits. Interestingly, they conclude that there are important problems, particularly those related

to assessing public policy, such as identiﬁcation and implementation in the context of structural, dynamic and high-dimensional models, which remain to be

solved.

In Part VI, the theme of the importance of economic policy is continued, but

with the emphasis now on monetary policy and macroeconomic policy, which

remain of continued importance. Starting in the 1970s and continuing into the

1990s, the development of macroeconometric models for policy purposes was a

highly regarded area; during that period computing power was developing primarily through mainframe computers, allowing not so much the estimation as the

simulation of macroeconomic models of a dimension that had not been previously

contemplated. Government treasuries, central banks and some non-governmental

agencies developed their own empirical macro-models comprising hundreds of

equations. Yet, these models failed to live up to their promise, either wholly or in

part. For some periods there was an empirical failure, the models simply not being

good enough; but, more radically, the theoretical basis of the models was often

quite weak, at least relative to the theory of the optimizing and rational agent and

ideas of intertemporal general equilibrium.

In Chapter 16, Carlo Favero expands upon this theme, especially as it relates to

the econometrics of monetary policy and the force of the critiques by Lucas (1976)

and Sims (1980). A key distinction in the dissection of the modeling corpse is

between structural identiﬁcation and statistical identiﬁcation. The former relates to

the relationship between the structural parameters and the statistical parameters in

the reduced form, while the latter relates to the properties of the statistical or empirical model which represents the data. Typically, structural identiﬁcation is achieved

xxii Editors’ Introduction

by parametric restrictions seeking to classify some variables as “exogenous,” a task

that some have regarded as misguided (or indeed even “impossible”). Further, a

failure to assess the validity of the reduction process in going from the (unknown)

data-generating process to a statistical representation, notwithstanding criticisms

related to structural identiﬁcation, stored up nascent empirical failure awaiting the

macreconometric model. Developments in cointegration theory and practice have

“tightened” up the speciﬁcation of empirical macromodels, and DSGE models, preferred theoretically by some, have provided an alternative “modellus operandi.”

Subsequently, the quasi-independence of some central banks has heightened the

practical importance of questions such as “How should a central bank respond to

shocks in macroeconomic variables?” (Favero, Chapter 16). In practice, although

DSGE models are favored for policy analysis, in their empirical form the VAR

reappears, but with their own set of issues. Favero considers such practical developments as calibration and model evaluation, the identiﬁcation of shocks, impulse

responses, structural stability of the parameters, VAR misspeciﬁcation and factor

augmented VARs. A summary and analysis of Sims’ (2002) small macroeconomic

model (Appendix A) helps the reader to understand the relationship between an

optimizing speciﬁcation and the resultant VAR model.

In Chapter 17, Gunnar Bårdsen and Ragnar Nymoen provide a paradigm for

the construction of a dynamic macroeconometric model, which is then illustrated with a small econometric model of the Norwegian economy that is used

for policy analysis. Bårdsen and Nymoen note the two central critiques of “failed”

macroeconometric models: the Lucas (1976) critique and the Clements and Hendry

(1999) analysis of forecast failure involving “location” shifts (rather than behavioral parameter shifts). But these critiques have led to different responses; ﬁrst, the

move to explicit optimizing models (see Chapter 16); and, alternatively, to greater

attention to the effects of regime shifts, viewing the Lucas critique as a possibility

theorem rather than a truism (Ericsson and Irons, 1995). Whilst it is de rigueur

to accept that theory is important, Bårdsen and Nymoen consider whether “theory” provides the (completely) correct speciﬁcation or whether it simply provides a

guideline for the speciﬁcation of an empirical model. In their approach, the underlying economic model is nonlinear and speciﬁed in continuous time; hence, the

ﬁrst practical steps are linearization and discretization, which result in an equilibrium correction model (EqCM). Rather than remove the data trends, for example

by applying the HP ﬁlter, the common trends are accounted for through a cointegration analysis. The approach is illustrated step by step by building a small-scale

econometric model of the Norwegian economy, which incorporates the ability to

analyze monetary policy; for example, an increase in the market rate, which shows

the channels of the operation of monetary policy. Further empirical analysis of the

New Keynesian Phillips curve provides an opportunity to illustrate their approach

in another context. In summary, Bårdsen and Nymoen note that cointegration

analysis takes into account non-stationarities that arise through unit roots, so that

forecast failures are unlikely to be attributable to misspeciﬁcation for that reason.

In contrast to the econometric models of the 1970s, the real challenges arise from

non-stationarities in functional relationships due to structural breaks; however,

Terence C. Mills and Kerry Patterson

xxiii

there are ways to “robustify” the empirical model and forecasts from it so as to

mitigate such possibilities, although challenges remain in an area that continues

to be of central importance in economic policy.

One of the key developments in monetary policy in the UK and elsewhere in

the last decade or so has been the move to give central banks a semi-autonomous

status. In part, this was thought to avoid the endogenous “stop–go” cycle driven by

political considerations. It also carried with it the implication that it was monetary

policy, rather than ﬁscal policy, which would become the major macroeconomic

policy tool, notwithstanding the now apparent practical limitations of such a

move. In Chapter 18, Brian Henry provides an overview of the institutional and

theoretical developments in the UK in particular, but with implications for other

countries that have taken a similar route. The key question that is addressed in

this chapter is whether regime changes, such as those associated with labor market

reforms, inﬂation targeting and instrument independence for the Bank of England, have been the key factors in dampening the economic cycle and improving

inﬂation, unemployment and output growth, or whether the explanation is more

one of beneﬁcial international events (the “good luck” hypothesis) and monetary

policy mistakes. Henry concludes, perhaps controversially, that the reforms to the

labor market and to the operation of the central bank are unlikely to have been the

fundamental reasons for the improvement in economic performance. He provides

an econometric basis for these conclusions, which incorporates a role for international factors such as real oil prices and measures of international competitiveness.

Once these factors are taken into account, the “regime change” explanation loses

force.

The growth of ﬁnancial econometrics in the last two decades was noted in the

ﬁrst volume of this Handbook. Indeed, this development was recognized in the

award of the 2003 Nobel Prize in Economics (jointly with Sir Clive Granger) to

Robert Engle for “methods of analyzing economic time series with time-varying

volatility (ARCH).” Part VII of this volume reﬂects this development and is thus

devoted to applications in the area of ﬁnancial econometrics.

In Chapter 19, George Dotsis, Raphael Markellos and Terence Mills consider

continuous-time stochastic volatility models. What is stochastic volatility? To

answer that question, we start from what it is not. Consider a simple model of an

asset price, Y(t), such as geometric Brownian motion, which in continuous time

takes the form of the stochastic differential equation dY(t) = μY(t) + σ Y(t)dW(t),

2

where W(t) is a standard Brownian motion (BM) input; then σ (or σ ) is the volatility parameter that scales the stochastic BM contribution to the diffusion of Y(t).

In this case the volatility parameter is constant, although the differential equation

is stochastic. However, as Dotsis et al. note, a more appropriate speciﬁcation for

the accepted characteristics of ﬁnancial markets is a model in which volatility

also evolves stochastically over time. For example, if we introduce the variance

√

function v(t), then the simple model becomes dY(t) = μY(t) + v(t)Y(t)dW(t),

and this embodies stochastic volatility. Quite naturally, one can then couple this

equation with one that models the diffusion over time of the variance function.

ARCH/GARCH models are one way to model time-varying volatility, but there are

xxiv Editors’ Introduction

a number of other attractive speciﬁcations; for example, jump diffusions, afﬁne

diffusions, afﬁne jump diffusions and non-afﬁne diffusions. In motivating alternative speciﬁcations, Dotsis et al. note some key empirical characteristics in ﬁnancial

markets that underlie the rationale for stochastic volatility models, namely fat

tails, volatility clustering, leverage effects, information arrivals, volatility dynamics and implied volatility. The chapter then continues by covering such issues as

speciﬁcation, estimation and inference in stochastic volatility models. A comparative evaluation of ﬁve models applied to the S&P 500, for daily data over the

period 1990–2007, is provided to enable the reader to see some of the models “in

action.”

One of the most signiﬁcant ideas in the area of ﬁnancial econometrics is that the

underlying stochastic process for an asset price is a martingale. Consider a stochastic process X = (Xt , Xt−1 , . . .), which is a sequence of random variables; then the

martingale property is that the expectation (at time t − 1) of Xt , conditional on the

information set It−1 = (Xt−1 , Xt−2 , . . .), is Xt−1 ; that is, E(Xt |It−1 ) = Xt−1 (almost

surely), in which case, X is said to be a martingale (the deﬁnition is sometimes

phrased in terms of the σ -ﬁeld generated by It−1 , or indeed some other “ﬁltration”). Next, deﬁne the related process Y = ( Xt , Xt−1 , . . .); then Y is said to be a

martingale difference sequence (MDS). The martingale property for X translates to

the property for Y that E(Yt |It−1 ) = 0 (see, for example, Mikosch, 1998, sec. 1.5).

This martingale property is attractive from an economic perspective because of its

link to efﬁcient markets and rational expectations; for example, in terms of X, the

martingale property says that the best predictor, in a minimum mean squared error

(MSE) sense, of Xt is Xt−1 .

In Chapter 20, J. Carlos Escanciano and Ignacio Lobato consider tests of the

martingale difference hypothesis (MDH). The MDH generalizes the MDS condition

to E(Yt |It−1 ) = μ, where μ is not necessarily zero; it implies that past and current

information (as deﬁned in It ) are of no value, in an MSE sense, in forecasting future

values of Yt . Tests of the MDH can be seen as being translated to the equivalent

form given by E[(Yt − μ)w(It−1 )], where w(It−1 ) is a weighting function. A useful

means of organizing the extant tests of the MDH is in terms of the type of functions

w(.) that are used. For example, if w(It−1 ) = Yt−j , j ≥ 1, then the resulting MDH

test is of E[(Yt − μ)Yt−j ] = 0, which is just the covariance between Yt and Yt−j .

This is just one of a number of tests, but it serves to highlight some generic issues.

In principle, the condition should hold for all j ≥ 1 but, practically, j has to be

truncated to some ﬁnite value. Moreover, this is just one choice of w(It−1 ), whereas

the MDH condition is not so restricted. Escanciano and Lobato consider issues such

as the nature of the conditioning set (ﬁnite or inﬁnite), robustifying standard test

statistics (for example, the Ljung–Box and Box–Pierce statistics), and developing

tests in both the time and frequency domains; whilst standard tests are usually

of linear dependence, for example autocorrelation based tests, it is important to

consider tests based on nonlinear dependence. To put the various tests into context,

the chapter includes an application to four daily and weekly exchange rates against

the US dollar. The background to this is that the jury is out in terms of a judgment

on the validity of the MDH for such data; some studies have found against the