Co-Integration for the Applied Economist Book

List of Tables x

List of Figures and Screens xiii

Preface to the First Edition xiv

Preface to the Second Edition xvi

Notes on Contributors xviii

1 Introduction B. Bhaskara Rao 1

1.1 Introduction 1

1.2 Unit roots and cointegration 1

1.3 Economic implications 3

1.4 An overview of the papers 5

1.5 Concluding observations 8

2 A Primer on Cointegration with an Application to Money and Income David A. Dickey Dennis W. Jansen Daniel L. Thornton 10

2.1 Introduction 10

2.2 Testing for cointegration: a general framework 10

2.2.1 Locating stationary linear combination of variables 12

2.2.2 Multiple cointegrating vectors 13

2.2.3 Tests for cointegration and their relation to unit root tests 15

2.3 Is there an economic interpretation of cointegration vectors? 16

2.3.1 Cointegration with exogenous variables 16

2.3.2 Should there be many or few cointegrating vectors? 20

2.4 Alternative tests for cointegration 21

2.4.1 A note about distributions 22

2.4.2 Other approaches to cointegration 23

2.5 An application of cointegration: the demand for money 24

2.5.1 The velocity of M1 and M2 25

2.5.2 The velocity of the monetary base 28

2.5.3 Empirical results 28

2.5.4 Tests for the order of integration 29

2.5.5 Tests for cointegration using three methodologies 29

2.5.6 Cointegration using alternative monetary aggregates 32

2.5.7 Cointegration and the monetary base 34

2.6 Summary and conclusions 35

Appendix to Chapter 2 36

3 Unit Roots and Cointegration for the Economist Darryl Holden Roger Perman 43

3.1 Introduction 43

3.2 Stationarity and unit roots 45

3.2.1 Stationary time series 45

3.2.2 The first order autoregressiveprocess: AR(1) 45

3.2.3 Second order autoregressive case: AR(2) 50

3.3 Testing for unit roots 51

3.3.1 The Dickey-Fuller tests 51

3.3.2 The Augmented Dickey-Fuller regression 55

3.3.3 A suggested sequential procedure for unit root testing 56

3.3.4 Phillips and Perron tests 59

3.3.5 Unit root tests and structural breaks 61

3.3.6 Trend and difference stationarity 63

3.4 The error correction mechanism (ECM) 64

3.5 Cointegration 66

3.5.1 The cointegrating regression 70

3.5.2 Testing for cointegration 71

3.5.3 Estimating the ECM 72

3.5.4 Johansen procedure 74

3.6 Cointegration and econometric modelling 80

3.7 Concluding comments 83

Appendix to Chapter 3 84

4 The Significance of Unit Roots and the Pitfalls of Mechanical Statistics Ron Smith 101

4.1 Introduction 101

4.2 Mechanical statistics 103

4.3 Applied econometrics 104

4.4 Significance 107

4.5 Unit roots 109

4.6 VARs, error correction and cointegration 115

4.7 Weak exogeneity 122

4.8 Identification 124

4.9 Conclusions 127

5 Unit Roots and Structural Breaks: A Survey of the Literature Joseph P. Byrne Roger Perman 129

5.1 Introduction 129

5.2 Unit roots and ADF tests 130

5.3 Exogenous structural breaks 131

5.4 Endogenous structural breaks 132

5.5 Non-linear breaks and GLS detrending 134

5.6 Multiple structural breaks 135

5.6.1 Two structural breaks 136

5.6.2 Multiple breaks 136

5.7 Unit roots and structural breaks: applied papers 137

5.8 Other issues 138

5.9 Conclusion 139

5.10 Software 141

6 New Unit Root Tests Designed for the Trend-Break Stationary Alternative: Simulation Evidence and Empirical Applications Amit Sen 143

6.1 Introduction 143

6.2 Model and test statistics 145

6.3 Finite sample size and power 159

6.4 Empirical applications 188

6.4.1 Extended Nelson-Plosser data set 188

6.4.2 Real per capita GDP for 18 OECD countries 191

6.5 Conclusions 192

Appendix A 192

Appendix B 193

7 How to Deal with Structural Breaks in Practical Cointegration Analysis? Roselyne Joyeux 195

7.1 Introduction 195

7.2 Univariate case 196

7.2.1 Shift in intercept model 196

7.2.2 Shift in mean and trend model 198

7.2.3 Generalization to an AR(k) process 199

7.2.4 Generalization to the case of more than one shift 199

7.3 Multivariate case 200

7.3.1 Shift in intercept model: none of the p time series have a deterministic trend 202

7.3.2 Some or all of the time series follow a trending pattern 203

7.3.3 Some or all of the time series follow a trending pattern in each sub-sample and the cointegrating relations are stationary in each sub-sample (with possibly a broken constant level); trend breaks are allowed only in the non-stationary series 203

7.3.4 Unit root tests 203

7.4 Empirical illustration: A German money-demand system 203

7.4.1 Description 203

7.4.2 The analysis 205

7.5 Conclusion 213

Appendix to Chapter 7 213

7A.1 Specification of the model: deterministic components and exogenous variables 215

7A.2 Cointegration tests 215

7A.3 Empirical illustration: a German money-demand system 216

7A.4 Other important matters 221

8 Panel Cointegration Analysis: An Empirical Example N.R. Vasudeva Murthy 222

8.1 Introduction 222

8.2 Model specification, data and cointegration analysis 224

8.3 Empirical results 228

8.4 Conclusions 233

Appendix to Chapter 8 233

References 245

Index 257