This book is wide-ranging in its account of literature on cointegration and the modelling of integrated processes (those which accumulate the effects of past shocks). Data series which display integrated behavior are common in economics, although techniques appropriate to analyzing such data are relatively new, with few existing expositions of the literature. This book explores relationships among integrated data series and their use in dynamic econometric modelling. The concepts of cointegration and error-correction models are fundamental components of the modelling strategy. This area of time series econometrics has grown in importance over the past decade and is of interest to both econometric theorists and applied econometricians. By explaining the important concepts informally and presenting them formally, the book bridges the gap between purely descriptive and purely theoretical accounts of the literature. The work describes the asymptotic theory of integrated processes and uses the tools provided by this theory to develop the distributions of estimators and test statistics. It emphasizes practical modelling advice and the use of techniques for systems estimation. A knowledge of econometrics, statistics, and matrix algebra at the level of a final-year undergraduate or first-year undergraduate course in econometrics is sufficient for most of the book. Other mathematical tools are described as they occur. About the SeriesAdvanced Texts in Econometrics is a distinguished and rapidly expanding series in which leading econometricians assess recent developments in such areas as stochastic probability, panel and time series data analysis, modeling, and cointegration. In both hardback and affordable paperback, each volume explains the nature and applicability of a topic in greater depth than possible in introductory textbooks or single journal articles. Each definitive work is formatted to be as accessible and convenient for those who are not familiar with the detailed primary literature.
Author(s): Anindya Banerjee, Juan Dolado, J. W. Galbraith, David Hendry
Year: 1993
Language: English
Pages: 352
Contents......Page 8
Notational Conventions, Symbols, and Abbreviations......Page 12
1. Introduction and Overview......Page 16
1.1. Equilibrium relationships and the long run......Page 17
1.2. Stationarity and equilibrium relationships......Page 19
1.3. Equilibrium and the specification of dynamic models......Page 20
1.4. Estimation of long-run relationships and testing for orders of integration and co-integration......Page 23
1.5. Preliminary concepts and definitions......Page 25
1.6. Data representation and transformations......Page 43
1.7. Examples: typical ARMA processes......Page 47
1.8. Empirical time series: money, prices, output, and interest rates......Page 55
1.9. Outline of later chapters......Page 57
Appendix......Page 58
2 Linear Transformations, Error Correction, and the Long Run in Dynamic Regression......Page 61
2.1. Transformations of a simple model......Page 63
2.2. The error-correction model......Page 65
2.3. An example......Page 67
2.4. Bdrdsen and Bewley transformations......Page 68
2.5. Equivalence of estimates from different transformations......Page 70
2.6. Homogeneity and the ECM as a linear transformation of the ADL......Page 75
2.7. Variances of estimates of long-run multipliers......Page 76
2.8. Expectational variables and the interpretation of long-run solutions......Page 79
3 Properties of Integrated Processes......Page 84
3.1. Spurious regression......Page 85
3.2. Trends and random walks......Page 96
3.3. Some statistical features of integrated processes......Page 99
3.4. Asymptotic theory for integrated processes......Page 101
3.5. Using Wiener distribution theory......Page 106
3.6. Near-integrated processes......Page 110
4. Testing for a Unit Root......Page 114
4.1. Similar tests and exogenous regressors in the DGP......Page 119
4.2. General dynamic models for the process of interest......Page 121
4.3. Non-parametric tests for a unit root......Page 123
4.4. Tests on more than one parameter......Page 128
4.5. Further extensions......Page 134
4.6. Asymptotic distributions of test statistics......Page 138
5. Co-integration......Page 151
5.1. An example......Page 152
5.2. Polynomial matrices......Page 155
5.3. Integration and co-integration: formal definitions and theorems......Page 160
5.5. Alternative representations of co-integrated variables: two examples......Page 168
5.6. Engle–Granger two-step procedure......Page 172
6. Regression with Integrated Variables......Page 177
6.1. Unbalanced regressions and orthogonality tests......Page 179
6.2. Dynamic regressions......Page 183
6.3. Functional forms and transformations......Page 207
Appendix: Vector Brownian Motion......Page 215
7. Co-integration in Individual Equations......Page 219
7.1. Estimating a single co-integrating vector......Page 220
7.2. Tests for co-integration in a single equation......Page 221
7.3. Response surfaces for critical values......Page 226
7.4. Finite-sample biases in OLS estimates......Page 229
7.5. Powers of single-equation co-integration tests......Page 245
7.8. A fully modified least-squares estimator......Page 255
7.7. Fully modified estimation......Page 254
7.9. Dynamic specification......Page 257
7.10. Examples......Page 259
Appendix: Covariance Matrices......Page 267
8. Co-integration in Systems of Equations......Page 270
8.1. Co-integration and error correction......Page 272
8.2. Estimating co-integrating vectors in systems......Page 276
8.3. Inference about the co-integration space......Page 281
8.4. An empirical illustration......Page 283
8.5. Extensions......Page 286
8.6. A second example of the Johansen maximum likelihood approach......Page 307
8.7. Asymptotic distributions of estimators of co-integrating vectors in I(1) systems......Page 308
9.1. Summary......Page 314
9.2. The invariance of co-integrating vectors......Page 315
9.3. Invariance of co-integration under seasonal adjustment......Page 316
9.4. Structured time-series models and co-integration......Page 318
9.5. Recent research on integration and co-integration......Page 319
9.6. Reinterpreting econometrics time-series problems......Page 322
References......Page 326
Acknowledgements for Quoted Extracts......Page 336
I......Page 338
Y......Page 339
C......Page 340
F......Page 341
N......Page 342
T......Page 343
W......Page 344
