In the last decade, there have been rapid and enormous developments in the field of unit roots and cointegration, but this progress has taken divergent directions and has been subjected to criticism from outside the field. This book responds to those criticisms, clearly relating cointegration to economic theories and describing cointegrated regression as a revolution in econometric methods for macroeconomics. It provides a guide for the selection of appropriate inference methods to study macroeconomic relations. The discussion of unit roots and cointegration starts from first principles, builds up explanations of concepts and techniques step-by-step, and ultimately shows how the techniques have been applied to economic studies.
Author(s): Michio Hatanaka
Series: Advanced Texts in Econometrics
Publisher: Oxford University Press(UK)
Year: 1996
Language: English
Pages: 307
Contents......Page 8
List of figures......Page 12
PART I: UNIT-ROOT TESTS IN UNIVARIATE ANALYSIS......Page 14
1.1 Stochastic Trend......Page 16
1.2 Stochastic Trend as a Logical Implication of an Economic Theory?......Page 22
1.3 Influences upon the Testing of Economic Theories......Page 23
1.4 Overview of Part I......Page 26
2.1 Basic Discrimination......Page 29
2.2 Long-Run Component......Page 30
2.3 Dominating Root of Characteristic Polynomial......Page 35
2.4 Non-Separate Hypotheses......Page 37
2.5 Time Aggregation and Other Remarks on the Data......Page 38
3.1 Non-parametric Variance Ratios and Mean-Reverting......Page 41
3.2 Difficulty of Discrimination through the Non-parametric Variance Ratios......Page 43
3.3 Time-Series Decomposition......Page 46
3.4 Parametric MA Unit-Root Test: A Test for Trend Stationarity against Difference Stationarity......Page 47
4.1 Pure Random Walk without a Drift......Page 53
4.2 Pure Random Walk possibly with a Drift......Page 57
5.1 A Method that Does not Work......Page 60
5.2 Dickey-Fuller Test......Page 61
5.3 The Case where the Deterministic Trend is Confined to a Constant......Page 63
6.1 Deterministic Trends......Page 64
6.2 Series Correlations in Δx[sub(t)]......Page 67
6.3 MA Unit-Root Test......Page 72
7.1 The Case where Δx[sub(t)], is an AR......Page 76
7.2 ARMA in General and the Schwert ARMA......Page 77
7.3 Miscellaneous Remarks......Page 80
Highlights of Chapters 4-7......Page 83
8.1 Various Modes of Deterministic Trends......Page 87
8.2 Encompassing and 'General-to-Specific' Principles on the Model Selection......Page 90
8.3 Simulation Studies on the Comparison of P-values......Page 97
9. Results of the Model Selection Approach......Page 103
9.1 Deterministic Trends Amenable to the DS and the TS......Page 104
9.2 Discrimination between TS and DS......Page 105
10.1 Differences between the Bayesian and the Classic Theories......Page 115
10.2 Different Versions of the Hypotheses......Page 117
10.3 Problems Associated with the First Version......Page 118
10.4 Point Null Hypotheses......Page 122
10.5 Results in the Second and the Third Versions......Page 125
PART II: CO-INTEGRATION ANALYSIS IN ECONOMETRICS......Page 128
Overview......Page 130
11.1 Economic Models and Statistical Models......Page 133
11.2 Weak Exogeneity......Page 137
11.3 Granger Non-Causality......Page 142
12. Conceptual Framework of the Co-Integration and its Relation to Economic Theories......Page 148
12.1 Co-integration in the MA Representation......Page 149
12.2 Granger Representation Theorem......Page 153
12.3 Economic Theory and Co-integration......Page 163
Highlights of Chapter 12......Page 174
13. Asymptotic Inference Theories on Co-Integrated Regressions......Page 177
13.1 Pure Random Walk......Page 179
13.2 Deterministic Polynomial Trends......Page 191
13.3 Serially Correlated Case......Page 200
13.4 Miscellaneous Remarks including Direction of Co-integration......Page 206
13.5 A Priori Specified Co-integrating Vector......Page 211
13.6 Shortcomings in Many Past Empirical Studies......Page 212
Highlights of Chapter 13......Page 214
14. Inference on Dynamic Econometric Models......Page 217
14.1 Hendry Model with the Two-Step Method......Page 220
14.2 Dynamic Equation with the Two-Step Method......Page 222
14.3 Hendry Model with the Single-Step Method......Page 224
14.4 Dynamic Equation with the Single-Step Method......Page 228
15. Maximum-Likelihood Inference Theory of Co-Integrated VAR......Page 232
15.1 Determination of Co-integration Rank......Page 234
15.2 Testing for Restrictions on the Co-integration Space......Page 243
15.4 Weak Exogeneity and Granger Non-causality......Page 249
15.5 Applications......Page 254
Appendix 1 Spectral Analysis......Page 260
Appendix 2 Wiener (Brownian Motion) Process......Page 262
Appendix 3 Asymptotic Theories involving a Linear Deterministic Trend......Page 264
Appendix 4 OLS Estimator of Difference-Stationary Autoregressive Process......Page 271
Appendix 5 Mathematics for the VAR, VMA, and VARMA......Page 273
Appendix 6 Fully Modified Least-Squares Estimator......Page 278
References......Page 282
I......Page 302
W......Page 303
G......Page 304
L......Page 305
S......Page 306
Z......Page 307
