The Cointegrated VAR Model: Methodology and Applications

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OUP Oxford, Dec 7, 2006 - Business & Economics - 480 pages
This valuable text provides a comprehensive introduction to VAR modelling and how it can be applied. In particular, the author focuses on the properties of the Cointegrated VAR model and its implications for macroeconomic inference when data are non-stationary. The text provides a number of insights into the links between statistical econometric modelling and economic theory and gives a thorough treatment of identification of the long-run and short-run structure as well as of the common stochastic trends and the impulse response functions, providing in each case illustrations of applicability. This book presents the main ingredients of the Copenhagen School of Time-Series Econometrics in a transparent and coherent framework. The distinguishing feature of this school is that econometric theory and applications have been developed in close cooperation. The guiding principle is that good econometric work should take econometrics, institutions, and economics seriously. The author uses a single data set throughout most of the book to guide the reader through the econometric theory while also revealing the full implications for the underlying economic model. To test ensure full understanding the book concludes with the introduction of two new data sets to combine readers understanding of econometric theory and economic models, with economic reality.
 

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Contents

12
121 Identification when data are nonstationary
122 Identifying restrictions1
123 Formulation of identifying hypotheses and degrees of freedom
124 Justidentifying restrictions
125 Overidentifying restrictions
126 Lack of identification
127 Recursive tests of α and β

22 Inflation and money growth
23 The time dependence of macroeconomic data
24 A stochastic formulation
treating prices as I2
treating prices as I1
27 Concluding remarks
3
31 A single timeseries process
32 A vector process
33 Reviewing some useful results
34 Deriving the VAR1
35 Interpreting the VAR model
36 The dynamic properties of the VAR process
37 Concluding remarks
Part II
4
41 Likelihoodbased estimation in the unrestricted VAR
42 Three different ECM representations
43 Misspecification tests
44 Concluding remarks
5
51 Defining integration and cointegration
52 An intuitive interpretation of Π αβ
53 Common trends and the moving average representation
54 From the AR to the MA representation
55 Pulling and pushing forces
56 Concluding discussion
6
62 A trend and a constant in the VAR
63 Five cases
64 The MA representation with deterministic components
65 Dummy variables in a simple regression model
66 Dummy variables and the VAR
67 An illustrative example
68 Conclusions
7
72 Derivation of the ML estimator
73 Normalization
74 The uniqueness of the unrestricted estimates
75 An illustration
76 Interpreting the results
77 Concluding remarks
8
81 The LR test for cointegration rank
82 The asymptotic tables with a trend and a constant in the model
83 The role of dummy variables for the asymptotic tables
84 Similarity and rank determination
a difficult choice
86 An illustration based on the Danish data
87 Concluding remarks
Part III
9
91 Diagnosing parameter nonconstancy
92 Forward recursive tests
93 Backward recursive tests
94 Concluding remarks
10
101 Formulating hypotheses as restrictions on β
102 Same restriction on all β
103 Some β vectors assumed known
104 Only some coefficients are restricted
105 Revisiting the scenario analysis
11
111 Longrun weak exogeneity
112 Weak exogeneity and partial models
113 Testing a known vector in α
114 Concluding remarks
Part IV
128 Concluding discussion
13
131 Formulating identifying restrictions
132 Interpreting shocks
133 Which economic questions?
134 Restrictions on the shortrun reducedform model
135 The VAR in triangular form
136 Imposing general restrictions on A0
137 A partial system
138 Concluding remarks
14
141 The common trends representation
142 The unrestricted MA representation
143 The MA representation subject to restrictions on α and β
144 Imposing exclusion restrictions on β
145 Assessing the economic model scenario
146 Concluding remarks
15
151 Reparametrization of the VAR model
152 Separation between transitory and permanent shocks
153 How to formulate and interpret structural shocks
154 An illustration
155 Are the labels credible?
Part V
16
161 Linking the I1 and the I2 model
162 Stochastic and deterministic trends in the nominal variables
163 I2 symptoms in I1 models
164 Is the nominaltoreal transformation acceptable?
165 Concluding remarks
17
171 Structuring the I2 model
172 Deterministic components in the I2 model
173 ML estimation and some useful parametrizations
174 Estimating the I2 model
175 Concluding discussion
18
181 Testing price homogeneity
182 Assessing the I1 results within the I2 model
183 An empirical scenario for nominal money and prices
184 Concluding discussion
Part VI
19
191 The generaltospecific and the VAR
192 The specifictogeneral in the choice of variables
193 Gradually increasing the information set
194 Combining partial systems
195 Introducing the new data
20
201 Economic background
202 The data and the models
the EMS regime
The postBrettonWoods regime
205 Concluding discussion
21
211 International parity conditions
212 The data and the models
213 Analysing the longrun structure
214 Concluding remarks
22
221 The full model estimates
222 What have we learnt about inflationary mechanisms?
223 Concluding discussion
APPENDIX A
APPENDIX B
Bibliography
Index
Copyright

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About the author (2006)

Katarina Juselius obtained her Ph.D from the Swedish School of Economics, Helsinki in 1983. In 1985 she became Associate Professor at the University of Copenhagen and in 1996 she was appointed the Chair of Macroeconometrics. She has published extensively on the methodology of Cointegrated VAR Models with applications to Monetary Transmission Mechanisms, Policy Control Rules, Price Linkages, Wage-, Price, and Unemployment Dynamics. She has been the leader of numerous research projects, and has been on the editorial boards of the International Journal of Forecasting, the Journal of Business and Economic Statistics, and is presently serving the Journal of Economic Methodology. In 1995-98 she was a member of the Danish Social Sciences Research Council and is presently a member of the EUROCORES committee at the European Science Foundation.

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