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Cointegrated VAR Model: Methodology and Applications [Pehme köide]

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(Professor at the Institute of Economics, University of Copenhagen)
  • Formaat: Paperback / softback, 478 pages, kõrgus x laius x paksus: 245x170x25 mm, kaal: 806 g, numerous tables, line drawings and mathematical examples
  • Sari: Advanced Texts in Econometrics
  • Ilmumisaeg: 07-Dec-2006
  • Kirjastus: Oxford University Press
  • ISBN-10: 0199285675
  • ISBN-13: 9780199285679
Teised raamatud teemal:
Cointegrated VAR Model: Methodology and ApplicationsSuurem pilt
  • Formaat: Paperback / softback, 478 pages, kõrgus x laius x paksus: 245x170x25 mm, kaal: 806 g, numerous tables, line drawings and mathematical examples
  • Sari: Advanced Texts in Econometrics
  • Ilmumisaeg: 07-Dec-2006
  • Kirjastus: Oxford University Press
  • ISBN-10: 0199285675
  • ISBN-13: 9780199285679
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780199285679.html
Märksõnad:
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.
Preface vii
I Bridging economics and econometrics 1
1 Introduction
3
1.1 On the choice of economic models
4
1.2 Theoretical, true and observable variables
6
1.3 Testing a theory as opposed to a hypothesis
7
1.4 Experimental design in macroeconomics
8
1.5 On the choice of empirical example
9
2 Models and relations in economics and econometrics
13
2.1 The VAR approach and theory-based models
14
2.2 Inflation and money growth
15
2.3 The time dependence of macroeconomic data
18
2.4 A stochastic formulation
21
2.5 Scenario analyses: treating prices as I(2)
27
2.6 Scenario analyses: treating prices as I(1)
32
2.7 Concluding remarks
32
3 The probability approach in econometrics, and the VAR
35
3.1 A single time-series process
35
3.2 A vector process
38
3.2.1 An illustration
40
3.3 Reviewing some useful results
42
3.4 Deriving the VAR
43
3.5 Interpreting the VAR model
46
3.6 The dynamic properties of the VAR process
48
3.6.1 The roots of the characteristic function
48
3.6.2 Calculating the eigenvalue roots using the companion matrix
50
3.6.3 Illustration
51
3.7 Concluding remarks
52
II Specifying the VAR model 53
4 The unrestricted VAR
55
4.1 Likelihood-based estimation in the unrestricted VAR
55
4.1.1 The estimates of the unrestricted VAR(2) for the Danish data
59
4.2 Three different ECM representations
60
4.2.1 The ECM formulation with m = 1
61
4.2.2 The ECM formulation with m = 2
63
4.2.3 ECM representation in acceleration rates, changes and levels
64
4.2.4 The relationship between the different VAR formulations
65
4.3 Misspecification tests
66
4.3.1 Specification checking
66
4.3.2 Residual correlations and information criteria
66
4.3.3 Tests of residual autocorrelation
73
4.3.4 Tests of residual heteroscedasticity
74
4.3.5 Normality tests
75
4.4 Concluding remarks
77
5 The cointegrated VAR model
79
5.1 Defining integration and cointegration
79
5.2 An intuitive interpretation of II = α&beta:'
80
5.3 Common trends and the moving average representation
84
5.4 From the AR to the MA representation
85
5.5 Pulling and pushing forces
88
5.6 Concluding discussion
90
6 Deterministic components in the I(1) model
93
6.1 A trend and a constant in a simple dynamic regression model
93
6.2 A trend and a constant in the VAR
95
6.3 Five cases
99
6.4 The MA representation with deterministic components
100
6.5 Dummy variables in a simple regression model
102
6.6 Dummy variables and the VAR
104
6.7 An illustrative example
109
6.8 Conclusions
112
7 Estimation in the 1(1) model
115
7.1 Concentrating the general VAR model
115
7.2 Derivation of the ML estimator
117
7.3 Normalization
120
7.4 The uniqueness of the unrestricted estimates
120
7.5 An illustration
121
7.6 Interpreting the results
124
7.7 Concluding remarks
128
8 Determination of cointegration rank
131
8.1 The LR test for cointegration rank
131
8.2 The asymptotic tables with a trend and a constant in the model
134
8.3 The role of dummy variables for the asymptotic tables
139
8.4 Similarity and rank determination
139
8.5 The cointegration rank: a difficult choice
140
8.6 An illustration based on the Danish data
143
8.7 Concluding remarks
145
III Testing hypotheses on cointegration 147
9 Recursive tests of constancy
149
9.1 Diagnosing parameter non-constancy
149
9.2 Forward recursive tests
151
9.2.1 The recursively calculated log likelihood
151
9.2.2 Recursively calculated trace test statistics
153
9.2.3 Recursively calculated eigenvalues λi
154
9.2.4 The fluctuations test
157
9.2.5 The max test of constant β
159
9.2.6 Tests of 'βt equals a known β
160
9.2.7 Recursively calculated prediction tests
163
9.3 Backward recursive tests
164
9.3.1 Log likelihood function
165
9.3.2 The trace test statistics
166
9.3.3 The log transformed eigenvalues
166
9.3.4 Fluctuations tests
166
9.3.5 Max test of constant β
167
9.3.6 Test of βt equal to a known β
167
9.3.7 Backward predictions tests
167
9.4 Concluding remarks
170
10 Testing restrictions on β
173
10.1 Formulating hypotheses as restriction on β
173
10.2 Same restriction on all β
175
10.2.1 Illustrations
178
10.3 Some β vectors assumed known
183
10.3.1 Illustrations
185
10.4 Only some coefficients are restricted
186
10.4.1 Illustrations
187
10.5 Revisiting the scenario analysis
190
11 Testing restrictions on α
193
11.1 Long-run weak exogeneity
193
11.1.1 Empirical illustrations
196
11.2 Weak exogeneity and partial models
197
11.2.1 Illustration
198
11.3 Testing a known vector in &alpha'
200
11.3.1 Illustration
202
11.4 Concluding remarks
203
IV Identification 205
12 Identification of the long-run structure
207
12.1 Identification when data are non-stationary
207
12.2 Identifying restrictions
209
12.3 Formulation of identifying hypotheses and degrees of freedom
212
12.4 Just-identifying restrictions
216
12.5 Over-identifying restrictions
219
12.6 Lack of identification
221
12.7 Recursive tests of α and β
224
12.8 Concluding discussion
228
13 Identification of the short-run structure
229
13.1 Formulating identifying restrictions
230
13.2 Interpreting shocks
231
13.3 Which economic questions?
232
13.4 Restrictions on the short-run reduced-form model
236
13.5 The VAR in triangular form
240
13.6 Imposing general restrictions on A0
243
13.6.1 Is a current effect empirically identifiable?
243
13.6.2 Illustration 1: Lack of empirical identification
245
13.6.3 Illustration 2: The problem of weak instruments
245
13.6.4 Illustration 3: The preferred structure
249
13.7 A partial system
252
13.8 Concluding remarks
252
14 Identification of common trends
255
14.1 The common trends representation
255
14.2 The unrestricted MA representation
258
14.3 The MA representation subject to restrictions on α and β
262
14.4 Imposing exclusion restrictions on βperpendicular
266
14.5 Assessing the economic model scenario
268
14.6 Concluding remarks
272
15 Identification of a structural MA model
275
15.1 Reparametrization of the VAR, model
275
15.2 Separation between transitory and permanent shocks
277
15.3 How to formulate and interpret structural shocks
279
15.4 An illustration
282
15.5 Are the labels credible?
286
V The I(2) model 289
16 Analysing I(2) data with the I(1) model
291
16.1 Linking the I(1) and the I(2) model
292
16.2 Stochastic and deterministic trends in the nominal variables
293
16.3 I(2) symptoms in I(1) models
297
16.3.1 The characteristic roots of the model
298
16.3.2 The graphs of the cointegration relations
299
16.4 Is the nominal-to-real transformation acceptable?
302
16.4.1 Transforming I(2) data to I(1)
302
16.4.2 Testing long-run price homogeneity
303
16.5 Concluding remarks
308
17 The 1(2) model: Specification and estimation
311
17.1 Structuring the I(2) model
312
17.2 Deterministic components in the I(2) model
314
17.2.1 Restricting the constant term and the trend
315
17.2.2 Restricting a broken trend and the dummy variables
316
17.3 ML estimation and some useful parametrizations
318
17.3.1 The two-step procedure
318
17.3.2 The ML procedure
318
17.3.3 Decomposing the &Gamma: and the Π matrix
320
17.4 Estimating the I(2) model
322
17.4.1 Determining the two reduced rank indices
322
17.4.2 The unrestricted I(2) estimates
326
17.5 Concluding discussion
329
18 Testing hypotheses in the I(2) model
331
18.1 Testing price homogeneity
332
18.1.1 Long-run price homogeneity
332
18.1.2 Medium-run price homogeneity
333
18.2 Assessing the 1(1) results within the I(2) model
335
18.2.1 Testing the restrictions of the I(1) model
335
18.2.2 A data consistent long-run structure
339
18.3 An empirical scenario for nominal money and prices
340
18.4 Concluding discussion
343
VI A methodological approach 345
19 Specific-to-general and general-to-specific
347
19.1 The general-to-specific and the VAR
347
19.2 The specific-to-general in the choice of variables
348
19.3 Gradually increasing the information Set
349
19.4 Combining partial systems
352
19.5 Introducing the new data
354
20 Wage, price, and unemployment dynamics
359
20.1 Economic background
359
20.1.1 Centralized wage bargaining and an aggregate wage relation
361
20.1.2 The price wedge, productivity and unemployment
363
20.1.3 Phillips-curve type relations
365
20.2 The data and the models
368
20.3 Empirical analysis: the EMS regime
371
20.3.1 Specification testing
371
20.3.2 The overall tests
373
20.3.3 Exploiting the information in the Π matrix
375
20.3.4 Identifying the long-run structure
377
20.4 Empirical analysis: The post-Bretton-Woods regime
380
20.4.1 Specification tests
380
20.4.2 Investigating the Π matrix
382
20.4.3 An identified long-run structure
383
20.5 Concluding discussion
385
21 Foreign transmission effects: Denmark versus Germany
387
21.1 International parity conditions
388
21.2 The data and the models
395
21.2.1 Rank determination
396
21.2.2 Tests of a unit vector in β and zero row and a unit vector in α
397
21.3 Analysing the long-run structure
399
21.3.1 Identifying the long-run relations
399
21.3.2 The common driving t rends
401
21.4 Concluding remarks
401
22 Collecting the threads
403
22.1 The full model estimates
404
22.1.1 Some general results
406
22.1.2 A more detailed analysis
407
22.1.3 Comparing the two periods
408
22.2 What have we learnt about inflationary mechanisms?
410
22.2.1 Main findings
410
22.2.2 Do we now understand previous puzzles better?
412
22.2.3 Which theories seem empirically relevant?
414
22.2.4 About the VAR analysis and the theory model
415
22.3 Concluding discussion
416
Appendix A The asymptotic tables for cointegration rank 419
Appendix B A roadmap for writing an empirical paper 423
Bibliography 425
Index 439


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.