## The Cointegrated VAR Model: Methodology and ApplicationsThis 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

15 On the choice of empirical example | |

2 | |

21 The VAR approach and theorybased models | |

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 | |

### Other editions - View all

The Cointegrated VAR Model:Methodology and Applications: Methodology and ... Katarina Juselius No preview available - 2006 |

The Cointegrated VAR Model: Methodology and Applications Katarina Juselius No preview available - 2006 |

### Common terms and phrases

analysis assumption behaviour bond rate broken linear trend cointegration rank cointegration relations common stochastic trends common trends condition constant corresponds covariance covariance matrix Danish data defined deterministic components dynamics econometric economic effects eigenvalues empirical model empirical shocks equilibrium correcting estimated example formulation graphs hypothesis identifying restrictions illustrate impose inflation rate information set interest rate spread interpretation Johansen Juselius just-identifying likelihood function long-run price homogeneity long-run relations long-run structure lower panel macroeconomic matrix monetary money demand relation nominal interest rates nominal money non-stationary over-identifying p-value parameters permanent shocks Phillips curve price wedge real exchange rate real income real interest rates real money stock recursive reduced rank residuals sample period Section shift dummy short-term interest rate significant specification suggest test statistic theoretical trace test transitory shocks unemployment rate unit roots unrestricted upper panel VAR model vector process whereas zero restrictions