## 1. Introduction

## 2. Econometric Foundations

#### 2.1. Econometric Theory and Economic Applications

#### 2.2. Developing a User Friendly Software

## 3. The CVAR as an Empirical Methodology

#### 3.1. Confronting Theories with Data

#### 3.2. Linking Theory and Evidence: A Bridging Principle

#### 3.3. Haavelmo’s Probability Approach and the CVAR

## 4. Early Applications

#### 4.1. Is Inflation a Monetary Phenomenon?

#### 4.2. Is Inflation Imported?

#### 4.3. CPI Inflation and Excessive Wage Claims

#### 4.4. Combining the Results: A Proposal for a Large-Scale Macro Model

## 5. Towards a New Methodological Approach

#### 5.1. Long Swings in Financial Market Behavior

#### 5.2. Persistent Movements and Time-Varying Coefficients

#### 5.3. Real Exchange Rate Persistence and the Real Economy

#### 5.4. Crises Periods and Comparative Studies

## 6. Some Reflections

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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1. | Sadly, Clive left us already in 2009, all too early. |

2. | Google scholar records 18132 citation in November 2020. |

3. | Such assumptions are, for example, long-run proportionality, exogeneity and endogeneity status, expectation formation, and so on. |

4. | |

5. | Many years later I revised my thinking on this: inflation is in fact a monetary problem, but after deregulation of capital movements, it is asset price inflation and house price inflation and not CPI inflation that react strongly on excess liquidity. |

6. | More than twenty years later, Johansen and Juselius (2014) showed that the invariance property was also valid for common stochastic trends, albeit in a slightly more complicated way. While the labeling of the estimated shocks changes when the information set is expanded, the stochastic trend(s) of the small model remain the same in the expanded model. Assume, for example, that the Danish bond rate is strongly exogenous in a domestic VAR model for Denmark and, thus, a common stochastic trend. Now, if the shocks to the Danish bond rate originate from shocks to the German bond rate and the German bond rate is added to the model, then the German rate becomes the “new” common stochastic trend. However, it is basically the same as the old one. |

7. | Johansen et al. (2010) subsequently report a full-fledged I(2) analysis. |

8. | The variables in the figure are defined as follows: w is nominal manufacturing wages, ${p}_{c}$ is consumer prices, ${p}_{y}$ is the price of output, c is productivity, u is unemployment, ${R}_{b}$ is the long-term bond rate, ${R}_{d}$ is the deposit rate, $\Delta p$ is CPI inflation, m is money stock, y is real GDP, q is the real exchange rate, a superscript ${}^{f}$ stands for foreign country, and a superscript ${}^{*}$ for an equilibrium value. A more detailed account can be found in Juselius (2006, Part VI). |

9. | In the dollar euro market, around 75% of all transactions are purely speculative. The remaining 25% are related to the trade in exports and imports but, due to forward contracts, future expectations play a significant role. |

10. | |

11. | The division into groups depended on whether foreign aid and the macro-economy—measured by GDP, investment, private consumption, and government expenditure—(1) had been unrelated in the long run; (2) whether aid had no long-run effect on the macro-economy—tested as a unit vector in $\alpha $—but the latter had been influencing aid; (3) whether aid has been exogenous with respect to the macro economy and finally; or (4) whether aid and the macro-economy have been tied together in an interdependent relationship. |

12. | This, in my view, is a sure proof that the person in question has never performed a proper CVAR analysis. Hundreds of students in the Copenhagen summer schools, who have struggled to make a well-specified CVAR deliver results in accordance with their favorite economic model—often without success—would certainly nod in agreement. |

**Figure 1.**Using cointegration relations from partial models as the main economic determinants in a large macroeconomic model.

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