Theory Coherent Shrinkage of Time Varying Parameters in VARs: A Appendixby@keynesian

# Theory Coherent Shrinkage of Time Varying Parameters in VARs: A Appendix

September 4th, 2024

Andrea Renzetti, Department of Economics, Alma Mater Studiorium Universit`a di Bologna, Piazza Scaravilli 2, 40126 BologNA, Italy. Theory coherent TVP-VAR can be re-written as: (https://cdn.hackernoon.com/images/fWZa4tUiBGemnqQfBGgCPf9594N2-hpd31y3.png)

Andrea Renzetti, Department of Economics, Alma Mater Studiorium Universit`a di Bologna, Piazza Scaravilli 2, 40126 Bologna, Italy.

Abstract and Introduction

Theory coherent TVP-VAR

Forecasting with the TC-TVP-VAR

Response analysis at the ZLB with the TC-TVP-VAR

Conclusion and References

A Appendix

## A Appendix

### A.1.1 Time Varying Parameters by dummy observations

Starting from:

we can write the TVP-VAR in static compact form as:

Suppose we want to specify independent RW stochastic processes for all the coefficients in Φ as:

This is just another way of writing:

### A.1.3 Integrating constant of the theory coherent prior

The integrating constant of the Normal-Inverse-Wishart prior

### A.1.4 Conditional distribution of theory coherent prior

Considering the three first blocks we get

### A.1.5 Marginal likelihood and fit-complexity trade off

The marginal likelihood is given by:

Following the same steps as in (Giannone et al. 2015) it can be re-written as :

### A.2.2 Competing models in the forecasting exercise

The competing models in the out of sample forecasting exercise in Section 3 are

• A constant parameters VAR with flat prior.

• A constant parameters VAR with Normal Inverse-Wishart prior.

• A TVP-VAR model

The VAR with Normal Inverse-Wishart prior is given by:

### A.3 Medium scale New Keynesian model

The model is taken from Del Negro et al. (2015) and it is a version of the popular medium scale New Keynesian model in Smets et al. (2007). The set of log-linearized equilibrium conditions of the model is

This paper is available on arxiv under CC 4.0 license.

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