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

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

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September 4th, 2024
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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)
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STORY’S CREDIBILITY

Academic Research Paper

Academic Research Paper

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

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 Theory Coherent TVP-VAR

A.1.1 Time Varying Parameters by dummy observations

Starting from:


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


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


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This is just another way of writing:


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A.1.2 Population moments

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A.1.3 Integrating constant of the theory coherent prior

The integrating constant of the Normal-Inverse-Wishart prior


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A.1.4 Conditional distribution of theory coherent prior

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Considering the three first blocks we get


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A.1.5 Marginal likelihood and fit-complexity trade off

The marginal likelihood is given by:


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


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A.1.6 Formulas with distinct λj for j = 1, . . . ,K

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A.2 Small scale New Keynesian model for the forecasting exercise

A.2.1 Data

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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:


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A.2.3 Prior for the DSGE parameters

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A.2.4 Posterior estimate for the DSGE parameters and IRFs from the TC-TVPVAR

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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


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This paper is available on arxiv under CC 4.0 license.



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