This content originally appeared on HackerNoon and was authored by Keynesian Technology
:::info Andrea Renzetti, Department of Economics, Alma Mater Studiorium Universit`a di Bologna, Piazza Scaravilli 2, 40126 Bologna, Italy.
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Table of Links
Forecasting with the TC-TVP-VAR
Response analysis at the ZLB with the TC-TVP-VAR
A Appendix
A.1 Theory Coherent TVP-VAR
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.1.2 Population moments
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.1.6 Formulas with distinct λj for j = 1, . . . ,K
A.2 Small scale New Keynesian model for the forecasting exercise
A.2.1 Data
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.2.3 Prior for the DSGE parameters
A.2.4 Posterior estimate for the DSGE parameters and IRFs from the TC-TVPVAR
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
\
\
\
:::info This paper is available on arxiv under CC 4.0 license.
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This content originally appeared on HackerNoon and was authored by Keynesian Technology
Keynesian Technology | Sciencx (2024-09-04T23:00:13+00:00) Theory Coherent Shrinkage of Time Varying Parameters in VARs: A Appendix. Retrieved from https://www.scien.cx/2024/09/04/theory-coherent-shrinkage-of-time-varying-parameters-in-vars-a-appendix/
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