## SYSTEM PRIORS

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System priors are an intuitive way of specifying economically-meaningful priors about the properties of the model, not just about its individual coefficients. System priors have been used to estimate flag-ship models at the

System priors are priors about "system properties" of your model, say economic models. These system properties are then function of multiple, possibly all, parameters in the model. For instance, you can have a prior about the impulse-responses, about policy experiments, or about the share of variance an output gap should have at business-cycle frequencies...

In most Bayesian settings, the likelihood function, \(L(\theta|Y)\), is updated by the priors on the parameters, \(p(\theta)\). Most often, the priors on parameters are a sequence of marginal, independent priors about the elements of \(\theta\), \(\theta_{1},\dots , \theta_{N}\).

With system priors, we have a view about some function of the parameters, \(S = h(\theta|M)\), given the model M. The marginal-parameter priors, \(p_{m}(\theta)\) are then updated with the information about the system property, \(S\), to get the "composite prior"

\[p_{c}(\theta|S,M) \propto p(h(\theta|M)) \times p_{m}(\theta).\]

Posterior computation with system priors are then simply a multi-step application of Bayesian updating, where marginal parameter priors are updated with the priors about system properties, which are in turn updated by the observed data:

\[p(\theta|Y) \propto L(\theta|Y) \times p_{s}(h(\theta)|M) \times p_{m}(\theta). \]

Interested in learning more? Please, read the papers or contact me.

**SYSTEM PRIORS**with Jaromir Benes, Miroslav Plasil, and Jan Bruha.System priors are an intuitive way of specifying economically-meaningful priors about the properties of the model, not just about its individual coefficients. System priors have been used to estimate flag-ship models at the

**International Monetary Fund**(IMF) and at the**European Central Bank**(ECB). See a short introduction to system priors below...**PAPERS:****System Priors for Econometric Time Series**[pdf] (2016/2017 with M. Plasil)**IMF Working Paper WP/16/231**[CNB WP 2017 updated version]*Economics Letters*version [pdf]:-
joint with Jaromir Benes)**System Priors****-- Formulating priors about DSGE models properties**, (**[**pdf**],****IMF Working Paper WP/13/257****[**pdf**],**slides IMF-ICD Nov 2017 [pdf]**.** **Forecasting and Policy Analysis with Trend-Cycle Bayesian VARs**[draft] -- system priors for vector auto-regressions (VARs)

**The New Area-Wide Model II:****an extended version of the ECB’s micro-founded model for forecasting and policy analysis with a financial sector [**pdf**]**, by G. Coenen, P. Karadi, S. Schmidt, and A. Warne, ECB WP No 2200 / November 2018.**Wickens, Michael R. & Pagan, Adrian**, 2019. "Checking if the Straitjacket Fits," CEPR Discussion Papers 14140, C.E.P.R. Discussion Papers.

**CODE:****IRIS [Matlab, Octave] Implementation of general System priors [zip].**Example of having a system prior about a sacrifice ratio in a real-world DNK gap model. This implementation is general and allows for likelihood or non-likelihood estimation with system priors, automated calibration based on system features/priors, etc. Supports also TC-BVAR models for system priors for VARs. A small introduction to the codes with examples is here:**System priors on top of IRIS: Estimation, Calibration, and Testing [pdf]**.

**Dynare [Matlab, Octave] implementation of general System priors [zip].**System priors code for DSGE models in Dynare. Installation and use is documented and illustrated with the AR(2) example. Note, this is a simple Dynare workaround, not a documented feature...

**GNU R implementation of system priors for the AR(2) model by Miroslav Plasil**AR(2) example from the paper.

**YADA [Matlab] by Anders Warne (ECB) features implementation of system priors.**No examples, a full-blown and ready-to-use implementation in the YADA toolbox developed at the European Central Bank (ECB).

**What are the***system priors*?System priors are priors about "system properties" of your model, say economic models. These system properties are then function of multiple, possibly all, parameters in the model. For instance, you can have a prior about the impulse-responses, about policy experiments, or about the share of variance an output gap should have at business-cycle frequencies...

In most Bayesian settings, the likelihood function, \(L(\theta|Y)\), is updated by the priors on the parameters, \(p(\theta)\). Most often, the priors on parameters are a sequence of marginal, independent priors about the elements of \(\theta\), \(\theta_{1},\dots , \theta_{N}\).

With system priors, we have a view about some function of the parameters, \(S = h(\theta|M)\), given the model M. The marginal-parameter priors, \(p_{m}(\theta)\) are then updated with the information about the system property, \(S\), to get the "composite prior"

\[p_{c}(\theta|S,M) \propto p(h(\theta|M)) \times p_{m}(\theta).\]

Posterior computation with system priors are then simply a multi-step application of Bayesian updating, where marginal parameter priors are updated with the priors about system properties, which are in turn updated by the observed data:

\[p(\theta|Y) \propto L(\theta|Y) \times p_{s}(h(\theta)|M) \times p_{m}(\theta). \]

Interested in learning more? Please, read the papers or contact me.

**Disclaimer:**

**The views expressed herein are those of the author and should not be attributed to the International Monetary Fund, its Executive Board, or its management.**