Forecasting with High‐Dimensional Panel VARs

Q: What does the author propose to do to reduce the computational burden of the panel VAR?

2As the authors explain later in this paper, this hierarchical prior pools certain VAR coefficients by country or by variable, and results in a lower-dimensional VAR which greatly reduces the computational burden.

Question

1. What contributions have the authors mentioned in the paper "Forecasting with high-dimensional panel vars∗" ?

2. What is the popular approach to dimension reduction in Bayesian vector autoregressions?

3. What is the common ground of all these modelling approaches?

4. How many countries registered inflation rates in the eurozone in 2014?

Accepted Answer

This paper develops methods for estimating and forecasting in Bayesian panel vector autoregressions of large dimensions with time-varying parameters and stochastic volatility.. The authors exploit a hierarchical prior that takes into account possible pooling restrictions involving both VAR coefficients and the error covariance matrix, and propose a Bayesian dynamic learning procedure that controls for various sources of model uncertainty.. The authors use their methods to forecast inflation rates in the eurozone and show that these forecasts are superior to alternative methods for large vector autoregressions.

Accepted Answer

A popular approach to dimension reduction in Bayesian vector autoregressions is to use hierarchical priors that induce shrinkage in the parameters.

Accepted Answer

The common ground of all these modelling approaches is the need to account for the panel structure in the data, and explicitly model inter-dependencies and commonalities in the units (countries or individuals).

Accepted Answer

For instance, in December 2014, most of the eurozone were experiencing deflation and no country registered an inflation rate above 1%.

Accepted Answer

the use of simulation methods means that the authors consider only structural analysis (not much more computationally-intensive recursive forecasting) using 27-variable PVARs.

Accepted Answer

The novelties of their approach are that i) the authors tackle in one integrated setting all concerns pertaining to out-of-sample forecasting, such as controlling for over-fitting and dealing with model uncertainty; ii) the authors allow for empirically relevant extensions that account for structural breaks and changing volatilities; and iii) the authors do so in a computationally efficient way, building on previous work by Koop and Korobilis (2013) for single-country VARs.

Accepted Answer

Since the authors wish to forecast at horizon h > 1 and calculate predictive likelihoods, the authors use predictive simulation for longer forecast horizons.

Accepted Answer

The i-th equation of the PVAR with p lags takes the formyit = A 1 iYt−1 + ...+ A p iYt−p + uit, (1)where Aji for j = 1, .., p are G×NG matrices PVAR coefficients for country i.

Accepted Answer

Improving on the inference of Canova and Ciccarelli (2009), the authors allow for the TVPPVAR error covariance matrix to be time-varying and use EWMA filtering methods to estimate it as:Σ̂t = κΣ̂t−1 + (1− κ) ũtũ′t,where ũtũ ′ t = (I + σ 2X ′tXt) −1 [( Yt − X̃ ′tE (θt|Dt−1) )( Yt − X̃ ′tE (θt|Dt−1) )′] , E (θt|Dt−1) is produced by the Kalman filter and 0 < κ ≤

Accepted Answer

2As the authors explain later in this paper, this hierarchical prior pools certain VAR coefficients by country or by variable, and results in a lower-dimensional VAR which greatly reduces the computational burden.

Accepted Answer

Repeatedly running such an algorithm on an expanding window of data, as is typically done in a recursive forecasting exercise, multiplies this burden by hundreds in many applications.

Accepted Answer

A popular way to introduce such pooling in PVARs that will result in efficient shrinkage, is described in Canova and Ciccarelli (2009, 2013).

Forecasting with High‐Dimensional Panel VARs

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Most frequently asked questions

1. What contributions have the authors mentioned in the paper "Forecasting with high-dimensional panel vars∗" ?

2. What is the popular approach to dimension reduction in Bayesian vector autoregressions?

3. What is the common ground of all these modelling approaches?

4. How many countries registered inflation rates in the eurozone in 2014?

5. What does the author consider to be a more computationally intensive method?

6. What are the novelties of the approach?

7. What is the way to calculate the horizon of the forecast?

8. What is the i-th equation of the PVAR with p lags?

9. What is the simplest way to estimate the TVPPVAR error covariance matrix?

10. What does the author propose to do to reduce the computational burden of the panel VAR?

11. How many times does it take to run a recursive forecasting exercise?

12. What is the popular way to introduce pooling in a PVAR?

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Citations

Forecasting crude oil real prices with averaging time-varying VAR models

The Nexus between Economic Complexity and Energy Consumption under the Context of Sustainable Environment: Evidence from the LMC Countries.

Monetary policy and bubbles in G7 economies using a panel VAR approach: Implications for sustainable development

A multi-country dynamic factor model with stochastic volatility for euro area business cycle analysis.

Penalized estimation of panel vector autoregressive models: A panel LASSO approach

References

Regression Shrinkage and Selection via the Lasso

Time Varying Structural Vector Autoregressions and Monetary Policy

Time Series Analysis by State Space Methods

Testing the equality of prediction mean squared errors

Drifts and volatilities: monetary policies and outcomes in the post WWII US

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