Large Vector Autoregressions with Stochastic Volatility and Flexible Priors

Carriero, Andrea; Clark, Todd E.; Marcellino, Massimiliano

doi:10.26509/frbc-wp-201617

Cited by 22 publications

(26 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In most empirical macroeconomic applications, there is evidence of changes in volatility (although the mixed‐frequency VAR literature has mostly ignored this issue and worked with homoskedastic models). In this paper we adopt a popular multivariate stochastic volatility specification (see Carriero, Clark, & Marcellino, ; Cogley & Sargent, ). This decomposes the error covariance matrix as follows:

{normalΣ}_{t}^{- 1} = {boldL}^{^{'}} {boldD}_{t}^{- 1} boldL,

where

boldL

n \times n

lower triangular matrix with a diagonal of ones:

boldL = ([], \begin{matrix} center center center center \\ array 1 & array 0 & array \dots & array 0 \\ array a_{1, 1} & array 1 & array & array ⋮ \\ array ⋮ & array ⋱ & array ⋱ & array 0 \\ array a_{n, 1} & array & array a_{n, n - 1} & array 1 \end{matrix}),

and we define

bolda = {false(a_{1, 1}, a_{2, 1}, \dots, a_{n, 1}, a_{2, 1}, \dots, a_{n, n - 1} false)}^{'}

as an

m \times 1

vector.…”

Section: Mixed‐frequency Econometric Methodsmentioning

confidence: 99%

Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970

Koop

McIntyre

Mitchell

et al. 2020

J of Applied Econometrics

View full text Add to dashboard Cite

Summary Output growth estimates for regions of the UK are currently published at an annual frequency only, released with a long delay, and offer limited historical coverage. To improve the regional database this paper develops a mixed‐frequency multivariate model and uses it to produce consistent estimates of quarterly regional output growth dating back to 1970. We describe how these estimates are updated and evaluated on an ongoing, quarterly basis to publish online (at www.escoe.ac.uk/regionalnowcasting) more timely regional growth estimates. We illustrate how the new quarterly data can contribute to our historical understanding of business cycle dynamics and connectedness between regions.

show abstract

{normalΣ}_{t}^{- 1} = {boldL}^{^{'}} {boldD}_{t}^{- 1} boldL,

where

boldL

n \times n

lower triangular matrix with a diagonal of ones:

boldL = ([], \begin{matrix} center center center center \\ array 1 & array 0 & array \dots & array 0 \\ array a_{1, 1} & array 1 & array & array ⋮ \\ array ⋮ & array ⋱ & array ⋱ & array 0 \\ array a_{n, 1} & array & array a_{n, n - 1} & array 1 \end{matrix}),

and we define

bolda = {false(a_{1, 1}, a_{2, 1}, \dots, a_{n, 1}, a_{2, 1}, \dots, a_{n, n - 1} false)}^{'}

as an

m \times 1

vector.…”

Section: Mixed‐frequency Econometric Methodsmentioning

confidence: 99%

Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970

Koop

McIntyre

Mitchell

et al. 2020

J of Applied Econometrics

View full text Add to dashboard Cite

show abstract

“…For notational simplicity, let Π denote the collection of the VAR's coefficients. Note also that, to speed computation, we estimate the model with the triangularization approach developed in Carriero, Clark, and Marcellino (2016b). Estimates derived from the BVAR-SV model are based on samples of 5,000 retained draws, obtained by sampling a total of 30,000 draws, discarding the first 5,000, and retaining every 5th draw of the post-burn sample.…”

Section: Bvar-sv Modelmentioning

confidence: 99%

“…To speed computation, we estimate the model with the triangularization approach developed in Carriero, Clark, and Marcellino (2016b), using an independent Normal-Wishart prior. 5…”

Section: Impulse Response Estimates From Two-step Approachmentioning

confidence: 99%

“…For the VAR coefficients Π, with smaller models it is common to rely on a GLS solution for the posterior mean (e.g., Carriero, Clark, and Marcellino 2016a). However, with large models it is far faster to exploit the triangularization -obtaining the same posterior provided by standard system solutions -developed in Carriero, Clark, and Marcellino (2016b) and estimate the VAR coefficients on an equation-by-equation basis.…”

Section: Coefficient Priors and Posteriorsmentioning

confidence: 99%

“…In this subsection we briefly summarize the VAR triangularization that is needed to handle a large system with asymmetric priors and time-varying volatilities, such as the model used here. 7 More details can be found in Carriero, Clark, and Marcellino (2016b). With the triangularization, the estimation algorithm will block the conditional posterior distribution of the system of VAR coefficients in n different blocks.…”

Section: Triangularization For Estimationmentioning

confidence: 99%

See 2 more Smart Citations

Assessing International Commonality in Macroeconomic Uncertainty and its Effects

Clark

Carriero²,

Marcellino³

2018

Working Paper (Federal Reserve Bank of Cleveland)

Self Cite

View full text Add to dashboard Cite

This paper uses a large vector autoregression (VAR) to measure international macroeconomic uncertainty and its effects on major economies, using two datasets, one with GDP growth rates for 19 industrialized countries and the other with a larger set of macroeconomic indicators for the U.S., euro area, and U.K. Using basic factor model diagnostics, we fi rst provide evidence of signifi cant commonality in international macroeconomic volatility, with one common factor accounting for strong comovement across economies and variables. We then turn to measuring uncertainty and its effects with a large VAR in which the error volatilities evolve over time according to a factor structure. The volatility of each variable in the system refl ects time-varying common (global) components and idiosyncratic components. In this model, global uncertainty is allowed to contemporaneously affect the macroeconomies of the included nations-both the levels and volatilities of the included variables. In this setup, uncertainty and its effects are estimated in a single step within the same model. Our estimates yield new measures of international macroeconomic uncertainty, and indicate that uncertainty shocks (surprise increases) lower GDP and many of its components, adversely affect labor market conditions, lower stock prices, and in some economies lead to an easing of monetary policy.

show abstract

Steady‐state modeling and macroeconomic forecasting quality

Louzis

2018

J of Applied Econometrics

View full text Add to dashboard Cite

Vector autoregressions (VARs) with informative steady-state priors are standard forecasting tools in empirical macroeconomics. This study proposes (i) an adaptive hierarchical normal-gamma prior on steady states, (ii) a time-varying steady-state specification which accounts for structural breaks in the unconditional mean, and (iii) a generalization of steady-state VARs with fat-tailed and heteroskedastic error terms. Empirical analysis, based on a real-time dataset of 14 macroeconomic variables, shows that, overall, the hierarchical steady-state specifications materially improve out-of-sample forecasting for forecasting horizons longer than 1 year, while the time-varying specifications generate superior forecasts for variables with significant changes in their unconditional mean.

show abstract

Large Vector Autoregressions with Stochastic Volatility and Flexible Priors

Cited by 22 publications

References 21 publications

Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970

Regional output growth in the United Kingdom: More timely and higher frequency estimates from 1970

Assessing International Commonality in Macroeconomic Uncertainty and its Effects

Steady‐state modeling and macroeconomic forecasting quality

Contact Info

Product

Resources

About