<p>We combine Bayesian Model Averaging (BMA) with Vector Autoregressive (VAR) models—two widely used econometric tools. A key novelty of this study is the integration of these methods within the <Emphasis FontCategory="NonProportional">gretl</Emphasis> framework. Bayesian Model Averaging has a well-established foundation in econometrics and has been extensively studied in the literature (e.g., Kass and Raftery (J Am Stat Assoc 90(430):773–795, 1995, <a href="https://doi.org/10.1080/01621459.1995.10476572">https://doi.org/10.1080/01621459.1995.10476572</a>), Raftery (Sociol Methodol 25:111–163, 1995), Raftery (Biometrika 83(2):251–266, 1996, <a href="https://doi.org/10.1093/biomet/83.2.251">https://doi.org/10.1093/biomet/83.2.251</a>), Fernández et al. (J Econom 100(2):381–427, 2001a, <a href="https://doi.org/10.1016/S0304-4076(00)00076-2">https://doi.org/10.1016/S0304-4076(00)00076-2</a>), Fernández et al. (J Appl Econom 16(5):563–576, 2001b, <a href="https://doi.org/10.1002/jae.623">https://doi.org/10.1002/jae.623</a>), Ley and Steel (J Macroecon 29(3):476–493, 2007, <a href="https://doi.org/10.1016/j.jmacro.2006.12.002">https://doi.org/10.1016/j.jmacro.2006.12.002</a>), Ley and Steel (J Appl Economet 24(4):651–674, 2009, <a href="https://doi.org/10.1002/jae.1057">https://doi.org/10.1002/jae.1057</a>), Steel (J Econ Lit 58(3):644–719, 2020, <a href="https://doi.org/10.1257/jel.20191385">https://doi.org/10.1257/jel.20191385</a>). BMA addresses model uncertainty by averaging over a set of competing models, weighting each model’s contribution by its explanatory power. We adopt natural conjugate priors, allowing for closed-form calculations of marginal data densities—an essential component in assessing model fit. This approach enables efficient model comparison and selection.VAR models, in turn, are a fundamental class of multivariate time series models used to capture dynamic inter-dependencies among multiple economic or financial variables (Koop and Korobilis in Found Trends® Econom 3(4):267–358, 2010a, <a href="https://doi.org/10.1561/0800000013">https://doi.org/10.1561/0800000013</a>; (Karlsson in: Handbook of economic forecasting, 791–897, 2013, <a href="https://doi.org/10.1016/B978-0-444-62731-5.00015-4">https://doi.org/10.1016/B978-0-444-62731-5.00015-4</a>). As an empirical illustration, we demonstrate the functionality of the package and assess its computational performance using a small-scale model drawn from Giannone et al. (Rev Econ Stat 97(2):436–451, 2015). The model includes three monetary variables: real GDP, the GDP deflator, and the federal funds rate. We present standard BMA outputs, including posterior inclusion probabilities, average parameter estimates, forecasts, and impulse response functions–core components of VAR model analysis. Combined with our implementation of marginal data density calculations, adapted from the original <Emphasis FontCategory="NonProportional">MATLAB</Emphasis> code in Giannone et al. (Rev Econ Stat 97(2):436–451, 2015), our solution enables highly efficient computation.</p>

Bayesian model averaging for VAR models: gretl-based implementation

期刊论文
发表日期：

2026年1月31日

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Marcin Błażejowski,
Paweł Kufel,
Jacek Kwiatkowski

摘要

We combine Bayesian Model Averaging (BMA) with Vector Autoregressive (VAR) models—two widely used econometric tools. A key novelty of this study is the integration of these methods within the gretl framework. Bayesian Model Averaging has a well-established foundation in econometrics and has been extensively studied in the literature (e.g., Kass and Raftery (J Am Stat Assoc 90(430):773–795, 1995, https://doi.org/10.1080/01621459.1995.10476572), Raftery (Sociol Methodol 25:111–163, 1995), Raftery (Biometrika 83(2):251–266, 1996, https://doi.org/10.1093/biomet/83.2.251), Fernández et al. (J Econom 100(2):381–427, 2001a, https://doi.org/10.1016/S0304-4076(00)00076-2), Fernández et al. (J Appl Econom 16(5):563–576, 2001b, https://doi.org/10.1002/jae.623), Ley and Steel (J Macroecon 29(3):476–493, 2007, https://doi.org/10.1016/j.jmacro.2006.12.002), Ley and Steel (J Appl Economet 24(4):651–674, 2009, https://doi.org/10.1002/jae.1057), Steel (J Econ Lit 58(3):644–719, 2020, https://doi.org/10.1257/jel.20191385). BMA addresses model uncertainty by averaging over a set of competing models, weighting each model’s contribution by its explanatory power. We adopt natural conjugate priors, allowing for closed-form calculations of marginal data densities—an essential component in assessing model fit. This approach enables efficient model comparison and selection.VAR models, in turn, are a fundamental class of multivariate time series models used to capture dynamic inter-dependencies among multiple economic or financial variables (Koop and Korobilis in Found Trends® Econom 3(4):267–358, 2010a, https://doi.org/10.1561/0800000013; (Karlsson in: Handbook of economic forecasting, 791–897, 2013, https://doi.org/10.1016/B978-0-444-62731-5.00015-4). As an empirical illustration, we demonstrate the functionality of the package and assess its computational performance using a small-scale model drawn from Giannone et al. (Rev Econ Stat 97(2):436–451, 2015). The model includes three monetary variables: real GDP, the GDP deflator, and the federal funds rate. We present standard BMA outputs, including posterior inclusion probabilities, average parameter estimates, forecasts, and impulse response functions–core components of VAR model analysis. Combined with our implementation of marginal data density calculations, adapted from the original MATLAB code in Giannone et al. (Rev Econ Stat 97(2):436–451, 2015), our solution enables highly efficient computation.