© Andrzej Kocięcki, Michele Ca’ Zorzi, Michał Rubaszek. Article available under the CC BY-SA 4.0 licence
The paper provides a Bayesian methodological framework for the estimation of structural vector autoregression (SVAR) models with recursive identification schemes that allows for the inclusion of overidentifying restrictions. The proposed framework enables the researcher (i) to elicit the prior on non-zero contemporaneous relations between economic variables and (ii) to derive an analytical expression for the posterior distribution and marginal data density. We illustrate our methodological framework by estimating a New-Keynesian SVAR model for Poland.
structural VAR, Bayesian inference, overidentifying restrictions
C11; C32; E47
Bańbura, M., Giannone, D., & Reichlin, L. (2010). Large Bayesian vector autoregressions. Journal of Applied Econometrics, 25(1), 71–92. https://doi.org/10.1002/jae.1137.
Baumeister, C., & Hamilton, J. D. (2015). Sign restrictions, structural vector autoregressions, and useful prior information. Econometrica, 83(5), 1963–1999. https://doi.org/10.3982/ECTA12356.
Baumeister, C., & Hamilton, J. D. (2019). Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks. American Economic Review, 109(5), 1873–1910. https://doi.org/10.1257/aer.20151569.
Christiano, L. J., Eichenbaum, M., & Evans, C. L. (1999). Monetary policy shocks: What have we learned and to what end?. In J. B. Taylor & M. Woodford (Eds.), Handbook of Macroeconomics (vol. 1, part A, pp. 65–148). https://doi.org/10.1016/S1574-0048(99)01005-8.
Christiano, L. J., Eichenbaum, M., & Evans, C. L. (2005). Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy. Journal of Political Economy, 113(1), 1–45. https://doi.org/10.1086/426038.
Crump, R. K., Eusepi, S., Giannone, D., Qian, E., & Sbordone, A. M. (2025). A Large Bayesian VAR of the U.S. Economy. International Journal of Central Banking, 21(2), 351–409. https://www.ijcb.org/journal/ijcb25q2a8.pdf.
Giannone, D., Lenza, M., & Primiceri, G. E. (2015). Prior Selection for Vector Autoregressions. The Review of Economics and Statistics, 97(2), 436–451. https://doi.org/10.1162/REST_a_00483.
Kadiyala, K. R., & Karlsson, S. (1997). Numerical methods for estimation and inference in Bayesian VAR-models. Journal of Applied Econometrics, 12(2), 99–132. https://doi.org/10.1002/(SICI)1099-1255(199703)12:2%3C99::AID-JAE429%3E3.0.CO;2-A.
Litterman, R. B. (1986). Forecasting with Bayesian vector autoregressions: five years of experience. Journal of Business & Economic Statistics, 4(1), 25–38. https://doi.org/10.2307/1391384.
Orphanides, A. (2003). Monetary policy evaluation with noisy information. Journal of Monetary Economics, 50(3), 605–631. https://doi.org/10.1016/S0304-3932(03)00027-8.
Rubaszek, M., Szafranek, K., & Uddin, G. S. (2021). The dynamics and elasticities on the U.S. natural gas market. A Bayesian Structural VAR analysis. Energy Economics, 103. https://doi.org/10.1016 /j.eneco.2021.105526 .
Sims, C. A. (2003). Comments on Smets and Wouters. https://archive.riksbank.se/Upload/Dokument_riksbank/Kat_foa/smets.pdf.
Sims, C. A, & Zha, T. (1998). Bayesian methods for dynamic multivariate models. International Economic Review, 39(4), 949–968. https://doi.org/10.2307/2527347.
Uhlig, H. (2005). What are the effects of monetary policy on output? Results from an agnostic identification procedure. Journal of Monetary Economics, 52(2), 381–419. https://doi.org/10.1016 /j.jmoneco.2004.05.007 .
Waggoner, D. F., & Zha, T. (2003). A Gibbs sampler for structural vector autoregressions. Journal of Economic Dynamics and Control, 28(2), 349–366. https://doi.org/10.1016/S0165-1889(02)00168-9.