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Research Article

Estimating Posterior Sensitivities with Application to Structural Analysis of Bayesian Vector Autoregressions

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References

  • Albert, J. H., and Chib, S. (1993), “Bayesian Analysis of Binary and Polychotomous Response Data,” Journal of the American Statistical Association, 88, 669–679. DOI: 10.1080/01621459.1993.10476321.
  • Amir-Ahmadi, P., Matthes, C., and Wang, M.-C. (2018), “Choosing Prior Hyperparameters: With Applications to Time-Varying Parameter Models,” Journal of Business & Economic Statistics, 38, 124–136. DOI: 10.1080/07350015.2018.1459302.
  • Baumeister, C., and 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, 1873–1910. DOI: 10.1257/aer.20151569.
  • Baumeister, C., Korobilis, D., and Lee, T. K. (2020), “Energy Markets and Global Economic Conditions,” The Review of Economics and Statistics, 104, 1–45.
  • Berger, J. O., Insua, D. R., and Ruggeri, F. (2000), “Bayesian Robustness,” in Robust Bayesian Analysis, eds. D. R. Insua and F. Ruggeri, pp. 1–32, New York: Springer.
  • Blanchard, O., and Perotti, R. (2002), “An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output,” the Quarterly Journal of Economics, 117, 1329–1368. DOI: 10.1162/003355302320935043.
  • Bou-Rabee, N., Eberle, A., and Zimmer, R. (2020), “Coupling and Convergence for Hamiltonian Monte Carlo,” The Annals of Applied Probability, 30, 1209–1250. DOI: 10.1214/19-AAP1528.
  • Briggs, A. D., Mytton, O. T., Kehlbacher, A., Tiffin, R., Elhussein, A., Rayner, M., Jebb, S. A., Blakely, T., and Scarborough, P. (2017), “Health Impact Assessment of the UK Soft Drinks Industry Levy: A Comparative Risk Assessment Modelling Study,” The Lancet Public Health, 2, e15–e22. DOI: 10.1016/S2468-2667(16)30037-8.
  • Camacho, M., Gadea, M. D., and Gómez-Loscos, A. (2020), “A New Approach to Dating the Reference Cycle,” Journal of Business & Economic Statistics, 40, 66–81. DOI: 10.1080/07350015.2020.1773834.
  • Carriero, A., Clark, T. E., and Marcellino, M. (2019), “Large Bayesian Vector Autoregressions with Stochastic Volatility and Non-Conjugate Priors,” Journal of Econometrics, 212, 137–154. DOI: 10.1016/j.jeconom.2019.04.024.
  • Carter, C. K., and Kohn, R. (1994), “On Gibbs Sampling for State Space Models,” Biometrika, 81, 541–553. DOI: 10.1093/biomet/81.3.541.
  • Chib, S., and Ergashev, B. (2009), “Analysis of Multifactor Affine Yield Curve Models,” Journal of the American Statistical Association, 104, 1324–1337. DOI: 10.1198/jasa.2009.ap08029.
  • Cui, Z., Fu, M. C., Hu, J.-Q., Liu, Y., Peng, Y. and Zhu, L. (2020), “On the Variance of Single-Run Unbiased Stochastic Derivative Estimators,” INFORMS Journal on Computing, 32, 390–407.
  • De Jong, R. M. (1995), “Laws of Large Numbers for Dependent Heterogeneous Processes,” Econometric Theory, 11, 347–358. DOI: 10.1017/S0266466600009208.
  • Del Negro, M., and Schorfheide, F. (2008), “Forming Priors for DSGE Models (and How it Affects the Assessment of Nominal Rigidities),” Journal of Monetary Economics, 55, 1191–1208. DOI: 10.1016/j.jmoneco.2008.09.006.
  • Diebold, F. X., and Li, C. (2006), “Forecasting the Term Structure of Government Bond Yields,” Journal of Econometrics, 130, 337–364. DOI: 10.1016/j.jeconom.2005.03.005.
  • Doan, T., Litterman, R., and Sims, C. (1984), “Forecasting and Conditional Projection Using Realistic Prior Distributions,” Econometric Reviews, 3, 1–100. DOI: 10.1080/07474938408800053.
  • Durbin, J., and Koopman, S. J. (2002), “A Simple and Efficient Simulation Smoother for State Space Time Series Analysis,” Biometrika, 89, 603–616. DOI: 10.1093/biomet/89.3.603.
  • Durmus, A., and Moulines, E. (2017), “Nonasymptotic Convergence Analysis for the Unadjusted Langevin Algorithm,” The Annals of Applied Probability, 27, 1551–1587. DOI: 10.1214/16-AAP1238.
  • Frühwirth-Schnatter, S. (1994), “Data Augmentation and Dynamic Linear Models,” Journal of Time Series Analysis, 15, 183–202. DOI: 10.1111/j.1467-9892.1994.tb00184.x.
  • Giannone, D., Lenza, M., and Primiceri, G. E. (2015), “Prior Selection for Vector Autoregressions,” Review of Economics and Statistics, 97, 436–451. DOI: 10.1162/REST_a_00483.
  • Giles, M., and Glasserman, P. (2006), “Smoking Adjoints: Fast Monte Carlo Greeks,” Risk, 19, 88–92.
  • Giordano, R., Broderick, T., and Jordan, M. I. (2017), “Covariances, Robustness, and Variational Bayes,” arXiv preprint arXiv:1709.02536.
  • Glasserman, P. (2013), Monte Carlo Methods in Financial Engineering (Vol. 53), New York: Springer.
  • Glasserman, P., and Liu, Z. (2010), “Estimating Greeks in Simulating lévy-driven Models,” Journal of Computational Finance, 14, 3. DOI: 10.21314/JCF.2010.210.
  • Greenberg, E. (2012), Introduction to Bayesian Econometrics, Cambridge: Cambridge University Press.
  • Griewank, A., and Walther, A. (2008), Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation (Vol. 105), Philadelphia: SIAM.
  • Gustafson, P. (2000), “Local Robustness in Bayesian Analysis,” in Robust Bayesian Analysis, Springer, pp. 71–88.
  • Hauzenberger, N., Huber, F., Marcellino, M., and Petz, N. (2021), “Gaussian Process Vector Autoregressions and Macroeconomic Uncertainty,” arXiv preprint arXiv:2112.01995.
  • Homescu, C. (2011), “Adjoints and Automatic (Algorithmic) Differentiation in Computational Finance,” Available at SSRN: DOI: 10.2139/ssrn.1828503.
  • Huber, F., and Feldkircher, M. (2019), “Adaptive Shrinkage in Bayesian Vector Autoregressive Models,” Journal of Business & Economic Statistics, 37, 27–39. DOI: 10.1080/07350015.2016.1256217.
  • Jacobi, L., Nghiem, N., Ramirez Hassan, A., and Blakely, T. (2021), “Food Price Elasticities for Policy Interventions: Estimates from a Virtual Experiment in a Multistage Demand Analysis with (Expert) Prior Information,” Economic Record (forthcoming). DOI: 10.1111/1475-4932.12640.
  • Jacobi, L., Wagner, H., and Frühwirth-Schnatter, S. (2016), “Bayesian Treatment Effects Models with Variable Selection for Panel Outcomes with an Application to Earnings Effects of Maternity Leave,” Journal of Econometrics, 193, 234–250. DOI: 10.1016/j.jeconom.2016.01.005.
  • Jarociński, M., and Marcet, A. (2019), “Priors about Observables in Vector Autoregressions,” Journal of Econometrics, 209, 238–255. DOI: 10.1016/j.jeconom.2018.12.023.
  • Karlsson, S. (2013), “Forecasting with Bayesian Vector Autoregression,” in Handbook of Economic Forecasting (Vol. 2), Elsevier, pp. 791–897.
  • Koop, G., and Korobilis, D. (2010), Bayesian Multivariate Time Series Methods for Empirical Macroeconomics, Delft: Now Publishers Inc.
  • Kwok, C. F., Zhu, D., and Jacobi, L. (2020), ADtools: Automatic Differentiation Toolbox. R package version 0.5.4, https://cran.r-project.org/package=ADtools.
  • Kwok, C. F., Zhu, D., and Jacobi, L. (2022), “An Analysis of Vectorised Automatic Differentiation for Statistical Applications,” Available at SSRN.
  • L’Ecuyer, P. (1990), “A Unified View of the ipa, sf, and lr Gradient Estimation Techniques,” Management Science, 36, 1364–1383.
  • Litterman, R. B. (1986), “Forecasting with Bayesian Vector Autoregressions—Five Years of Experience,” Journal of Business & Economic Statistics, 4, 25–38. DOI: 10.2307/1391384.
  • Morley, J., and Wong, B. (2017), “Estimating and Accounting for the Output Gap with Large Bayesian Vector Autoregressions,” CAMA working paper, 46.
  • Müller, U. K. (2012), “Measuring Prior Sensitivity and Prior Informativeness in Large Bayesian Models,” Journal of Monetary Economics, 59, 581–597. DOI: 10.1016/j.jmoneco.2012.09.003.
  • Peng, Y., Fu, M. C., Hu, J.-Q., and Heidergott, B. (2018), “A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural Parameters,” Operations Research, 66, 487–499. DOI: 10.1287/opre.2017.1674.
  • Pérez, C., Martin, J., and Rufo, M. (2006), “MCMC-based Local Parametric Sensitivity Estimations,” Computational Statistics & Data Analysis, 51, 823–835. DOI: 10.1016/j.csda.2005.09.005.
  • Primiceri, G. E. (2005), ‘Time Varying Structural Vector Autoregressions and Monetary Policy,” The Review of Economic Studies, 72, 821–852. DOI: 10.1111/j.1467-937X.2005.00353.x.
  • Raghunathan, M. S. (1979), “A Proof of Oseledec’s Multiplicative Ergodic Theorem,” Israel Journal of Mathematics, 32, 356–362. DOI: 10.1007/BF02760464.
  • Ramey, V. A. (2019), “Ten Years After the Financial Crisis: What Have We Learned from the Renaissance in Fiscal Research?” Journal of Economic Perspectives, 33, 89–114. DOI: 10.1257/jep.33.2.89.
  • Roos, M., Martins, T. G., Held, L., Rue, H., et al. (2015), “Sensitivity Analysis for Bayesian Hierarchical Models,” Bayesian Analysis, 10, 321–349. DOI: 10.1214/14-BA909.
  • Townsend, J., Koep, N., and Weichwald, S. (2016), “Pymanopt: A Python Toolbox for Optimization on Manifolds Using Automatic Differentiation,” The Journal of Machine Learning Research, 17, 4755–4759.