Robust Bayesian Analysis for Econometrics

doi:10.1017/9781009589727.007

Chapter 4 - Robust Bayesian Analysis for Econometrics

from Part III - Frontiers of Time-Series Econometrics

Published online by Cambridge University Press: 11 November 2025

Raffaella Giacomini ,

Toru Kitagawa and

Matthew Read

Edited by

Victor Chernozhukov ,

Johannes Hörner ,

Eliana La Ferrara and

Iván Werning

Show author details

Victor Chernozhukov: Affiliation:
Massachusetts Institute of Technology
Johannes Hörner: Affiliation:
Yale University, Connecticut
Eliana La Ferrara: Affiliation:
Harvard University, Massachusetts
Iván Werning: Affiliation:
Massachusetts Institute of Technology

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Every 5 years, the World Congress of the Econometric Society brings together scholars from around the world. Leading scholars present state-of-the-art overviews of their areas of research, offering newcomers access to key research in economics. Advances in Economics and Econometrics: Twelfth World Congress consists of papers and commentaries presented at the Twelfth World Congress of the Econometric Society. This two-volume set includes surveys and interpretations of key developments in economics and econometrics, and discussions of future directions for a variety of topics, covering both theory and application. The first volume addresses such topics as contract theory, industrial organization, health and human capital, as well as racial justice, while the second volume includes theoretical and applied papers on climate change, time-series econometrics, and causal inference. These papers are invaluable for experienced economists seeking to broaden their knowledge or young economists new to the field.

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Type: Chapter
Information: Advances in Economics and Econometrics
Twelfth World Congress
, pp. 117 - 157

DOI: https://doi.org/10.1017/9781009589727.007 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2026

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References

Amir-Ahmadi, P., and Drautzburg, T. (2021). “Identification and inference with ranking restrictions,” Quantitative Economics, 12, 1–39.10.3982/QE1277CrossRef Google Scholar

Andrews, I., Gentzkow, M., and Shapiro, J. M. (2017). “Measuring the sensitivity of parameter estimates to estimation moments,” Quarterly Journal of Economics, 132, 1553–1592.10.1093/qje/qjx023CrossRef Google Scholar

Andrews, I., Gentzkow, M., and Shapiro, J. M. (2020). “On the informativeness of descriptive statistics for structural estimates,” Econometrica, 88, 2231–2258.10.3982/ECTA16768CrossRef Google Scholar

Arias, J. E., Caldara, D., and Rubio-Ramírez, J. F. (2019). “The systematic component of monetary policy in SVARs: An agnostic identification procedure,” Journal of Monetary Economics, 101, 1–13.10.1016/j.jmoneco.2018.07.011CrossRef Google Scholar

Arias, J. E., Rubio-Ramírez, J. F., and Waggoner, D. F. (2018). “Inference based on SVARs identified with sign and zero restrictions: Theory and applications,” Econometrica, 86, 685–720.10.3982/ECTA14468CrossRef Google Scholar

Armstrong, T. B., and Kolesár, M. (2021). “Sensitivity analysis using approximate moment condition models,” Quantitative Economics, 12, 77–108.10.3982/QE1609CrossRef Google Scholar

Artstein, Z. (1983). “Distributions of random sets and random selections,” Israel Journal of Mathematics, 46, 313–324.10.1007/BF02762891CrossRef Google Scholar

Bacchiocchi, E., and Kitagawa, T. (2020). “Locally-but not globally-identified SVARs.” cemmap Working Paper CWP40/20.Google Scholar

Barankin, E. (1960). “Sufficient parameters: Solution of the minimal dimensionality problem,” Annals of the Institute of Statistical Mathematics, 12, 91–118.10.1007/BF01733119CrossRef Google Scholar

Baumeister, C., and Hamilton, J. D. (2015). “Sign restrictions, structural vector autore-gressions, and useful prior information,” Econometrica, 83, 1963–1999.10.3982/ECTA12356CrossRef Google Scholar

Berger, J. O. (1984). “The robust Bayesian viewpoint.” In Kadane, J. (ed.), Robustness of Bayesian Analysis. Amsterdam: North-Holland, pp. 1–32.Google Scholar

Berger, J. O. (1985). Statistical Decision Theory and Bayesian Analysis, 2nd ed. New York: Springer.10.1007/978-1-4757-4286-2CrossRef Google Scholar

Berger, J. O., and Berliner, L. M. (1986). “Robust Bayes and empirical Bayes analysis with ε-contaminated priors,” The Annals of Statistics, 14, 461–486.10.1214/aos/1176349933CrossRef Google Scholar

Berger, J. O. (1994). “An overview of robust Bayesian analysis,” TEST, 3, 5–58.10.1007/BF02562676CrossRef Google Scholar

Betrò, B., and Ruggeri, F. (1992). “Conditional Γ-minimax actions under convex losses,” Communications in Statistics, Part A – Theory and Methods, 21, 1051–1066.10.1080/03610929208830830CrossRef Google Scholar

Bonhomme, S., and Weidner, M. (2022). “Minimizing sensitivity to model misspecification,” Quantitative Economics, 13, 907–954.10.3982/QE1930CrossRef Google Scholar

Brown, L. D., and Purves, R. (1973). “Measurable selections of extrema,” Annals of Statistics, 1, 902–912.10.1214/aos/1176342510CrossRef Google Scholar

Chamberlain, G. (2000). “Econometric applications of maxmin expected utilities,” Journal of Applied Econometrics, 15, 625–644.10.1002/jae.583CrossRef Google Scholar

Chamberlain, G., and Leamer, E. E. (1976). “Matrix weighted averages and posterior bounds,” Journal of the Royal Statistical Society, Series B (Methodological), 38, 73–84.10.1111/j.2517-6161.1976.tb01569.xCrossRef Google Scholar

Chen, X., Christensen, T. M., and Tamer, E. (2018). “Monte Carlo confidence sets for identified sets,” Econometrica, 86, 1965–2018.10.3982/ECTA14525CrossRef Google Scholar

Chib, S., and Jeliazkov, I. (2001). “Likelihoods from the Metropolis Hastings output,” Journal of the American Statistical Association, 96, 270–281.10.1198/016214501750332848CrossRef Google Scholar

Christensen, T. M., and Connault, B. (2023). “Counterfactual sensitivity and robustness,” Econometrica, 91, 263–298.10.3982/ECTA17232CrossRef Google Scholar

Christiano, L. J., Eichenbaum, M., and Evans, C. L. (1999). “Monetary policy shocks: What have we learned and to what end?” In Taylor, J. B. and Woodford, M. (eds.), Handbook of Macroeconomics, vol. 1, Part A. Amsterdam: Elsevier, pp. 65–148.10.1016/S1574-0048(99)01005-8CrossRef Google Scholar

DasGupta, A., and Studden, W. J. (1989). “Frequentist behavior of robust Bayes estimates of normal means,” Statistics and Decisions, 7, 333–361.Google Scholar

Del Negro, M., and Schorfheide, F. (2011). “Bayesian macroeconometrics.” In Geweke, J., Koop, G., and Dijk, H. V. (eds.), Oxford Handbook of Bayesian Econometrics. Oxford: Oxford University Press, pp. 293–389.Google Scholar

Denneberg, D. (1994). Non-additive Measure and Integral. Dordrecht: Kluwer Academic.10.1007/978-94-017-2434-0CrossRef Google Scholar

Dey, D. K., and Micheas, A. C. (2000). “Ranges of posterior expected losses and ε-robust actions.” In Ríos Insua, D. and Ruggeri, F. (eds.), Robust Bayesian Analysis. New York: Springer, pp. 145–159.10.1007/978-1-4612-1306-2_8CrossRef Google Scholar

Ellsberg, D. (1961). “Risk, ambiguity, and the Savage axioms,” Quarterly Journal of Economics, 75, 643–669.10.2307/1884324CrossRef Google Scholar

Gafarov, B., Meier, M., and Montiel Olea, J. L. (2018). “Delta-method inference for a class of set-identified SVARs,” Journal of Econometrics, 203, 316–327.10.1016/j.jeconom.2017.12.004CrossRef Google Scholar

Geweke, J. (1999). “Simulation methods for Bayesian econometric models: Inference, development, and communication,” Econometric Reviews, 18, 1–126.10.1080/07474939908800428CrossRef Google Scholar

Giacomini, R., and Kitagawa, T. (2021). “Robust Bayesian inference for set-identified models,” Econometrica, 89, 1519–1556.10.3982/ECTA16773CrossRef Google Scholar

Giacomini, R., Kitagawa, T., and Read, M. (2022a). “Robust Bayesian inference in proxy SVARs,” Journal of Econometrics, 228(1), 107–126.10.1016/j.jeconom.2021.02.003CrossRef Google Scholar

Giacomini, R., Kitagawa, T., and Uhlig, H. (2019). “Estimation under ambiguity.” cemmap Working Paper CWP24/19.10.1920/wp.cem.2019.2419CrossRef Google Scholar

Giacomini, R., Kitagawa, T., and Volpicella, A. (2022b). “Uncertain identification,” Quantitative Economics, 13(1), 95–123.10.3982/QE1671CrossRef Google Scholar

Gilboa, I., and Schmeidler, D. (1993). “Updating ambiguous beliefs,” Journal of Economic Theory, 59, 33–49.10.1006/jeth.1993.1003CrossRef Google Scholar

Good, I. J. (1965). The Estimation of Probabilities. Cambridge, MA: MIT Press.Google Scholar

Gustafson, P. (2000). “Local robustness in Bayesian analysis.” In Ríos Insua, D. and Ruggeri, F. (eds.), Robust Bayesian Analysis. New York: Springer, pp. 71–88.10.1007/978-1-4612-1306-2_4CrossRef Google Scholar

Hansen, L. P., and Sargent, T. J. (2001). “Robust control and model uncertainty,” American Economic Review, 91, 60–66.10.1257/aer.91.2.60CrossRef Google Scholar

Ho, P. (2023). “Global robust Bayesian analysis in large models,” Journal of Econometrics, 235, 608–642.10.1016/j.jeconom.2022.06.004CrossRef Google Scholar

Huber, P. J. (1973). “The use of Choquet capacities in statistics,” Bulletin of the International Statistical Institute, 45, 181–191.Google Scholar

Huber, P. J., and Ronchetti, E. M. (2009). Robust Statistics, 2nd ed. New York: Wiley.10.1002/9780470434697CrossRef Google Scholar

Kitamura, Y., Otsu, T., and Evdokimov, K. (2013). “Robustness, infinitesimal neighborhoods, and moment restrictions,” Econometrica, 81, 1185–1201.Google Scholar

Kline, B., and Tamer, E. (2016). “Bayesian inference in a class of partially identified models,” Quantitative Economics, 7, 329–366.10.3982/QE399CrossRef Google Scholar

Koopmans, T. C., and Reiersol, R. (1950). “The identification of structural characteristics,” Annals of Mathematical Statistics, 21, 165–181.10.1214/aoms/1177729837CrossRef Google Scholar

Kudō, H. (1967). “On partial prior information and the property of parametric sufficiency.” In Cam, L. L. and Neyman, J. (eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 251–265.Google Scholar

Lavine, M., Wasserman, L., and Wolpert, R. L. (1991). “Bayesian inference with specified marginals,” Journal of the American Statistical Association, 86, 964–971.10.1080/01621459.1991.10475139CrossRef Google Scholar

Leamer, E. E. (1978). Specification Searches. New York: Wiley.Google Scholar

Leamer, E. E. (1982). “Sets of posterior means with bounded variance priors,” Econo-metrica, 50, 725–736.10.2307/1912610CrossRef Google Scholar

Liao, Y., and Simoni, A. (2013). “Semi-parametric Bayesian partially identified models based on support function.” arXiv:1212.3267.Google Scholar

Manski, C. F. (1981). “Learning and decision making when subjective probabilities have subjective domains,” Annals of Statistics, 9, 59–65.10.1214/aos/1176345332CrossRef Google Scholar

Manski, C. F. (2000). “Identification problems and decisions under ambiguity: Empirical analysis of treatment response and normative analysis of treatment choice,” Journal of Econometrics, 95, 415–442.10.1016/S0304-4076(99)00045-7CrossRef Google Scholar

Mertens, K., and Ravn, M. O. (2013). “The dynamic effects of personal and corporate income tax changes in the United States,” American Economic Review, 103, 1212–1247.10.1257/aer.103.4.1212CrossRef Google Scholar

Molchanov, I. (2005). Theory of Random Sets. London: Springer.Google Scholar

Molchanov, I., and Molinari, F. (2018). Random Sets in Econometrics. Cambridge: Cambridge University Press.10.1017/9781316392973CrossRef Google Scholar

Moon, H. R., and Schorfheide, F. (2011). “Bayesian and frequentist inference in partially identified models.” NBER Working Paper No. 14882.Google Scholar

Moon, H. R., and Schorfheide, F. (2012). “Bayesian and frequentist inference in partially identified models,” Econometrica, 80, 755–782.Google Scholar

Moreno, E., and Cano, J. A. (1995). “Classes of bidimensional priors specified on a collection of sets: Bayesian robustness,” Journal of Statistical Inference and Planning, 46, 325–334.10.1016/0378-3758(94)00134-HCrossRef Google Scholar

Müller, U. K. (2012). “Measuring prior sensitivity and prior informativeness in large Bayesian models,” Journal of Monetary Economics, 59, 581–597.10.1016/j.jmoneco.2012.09.003CrossRef Google Scholar

Norets, A., and Tang, X. (2014). “Semiparametric inference in dynamic binary choice models,” Review of Economic Studies, 81, 1229–1262.10.1093/restud/rdt050CrossRef Google Scholar

Peterson, I. R., James, M. R., and Dupuis, P. (2000). “Minimax optimal control of stochastic uncertain systems with relative entropy constraints,” ISSS Transactions on Automatic Control, 45, 398–412.10.1109/9.847720CrossRef Google Scholar

Pires, C. P. (2002). “A rule for updating ambiguous beliefs,” Theory and Decision, 33, 137–152.10.1023/A:1021255808323CrossRef Google Scholar

Poirier, D. J. (1998). “Revising beliefs in nonidentified models,” Econometric Theory, 14, 483–509.10.1017/S0266466698144043CrossRef Google Scholar

Read, M. (2022). “Algorithms for inference in SVARs identified with sign and zero restrictions,” The Econometrics Journal, 25, 699–718.10.1093/ectj/utac009CrossRef Google Scholar

Rieder, H. (1994). Robust Asymptotic Statistics. New York: Springer.10.1007/978-1-4684-0624-5CrossRef Google Scholar

Ríos Insua, D., and Ruggeri, F. (eds.) (2000). Robust Bayesian Analysis. New York: Springer.10.1007/978-1-4612-1306-2CrossRef Google Scholar

Robbins, H. (1956). “An empirical Bayes approach to statistics,” Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, pp. 157–163.Google Scholar

Rothenberg, T. J. (1971). “Identification in parametric models,” Econometrica, 39, 577–591.10.2307/1913267CrossRef Google Scholar

Rubio-Ramírez, J. F., Waggoner, D. F., and Zha, T. (2010). “Structural vector autoregres-sions: Theory of identification and algorithms for inference,” Review of Economic Studies, 77, 665–696.10.1111/j.1467-937X.2009.00578.xCrossRef Google Scholar

Schmeidler, D. (1989). “Subjective probability and expected utility without additivity,” Econometrica, 57, 571–587.10.2307/1911053CrossRef Google Scholar

Shyamalkumar, N. D. (2000). “Likelihood robustness.” In Ríos Insua, D. and Ruggeri, F. (eds.), Robust Bayesian Analysis. New York: Springer, pp. 127–143.10.1007/978-1-4612-1306-2_7CrossRef Google Scholar

Sims, C. A., Waggoner, D. F., and Zha, T. (2008). “Methods for inference in large multiple-equation Markov-switching models,” Journal of Econometrics, 146, 255–274.10.1016/j.jeconom.2008.08.023CrossRef Google Scholar

Sivaganesan, S., and Berger, J. O. (1989). “Ranges of posterior measures for priors with unimodal contaminations,” Annals of Statistics, 17, 868–889.10.1214/aos/1176347148CrossRef Google Scholar

Stock, J. H., and Watson, M. W. (2018). “Identification and estimation of dynamic causal effects in macroeconomics using external instruments,” The Economic Journal, 128, 917–948.10.1111/ecoj.12593CrossRef Google Scholar

Uhlig, H. (2005). “What are the effects of monetary policy on output? Results from an agnostic identification procedure,” Journal of Monetary Economics, 52, 381–419.10.1016/j.jmoneco.2004.05.007CrossRef Google Scholar

Uhlig, H. (2017). “Shocks, sign restrictions, and identification.” In Honoré, B., Pakes, A., Piazzesi, M., and Samuelson, L. (eds.), Advances in Economics and Econometrics: Eleventh World Congress. Cambridge: Cambridge University Press, pp. 95–127.10.1017/9781108227223.004CrossRef Google Scholar

Vidakovic, B. (2000). “Γ-Minimax: A paradigm for conservative robust Bayesians.” In Ríos Insua, D. and Ruggeri, F. (eds.), Robust Bayesian Analysis. New York: Springer, pp. 241–259.10.1007/978-1-4612-1306-2_13CrossRef Google Scholar

Wald, A. (1950). Statistical Decision Functions. New York: Wiley.Google Scholar

Wasserman, L. A. (1990). “Prior envelopes based on belief functions,” The Annals of Statistics, 18, 454–464.10.1214/aos/1176347511CrossRef Google Scholar

Watson, J., and Holmes, C. (2016). “Approximate models and robust decisions,” Statistical Science, 31, 465–489.Google Scholar

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