Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix

Econometrica

Volumn 81, Issue 5, 2013, Pages 1805-1849

  Müller, Ulrich K ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

Interval estimation; Posterior variance; Pseudo true parameter value; Quasi likelihood

Indexed keywords

EID: 84889092135     PISSN: 00129682     EISSN: 14680262     Source Type: Journal    
DOI: 10.3982/ECTA9097     Document Type: Article

References (48)

1. Andrews, D. W. K. (1987): "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers, " Econometrica, 55, 1465-1471. DOI: 10.2307/1913568
2. Bayarri, M. J., and J. O. Berger (1997): "Measures of Surprise in Bayesian Analysis, " Working Paper 97-46, Duke University .
3. Berger, J. O. (1985): Statistical Decision Theory and Bayesian Analysis (Second Ed.). New York : Springer-Verlag. DOI: 10.1007/978-1-4757-4286-2
4. Berk, R. H. (1966): "Limiting Behavior of Posterior Distributions When the Model Is Incorrect, " Annals of Mathematical Statistics, 37, 51-58. DOI: 10.1214/aoms/1177699597
5. Berk, R. H. (1970): "Consistency a posteriori, " Annals of Mathematical Statistics, 41, 894-906. DOI: 10.1214/aoms/1177696967
6. Boos, D. D., and J. F. Monahan (1986): "Bootstrap Methods Using Prior Information, " Biometrika, 73, 77-83. DOI: 10.1093/biomet/73.1.77
7. Box, G. E. P. (1980): "Sampling and Bayes' Inference in Scientific Modelling, " Journal of the Royal Statistical Society, Ser. A, 143, 383-430. DOI: 10.2307/2982063
8. Bunke, O., and X. Milhaud (1998): "Asymptotic Behavior of Bayes Estimates Under Possibly Incorrect Models, " The Annals of Statistics, 26, 617-644. DOI: 10.1214/aos/1028144851
9. Chen, C. (1985): "On Asymptotic Normality of Limiting Density Functions With Bayesian Implications, " Journal of the Royal Statistical Society, Ser. B, 47, 540-546.
10. Chow, G. C. (1984): "Maximum-Likelihood Estimation of Misspecified Models, " Economic Modelling, 1, 134-138. DOI: 10.1016/0264-9993(84)90001-4
11. Christiano, L. J. (2007): "Comment, " Journal of Business & Economic Statistics, 25, 143-151. DOI: 10.1198/073500107000000061
12. Del Negro, M., and F. Schorfheide (2004): "Priors From General Equilibrium Models for VARs, " International Economic Review, 45, 643-673. DOI: 10.1111/j.1468-2354.2004.00139.x
13. Doksum, K. A., and A. Y. Lo (1990): "Consistent and Robust Bayes Procedures for Location Based on Partial Information, " The Annals of Statistics, 18, 443-453. DOI: 10.1214/aos/1176347510
14. Domowitz, I., and H. White (1982): "Misspecified Models With Dependent Observations, " Journal of Econometrics, 20, 35-58. DOI: 10.1016/0304-4076(82)90102-6
15. Dudley, R. M. (2002): Real Analysis and Probability. Cambridge, U.K. : Cambridge University Press. DOI: 10.1017/CBO9780511755347
16. Fahrmeir, L., and G. Tutz (2001): Multivariate Statistical Modelling Based on Generalized Linear Models. New York : Springer-Verlag. DOI: 10.1007/978-1-4757-3454-6
17. Freedman, D. A. (2006): "On the So-Called 'Huber Sandwich Estimator' and 'Robust Standard Errors', " The American Statistician, 60, 299-302. DOI: 10.1198/000313006X152207
18. Gelman, A., X. Meng, and H. Stern (1996): "Posterior Predictive Assessment of Model Fitness via Realized Discrepancies, " Statistica Sinica, 6, 733-807.
19. Gelman, A., J. B. Carlin, H. S. Stern, and D. B. Rubin (2004): Bayesian Data Analysis (Second Ed.). Boca Raton, FL : Chapman & Hall/CRC.
20. Geweke, J. (2005): Contemporary Bayesian Econometrics and Statistics. Hoboken, NJ : Wiley. DOI: 10.1002/0471744735
21. Gourieroux, C., A. Monfort, and A. Trognon (1984): "Pseudo Maximum Likelihood Methods: Theory, " Econometrica, 52, 681-700. DOI: 10.2307/1913471
22. Hall, P., and C. C. Heyde (1980): Martingale Limit Theory and Its Applications. New York : Academic Press.
23. Hartigan, J. (1983): Bayes Theory. New York : Springer. DOI: 10.1007/978-1-4613-8242-3
24. Huber, P. (1967): "The Behavior of the Maximum Likelihood Estimates Under Nonstandard Conditions, " in Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley : University of California Press, 221-233.
25. Jeganathan, P. (1995): "Some Aspects of Asymptotic Theory With Applications to Time Series Models, " Econometric Theory, 11, 818-887. DOI: 10.1017/S0266466600009907
26. Kim, J. (2002): "Limited Information Likelihood and Bayesian Analysis, " Journal of Econometrics, 107, 175-193. DOI: 10.1016/S0304-4076(01)00119-1
27. Kleijn, B. J. K., and A. W. Van der Vaart (2012): "The Bernstein-Von-Mises Theorem Under Misspecification, " Electronic Journal of Statistics, 6, 354-381. DOI: 10.1214/12-EJS675
28. Kwan, Y. K. (1999): "Asymptotic Bayesian Analysis Based on a Limited Information Estimator, " Journal of Econometrics, 88, 99-121. DOI: 10.1016/S0304-4076(98)00024-4
29. Lancaster, T. (2003): "A Note on Bootstraps and Robustness, " Working Paper, Brown University .
30. Lieb, E. H., and M. Loss (2001): Analysis (Second Ed.). Providence, RI : American Mathematical Society.
31. Lubik, T., and F. Schorfheide (2004): "Testing for Indeterminacy: An Application to U.S. Monetary Policy, " American Economic Review, 94, 190-217. DOI: 10.1257/000282804322970760
32. Moran, P. A. P. (1948): "Rank Correlation and Product-Moment Correlation, " Biometrika, 35, 203-206.
33. Müller, U. K. (2013): "Supplement to 'Risk of Bayesian Inference in Misspecified Models, and the Sandwich Covariance Matrix', " Econometrica Supplemental Material, 81, http://www.econometricsociety.org/ecta/supmat/9097_data_and_programs.zip.
34. Newey, W. K., and K. West (1987): "A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix, " Econometrica, 55, 703-708. DOI: 10.2307/1913610
35. Pelenis, J. (2010): "Bayesian Semiparametric Regression, " Working Paper, Princeton University .
36. Pratt, J. W., H. Raiffa, and R. Schlaifer (1965): Introduction to Statistical Decision Theory. New York : Wiley.
37. Royall, R., and T. Tsou (2003): "Interpreting Statistical Evidence by Using Imperfect Models: Robust Adjusted Likelihood Functions, " Journal of the Royal Statistical Society, Ser. B, 65, 391-404. DOI: 10.1111/1467-9868.00392
38. Schennach, S. M. (2005): "Bayesian Exponentially Tilted Empirical Likelihood, " Biometrika, 92, 31-46. DOI: 10.1093/biomet/92.1.31
39. Schervish, M. J. (1995): Theory of Statistics. New York : Springer.
40. Schorfheide, F. (2008): "DSGE Model-Based Estimation of the New Keynesian Phillips Curve, " FRB Richmond Economic Quarterly, 94, 397-433.
41. Shalizi, C. R. (2009): "Dynamics of Bayesian Updating With Dependent Data and Misspecified Models, " Electronic Journal of Statistics, 3, 1039-1074. DOI: 10.1214/09-EJS485
42. Silverman, B. W. (1986): Density Estimation. London : Chapman & Hall.
43. Stafford, J. E. (1996): "A Robust Adjustment of the Profile Likelihood, " The Annals of Statistics, 24, 336-352. DOI: 10.1214/aos/1033066212
44. Szpiro, A. A., K. M. Rice, and T. Lumley (2010): "Model-Robust Regression and a Bayesian 'Sandwich' Estimator, " The Annals of Applied Statistics, 4, 2099-2113. DOI: 10.1214/10-AOAS362
45. Van der Vaart, A. W. (1998): Asymptotic Statistics. Cambridge, U.K. : Cambridge University Press.
46. White, H. (1980): "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity, " Econometrica, 48, 817-830. DOI: 10.2307/1912934
47. White, H. (1982): "Maximum Likelihood Estimation of Misspecified Models, " Econometrica, 50, 1-25. DOI: 10.2307/1912526
48. Zellner, A. (1997): "The Bayesian Method of Moments (BMOM): Theory and Applications, " in Applying Maximum Entropy to Econometric Problems. Advances in Econometrics, Vol. 12, ed. by T. B. Fomby and R. C. Hill . Bingley : Emerald Group Publishing, 85-105. DOI: 10.1108/S0731-9053(1997)0000012005