Bayesian Approach and Identification

Kociecki, Andrzej (2013): Bayesian Approach and Identification.

Abstract

The paper aims at systematic placement of identification concept within Bayesian approach. Pointing to some deficiencies of the standard Bayesian language to describe identification problem we propose several useful characterizations that seem to be intuitively sound and attractive given their potential applications. We offer comprehensive interpretations for them. Moreover we introduce the concepts of uniform, marginal and faithful identification. We argue that all these concepts may have practical significance. Our theoretical development is illustrated with a number of simple examples and one real application i.e. Structural VAR model.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bayesian, Identification
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation

References

Barankin, E.W. (1960), “Sufficient Parameters: Solution of the Minimal Dimensionality Problem”, Annals of the Institute of Statistical Mathematics, 12, pp. 91–118.

Bowden, R. (1973), “The Theory of Parametric Identification”, Econometrica, 41, pp. 1069–1074.

Canova, F. and L. Sala (2009), “Back to Square One: Identification Issues in DSGE Models”, Journal of Monetary Economics, 56, pp. 431–449.

Christiano, L.J., M. Eichenbaum and R. Vigfusson (2006), “Assessing Structural VARs”, in. D. Acemoglu, K. Rogoff and M. Woodford, eds., NBER Macroeconomics Annual 2006, vol. 21, MIT Press.

Cooley, T.F. and M. Dwyer (1998), “Business Cycle Analysis Without Much Theory: A Look at Structural VARs”, Journal of Econometrics, 83, pp. 57–88.

Cooley, T.J. and S.F. LeRoy (1985), “Atheoretical Macroeconomics: A Critique”, Journal of Monetary Economics, 16, pp. 283–308.

Dawid, A. P. (1979), “Conditional Independence in Statistical Theory” (with discussion), Journal of the Royal Statistical Society, Ser. B, 41, pp. 1–31.

De Finetti, B. (1974), Theory of Probability, vol. I, John Wiley & Sons, Chichester.

Drèze, J.H. (1962), “The Bayesian Approach to Simultaneous Equations Estimation”, ONR Research Memorandum 67, The Technological Institute, Northwestern University.

Drèze, J.H. (1972), “Econometrics and Decision Theory”, Econometrica, 40, pp. 1–17.

Drèze, J.H. (1974), “Bayesian Theory of Identification in Simultaneous Equations Models”, in: S.E. Fienberg and A. Zellner, eds., Studies in Bayesian Econometrics and Statistics, North–Holland Pub. Co., Amsterdam.

Drèze, J.H. (1976), “Bayesian Limited Information Analysis of the Simultaneous Equations Model”, Econometrica, 44, pp. 1045–1075.

Drèze, J.H. and M. Mouchart (1990), “Tales of Testing Bayesians”, in: R.A.L. Carter, J. Dutta and A. Ullah, eds., Contributions to Econometric Theory and Application, Springer–Verlag, New York.

Drèze, J.H. and J–F. Richard (1983), “Bayesian Analysis of Simultaneous Equation Systems”, in: Z. Griliches and M.D. Intriligator, eds., Handbook of Econometrics, vol. I, North–Holland Pub. Co., Amsterdam.

Fernández–Villaverde, J., J.F. Rubio–Ramírez and T.J. Sargent (2005), “A,B,C’s (and D)’s for Understanding VARS”, New York University, Working Paper.

Fisher, F.M. (1966), The Identification Problem in Econometrics, McGraw–Hill, New York.

Florens, J–P., M. Mouchart and J–M. Rolin (1990), Elements of Bayesian Statistics, Marcel Dekker, Inc., New York.

Galí, J., M. Gertler and J.D. López–Salido (2005), “Robustness of the Estimates of the Hybrid New Keynesian Phillips Curve”, Journal of Monetary Economics, 52, pp. 1107–1118.

Gelfand, A.E. and S.K. Sahu (1999), “Identifiability, Improper Priors, and Gibbs Sampling for Generalized Linear Models”, Journal of the American Statistical Association, 94, pp. 247–253.

Good, I.J. (1960), “Weight of Evidence, Corroboration, Explanatory Power, Information and the Utility of Experiments”, Journal of the Royal Statistical Society, series B, 22, pp. 319–331.

Good, I.J. (1966), “A Derivation of the Probabilistic Explication of Information”, Journal of the Royal Statistical Society, series B, 28, pp. 578–581.

Gupta, A.K. and D.K. Nagar (2000), Matrix Variate Distributions, Chapman & Hall/CRC, Boca Raton.

Gustafson, P. (2005), “On Model Expansion, Model Contraction, Identifiability and Prior Information: Two Illustrative Scenarios Involving Mismeasured Variables”, Statistical Science, 20, pp. 111–129.

Gustafson, P. (2009), “What Are the Limits of Posterior Distributions Arising from Nonidentied Models, and Why Should We Care?”, Journal of the American Statistical Association, 104, pp. 1682–1695.

Haavelmo, T. (1944), “The Probability Approach in Econometrics”, Econometrica, 12, pp. 1–115.

Hamilton, A.G. (1978), Logic for Mathematicians, Cambridge University Press, Cambridge.

Hansen, L.P. and T.J. Sargent (1991), “Two Difficulties in Interpreting Vector Autoregressions”, in: L.P. Hansen and T.J. Sargent, Rational Expectations Econometrics, Westview Press.

Hsiao, C. (1983) “Identification”, in: Z. Griliches and M.D. Intriligator, eds., Handbook of Econometrics, vol. I, North–Holland Pub. Co., Amsterdam.

Kadane, J.B. (1974), “The Role of Identification in Bayesian Theory”, in: S.E. Fienberg and A. Zellner, eds., Studies in Bayesian Econometrics and Statistics, North–Holland Pub. Co., Amsterdam.

King, R.G. and M.W. Watson (1997), “Testing Long–Run Neutrality”, Federal Reserve Bank of Richmond Economic Quarterly, vol. 83/3.

Kocięcki, A. (2011), “Algebraic Theory of Identification in Parametric Models”, National Bank of Poland, Working Paper no. 88.

Koop, G., H.M. Pesaran and R.P. Smith (2011), “On Identification of Bayesian DSGE Models”, Journal of Business and Economic Statistics, forthcoming.

Kraay, A. (2012), “Instrumental Variables Regressions with Uncertain Exclusion Restrictions: A Bayesian Approach”, Journal of Applied Econometrics, 27, pp. 108–128.

Leamer, E.E. (1978), Specification Searches: Ad Hoc Inference with Nonexperimental Data, John Wiley & Sons, New York.

Leeper, E.M., C.A. Sims and T. Zha (1996), “What Does Monetary Policy Do?” with discussion, Brookings Papers on Economic Activity, 2, pp. 1–78.

Leeper, E.M. and T. Zha (2002), “Empirical Analysis of Policy Interventions”, NBER working paper no. 9063.

Liu, T–C. (1960), “Underidentification, Structural Estimation and Forecasting”, Econometrica, 28, pp. 855–865.

Lucas, R.E. and N.L. Stokey (1987), “Money and Interest in a Cash–in–Advance Economy”, Econometrica, 55, pp. 491–513.

Maddala, G.S. (1976), “Weak Priors and Sharp Posteriors in Simultaneous Equation Models”, Econometrica, 44, pp. 345–251.

Morales, J–A. (1971), Bayesian Full Information Structural Analysis, Springer–Verlag, Berlin.

Müller, U.K. (2012), “Measuring Prior Sensitivity and Prior Informativeness in Large Bayesian Models”, Journal of Monetary Economics, 59, pp. 581–597.

Oulhaj A. and M. Mouchart (2003), “Partial Sufficiency with Connection to the Identification Problem”, Metron, 61, pp. 267–283.

Poirier, D.J. (1998), “Revising Beliefs in Nonidentified Models”, Econometric Theory, 14, pp. 483–509.

Prakasa Rao, B.L.S. (1992), Identifiability in Stochastic Models: Characterization of Probability Distributions, Academic Press, Inc.

Ravenna, F. (2007), “Vector Autoregressions and Reduced Form Representations of DSGE Models”, Journal of Monetary Economics, 54, pp. 2048–2064.

Ríos–Rull, J–V., F. Schorfheide, C. Fuentes–Albero, M. Kryshko and R. Santaeulàlia–Llopis (2012), “Methods versus Substance: Measuring the Effects of Technology Shocks”, Journal of Monetary Economics, 59, pp. 826–846.

Rothenberg, T.J. (1971), “Identification in Parametric Models”, Econometrica, 39, pp. 577–591.

Rothenberg, T.J. (1973), Efficient Estimation with A Priori Information, Yale University Press, New Heaven and London.

Rubio–Ramírez, J.F, D.F. Waggoner and T. Zha (2010), “Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference”, The Review of Economic Studies, 77, pp. 665–696.

Sims, C.A. (2007), “Thinking about Instrumental Variables”, manuscript, available at http://sims.princeton.edu/yftp/IV/IV.pdf.

Sims, C.A. and T. Zha (2006), “Does Monetary Policy Generate Recessions?”, Macroeconomic Dynamics, 10, pp. 231–272.

Zellner, A. (1971), An Introduction to Bayesian Inference in Econometrics, John Wiley & Sons, New York.