Advertisement

Measuring public inflation perceptions and expectations in the UK

  • Yasutomo MurasawaEmail author
Article

Abstract

The Bank of England Inflation Attitudes Survey asks individuals about their inflation perceptions and expectations in eight intervals including an indifference limen. This paper studies fitting a mixture normal distribution to such interval data, allowing for multiple modes. Bayesian analysis is useful since ML estimation may fail. A hierarchical prior helps to obtain a weakly informative prior. The No-U-Turn Sampler speeds up posterior simulation. Permutation invariant parameters are free from the label switching problem. The paper estimates the distributions of public inflation perceptions and expectations in the UK during 2001Q1–2017Q4. The estimated means are useful for measuring information rigidity.

Keywords

Bayesian Indifference limen Information rigidity Interval data Normal mixture No-U-Turn Sampler 

JEL Classification

C11 C25 C46 C82 E31 

Notes

References

  1. Albert JH, Chib S (1993) Bayesian analysis of binary and polychotomous response data. J Am Stat Assoc 88:669–679.  https://doi.org/10.2307/2290350 CrossRefGoogle Scholar
  2. Alston CL, Mengersen KL (2010) Allowing for the effect of data binning in a Bayesian normal mixture model. Comput Stat Data Anal 54:916–923.  https://doi.org/10.1016/j.csda.2009.10.003 CrossRefGoogle Scholar
  3. Armantier O, Bruine de Bruin W, Potter S, Topa G, van der Klaauw W, Zafar B (2013) Measuring inflation expectations. Ann Rev Econ 5:273–301.  https://doi.org/10.1146/annurev-economics-081512-141510 CrossRefGoogle Scholar
  4. Betancourt M, Girolami M (2015) Hamiltonian Monte Carlo for hierarchical models. In: Upadhyay SK, Singh U, Dey DK, Loganathan A (eds) Current trends in Bayesian methodology with applications, chap 4. CRC Press, Boca Raton, pp 79–102CrossRefGoogle Scholar
  5. Biernacki C (2007) Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures for grouped data and behavior of the EM algorithm. Scand J Stat 34:569–586.  https://doi.org/10.1111/j.1467-9469.2006.00553.x CrossRefGoogle Scholar
  6. Binder CC (2017) Measuring uncertainty based on rounding: new method and application to inflation expectations. J Monet Econ 90:1–12.  https://doi.org/10.1016/j.jmoneco.2017.06.001 CrossRefGoogle Scholar
  7. Blanchflower DG, MacCoille C (2009) The formation of inflation expectations: an empirical analysis for the UK. Working Paper 15388, National Bureau of Economic Research.  https://doi.org/10.3386/w15388
  8. Chen MH, Dey DK (2000) Bayesian analysis for correlated ordinal data models. In: Dey DK, Ghosh SK, Mallick BK (eds) Generalized linear models: a Bayesian perspective, chap 8. Marcel Dekker, New York, pp 133–157Google Scholar
  9. Chib S, Greenberg E (1995) Understanding the Metropolis–Hastings algorithm. Amn Stat 4:327–335.  https://doi.org/10.1080/00031305.1995.10476177 Google Scholar
  10. Coibion O, Gorodnichenko Y (2015) Information rigidity and the expectations formation process: a simple framework and new facts. Am Econ Rev 105:2644–2678.  https://doi.org/10.1257/aer.20110306 CrossRefGoogle Scholar
  11. Cowles MK (1996) Accelerating Monte Carlo Markov chain convergence for cumulative-link generalized linear models. Stat Comput 6:101–111.  https://doi.org/10.1007/BF00162520 CrossRefGoogle Scholar
  12. Frühwirth-Schnatter S (2004) Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques. Econom J 7:143–167.  https://doi.org/10.1111/j.1368-423x.2004.00125.x CrossRefGoogle Scholar
  13. Frühwirth-Schnatter S (2006) Finite mixture and Markov switching models. Springer, New YorkGoogle Scholar
  14. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB (2014) Bayesian data analysis, 3rd edn. CRC Press, Boca RatonGoogle Scholar
  15. Geweke J (2007) Interpretation and inference in mixture models: simple MCMC works. Comput Stat Data Anal 51:3529–3550.  https://doi.org/10.1016/j.csda.2006.11.026 CrossRefGoogle Scholar
  16. Gronau QF, Sarafoglou A, Matzke D, Ly A, Boehm U, Marsman M, Leslie DS, Forster JJ, Wagenmakers EJ, Steingroever H (2017) A tutorial on bridge sampling. J Math Psychol 81:80–97.  https://doi.org/10.1016/j.jmp.2017.09.005 CrossRefGoogle Scholar
  17. Hall AR (2005) Generalized method of moments. Oxford University Press, OxfordGoogle Scholar
  18. Hoffman MD, Gelman A (2014) The No-U-Turn Sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res 15:1593–1623Google Scholar
  19. Jeffreys H (1961) Theory of probability, 3rd edn. Clarendon Press, OxfordGoogle Scholar
  20. Kamada K, Nakajima J, Nishiguchi S (2015) Are household inflation expectations anchored in Japan? Working paper 15-E-8, Bank of JapanGoogle Scholar
  21. Kiefer J, Wolfowitz J (1956) Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Ann Math Stat 27:887–906.  https://doi.org/10.1214/aoms/1177728066 CrossRefGoogle Scholar
  22. Lahiri K, Zhao Y (2015) Quantifying survey expectations: a critical review and generalization of the Carlson–Parkin method. Int J Forecast 31:51–62.  https://doi.org/10.1016/j.ijforecast.2014.06.003 CrossRefGoogle Scholar
  23. Liu JS, Sabatti C (2000) Generalized Gibbs sampler and multigrid Monte Carlo for Bayesian computation. Biometrika 87:353–369.  https://doi.org/10.1093/biomet/87.2.353 CrossRefGoogle Scholar
  24. Lombardelli C, Saleheen J (2003) Public expectations of UK inflation. Bank Engl Q Bull 43:281–290Google Scholar
  25. Mankiw NG, Reis R (2002) Sticky information versus sticky prices: a proposal to replace the new Keynesian Phillips curve. Q J Econ 117:1295–1328.  https://doi.org/10.1162/003355302320935034 CrossRefGoogle Scholar
  26. Mankiw NG, Reis R, Wolfers J (2004) Disagreement about inflation expectations. In: Gertler M, Rogoff K (eds) NBER macroeconomics annual 2003, vol 18. MIT Press, Cambridge, pp 209–248Google Scholar
  27. Manski CF (2004) Measuring expectations. Econometrica 72:1329–1376.  https://doi.org/10.1111/j.1468-0262.2004.00537.x CrossRefGoogle Scholar
  28. Manski CF, Molinari F (2010) Rounding probabilistic expectations in surveys. J Bus Econ Stat 28:219–231.  https://doi.org/10.1198/jbes.2009.08098 CrossRefGoogle Scholar
  29. Meng XL, Schilling S (2002) Warp bridge sampling. J Comput Graph Stat 11:552–586.  https://doi.org/10.1198/106186002457 CrossRefGoogle Scholar
  30. Murasawa Y (2013) Measuring inflation expectations using interval-coded data. Oxf Bull Econ Stat 75:602–623.  https://doi.org/10.1111/j.1468-0084.2012.00704.x CrossRefGoogle Scholar
  31. Nandram B, Chen MH (1996) Reparameterizing the generalized linear model to accelerate Gibbs sampler convergence. J Stat Comput Simul 54:129–144.  https://doi.org/10.1080/00949659608811724 CrossRefGoogle Scholar
  32. Nardo M (2003) The quantification of qualitative survey data: a critical assessment. J Econ Surv 17:645–668.  https://doi.org/10.1046/j.1467-6419.2003.00208.x CrossRefGoogle Scholar
  33. Neal RM (2011) MCMC using Hamiltonian dynamics. In: Brooks S, Gelman A, Jones GL, Meng XL (eds) Handbook of Marcov Chain Monte Carlo, handbooks of modern statistical methods, chap 5. Chapman & Hall/CRC, Boca Raton, pp 113–162Google Scholar
  34. Papaspiliopoulos O, Roberts GO, Sköld M (2003) Non-centered parameterisations for hierarchical models and data augmentation. In: Bernardo JM, Bayarri MJ, Berger JO, Dawid AP, Heckerman D, Smith AFM, West M (eds) Bayesian statistics, vol 7. Oxford University Press, Oxford, pp 307–326Google Scholar
  35. Papaspiliopoulos O, Roberts GO, Sköld M (2007) A general framework for the parametrization of hierarchical models. Stat Sci 22:59–73.  https://doi.org/10.1214/088342307000000014 CrossRefGoogle Scholar
  36. Pesaran MH, Weale M (2006) Survey expectations. In: Elliot G, Granger CWJ, Timmermann A (eds) Handbook of economic forecasting, chap 14, vol 1. Elsevier, Amsterdam, pp 715–776.  https://doi.org/10.1016/S1574-0706(05)01014-1 CrossRefGoogle Scholar
  37. R Core Team (2018) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/. Accessed 19 June 2018
  38. Richardson S, Green PJ (1997) On Bayesian analysis of mixtures with an unknown number of components (with discussion). J R Stat Soc Ser B (Stat Methodol) 59:731–792.  https://doi.org/10.1111/1467-9868.00095 CrossRefGoogle Scholar
  39. Sinclair P (ed) (2010) Inflation expectations. Routledge, LondonGoogle Scholar
  40. Stan Development Team (2018) RStan: the R interface to Stan. http://mc-stan.org/, R package version 2.17.3. Accessed 19 June 2018
  41. Terai A (2010) Estimating the distribution of inflation expectations. Econ Bull 30:315–329Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EconomicsKonan UniversityKobeJapan

Personalised recommendations