Measuring the Distributions of Public Inflation Perceptions and Expectations in the UK

Murasawa, Yasutomo (2017): Measuring the Distributions of Public Inflation Perceptions and Expectations in the UK.

Abstract

The Bank of England/GfK NOP Inflation Attitudes Survey asks individuals about their inflation perceptions and expectations in eight ordered categories with known boundaries except for an indifference limen. With enough categories for identification, one can fit a mixture distribution to such data, which can be multi-modal. Thus Bayesian analysis of a normal mixture model for interval data with an indifference limen is of interest. This paper applies the No-U-Turn Sampler (NUTS) for Bayesian computation, and estimates the distributions of public inflation perceptions and expectations in the UK during 2001Q1--2015Q4. The estimated means are useful for measuring information rigidity.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bayesian, Indifference limen, Information rigidity, Interval data, Normal mixture, No-U-turn sampler
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C46 - Specific Distributions ; Specific Statistics; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C82 - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data ; Data Access; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E31 - Price Level ; Inflation ; Deflation

References

Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88, 669-679.

Alston, C. L., & Mengersen, K. L. (2010). Allowing for the effect of data binning in a Bayesian normal mixture model. Computational Statistics & Data Analysis, 54, 916-923.

Armantier, O., Bruine de Bruin, W., Potter, S., Topa, G., van der Klaauw, W., & Zafar, B. (2013). Measuring inflation expectations. Annual Review of Economics, 5, 273-301.

Betancourt, M., & Girolami, M. (2015). Hamiltonian Monte Carlo for hierarchical models. In S. K. Upadhyay, U. Singh, D. K. Dey, & A. Loganathan (Eds.), Current trends in Bayesian methodology with applications (pp. 79-102). CRC Press.

Biernacki, C. (2007). Degeneracy in the maximum likelihood estimation of univariate Gaussian mixtures for grouped data and behavior of the EM algorithm. Scandinavian Journal of Statistics, 34, 569-586.

Binder, C. C. (2015). Measuring uncertainty based on rounding: New method and application to inflation expectations. (Available at SSRN)

Blanchflower, D. G., & MacCoille, C. (2009). The formation of inflation expectations: An empirical analysis for the UK. Working Paper No. 15388. National Bureau of Economic Research.

Chen, M.-H., & Dey, D. K. (2000). Bayesian analysis for correlated ordinal data models. In D. K. Dey, S. K. Ghosh, & B. K. Mallick (Eds.), Generalized linear models: A Bayesian perspective (pp. 133-157). Marcel Dekker.

Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. American Statistician, 4, 327-335.

Coibion, O., & Gorodnichenko, Y. (2015). Information rigidity and the expectations formation process: A simple framework and new facts. American Economic Review, 105, 2644-2678.

Cowles, M. K. (1996). Accelerating Monte Carlo Markov chain convergence for cumulative-link generalized linear models. Statistics and Computing, 6, 101-111.

Fruhwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. Springer.

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2014). Bayesian data analysis (3rd ed.). CRC Press.

Geweke, J. (2007). Interpretation and inference in mixture models: Simple MCMC works. Computational Statistics & Data Analysis, 51, 3529-3550.

Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn Sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15, 1593-1623.

Kamada, K., Nakajima, J., & Nishiguchi, S. (2015). Are household inflation expectations anchored in Japan? Working Paper No. 15-E-8. Bank of Japan.

Kiefer, J., & Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Annals of Mathematical Statistics, 27, 887-906.

Lahiri, K., & Zhao, Y. (2015). Quantifying survey expectations: A critical review and generalization of the Carlson-Parkin method. International Journal of Forecasting, 31, 51-62.

Liu, J. S., & Sabatti, C. (2000). Generalized Gibbs sampler and multigrid Monte Carlo for Bayesian computation. Biometrika, 87, 353-369.

Lombardelli, C., & Saleheen, J. (2003). Public expectations of UK inflation. Bank of England Quarterly Bulletin, 43, 281-290.

Mankiw, N. G., & Reis, R. (2002). Sticky information versus sticky prices: A proposal to replace the new Keynesian Phillips curve. Quarterly Journal of Economics, 117, 1295-1328.

Mankiw, N. G., Reis, R., & Wolfers, J. (2004). Disagreement about inflation expectations. In M. Gertler & K. Rogoff (Eds.), NBER macroeconomics annual 2003 (Vol. 18, pp. 209-248). MIT Press.

Manski, C. F. (2004). Measuring expectations. Econometrica, 72, 1329-1376.

Manski, C. F., & Molinari, F. (2010). Rounding probabilistic expectations in surveys. Journal of Business & Economic Statistics, 28, 219-231.

Murasawa, Y. (2013). Measuring inflation expectations using interval-coded data. Oxford Bulletin of Economics and Statistics, 75, 602-623.

Nandram, B., & Chen, M.-H. (1996). Reparameterizing the generalized linear model to accelerate Gibbs sampler convergence. Journal of Statistical Computation and Simulation, 54, 129-144.

Nardo, M. (2003). The quantification of qualitative survey data: A critical assessment. Journal of Economic Surveys, 17, 645-668.

Neal, R. M. (2011). MCMC using Hamiltonian dynamics. In S. Brooks, A. Gelman, G. L. Jones, & X.-L. Meng (Eds.), Handbook of Marcov chain Monte Carlo (pp. 113-162). Chapman & Hall/CRC.

Papaspiliopoulos, O., Roberts, G. O., & Skold, M. (2003). Non-centered parameterisations for hierarchical models and data augmentation. In J. M. Bernardo et al. (Eds.), Bayesian statistics 7 (pp. 307-326). Oxford University Press.

Papaspiliopoulos, O., Roberts, G. O., & Skold, M. (2007). A general framework for the parametrization of hierarchical models. Statistical Science, 22, 59-73.

Pesaran, M. H., & Weale, M. (2006). Survey expectations. In G. Elliot, C. W. J. Granger, & A. Timmermann (Eds.), Handbook of economic forecasting (Vol. 1, pp. 715-776). Amsterdam: Elsevier.

R Core Team. (2016). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Retrieved from https://www.R-project.org

Richardson, S., & Green, P. J. (1997). On Bayesian analysis of mixtures with an unknown number of components (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59, 731-792.

Sinclair, P. (Ed.). (2010). Inflation expectations. Routledge.

Stan Development Team. (2016). RStan: the R interface to Stan. Retrieved from http://mc-stan.org/ (R package version 2.14.1)

Terai, A. (2010). Estimating the distribution of inflation expectations. Economics Bulletin, 30, 315-329.