On the evolution of the united kingdom price distributions. (English) Zbl 1412.62198

Summary: We propose a functional principal components method that accounts for stratified random sample weighting and time dependence in the observations to understand the evolution of distributions of monthly micro-level consumer prices for the United Kingdom (UK). We apply the method to publicly available monthly data on individual-good prices collected in retail stores by the UK Office for National Statistics for the construction of the UK Consumer Price Index from March 1996 to September 2015. In addition, we conduct Monte Carlo simulations to demonstrate the effectiveness of our methodology. Our method allows us to visualize the dynamics of the price distribution and uncovers interesting patterns during the sample period. Further, we demonstrate the efficacy of our methodology with an out-of-sample forecasting algorithm which exploits the time dependence of distributions. Our out-of-sample forecasts compares favorably with the random walk forecast.


62P20 Applications of statistics to economics
62H25 Factor analysis and principal components; correspondence analysis
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[1] Alvarez, F., Le Bihan, H. and Lippi, F. (2016). The real effects of monetary shocks in sticky price models: A sufficient statistic approach. Am. Econ. Rev.106 2817-51. DOI:10.1257/aer.20140500.
[2] Ball, L. and Mankiw, N. G. (1995). Relative-price changes as aggregate supply shocks. Q. J. Econ.110 161. DOI:10.2307/2118514. · Zbl 0827.90034 · doi:10.2307/2118514
[3] Bellhouse, D. R. and Stafford, J. E. (1999). Density estimation from complex surveys. Statist. Sinica9 407-424. · Zbl 0921.62041
[4] Benko, M., Härdle, W. and Kneip, A. (2009). Common functional principal components. Ann. Statist.37 1-34. · Zbl 1169.62057 · doi:10.1214/07-AOS516
[5] Berger, D. and Vavra, J. (2018). Dynamics of the U.S. price distribution. Eur. Econ. Rev.103 60-82.
[6] Bils, M. and Klenow, P. J. (2004). Some evidence on the importance of price stickiness. J. Polit. Econ.112 947-987.
[7] Buskirk, T. D. (1998). Nonparametric density estimation using complex survey data. In Proceedings of the Survey Research Methods Section 799-801. Amer. Statist. Assoc., Alexandria, VA.
[8] Buskirk, T. D. (1999). Using nonparametric methods for density estimation with complex survey data. Ph.D. dissertation, Arizona State Univ.
[9] Buskirk, T. D. and Lohr, S. L. (2005). Asymptotic properties of kernel density estimation with complex survey data. J. Statist. Plann. Inference128 165-190. · Zbl 1058.62032 · doi:10.1016/j.jspi.2003.09.036
[10] Canty, A. J. and Davison, A. C. (1999). Resampling-based variance estimation for labour force surveys. Statistician48 379-391.
[11] Castro Camilo, D. and de Carvalho, M. (2017). Spectral density regression for bivariate extremes. Stoch. Environ. Res. Risk Assess.31 1603-1613.
[12] Chen, H. A., Levy, D., Ray, S. and Bergen, M. (2008). Asymmetric price adjustment in the small. J. Econ. Perspect.55 728-737.
[13] Chu, B. M., Huynh, K. P., Jacho-Chávez, D. T. and Kryvtsov, O. (2018). Supplement to “On the evolution of the United Kingdom price distributions.” DOI:10.1214/18-AOAS1172SUPP. · Zbl 1412.62198
[14] Debelle, G. and Lamont, O. (1997). Relative price variability and inflation: Evidence from U.S. cities. J. Polit. Econ.105 132-152.
[15] Dhyne, E., Alvarez, L., Le Bihan, H., Veronese, G., Dias, D., Hoffmann, J., Jonker, N., Lunnemann, P., Rumler, F. and Vilmunen, J. (2006). Price changes in the euro area and the United States: Some facts from individual consumer price data. J. Econ. Perspect.20 171-192.
[16] Duin, R. P. W. (1976). On the choice of smoothing parameters for parzen estimators of probability density functions. IEEE Trans. Comput.25 1175-1179. · Zbl 0359.93035 · doi:10.1109/TC.1976.1674577
[17] Gagnon, E. (2009). Price setting during low and high inflation: Evidence from Mexico. Q. J. Econ.124 1221-1263.
[18] Vavra, J. S. (2011). Inflation dynamics and time-varying volatility: new evidence and an Ss interpretation. Q. J. Econ.129 215-258. · Zbl 1400.91360 · doi:10.1093/qje/qjt027
[19] Huynh, K. P. and Jacho-Chávez, D. T. (2010). Firm size distributions through the lens of functional principal components analysis. J. Appl. Econometrics25 1211-1214.
[20] Huynh, K. P., Jacho-Chávez, D. T., Petrunia, R. J. and Voia, M. (2011). Functional principal component analysis of density families with categorical and continuous data on Canadian entrant manufacturing firms. J. Amer. Statist. Assoc.106 858-878. · Zbl 1229.62156 · doi:10.1198/jasa.2011.ap10111
[21] Huynh, K. P., Jacho-Chávez, D. T., Kryvtsov, O., Shepotylo, O. and Vakhitov, V. (2016). The evolution of firm-level distributions for Ukrainian manufacturing firms. J. Comp. Econ.44 148-162.
[22] Hyndman, R. J., Bashtannyk, D. M. and Grunwald, G. K. (1996). Estimating and visualizing conditional densities. J. Comput. Graph. Statist.5 315-336.
[23] Hyndman, R. J. and Khandakar, Y. (2008). Automatic time series forecasting: The forecast package for R. J. Stat. Softw.27 1-22.
[24] Kaplan, G. and Menzio, G. (2015). The morphology of price dispersion. Internat. Econom. Rev.56 1165-1206. · Zbl 1404.91108 · doi:10.1111/iere.12134
[25] Klenow, P. J. and Kryvtsov, O. (2008). State-dependent or time-dependent pricing: Does it matter for recent U.S. inflation? Q. J. Econ.123 863-904.
[26] Klenow, P. J. and Malin, B. (2010). Microeconomic evidence on price-setting. In Handbook of Monetary Economics (B. M. Friedman and M. Woodford, eds.) 3 231-284 6. Elsevier, Amsterdam.
[27] Kneip, A. and Utikal, K. J. (2001). Inference for density families using functional principal component analysis. J. Amer. Statist. Assoc.96 519-542. · Zbl 1019.62060 · doi:10.1198/016214501753168235
[28] Kryvtsov, O. (2016). Is there a quality bias in the Canadian CPI? Evidence from microdata. Can. J. Econ.49 1401-1424.
[29] Lach, S. and Tsiddon, D. (1992). The behavior of prices and inflation: An empirical analysis of disaggregated price data. J. Polit. Econ.100 349-389.
[30] Midrigan, V. (2011). Menu costs, multiproduct firms, and aggregate fluctuations. Econometrica79 1139-1180. · Zbl 1259.91067 · doi:10.3982/ECTA6735
[31] Nakamura, E. and Steinsson, J. (2008). Five facts about prices: A reevaluation of menu cost models. Q. J. Econ.123 1415-1464.
[32] Nakamura, E. and Steinsson, J. (2013). Price rigidity: Microeconomic evidence and macroeconomic implications. Ann. Rev. Econ.213 133-163.
[33] Peterson, B. and Shi, S. (2004). Money, price dispersion and welfare. Econom. Theory24 907-932. · Zbl 1084.91045 · doi:10.1007/s00199-003-0465-1
[34] Piessens, R., de Doncker-Kapenga, E., Überhuber, C. W. and Kahaner, D. K. (1983). QUADPACK: A Subroutine Package for Automatic Integration. Springer Series in Computational Mathematics1. Springer, Berlin. · Zbl 0508.65005
[35] Rosenblatt, M. (1956). A central limit theorem and a strong mixing condition. Proc. Natl. Acad. Sci. USA42 43-47. · Zbl 0070.13804 · doi:10.1073/pnas.42.1.43
[36] Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall, London. · Zbl 0617.62042
[37] Thorarinsdottir, T. L., Gneiting, T. and Gissibl, N. (2013). Using proper divergence functions to evaluate climate models. SIAM/ASA J. Uncertain. Quantificat.1 522-534. · Zbl 1401.60067 · doi:10.1137/130907550
[38] Tran, L. T. (1990). Kernel density estimation on random fields. J. Multivariate Anal.34 37-53. · Zbl 0709.62085 · doi:10.1016/0047-259X(90)90059-Q
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