A State Space Approach to Extracting the Signal From Uncertain Data

Abstract

Most macroeconomic data are uncertain -they are estimates rather than perfect measures of underlying economic variables. One symptom of that uncertainty is the propensity of statistical agencies to revise their estimates in the light of new information or methodological advances. This paper sets out an approach for extracting the signal from uncertain data. It describes a two-step estimation procedure in which the history of past revisions are first used to estimate the parameters of a measurement equation describing the official published estimates. These parameters are then imposed in a maximum likelihood estimation of a state space model for the macroeconomic variable.Keywords: Real-time data analysis; State space models; Data uncertainty; Data revisions JEL codes: C32, C53 * This paper represents the views and analysis of the authors and should not be thought to represent those of the Bank of England, Monetary Policy Committee, or any other organisation to which the authors are affiliated. We would like to thank the associate editor for extremely helpful comments on an early version of the paper. We have further benefited from helpful comments from Andrew Blake, Spencer Dale, Kevin Lee, Lavan Mahadeva, Tony Yates and Shaun Vahey. We would also like to thank Simon Van Norden for his constructive and incisive comments especially on the relation between our model and comparable recent models in the literature.

Measuring the effects of expectations shocks

“…6 It may be tempting to discount the importance of accounting for data revisions, but data revisions can be large relative to the variability in the series (see, e.g., Aruoba (2008)). Croushore (2011bCroushore ( , 2011a provide review articles, and Jacobs and van Norden (2011), Cunningham et al (2009), Kishor and Koenig (2012) and Garratt et al (2008) are key papers considering various ways of modelling data subject to revision, and Clements and Galvão (2019) provide a recent review.…”

“…We show how to obtain impulse response estimates under two assumptions. The …rst one is that after many rounds of revisions, we observe the 'true'values (as in, e.g., Cunningham, Eklund, Je¤ery, Kapetanios and Labhard (2009), Kishor and Koenig (2012) and Garratt, Lee, Mise and Shields (2008)) and the second that 'true' values are never observed (as in, e.g., Jacobs and van Norden (2011)).…”

Testing for News and Noise in Non-Stationary Time Series Subject to Multiple Historical Revisions

“…Recently, Clements and Galvão (2013) extended the Jacobs and van Norden (2011) framework by allowing for revision bias. The alternative state-space forms of Cunningham et al (2012) and Kishor and Koenig (2012) should in principle be able to do the same. Fixler and Nalewaik (2009) propose an alternative test, whose properties still have to be explored.…”

Real-time analysis on Japan’s labor productivity

“…Fan charts illustrate probability distributions of future revisions over history, as well as those of projection itself. Cunningham et al (2007) construct a model used for creating probability distributions of future revisions to the past data. Predicting revisions that are likely to happen in the future is called as ''backcasting.''…”

“…For instance, for the United Kingdom, Ashley et al (2005) report that survey data are significantly helpful to predict the revisions to GDP. Cunningham et al (2007) construct a state-space model with survey data to predict revisions to GDP. 17,18 Table 5c and d show that the coefficient on the Tankan diffusion index is positive and significant at the 5% level, both with the preliminary estimates and with the first annual revisions.…”