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Empirical Economics

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18-06-2018

Output gaps, inflation and financial cycles in the UK

Authors: Marko Melolinna, Máté Tóth

Published in: Empirical Economics | Issue 3/2019

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Abstract

This paper aims at constructing potential output and output gap measures for the UK which are pinned down by macroeconomic relationships as well as financial indicators. The exercise is based on a parsimonious unobserved components model which is estimated via Bayesian methods where the time-paths of unobserved variables are extracted with the Kalman filter. The resulting measures track current narratives on macroeconomic cycles and trends in the UK reasonably well. The inclusion of summary indicators of financial conditions leads to a more optimistic view on the path of UK potential output after the crisis and adds value to the model via improving its real-time performance. The models augmented with financial conditions have some real-time wage inflation forecasting ability over the monetary policy-relevant 2- to 3-year horizon during the last 15 years. Finally, we also introduce a new approach to construct financial conditions indices, with emphasis on their real-time performance and ability to track the evolution of macro-financial imbalances. Our results can be relevant from both monetary and macro-prudential policy perspectives.

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For an analysis of some current methods used for policy purposes in the UK, see OBR (2014) and for an example of a more complex production function type approach, see Fernald (2012).

For more details on state space models and the Kalman filter, see e.g. Kalman (1960) and Durbin and Koopman (2001).

See e.g. van Norden and Orphanides (2004).

See Havik et al. (2014).

In fact, for the UK, a number of relevant macroeconomic time series have become less volatile since the introduction of inflation targeting in 1992. For example, the standard deviation of a HP-filtered measure of the output gap in 1992 to 2014 is half of its level in 1970 to 1991, while the standard deviation of core inflation is one-fourths of its level in 1970 to 1991.

For a detailed overview on the information content of the long-term unemployment rate with respect to the NAIRU (or trend unemployment rate), see Rusticelli (2014).

For an introduction to dynamic factor models of this type, see e.g. Stock and Watson (1991). In fact, we experiment with two different financial condition indices (see details in Appendix 2).

See Appendix 1 for the equations of the state space representation of the UCM. See also Tóth (2015).

For details of data used in the analysis, see Appendix 3.

This is sometimes referred to as a “local linear trend” decomposition, see e.g. Harvey et al. (1998).

See Benes et al. (2010) for a similar approach.

The original formulation of the Phillips curve included wage instead of price inflation (see Phillips 1958). We experimented with different measures of inflation; the main results are relatively robust to the different measures.

Estimation and filtering have been implemented in Matlab with the help of the Iris-toolbox, see: J. Benes, M. K. Johnston, and S. Plotnikov, IRIS Toolbox Release 20150318 (Macroeconomic modelling toolbox). The software is available at http://www.iris-toolbox.com.

We also experimented with larger values for the hyper-parameters of trends and cycles, whilst holding their relative values constant. The results are very similar.

One alternative to this approach is a computationally less-intensive Gibbs sampling, which can be thought of as a Metropolis–Hastings algorithm with a special proposal distribution that is always accepted (see e.g. Robert and Casella 2004). This would have required the usage of (possibly truncated) normal prior densities for the coefficients to be estimated and thus would have limited our choice of priors. Due to the presence of AR(1) terms and our prior views on the sign of the non-AR coefficients in the state equations, we did not find it useful to restrict ourselves to normal priors and the Gibbs sampler.

Median values are close to mean values, so there is no qualitative difference between the results using any of these measures. However, in the case of asymmetry the median is typically considered as the more representative moment of the distribution.

See Jarocinski and Lenza (2016), for a similar approach.

We define pseudo-real-time as filtered real-time estimation of the models, using latest vintage (2014Q4) data. In Sect. 3.2, we use vintage real-time GDP data and quarterly re-estimation of the models to test the fully fledged real-time performance of the models.

However, it is notable how weak net lending and credit dynamics (an important variable in the FCIs) remained at the end of the sample.

For example, OECD, in its June 2015 Economic Outlook, estimated the trend output in the UK at between 2 and 2.5% 2004 to 2006, and at 1.8% in 2014.

See, for example, Grant and Chan (2017) and Luo and Startz (2014), who, using unobserved components models, find evidence that there was a break in US trend GDP growth around the beginning of the financial crisis.

Of course, not even this exercise can replicate the true nature of uncertainty as no account is taken of actual vintage price/wage inflation and unemployment rate data (for which revisions are relatively small, however) nor of the uncertainty related to availability of current modelling techniques at each point in time.

The inclusion of the forward-looking element does not have a large effect on the real-time output gap estimates nor the performance of these estimates, although it does have some effect on the level of the gap at the end of the sample. The results for the B1 model are not reported in this section, as they are very close to the B2 model.

This is also true for the estimates of trend unemployment, but we do not report the results here, as this is not the focus of our study.

The models are first estimated with data up to 2004q4, and then, a forecast is produced for each quarter for a three-year period forward. The estimation period is then rolled forward quarter by quarter. Forecasting performance against a simple random walk assumption can then be assessed with standard tools, like root-mean-square errors (RMSE) and Theil U (the relative RMSE of a UCM versus that of a random walk assumption). It is also worth noting that in the FCI models, the dynamic factor model for the FCI is executed in real time to allow only for financial markets data up to the examined point in time to affect the FCI estimate.

This choice is also in line with the original formulation of the Phillips curve (see Phillips (1958)).

For brevity, only Figures for the FCI models are reported here. Other results are available from the authors on request.

See, for example, Guichard et al. (2009), Matheson (2012), and Darracq-Paries et al. (2014).

The smoothing is not crucial for the results of the FCI model presented in this paper, but it slightly improves the real-time performance of the FCI as well as smoothing the short-term volatility.

For details on the construction of the time series, see Speigner (2014).

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Title: Output gaps, inflation and financial cycles in the UK
Authors: Marko Melolinna
Máté Tóth
Publication date: 18-06-2018
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 3/2019
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-018-1498-4

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