Monetary policy makers need to know whether the economy is operating above or below its supply capacity. If the economy is operating above its supply capacity, inflation is likely to rise, and vice versa. A crucial component of supply capacity is the labour productivity trend but we cannot observe this directly. We have to estimate it. Thankfully, there are ways of splitting observed macroeconomic time series into estimated trend and cyclical components. Using a variety of methods on UK data, I find that UK productivity growth over the period 1991 to 2018 has been structurally, rather than cyclically, weak since the financial crisis. And, UK trend productivity has been strongly correlated with trend productivity in other advanced economies.
In a recent Working Paper, my co-author and I studied the recent weakness in labour productivity in the United Kingdom. The black line in Chart 1 shows that labour productivity – defined as output per hour worked – has stagnated since around 2008. This stagnation has received much attention in the blogosphere, including in blogs by Kimball et al (2013), Lewis (2018), Schneider (2018) and Wren-Lewis (2017). We wanted to see if structural or cyclical components of the data could better explain this weakness. One popular method for splitting data into its trend and cycle components is to use unobserved components models (UCM). (For some examples of this see Morley et al (2003), Mitra and Sinclair (2012) and Grant and Chan (2017).) We introduce a set of one-variable (univariate) and two-variable (bivariate) models that allow us to estimate trends and cycles for the productivity data.
The univariate models we use only have UK productivity as an observable time series, while we add productivity in peer economies in the bivariate versions. We also use Bayesian techniques to estimate the models. Bayesian techniques allow us to feed prior information into the estimation. For example, we could have a view on the size of a particular parameter of the model (like how productivity depends on its own lagged value), and we can express this as a prior for the model. We can also express our views on how confident we are in our prior beliefs by adjusting the ‘tightness’ of the prior: the more confident we are, the tighter the prior. Bayesian estimation then lets the actual data either move the estimated (posterior) parameter value away from the prior or keep it close to it. It does this by maximising the likelihood of the data, given the priors and the model that we are using.
Furthermore, in these types of models, it is possible to model directly the correlation between shocks to the trend and the cycle. People have different views about this issue. Some think that the trend is a long-term phenomenon uncorrelated with short-term cyclical variations around the trend. But others think that trends and cycles can be correlated, either positively or negatively. The correlation could be positive, for example, if cyclical shocks have a persistent effect on the trend. Arguably, this happened in the financial crisis in the 2000’s. On the other hand, the correlation could be negative. For example, a technological improvement could imply higher trend productivity immediately (ie, a positive shock to the trend). But, if actual productivity only catches up later, this would look like a negative cyclical shock.
The framework we use has the advantage that we can calculate the likelihood of each model and so assess our choice of priors. This turns out to be very important. Our priors for the correlation between, and the relative volatility of, trend and cycle shocks turn out to affect the smoothness of the estimated trend, our main interest. In our data, if the prior is set to be consistent with a smooth trend, then we find that non-correlated UC models, with no parameterised correlation between the trend and cycle shocks, or correlated models with strongly smoothed trends are the likeliest to fit the data. This typically results in a relatively smooth estimated trend. On the other hand, if the prior allows for a more volatile trend, then by far the most likely models are generally the ones allowing for correlation between the trend and the cycle shocks, rather than non-correlated UC models. This causes the resulting estimated trend to be relatively more volatile.
An example of two trends in a univariate model allowing for correlation between the trend and the cycle shocks is shown in Chart 1. By varying the prior for the relative volatility of the trend and the cycle, we can obtain very different estimates of the trend. If we set a relatively smooth trend as a prior, the estimated trend is nearly a straight line. At the other extreme, if we set a relatively volatile trend, the estimated trend is near the data. This shows that one needs to be very careful when setting priors in these types of models.
Chart 1: UK productivity data and its trend from selected univariate model specifications (1991 Q1=100)
Notes: Productivity defined as UK GDP divided by total hours worked in the UK economy. The red and green lines show different estimated trends for this series based on two alternative priors for the volatility of shocks to this trend in a correlated UCM.
Sources: ONS and author’s calculations.
Whichever of our models is used, our evidence suggests that the trend productivity growth rate in the United Kingdom has been substantially weaker since the financial crisis (Chart 2). This result is consistent with other studies finding an important role for structural drivers in explaining UK productivity dynamics in recent years. (See, for example, Goodridge et al (2016) and Oulton and Sebastiá-Barriel (2017).) Given that our approach is more focused on empirical observations about aggregate trends than most other studies on this topic, it is encouraging that the main conclusion is similar.
We also find evidence that there is a significant positive correlation between shocks to UK trend productivity and those of other advanced economies. These positive correlations between trends appear to have become stronger since the financial crisis, which is consistent with the view of synchronised global shocks affecting macroeconomic dynamics more now than before the crisis (see Chart 3).
Chart 2: Average pre and post-crisis trend productivity growth rates (year-on-year %) – selected models
Note: The chart shows the range of highest and lowest average trend productivity growth rates from four different UCM models on UK productivity.
Source: Author’s calculations.
Chart 3: Trend correlation coefficient for UK and US productivity
Notes: The chart shows the rolling correlation coefficient of UK and US productivity trend shocks from a bivariate UCM. Dashed lines are 90% confidence intervals.
Source: Author’s calculations.
Our results are consistent with a relatively pessimistic view of post-financial crisis productivity dynamics in the UK. The weakness of trend productivity growth appears to be consistent with a secular, long-term stagnation type narrative. All is not lost though – things can change quickly. It is possible that positive real economy shocks could quickly lead to an improvement in trend productivity. (See, for example, Carney (2018) and Haldane (2018) for remarks on the effects of technological progress.) More structural models and views on future technological progress are needed to formulate forecasts for that; our model – like any time series model, no matter how sophisticated – is a reflection of past, not future data dynamics. But, it can still help monetary policy makers know where the economy is operating relative to its current supply potential. Improving the economy’s supply potential is likely to require structural policies that are beyond their scope.
Marko Melolinna works in the Bank’s Structural Economics Division.
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