Wednesday, 8 November 2017

Breaking point

In the context of the debate on productivity, I was recently asked by a non-economist why economists tend to assume mean reversion when it is clear there has been a structural break in the series. It is a very good question and goes to the heart of a major problem in the business of forecasting. Most of our forecasting models are based on linear (or log-linearised) relationships whose forecast performance is conditioned by historical experience. Therefore, if a relationship has tended to mean-revert in the past, the model will assume it does so in future. As a consequence, we cannot easily deal with structural breaks in economic relationships. To put it another way, even if the data deviates from past performance for a prolonged period of time, it is dangerous to assume that there has been a permanent shift since it is entirely possible that it will soon snap back.

It takes a lot to convince economists that there has been a change in trends. In a classic 1961 paper[1], Lawrence Klein and Richard Kosobud noted that much of macroeconomics is based on five “great ratios” in which the relationships between variables can be assumed to be stable. These five ratios are (i) the savings-income ratio; (ii) the capital-output ratio; (iii) labour's share of income; (iv) income velocity of circulation and (v) the capital-labour ratio. But what might have been true almost six decades ago is no longer the case. Labour’s share in income has fallen sharply in the Anglo-Saxon economies over recent years whilst recent experience has shown big shifts in the capital-output ratio, which resulted in the productivity puzzle. However, these old ideas die hard and whilst we try to ensure that we do not stick to outdated precepts, relationships often change so imperceptibly slowly that it is difficult to be sure whether we are witnessing a cyclical shift or a secular trend.

The problem is well-known in economics and has been much-studied. In my introductory econometrics classes one of the first statistical tests to which I was introduced was the Chow test for structural breaks which assesses whether the coefficients derived from regressions on two different parts of the dataset are equal. Although it is pretty simple stuff, a look at UK year-on-year employment and GDP growth over the period 1980 to 2016 nicely highlights the nature of the problem. A quick glance at the chart certainly suggests that there has been a change in the trend relationship (chart). But it is really not that simple.

Suppose in 2013 a policymaker began to be concerned about the nature of the relationship and suspected there was a break in the historical trend. In early 2013, the intelligent policymaker has quarterly data through to end-2012 and decides to estimate a simple econometric equation using the EViews software over the period 1980 to 2012 (132 observations) in order to test their hypothesis. But conducting a Chow test for a structural break at the end of 2008, 2009 and 2010 does not yield any evidence of a break. The data-driven policymaker would thus conclude that this is problem to keep under observation but it is not yet time to press the panic button. A year later, in early 2014, the policymaker runs the analysis again with an additional four quarters of data (136 observations) but still finds no evidence of a structural break in the relationship. But by early 2015, our policymaker runs the analysis on data through end-2014 and finds some evidence of a break in the data at the end of 2009. By the time we get to early 2016 – three years after they suspect a problem – the statistical evidence is unambiguous: There has been a change in the relationship between GDP growth and employment.

The first point to make clear here is that a cautious policymaker has to wait for evidence that there has been a productivity shift – even if they suspected that something was amiss, they cannot make inferences on a relatively small amount of data because they do not know whether the shift is temporary or permanent. But even when the statistical evidence is clear, we cannot simply jump to conclusions – the blip in the productivity figures could vanish just as suddenly as it appeared. For example, if labour shortages begin to manifest themselves, companies can only increase output by increasing capital investment rather than relying on labour. This will mean GDP grows more rapidly than employment in which case labour productivity figures would begin to look much stronger.

As noted above, this is a simplistic exercise and there are better statistical ways to assess whether there are breaks in a data series, but it does highlight an important point: In a world where we require empirical evidence before making policy changes, we sometimes have to wait a long time to build up sufficient information before we are even half sure that we are doing the right thing. Whilst the BoE and OBR are criticised for failing to foresee these trend shifts in economic performance, anyone who has ever tried modelling and forecasting when trends are changing will tell you that it is much harder than it looks.



[1] Klein, L.R. and R. F. Kosobud (1961) ‘Some Econometrics of Growth: Great Ratios of Economics,’ Quarterly Journal of Economics (75), 173-198

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