Potential supply, the output gap and inflation

Stephen Millard

Potential supply matters!  If an economy is producing less output than it could, then there are resources that are being wasted.  And when these resources are human – that is unemployment – this carries an additional social cost.  But why, specifically, should it matter for an inflation-targeting central bank?  Presumably, because it is a good indicator of inflationary pressure!  The trouble is that there are good reasons to think that this is not actually the case.  And economic theory suggests there is a much better measure of inflationary pressure we can use.

A central bank attempting to achieve a 2% inflation target in the medium term will want to set its tools so as to ensure that the growth of nominal demand over the medium term  ̶  which its tools affect – is 2% higher than the growth rate of real supply over the medium term.  Of course, to do that you need to know what is driving the growth rate of real supply;  hence, the need to calculate potential supply.

So far, so good.  But then how do we measure potential supply and its growth rate?  In a closed economy, the level of potential supply can be built up from natural resources, the capital stock and the potential labour force adjusted for the fact that there will always be some level of unemployment (the natural rate) reflecting the fact that it takes time and effort for workers to find jobs and for firms to find the workers they need.  The growth rate of potential supply will then reflect investment in capital and population growth, as well as the evolution of total factor productivity.  (Of course, understanding current movements in total factor productivity and projecting this forward is really difficult and has been the subject of much debate of late;  but I’ll leave that one for another time.)

But life is not that simple …

Although this ‘bottom up’ approach to potential supply sounds quite reasonable – and is clearly the right approach to use in a discussion of whether resources are being wasted – it does have some problems in the context of using it to construct a measure of inflationary pressure:

1) There may be real frictions in the economy that mean the level of output that is neutral from an inflation point of view will lie beneath this measure of potential.  I’ve already mentioned the search frictions in the labour market that are captured by the natural rate of unemployment;  another example would be a lack of competition leading to rent-seeking behaviour and lower than socially efficient output.  In this case, it has to be the responsibility of government policy more widely to eliminate these frictions, raising output and more fully utilising the economy’s resources (including people).

2) Supply in an open economy can be increased through increased imports (including, importantly in the UK context, migrant workers) and, unlike the case for capital and domestic labour, the amount of ‘potential imports’ is not fixed at any point in time.  I should be clear here that I am thinking about the supply of final consumer goods (as opposed to GDP, a measure of the value added to imports by labour and capital), since it is their price – and not the GDP deflator – that goes into the Inflation Target in the United Kingdom.

For both of these reasons, the gap between actual output and this ‘bottom up’ measure of potential may be completely unrelated to inflation.  And this is why the ‘output gap’ in the sorts of theoretical economic models used in central banks (eg, COMPASS) is measured as the gap between actual output and its ‘flexible price’ value:  that is, what output would be produced given world prices and assuming domestic firms could set whatever price they wanted to for their output and workers whatever wage.  So, an alternative way of getting at ‘potential output’ is to use such a model and actual data to calculate the implied ‘flexible price’ output.  The problem with doing that is that these calculations will be model specific and are quite hard to communicate!

Is there an alternative?

Can we, instead, construct a ‘top down’ measure of potential supply?  One approach is to construct a trend using data on actual output and there are a wide variety of ways of doing this:  eg, the Hodrick-Prescott Filter, the Beveridge-Nelson decomposition, the Christiano-Fitzgerald filter, etc.  Unfortunately though, this approach falls foul of the same critiques as earlier:  trend GDP is not a good measure of potential gross output in an open economy and, anyway, the gap between actual GDP and trend GDP may not be a good indicator of future inflation as shown by Orphanides and van Norden.

Maybe, then, the answer is not to worry about the relationship between your measure of potential output and trend output (or inputs) but rather just to aim to extract that part of output that is most highly correlated with future inflation.  This is the thinking that underlies the multivariate approaches set out in Section 4 of the OBR’s working paper on Output gap measurement.  Again, though, these approaches will tend to produce model-specific estimates that will not always be that easy to explain and Orphanides and van Norden have also shown that these estimates produced in real time have not performed well in the past.

Back to what matters for inflation

So, I’m afraid I’m inexorably drawn to the conclusion that, if we are interested in an indicator of inflationary pressure, attempting to calculate potential output (and the output gap) is not the way to go.  Thankfully, economic theory suggests that there is a better measure of inflationary pressure:  specifically, real marginal cost relative to equilibrium or, equivalently, a measure of mark-ups relative to desired.  The intuition is the following.  If mark-ups are low, firms will want to raise their prices by more – ie, inflationary pressure will be larger – so as to restore mark-ups to their desired level;  if mark-ups are high, competitive pressures will mean that firms will raise prices by less – ie, inflationary pressure will be lower – and mark-ups will fall.

With minimal assumptions (constant elasticity of output with respect to labour input), real marginal cost will be equivalent to the labour share (in gross output) relative to its average, and we have data on this.  This reasoning led to a large body of empirical work on the New Keynesian Phillips Curve (NKPC)  including contributions by, inter alia, Gali, Gertler and Lopez-Salido and Sbordone.  These authors argue that the evidence suggests the labour share – when combined with information from lagged and future expected inflation – actually helps explain movements in inflation.  That said, other authors have challenged just how successful this approach has been.  In particular, Rudd and Whelan have argued that the labour share moves countercyclically, contrary to what is assumed in the derivation of the NKPC, that the estimated coefficient on the labour share is almost invariably insignificant, and, most importantly, the fit of an estimated NKPC is no better than that of a univariate autoregressive model for inflation.

But, if like me you do accept the main point of the theory – viz. that it is cost pressures that determine inflation – then there is an alternative to relying on a model-based measure of real marginal cost:  you could just go and ask firms where they think their margins are relative to where they want to be!

And back to the output gap

One criticism of this approach, though, is that by the time costs are rising, and margins are squeezed, it is too late for the central bank to ward off the ensuing inflation.  Instead, central banks should look to leading indicators of rises in costs, and, to the extent that labour costs form a large proportion of total costs, leading indicators of rises in unit labour costs in particular.  The unemployment rate is one such indicator, and it is straightforward to think of an argument that the other components of the ‘bottom up’ output gap measure reveal additional information about future wage growth.  That said, the message that other costs – and, in particular, import and energy costs – are important for inflation suggests the need to be very careful in how the information contained in the output gap is interpreted;  it certainly is not a sufficient statistic for inflationary pressure!


What’s the answer?  To my mind, central banks should worry less about trying to measure the output gap when forecasting inflation and concentrate on assessing the pressure of costs on firms’ margins.  This will enable them to control inflation.  Controlling inflation will ensure that output remains close to its equilibrium, with the result that the central bank is doing as much as it can to minimise wasted resources within the economy.

Stephen Millard works in the Bank’s Structural Economic Analysis Division.

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3 thoughts on “Potential supply, the output gap and inflation

  1. It’s thirty five years since stagflation, caused by a peak c66% wage share of GDP, was addressed by supply side initiatives and restrictions on collective bargaining. The long term downward pressure on wages, compounded by globalisation, has left developed consumer economies running on credit and fumes from a low wage share. At some point in the middle of the time series we found a sweet spot in the split of rewards to capital and labour. What was it and, if that were taken as a target, 2.0 would follow if the monetary right and fiscal left hands could shake on it. Where do we find an agreed, regularly reported measure of wage / capital share of GDP in order to benchmark the effectiveness of innovation in the toolkit of policy drivers?

  2. Good post.

    The P-MC margin approach does have two problems though. Or rather, it makes two implicit assumptions that might not work:

    1. It assumes the elasticity of the average individual firm’s demand curve stays the same over time. If demand because more elastic, for example, that P-MC margin would shrink, without creating upward pressure on P.

    2. It assumes prices are stickier than wages, so that MC rises first, and then P rises second (unless the CB takes offsetting action). If we make the opposite assumption, then a fall in the P-MC margin would imply deflationary pressures (wages and hence MC will fall, but haven’t fallen yet).

  3. I think an inflation targeting central bank should — wait for it — target inflation. When the price level is below the trend produced by the inflation target, central banks start buying stuff: ST assets, LT assets, private sector assets, foreign exchange or whatever until the price level is back on target. If the price level goes above target, the central bank starts selling stuff.

    The need for a view on what the trend in potential real income is comes in when setting the inflation target, not in month to month management and not for predicting short term fluctuations in the inflation rate.

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