Category Archives: Macroeconomics

What can regional data tell us about the UK Phillips Curve?

Alex Tuckett

The Phillips Curve (PC) is an old concept in economics, but it is a durable one. The simple idea behind the PC is that the lower the rate of unemployment, the faster wages will grow. If the PC has changed over time, that can have important implications for monetary policymakers. Analysis of regional UK data suggests that the PC has shifted down over time, but has not necessarily become flatter. Higher levels of educational attainment are likely to have contributed to this shift.

Despite its age, the PC remains central to the way that Central Banks attempt to control inflation. In most advanced economies wages are the most important component of domestic costs, so stabilising wage inflation should be sufficient to stabilise price inflation. In turn, the PC says that stabilising wage growth can be achieved by stabilising unemployment. So to meet an inflation target, Central Banks just need to change interest rates to keep the economy growing steadily and prevent unemployment getting too high – or low.

Reality is rarely that simple. Central Banks often face external cost shocks, such as large movements in commodity prices or exchange rates, which can move inflation and unemployment in opposite directions. In this case, Central Banks face a ‘trade-off’ between stabilising inflation or unemployment. The PC determines the terms of that trade-off.

A number of economists and policymakers have argued that the PC has become flatter or disappeared – in other words, a given change in unemployment has less effect on inflation. There could be a number of reasons for such a ‘flattening’: changes in the labour market, greater integration of the global economy or more credible policy frameworks.

If true, this flattening in the Phillips Curve may be a mixed blessing. On the one hand, a shock to the economy that changes unemployment will not move inflation too far from target. Set against that, trade-offs are more painful when the PC is flat. Suppose inflation is high because the exchange rate has depreciated. With a flat PC, bringing inflation back to target would require a larger increase in unemployment.

Regional data can potentially be a helpful source of information about the stability of the PC, and has been used to analyse this question for the US (as well as other questions about the labour market). It provides more data points, making it easier to look for changes in parameters. And regional variation can be used to explore potential reasons for changes. In this post I investigate what regional data for the UK can tell us about how – and why – the PC may have shifted in the UK over the past 20 years.

Has the Phillips Curve remained stable in the UK?

Phillips Curves are normally estimated on macroeconomic data for wage growth and the unemployment rate at a national level, but the same principal can be applied to regional level data, using panel techniques.  Figure 1 shows the results of fitting a simple Phillips Curve relationship for the UK using either Local Authority (LA) level data (column (1)) or NUTS1 level data (which divides the UK into twelve nations or regions – column (4)), using a fixed effects panel estimator. The growth rate of median hourly wages is negatively affected by the rate of unemployment in the previous year; an increase in the unemployment rate of 1 percentage point results in wage growth that is roughly 0.5 percentage points weaker.

Figure 1: Phillips Curves estimated on regional data

All regressions estimated on annual data, and include geographic fixed effects. Wage growth is median hourly wages for full-time workers, resident basis for LA, workplace basis for NUTS1.  *** Significantly different from zero at 1% probability **5% probability * 10% probability.

Are these parameters stable over the sample? Whether the level of the PC has changed over time can be tested by including a time trend in the regression, as shown in Columns (2) and (5) of Figure 1. The trend is negative, and highly significant. Over the sample, the same level of unemployment has been associated with lower wage growth. An alternative model, which allows a discrete shift in the PC, finds a lower level after the crisis than before.

Columns (3) and (6) look for evidence that the curve has become flatter, instead of (or in addition to) moving downwards, by allowing the coefficient on unemployment to change over time. The results indicate that, if anything, the slope of the Phillips Curve appears to have trended downwards (become steeper) over time, although the coefficient is very close to zero and not significant.

Another way to assess whether the slope of the PC has changed over time is to use rolling regressions – estimating a PC over successively later samples and seeing how the slope coefficient changes, as in Leduc and Wilson (2017). Figure 2 shows the slope parameter of the PC estimated over rolling seven year periods, and how this estimate has changed over time. The curve appears to steepen during the financial crisis; indeed it is difficult to find a downward slope for sample windows prior to the crisis. This probably illustrates the effect of sample selection – it is difficult to estimate the PC over a period with no recession, even with regional data.

Figure 2: rolling estimates of the slope of the Phillips Curve

 β coefficient in regression  median hourly pay growth = α + β* lagged unemployment rate + θ*lagged National CPI Inflation rate. Dotted lines show 90% confidence interval around the fixed-effects panel estimate. Regressions estimated over 7-year overlapping windows, for instance 2017 values are estimated on 2001-17 data.

There is some tentative evidence that the PC has become flatter over the past few years. However this could easily be the flip side of the same sample coin – as the Great Recession moves further into the rear-view mirror, it becomes harder to identify cyclical relationships. Overall there is stronger evidence for there being a drop, not a tilt, in the UK wage Phillips Curve.

Why has the Phillips Curve changed?

What could have caused such a drop?  Slower productivity growth is probably part of the story. However, if aggregate productivity growth is added to the panel equations there remains a significant downward trend.

Phillips Curve models often include a measure of the ‘unemployment gap’, instead of simply unemployment. The idea is that there is a ‘natural rate’ of unemployment – often termed the NAIRU, or U* – at which wage inflation should be consistent with the inflation target. U* is not directly observable; it can only be estimated. The evidence presented above – that the constant term in the PC has fallen – can be interpreted as a fall in U*.

Why has U* fallen? As outlined in Saunders (2017), there are a number of possible reasons: changes to the benefits system, the rise of the ‘gig economy’, demographics (Tuzeman (2017)), inward migration, and the increase in educational attainment. Educational attainment is a particularly compelling candidate. Workers with more education have higher participation rates and lower unemployment rates on average. This could be for a number of reasons. Higher levels of formal education may make workers more effective at finding and applying for jobs; make it easier to make the transition into occupations or industries where employment is growing; or shift the mix of jobs in the economy towards occupations which are more secure.

Regional data is well suited to testing the idea that higher educational attainment may have lowered U*. In Figure 3 I show what happens when a measure of educational attainment (the share of the population with degree-level education) is introduced into the Phillips Curve equations.  Education seems to shift the PC downwards (see columns (1) and (3)). However, educational attainment increases in almost all of the Local Authorities and regions over the last 12 years, so the result may spuriously reflect a more general downward trend in wage growth. Columns (2) and (4) test this by including a time trend in the equations; although smaller, the effect of education remains statistically significant.  Educational attainment also remains significant if productivity growth is included instead of a time-trend.

Figure 3: has educational attainment shifted the Phillips Curve?

All regressions estimated on annual data, and include geographic fixed effects. Wage growth is median hourly wages for full-time workers, resident basis for LA, workplace basis for NUTS1.  *** Significantly different from zero at 1% probability **5% probability * 10% probability.

This is a conditional result, which does not mean that education lowers wages. A more intuitive way to put it is that rising educational attainment has reduced U*, allowing for unemployment to be lower without causing wage growth that is too high for the inflation target. The net effect on wages could easily be positive.

Based on the LA level results, rising levels of educational attainment can explain a fall in U* of around 1ppt over the last 12 years. The estimated effects are even larger with mean wages, or using NUTS1 data.

Will U* continue to fall?

Average levels of educational attainment in the workforce are likely to continue to increase over the next two decades.  As older workers retire from the workforce, the average level of educational attainment for the workforce as a whole will increase, even without any further increase in the proportion of school leaves going to university. Figure 4 shows a projection for how the share of graduates in the workforce could progress, under a few other simple assumptions. If levels of education continue to rise as projected in Figure 4, then this should reduce U* by around ½ ppt over the next 15 years.

Figure 4: projections for share of graduates in 16-64 population

Assumes that number of new graduations remains a constant share of the 21-24 year old population. Baseline projection assumes net migration is neutral for educational attainment. Migration variant assumes migration continues at levels in year to June 2017, and rates of higher education amongst graduates are as estimated in ONS analysis. Both projections assume mortality rates are equal for graduates and non-graduates.

To summarise, analysis of regional data suggests that the Phillips Curve has shifted down in the UK – that is, U* has fallen. Higher levels of educational attainment can partly explain this downward shift. There is little evidence that the Phillips Curve has become flatter.

Alex Tuckett works in the Bank’s External MPC unit.

If you want to get in touch, please email us at or leave a comment below.

Comments will only appear once approved by a moderator, and are only published where a full name is supplied.Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.

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Bitesize: UK real interest rates over the past three centuries

John Lewis

How low are UK real interest rates by historical standards? Using the Bank’s Millennium of Macroeconomic Data, I compute real bank rate, mortgage rates, and 10-year government bond yields over time.

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The UK’s productivity puzzle is in the top tail of the distribution

Patrick Schneider

UK productivity growth has been puzzlingly slow since the crisis. After averaging 2% every year in the pre-crisis decade, growth in labour productivity (output per hour worked) has slowed to an average of only 0.5%. Extensive research and commentary on the productivity puzzles has suggested myriad causes for the malaise – including ‘zombie’ firms hoarding resources, sluggish investment in the face of uncertainty, mismeasurement and more – and have dismissed others that no longer seem plausible – including temporary labour hoarding. Using firm-level data, I show that slower aggregate growth is entirely driven by the more productive firms in the economy.

In apparent contrast to my results, recent arguments have focused on the role that the weakest firms play in keeping down aggregate productivity. For example, Andy Haldane highlighted the ‘long tail of low-productivity companies’, which drags on the aggregate, in a speech last year and the OECD has published several papers (e.g. here [pdf] and here) analysing the divergence of the top end of the productivity distribution (‘frontier’ firms) from the rest (‘laggards’).

These ideas have been very influential. But unproductive firms are not responsible for all of the UK’s issues. Using a new method that links aggregate productivity to its distribution across workers, I found that the slowdown in productivity growth is isolated in the top tail of the distribution of productivity across workers. The most productive firms are failing to improve on each other at the same rate as their predecessors did.

You can see this in Chart 1 – the two lines track the average, annual change in productivity at different parts of the distribution across workers, before and after the crisis. The post-crisis line is well below the pre-crisis one, but only toward the right, the top tail of the distribution. Surprisingly, the bottom end of the distribution appears to have been growing faster in recent years than it was leading up to the crisis.

Chart 1: Av. annual change in productivity, by centile of the productivity level distribution

The beauty of this chart is that the average height of each line is about equal to the change in the aggregate – so we can see which part of the distribution is moving (or not) to cause the aggregate to move. And, again, it’s the top end that’s doing the work. This fact doesn’t explain the puzzle. As with any statistical decomposition, we’re brought no closer to the why of the issue, but the where is a little clearer.

That’s about all I have to say. The rest of this post provides the working behind Chart 1. In the next section, I sketch the method I used, and then I take it to UK data, giving a bit more flavour to the result, ending up right back at Chart 1.

One thing this extra detail does is to confirm the headline results in Andy’s speech and the OECD’s papers. You can see the long tail of low productivity firms in Chart 4, and the divergence of the top end of the distribution from the rest in Chart 1. But in the data we have, these features are always there. So they can’t be to blame for the slowdown in growth. Indeed, if anything, the increasing dispersion is where aggregate growth usually comes from. In this light, the UK growth puzzle is there because the increasing dispersion has slowed down since the crisis.

The method (for the interested reader)

So how did I get to Chart 1?

Aggregate labour-productivity (value-added per worker) is usually measured by taking a labour-weighted average of firm-level productivity.  But it can also be approximated by the average of a number (Q) of equally spaced quantiles (as I outline in a forthcoming working paper). So, for example, we could measure aggregate productivity by taking the average of the 1st through 99th centiles of the distribution. More explicitly

\Pi = \frac{VA}{L}=\sum_{i} \frac{l_i}{L} \pi_i \approx \frac{1}{Q} \sum_{j} q^{\pi}(j)

where i and j represent firms and quantiles, \pi is productivity, va is value-added and l is labour. q^{\pi}(j) is the quantile function of productivity across workers, it picks out the productivity of the worker who is more productive than exactly j/Q of the others.

(Aside: we need to be careful to work with the correct distribution. The key is that aggregate productivity is the mean of the distribution across workers. Because we usually measure productivity at the firm level, we need to use labour weights to adjust the calculation to the right distribution.)

With this approximation, we can measure changes in the aggregate by averaging over changes in the centiles as well. Using the formula below, we can see which part of the distribution is moving (or not) to cause the aggregate to move.

\Delta \Pi \approx \frac{1}{Q} \sum_{j} \Delta q^{\pi}(j)

Note that we’re tracking growth in the distribution here – not growth in firms, nor the distribution of firm growth, so it could be that parts of the distribution move around or stay still, but the firms that are located there are shifting around a lot.

The data (for the still interested reader)

So now that we have the method in hand, let’s apply it to UK data.

I’m using ONS firm-level microdata (combining ARDx with ABS 2015), and measuring productivity as real value-added (using 2-digit sector deflators) per employee.

This dataset doesn’t cover the whole economy – the surveys only try to cover the non-financial business economy (which is a shame given the importance of finance in the growth puzzle) and some other sectors only pop up from 2009, so I had to cut these from the whole dataset for consistency. Because of these survey limitations, the ‘aggregate’ in the below results is a subset of the overall UK aggregate economy.

OK so let’s first check how close the approximation is. The charts below show actual productivity and its growth as measured from the micro-data, compared with the approximation. As you can see in Chart 2, the approximation has a consistent negative bias, because cutting out the top 1% drops some very large outliers, but the growth path is about right (Chart 3).

Chart 2: Aggregate productivity and its centile approximation (level)

Chart 3: Aggregate productivity and its centile approximation (growth)


Now that we know the approximation matches the aggregate patterns pretty well, we can look at the distributions underlying these aggregate figures. And we find:

1. The productivity distribution is highly skewed (chart 4), so the top tail has a very strong influence on the aggregate.

The distribution has a long tail of workers in unproductive firms at the bottom, and workers in a collection of the ‘happy few’ extremely productive firms at the top. This is a well-known feature of the productivity distribution, regardless of whether we weight by labour or not. An implication of this shape is that the top tail has a very strong influence on the level of aggregate productivity in any given year, just as large outliers will push up on any average.

Chart 4: Most of the distribution is stable over time

2. The top tail has an even greater influence on changes in aggregate productivity from year to year.

Over 70% of the growth in aggregate productivity between 2003 and 2015 was driven by the top two deciles.  This is because the rest of the distribution doesn’t move around much; at least not in magnitudes that compare to movements in the upper tail (chart 4). Incidentally, this is the same thing as the OECD’s observation that the top tail is diverging from the rest.

3. The productivity puzzle (slower aggregate growth after the crisis than before) is located in the top tail of the distribution.

We can locate the growth puzzle by comparing changes in the pre- and post-crisis periods. Chart 5 is a reproduction of chart 1 with an extra line; it shows the average annual change of each centile over three distinct periods – the pre-crisis years (2004-07), the crisis (2008-09) and the post-crisis period (2010-15).

To read the chart, pick a centile and the three lines show how that part of the distribution changed, on average, over these different periods. For example, the median grew at about the same rate pre- and post-crisis, and had quite a drop during the crisis.

Chart 5: Average annual change in productivity by centile

The growth puzzle is the gap between the pre- and post-crisis lines. The chart shows that lower sections of the distribution have actually grown faster post-crisis than they did before it (pink line above the navy) and so cannot be driving the puzzle. By contrast, the top two deciles grew far slower (pink line below the navy) and therefore this is where the growth puzzle is located.

This work contains statistical data from ONS which is Crown Copyright. The use of the ONS statistical data in this work does not imply the endorsement of the ONS in relation to the interpretation or analysis of the statistical data. This work uses research datasets which may not exactly reproduce National Statistics aggregates.

Patrick Schneider works in the Bank’s Structural Economic Analysis Division.

If you want to get in touch, please email us at or leave a comment below.

Comments will only appear once approved by a moderator, and are only published where a full name is supplied.Bank Underground is a blog for Bank of England staff to share views that challenge – or support – prevailing policy orthodoxies. The views expressed here are those of the authors, and are not necessarily those of the Bank of England, or its policy committees.


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How does monetary policy affect the distribution of income and wealth?

Philip Bunn, Alice Pugh and Chris Yeates

Following the onset of the financial crisis, the Monetary Policy Committee (MPC) cut interest rates to historically low levels and launched a programme of quantitative easing (QE) to support the UK economy. How did this exceptional period of monetary policy affect different households in the UK? Did it increase or decrease inequality?  Although existing differences in income and wealth means that the impact in cash terms varied substantially between households, in a recent staff working paper we find that monetary policy had very little impact on relative measures of inequality. Compared to what would have otherwise happened, younger households are estimated to have benefited most from higher income in cash terms, while older households gained more from higher wealth.

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Can central bankers become Superforecasters?

Aakash Mankodi and Tim Pike

Tetlock and Gardner’s acclaimed work on Superforecasting provides a compelling case for seeing forecasting as a skill that can be improved, and one that is related to the behavioural traits of the forecaster. These so-called Superforecasters have in recent years been pitted against experts ranging from U.S intelligence analysts to participants in the World Economic Forum, and have performed on par or better by accurately predicting the outcomes of a broad range of questions. Sounds like music to a central banker’s ears? In this post, we examine the traits of these individuals, compare them with economic forecasting and draw some related lessons. We conclude that considering the principles and applications of Superforecasting can enhance the work of central bank forecasting.

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Population ageing and the macroeconomy

Noëmie Lisack, Rana Sajedi and Gregory Thwaites

An unprecedented ageing process is unfolding in industrialised economies. The share of the population over 65 has gone from 8% in 1950 to almost 20% in 2015, and is projected to keep rising. What are the macroeconomic implications of this change? What should we expect in the coming years? In a recent staff working paper, we link population ageing to several key economic trends over the last half century: the decline in real interest rates, the rise in house prices and household debt, and the pattern of foreign asset holdings among advanced economies. The effects of demographic change are not expected to reverse so long as longevity, and in particular the average time spent in retirement, remains high.

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Stirred, not shaken: how market interest rates have been reacting to economic data surprises

Jeremy Franklin, Scott Woldum, Oliver Wood and Alex Parsons

How do markets react to the release of economic data? We use a set of machine learning and statistical algorithms to try to find out.  In the period since the EU referendum, we find that UK data outturns have generally been more positive than market expectations immediately prior to their release. At the same time, the responsiveness of market interest rates to those data surprises fell below historic averages.  The sensitivity of market rates has also been below historic averages in the US and Euro area, suggesting international factors may also have played a role. But there are some signs that the sensitivity has increased over the past year in the UK.

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Voting with their wallets? Consumer expectations after the EU referendum

Tamara Li, Nicola Shadbolt, Thomas Stratton and Gregory Thwaites

Consumption growth remained fairly steady in the immediate aftermath of the UK vote to leave the European Union in June 2016. But how did consumer expectations evolve in the first months after the referendum? We show with the Bank’s in-house household survey that ‘Leavers’ became more positive about the economy and their own financial situation after the referendum, with the opposite true for ‘Remainers’, and that this was reflected in spending by the two groups. But the size of the effect was small.

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Who’s driving consumer credit growth?

Ben Guttman-Kenney, Liam Kirwin, Sagar Shah

Consumer credit growth has raised concern in some quarters. This type of borrowing – which covers mainstream products such as credit cards, motor finance, personal loans and less mainstream ones such as rent-to-own agreements – has been growing at a rapid 10% a year. What’s been driving this credit growth, and how worried should policymakers be?

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How does uncertainty affect how UK firms invest?

Marko Melolinna and Srdan Tatomir

Uncertainty is in the spotlight again. And the MPC believe it is an important factor influencing the slowdown in domestic demand (August 2017 Inflation Report). Previous work by Haddow et al. (2013) has found a composite aggregate indicator of uncertainty combining several different variables that does appear to have explanatory power for GDP growth; but as Kristin Forbes notes these measures correlate better with consumption than investment. So in this blog post, we look at firm-level data to explore measures of uncertainty that matter for how firms invest in the United Kingdom. Our aggregate measure of uncertainty has a better forecast performance for investment than the composite aggregate indicator does.

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