UK Labour Productivity and Output Composition

One of the oddities of the UK economic data which has attracted some comment recently is the rise in recorded employment despite weak growth in real output.  The implication is that labour productivity in the UK appears to be declining.

The graph below shows year on year change in overall labour productivity since 1997, together with a two year moving average.  Although this moves around a bit, there does appear to be a permanent fall in productivity growth from around 2008 onwards.

 

As always, this is probably a complex phenomenon with numerous explanations.  I thought I'd look at just one possible reason, being a change in composition of UK output.

Shortly after I'd done my analysis, I came across this publication by the IFS where they also considered this issue.  Interestingly, they came to the opposite conclusion to me, so I thought it would be useful to set out what I did and then look at the reason for the different result.

Anyway, what I did was a little analysis based on the breakdown of value added by industry.  First of all, I took the real output and employment measures for each industry and calculated the actual industry specific productivity for each year.  I then took the average rate of productivity growth in each industry and calculated a trend path for productivity in each, i.e. what productivity would have been in each industry in each year had it grown had a constant rate (using 2010 Q4 as the reference period in line with the output figures).  This fixed productivity growth rate is different for each industry.  Productivity grows quicker in some industries like manufacturing than in others like education.

I used these industry specific trend productivity series to calculate what employment would have been in each year using the actual output data and then combined this to get a counterfactual overall productivity.  The results are shown in the graph below, together with the two year moving average.

 

What this graph shows is what overall productivity would have been had each industry seen constant productivity growth across this period, but given the actual change in output pattern.  Although the timing is not quite the same, this graph also depicts a clear drop in overall productivity in recent years.  This is entirely attributable to the change in output composition.  It reflects the fact that UK output has shifted towards industries with lower normal productivity growth.

I was rather intrigued to find that the IFS had come up with the opposite conclusion. Their own assessment concluded that output composition had the opposite effect and should in fact have increased average productivity.  A closer look revealed why we were getting different results.

For my own analysis I used the actual ouput figures (chained volume measures 2010 reference year) together with counterfactual productivity to derive a counterfactual set of employment data for each industry.  However, rather than using actual output data, the IFS used actual employment data.  Although they don't explicitly calculate any counterfactual output data, this is implicitly what they are doing.

These two ways will certainly produce different results.  What is more, the IFS method will always be more likely to get the result they got than the method I used.  Each method tends to skew the results in opposite directions.

A little example helps illustrate this.  Assume an economy has two industries, goods and services, each employing 100 people and each producing 1,000 units of output in year 1.  So productivity is 10 units per head in each industry.  Now let's assume that in year 2, productivity in the goods industry increases to 20 units per head, but in services, it stays the same.  What happens to average productivity depends on what happens to output composition.

Firstly, we should note that if overall output levels stayed the same, employment would fall to 50 in the goods industry and stay the same in the services industry, giving an overall fall in employment.  Average productivity will have risen.  

Although it makes no difference to the average productivity measure, if we wanted to assume full employment we could increase output and employment equally in both industries.  The result would be higher output of both goods and services, but an overall shift of employment from goods to services.  More people would be employed in services and fewer in making goods.  Using my numbers that would mean output of 1,333 in each industry produced by 67 people making goods and 133 providing services.  Total output of 2,667 with 200 of workers implies overall productivity of 13.3 per head.

The alternative way of looking at it is to assume that each industry continues to employ the same number of people.  The economy is now producing 2,000 of goods but still only 1,000 of services.  200 workers producing output of 3,000 implies average productivity of 15.0 per head.

This is why I got a different result to the IFS.  I used the first method and they used the second.  The second will always give a higher positive estimate of the compositional impact on productivity because it automatically puts a higher weight on industries with higher productivity growth.  For comparison purposes, I carried out my type of analysis, but used actual employment and counterfactual output.  The results are shown in the graph below and they do indeed suggest the reverse effect. 

 

It is not an easy question which method is better.  One way will always overestimate the effect and the other will always underestimate it.  However, having looked at both, I think I still tend to prefer mine.  The IFS method assumes that output composition is driven by employment composition, rather than the other way around.  This does not seem realistic to me.  The pattern I would expect to see would me more like that I described in the first scenario of my simple example.  If an industry has high productivity growth, this is more likely to lead to a reduction in its share of overall employment, than it is to an increase in its share of output.  The composition of output growth is driven primarily by income elasticities.  Although the pattern is complicated, I think the UK data supports this view.

Nevertheless, I acknowledge that there is no perfectly right way to do this.  Each method has its bias.  However, my own conclusion from this exercise would be that the compositional effect has been a factor in what has happened to UK productivity and that it is material, although it can at best only a explain a part of what we observe.

Data from tables B1 and B2 of the Quarterly National Accounts and EMP13