# Chapter 6 Productivity

What is productivity and why it is important?

What are the main productivity measures, and how do they relate to each other?

How productive is the UK, and how does it compare with other countries?

Which sectors and firms have the highest (and lowest) productivity?

What is the productivity puzzle, and what explains it?

Can we improve the way we measure productivity?

## 6.1 Introduction

Paul Krugman, an economist who won the Nobel prize, is regularly quoted as saying “Productivity isn’t everything, but in the long run, it’s almost everything.” What he meant by that is that productivity growth (or its absence) has a major influence on the quantity and quality of goods and services available to us and so, ultimately, our standard of living. If we are interested in raising people’s standard of living, we need to be equally interested in raising productivity. It is as simple as that.

We all have an intuitive sense of productivity. At aggregate level, as discussed in Chapter 2, we often measure this as gross domestic product (GDP). But what does it mean to scale that up to the whole economy? How would you measure it?

A key feature of any economy is the amount of output it is producing. At aggregate level, we often measure this as Gross Domestic Product (GDP). Essentially, it is the aggregate amount of goods and services that have been produced and that are available for consumption, or for investment which may lead to higher output in future.

factors of production
These are the inputs into the production process in order to produce output. These include the amount of labour and capital available. This covers tangible capital, such as machines and buildings, but also intangible capital such as the stock of human education.

At any time, the economy will have available to it a given set of factor endowments that can be used to generate this production. These are known as factors of production.

At individual firm level the amount and combination of factors employed can usually be varied; a firm producing drainpipes can produce more of them if it wishes by employing more people, or it can buy new machines so that its existing staff can produce more pipes.

At whole economy level, however, the factor endowments are more often fixed. Other things being equal, if one firm is employing more staff, it is likely to be attracting them from a different firm.

productivity
Productivity is the relationship between inputs and outputs in the economy – it captures how efficiently production inputs are being used to produce a given level of output, capturing how much output is generated per unit of input. The most recognised measure is labour productivity, which captures the amount of output per worker or per hour worked. Productivity plays a key part in determining a country’s long-term economic growth.

Aggregate factor endowments are not absolutely fixed. Working populations do change over time, as we saw in the previous chapter, and capital can be increased by means of investment. But, over time, the greatest scope for increasing output is likely to come from using given factors of production – production inputs – more efficiently. Essentially, it is the degree of such efficiency that represents productivity.

### The Solow-Swan growth model

The key model for how productivity growth happens was developed by Robert Solow in 1956. Trevor Swan also independently developed the growth model. The model focuses on exogenous growth by analysing changes in the workforce, the savings rate and the rate of technological progress.

The model demonstrates that output growth is linked to the growth in inputs (labour and capital) as well as new ideas and new technology. While labour is dependent on the population, the level of capital is driven by savings (as savings are equal to investment), so an economy can grow faster by saving more, leading to more capital per worker.

Importantly, the Solow-Swan model also demonstrates that technological advances and improvements in the productivity rate of labour and/or capital will produce higher rates of growth.

As we shall see, however, productivity growth has not been a positive story in recent years, and this is a matter for concern. Before we turn to these issues, we need to consider a little more carefully what productivity is and how it can be measured.

## 6.2 What is productivity?

At its simplest, productivity is the results you receive for the effort you put in: outputs from a certain level of inputs. Put another way, productivity is the rate of conversion of inputs to outputs.

From an economic viewpoint, an output is a good or service that an organisation produces, and an input is a resource that is used in the production of that good or service. For a firm, labour (workers) and capital (machines and so on) are the most important inputs.

### 6.2.1 The Cobb-Douglas production function

These elements were formalised by Charles Cobb and Paul Douglas. In a seminal article in the 1920s, they proposed a stylised algebraic representation of the production process:

$Y = f(K,L)$

On the face of it, this formula is pretty simple. It states that output (or production, represented by Y) is a function of the amount of capital (K) and labour (L) used in the production process. It is also quite general. But Cobb and Douglas went on to make their formula more specific.

$Y = AK^{\propto}L^{1 - \propto}$

This was intended to deal with two issues:

1. The relative importance of labour and capital in producing output. This is captured in the parameter $$\propto$$. If $$\propto$$ was zero, then only labour would be relevant to producing output, and capital would drop out of the formula. At the other end of the scale, if $$\propto$$ was one, then only capital would be relevant. Intermediate values of $$\propto$$ represent situations between these two extremes. The idea was that empirical evidence could be used to estimate the actual value of $$\propto$$ in a given economy. At a more granular level, some industries, such as oil and gas extraction, are heavily reliant on a high ratio of capital to labour, whereas others, such as many service industries, are more reliant on labour inputs. The former would have a relatively high value of $$\propto$$ and the latter a lower one.
2. The level of productivity. This is A in the equation. If we assume A is constant, then a firm can increase its level of output only by increasing its levels of capital and labour. As we noted above, however, at aggregate level at least, there will be limits to the extent that this is possible. So attention focuses on A. To what extent can output be increased by a higher level of A – in other words, supported by higher productivity?

### 6.2.2 What Cobb-Douglas tells us about productivity

The formula makes it obvious that, while there are a number of ways productivity might be improved, two of the most obvious ones will be:

You can read Cobb and Douglas’s original paper:

Cobb C W, Douglas P H (1928), ‘A theory of production’, American Economic Review, Volume 18, Number 1, Supplement, pages 139 to 165

Nearly a hundred years on, the Cobb-Douglas formulation has been found to be consistently a good way to capture and approximate reality. It is simple and easy to apply.

It has some inflexibilities though and, when studying productivity, you may see other production function formulations too. Examples include the Constant Elasticity of Substitution model (CES) and the Translog model.

• Changes in the way firms mix or organise production factors. Henry Ford’s car-assembly production line is a good example. Prior to Ford’s innovation, those working in car factories would do various jobs, fetching the tools they needed at the appropriate time. With the production line, the car moved instead of the people, and workers could focus on just one element of production. Or, an earlier example is given by Adam Smith’s description of a pin factory, where changing the organisation of production increased specialisation and productivity. The level of capital and labour might have been the same in each case, but the production line and the better pin factory organisation led to far more cars or pins being produced.
• Advances in technology (and the extent to which these can be implemented). A farmer with a tractor and modern plough is not surprisingly likely to be more productive than his (or her) medieval counterpart with only an ox and a badly designed implement. The productivity of Henry Ford’s production line has no doubt been greatly enhanced over time by the introduction of progressively better machine tools, industrial robots, and so on.

## 6.3 Measuring productivity

Let’s consider a stylised example of a hypothetical bakery called Daily Bread. We will look at the various measures of productivity that can relate to its operations and how, by working through the other components of the Cobb-Douglas formula, we can arrive at estimates of A – productivity itself.

To illustrate the calculations, we will look at two ways in which Daily Bread could operate: one involving a single shift working and one with a double shift. We can then calculate what change in productivity is generated by a change between these two modes.

Gross Value Added (GVA) is the value generated by any unit engaged in the production of goods and services. It measures the contribution to the economy of each individual producer, industry or sector. Simplistically it is the value of the amount of goods and services that have been produced, less the cost of all inputs and raw materials that are directly attributable to that production.

The key point here is that productivity is essentially a ratio of outputs (Y in our Cobb-Douglas formulation above) to inputs ($$K^{\propto}L^{1 - \propto}$$). The output side we can deal with quite quickly. What we are concerned with is the gross value added from the economy’s production processes, as discussed in Chapter 2 (see Sections 2.2.1 and 2.2.2).

Furthermore, since we are interested in real living standards, we are mainly interested in the volume measure of GVA (see Chapter 2), abstracting from movement in price levels. Measuring output is far from straightforward. But in our context of measuring productivity, there are no new issues beyond those discussed in Chapter 2.

The new questions are how to measure the inputs, which are the factors of production such as labour and capital.

### 6.3.1 Measuring labour productivity

labour productivity
The total output produced relative to the amount of labour used to produce it, capturing the efficiency of the workforce. It reflects output per unit of labour input. There are several possible measures of labour, including the number of employees, the number of jobs or the number of hours worked.

Labour productivity is a commonly used measure for productivity as a whole. It can be thought of as productivity of labour without regard to what is happening to capital. In the short term at least, capital is likely to be pretty fixed, so this may not be an unreasonable assumption if we want to estimate Daily Bread’s productivity.

The bakery produces output: loaves of bread. For simplicity we assume that all Daily Bread’s loaves are the same size and quality. We can measure its output by counting the number of loaves it bakes in 24 hours.

Daily Bread uses inputs in the form of labour, capital (its baking oven and premises it operates in), and materials including flour, yeast and salt. We will assume the capital component is fixed, so Daily Bread can vary its output of loaves only by varying the amount of labour and materials used. The capacity of the oven is limited to 100 loaves per hour, and we might assume that a skilled baker can operate at the same rate, mixing and preparing the dough for the next 100 loaves while the previous batch is in the oven.

Suppose our baker works eight hours a day, and that the first hour each day is spent preparing the first batch of loaves for baking and the last hour for cleaning up, ordering materials and so on. This implies six hour-long baking cycles per day, and if we assume that Daily Bread’s skilled baker works at full capacity, output is 600 loaves per day.

Suppose also that Daily Bread employs a sales assistant to sell the output. The sales assistant works for seven hours a day, as there is no bread to sell in the first hour. (Note, that while the baker might physically produce loaves of bread, the sales assistant provides the vital service of marketing them to customers, and productivity in this example depends on selling bread as well as making it.)

In this scenario, output is 600 loaves per day, hours worked, by the baker and sales assistant together, would be 15, so (daily) labour productivity would be 600 divided by 15, or 40 loaves per hour. We set this out in Figure 6.1.

Labour input (hours) Output (loaves) Labour productivity (loaves per hour)
Bakers 8
Sales Assistants 7
Total 15 600 40.0

Figure 6.1 Single shift working at the Daily Bread bakery

Single shift working at the Daily Bread bakery

If productivity depends only on labour inputs, how might it change?

Imagine that the baker and the sales assistant each want to work fewer hours. The baker works seven hours, so the sales assistant works six hours each day.

Two hours per day are needed for preparation and cleaning up, so there are now five one hour baking cycles. Output would be 500 loaves, hours worked would be 13, and labour productivity falls to 500 divided by 13. Daily Bread’s productivity would be 38.5 loaves per hour instead of 40.

Now imagine the head baker goes on holiday, and a less skilled baker takes over. This baker can prepare only 90 loaves per hour, rather than 100. In the eight-hour shift, that implies 540 loaves a day, but both staff members work the same hours. So labour productivity would be 540 divided by 15. It falls to 36 loaves per hour while the head baker is on holiday.

If the CEO of Daily Bread wanted to improve productivity, one obvious way would be to ask the staff to work longer hours. But our baker doesn’t want to work more hours. And so the decision is made to institute a double shift.

In the new environment, the head baker works 7 hours per day. Daily Bread recruits another equally efficient baker who takes over at the end of his or her shift. If the second baker also works 7 hours per day, at full capacity of 100 loaves per hour, then daily output will increase to 1,200 loaves (12 baking cycles, as two hours per day would still be required for preparation and clean up).

Of course that means a second sales assistant, so that sales can take place over 13 hours rather than 7 hours. So total hours worked would be 27, and labour productivity would be 1,200 divided by 27. Productivity jumps to 44.4 loaves per hour (Figure 6.2).

Labour input (hours) Output (loaves) Labour productivity (loaves per hour)
Bakers 14
Sales Assistants 13
Total 27 1,200 44.4

Figure 6.2 Double shift working at the Daily Bread bakery

Double shift working at the Daily Bread bakery

This increase in labour productivity reflects increased efficiency in the use of labour and capital, for example, by reducing the proportion of down-time relative to baking cycles.

The change from single to double shift working has raised productivity from 40.0 to 44.4 loaves per hour worked. But how should we express this as a change? We use natural logarithmic changes, which are the same whether you are measuring an increase or a decrease, unlike arithmetic percentage changes.

### How it’s done Logarithmic changes vs percentage changes

The usual way to measure changes is to calculate the percentage change. As it happens, 44.4 is exactly 11% higher than 40, so we might say the improvement in productivity has been 11%. But we could just as well turn the calculation round and consider the reduction in productivity that single shift working represents as compared with that of the double shift. The percentage reduction would be given by (100(1 – 40/44)) or 9.1%.

Are we to say that the change in productivity between the two modes of working is 11% or 9.1%, or something else?

As we can see, arithmetic percentages can lead to ambiguity and confusion. So let us consult the guidance published by Measuring Productivity. OECD Manual: Measurement of Aggregate and Industry-level Productivity Growth.

This is detailed, comprehensive and informative, if not necessarily the best holiday reading, and it suggests that productivity change should normally be expressed in logarithmic percentages rather than arithmetic ones.

If we consider the increase in double shift working over single shift, the logarithmic percentage change is given by

ln(44) – ln(40) = 9.5 log percent

or, the other way round, the reduction in productivity obtained by the single shift compared with the double shift is

ln(40) – ln(44) = –9.5 log percent

Either way round, the change in productivity is 9.5 log percent, with no ambiguity.

Measures of labour productivity often only go this far, calculating the productivity of the economy (or the bakery) by dividing the volume of output (number of loaves of bread) by the total amount of labour used (hours worked). This is the measure most often reported, partly because it is fairly simple.

multi-factor productivity (MFP)
Multi-factor productivity reflects the overall efficiency with which labour and capital inputs are used together in the production process. It is recorded in a growth accounting framework, in which the growth in MFP is measured as a residual – that is, the part of GDP growth that cannot be explained by changes in labour and capital inputs. It is also called total factor productivity or TFP.

But we can do better and get closer to a true measure of productivity, often known as multi-factor productivity (MFP). We come back to this in Section 6.3.5. The intervening sections prepare the other groundwork needed for this.

### 6.3.2 Measuring labour quality

At Daily Bread, the replacement baker could not produce as many loaves in an hour as the permanent baker, because he was less skilled and probably therefore attracted a lower wage rate. The difference in the quality of labour could be measured. But often differences in the labour input from different types of workers are not taken into account when we calculate labour productivity, even though it may be important.

This section introduces quality-adjusted labour input, which breaks down labour input into hours worked and labour quality.

An input into estimating multi-factor productivity (MFP). QALI accounts for changes in the composition (or “quality”) of the employed workforce as well as changes in hours worked. It weights hours worked by different types of workers by their relative income share, reflecting their contribution to economic production.

The measure known as quality-adjusted labour input (QALI) attempts to take into account differences in types of labour. Economic theory suggests that wages reflect the value that labour adds to production. For example, a skilled sheep shearer is likely to be able to shear more sheep in a given time than a general farm labourer tackling a sheep for the first time (and many more sheep than most of us could shear). And so, on a farm, employing an experienced sheep shearer is likely to produce more output (and thus more value added) in a given time than if you employed an economist to do the job. But, for farm work, the shearer’s hourly wages would be correspondingly higher as well.

A QALI measure accounts for these variations in labour composition or “quality” by weighting the hours worked of different worker types by their relative pay shares, that is, their shares of the total wage bill.

Back at Daily Bread, the head baker and the sales assistant are working together in a single shift, and two skilled bakers and two sales assistants sometimes work in a double shift. Let’s assume that the training and experience required of a baker is reflected in a going rate for bakers of £12 per hour, while the going rate for sales assistants is lower, at £8 per hour.

Figure 6.3 will incorporate this information.

Törnqvist index
A Törnqvist index is a form of index where the weight is constructed using an average of the relevant variable in the current and base period. As such, it is a symmetric index as it gives equal weight to both periods.

But we need to be more specific as to how we are going to incorporate these apparent quality differences. The international guidance recommends that doing so should be based on a Törnqvist index (see the Appendix 2C, “Index Numbers” for a reminder of what this means).

Using this formula, the change in the quality-adjusted labour input between two periods is given as Qtt−1 where

Qtt−1 = Pi (Hours workedit / Hours workedit−1) (Weightit + Weightit−1 /2)

and

Hours workedit is the hours worked by the ith group in period t. (In our case, we have only two groups: bakers when i = 1 and sales assistants when i = 2)

Weightit is the share of the total pay bill in period t earned by the ith group.

Let’s now take the Daily Bread example where it was using the single shift work pattern in period 1 but moved to a double shift in period 2. What happens to the quality of the labour input between the two periods? Applying the formula to the data (see Figure 6.3a):

• It takes the change in hours worked by a particular group from one time period to another.
• It multiplies this by that group’s average share of the wage bill over the two periods.
• This provides the growth in quality adjusted labour input from one period to another.

Intuitively, this gives us what we want. The QALI rises if the hours worked by the higher wage workers (in our case, the bakers) increases faster than the total hours worked.

Once more, we can also simplify the calculation by working in natural logarithmic terms. If we work in terms of log Qtt−1, we can change the formula to become more straightforward. The log change in QALI then becomes the change in hours worked expressed as logarithms, weighted as before by the average income shares.

Applying the formula to the data (see Figure 6.3):

• The average pay shares are calculated as simple arithmetic averages between the two working regimes. For bakers this is (63.2 + 61.8)/2 or 62.5%. For sales assistants, the same calculation comes to 37.5%.
• For the change in hours, it is convenient to work in log percentage change terms for the reasons discussed above. So for bakers, the change is ln(14) – ln(8) or 56 (log) percent. For sales assistants, the equivalent calculation is ln(13) – ln(7) or 61.9 (log) percent. In accordance with the formula, we then multiply the average pay share and the log change in hours for both bakers and sales assistants. The change in the QALI for our bakery is then given as the sum of these two products. In our example, as we see from Figure 6.3b, the change in QALI between the double and single shift cases is some 58.2 (log) percent.
Scenario Worker types Labour input
(hours)
Pay
(£/hour)
Pay bill
(£/day)
Pay shares (%)
Single shift working Bakers 8 12 96 63.2
Sales Assistants 7 8 56 36.8
Total 15 152 100.0
Double shift working Bakers 14 12 168 61.8
Sales Assistants 13 8 104 38.2
Total 27 272 100.0

Average pay shares (%) Change in hours (log%) Change in QALI (log%)
Bakers 62.5 56.0 35.0
Sales Assistants 37.5 61.9 23.2
Total 100 58.8 58.2

Figure 6.3b Change from single to double shift working at Daily Bread

Change from single to double shift working at Daily Bread

What does this tell us? If we made no distinction between hours supplied by the bakers and the sales assistants, we see total hours worked under the double shift system comes to 27 as against 15 with the single shift. So the increase in hours worked is log(27) less log(15) or 58.8 (log) percent. This is more than the increase we calculated in the QALI.

Another way of putting this is that the labour composition or “quality” has declined by 0.6 (= 58.8 − 58.2) (log)% in the double shift regime.

The key to what is going on is to look at the composition of the workers in the two cases. In the single shift illustration, there were 8 high-skilled (high-cost) worker hours and 7 low-skilled (low-cost) ones. In the double shift illustration, there are 14 high-skilled and 13 low-skilled worker hours. The ratio of high- to low-skilled worker hours is reduced.

The double shift system has allowed relative economising on the high-cost labour input. That saving is a further factor contributing to the higher productivity that the double shift system allows, and that is what our analysis is picking up.

### 6.3.3 Measuring the contribution of capital inputs

capital input
Capital input includes anything that provides a means of producing output without being completely used up in the production process.

So far, we have focused entirely on labour inputs. The next stage is to take account of capital inputs to the production process.

At Daily Bread, it is easy to see the capital inputs. They include the oven and the building that the baker and the sales assistant work in.

Are the ingredients like flour capital inputs? No, because once flour is used to make a loaf of bread, the same flour cannot be used again to produce another loaf of bread. These are intermediate goods, as discussed in Chapter 2 on GDP.

capital services
These are flows of productive services from capital assets, rather than the capital stock of those assets. They are directly comparable to flows of labour services measured by QALI.

For productivity purposes, we measure capital inputs by estimating the services they provide. In principle, measurement of capital services requires lots of information on the accumulation of capital assets over time, as well as a number of assumptions on the lives of different types of assets, how the productive efficiency of assets changes over their lifetimes, and the nature of the returns on capital.

However, we can cut through this complexity by noting that the value of the capital services a firm uses is the same as the costs that firms would pay if they were to rent all their capital assets in competitive markets.

Taking this further, we can consider the two costs that an owner of capital would incur, that he or she needs to recover from the rental charged:

• Opportunity cost. An investment in one particular piece of capital by definition precludes that money from being invested in some other item of capital which would offer a rate of return. In our example, tying up your money in the Daily Bread’s ovens means the loss of an investment return elsewhere.
• Depreciation. Various kinds of capital assets have different rates of depreciation. Computers or vehicles wear out quite quickly over time, just from repeated use. Other assets such as buildings will be less susceptible to such wear and tear. But they may still be subject to obsolescence if they become less suitable over time. The baker’s building is not likely to wear out, but it may become obsolete because it is not capable of housing the volume of production the baker requires. Or it may not be suitable for accommodating new ways of baking loaves, with the new technologies involved for doing so.

In a competitive rental market for capital, these costs will be reflected in the market rental rate that emerges. Let’s agree the market rent paid by our Daily Bread on its capital is a fair reflection of the capital services provided by these assets. For illustration, we assume that the costs to Daily Bread are:

• Premises: £75 per day
• Oven and associated equipment: £13 per day plus £10 for each hour that it is used.

The different rental payments for the two types of capital reflect the fact that you don’t pay a higher rent to your landlord if you use the building more because it doesn’t wear out, whereas equipment such as ovens will suffer wear and tear and have to be replaced sooner if they are used more intensively.

Figure 6.4a summarises these assumptions.

Asset types Charge unit Cost
(£/charge unit)
Cost (£/day) Cost shares (%)
Single shift working Premises Day 75 75 50.7
Oven etc. Day plus hours used 13 per day plus 10 per hour 73 49.3
Total 148 100.0
Double shift working Premises Day 75 75 36.1
Oven etc. Day plus hours used 13 per day plus 10 per hour 133 63.9
Total 208 100.0

Figure 6.4a Introducing capital services

Introducing capital services

Asset types Charge unit Cost
(£/charge unit)
Cost (£/day) Cost shares (%)
Single shift working Premises Day 75 75 50.7
Oven etc. Day plus hours used 13 per day plus 10 per hour 73 49.3
Total 148 100.0
Double shift working Premises Day 75 75 36.1
Oven etc. Day plus hours used 13 per day plus 10 per hour 133 63.9
Total 208 100.0

Figure 6.4aa A single shift

A single shift

The premises’ cost is £75 per day. The cost of the ovens, etc., is £13 plus £10 for each of the six hour-long bakes carried out under that shift arrangement, or £73.

Asset types Charge unit Cost
(£/charge unit)
Cost (£/day) Cost shares (%)
Single shift working Premises Day 75 75 50.7
Oven etc. Day plus hours used 13 per day plus 10 per hour 73 49.3
Total 148 100.0
Double shift working Premises Day 75 75 36.1
Oven etc. Day plus hours used 13 per day plus 10 per hour 133 63.9
Total 208 100.0

Figure 6.4ab A single shift

A single shift

So the total capital services used under this system is £148 per day.

Asset types Charge unit Cost
(£/charge unit)
Cost (£/day) Cost shares (%)
Single shift working Premises Day 75 75 50.7
Oven etc. Day plus hours used 13 per day plus 10 per hour 73 49.3
Total 148 100.0
Double shift working Premises Day 75 75 36.1
Oven etc. Day plus hours used 13 per day plus 10 per hour 133 63.9
Total 208 100.0

Figure 6.4ac A double shift

A double shift

The cost of the premises is the same at £75 a day. But there are now 12 bake cycles each day and so the cost of the ovens, etc., rises to £133.

Asset types Charge unit Cost
(£/charge unit)
Cost (£/day) Cost shares (%)
Single shift working Premises Day 75 75 50.7
Oven etc. Day plus hours used 13 per day plus 10 per hour 73 49.3
Total 148 100.0
Double shift working Premises Day 75 75 36.1
Oven etc. Day plus hours used 13 per day plus 10 per hour 133 63.9
Total 208 100.0

A double shift

The total capital services used with the double shift system come to £208.

We can now use this information to calculate the change in capital services between the two patterns of shift working. To be consistent with the information we calculated for quality adjusted labour input, we want this change to be in natural log percentage terms and we can apply the same formula for this purpose (Figure 6.4b):

Asset types Average cost shares (%) Change in costs (log %) Change in capital services (log %)
Premises 43.4 0.0 0.0
Oven etc. 56.6 60.0 34.0
Total 100.0 34.0 34.0

Figure 6.4b Change from single to double shift working

Change from single to double shift working

Asset types Average cost shares (%) Change in costs (log %) Change in capital services (log %)
Premises 43.4 0.0 0.0
Oven etc. 56.6 60.0 34.0
Total 100.0 34.0 34.0

Figure 6.4ba Premises

Premises

We can calculate the average cost share between the two cases as (50.7 + 36.1)/2 or 43.4%. But as it happens, in this particular case, this is academic because the change in costs for premises is zero. So the product is also zero.

Asset types Average cost shares (%) Change in costs (log %) Change in capital services (log %)
Premises 43.4 0.0 0.0
Oven etc. 56.6 60.0 34.0
Total 100.0 34.0 34.0

Figure 6.4bb Ovens

Ovens

The average cost share is 56.6%. This time, it does matter. The log change in costs is given by ln(133) – ln(73) which gives a change of 60 (log) percent. The change in capital services is given as the product of the average cost share and this change in cost. So the change in capital services in respect of ovens, etc., is 34.0 (log) percent.

Asset types Average cost shares (%) Change in costs (log %) Change in capital services (log %)
Premises 43.4 0.0 0.0
Oven etc. 56.6 60.0 34.0
Total 100.0 34.0 34.0

Figure 6.4bc Total

Total

The total change in capital services is the sum of those for premises and ovens, etc. This is also 34.0%, because there is no change stemming from use of premises.

At first sight, this increase in capital services in moving to a double shift system may seem counter-intuitive: after all, the amount of physical capital employed has not changed. But in moving to double shift working, the bakery is using its physical capital more intensively and therefore the flow of capital services has increased. The greater number of baking cycles will have increased the wear and tear on the ovens, and this is reflected in the higher capital cost that has to be borne.

We should note that the example in Figure 6.4 relies on rental charges fairly reflecting the value of each type of capital. In the real world, rental markets for capital assets are often non-existent and most capital assets are owned directly by the firms that use them, albeit often financed by borrowing.

Moreover, even where rental markets exist, rental prices may be unrepresentative, as they might include bundled labour services (such as an operator that is supplied with a crane) and profit margins for the rental organisation. Long-term rentals will typically include an allowance for general inflation, which we are not including in our simplified scenarios.

### 6.3.4 Calculating labour and capital shares

labour share
The labour share of income estimates the income received by labour in the generation of value added, which includes compensation of employees.
capital share
The capital share of income estimates the income received by capital in the generation of value added, which includes gross operating surplus.

So far, we have separately measured the changes in quality-adjusted labour input and capital services between the two scenarios. Recalling the Cobb-Douglas formula in Section 6.2.1, to calculate productivity, we need a combined measure of inputs, and we get that by weighting together labour and capital inputs. For this, we need the labour share and the capital share, which are usually taken to be the shares of the costs of production.

Before accounting for the labour and capital shares, we need to properly account for our bakery’s output. Earlier, we thought about output as the number of loaves of bread. In this section, and the next, we will need to go back to monetary values, so we will need to think about the price of a loaf.

Let’s assume that each loaf is sold for £1. So total revenue (gross output) from the 600 loaves in the single shift pattern is £600 a day, and from the 1,200 loaves in the double shift system, daily revenue is £1,200.

However, the bakery will also incur the cost of the ingredients to make the loaves – the intermediate inputs. Let’s assume these are 50p for every loaf. So half of the revenue is eaten up by intermediate costs, and gross value added (the value of the output added deducting intermediate costs) is half the revenue – £300 a day in the single shift system, and £600 with double shifts.

Gross value added generated by the business goes to three main places:

• The costs of labour. Workers get their wages and salaries.
• Taxes to the government. Think of this as the taxes on production.
• Operating surplus. The part that is left over is effectively money the business has earned from using its capital equipment, but also money that can be spent buying new capital assets when the current ones eventually wear out. This “left over” money is often referred to as profit, but in economic statistics it is referred to as “operating surplus” – the surplus money from business operations. Note that for the purposes of this section, this is capital income.

We are now in a position to calculate the labour and capital shares of the production costs. In the Cobb-Douglas production function, the capital share is α and the labour share is 1 minus α. Since they must add up to 1, we can just as well find the labour share and calculate the capital share as I minus that. This is easier so that is what we will do.

Based on the selling price of our loaves, and the costs of intermediates, and the costs of the wages of the bakers and shop assistants from Figure 6.3, we have all we need. This calculation is summarised in Figure 6.5.

Scenario GVA (£/day) Labour costs (£/day) Labour costs (% of GVA) Average labour cost share (%) Average capital cost share (%)
Single shift working 300 152 50.7
Double shift working 600 272 45.3
Average       48.0 52.0

Figure 6.5 Labour and capital shares

Labour and capital shares

Scenario GVA (£/day) Labour costs (£/day) Labour costs (% of GVA) Average labour cost share (%) Average capital cost share (%)
Single shift working 300 152 50.7
Double shift working 600 272 45.3
Average       48.0 52.0

This is £300 a day in the single shift system, and £600 a day in the double shift system.

Scenario GVA (£/day) Labour costs (£/day) Labour costs (% of GVA) Average labour cost share (%) Average capital cost share (%)
Single shift working 300 152 50.7
Double shift working 600 272 45.3
Average       48.0 52.0

Figure 6.5b Labour costs

Labour costs

From Figure 6.3, we know the wage bill costs per day are £152 per day and £272 per day under the one and two shift modes of working respectively.

Scenario GVA (£/day) Labour costs (£/day) Labour costs (% of GVA) Average labour cost share (%) Average capital cost share (%)
Single shift working 300 152 50.7
Double shift working 600 272 45.3
Average       48.0 52.0

Figure 6.5c The labour share of output

The labour share of output

This is 50.7% in the single shift system, and 45.3% with double shifts.

Scenario GVA (£/day) Labour costs (£/day) Labour costs (% of GVA) Average labour cost share (%) Average capital cost share (%)
Single shift working 300 152 50.7
Double shift working 600 272 45.3
Average       48.0 52.0

Figure 6.5d The average labour share

The average labour share

This is therefore 48.0% and the capital share by implication is 52.0%. These calculations are important for the Törnqvist index formula noted above.

At Daily Bread the labour cost share is 48%, averaged over the two scenarios. The typical real-life labour share in the UK economy is around two-thirds.1

### 6.3.5 Bringing it all together

The measurements for labour and capital input noted above form part of a growth accounting framework that comes directly from the Cobb-Douglas production function. Each part of the function needs to be accounted for to determine its contribution to growth.

Revisiting the formula, we can see that so far, we’ve discussed output (Y), the labour (L) and capital (K) inputs and the weights ($$\propto$$ and (1−$$\propto$$)) we apply to each of them.

$Y = AK^{\propto}L^{1 - \propto}$

The remaining element is the A, which, as we have mentioned, is productivity, and which we want to quantify.

So we can see:

• We have an increase in output given in log percentage terms by $$\ln\left(300\right) −\ln\left(150\right)$$ or 69.3 log percent
• The change in the QALI input weighted by its cost share is 27.9 log percent
• The corresponding change in capital inputs weighted by their cost share is 17.7 log percent.

So we can now straightforwardly control the improvement in output that is not due either to increased capital or labour inputs as (69.3 − 27.9 − 17.7) = 23.7 log percent. This is therefore exactly the change in multi-factor productivity that we wanted to calculate – it is the change in A in the Cobb-Douglas formula.

The fact that it is positive suggests that the single shift mode of working was inefficient. The bakery became more productive by using its fixed capital – its premises and the fixed element of its baking equipment – more intensively under the double-shift work pattern.

Back at Daily Bread, we now have all we need to calculate the change in A when it moves from single to double shift working, shown in Figure 6.6.

Change in output (GVA) (log%) Weighted change in QALI (log%) Weighted change in capital services (log%) Change in MFP (%)
69.3 27.9 17.7 23.7
Change in QALI (log%) Labour cost share (%) Change in capital services (log%) Capital cost share (%)
58.2 48.0 34.0 52.0

Figure 6.6 Decomposition of change in output for Daily Bread

Decomposition of change in output for Daily Bread

Change in output (GVA) (log%) Weighted change in QALI (log%) Weighted change in capital services (log%) Change in MFP (%)
69.3 27.9 17.7 23.7
Change in QALI (log%) Labour cost share (%) Change in capital services (log%) Capital cost share (%)
58.2 48.0 34.0 52.0

Figure 6.6a The increase in output (measured by gross value Added)

The increase in output (measured by gross value Added)

In log percent terms, this is given by ln(600) less ln(300) or 69.3 log percent.

Change in output (GVA) (log%) Weighted change in QALI (log%) Weighted change in capital services (log%) Change in MFP (%)
69.3 27.9 17.7 23.7
Change in QALI (log%) Labour cost share (%) Change in capital services (log%) Capital cost share (%)
58.2 48.0 34.0 52.0

Figure 6.6b The (log) change in quality-adjusted labour input (QALI)

The (log) change in quality-adjusted labour input (QALI)

The figure in Figure 6.3 (58.2%) multiplied by the labour share in Figure 6.5 (48.0%) gives a weighted contribution of 27.9% to the change in output.

Change in output (GVA) (log%) Weighted change in QALI (log%) Weighted change in capital services (log%) Change in MFP (%)
69.3 27.9 17.7 23.7
Change in QALI (log%) Labour cost share (%) Change in capital services (log%) Capital cost share (%)
58.2 48.0 34.0 52.0

Figure 6.6c The (log) change in capital services

The (log) change in capital services

The figure in Figure 6.4 (34.0%) multiplied by the capital share in Figure 6.5 (52.0%) gives a weighted contribution of 17.7%.

Change in output (GVA) (log%) Weighted change in QALI (log%) Weighted change in capital services (log%) Change in MFP (%)
69.3 27.9 17.7 23.7
Change in QALI (log%) Labour cost share (%) Change in capital services (log%) Capital cost share (%)
58.2 48.0 34.0 52.0

Figure 6.6d The change in productivity between our two scenarios

The change in productivity between our two scenarios

This is the residual change in output that cannot be explained by the change in inputs. Subtracting the contributions due to changes in labour and capital inputs from the change in output leaves a residual of 23.7 log percent that cannot be attributed to changes in inputs and therefore represents a change in MFP.

The figure of 23.7% is the productivity improvement that moving from single to double shift at Daily Bread provides.

## 6.4 UK productivity: A set of paradoxes

In the introduction, we argued that what is happening to productivity is of primary importance not least as the overriding medium-term influence on people’s standard of living. Having looked at the various productivity measures and how they relate to each other, and how in practice they can be measured, it is now time to consider what the experience has been in the UK.

In the context of the UK, the discussion can be ordered around some paradoxes.

1. Low UK productivity. Why has the UK had apparently poor productivity as compared with similar countries?

For a long time, the UK “productivity puzzle” referred to this question. But now we have two more:

1. A productivity slowdown. Since the 2008/09 financial crisis, UK productivity growth has been a fraction of that in previous decades.
2. Persistent differences in productivity between firms. This occurs even within the same sector and appears to be large. So apparently low-productivity firms are not learning by observing high-productivity firms.

We will look at each of these paradoxes in turn.

### 6.4.1 Paradox 1: International comparisons

#### ONS Resource

The ONS publishes periodic comparisons of productivity achieved in the major economies, based as far as possible on OECD methodologies and data. For example, see International comparisons of UK productivity (ICP), final estimates.

Figure 6.8 makes use of the International Comparisons of Productivity measures produced by the ONS. This chart shows UK productivity in 2019 as 100 and the value for the other G7 countries relative to it. Productivity in Italy and Canada is around 3% and 8% lower than in the UK respectively, while Japan was over 23% lower. But in the other three G7 countries, productivity was higher than in the UK – in the case of the US more than a fifth higher. Taking an average of other G7 countries weighted by their economy’s size, UK productivity was around 11% lower than these economic competitors.

These relative positions to UK productivity observed in 2019 have been largely stable over time, as shown in Figure 6.9. With a few gyrations from year to year, the overall picture remains broadly similar over the last two decades.

As against the rest of the G7 as a whole, the UK has become, if anything, marginally less productive relatively. This failure of the UK to improve its comparative productivity position comes in the face of continuing government programmes intended to address the issue.

#### Policies to boost productivity growth

Successive governments since the 1960s have recognised the productivity problem and have adopted policies and programmes designed to improve matters. The Department for Business, Energy, and Industrial Strategy (BEIS) as it is now called, formerly the Department for Business, Innovation and Skills, has been the home of many of these. Policies have generally aimed to increase capital investment by businesses, increase business innovation (through research and development (R&D) and science), or make finance more available for small and medium sized enterprises (SMEs). There have been many policies in recent decades, including the following:

• R&D tax credits for SMEs were introduced in 2000, and for large firms’ in 2002.
• Increased capital investment tax allowances for SMEs were introduced in the early 2000s.
• The Lambert Review of business-university collaboration was undertaken in 2003, resulting in the 10-year science framework.
• The Plan for Growth was published alongside the Budget in 2011.
• The Heseltine review of 2012 led to the creation of the Regional Growth Fund, and increased power for local authorities and Local Economic Partnerships.
• The British Business Bank in was established in 2014.
• The Fixing the Foundations policy of 2015 focused on long-term investment and promoting a dynamic economy.
• The UK’s Industrial Strategy of 2017 aimed to boost productivity by backing businesses to create good jobs and increase the earning power of people throughout the UK with investment in skills, industries and infrastructure.

The current policy framework is set out in The UK’s Build Back Better: our plan for growth published in 2021.

These policy frameworks were no doubt constructed in accordance with the best evidence and appear to have targeted important issues. But all we can see is what actually happened. We do not have the counterfactual figures on what would have been the outcome in the absence of such policies. The position might have looked much worse. All the same, it seems clear that over a long period, successive policies have failed to improve the UK’s comparative productivity performance.

Diagnosing the causes of this persistent weakness is problematic, because the UK scores well when we look at most of the likely reasons for it:

• Inflexibilities in the product market? An example would be a lack of competitive pressure failing to drive out inefficient, low productivity practices. Yet, in most of its assessments, the OECD rates the UK as having a comparatively well-functioning product market, with well-targeted competition and regulatory systems.
• A lack of foreign direct investment? As discussed in Chapter 9 (trade), one of the most powerful sources of innovation to drive productivity is foreign direct investment (FDI). Overseas concerns investing in the UK often bring know-how to go with their investment. But a lack of inward FDI cannot explain low productivity in the UK, as the UK has one of the highest rates of FDI in the world.
• An inflexible labour market? As discussed in Chapter 5 on labour, the UK labour market is very flexible and dynamic by international comparison. This should allow labour to be transferred quite quickly from low-productivity areas to those with more productive possibilities.
• Low education standards? The UK scores more poorly for its degree of educational attainment. That said, it generally scores higher than the OECD average. In 2020 its performance was not statistically significantly different from that of the United States or Germany. So it is hard to see that this factor alone could explain the far better productivity enjoyed in those two countries.
• Poor infrastructure? Investment in transport such as the rail and road systems has been limited by fiscal stringency over long periods of time. To the extent that transport issues hamper movement of goods around the economy, this could well have a detrimental effect on productivity. On the other hand, in a modern economy dominated by the service sector, the communications and information infrastructures may be at least as important determinants. On most measures such as access to broadband or digital literacy, the UK does not seem unduly badly placed, at least as compared with other G7 countries.

One well-regarded comparative assessment of educational attainment in different countries is provided by the OECD’s Programme for International Student Assessment (PISA), which has run every three years for over two decades. However, PISA 2021 was postponed and is due to be released in 2022. It assesses 15-year-old students in mathematics, science, and reading, in a consistent way across countries. In the 2018 exercise, the UK ranked in the mid-teens of 79 countries across the board – a small improvement on the previous rankings.

In this light, it is hard to discern a clear explanation of the persistent low UK productivity relative to most other countries. To make matters worse, it has now been joined by the second of the trio of puzzles: the sharp deceleration of UK productivity growth since 2007.

### 6.4.2 Paradox 2: The collapse in productivity growth

Until around 2007, UK productivity was growing at a steady rate of around 2% a year. As we have seen, this turned out not to be sufficiently fast to close the gap in productivity performance between the UK and other G7 countries. But it did nevertheless support a long-term increase in real wages and living standards. Moreover, it was a well-established trend: productivity had been growing at this rate or a little higher for the previous six decades.

But from 2007 onwards, there was a sharp break in behaviour. Productivity growth slowed to much lower rates. In fact, by the end of 2021, productivity was estimated to be only 7% higher than it had been at the end of 2007. The implied average growth of 0.5% a year is clearly much lower than what had preceded it. The suddenness of the break is demonstrated clearly in Figure 6.10.

The blue line shows the actual path estimated for productivity, with the break in growth rates clearly visible. The dotted line projects the levels of productivity that would have been achieved, had growth been sustained at the levels of the previous 60 years. As a matter of straightforward arithmetic, we can then calculate the “productivity gap” – the shortfall in productivity as a result of this mysterious change in behaviour. By the end of 2021, this came to some 19%. By equally simple arithmetic, we can then derive an estimate of “missing output”, how much more GDP or national income there would have been had productivity continued to grow as before. This equates to over £400 billion, which is clearly a very large amount of money: to put it in context, it would represent enough missing national income to finance the National Health Service in its entirety each year more than twice over.

#### What caused this abrupt break in productivity growth?

Many theories have been advanced to explain this break, but none has reached consensus – it is possible that there is no single explanatory factor, but rather a combination of things that have come together. Based on Figure 6.10, it is clear that explanations must be sufficiently large to explain the considerable break in the time series; come into effect around 2007 (or at least increase notably from this point onwards); be ongoing or long-lasting; and be apparent in many developed countries, but especially pronounced in the UK.

Some theories that were popular shortly after the 2007/08 economic downturn have since fallen out of favour:

• Too many zombies? The fall-out from the financial crisis, especially the record low interest rates, allowed many unproductive companies to linger in the economy. Economic well-being would presumably have been improved if such “zombie companies”, as they were known at the time, had been allowed to fail and close, and the resources they used reallocated to more productive uses. Unproductive companies may have continued to operate for a few years, but this seems unlikely to have persisted for more than a decade.
• The decline of productive industries? The North Sea Oil industry was very productive pre-2007. There has been increased regulation on the financial industry since the crisis. But this seems too narrow to be sufficient – these industries make up too small a fraction of the UK economy to explain the overall experience.
• Financial intermediation has not been as efficient since the financial crisis? Banks and other financial intermediaries have a classic role of channelling savings into productive investment opportunities. Banks, for example, take deposits from savers and then use the proceeds in part to advance funds to firms wanting to finance (hopefully) productive investment. Since the financial crisis, new lending to firms has remained at only a fraction of the levels seen before the crisis. The argument would be that firms have not had the finance available to make investments which would allow them to improve their productivity. But the financial intermediation argument is undermined by surveys designed to elicit the barriers and problems that firms see themselves as facing. They consistently suggest that lack of financing opportunities has not been a major concern or constraint. Equally, the financial institutions typically cite lack of profitable investment opportunities as the reason for their continued sluggish lending, rather than their inability to provide finance which would enable worthwhile investment to be undertaken. For these reasons, it is hard to see shortage of finance as the major reason for the poor productivity performance of recent years.
• Are we measuring productivity incorrectly? The argument goes that the modern economy, particularly under the impact of digitalisation, has become increasingly complex and hard to measure. So perhaps the “missing output” is actually there, but is not being picked up by the statistical measures. Certainly, as we have seen above and from previous chapters, there is no shortage of issues in regard to accurate measurement. But as an explanation of the productivity puzzle, this theory has serious shortcomings. One is the sheer scale of the productivity gap to be explained. There may well be errors in the recording of economic output, but it is hard to give credence to such errors now amounting to nearly a fifth of recorded GDP. Secondly, and more telling, if the economy was becoming more complex over time, then why did this impact on productivity measurement only in such a clear cliff edge as the change of behaviour from 2007 would imply? Furthermore, since a productivity slowdown has been experienced, to a greater or lesser extent, in most developed countries, this explanation would require a sudden cliff-edge divergence of measurement and reality in a large number of countries. This would seem too much of a coincidence to be plausible.

Robert Gordon summarises his argument in relation to the US in this book:

Gordon R (2016), The rise and fall of American growth, Princeton University Press

Other explanations, based on the slowdown in investment, are more credible:

• There’s less innovation in which to invest. The slowdown in business investment may be because there is nothing new worth investing in – Robert Gordon, an eminent economist, argues that there is no current equivalent of the industrial revolution and that everything worth inventing has been invented already!
• A failure to invest in innovation based on the macroeconomic situation. Slow international trade growth and restrictive fiscal policies may have impacted adversely on entrepreneurs’ willingness to invest.

#### ONS Resource

Read more about the various explanations for the productivity puzzle in the ONS article on Productivity measurement, and see the further reading section for more accounts of the arguments.

Macroeconomic explanations have not so far been underpinned by extensive empirical testing that might serve to confirm or refute them. But these macro-based theories may explain the sharp break in behaviour since the financial crisis, because a change in microeconomic factors alone are an implausible explanation. We cannot argue that skills or management practices changed suddenly for the worse in 2008.

Examples of research arguing that the failure to invest in innovation is driving low investment:

Carlin W, Soskice D (2018), ‘Stagnant productivity and low unemployment: Stuck in a Keynesian equilibrium’, Oxford Review of Economic Policy 34

Oulton N (2019), ‘The UK (and Western) productivity puzzle: Does Arthur Lewis hold the key?’, International Productivity Monitor, Voume.36, pages 110 to 141

### 6.4.3 Paradox 3: The behaviour of disaggregated productivity

We have focused on experience at the level of the whole economy. But it is instructive to look at what has been happening at lower levels of aggregation – by sector or by individual firm, for example.

#### ONS Resource

In the UK, the main source of information on individual business is the Annual Business Survey (ABS) carried out each year by the ONS of around 62,000 respondents. The ABS covers the non-financial business sector and relates to approximately two-thirds of the UK economy. It provides information on businesses’ turnover and intermediate purchases to give a good approximation to their gross value added. This approximation is called aGVA.

In addition, the Interdepartmental Business Register (IDBR) can be used to derive employment information about the firms responding to the ABS. The Business Register Employment Survey and HMRC records are both used to provide this employment information.

The Interdepartmental Business Register (IDBR) is a comprehensive list of UK businesses – around 2.7 million businesses in all sectors of the economy – used by government for statistical purposes, and it provides the sampling frame for business surveys such as the ABS. The two main sources of input are value added tax (VAT) and pay as you earn (PAYE) records from HMRC, with additional information coming from Companies House, Dun and Bradstreet and ONS business surveys. The main characteristics that are covered by the IDBR are:

• employment (various size bands)
• geography
• industry
• domestic or foreign ownership.

Together, these sources allow the construction of reasonable productivity estimates by individual firm, computed as aGVA divided by the employment headcount.

In 2021, the ONS published an article ‘Firm-level labour productivity measures from the Annual Business Survey, Great Britain: 1998 to 2019’. This article contains a wealth of interesting analysis, with the main results summarised in Figure 6.11.

Classification Sub-classification GVA (£000)
Industry Accommodation and food services 19
Human health and social work activities 21
Retail 28
Transport and storage 42
Real estate 46
Construction 47
Manufacturing 51
Professional, scientific and technical services 51
Information and communication 79
Firm size
(by employment band)
1 to 9 employees 23
10 to 49 31
50 to 99 36
100 to 249 39
250 to 99 39
1,000 and over 30
Age of firm 2 years or younger 24.5
3 to 5 years 28.0
6 to 10 years 25.5
11 to 20 years 29.5
21 years and older 31.5
By ownership of firm Domestically owned 28
Foreign owned (EU) 45
Foreign owned (Non-EU) 44

Figure 6.11 Average (median) aGVA per worker by firm characteristics in 2019, £000s

Average (median) aGVA per worker by firm characteristics in 2019, £000s

There is a clear difference in productivity levels between various sectors of the economy and an interesting relationship between productivity and firm size.

For the most part, there is a positive relationship between size and productivity. The productivity of the median firm with between 250 and 999 employed was some 73% higher than those of the smallest firms. The exception to this trend is the lower productivity of firms that employ more than 1,000 as compared with the 250 to 999 band. But this is likely to be explained by the fact that this group has a high representation of businesses in sectors where productivity is typically lower than average, such as the retail industry.

One possible explanation of this positive relationship may be that larger firms are able to exploit economies of scale, reducing the proportional impact of their overheads and other fixed costs. At least as plausible, however, is the likely correlation between firm size and age. Some smaller firms may be relatively new firms that are still in the process of discovering and exploiting the efficiencies that are open to them. Some confirmation of this possibility is provided by looking at the relationship between firm age and average productivity.

A clear feature of the table is the lower productivity of young firms. Broadly, firms having been in existence for less than three years have productivity around a fifth lower than those of older firms. There is not much change, however, once firms have been in existence for more than three years. So if there is a “learning period” for new firms, this may be the extent of it.

At face value, ownership highlights striking differences. Firms with ownership within the EU have productivity on average 64% higher than that of domestically owned firms. Firms with ownership outside the EU similarly have productivity around 60% higher than domestically owned enterprises. In part, this may reflect the fact that foreign owned firms have greater access to world class know-how and technologies. As discussed in Chapter 9, and as noted earlier in this chapter, one of the clear advantages of countries receiving foreign direct investment is precisely this access to productive know-how. It may be this factor that is showing up in the productivity figures.

At the same time, care needs to be taken in interpreting ownership data. Young and small firms are more likely than larger or older enterprises to be domestically owned. As we have seen, these are likely to have lower productivity in any case. Furthermore, some reverse causation may be in operation. Overseas investors may be more prepared to invest in, and seek ownership of, high productivity firms than they would in respect of lower productivity ones. In that case, foreign ownership would be the consequence of firms having relatively high productivity, rather than the causal influence.

These analyses of the stories behind the aggregate figures for productivity are of great interest. But perhaps the most interesting feature relates to the distribution of productivity performance between different firms, which reveals what some describe as the third “productivity puzzle”. Figure 6.12 gives one such demonstration of UK experience.

The horizontal axis shows the range of aGVA per worker achieved by firms included in the ABS. The “kernel densities” represent the proportion of employees whose firms achieve that level of productivity. By definition, the sum of all these kernel densities comes to one. The dotted lines represent the mean productivity achieved by the average employee. The kernel densities distribution is shown for selected years between 1998 and 2018.

There are several striking features revealed by the chart.

• There is an enormous spread of productivity. The productivity performance of firms achieving the highest productivity is seven or eight times the mean productivity achieved. At the opposite end of the scale, there is a large tail of firms that achieve low productivity, or, in a few cases, negative productivity, implying that they achieved negative value added and presumably made losses.
• The curve is not symmetric. The low performing tail – firms achieving below mean productivity – is much heavier than the high performing tail. There is some evidence that this feature applies to the UK to a greater extent than may be the case in other countries.
• Stability over time. The wide spread of apparent performance has remained a feature from 1998 till 2018, and so too has the characteristic heavy low performing tail relative to the high performing one.

Taken together, these findings characterise the third productivity puzzle: the remarkable spread of productivity across different businesses, even fairly similar ones, and the lack of convergence over time.

This raises some important issues of policy relevance:

• Should policies designed to improve productivity be more targeted at the low performing tail? Given its size, only a small average productivity improvement achieved by low performing firms would result in a substantial improvement at aggregate level.
• Why has the wide range of performance persisted over time? If firm A can apparently achieve productivity a multiple larger than that of firm B, why can the latter not adopt the practices and behaviours of the former and achieve the same success? Benchmarking and learning from best practice might be expected to achieve just this effect. But this appears not to have happened over an extended period of time; the wide dispersion of performance has remained largely unchanged. These are live policy issues which are currently largely unresolved.

## 6.5 Improving productivity measurement

Given its importance in relation to people’s standard of living, productivity will remain a key issue for the UK economy for the foreseeable future. The future development of productivity statistics will be guided by the need for a better understanding of what drives productivity and the design of policies to improve the outcome.

### 6.5.1 Double deflation

double deflation
Double deflation is considered the best approach to producing volume estimates of gross value added (GVA). For every industry, the current price estimate of its output is deflated by a price index for output and the current price estimate of its inputs is deflated by an input price index. That is, outputs are deflated using deflators for the product produced, while the goods and services that are used as inputs to the production are deflated using relevant specific product deflators.

Since the numerator for productivity calculation is gross value added, the research agenda will be closely linked to the agenda for measuring the economy’s output in changing modern circumstances. But, in one sense, there is nothing additional from a productivity point of view here, over and above the issues discussed in the chapters of this book on GDP and hard to measure sectors. However, there is one issue in the context of improved measurement of GDP that is particularly important for measuring productivity, namely double deflation.

In June 2021, the ONS published early research findings into the production of alternative estimates of GDP in a new framework, including experimental estimates of double-deflated industry-level gross value added (GVA). Estimates were produced for the period 1997 to 2018 in the UK. These impacts reflect broader improvements to how the balancing of current price and volume estimates of GDP in the supply and use tables (SUTs) framework has been undertaken for these experimental estimates. That is, these estimates do not simply reflect the removal of single deflation bias.

In measuring GDP by the output route, ONS has used turnover as a proxy for value added and used a single deflator to obtain volume measures. It would clearly be preferable, as reflected in the international guidance, for the intermediate inputs into production processes to be deflated by an appropriate price index and for the gross outputs to be separately deflated by its own appropriate deflator. The volume of GVA under such double deflation is then the difference between the deflated output and the deflated inputs.

Arguably, this is important at whole economy level only in the short term. When available, the expenditure measure of GDP is to be preferred to the output measure, and the expenditure measure is reasonably well deflated already. But at sub-aggregate level, double deflation is of much more importance. Obtaining accurate estimates of the value added for particular sectors and individual firms requires the volumes of the gross output they produce and of the inputs they use to be measured accurately. Without double deflation, this is unlikely to be achieved. Going back to our example of the bakery, there is no reason to suppose that movements in the prices of loaves will be the same as those in the price of the flour and other intermediate inputs that are used in the production of the bread.

### 6.5.2 Missing capitals

Traditionally, economic analysis has concentrated on physical capital. At Daily Bread we regarded capital as the premises and ovens that are used to bake the bread. But there are other forms of capital which are equally relevant to economic production:

• Intangible capital. Firms invest not just in physical assets but in a range of other items such as developing software and systems, wider forms of intellectual property and building up their brand image. Any or all of these assets may be important for the productivity that they achieve, so it is important the data and analysis should take them fully into account.
• Human capital. Perhaps even more important is the stock of skills and know-how that individuals possess as a result of their education, training and experience. Clearly, baking bread requires an oven and premises, but it also depends crucially on the baker’s skill and experience and, for that matter, on the sales assistants’ abilities and experience in marketing the product successfully. Work is going on around the world to provide indicators and estimates of human capital. So again, it is important that productivity analysis should take such estimates fully into account.
• Natural capital. This is the stock of assets provided by nature that are often integrally related to production, as is discussed further in Chapter 11. Daily Bread, for example, will be dependent on a continuing supply of high quality flour, which in turn may depend on climate and soil quality. In the opposite direction, the bakery may well have an effect on natural assets. It will use energy, the generation of which will have implications for the environment. It may also produce carbon dioxide or other emissions in the course of its operations, and it is important to be aware of these. For these reasons, productivity analysis will increasingly need to take account of natural capital.

## 6.6 Summary

We began this chapter by setting out what productivity is, but also stressing its importance beyond being an economic ratio of technical interest only. On the contrary, as Paul Krugman reiterated, productivity – or the lack of it – is the crucial determinant of people’s material well-being.

Having considered various key measures of productivity and how they relate to one another, we also considered UK experience in recent years. Bluntly, it is far from reassuring. UK productivity remains low by comparison with most other comparable countries. At the same time, we have seen a sharp break from the growth trend of previous decades, with productivity essentially being on a flat plateau since 2007. This has consequences for our standard of living as well, for example, in the way it affects the government’s ability to finance growing demands on the NHS and other public services.

Understanding why productivity has evolved as it has is probably described as, at best, a work in progress. We have a clear picture of what has been happening and some pointers as to what may be significant determinants. But, to date, no fully convincing explanation has emerged.

In this context, compilation of high-quality estimates and measures of productivity growth will not, on its own, provide the fully convincing explanations that are needed. But it is also the case that without such quantitative evidence being available, progress in understanding and addressing these issues will be severely hampered. Accordingly, accurate measurement of productivity will remain a central agenda for the foreseeable future.