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# TFP vis-à-vis Labour Productivity - why TFP is the best measure of productivity in the digital age

## Intro

Economists operate with two measures of productivity – labour productivity and total factor productivity. The two are sometimes used more or less interchangeably, seemingly without people realising they are actually quite different. In the work we currently do on disruptive technologies, understanding how they differ is very important, hence this research paper.

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## Labour productivity

Labour productivity is a measure of total output per hour worked. In other words, it is a measure of how productive the labour force is. Think about how you would measure total output in an economy. We can probably all agree that:

(i) Total Output = Number of Hours Worked * Output per Hour

Now, by rearranging (i), assuming that output per hour is just a synonym for labour productivity, you can see that labour productivity is a measure of total output divided by labour input:

(ii) Labour Productivity = Total Output / Number of Hours Worked

Total output is another name for GDP, and I can prove (but won’t do it now) that any change in the number of hours worked is virtually identical to any change in the size of the workforce in aggregate. By using some simple maths, I therefore find that:

(iii) DeltaGDP ≈ DeltaWorkforce + DeltaLabour Productivity

Equation (iii) explains why labour productivity is important to GDP growth or, at least, why it has been important up to this point. That may all change as robots increasingly replace humans in the work process, but more on that later.

## Total factor productivity

Total factor productivity (TFP) is a measure of how output in an economy is affected by both labour and capital. It effectively measures how efficiently those two input factors are utilised in the work process. In most TFP models, labour is allocated the weight of 70% and capital 30%.

Think about it this way: Assuming the input from labour is constant from one year to the next, TFP will only improve if GDP grows faster than the capital stock. In other words, throwing more capital into the work process, for example by replacing humans with robots, won’t necessarily have a positive impact on TFP unless the net gain (from more capital but less labour) is positive.

Let’s stay with that example for a few seconds. As robots replace humans, labour productivity will most likely rise, but TFP could fall unless GDP more than offsets the capital spent on robots. At the very least, the two measures of productivity could lead to very different results.

In an increasingly digitised economy where capital matters more and labour less, it is therefore important that we increasingly zoom in on TFP when we assess productivity in society. TFP is measured as follows:

(iv)         TFP = Total Output / Weighted Average of Inputs

In other words, TFP is a measure of total output divided by total input with the (quantifiable) input factors being labour and capital. In fact, TFP is affected by other input factors than those two (Exhibit 1). Factors such as the quality of the infrastructure, environmental regulations and the quality of the educational system also matter a great deal, and the list is long. In practice, though, the two input factors used in almost all TFP models are capital and labour.

In economic theory, the Cobb-Douglas production function is typically used to represent total output, i.e.:

(v) TFP = Y/(K^(alpha)*L^(beta))

where Y is total output, K is capital, α is the output elasticity of capital, L is labour and ß is the output elasticity of labour. Now, TFP represents the increase in total output that is not the result of an increase or a drop in those two input factors.

It is actually more relevant to look at the change in productivity over time than to look at an absolute number. In that respect, the following equation comes handy:

(vi) (DeltaY)/Y = alpha(DeltaK)/K+beta(DeltaL)/L+(DeltaTFP)/(TFP)

which measures the relationship between growth in total output, growth in capital and labour, and growth in TFP.

## How the two measures compare

As I stated earlier, the two measures of productivity do not always go hand in hand and I suspect that, in an increasingly digitised world, that will happen more frequently.

Labour productivity first: In the UK, since the Global Financial Crisis, labour productivity, when measured as output per hour worked, has been virtually unchanged (Exhibit 2) and is now approximately 15% below the G7 average with only Italy underperforming the UK.

Much lower labour productivity in the UK when compared to the rest of G7 could quite conceivably be the result of very low penetration of advanced robotics in the UK manufacturing industry. As you can see from Exhibit 3 below, the UK is nowhere near the top in terms of the number of robots installed per 10,000 employees in the manufacturing industry.

When my book was published in March 2018, I used data from 2015, showing that the UK was in 22nd place back then with 71 robots per 10,000 employees. Although I do not hold any more recent data on the UK, I know it is still outside the top 20, which has had the net effect of reducing the level of international competitiveness of UK manufacturing companies.

Switching to TFP, neither has that measure of productivity performed particularly well in the UK since the Global Financial Crisis (Exhibit 4), and the reason could be at least partially the same, but another dynamic is worth pointing out.

More and more capital is misallocated in the UK, and that has particularly been the case in the years since the Global Financial Crisis. Vast amounts of capital that could, and should, be deployed productively have instead been deployed unproductively.

When the supply of risk-willing capital is finite – and it almost always is –then TFP will be negatively affected by more and more capital being misallocated. The list is long, but allow me to mention just a few sources of misallocated capital:

1.  Massive amounts of property speculation - predominantly buy-to-let in and around London.
2. The growing tendency of capital owners preferring to pocket profits rather than re-investing them (which could also explain why the penetration of robots is so low in the UK).
3. The rising cost of servicing the growing populace of elderly in society – it is both expensive and non-productive (at least in economic terms).
4. The rising cost of servicing the growing mountain of debt.

The UK has been affected by all these four factors but by the first two more than most other countries; i.e. nobody should be surprised that more capital has been misallocated here than elsewhere which explains the poor performance of TFP.

## Conclusion

All this becomes relevant when zooming in on countries and companies likely to benefit from the digital revolution, and it would be rather naïve to assume that the digital revolution is limited to the manufacturing industry. Take the recent collapse of Thomas Cook – the biggest travel company in the world. Well, until a few weeks ago, it certainly was, but Thomas Cook did a terrible job, adjusting to the digital age, and the company paid the ultimate price for that mistake.

Going forward, you would want to invest in countries (and in companies) where TFP is relatively high and where the penetration of advanced robotics is well above average. Regrettably, the UK doesn’t do particularly well in either category.

Niels C. Jensen

8 October 2019