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Video Summary: Multi-factor Productivity

Released: 23 January 2014

This is a transcript of the video podcast which can be viewed at:


This is a short video providing an overview of Multi-factor productivity and how it is calculated.

Production Function

Let’s begin by looking at output. The two main components of output are labour and capital. Labour describes inputs such as workers or hours, whilst capital includes offices, factories and machinery.  Output can be determined by this equation, which is known as the production function. Here, in broad terms, Y represents output, K is represents capital, and L represents labour. The powers on K and L represent income shares However there is another contributor to output growth.  The A represents Multi-factor Productivity.  Multi-factor productivity, or MFP, is also known as ‘total factor productivity’, and the ‘Solow residual’, we can describe MFP as the part of change in output which cannot be explained by changes in capital or labour input.  Once we account for the contributions of change in capital and labour out of change in output, we are left with MFP.

Indicative Estimates

The Office for National Statistics measures estimates of both factor inputs of capital and labour.  To measure estimates of capital, we use VICS, the Volume Index of Capital Services. And to measure estimates of labour, we use QALI, which is Quality Adjusted Labour Input.  VICS and QALI provide a more complete picture of the inputs of capital and labour respectively.  They adjust the data for changes in the quality of labour and capital as well as observing differences and measuring the growth.  ONS also measures output.  For calculating MFP we look at Gross Value Added (GVA) which measures the total contribution to the economy of each individual producer, industry or sector. GVA takes away intermediate expenditure, and the result is known as value added

Growth Accounting

Growth accounting is how we measure Multi-factor productivity.  It was first introduced in 1957 by economist Robert Solow in his paper ‘Technical Change and the Aggregate Production Function’.  He was able to calculate the growth in MFP, calling it the ‘disembodied technical change'.  Let’s simplify this. What he said was if we decompose the growth of an economy’s output into that which is due to capital, and into that which is due to labour, and then What he said was if we decompose the growth of an economy’s output into that which is due to growth in capital input, and into that which is due to growth in labour input, and then take them both away, what we are left with, the unaccounted growth, is the growth in MFP.

Multi-factor Productivity

ONS calculates the growth in MFP using Solow’s theory of growth accounting.  We take the growth rate of GVA, and then take away the growth in VICS and the growth in QALI.  This leaves us with the ‘unexplained growth’ – which is the growth in MFP.  Let’s take an example of this. If the growth rate for GVA is 2%, the growth rate in VICS is 1% and the growth rate in QALI is 0.7%, we are able to calculate that the growth in MFP is 0.3%.  Let’s take a look at what the latest data shows us. This chart shows us the breakdown of GVA growth in percentage points up to 2012.  The blue bars show growth in capital input, which is accounted for by VICS.  The green bars show growth in hours worked and the yellow bars show growth in labour composition, both of which are accounted for by QALI.  The blue line shoes output growth for each year.  What remains is the growth in multi-factor productivity which can be seen by the red bars.  We can see since the recession in 2008, growth in MFP has remained negative, whilst labour inputs have grown.


This is a short video providing an overview of Multi-factor productivity and how it is calculated.

Source: Office for National Statistics

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