What are the approaches to the measurement of total factor productivity?

Approaches to the measurement of total factor productivity

Total-factor productivity (TFP) is a variable which accounts for effects in total output not caused by inputs. For example, a year with unusually good weather will tend to have higher output, because bad weather “hinders agricultural output.

A variable like weather does not directly relate to unit inputs, so weather is considered a total-factor productivity variable.

The equation below (in Cobb-Douglas form) represents total output (Y) as a function of total-factor productivity (A), capital input (K), labour input (L), and the two inputs’ respective shares of output (a and P are the capital input share of contribution for K and L respectively).

An increase in either A, K or L will lead to an increase in output. While capital and labour input are tangible, total-factor productivity appears to be more intangible as it can range from technology to knowledge of worker (human capital).

Technology Growth and Efficiency are regarded as two of the biggest sub-sections of Total Factor Productivity, the former possessing “special” inherent features such as positive externalities and non- rivalness which enhance its position as a driver of economic growth.

Total Factor Productivity is often seen as the real driver of growth within an economy and studies reveal that whilst labour and investment are important contributors, Total Factor Productivity may account for up to 60% of growth within economies.

There are two different methods to the measurement of TFP: growth accounting and econometric. Within these, there are five widely used approaches that can be categorised into three broad classes.

The first two, index numbers and data envelopment analysis, are flexible in the specification of technology, but do not allow for measurement errors in the data. The other three are econometric methods that calculate productivity from an estimated production function.

Data Envelopment Analysis (DEA):

The first approach to productivity measurement is completely nonparametric and uses linear programming. It dates back to Farrell and it was operationalised by Chames, Cooper, and Rhodes.

No particular production function is assumed. Instead, the ratio of a linear combination of outputs over a linear combination of inputs is compared across observations. While there is no theoretical justification for the linear aggregation, it is natural in an activities analysis framework.

This approach has some drawbacks. The flexibility in weighting can be a drawback. It has the implication that each firm with the highest output-input ratio for any combination of outputs and inputs will be considered efficient.

The method is not stochastic, which is demanding on the data and makes the method sensitive to outliers. One might object to the label “100% efficient” for the best practice firms in the sample. In some situations no firm might be efficient, e.g. due to regulation.

Index Numbers (TFP):

The second approach provides a theoretically motivated aggregation method for inputs and outputs, while remaining fairly sceptic on the shape of the underlying technology.

According to this approach, under a number of assumptions, it is possible to calculate the term ‘A’ at (1) from observables, without having to specify the exact production function, nor forcing it to be uniform across observations.

The work of Solow and Diewert are considered important that refer to two types of index numbers respectively. One is Solow index and the other is Translog Index.

Solow Index:

Let Y denote output (value added), L labour input and K capital input. Let be the income share of capital in value added. Then, the Solow index of TFP is given by the following equation:

In the above equation, lnY is the growth rate of output, InL is the growth rate of labour input and InK is the growth rate of capital input. InA is the growth rate of total factor productivity.

Solow index assumes the elasticity of substitution between labour and capital to be equal to one. In other words, the assumption is that if wage rate goes up by 5 per cent, then employment will fall by 5 per cent. The assumption of unitary elasticity of substitution implies that the income shares of labour and capital remain constant.

Translog index:

The translog index of TFP does not make rigid assumptions about elasticity of substitution between factors of production. It allows for variable elasticity of substitution. Moreover, this index does not require technological progress to be Hicks-neutral where increase in the marginal productivity of labour and capital is proportional.

The translog index provides an estimate of the shift of the production function even if the technological change is non- neutral i.e. it is labour-saving or capital-saving in character.

The translog index of TFP growth is given by the following equation: A in TFP, =

In the above equation, Y is output, L labour and K capital. SL is income share of labour and SK denotes income share of capital. A’lnTFP is the rate of technological change or the rate of growth of total factor productivity.

One of the main advantages of the index number approach is the ease of calculation. Also, the specification of technology is flexible; allowing firms to produce with different technologies, and the method can easily handle multiple outputs and a large number of inputs.

The main disadvantages are the requirements on data quality and the assumptions regarding firm behaviour and market structure.

It is impossible to account for measurement errors or to deal with outliers, except for some ad hoc trimming of the data. Factor prices information and returns to scale have to be estimated or available independently.

Econometric Methods:

Third approach is the use of econometric methods in order to measure productivity. In the econometric approach, we apply regression analysis to estimate a production function and get the rate of technological progress from the estimated production function. The Cobb-Douglas production function is commonly been used in productivity studies.

Some researchers have done some variations by using different procedures such as Instrumental Variable Estimation (IVE), Stochastic Frontier Estimation (SF) and last but not the least some Semi- parametric procedures to address the issue of productivity.

A detailed analysis of these methods is, however, outside the purview of this unit approach also has some limitations. It assumes that same rate of technological progress for all the years under study. The estimates of the rate of technological change are often seriously affected by the problem of multicollinearity.